{
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    "attribution": "lithium-niobate.com data compiled by Wentao Jiang; cite the original sources listed per value.",
    "count": 49,
    "data_version": "0.1.0",
    "documentation": "https://lithium-niobate.com/api/openapi.json",
    "license": {
      "id": "CC-BY-4.0",
      "name": "Creative Commons Attribution 4.0 International",
      "url": "https://creativecommons.org/licenses/by/4.0/"
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          "s24 = -s14",
          "s55 = s44",
          "s56 = 2 s14",
          "s66 = 2 (s11 - s12)"
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      "tensor": "elastic-compliance-sE",
      "unit": {
        "display": "1e-12 m^2/N",
        "ucum": "10*-12.m2/N"
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      "name": "Elastic compliance at constant electric field",
      "notes": "s14 < 0 goes with c14 > 0. Temperature coefficients (1e-4 /C): s11 1.66, s12 0.28, s13 1.94, s14 1.33, s33 1.60, s44 2.05.",
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        "locator": "Table 5, p. 200",
        "original_reference": "Smith & Welsh, J. Appl. Phys. 42, 2219 (1971)",
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        "transcribed": "2026-10-25"
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        "point_group": "3m",
        "relations": [
          "s22 = s11",
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          "s24 = -s14",
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          "s66 = 2 (s11 - s12)"
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      },
      "tensor": "elastic-compliance-sE",
      "unit": {
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        "ucum": "10*-12.m2/N"
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        "order": [
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    {
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        "z_sign_definition": "+c points out of the face that becomes negative on compression; equivalently it becomes positive on cooling (weis1985 pp. 192-193)"
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      "name": "Elastic compliance at constant electric field",
      "provenance": {
        "locator": "Table 5, p. 200",
        "original_reference": "Warner, Onoe, Coquin, JASA 42, 1223 (1967)",
        "source_id": "weis1985",
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        "transcribed": "2026-10-25"
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        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "s22 = s11",
          "s23 = s13",
          "s24 = -s14",
          "s55 = s44",
          "s56 = 2 s14",
          "s66 = 2 (s11 - s12)"
        ]
      },
      "tensor": "elastic-compliance-sE",
      "unit": {
        "display": "1e-12 m^2/N",
        "ucum": "10*-12.m2/N"
      },
      "variant": "unspecified",
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      "voigt_convention": {
        "full_from_voigt": "s_ijkl = s_IJ x (1 if I<=3 else 1/2) x (1 if J<=3 else 1/2) (engineering shear strain)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
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        "shear_strain": "engineering"
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    {
      "conditions": {
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      "consistency": [
        {
          "check": "piezo-stiffened longitudinal velocity along Z, sqrt((c33 + e33^2/eps33^S)/rho), kushibiki1999 constants and density",
          "result": "7328.6 m/s (unstiffened 7102.1 m/s); measured 7328.20 m/s (kushibiki1999 Table II)",
          "status": "C"
        }
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      "frame": {
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        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "not stated in this record; tensor form matches this frame by symmetry"
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            ],
            [
              59.85,
              0.0,
              0.0
            ]
          ],
          [
            [
              7.83,
              0.0,
              0.0
            ],
            [
              0.0,
              -7.83,
              59.85
            ],
            [
              0.0,
              59.85,
              0.0
            ]
          ],
          [
            [
              67.99,
              0.0,
              0.0
            ],
            [
              0.0,
              67.99,
              0.0
            ],
            [
              0.0,
              0.0,
              234.18
            ]
          ]
        ]
      ],
      "id": "elastic-stiffness-cE/cln/kushibiki1999",
      "independent": {
        "c11": {
          "uncertainty": {
            "type": "stated",
            "value": 0.03
          },
          "value": 198.86
        },
        "c12": {
          "uncertainty": {
            "type": "stated",
            "value": 0.04
          },
          "value": 54.67
        },
        "c13": {
          "uncertainty": {
            "type": "stated",
            "value": 0.55
          },
          "value": 67.99
        },
        "c14": {
          "uncertainty": {
            "type": "stated",
            "value": 0.02
          },
          "value": 7.83
        },
        "c33": {
          "uncertainty": {
            "type": "stated",
            "value": 0.75
          },
          "value": 234.18
        },
        "c44": {
          "uncertainty": {
            "type": "stated",
            "value": 0.01
          },
          "value": 59.85
        }
      },
      "kind": "tensor",
      "name": "Elastic stiffness at constant electric field",
      "notes": "The source also lists c66 = 72.09 +- 0.02 GPa; the 3m relation (c11 - c12)/2 gives 72.095. In the same table LiTaO3 has c14 = -10.75 GPa.",
      "provenance": {
        "source_id": "kushibiki1999",
        "status": "P",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 4,
      "scale": 1,
      "symbol": "c^E",
      "symmetry_form": {
        "form": [
          [
            "c11",
            "c12",
            "c13",
            "c14",
            "0",
            "0"
          ],
          [
            "c12",
            "c11",
            "c13",
            "-c14",
            "0",
            "0"
          ],
          [
            "c13",
            "c13",
            "c33",
            "0",
            "0",
            "0"
          ],
          [
            "c14",
            "-c14",
            "0",
            "c44",
            "0",
            "0"
          ],
          [
            "0",
            "0",
            "0",
            "0",
            "c44",
            "c14"
          ],
          [
            "0",
            "0",
            "0",
            "0",
            "c14",
            "(c11-c12)/2"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "c22 = c11",
          "c23 = c13",
          "c24 = -c14",
          "c55 = c44",
          "c56 = c14",
          "c66 = (c11 - c12)/2"
        ]
      },
      "tensor": "elastic-stiffness-cE",
      "unit": {
        "display": "GPa",
        "qudt": "http://qudt.org/vocab/unit/GigaPA",
        "ucum": "GPa"
      },
      "variant": "cln",
      "variant_note": "SAW-grade congruent",
      "voigt": [
        [
          198.86,
          54.67,
          67.99,
          7.83,
          0.0,
          0.0
        ],
        [
          54.67,
          198.86,
          67.99,
          -7.83,
          0.0,
          0.0
        ],
        [
          67.99,
          67.99,
          234.18,
          0.0,
          0.0,
          0.0
        ],
        [
          7.83,
          -7.83,
          0.0,
          59.85,
          0.0,
          0.0
        ],
        [
          0.0,
          0.0,
          0.0,
          0.0,
          59.85,
          7.83
        ],
        [
          0.0,
          0.0,
          0.0,
          0.0,
          7.83,
          72.095
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "C_ijkl = c_IJ, I = V(ij), J = V(kl)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "conditions": {
        "electrical_boundary": "E"
      },
      "frame": {
        "convention": "unstated",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "not stated in this record; tensor form matches this frame by symmetry"
      },
      "full": [
        [
          [
            [
              199.0,
              0.0,
              0.0
            ],
            [
              0.0,
              54.7,
              7.9
            ],
            [
              0.0,
              7.9,
              70.0
            ]
          ],
          [
            [
              0.0,
              72.15,
              7.9
            ],
            [
              72.15,
              0.0,
              0.0
            ],
            [
              7.9,
              0.0,
              0.0
            ]
          ],
          [
            [
              0.0,
              7.9,
              59.9
            ],
            [
              7.9,
              0.0,
              0.0
            ],
            [
              59.9,
              0.0,
              0.0
            ]
          ]
        ],
        [
          [
            [
              0.0,
              72.15,
              7.9
            ],
            [
              72.15,
              0.0,
              0.0
            ],
            [
              7.9,
              0.0,
              0.0
            ]
          ],
          [
            [
              54.7,
              0.0,
              0.0
            ],
            [
              0.0,
              199.0,
              -7.9
            ],
            [
              0.0,
              -7.9,
              70.0
            ]
          ],
          [
            [
              7.9,
              0.0,
              0.0
            ],
            [
              0.0,
              -7.9,
              59.9
            ],
            [
              0.0,
              59.9,
              0.0
            ]
          ]
        ],
        [
          [
            [
              0.0,
              7.9,
              59.9
            ],
            [
              7.9,
              0.0,
              0.0
            ],
            [
              59.9,
              0.0,
              0.0
            ]
          ],
          [
            [
              7.9,
              0.0,
              0.0
            ],
            [
              0.0,
              -7.9,
              59.9
            ],
            [
              0.0,
              59.9,
              0.0
            ]
          ],
          [
            [
              70.0,
              0.0,
              0.0
            ],
            [
              0.0,
              70.0,
              0.0
            ],
            [
              0.0,
              0.0,
              240.0
            ]
          ]
        ]
      ],
      "id": "elastic-stiffness-cE/unspecified/andrushchak2009",
      "independent": {
        "c11": {
          "value": 199
        },
        "c12": {
          "value": 54.7
        },
        "c13": {
          "value": 70.0
        },
        "c14": {
          "value": 7.9
        },
        "c33": {
          "value": 240
        },
        "c44": {
          "value": 59.9
        }
      },
      "kind": "tensor",
      "name": "Elastic stiffness at constant electric field",
      "provenance": {
        "source_id": "andrushchak2009",
        "status": "S",
        "transcribed": "2026-10-25",
        "via": "bouchy2022"
      },
      "public": true,
      "rank": 4,
      "scale": 1,
      "symbol": "c^E",
      "symmetry_form": {
        "form": [
          [
            "c11",
            "c12",
            "c13",
            "c14",
            "0",
            "0"
          ],
          [
            "c12",
            "c11",
            "c13",
            "-c14",
            "0",
            "0"
          ],
          [
            "c13",
            "c13",
            "c33",
            "0",
            "0",
            "0"
          ],
          [
            "c14",
            "-c14",
            "0",
            "c44",
            "0",
            "0"
          ],
          [
            "0",
            "0",
            "0",
            "0",
            "c44",
            "c14"
          ],
          [
            "0",
            "0",
            "0",
            "0",
            "c14",
            "(c11-c12)/2"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "c22 = c11",
          "c23 = c13",
          "c24 = -c14",
          "c55 = c44",
          "c56 = c14",
          "c66 = (c11 - c12)/2"
        ]
      },
      "tensor": "elastic-stiffness-cE",
      "unit": {
        "display": "GPa",
        "qudt": "http://qudt.org/vocab/unit/GigaPA",
        "ucum": "GPa"
      },
      "variant": "unspecified",
      "voigt": [
        [
          199.0,
          54.7,
          70.0,
          7.9,
          0.0,
          0.0
        ],
        [
          54.7,
          199.0,
          70.0,
          -7.9,
          0.0,
          0.0
        ],
        [
          70.0,
          70.0,
          240.0,
          0.0,
          0.0,
          0.0
        ],
        [
          7.9,
          -7.9,
          0.0,
          59.9,
          0.0,
          0.0
        ],
        [
          0.0,
          0.0,
          0.0,
          0.0,
          59.9,
          7.9
        ],
        [
          0.0,
          0.0,
          0.0,
          0.0,
          7.9,
          72.15
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "C_ijkl = c_IJ, I = V(ij), J = V(kl)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "conditions": {
        "electrical_boundary": "E",
        "method": "resonant ultrasound spectroscopy",
        "temperature_C": 30
      },
      "frame": {
        "convention": "unstated",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "not stated in this record; tensor form matches this frame by symmetry"
      },
      "full": [
        [
          [
            [
              199.5,
              0.0,
              0.0
            ],
            [
              0.0,
              55.27,
              8.7
            ],
            [
              0.0,
              8.7,
              67.67
            ]
          ],
          [
            [
              0.0,
              72.115,
              8.7
            ],
            [
              72.115,
              0.0,
              0.0
            ],
            [
              8.7,
              0.0,
              0.0
            ]
          ],
          [
            [
              0.0,
              8.7,
              59.48
            ],
            [
              8.7,
              0.0,
              0.0
            ],
            [
              59.48,
              0.0,
              0.0
            ]
          ]
        ],
        [
          [
            [
              0.0,
              72.115,
              8.7
            ],
            [
              72.115,
              0.0,
              0.0
            ],
            [
              8.7,
              0.0,
              0.0
            ]
          ],
          [
            [
              55.27,
              0.0,
              0.0
            ],
            [
              0.0,
              199.5,
              -8.7
            ],
            [
              0.0,
              -8.7,
              67.67
            ]
          ],
          [
            [
              8.7,
              0.0,
              0.0
            ],
            [
              0.0,
              -8.7,
              59.48
            ],
            [
              0.0,
              59.48,
              0.0
            ]
          ]
        ],
        [
          [
            [
              0.0,
              8.7,
              59.48
            ],
            [
              8.7,
              0.0,
              0.0
            ],
            [
              59.48,
              0.0,
              0.0
            ]
          ],
          [
            [
              8.7,
              0.0,
              0.0
            ],
            [
              0.0,
              -8.7,
              59.48
            ],
            [
              0.0,
              59.48,
              0.0
            ]
          ],
          [
            [
              67.67,
              0.0,
              0.0
            ],
            [
              0.0,
              67.67,
              0.0
            ],
            [
              0.0,
              0.0,
              235.2
            ]
          ]
        ]
      ],
      "id": "elastic-stiffness-cE/unspecified/ogi2002",
      "independent": {
        "c11": {
          "uncertainty": {
            "type": "stated",
            "value": 0.2
          },
          "value": 199.5
        },
        "c12": {
          "uncertainty": {
            "type": "stated",
            "value": 0.13
          },
          "value": 55.27
        },
        "c13": {
          "uncertainty": {
            "type": "stated",
            "value": 0.26
          },
          "value": 67.67
        },
        "c14": {
          "uncertainty": {
            "type": "stated",
            "value": 0.2
          },
          "value": 8.7
        },
        "c33": {
          "uncertainty": {
            "type": "stated",
            "value": 0.4
          },
          "value": 235.2
        },
        "c44": {
          "uncertainty": {
            "type": "stated",
            "value": 0.04
          },
          "value": 59.48
        }
      },
      "kind": "tensor",
      "name": "Elastic stiffness at constant electric field",
      "notes": "Source lists c66 = 72.10 +- 0.01 GPa.",
      "provenance": {
        "source_id": "ogi2002",
        "status": "P",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 4,
      "scale": 1,
      "symbol": "c^E",
      "symmetry_form": {
        "form": [
          [
            "c11",
            "c12",
            "c13",
            "c14",
            "0",
            "0"
          ],
          [
            "c12",
            "c11",
            "c13",
            "-c14",
            "0",
            "0"
          ],
          [
            "c13",
            "c13",
            "c33",
            "0",
            "0",
            "0"
          ],
          [
            "c14",
            "-c14",
            "0",
            "c44",
            "0",
            "0"
          ],
          [
            "0",
            "0",
            "0",
            "0",
            "c44",
            "c14"
          ],
          [
            "0",
            "0",
            "0",
            "0",
            "c14",
            "(c11-c12)/2"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "c22 = c11",
          "c23 = c13",
          "c24 = -c14",
          "c55 = c44",
          "c56 = c14",
          "c66 = (c11 - c12)/2"
        ]
      },
      "tensor": "elastic-stiffness-cE",
      "unit": {
        "display": "GPa",
        "qudt": "http://qudt.org/vocab/unit/GigaPA",
        "ucum": "GPa"
      },
      "variant": "unspecified",
      "voigt": [
        [
          199.5,
          55.27,
          67.67,
          8.7,
          0.0,
          0.0
        ],
        [
          55.27,
          199.5,
          67.67,
          -8.7,
          0.0,
          0.0
        ],
        [
          67.67,
          67.67,
          235.2,
          0.0,
          0.0,
          0.0
        ],
        [
          8.7,
          -8.7,
          0.0,
          59.48,
          0.0,
          0.0
        ],
        [
          0.0,
          0.0,
          0.0,
          0.0,
          59.48,
          8.7
        ],
        [
          0.0,
          0.0,
          0.0,
          0.0,
          8.7,
          72.115
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "C_ijkl = c_IJ, I = V(ij), J = V(kl)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "conditions": {
        "electrical_boundary": "E"
      },
      "frame": {
        "convention": "unstated",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "not stated in this record; tensor form matches this frame by symmetry"
      },
      "full": [
        [
          [
            [
              198.4,
              0.0,
              0.0
            ],
            [
              0.0,
              54.72,
              7.88
            ],
            [
              0.0,
              7.88,
              65.13
            ]
          ],
          [
            [
              0.0,
              71.84,
              7.88
            ],
            [
              71.84,
              0.0,
              0.0
            ],
            [
              7.88,
              0.0,
              0.0
            ]
          ],
          [
            [
              0.0,
              7.88,
              59.65
            ],
            [
              7.88,
              0.0,
              0.0
            ],
            [
              59.65,
              0.0,
              0.0
            ]
          ]
        ],
        [
          [
            [
              0.0,
              71.84,
              7.88
            ],
            [
              71.84,
              0.0,
              0.0
            ],
            [
              7.88,
              0.0,
              0.0
            ]
          ],
          [
            [
              54.72,
              0.0,
              0.0
            ],
            [
              0.0,
              198.4,
              -7.88
            ],
            [
              0.0,
              -7.88,
              65.13
            ]
          ],
          [
            [
              7.88,
              0.0,
              0.0
            ],
            [
              0.0,
              -7.88,
              59.65
            ],
            [
              0.0,
              59.65,
              0.0
            ]
          ]
        ],
        [
          [
            [
              0.0,
              7.88,
              59.65
            ],
            [
              7.88,
              0.0,
              0.0
            ],
            [
              59.65,
              0.0,
              0.0
            ]
          ],
          [
            [
              7.88,
              0.0,
              0.0
            ],
            [
              0.0,
              -7.88,
              59.65
            ],
            [
              0.0,
              59.65,
              0.0
            ]
          ],
          [
            [
              65.13,
              0.0,
              0.0
            ],
            [
              0.0,
              65.13,
              0.0
            ],
            [
              0.0,
              0.0,
              227.9
            ]
          ]
        ]
      ],
      "id": "elastic-stiffness-cE/unspecified/ogi2002-kovacs1990",
      "independent": {
        "c11": {
          "value": 198.4
        },
        "c12": {
          "value": 54.72
        },
        "c13": {
          "value": 65.13
        },
        "c14": {
          "value": 7.88
        },
        "c33": {
          "value": 227.9
        },
        "c44": {
          "value": 59.65
        }
      },
      "kind": "tensor",
      "name": "Elastic stiffness at constant electric field",
      "provenance": {
        "locator": "Table III",
        "original_reference": "Kovacs et al., IEEE Ultrasonics Symposium 1990",
        "source_id": "ogi2002",
        "status": "S",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 4,
      "scale": 1,
      "symbol": "c^E",
      "symmetry_form": {
        "form": [
          [
            "c11",
            "c12",
            "c13",
            "c14",
            "0",
            "0"
          ],
          [
            "c12",
            "c11",
            "c13",
            "-c14",
            "0",
            "0"
          ],
          [
            "c13",
            "c13",
            "c33",
            "0",
            "0",
            "0"
          ],
          [
            "c14",
            "-c14",
            "0",
            "c44",
            "0",
            "0"
          ],
          [
            "0",
            "0",
            "0",
            "0",
            "c44",
            "c14"
          ],
          [
            "0",
            "0",
            "0",
            "0",
            "c14",
            "(c11-c12)/2"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "c22 = c11",
          "c23 = c13",
          "c24 = -c14",
          "c55 = c44",
          "c56 = c14",
          "c66 = (c11 - c12)/2"
        ]
      },
      "tensor": "elastic-stiffness-cE",
      "unit": {
        "display": "GPa",
        "qudt": "http://qudt.org/vocab/unit/GigaPA",
        "ucum": "GPa"
      },
      "variant": "unspecified",
      "voigt": [
        [
          198.4,
          54.72,
          65.13,
          7.88,
          0.0,
          0.0
        ],
        [
          54.72,
          198.4,
          65.13,
          -7.88,
          0.0,
          0.0
        ],
        [
          65.13,
          65.13,
          227.9,
          0.0,
          0.0,
          0.0
        ],
        [
          7.88,
          -7.88,
          0.0,
          59.65,
          0.0,
          0.0
        ],
        [
          0.0,
          0.0,
          0.0,
          0.0,
          59.65,
          7.88
        ],
        [
          0.0,
          0.0,
          0.0,
          0.0,
          7.88,
          71.84
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "C_ijkl = c_IJ, I = V(ij), J = V(kl)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "conditions": {
        "electrical_boundary": "E"
      },
      "frame": {
        "convention": "IRE-1949",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "+c points out of the face that becomes negative on compression; equivalently it becomes positive on cooling (weis1985 pp. 192-193)"
      },
      "full": [
        [
          [
            [
              200.0,
              0.0,
              0.0
            ],
            [
              0.0,
              54.0,
              8.0
            ],
            [
              0.0,
              8.0,
              60.0
            ]
          ],
          [
            [
              0.0,
              73.0,
              8.0
            ],
            [
              73.0,
              0.0,
              0.0
            ],
            [
              8.0,
              0.0,
              0.0
            ]
          ],
          [
            [
              0.0,
              8.0,
              60.0
            ],
            [
              8.0,
              0.0,
              0.0
            ],
            [
              60.0,
              0.0,
              0.0
            ]
          ]
        ],
        [
          [
            [
              0.0,
              73.0,
              8.0
            ],
            [
              73.0,
              0.0,
              0.0
            ],
            [
              8.0,
              0.0,
              0.0
            ]
          ],
          [
            [
              54.0,
              0.0,
              0.0
            ],
            [
              0.0,
              200.0,
              -8.0
            ],
            [
              0.0,
              -8.0,
              60.0
            ]
          ],
          [
            [
              8.0,
              0.0,
              0.0
            ],
            [
              0.0,
              -8.0,
              60.0
            ],
            [
              0.0,
              60.0,
              0.0
            ]
          ]
        ],
        [
          [
            [
              0.0,
              8.0,
              60.0
            ],
            [
              8.0,
              0.0,
              0.0
            ],
            [
              60.0,
              0.0,
              0.0
            ]
          ],
          [
            [
              8.0,
              0.0,
              0.0
            ],
            [
              0.0,
              -8.0,
              60.0
            ],
            [
              0.0,
              60.0,
              0.0
            ]
          ],
          [
            [
              60.0,
              0.0,
              0.0
            ],
            [
              0.0,
              60.0,
              0.0
            ],
            [
              0.0,
              0.0,
              243.0
            ]
          ]
        ]
      ],
      "id": "elastic-stiffness-cE/unspecified/weis1985-nakagawa1973",
      "independent": {
        "c11": {
          "value": 200
        },
        "c12": {
          "value": 54
        },
        "c13": {
          "value": 60
        },
        "c14": {
          "value": 8
        },
        "c33": {
          "value": 243
        },
        "c44": {
          "value": 60
        }
      },
      "kind": "tensor",
      "name": "Elastic stiffness at constant electric field",
      "provenance": {
        "locator": "Table 6, p. 200",
        "original_reference": "Nakagawa et al. 1973",
        "source_id": "weis1985",
        "status": "P-comp",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 4,
      "scale": 1,
      "symbol": "c^E",
      "symmetry_form": {
        "form": [
          [
            "c11",
            "c12",
            "c13",
            "c14",
            "0",
            "0"
          ],
          [
            "c12",
            "c11",
            "c13",
            "-c14",
            "0",
            "0"
          ],
          [
            "c13",
            "c13",
            "c33",
            "0",
            "0",
            "0"
          ],
          [
            "c14",
            "-c14",
            "0",
            "c44",
            "0",
            "0"
          ],
          [
            "0",
            "0",
            "0",
            "0",
            "c44",
            "c14"
          ],
          [
            "0",
            "0",
            "0",
            "0",
            "c14",
            "(c11-c12)/2"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "c22 = c11",
          "c23 = c13",
          "c24 = -c14",
          "c55 = c44",
          "c56 = c14",
          "c66 = (c11 - c12)/2"
        ]
      },
      "tensor": "elastic-stiffness-cE",
      "unit": {
        "display": "GPa",
        "qudt": "http://qudt.org/vocab/unit/GigaPA",
        "ucum": "GPa"
      },
      "variant": "unspecified",
      "voigt": [
        [
          200.0,
          54.0,
          60.0,
          8.0,
          0.0,
          0.0
        ],
        [
          54.0,
          200.0,
          60.0,
          -8.0,
          0.0,
          0.0
        ],
        [
          60.0,
          60.0,
          243.0,
          0.0,
          0.0,
          0.0
        ],
        [
          8.0,
          -8.0,
          0.0,
          60.0,
          0.0,
          0.0
        ],
        [
          0.0,
          0.0,
          0.0,
          0.0,
          60.0,
          8.0
        ],
        [
          0.0,
          0.0,
          0.0,
          0.0,
          8.0,
          73.0
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "C_ijkl = c_IJ, I = V(ij), J = V(kl)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "conditions": {
        "electrical_boundary": "E"
      },
      "frame": {
        "convention": "IRE-1949",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "+c points out of the face that becomes negative on compression; equivalently it becomes positive on cooling (weis1985 pp. 192-193)"
      },
      "full": [
        [
          [
            [
              203.0,
              0.0,
              0.0
            ],
            [
              0.0,
              57.3,
              8.5
            ],
            [
              0.0,
              8.5,
              75.2
            ]
          ],
          [
            [
              0.0,
              72.85,
              8.5
            ],
            [
              72.85,
              0.0,
              0.0
            ],
            [
              8.5,
              0.0,
              0.0
            ]
          ],
          [
            [
              0.0,
              8.5,
              59.5
            ],
            [
              8.5,
              0.0,
              0.0
            ],
            [
              59.5,
              0.0,
              0.0
            ]
          ]
        ],
        [
          [
            [
              0.0,
              72.85,
              8.5
            ],
            [
              72.85,
              0.0,
              0.0
            ],
            [
              8.5,
              0.0,
              0.0
            ]
          ],
          [
            [
              57.3,
              0.0,
              0.0
            ],
            [
              0.0,
              203.0,
              -8.5
            ],
            [
              0.0,
              -8.5,
              75.2
            ]
          ],
          [
            [
              8.5,
              0.0,
              0.0
            ],
            [
              0.0,
              -8.5,
              59.5
            ],
            [
              0.0,
              59.5,
              0.0
            ]
          ]
        ],
        [
          [
            [
              0.0,
              8.5,
              59.5
            ],
            [
              8.5,
              0.0,
              0.0
            ],
            [
              59.5,
              0.0,
              0.0
            ]
          ],
          [
            [
              8.5,
              0.0,
              0.0
            ],
            [
              0.0,
              -8.5,
              59.5
            ],
            [
              0.0,
              59.5,
              0.0
            ]
          ],
          [
            [
              75.2,
              0.0,
              0.0
            ],
            [
              0.0,
              75.2,
              0.0
            ],
            [
              0.0,
              0.0,
              242.4
            ]
          ]
        ]
      ],
      "id": "elastic-stiffness-cE/unspecified/weis1985-smithwelsh1971",
      "independent": {
        "c11": {
          "value": 203.0
        },
        "c12": {
          "value": 57.3
        },
        "c13": {
          "value": 75.2
        },
        "c14": {
          "value": 8.5
        },
        "c33": {
          "value": 242.4
        },
        "c44": {
          "value": 59.5
        }
      },
      "kind": "tensor",
      "name": "Elastic stiffness at constant electric field",
      "notes": "cti1999 copies this set. Temperature coefficients (1e-4 /C): c11 -1.74, c12 -2.52, c13 -1.59, c14 -2.14, c33 -1.53, c44 -2.04 (weis1985 Table 6).",
      "provenance": {
        "locator": "Table 6, p. 200 (unit 1.0e11 N/m^2)",
        "original_reference": "Smith & Welsh, J. Appl. Phys. 42, 2219 (1971)",
        "source_id": "weis1985",
        "status": "P-comp",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 4,
      "scale": 1,
      "symbol": "c^E",
      "symmetry_form": {
        "form": [
          [
            "c11",
            "c12",
            "c13",
            "c14",
            "0",
            "0"
          ],
          [
            "c12",
            "c11",
            "c13",
            "-c14",
            "0",
            "0"
          ],
          [
            "c13",
            "c13",
            "c33",
            "0",
            "0",
            "0"
          ],
          [
            "c14",
            "-c14",
            "0",
            "c44",
            "0",
            "0"
          ],
          [
            "0",
            "0",
            "0",
            "0",
            "c44",
            "c14"
          ],
          [
            "0",
            "0",
            "0",
            "0",
            "c14",
            "(c11-c12)/2"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "c22 = c11",
          "c23 = c13",
          "c24 = -c14",
          "c55 = c44",
          "c56 = c14",
          "c66 = (c11 - c12)/2"
        ]
      },
      "tensor": "elastic-stiffness-cE",
      "unit": {
        "display": "GPa",
        "qudt": "http://qudt.org/vocab/unit/GigaPA",
        "ucum": "GPa"
      },
      "variant": "unspecified",
      "voigt": [
        [
          203.0,
          57.3,
          75.2,
          8.5,
          0.0,
          0.0
        ],
        [
          57.3,
          203.0,
          75.2,
          -8.5,
          0.0,
          0.0
        ],
        [
          75.2,
          75.2,
          242.4,
          0.0,
          0.0,
          0.0
        ],
        [
          8.5,
          -8.5,
          0.0,
          59.5,
          0.0,
          0.0
        ],
        [
          0.0,
          0.0,
          0.0,
          0.0,
          59.5,
          8.5
        ],
        [
          0.0,
          0.0,
          0.0,
          0.0,
          8.5,
          72.85
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "C_ijkl = c_IJ, I = V(ij), J = V(kl)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "conditions": {
        "electrical_boundary": "E"
      },
      "frame": {
        "convention": "IRE-1949",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "+c points out of the face that becomes negative on compression; equivalently it becomes positive on cooling (weis1985 pp. 192-193)"
      },
      "full": [
        [
          [
            [
              203.0,
              0.0,
              0.0
            ],
            [
              0.0,
              53.0,
              9.0
            ],
            [
              0.0,
              9.0,
              75.0
            ]
          ],
          [
            [
              0.0,
              75.0,
              9.0
            ],
            [
              75.0,
              0.0,
              0.0
            ],
            [
              9.0,
              0.0,
              0.0
            ]
          ],
          [
            [
              0.0,
              9.0,
              60.0
            ],
            [
              9.0,
              0.0,
              0.0
            ],
            [
              60.0,
              0.0,
              0.0
            ]
          ]
        ],
        [
          [
            [
              0.0,
              75.0,
              9.0
            ],
            [
              75.0,
              0.0,
              0.0
            ],
            [
              9.0,
              0.0,
              0.0
            ]
          ],
          [
            [
              53.0,
              0.0,
              0.0
            ],
            [
              0.0,
              203.0,
              -9.0
            ],
            [
              0.0,
              -9.0,
              75.0
            ]
          ],
          [
            [
              9.0,
              0.0,
              0.0
            ],
            [
              0.0,
              -9.0,
              60.0
            ],
            [
              0.0,
              60.0,
              0.0
            ]
          ]
        ],
        [
          [
            [
              0.0,
              9.0,
              60.0
            ],
            [
              9.0,
              0.0,
              0.0
            ],
            [
              60.0,
              0.0,
              0.0
            ]
          ],
          [
            [
              9.0,
              0.0,
              0.0
            ],
            [
              0.0,
              -9.0,
              60.0
            ],
            [
              0.0,
              60.0,
              0.0
            ]
          ],
          [
            [
              75.0,
              0.0,
              0.0
            ],
            [
              0.0,
              75.0,
              0.0
            ],
            [
              0.0,
              0.0,
              245.0
            ]
          ]
        ]
      ],
      "id": "elastic-stiffness-cE/unspecified/weis1985-warner1967",
      "independent": {
        "c11": {
          "value": 203
        },
        "c12": {
          "value": 53
        },
        "c13": {
          "value": 75
        },
        "c14": {
          "value": 9
        },
        "c33": {
          "value": 245
        },
        "c44": {
          "value": 60
        }
      },
      "kind": "tensor",
      "name": "Elastic stiffness at constant electric field",
      "provenance": {
        "locator": "Table 6, p. 200",
        "original_reference": "Warner, Onoe, Coquin, JASA 42, 1223 (1967)",
        "source_id": "weis1985",
        "status": "P-comp",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 4,
      "scale": 1,
      "symbol": "c^E",
      "symmetry_form": {
        "form": [
          [
            "c11",
            "c12",
            "c13",
            "c14",
            "0",
            "0"
          ],
          [
            "c12",
            "c11",
            "c13",
            "-c14",
            "0",
            "0"
          ],
          [
            "c13",
            "c13",
            "c33",
            "0",
            "0",
            "0"
          ],
          [
            "c14",
            "-c14",
            "0",
            "c44",
            "0",
            "0"
          ],
          [
            "0",
            "0",
            "0",
            "0",
            "c44",
            "c14"
          ],
          [
            "0",
            "0",
            "0",
            "0",
            "c14",
            "(c11-c12)/2"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "c22 = c11",
          "c23 = c13",
          "c24 = -c14",
          "c55 = c44",
          "c56 = c14",
          "c66 = (c11 - c12)/2"
        ]
      },
      "tensor": "elastic-stiffness-cE",
      "unit": {
        "display": "GPa",
        "qudt": "http://qudt.org/vocab/unit/GigaPA",
        "ucum": "GPa"
      },
      "variant": "unspecified",
      "voigt": [
        [
          203.0,
          53.0,
          75.0,
          9.0,
          0.0,
          0.0
        ],
        [
          53.0,
          203.0,
          75.0,
          -9.0,
          0.0,
          0.0
        ],
        [
          75.0,
          75.0,
          245.0,
          0.0,
          0.0,
          0.0
        ],
        [
          9.0,
          -9.0,
          0.0,
          60.0,
          0.0,
          0.0
        ],
        [
          0.0,
          0.0,
          0.0,
          0.0,
          60.0,
          9.0
        ],
        [
          0.0,
          0.0,
          0.0,
          0.0,
          9.0,
          75.0
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "C_ijkl = c_IJ, I = V(ij), J = V(kl)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "conditions": {
        "frequency_text": "high frequency",
        "mechanical_boundary": "S",
        "wavelength_nm": 633
      },
      "frame": {
        "convention": "unstated",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "not stated in this record; tensor form matches this frame by symmetry"
      },
      "full": [
        [
          [
            0.0,
            -3.0,
            9.0
          ],
          [
            -3.0,
            0.0,
            0.0
          ],
          [
            28.0,
            0.0,
            0.0
          ]
        ],
        [
          [
            -3.0,
            0.0,
            0.0
          ],
          [
            0.0,
            3.0,
            9.0
          ],
          [
            0.0,
            28.0,
            0.0
          ]
        ],
        [
          [
            28.0,
            0.0,
            0.0
          ],
          [
            0.0,
            28.0,
            0.0
          ],
          [
            0.0,
            0.0,
            31.0
          ]
        ]
      ],
      "id": "eo-rS/cln/cti1999",
      "independent": {
        "r13": {
          "value": 9
        },
        "r22": {
          "value": 3
        },
        "r33": {
          "value": 31
        },
        "r51": {
          "value": 28
        }
      },
      "kind": "tensor",
      "name": "Linear electro-optic (Pockels) coefficients, clamped (constant strain)",
      "notes": "Data sheet also lists r_c = 19 pm/V.",
      "provenance": {
        "source_id": "cti1999",
        "status": "V",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 3,
      "scale": 1,
      "symbol": "r^S",
      "symmetry_form": {
        "form": [
          [
            "0",
            "-r22",
            "r13"
          ],
          [
            "0",
            "r22",
            "r13"
          ],
          [
            "0",
            "0",
            "r33"
          ],
          [
            "0",
            "r51",
            "0"
          ],
          [
            "r51",
            "0",
            "0"
          ],
          [
            "-r22",
            "0",
            "0"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "r12 = -r22",
          "r23 = r13",
          "r42 = r51",
          "r61 = -r22"
        ]
      },
      "tensor": "eo-rS",
      "unit": {
        "display": "pm/V",
        "ucum": "pm/V"
      },
      "variant": "cln",
      "voigt": [
        [
          0.0,
          -3.0,
          9.0
        ],
        [
          0.0,
          3.0,
          9.0
        ],
        [
          0.0,
          0.0,
          31.0
        ],
        [
          0.0,
          28.0,
          0.0
        ],
        [
          28.0,
          0.0,
          0.0
        ],
        [
          -3.0,
          0.0,
          0.0
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "r_ijk = r_Ik, I = V(ij) (impermeability change d(eta)_ij = r_ijk E_k)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "conditions": {
        "mechanical_boundary": "S",
        "wavelength_nm": 633
      },
      "frame": {
        "convention": "IRE-1949",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "+c points out of the face that becomes negative on compression; equivalently it becomes positive on cooling (weis1985 pp. 192-193)"
      },
      "full": [
        [
          [
            0.0,
            -3.4,
            8.6
          ],
          [
            -3.4,
            0.0,
            0.0
          ],
          [
            28.0,
            0.0,
            0.0
          ]
        ],
        [
          [
            -3.4,
            0.0,
            0.0
          ],
          [
            0.0,
            3.4,
            8.6
          ],
          [
            0.0,
            28.0,
            0.0
          ]
        ],
        [
          [
            28.0,
            0.0,
            0.0
          ],
          [
            0.0,
            28.0,
            0.0
          ],
          [
            0.0,
            0.0,
            30.8
          ]
        ]
      ],
      "id": "eo-rS/cln/turner1966",
      "independent": {
        "r13": {
          "value": 8.6
        },
        "r22": {
          "value": 3.4
        },
        "r33": {
          "value": 30.8
        },
        "r51": {
          "value": 28
        }
      },
      "kind": "tensor",
      "name": "Linear electro-optic (Pockels) coefficients, clamped (constant strain)",
      "notes": "Turner 1966 also gives 6.5 (r13), 3.1 (r22), 28 (r33) and 23 (r51) pm/V at 3390 nm. r33 = 30.8-31 is the value most TFLN papers reuse.",
      "provenance": {
        "locator": "weis1985 Table 4, p. 199",
        "source_id": "turner1966",
        "status": "P-comp",
        "transcribed": "2026-10-25",
        "via": "weis1985"
      },
      "public": true,
      "rank": 3,
      "scale": 1,
      "symbol": "r^S",
      "symmetry_form": {
        "form": [
          [
            "0",
            "-r22",
            "r13"
          ],
          [
            "0",
            "r22",
            "r13"
          ],
          [
            "0",
            "0",
            "r33"
          ],
          [
            "0",
            "r51",
            "0"
          ],
          [
            "r51",
            "0",
            "0"
          ],
          [
            "-r22",
            "0",
            "0"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "r12 = -r22",
          "r23 = r13",
          "r42 = r51",
          "r61 = -r22"
        ]
      },
      "tensor": "eo-rS",
      "unit": {
        "display": "pm/V",
        "ucum": "pm/V"
      },
      "variant": "cln",
      "variant_note": "composition not stated in weis1985; volk2008 Table 1.2 lists the same clamped r33, r13, r22 (31, 8.6, 3.4) for CLN",
      "voigt": [
        [
          0.0,
          -3.4,
          8.6
        ],
        [
          0.0,
          3.4,
          8.6
        ],
        [
          0.0,
          0.0,
          30.8
        ],
        [
          0.0,
          28.0,
          0.0
        ],
        [
          28.0,
          0.0,
          0.0
        ],
        [
          -3.4,
          0.0,
          0.0
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "r_ijk = r_Ik, I = V(ij) (impermeability change d(eta)_ij = r_ijk E_k)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "conditions": {
        "mechanical_boundary": "S",
        "wavelength_nm": 633
      },
      "frame": {
        "convention": "IRE-1949",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "+c points out of the face that becomes negative on compression; equivalently it becomes positive on cooling (weis1985 pp. 192-193)"
      },
      "full": [
        [
          [
            0.0,
            -3.4,
            7.7
          ],
          [
            -3.4,
            0.0,
            0.0
          ],
          [
            18.2,
            0.0,
            0.0
          ]
        ],
        [
          [
            -3.4,
            0.0,
            0.0
          ],
          [
            0.0,
            3.4,
            7.7
          ],
          [
            0.0,
            18.2,
            0.0
          ]
        ],
        [
          [
            18.2,
            0.0,
            0.0
          ],
          [
            0.0,
            18.2,
            0.0
          ],
          [
            0.0,
            0.0,
            28.8
          ]
        ]
      ],
      "id": "eo-rS/unspecified/kaminow1980",
      "independent": {
        "r13": {
          "original_reference": "Turner, as cited in Kaminow et al. 1980",
          "value": 7.7
        },
        "r22": {
          "original_reference": "Turner, as cited in Kaminow et al. 1980",
          "value": 3.4
        },
        "r33": {
          "original_reference": "Turner, as cited in Kaminow et al. 1980",
          "value": 28.8
        },
        "r51": {
          "original_reference": "Kaminow et al. 1980",
          "value": 18.2
        }
      },
      "kind": "tensor",
      "name": "Linear electro-optic (Pockels) coefficients, clamped (constant strain)",
      "notes": "weis1985 calls the 1980 values probably the most accurate (fringing-field corrected). r51^S = 18.2 is 35% below the 28 of Turner 1966 and cti1999: shown as a spread, not blended. Kaminow 1980 itself not read.",
      "provenance": {
        "locator": "weis1985 Table 4, p. 199",
        "source_id": "kaminow1980",
        "status": "P-comp",
        "transcribed": "2026-10-25",
        "via": "weis1985"
      },
      "public": true,
      "rank": 3,
      "scale": 1,
      "symbol": "r^S",
      "symmetry_form": {
        "form": [
          [
            "0",
            "-r22",
            "r13"
          ],
          [
            "0",
            "r22",
            "r13"
          ],
          [
            "0",
            "0",
            "r33"
          ],
          [
            "0",
            "r51",
            "0"
          ],
          [
            "r51",
            "0",
            "0"
          ],
          [
            "-r22",
            "0",
            "0"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "r12 = -r22",
          "r23 = r13",
          "r42 = r51",
          "r61 = -r22"
        ]
      },
      "tensor": "eo-rS",
      "unit": {
        "display": "pm/V",
        "ucum": "pm/V"
      },
      "variant": "unspecified",
      "variant_note": "composition not stated in weis1985",
      "voigt": [
        [
          0.0,
          -3.4,
          7.7
        ],
        [
          0.0,
          3.4,
          7.7
        ],
        [
          0.0,
          0.0,
          28.8
        ],
        [
          0.0,
          18.2,
          0.0
        ],
        [
          18.2,
          0.0,
          0.0
        ],
        [
          -3.4,
          0.0,
          0.0
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "r_ijk = r_Ik, I = V(ij) (impermeability change d(eta)_ij = r_ijk E_k)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "conditions": {
        "frequency_text": "low frequency",
        "mechanical_boundary": "T",
        "wavelength_nm": 633
      },
      "frame": {
        "convention": "unstated",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "not stated in this record; tensor form matches this frame by symmetry"
      },
      "full": [
        [
          [
            0.0,
            -7.0,
            10.0
          ],
          [
            -7.0,
            0.0,
            0.0
          ],
          [
            33.0,
            0.0,
            0.0
          ]
        ],
        [
          [
            -7.0,
            0.0,
            0.0
          ],
          [
            0.0,
            7.0,
            10.0
          ],
          [
            0.0,
            33.0,
            0.0
          ]
        ],
        [
          [
            33.0,
            0.0,
            0.0
          ],
          [
            0.0,
            33.0,
            0.0
          ],
          [
            0.0,
            0.0,
            33.0
          ]
        ]
      ],
      "id": "eo-rT/cln/cti1999",
      "independent": {
        "r13": {
          "value": 10
        },
        "r22": {
          "value": 7
        },
        "r33": {
          "value": 33
        },
        "r51": {
          "value": 33
        }
      },
      "kind": "tensor",
      "name": "Linear electro-optic (Pockels) coefficients, unclamped (constant stress)",
      "notes": "Data sheet also lists r_c = 18 pm/V.",
      "provenance": {
        "source_id": "cti1999",
        "status": "V",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 3,
      "scale": 1,
      "symbol": "r^T",
      "symmetry_form": {
        "form": [
          [
            "0",
            "-r22",
            "r13"
          ],
          [
            "0",
            "r22",
            "r13"
          ],
          [
            "0",
            "0",
            "r33"
          ],
          [
            "0",
            "r51",
            "0"
          ],
          [
            "r51",
            "0",
            "0"
          ],
          [
            "-r22",
            "0",
            "0"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "r12 = -r22",
          "r23 = r13",
          "r42 = r51",
          "r61 = -r22"
        ]
      },
      "tensor": "eo-rT",
      "unit": {
        "display": "pm/V",
        "ucum": "pm/V"
      },
      "variant": "cln",
      "voigt": [
        [
          0.0,
          -7.0,
          10.0
        ],
        [
          0.0,
          7.0,
          10.0
        ],
        [
          0.0,
          0.0,
          33.0
        ],
        [
          0.0,
          33.0,
          0.0
        ],
        [
          33.0,
          0.0,
          0.0
        ],
        [
          -7.0,
          0.0,
          0.0
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "r_ijk = r_Ik, I = V(ij) (impermeability change d(eta)_ij = r_ijk E_k)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "conditions": {
        "mechanical_boundary": "T",
        "wavelength_nm": 633
      },
      "default": true,
      "frame": {
        "convention": "IRE-1949",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "+c points out of the face that becomes negative on compression; equivalently it becomes positive on cooling (weis1985 pp. 192-193)"
      },
      "full": [
        [
          [
            0.0,
            -6.81,
            10.0
          ],
          [
            -6.81,
            0.0,
            0.0
          ],
          [
            32.0,
            0.0,
            0.0
          ]
        ],
        [
          [
            -6.81,
            0.0,
            0.0
          ],
          [
            0.0,
            6.81,
            10.0
          ],
          [
            0.0,
            32.0,
            0.0
          ]
        ],
        [
          [
            32.0,
            0.0,
            0.0
          ],
          [
            0.0,
            32.0,
            0.0
          ],
          [
            0.0,
            0.0,
            32.2
          ]
        ]
      ],
      "id": "eo-rT/cln/weis1985",
      "independent": {
        "r13": {
          "notes": "sign explicitly positive in weis1985; Smakula & Claspy 1967 give 10.9",
          "original_reference": "Zook, Chen, Otto, APL 11, 159 (1967)",
          "value": 10.0
        },
        "r22": {
          "notes": "Lenzo et al. 1966 and Smakula 1967 give 6.7",
          "original_reference": "Zook, Chen, Otto, APL 11, 159 (1967)",
          "value": 6.81
        },
        "r33": {
          "notes": "Smakula & Claspy 1967 give 34.0",
          "original_reference": "Zook, Chen, Otto, APL 11, 159 (1967)",
          "value": 32.2
        },
        "r51": {
          "original_reference": "Bernal et al. 1966",
          "value": 32
        }
      },
      "kind": "tensor",
      "name": "Linear electro-optic (Pockels) coefficients, unclamped (constant stress)",
      "notes": "No 1550 nm EO values were found in any source read ( gap 4). Free (T) coefficients vary within +-5% with melt composition (Turner, Nash, Bridenbaugh 1970, via weis1985 p. 199); r22 varies with composition with a minimum near 48.9 mol% (volk2008 p. 150).",
      "provenance": {
        "locator": "Table 4, p. 199",
        "source_id": "weis1985",
        "status": "P-comp",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 3,
      "scale": 1,
      "symbol": "r^T",
      "symmetry_form": {
        "form": [
          [
            "0",
            "-r22",
            "r13"
          ],
          [
            "0",
            "r22",
            "r13"
          ],
          [
            "0",
            "0",
            "r33"
          ],
          [
            "0",
            "r51",
            "0"
          ],
          [
            "r51",
            "0",
            "0"
          ],
          [
            "-r22",
            "0",
            "0"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "r12 = -r22",
          "r23 = r13",
          "r42 = r51",
          "r61 = -r22"
        ]
      },
      "tensor": "eo-rT",
      "unit": {
        "display": "pm/V",
        "ucum": "pm/V"
      },
      "variant": "cln",
      "variant_note": "composition not stated in weis1985; volk2008 Table 1.2 lists the same values for CLN",
      "voigt": [
        [
          0.0,
          -6.81,
          10.0
        ],
        [
          0.0,
          6.81,
          10.0
        ],
        [
          0.0,
          0.0,
          32.2
        ],
        [
          0.0,
          32.0,
          0.0
        ],
        [
          32.0,
          0.0,
          0.0
        ],
        [
          -6.81,
          0.0,
          0.0
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "r_ijk = r_Ik, I = V(ij) (impermeability change d(eta)_ij = r_ijk E_k)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "conditions": {
        "wavelength_nm": 1060
      },
      "dk_scale": "legacy",
      "frame": {
        "convention": "unstated",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "not stated in this record; tensor form matches this frame by symmetry"
      },
      "full": [
        [
          [
            0.0,
            -3.0,
            -5.0
          ],
          [
            -3.0,
            0.0,
            0.0
          ],
          [
            -5.0,
            0.0,
            0.0
          ]
        ],
        [
          [
            -3.0,
            0.0,
            0.0
          ],
          [
            0.0,
            3.0,
            -5.0
          ],
          [
            0.0,
            -5.0,
            0.0
          ]
        ],
        [
          [
            -5.0,
            0.0,
            0.0
          ],
          [
            0.0,
            -5.0,
            0.0
          ],
          [
            0.0,
            0.0,
            -33.0
          ]
        ]
      ],
      "id": "nlo-d/cln/cti1999",
      "independent": {
        "d22": {
          "value": 3
        },
        "d31": {
          "value": -5
        },
        "d33": {
          "value": -33
        }
      },
      "kind": "tensor",
      "name": "Second-order nonlinear optical coefficients",
      "notes": "Pre-Shoji scale.",
      "provenance": {
        "source_id": "cti1999",
        "status": "V",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 3,
      "scale": 1,
      "symbol": "d (SHG)",
      "symmetry_form": {
        "form": [
          [
            "0",
            "0",
            "0",
            "0",
            "d31",
            "-d22"
          ],
          [
            "-d22",
            "d22",
            "0",
            "d31",
            "0",
            "0"
          ],
          [
            "d31",
            "d31",
            "d33",
            "0",
            "0",
            "0"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "Kleinman symmetry: d15 = d24 = d31",
          "d16 = d21 = -d22",
          "d32 = d31"
        ]
      },
      "tensor": "nlo-d",
      "unit": {
        "display": "pm/V",
        "ucum": "pm/V"
      },
      "variant": "cln",
      "voigt": [
        [
          0.0,
          0.0,
          0.0,
          0.0,
          -5.0,
          -3.0
        ],
        [
          -3.0,
          3.0,
          0.0,
          -5.0,
          0.0,
          0.0
        ],
        [
          -5.0,
          -5.0,
          -33.0,
          0.0,
          0.0,
          0.0
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "d_ijk = d_iJ, J = V(jk) (contracted SHG convention)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "conditions": {
        "note": "fundamental 1.06 um",
        "wavelength_nm": 1060
      },
      "dk_scale": "legacy",
      "frame": {
        "convention": "unstated",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "not stated in this record; tensor form matches this frame by symmetry"
      },
      "full": [
        [
          [
            0.0,
            -3.0,
            6.0
          ],
          [
            -3.0,
            0.0,
            0.0
          ],
          [
            6.0,
            0.0,
            0.0
          ]
        ],
        [
          [
            -3.0,
            0.0,
            0.0
          ],
          [
            0.0,
            3.0,
            6.0
          ],
          [
            0.0,
            6.0,
            0.0
          ]
        ],
        [
          [
            6.0,
            0.0,
            0.0
          ],
          [
            0.0,
            6.0,
            0.0
          ],
          [
            0.0,
            0.0,
            34.0
          ]
        ]
      ],
      "id": "nlo-d/cln/volk2008",
      "independent": {
        "d22": {
          "value": 3
        },
        "d31": {
          "value": 6
        },
        "d33": {
          "value": 34
        }
      },
      "kind": "tensor",
      "name": "Second-order nonlinear optical coefficients",
      "notes": "Legacy (pre-Shoji 1997) scale; the shoji1997 abstract states that many accepted standard values are overestimated. Kleinman symmetry assumed for the form (d15 = d31). Signs as listed (magnitudes).",
      "provenance": {
        "locator": "Table 1.2, p. 4",
        "original_reference": "Nikogosyan 2005",
        "source_id": "volk2008",
        "status": "P-comp",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 3,
      "scale": 1,
      "symbol": "d (SHG)",
      "symmetry_form": {
        "form": [
          [
            "0",
            "0",
            "0",
            "0",
            "d31",
            "-d22"
          ],
          [
            "-d22",
            "d22",
            "0",
            "d31",
            "0",
            "0"
          ],
          [
            "d31",
            "d31",
            "d33",
            "0",
            "0",
            "0"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "Kleinman symmetry: d15 = d24 = d31",
          "d16 = d21 = -d22",
          "d32 = d31"
        ]
      },
      "tensor": "nlo-d",
      "unit": {
        "display": "pm/V",
        "ucum": "pm/V"
      },
      "variant": "cln",
      "voigt": [
        [
          0.0,
          0.0,
          0.0,
          0.0,
          6.0,
          -3.0
        ],
        [
          -3.0,
          3.0,
          0.0,
          6.0,
          0.0,
          0.0
        ],
        [
          6.0,
          6.0,
          34.0,
          0.0,
          0.0,
          0.0
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "d_ijk = d_iJ, J = V(jk) (contracted SHG convention)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "conditions": {
        "note": "fundamental 1.06 um",
        "wavelength_nm": 1060
      },
      "dk_scale": "legacy",
      "frame": {
        "convention": "unstated",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "not stated in this record; tensor form matches this frame by symmetry"
      },
      "full": [
        [
          [
            0.0,
            -2.5,
            5.0
          ],
          [
            -2.5,
            0.0,
            0.0
          ],
          [
            5.0,
            0.0,
            0.0
          ]
        ],
        [
          [
            -2.5,
            0.0,
            0.0
          ],
          [
            0.0,
            2.5,
            5.0
          ],
          [
            0.0,
            5.0,
            0.0
          ]
        ],
        [
          [
            5.0,
            0.0,
            0.0
          ],
          [
            0.0,
            5.0,
            0.0
          ],
          [
            0.0,
            0.0,
            42.0
          ]
        ]
      ],
      "id": "nlo-d/sln/volk2008",
      "independent": {
        "d22": {
          "value": 2.5
        },
        "d31": {
          "value": 5
        },
        "d33": {
          "value": 42
        }
      },
      "kind": "tensor",
      "name": "Second-order nonlinear optical coefficients",
      "notes": "Legacy scale.",
      "provenance": {
        "locator": "Table 1.2, p. 4",
        "original_reference": "Nikogosyan 2005",
        "source_id": "volk2008",
        "status": "P-comp",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 3,
      "scale": 1,
      "symbol": "d (SHG)",
      "symmetry_form": {
        "form": [
          [
            "0",
            "0",
            "0",
            "0",
            "d31",
            "-d22"
          ],
          [
            "-d22",
            "d22",
            "0",
            "d31",
            "0",
            "0"
          ],
          [
            "d31",
            "d31",
            "d33",
            "0",
            "0",
            "0"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "Kleinman symmetry: d15 = d24 = d31",
          "d16 = d21 = -d22",
          "d32 = d31"
        ]
      },
      "tensor": "nlo-d",
      "unit": {
        "display": "pm/V",
        "ucum": "pm/V"
      },
      "variant": "sln",
      "variant_note": "near-stoichiometric",
      "voigt": [
        [
          0.0,
          0.0,
          0.0,
          0.0,
          5.0,
          -2.5
        ],
        [
          -2.5,
          2.5,
          0.0,
          5.0,
          0.0,
          0.0
        ],
        [
          5.0,
          5.0,
          42.0,
          0.0,
          0.0,
          0.0
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "d_ijk = d_iJ, J = V(jk) (contracted SHG convention)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "conditions": {
        "wavelength_nm": 1064
      },
      "frame": {
        "convention": "unstated",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "not stated in this record; tensor form matches this frame by symmetry"
      },
      "full": [
        [
          [
            0.0,
            -2.1,
            -4.3
          ],
          [
            -2.1,
            0.0,
            0.0
          ],
          [
            -4.3,
            0.0,
            0.0
          ]
        ],
        [
          [
            -2.1,
            0.0,
            0.0
          ],
          [
            0.0,
            2.1,
            -4.3
          ],
          [
            0.0,
            -4.3,
            0.0
          ]
        ],
        [
          [
            -4.3,
            0.0,
            0.0
          ],
          [
            0.0,
            -4.3,
            0.0
          ],
          [
            0.0,
            0.0,
            -27.0
          ]
        ]
      ],
      "id": "nlo-d/unspecified/zhu2021",
      "independent": {
        "d22": {
          "value": 2.1
        },
        "d31": {
          "value": -4.3
        },
        "d33": {
          "value": -27.0
        }
      },
      "kind": "tensor",
      "name": "Second-order nonlinear optical coefficients",
      "notes": "No reference given in the review table; scale not stated.",
      "provenance": {
        "locator": "Table 1",
        "source_id": "zhu2021",
        "status": "S",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 3,
      "scale": 1,
      "symbol": "d (SHG)",
      "symmetry_form": {
        "form": [
          [
            "0",
            "0",
            "0",
            "0",
            "d31",
            "-d22"
          ],
          [
            "-d22",
            "d22",
            "0",
            "d31",
            "0",
            "0"
          ],
          [
            "d31",
            "d31",
            "d33",
            "0",
            "0",
            "0"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "Kleinman symmetry: d15 = d24 = d31",
          "d16 = d21 = -d22",
          "d32 = d31"
        ]
      },
      "tensor": "nlo-d",
      "unit": {
        "display": "pm/V",
        "ucum": "pm/V"
      },
      "variant": "unspecified",
      "voigt": [
        [
          0.0,
          0.0,
          0.0,
          0.0,
          -4.3,
          -2.1
        ],
        [
          -2.1,
          2.1,
          0.0,
          -4.3,
          0.0,
          0.0
        ],
        [
          -4.3,
          -4.3,
          -27.0,
          0.0,
          0.0,
          0.0
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "d_ijk = d_iJ, J = V(jk) (contracted SHG convention)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "conditions": {
        "frequency_text": "> 10 MHz",
        "mechanical_boundary": "S"
      },
      "frame": {
        "convention": "unstated",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "not stated in this record; tensor form matches this frame by symmetry"
      },
      "full": [
        [
          44.0,
          0.0,
          0.0
        ],
        [
          0.0,
          44.0,
          0.0
        ],
        [
          0.0,
          0.0,
          27.9
        ]
      ],
      "id": "permittivity-S/cln/cti1999",
      "independent": {
        "eps11": {
          "value": 44
        },
        "eps33": {
          "value": 27.9
        }
      },
      "kind": "tensor",
      "name": "Relative permittivity, constant strain (clamped)",
      "provenance": {
        "source_id": "cti1999",
        "status": "V",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 2,
      "scale": 1,
      "symbol": "eps^S/eps0",
      "symmetry_form": {
        "form": [
          [
            "eps11",
            "0",
            "0"
          ],
          [
            "0",
            "eps11",
            "0"
          ],
          [
            "0",
            "0",
            "eps33"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "eps22 = eps11",
          "off-diagonal = 0"
        ]
      },
      "tensor": "permittivity-S",
      "unit": {
        "display": "relative (eps/eps0)",
        "qudt": "http://qudt.org/vocab/unit/UNITLESS",
        "ucum": "1"
      },
      "variant": "cln",
      "voigt": [
        [
          44.0,
          0.0,
          0.0
        ],
        [
          0.0,
          44.0,
          0.0
        ],
        [
          0.0,
          0.0,
          27.9
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "full[i][j] = M[i][j]",
        "order": [
          "x",
          "y",
          "z"
        ]
      }
    },
    {
      "conditions": {
        "frequency_text": "above acoustic resonances",
        "mechanical_boundary": "S",
        "method": "derived in the source's fit"
      },
      "default": true,
      "frame": {
        "convention": "unstated",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "not stated in this record; tensor form matches this frame by symmetry"
      },
      "full": [
        [
          44.9,
          0.0,
          0.0
        ],
        [
          0.0,
          44.9,
          0.0
        ],
        [
          0.0,
          0.0,
          26.7
        ]
      ],
      "id": "permittivity-S/cln/kushibiki1999",
      "independent": {
        "eps11": {
          "uncertainty": {
            "type": "stated",
            "value": 0.4
          },
          "value": 44.9
        },
        "eps33": {
          "uncertainty": {
            "type": "stated",
            "value": 0.3
          },
          "value": 26.7
        }
      },
      "kind": "tensor",
      "name": "Relative permittivity, constant strain (clamped)",
      "provenance": {
        "locator": "Table V",
        "source_id": "kushibiki1999",
        "status": "P",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 2,
      "scale": 1,
      "symbol": "eps^S/eps0",
      "symmetry_form": {
        "form": [
          [
            "eps11",
            "0",
            "0"
          ],
          [
            "0",
            "eps11",
            "0"
          ],
          [
            "0",
            "0",
            "eps33"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "eps22 = eps11",
          "off-diagonal = 0"
        ]
      },
      "tensor": "permittivity-S",
      "unit": {
        "display": "relative (eps/eps0)",
        "qudt": "http://qudt.org/vocab/unit/UNITLESS",
        "ucum": "1"
      },
      "variant": "cln",
      "variant_note": "SAW-grade congruent; composition not stated in the source",
      "voigt": [
        [
          44.9,
          0.0,
          0.0
        ],
        [
          0.0,
          44.9,
          0.0
        ],
        [
          0.0,
          0.0,
          26.7
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "full[i][j] = M[i][j]",
        "order": [
          "x",
          "y",
          "z"
        ]
      }
    },
    {
      "conditions": {
        "mechanical_boundary": "S"
      },
      "frame": {
        "convention": "unstated",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "not stated in this record; tensor form matches this frame by symmetry"
      },
      "full": [
        [
          44.0,
          0.0,
          0.0
        ],
        [
          0.0,
          44.0,
          0.0
        ],
        [
          0.0,
          0.0,
          29.0
        ]
      ],
      "id": "permittivity-S/cln/volk2008",
      "independent": {
        "eps11": {
          "value": 44
        },
        "eps33": {
          "value": 29
        }
      },
      "kind": "tensor",
      "name": "Relative permittivity, constant strain (clamped)",
      "provenance": {
        "locator": "Table 1.1, p. 3",
        "original_reference": "Tomeno & Matsumura, PRB 38, 606 (1988)",
        "source_id": "volk2008",
        "status": "P-comp",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 2,
      "scale": 1,
      "symbol": "eps^S/eps0",
      "symmetry_form": {
        "form": [
          [
            "eps11",
            "0",
            "0"
          ],
          [
            "0",
            "eps11",
            "0"
          ],
          [
            "0",
            "0",
            "eps33"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "eps22 = eps11",
          "off-diagonal = 0"
        ]
      },
      "tensor": "permittivity-S",
      "unit": {
        "display": "relative (eps/eps0)",
        "qudt": "http://qudt.org/vocab/unit/UNITLESS",
        "ucum": "1"
      },
      "variant": "cln",
      "voigt": [
        [
          44.0,
          0.0,
          0.0
        ],
        [
          0.0,
          44.0,
          0.0
        ],
        [
          0.0,
          0.0,
          29.0
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "full[i][j] = M[i][j]",
        "order": [
          "x",
          "y",
          "z"
        ]
      }
    },
    {
      "conditions": {
        "mechanical_boundary": "S"
      },
      "frame": {
        "convention": "IRE-1949",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "+c points out of the face that becomes negative on compression; equivalently it becomes positive on cooling (weis1985 pp. 192-193)"
      },
      "full": [
        [
          44.0,
          0.0,
          0.0
        ],
        [
          0.0,
          44.0,
          0.0
        ],
        [
          0.0,
          0.0,
          29.0
        ]
      ],
      "id": "permittivity-S/unspecified/weis1985-savage1966",
      "independent": {
        "eps11": {
          "value": 44
        },
        "eps33": {
          "value": 29
        }
      },
      "kind": "tensor",
      "name": "Relative permittivity, constant strain (clamped)",
      "provenance": {
        "locator": "Table 1, p. 197",
        "original_reference": "Savage, J. Appl. Phys. 37, 3071 (1966)",
        "source_id": "weis1985",
        "status": "P-comp",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 2,
      "scale": 1,
      "symbol": "eps^S/eps0",
      "symmetry_form": {
        "form": [
          [
            "eps11",
            "0",
            "0"
          ],
          [
            "0",
            "eps11",
            "0"
          ],
          [
            "0",
            "0",
            "eps33"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "eps22 = eps11",
          "off-diagonal = 0"
        ]
      },
      "tensor": "permittivity-S",
      "unit": {
        "display": "relative (eps/eps0)",
        "qudt": "http://qudt.org/vocab/unit/UNITLESS",
        "ucum": "1"
      },
      "variant": "unspecified",
      "voigt": [
        [
          44.0,
          0.0,
          0.0
        ],
        [
          0.0,
          44.0,
          0.0
        ],
        [
          0.0,
          0.0,
          29.0
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "full[i][j] = M[i][j]",
        "order": [
          "x",
          "y",
          "z"
        ]
      }
    },
    {
      "conditions": {
        "mechanical_boundary": "S"
      },
      "frame": {
        "convention": "IRE-1949",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "+c points out of the face that becomes negative on compression; equivalently it becomes positive on cooling (weis1985 pp. 192-193)"
      },
      "full": [
        [
          46.5,
          0.0,
          0.0
        ],
        [
          0.0,
          46.5,
          0.0
        ],
        [
          0.0,
          0.0,
          27.3
        ]
      ],
      "id": "permittivity-S/unspecified/weis1985-teague1975",
      "independent": {
        "eps11": {
          "value": 46.5
        },
        "eps33": {
          "value": 27.3
        }
      },
      "kind": "tensor",
      "name": "Relative permittivity, constant strain (clamped)",
      "provenance": {
        "locator": "Table 1, p. 197",
        "original_reference": "Teague, Rice, Gerson, J. Appl. Phys. 46, 2864 (1975)",
        "source_id": "weis1985",
        "status": "P-comp",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 2,
      "scale": 1,
      "symbol": "eps^S/eps0",
      "symmetry_form": {
        "form": [
          [
            "eps11",
            "0",
            "0"
          ],
          [
            "0",
            "eps11",
            "0"
          ],
          [
            "0",
            "0",
            "eps33"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "eps22 = eps11",
          "off-diagonal = 0"
        ]
      },
      "tensor": "permittivity-S",
      "unit": {
        "display": "relative (eps/eps0)",
        "qudt": "http://qudt.org/vocab/unit/UNITLESS",
        "ucum": "1"
      },
      "variant": "unspecified",
      "voigt": [
        [
          46.5,
          0.0,
          0.0
        ],
        [
          0.0,
          46.5,
          0.0
        ],
        [
          0.0,
          0.0,
          27.3
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "full[i][j] = M[i][j]",
        "order": [
          "x",
          "y",
          "z"
        ]
      }
    },
    {
      "conditions": {
        "mechanical_boundary": "S"
      },
      "frame": {
        "convention": "IRE-1949",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "+c points out of the face that becomes negative on compression; equivalently it becomes positive on cooling (weis1985 pp. 192-193)"
      },
      "full": [
        [
          44.3,
          0.0,
          0.0
        ],
        [
          0.0,
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          0.0
        ],
        [
          0.0,
          0.0,
          27.9
        ]
      ],
      "id": "permittivity-S/unspecified/weis1985-warner1967",
      "independent": {
        "eps11": {
          "value": 44.3
        },
        "eps33": {
          "value": 27.9
        }
      },
      "kind": "tensor",
      "name": "Relative permittivity, constant strain (clamped)",
      "notes": "ogi2002 Table III attributes 44.0 / 29.0 to Warner; weis1985 gives Warner 44.3 / 27.9 (attribution mismatch).",
      "provenance": {
        "locator": "Table 1, p. 197",
        "original_reference": "Warner, Onoe, Coquin, JASA 42, 1223 (1967)",
        "source_id": "weis1985",
        "status": "P-comp",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 2,
      "scale": 1,
      "symbol": "eps^S/eps0",
      "symmetry_form": {
        "form": [
          [
            "eps11",
            "0",
            "0"
          ],
          [
            "0",
            "eps11",
            "0"
          ],
          [
            "0",
            "0",
            "eps33"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "eps22 = eps11",
          "off-diagonal = 0"
        ]
      },
      "tensor": "permittivity-S",
      "unit": {
        "display": "relative (eps/eps0)",
        "qudt": "http://qudt.org/vocab/unit/UNITLESS",
        "ucum": "1"
      },
      "variant": "unspecified",
      "voigt": [
        [
          44.3,
          0.0,
          0.0
        ],
        [
          0.0,
          44.3,
          0.0
        ],
        [
          0.0,
          0.0,
          27.9
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "full[i][j] = M[i][j]",
        "order": [
          "x",
          "y",
          "z"
        ]
      }
    },
    {
      "conditions": {
        "mechanical_boundary": "S"
      },
      "frame": {
        "convention": "IRE-1949",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "+c points out of the face that becomes negative on compression; equivalently it becomes positive on cooling (weis1985 pp. 192-193)"
      },
      "full": [
        [
          43.9,
          0.0,
          0.0
        ],
        [
          0.0,
          43.9,
          0.0
        ],
        [
          0.0,
          0.0,
          23.7
        ]
      ],
      "id": "permittivity-S/unspecified/weis1985-yamada1967",
      "independent": {
        "eps11": {
          "value": 43.9
        },
        "eps33": {
          "value": 23.7
        }
      },
      "kind": "tensor",
      "name": "Relative permittivity, constant strain (clamped)",
      "notes": "Low end of eps33^S.",
      "provenance": {
        "locator": "Table 1, p. 197",
        "original_reference": "Yamada, Niizeki, Toyoda, Jpn. J. Appl. Phys. 6, 151 (1967)",
        "source_id": "weis1985",
        "status": "P-comp",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 2,
      "scale": 1,
      "symbol": "eps^S/eps0",
      "symmetry_form": {
        "form": [
          [
            "eps11",
            "0",
            "0"
          ],
          [
            "0",
            "eps11",
            "0"
          ],
          [
            "0",
            "0",
            "eps33"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "eps22 = eps11",
          "off-diagonal = 0"
        ]
      },
      "tensor": "permittivity-S",
      "unit": {
        "display": "relative (eps/eps0)",
        "qudt": "http://qudt.org/vocab/unit/UNITLESS",
        "ucum": "1"
      },
      "variant": "unspecified",
      "voigt": [
        [
          43.9,
          0.0,
          0.0
        ],
        [
          0.0,
          43.9,
          0.0
        ],
        [
          0.0,
          0.0,
          23.7
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "full[i][j] = M[i][j]",
        "order": [
          "x",
          "y",
          "z"
        ]
      }
    },
    {
      "conditions": {
        "frequency_text": "< 500 kHz",
        "mechanical_boundary": "T"
      },
      "frame": {
        "convention": "unstated",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "not stated in this record; tensor form matches this frame by symmetry"
      },
      "full": [
        [
          85.0,
          0.0,
          0.0
        ],
        [
          0.0,
          85.0,
          0.0
        ],
        [
          0.0,
          0.0,
          28.7
        ]
      ],
      "id": "permittivity-T/cln/cti1999",
      "independent": {
        "eps11": {
          "value": 85
        },
        "eps33": {
          "value": 28.7
        }
      },
      "kind": "tensor",
      "name": "Relative permittivity, constant stress (free)",
      "provenance": {
        "source_id": "cti1999",
        "status": "V",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 2,
      "scale": 1,
      "symbol": "eps^T/eps0",
      "symmetry_form": {
        "form": [
          [
            "eps11",
            "0",
            "0"
          ],
          [
            "0",
            "eps11",
            "0"
          ],
          [
            "0",
            "0",
            "eps33"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "eps22 = eps11",
          "off-diagonal = 0"
        ]
      },
      "tensor": "permittivity-T",
      "unit": {
        "display": "relative (eps/eps0)",
        "qudt": "http://qudt.org/vocab/unit/UNITLESS",
        "ucum": "1"
      },
      "variant": "cln",
      "voigt": [
        [
          85.0,
          0.0,
          0.0
        ],
        [
          0.0,
          85.0,
          0.0
        ],
        [
          0.0,
          0.0,
          28.7
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "full[i][j] = M[i][j]",
        "order": [
          "x",
          "y",
          "z"
        ]
      }
    },
    {
      "conditions": {
        "frequency_text": "low frequency (below acoustic resonances)",
        "mechanical_boundary": "T",
        "method": "measured"
      },
      "consistency": [
        {
          "check": "eps^T = eps^S + d e^T / eps0 from the kushibiki1999 eps^S, e and derived d",
          "result": "eps11^T = 83.3, eps33^T = 28.5 (measured 83.3, 28.5)",
          "status": "C"
        }
      ],
      "default": true,
      "frame": {
        "convention": "unstated",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "not stated in this record; tensor form matches this frame by symmetry"
      },
      "full": [
        [
          83.3,
          0.0,
          0.0
        ],
        [
          0.0,
          83.3,
          0.0
        ],
        [
          0.0,
          0.0,
          28.5
        ]
      ],
      "id": "permittivity-T/cln/kushibiki1999",
      "independent": {
        "eps11": {
          "uncertainty": {
            "type": "stated",
            "value": 0.8
          },
          "value": 83.3
        },
        "eps33": {
          "uncertainty": {
            "type": "stated",
            "value": 0.3
          },
          "value": 28.5
        }
      },
      "kind": "tensor",
      "name": "Relative permittivity, constant stress (free)",
      "provenance": {
        "locator": "Table IV",
        "source_id": "kushibiki1999",
        "status": "P",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 2,
      "scale": 1,
      "symbol": "eps^T/eps0",
      "symmetry_form": {
        "form": [
          [
            "eps11",
            "0",
            "0"
          ],
          [
            "0",
            "eps11",
            "0"
          ],
          [
            "0",
            "0",
            "eps33"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "eps22 = eps11",
          "off-diagonal = 0"
        ]
      },
      "tensor": "permittivity-T",
      "unit": {
        "display": "relative (eps/eps0)",
        "qudt": "http://qudt.org/vocab/unit/UNITLESS",
        "ucum": "1"
      },
      "variant": "cln",
      "variant_note": "SAW-grade congruent; composition not stated in the source",
      "voigt": [
        [
          83.3,
          0.0,
          0.0
        ],
        [
          0.0,
          83.3,
          0.0
        ],
        [
          0.0,
          0.0,
          28.5
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "full[i][j] = M[i][j]",
        "order": [
          "x",
          "y",
          "z"
        ]
      }
    },
    {
      "conditions": {
        "mechanical_boundary": "T"
      },
      "frame": {
        "convention": "unstated",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "not stated in this record; tensor form matches this frame by symmetry"
      },
      "full": [
        [
          84.0,
          0.0,
          0.0
        ],
        [
          0.0,
          84.0,
          0.0
        ],
        [
          0.0,
          0.0,
          30.0
        ]
      ],
      "id": "permittivity-T/cln/volk2008",
      "independent": {
        "eps11": {
          "value": 84
        },
        "eps33": {
          "value": 30
        }
      },
      "kind": "tensor",
      "name": "Relative permittivity, constant stress (free)",
      "notes": "Identical to the Savage 1966 set.",
      "provenance": {
        "locator": "Table 1.1, p. 3",
        "original_reference": "Tomeno & Matsumura, PRB 38, 606 (1988)",
        "source_id": "volk2008",
        "status": "P-comp",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 2,
      "scale": 1,
      "symbol": "eps^T/eps0",
      "symmetry_form": {
        "form": [
          [
            "eps11",
            "0",
            "0"
          ],
          [
            "0",
            "eps11",
            "0"
          ],
          [
            "0",
            "0",
            "eps33"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "eps22 = eps11",
          "off-diagonal = 0"
        ]
      },
      "tensor": "permittivity-T",
      "unit": {
        "display": "relative (eps/eps0)",
        "qudt": "http://qudt.org/vocab/unit/UNITLESS",
        "ucum": "1"
      },
      "variant": "cln",
      "voigt": [
        [
          84.0,
          0.0,
          0.0
        ],
        [
          0.0,
          84.0,
          0.0
        ],
        [
          0.0,
          0.0,
          30.0
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "full[i][j] = M[i][j]",
        "order": [
          "x",
          "y",
          "z"
        ]
      }
    },
    {
      "conditions": {
        "mechanical_boundary": "T"
      },
      "frame": {
        "convention": "IRE-1949",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "+c points out of the face that becomes negative on compression; equivalently it becomes positive on cooling (weis1985 pp. 192-193)"
      },
      "full": [
        [
          84.0,
          0.0,
          0.0
        ],
        [
          0.0,
          84.0,
          0.0
        ],
        [
          0.0,
          0.0,
          30.0
        ]
      ],
      "id": "permittivity-T/unspecified/weis1985-savage1966",
      "independent": {
        "eps11": {
          "value": 84
        },
        "eps33": {
          "value": 30
        }
      },
      "kind": "tensor",
      "name": "Relative permittivity, constant stress (free)",
      "provenance": {
        "locator": "Table 1, p. 197",
        "original_reference": "Savage, J. Appl. Phys. 37, 3071 (1966)",
        "source_id": "weis1985",
        "status": "P-comp",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 2,
      "scale": 1,
      "symbol": "eps^T/eps0",
      "symmetry_form": {
        "form": [
          [
            "eps11",
            "0",
            "0"
          ],
          [
            "0",
            "eps11",
            "0"
          ],
          [
            "0",
            "0",
            "eps33"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "eps22 = eps11",
          "off-diagonal = 0"
        ]
      },
      "tensor": "permittivity-T",
      "unit": {
        "display": "relative (eps/eps0)",
        "qudt": "http://qudt.org/vocab/unit/UNITLESS",
        "ucum": "1"
      },
      "variant": "unspecified",
      "voigt": [
        [
          84.0,
          0.0,
          0.0
        ],
        [
          0.0,
          84.0,
          0.0
        ],
        [
          0.0,
          0.0,
          30.0
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "full[i][j] = M[i][j]",
        "order": [
          "x",
          "y",
          "z"
        ]
      }
    },
    {
      "conditions": {
        "mechanical_boundary": "T"
      },
      "frame": {
        "convention": "IRE-1949",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "+c points out of the face that becomes negative on compression; equivalently it becomes positive on cooling (weis1985 pp. 192-193)"
      },
      "full": [
        [
          84.6,
          0.0,
          0.0
        ],
        [
          0.0,
          84.6,
          0.0
        ],
        [
          0.0,
          0.0,
          28.6
        ]
      ],
      "id": "permittivity-T/unspecified/weis1985-smithwelsh1971",
      "independent": {
        "eps11": {
          "value": 84.6
        },
        "eps33": {
          "value": 28.6
        }
      },
      "kind": "tensor",
      "name": "Relative permittivity, constant stress (free)",
      "notes": "weis1985 lists no S values for Smith & Welsh; ogi2002 attributes 44.3 / 27.9 to them (attribution mismatch).",
      "provenance": {
        "locator": "Table 1, p. 197",
        "original_reference": "Smith & Welsh, J. Appl. Phys. 42, 2219 (1971)",
        "source_id": "weis1985",
        "status": "P-comp",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 2,
      "scale": 1,
      "symbol": "eps^T/eps0",
      "symmetry_form": {
        "form": [
          [
            "eps11",
            "0",
            "0"
          ],
          [
            "0",
            "eps11",
            "0"
          ],
          [
            "0",
            "0",
            "eps33"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "eps22 = eps11",
          "off-diagonal = 0"
        ]
      },
      "tensor": "permittivity-T",
      "unit": {
        "display": "relative (eps/eps0)",
        "qudt": "http://qudt.org/vocab/unit/UNITLESS",
        "ucum": "1"
      },
      "variant": "unspecified",
      "voigt": [
        [
          84.6,
          0.0,
          0.0
        ],
        [
          0.0,
          84.6,
          0.0
        ],
        [
          0.0,
          0.0,
          28.6
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "full[i][j] = M[i][j]",
        "order": [
          "x",
          "y",
          "z"
        ]
      }
    },
    {
      "conditions": {
        "mechanical_boundary": "T"
      },
      "frame": {
        "convention": "IRE-1949",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "+c points out of the face that becomes negative on compression; equivalently it becomes positive on cooling (weis1985 pp. 192-193)"
      },
      "full": [
        [
          84.1,
          0.0,
          0.0
        ],
        [
          0.0,
          84.1,
          0.0
        ],
        [
          0.0,
          0.0,
          28.1
        ]
      ],
      "id": "permittivity-T/unspecified/weis1985-teague1975",
      "independent": {
        "eps11": {
          "value": 84.1
        },
        "eps33": {
          "value": 28.1
        }
      },
      "kind": "tensor",
      "name": "Relative permittivity, constant stress (free)",
      "provenance": {
        "locator": "Table 1, p. 197",
        "original_reference": "Teague, Rice, Gerson, J. Appl. Phys. 46, 2864 (1975)",
        "source_id": "weis1985",
        "status": "P-comp",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 2,
      "scale": 1,
      "symbol": "eps^T/eps0",
      "symmetry_form": {
        "form": [
          [
            "eps11",
            "0",
            "0"
          ],
          [
            "0",
            "eps11",
            "0"
          ],
          [
            "0",
            "0",
            "eps33"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "eps22 = eps11",
          "off-diagonal = 0"
        ]
      },
      "tensor": "permittivity-T",
      "unit": {
        "display": "relative (eps/eps0)",
        "qudt": "http://qudt.org/vocab/unit/UNITLESS",
        "ucum": "1"
      },
      "variant": "unspecified",
      "voigt": [
        [
          84.1,
          0.0,
          0.0
        ],
        [
          0.0,
          84.1,
          0.0
        ],
        [
          0.0,
          0.0,
          28.1
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "full[i][j] = M[i][j]",
        "order": [
          "x",
          "y",
          "z"
        ]
      }
    },
    {
      "conditions": {
        "mechanical_boundary": "T"
      },
      "frame": {
        "convention": "IRE-1949",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "+c points out of the face that becomes negative on compression; equivalently it becomes positive on cooling (weis1985 pp. 192-193)"
      },
      "full": [
        [
          85.2,
          0.0,
          0.0
        ],
        [
          0.0,
          85.2,
          0.0
        ],
        [
          0.0,
          0.0,
          28.7
        ]
      ],
      "id": "permittivity-T/unspecified/weis1985-warner1967",
      "independent": {
        "eps11": {
          "value": 85.2
        },
        "eps33": {
          "value": 28.7
        }
      },
      "kind": "tensor",
      "name": "Relative permittivity, constant stress (free)",
      "provenance": {
        "locator": "Table 1, p. 197",
        "original_reference": "Warner, Onoe, Coquin, JASA 42, 1223 (1967)",
        "source_id": "weis1985",
        "status": "P-comp",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 2,
      "scale": 1,
      "symbol": "eps^T/eps0",
      "symmetry_form": {
        "form": [
          [
            "eps11",
            "0",
            "0"
          ],
          [
            "0",
            "eps11",
            "0"
          ],
          [
            "0",
            "0",
            "eps33"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "eps22 = eps11",
          "off-diagonal = 0"
        ]
      },
      "tensor": "permittivity-T",
      "unit": {
        "display": "relative (eps/eps0)",
        "qudt": "http://qudt.org/vocab/unit/UNITLESS",
        "ucum": "1"
      },
      "variant": "unspecified",
      "voigt": [
        [
          85.2,
          0.0,
          0.0
        ],
        [
          0.0,
          85.2,
          0.0
        ],
        [
          0.0,
          0.0,
          28.7
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "full[i][j] = M[i][j]",
        "order": [
          "x",
          "y",
          "z"
        ]
      }
    },
    {
      "conditions": {
        "wavelength_nm": 633
      },
      "frame": {
        "convention": "unstated",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "not stated in this record; tensor form matches this frame by symmetry"
      },
      "full": [
        [
          [
            [
              -0.021,
              0.0,
              0.0
            ],
            [
              0.0,
              0.06,
              -0.052
            ],
            [
              0.0,
              -0.052,
              0.172
            ]
          ],
          [
            [
              0.0,
              -0.0405,
              -0.052
            ],
            [
              -0.0405,
              0.0,
              0.0
            ],
            [
              -0.052,
              0.0,
              0.0
            ]
          ],
          [
            [
              0.0,
              -0.109,
              0.121
            ],
            [
              -0.109,
              0.0,
              0.0
            ],
            [
              0.121,
              0.0,
              0.0
            ]
          ]
        ],
        [
          [
            [
              0.0,
              -0.0405,
              -0.052
            ],
            [
              -0.0405,
              0.0,
              0.0
            ],
            [
              -0.052,
              0.0,
              0.0
            ]
          ],
          [
            [
              0.06,
              0.0,
              0.0
            ],
            [
              0.0,
              -0.021,
              0.052
            ],
            [
              0.0,
              0.052,
              0.172
            ]
          ],
          [
            [
              -0.109,
              0.0,
              0.0
            ],
            [
              0.0,
              0.109,
              0.121
            ],
            [
              0.0,
              0.121,
              0.0
            ]
          ]
        ],
        [
          [
            [
              0.0,
              -0.109,
              0.121
            ],
            [
              -0.109,
              0.0,
              0.0
            ],
            [
              0.121,
              0.0,
              0.0
            ]
          ],
          [
            [
              -0.109,
              0.0,
              0.0
            ],
            [
              0.0,
              0.109,
              0.121
            ],
            [
              0.0,
              0.121,
              0.0
            ]
          ],
          [
            [
              0.141,
              0.0,
              0.0
            ],
            [
              0.0,
              0.141,
              0.0
            ],
            [
              0.0,
              0.0,
              0.118
            ]
          ]
        ]
      ],
      "id": "photoelastic-p/unspecified/andrushchak2009",
      "independent": {
        "p11": {
          "uncertainty": {
            "type": "stated",
            "value": 0.018
          },
          "value": -0.021
        },
        "p12": {
          "uncertainty": {
            "type": "stated",
            "value": 0.019
          },
          "value": 0.06
        },
        "p13": {
          "uncertainty": {
            "type": "stated",
            "value": 0.029
          },
          "value": 0.172
        },
        "p14": {
          "uncertainty": {
            "type": "stated",
            "value": 0.007
          },
          "value": -0.052
        },
        "p31": {
          "uncertainty": {
            "type": "stated",
            "value": 0.017
          },
          "value": 0.141
        },
        "p33": {
          "uncertainty": {
            "type": "stated",
            "value": 0.02
          },
          "value": 0.118
        },
        "p41": {
          "uncertainty": {
            "type": "stated",
            "value": 0.017
          },
          "value": -0.109
        },
        "p44": {
          "uncertainty": {
            "type": "stated",
            "value": 0.019
          },
          "value": 0.121
        }
      },
      "kind": "tensor",
      "name": "Photoelastic (strain-optic) coefficients",
      "provenance": {
        "locator": "sarabalis2020 Table I; mytsyk2021 Table 6",
        "source_id": "andrushchak2009",
        "status": "S",
        "transcribed": "2026-10-25",
        "via": "sarabalis2020"
      },
      "public": true,
      "rank": 4,
      "scale": 1,
      "symbol": "p",
      "symmetry_form": {
        "form": [
          [
            "p11",
            "p12",
            "p13",
            "p14",
            "0",
            "0"
          ],
          [
            "p12",
            "p11",
            "p13",
            "-p14",
            "0",
            "0"
          ],
          [
            "p31",
            "p31",
            "p33",
            "0",
            "0",
            "0"
          ],
          [
            "p41",
            "-p41",
            "0",
            "p44",
            "0",
            "0"
          ],
          [
            "0",
            "0",
            "0",
            "0",
            "p44",
            "p41"
          ],
          [
            "0",
            "0",
            "0",
            "0",
            "p14",
            "(p11-p12)/2"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "p22 = p11",
          "p23 = p13",
          "p24 = -p14",
          "p32 = p31",
          "p42 = -p41",
          "p55 = p44",
          "p56 = p41",
          "p65 = p14",
          "p66 = (p11 - p12)/2",
          "p_IJ is not symmetric (p14 != p41)"
        ]
      },
      "tensor": "photoelastic-p",
      "unit": {
        "display": "-",
        "qudt": "http://qudt.org/vocab/unit/UNITLESS",
        "ucum": "1"
      },
      "variant": "unspecified",
      "voigt": [
        [
          -0.021,
          0.06,
          0.172,
          -0.052,
          0.0,
          0.0
        ],
        [
          0.06,
          -0.021,
          0.172,
          0.052,
          0.0,
          0.0
        ],
        [
          0.141,
          0.141,
          0.118,
          0.0,
          0.0,
          0.0
        ],
        [
          -0.109,
          0.109,
          0.0,
          0.121,
          0.0,
          0.0
        ],
        [
          0.0,
          0.0,
          0.0,
          0.0,
          0.121,
          -0.109
        ],
        [
          0.0,
          0.0,
          0.0,
          0.0,
          -0.052,
          -0.0405
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "p_ijkl = p_IJ, I = V(ij), J = V(kl) (d(eta)_I = p_IJ S_J with engineering S_4..S_6)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "conditions": {
        "wavelength_nm": 633
      },
      "frame": {
        "convention": "unstated",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "not stated; the set is quoted with c14 > 0 (pitfall 2)"
      },
      "full": [
        [
          [
            [
              -0.023,
              0.0,
              0.0
            ],
            [
              0.0,
              0.076,
              0.057
            ],
            [
              0.0,
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              0.147
            ]
          ],
          [
            [
              0.0,
              -0.0495,
              0.057
            ],
            [
              -0.0495,
              0.0,
              0.0
            ],
            [
              0.057,
              0.0,
              0.0
            ]
          ],
          [
            [
              0.0,
              0.051,
              0.126
            ],
            [
              0.051,
              0.0,
              0.0
            ],
            [
              0.126,
              0.0,
              0.0
            ]
          ]
        ],
        [
          [
            [
              0.0,
              -0.0495,
              0.057
            ],
            [
              -0.0495,
              0.0,
              0.0
            ],
            [
              0.057,
              0.0,
              0.0
            ]
          ],
          [
            [
              0.076,
              0.0,
              0.0
            ],
            [
              0.0,
              -0.023,
              -0.057
            ],
            [
              0.0,
              -0.057,
              0.147
            ]
          ],
          [
            [
              0.051,
              0.0,
              0.0
            ],
            [
              0.0,
              -0.051,
              0.126
            ],
            [
              0.0,
              0.126,
              0.0
            ]
          ]
        ],
        [
          [
            [
              0.0,
              0.051,
              0.126
            ],
            [
              0.051,
              0.0,
              0.0
            ],
            [
              0.126,
              0.0,
              0.0
            ]
          ],
          [
            [
              0.051,
              0.0,
              0.0
            ],
            [
              0.0,
              -0.051,
              0.126
            ],
            [
              0.0,
              0.126,
              0.0
            ]
          ],
          [
            [
              0.157,
              0.0,
              0.0
            ],
            [
              0.0,
              0.157,
              0.0
            ],
            [
              0.0,
              0.0,
              0.141
            ]
          ]
        ]
      ],
      "id": "photoelastic-p/unspecified/mys2015-krupych2014",
      "independent": {
        "p11": {
          "value": -0.023
        },
        "p12": {
          "value": 0.076
        },
        "p13": {
          "value": 0.147
        },
        "p14": {
          "value": 0.057
        },
        "p31": {
          "value": 0.157
        },
        "p33": {
          "value": 0.141
        },
        "p41": {
          "value": 0.051
        },
        "p44": {
          "value": 0.126
        }
      },
      "kind": "tensor",
      "name": "Photoelastic (strain-optic) coefficients",
      "notes": "p14, p41 > 0 with c14 > 0 disagrees in sign with the weis1985 compilation of Avakyants.",
      "provenance": {
        "original_reference": "Krupych et al., Appl. Opt. 53, B1 (2014)",
        "source_id": "mys2015",
        "status": "S",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 4,
      "scale": 1,
      "symbol": "p",
      "symmetry_form": {
        "form": [
          [
            "p11",
            "p12",
            "p13",
            "p14",
            "0",
            "0"
          ],
          [
            "p12",
            "p11",
            "p13",
            "-p14",
            "0",
            "0"
          ],
          [
            "p31",
            "p31",
            "p33",
            "0",
            "0",
            "0"
          ],
          [
            "p41",
            "-p41",
            "0",
            "p44",
            "0",
            "0"
          ],
          [
            "0",
            "0",
            "0",
            "0",
            "p44",
            "p41"
          ],
          [
            "0",
            "0",
            "0",
            "0",
            "p14",
            "(p11-p12)/2"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "p22 = p11",
          "p23 = p13",
          "p24 = -p14",
          "p32 = p31",
          "p42 = -p41",
          "p55 = p44",
          "p56 = p41",
          "p65 = p14",
          "p66 = (p11 - p12)/2",
          "p_IJ is not symmetric (p14 != p41)"
        ]
      },
      "tensor": "photoelastic-p",
      "unit": {
        "display": "-",
        "qudt": "http://qudt.org/vocab/unit/UNITLESS",
        "ucum": "1"
      },
      "variant": "unspecified",
      "voigt": [
        [
          -0.023,
          0.076,
          0.147,
          0.057,
          0.0,
          0.0
        ],
        [
          0.076,
          -0.023,
          0.147,
          -0.057,
          0.0,
          0.0
        ],
        [
          0.157,
          0.157,
          0.141,
          0.0,
          0.0,
          0.0
        ],
        [
          0.051,
          -0.051,
          0.0,
          0.126,
          0.0,
          0.0
        ],
        [
          0.0,
          0.0,
          0.0,
          0.0,
          0.126,
          0.051
        ],
        [
          0.0,
          0.0,
          0.0,
          0.0,
          0.057,
          -0.0495
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "p_ijkl = p_IJ, I = V(ij), J = V(kl) (d(eta)_I = p_IJ S_J with engineering S_4..S_6)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "conditions": {
        "wavelength_nm": 633
      },
      "frame": {
        "convention": "unstated",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "not stated in this record; tensor form matches this frame by symmetry"
      },
      "full": [
        [
          [
            [
              -0.026,
              0.0,
              0.0
            ],
            [
              0.0,
              0.088,
              -0.083
            ],
            [
              0.0,
              -0.083,
              0.134
            ]
          ],
          [
            [
              0.0,
              -0.057,
              -0.083
            ],
            [
              -0.057,
              0.0,
              0.0
            ],
            [
              -0.083,
              0.0,
              0.0
            ]
          ],
          [
            [
              0.0,
              -0.151,
              0.145
            ],
            [
              -0.151,
              0.0,
              0.0
            ],
            [
              0.145,
              0.0,
              0.0
            ]
          ]
        ],
        [
          [
            [
              0.0,
              -0.057,
              -0.083
            ],
            [
              -0.057,
              0.0,
              0.0
            ],
            [
              -0.083,
              0.0,
              0.0
            ]
          ],
          [
            [
              0.088,
              0.0,
              0.0
            ],
            [
              0.0,
              -0.026,
              0.083
            ],
            [
              0.0,
              0.083,
              0.134
            ]
          ],
          [
            [
              -0.151,
              0.0,
              0.0
            ],
            [
              0.0,
              0.151,
              0.145
            ],
            [
              0.0,
              0.145,
              0.0
            ]
          ]
        ],
        [
          [
            [
              0.0,
              -0.151,
              0.145
            ],
            [
              -0.151,
              0.0,
              0.0
            ],
            [
              0.145,
              0.0,
              0.0
            ]
          ],
          [
            [
              -0.151,
              0.0,
              0.0
            ],
            [
              0.0,
              0.151,
              0.145
            ],
            [
              0.0,
              0.145,
              0.0
            ]
          ],
          [
            [
              0.177,
              0.0,
              0.0
            ],
            [
              0.0,
              0.177,
              0.0
            ],
            [
              0.0,
              0.0,
              0.07
            ]
          ]
        ]
      ],
      "id": "photoelastic-p/unspecified/rodrigues2023",
      "independent": {
        "p11": {
          "value": -0.026
        },
        "p12": {
          "value": 0.088
        },
        "p13": {
          "value": 0.134
        },
        "p14": {
          "value": -0.083
        },
        "p31": {
          "value": 0.177
        },
        "p33": {
          "value": 0.07
        },
        "p41": {
          "value": -0.151
        },
        "p44": {
          "value": 0.145
        }
      },
      "kind": "tensor",
      "name": "Photoelastic (strain-optic) coefficients",
      "notes": "Looks like a blend of the Avakyants and Coquin sets (observation).",
      "provenance": {
        "locator": "Eq. 8",
        "source_id": "rodrigues2023",
        "status": "S",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 4,
      "scale": 1,
      "symbol": "p",
      "symmetry_form": {
        "form": [
          [
            "p11",
            "p12",
            "p13",
            "p14",
            "0",
            "0"
          ],
          [
            "p12",
            "p11",
            "p13",
            "-p14",
            "0",
            "0"
          ],
          [
            "p31",
            "p31",
            "p33",
            "0",
            "0",
            "0"
          ],
          [
            "p41",
            "-p41",
            "0",
            "p44",
            "0",
            "0"
          ],
          [
            "0",
            "0",
            "0",
            "0",
            "p44",
            "p41"
          ],
          [
            "0",
            "0",
            "0",
            "0",
            "p14",
            "(p11-p12)/2"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "p22 = p11",
          "p23 = p13",
          "p24 = -p14",
          "p32 = p31",
          "p42 = -p41",
          "p55 = p44",
          "p56 = p41",
          "p65 = p14",
          "p66 = (p11 - p12)/2",
          "p_IJ is not symmetric (p14 != p41)"
        ]
      },
      "tensor": "photoelastic-p",
      "unit": {
        "display": "-",
        "qudt": "http://qudt.org/vocab/unit/UNITLESS",
        "ucum": "1"
      },
      "variant": "unspecified",
      "voigt": [
        [
          -0.026,
          0.088,
          0.134,
          -0.083,
          0.0,
          0.0
        ],
        [
          0.088,
          -0.026,
          0.134,
          0.083,
          0.0,
          0.0
        ],
        [
          0.177,
          0.177,
          0.07,
          0.0,
          0.0,
          0.0
        ],
        [
          -0.151,
          0.151,
          0.0,
          0.145,
          0.0,
          0.0
        ],
        [
          0.0,
          0.0,
          0.0,
          0.0,
          0.145,
          -0.151
        ],
        [
          0.0,
          0.0,
          0.0,
          0.0,
          -0.083,
          -0.057
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "p_ijkl = p_IJ, I = V(ij), J = V(kl) (d(eta)_I = p_IJ S_J with engineering S_4..S_6)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "conditions": {
        "wavelength_nm": 633
      },
      "frame": {
        "convention": "unstated",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "as compiled in weis1985 (IRE 1949 frame); the frame of the original Avakyants 1976 measurement is not verified"
      },
      "full": [
        [
          [
            [
              -0.026,
              0.0,
              0.0
            ],
            [
              0.0,
              0.09,
              -0.075
            ],
            [
              0.0,
              -0.075,
              0.133
            ]
          ],
          [
            [
              0.0,
              -0.058,
              -0.075
            ],
            [
              -0.058,
              0.0,
              0.0
            ],
            [
              -0.075,
              0.0,
              0.0
            ]
          ],
          [
            [
              0.0,
              -0.151,
              0.146
            ],
            [
              -0.151,
              0.0,
              0.0
            ],
            [
              0.146,
              0.0,
              0.0
            ]
          ]
        ],
        [
          [
            [
              0.0,
              -0.058,
              -0.075
            ],
            [
              -0.058,
              0.0,
              0.0
            ],
            [
              -0.075,
              0.0,
              0.0
            ]
          ],
          [
            [
              0.09,
              0.0,
              0.0
            ],
            [
              0.0,
              -0.026,
              0.075
            ],
            [
              0.0,
              0.075,
              0.133
            ]
          ],
          [
            [
              -0.151,
              0.0,
              0.0
            ],
            [
              0.0,
              0.151,
              0.146
            ],
            [
              0.0,
              0.146,
              0.0
            ]
          ]
        ],
        [
          [
            [
              0.0,
              -0.151,
              0.146
            ],
            [
              -0.151,
              0.0,
              0.0
            ],
            [
              0.146,
              0.0,
              0.0
            ]
          ],
          [
            [
              -0.151,
              0.0,
              0.0
            ],
            [
              0.0,
              0.151,
              0.146
            ],
            [
              0.0,
              0.146,
              0.0
            ]
          ],
          [
            [
              0.179,
              0.0,
              0.0
            ],
            [
              0.0,
              0.179,
              0.0
            ],
            [
              0.0,
              0.0,
              0.071
            ]
          ]
        ]
      ],
      "id": "photoelastic-p/unspecified/weis1985-avakyants1976",
      "independent": {
        "p11": {
          "value": -0.026
        },
        "p12": {
          "value": 0.09
        },
        "p13": {
          "value": 0.133
        },
        "p14": {
          "value": -0.075
        },
        "p31": {
          "value": 0.179
        },
        "p33": {
          "value": 0.071
        },
        "p41": {
          "value": -0.151
        },
        "p44": {
          "value": 0.146
        }
      },
      "kind": "tensor",
      "name": "Photoelastic (strain-optic) coefficients",
      "notes": "This is 'Set B' (also zhu2021). weis1985 lists these signed p14, p41 < 0 next to Smith & Welsh c14 > 0 in its IRE frame, without stating Avakyants' own frame; the sign pairing stays open until Avakyants 1976 is read. Measured p13, p33 include an indirect (piezo-EO) part whose size depends on the acoustic direction (N3).",
      "provenance": {
        "locator": "Table 7, p. 201",
        "original_reference": "Avakyants, Kiselev, Shchitkov, Sov. Phys. Solid State 18, 899 (1976)",
        "source_id": "weis1985",
        "status": "P-comp",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 4,
      "scale": 1,
      "symbol": "p",
      "symmetry_form": {
        "form": [
          [
            "p11",
            "p12",
            "p13",
            "p14",
            "0",
            "0"
          ],
          [
            "p12",
            "p11",
            "p13",
            "-p14",
            "0",
            "0"
          ],
          [
            "p31",
            "p31",
            "p33",
            "0",
            "0",
            "0"
          ],
          [
            "p41",
            "-p41",
            "0",
            "p44",
            "0",
            "0"
          ],
          [
            "0",
            "0",
            "0",
            "0",
            "p44",
            "p41"
          ],
          [
            "0",
            "0",
            "0",
            "0",
            "p14",
            "(p11-p12)/2"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "p22 = p11",
          "p23 = p13",
          "p24 = -p14",
          "p32 = p31",
          "p42 = -p41",
          "p55 = p44",
          "p56 = p41",
          "p65 = p14",
          "p66 = (p11 - p12)/2",
          "p_IJ is not symmetric (p14 != p41)"
        ]
      },
      "tensor": "photoelastic-p",
      "unit": {
        "display": "-",
        "qudt": "http://qudt.org/vocab/unit/UNITLESS",
        "ucum": "1"
      },
      "variant": "unspecified",
      "voigt": [
        [
          -0.026,
          0.09,
          0.133,
          -0.075,
          0.0,
          0.0
        ],
        [
          0.09,
          -0.026,
          0.133,
          0.075,
          0.0,
          0.0
        ],
        [
          0.179,
          0.179,
          0.071,
          0.0,
          0.0,
          0.0
        ],
        [
          -0.151,
          0.151,
          0.0,
          0.146,
          0.0,
          0.0
        ],
        [
          0.0,
          0.0,
          0.0,
          0.0,
          0.146,
          -0.151
        ],
        [
          0.0,
          0.0,
          0.0,
          0.0,
          -0.075,
          -0.058
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "p_ijkl = p_IJ, I = V(ij), J = V(kl) (d(eta)_I = p_IJ S_J with engineering S_4..S_6)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "conditions": {
        "wavelength_nm": 633
      },
      "frame": {
        "convention": "IRE-1949",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "+c points out of the face that becomes negative on compression; equivalently it becomes positive on cooling (weis1985 pp. 192-193)"
      },
      "full": [
        [
          [
            [
              -0.02,
              0.0,
              0.0
            ],
            [
              0.0,
              0.08,
              -0.08
            ],
            [
              0.0,
              -0.08,
              0.13
            ]
          ],
          [
            [
              0.0,
              -0.05,
              -0.08
            ],
            [
              -0.05,
              0.0,
              0.0
            ],
            [
              -0.08,
              0.0,
              0.0
            ]
          ],
          [
            [
              0.0,
              -0.15,
              0.12
            ],
            [
              -0.15,
              0.0,
              0.0
            ],
            [
              0.12,
              0.0,
              0.0
            ]
          ]
        ],
        [
          [
            [
              0.0,
              -0.05,
              -0.08
            ],
            [
              -0.05,
              0.0,
              0.0
            ],
            [
              -0.08,
              0.0,
              0.0
            ]
          ],
          [
            [
              0.08,
              0.0,
              0.0
            ],
            [
              0.0,
              -0.02,
              0.08
            ],
            [
              0.0,
              0.08,
              0.13
            ]
          ],
          [
            [
              -0.15,
              0.0,
              0.0
            ],
            [
              0.0,
              0.15,
              0.12
            ],
            [
              0.0,
              0.12,
              0.0
            ]
          ]
        ],
        [
          [
            [
              0.0,
              -0.15,
              0.12
            ],
            [
              -0.15,
              0.0,
              0.0
            ],
            [
              0.12,
              0.0,
              0.0
            ]
          ],
          [
            [
              -0.15,
              0.0,
              0.0
            ],
            [
              0.0,
              0.15,
              0.12
            ],
            [
              0.0,
              0.12,
              0.0
            ]
          ],
          [
            [
              0.17,
              0.0,
              0.0
            ],
            [
              0.0,
              0.17,
              0.0
            ],
            [
              0.0,
              0.0,
              0.07
            ]
          ]
        ]
      ],
      "id": "photoelastic-p/unspecified/weis1985-coquin",
      "independent": {
        "p11": {
          "value": -0.02
        },
        "p12": {
          "value": 0.08
        },
        "p13": {
          "value": 0.13
        },
        "p14": {
          "value": -0.08
        },
        "p31": {
          "value": 0.17
        },
        "p33": {
          "value": 0.07
        },
        "p41": {
          "value": -0.15
        },
        "p44": {
          "value": 0.12
        }
      },
      "kind": "tensor",
      "name": "Photoelastic (strain-optic) coefficients",
      "provenance": {
        "locator": "Table 7, p. 201",
        "original_reference": "Coquin, via Pinnow, Handbook of Lasers (1971)",
        "source_id": "weis1985",
        "status": "P-comp",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 4,
      "scale": 1,
      "symbol": "p",
      "symmetry_form": {
        "form": [
          [
            "p11",
            "p12",
            "p13",
            "p14",
            "0",
            "0"
          ],
          [
            "p12",
            "p11",
            "p13",
            "-p14",
            "0",
            "0"
          ],
          [
            "p31",
            "p31",
            "p33",
            "0",
            "0",
            "0"
          ],
          [
            "p41",
            "-p41",
            "0",
            "p44",
            "0",
            "0"
          ],
          [
            "0",
            "0",
            "0",
            "0",
            "p44",
            "p41"
          ],
          [
            "0",
            "0",
            "0",
            "0",
            "p14",
            "(p11-p12)/2"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "p22 = p11",
          "p23 = p13",
          "p24 = -p14",
          "p32 = p31",
          "p42 = -p41",
          "p55 = p44",
          "p56 = p41",
          "p65 = p14",
          "p66 = (p11 - p12)/2",
          "p_IJ is not symmetric (p14 != p41)"
        ]
      },
      "tensor": "photoelastic-p",
      "unit": {
        "display": "-",
        "qudt": "http://qudt.org/vocab/unit/UNITLESS",
        "ucum": "1"
      },
      "variant": "unspecified",
      "voigt": [
        [
          -0.02,
          0.08,
          0.13,
          -0.08,
          0.0,
          0.0
        ],
        [
          0.08,
          -0.02,
          0.13,
          0.08,
          0.0,
          0.0
        ],
        [
          0.17,
          0.17,
          0.07,
          0.0,
          0.0,
          0.0
        ],
        [
          -0.15,
          0.15,
          0.0,
          0.12,
          0.0,
          0.0
        ],
        [
          0.0,
          0.0,
          0.0,
          0.0,
          0.12,
          -0.15
        ],
        [
          0.0,
          0.0,
          0.0,
          0.0,
          -0.08,
          -0.05
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "p_ijkl = p_IJ, I = V(ij), J = V(kl) (d(eta)_I = p_IJ S_J with engineering S_4..S_6)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "frame": {
        "convention": "unstated",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "not stated in this record; tensor form matches this frame by symmetry"
      },
      "full": [
        [
          [
            0.0,
            -20.8,
            34.6
          ],
          [
            -20.8,
            0.0,
            0.0
          ],
          [
            34.6,
            0.0,
            0.0
          ]
        ],
        [
          [
            -20.8,
            0.0,
            0.0
          ],
          [
            0.0,
            20.8,
            34.6
          ],
          [
            0.0,
            34.6,
            0.0
          ]
        ],
        [
          [
            -0.85,
            0.0,
            0.0
          ],
          [
            0.0,
            -0.85,
            0.0
          ],
          [
            0.0,
            0.0,
            6.0
          ]
        ]
      ],
      "id": "piezo-strain-d/cln/cti1999",
      "independent": {
        "d15": {
          "value": 69.2
        },
        "d22": {
          "value": 20.8
        },
        "d31": {
          "value": -0.85
        },
        "d33": {
          "value": 6.0
        }
      },
      "kind": "tensor",
      "name": "Piezoelectric strain constants",
      "provenance": {
        "source_id": "cti1999",
        "status": "V",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 3,
      "scale": 1,
      "symbol": "d",
      "symmetry_form": {
        "form": [
          [
            "0",
            "0",
            "0",
            "0",
            "d15",
            "-2*d22"
          ],
          [
            "-d22",
            "d22",
            "0",
            "d15",
            "0",
            "0"
          ],
          [
            "d31",
            "d31",
            "d33",
            "0",
            "0",
            "0"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "d16 = -2 d22",
          "d21 = -d22",
          "d24 = d15",
          "d32 = d31"
        ]
      },
      "tensor": "piezo-strain-d",
      "unit": {
        "display": "pC/N",
        "ucum": "pC/N"
      },
      "variant": "cln",
      "voigt": [
        [
          0.0,
          0.0,
          0.0,
          0.0,
          69.2,
          -41.6
        ],
        [
          -20.8,
          20.8,
          0.0,
          69.2,
          0.0,
          0.0
        ],
        [
          -0.85,
          -0.85,
          6.0,
          0.0,
          0.0,
          0.0
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "d_ijk = d_iJ x (1 if J<=3 else 1/2) (engineering shear strain)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "default": true,
      "frame": {
        "convention": "unstated",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "not stated in this record; tensor form matches this frame by symmetry"
      },
      "full": [
        [
          [
            0.0,
            -20.2979,
            33.19025
          ],
          [
            -20.2979,
            0.0,
            0.0
          ],
          [
            33.19025,
            0.0,
            0.0
          ]
        ],
        [
          [
            -20.2979,
            0.0,
            0.0
          ],
          [
            0.0,
            20.2979,
            33.19025
          ],
          [
            0.0,
            33.19025,
            0.0
          ]
        ],
        [
          [
            -1.03662,
            0.0,
            0.0
          ],
          [
            0.0,
            -1.03662,
            0.0
          ],
          [
            0.0,
            0.0,
            8.68973
          ]
        ]
      ],
      "id": "piezo-strain-d/cln/kushibiki1999",
      "independent": {
        "d15": {
          "value": 66.3805
        },
        "d22": {
          "value": 20.2979
        },
        "d31": {
          "value": -1.03662
        },
        "d33": {
          "value": 8.68973
        }
      },
      "kind": "tensor",
      "name": "Piezoelectric strain constants",
      "notes": "Derived, not a published number. d15 66.4, d22 20.3, d31 -1.04, d33 8.7 pC/N. The hydrostatic d_h = 2 d31 + d33 from this set (about 6.6 pC/N) is within 5% of the measured 6.31 pC/N.",
      "provenance": {
        "derivation": "d = e s^E from the kushibiki1999 e and c^E sets, computed by scripts/build_data.py",
        "source_id": "kushibiki1999",
        "status": "C",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 3,
      "scale": 1,
      "symbol": "d",
      "symmetry_form": {
        "form": [
          [
            "0",
            "0",
            "0",
            "0",
            "d15",
            "-2*d22"
          ],
          [
            "-d22",
            "d22",
            "0",
            "d15",
            "0",
            "0"
          ],
          [
            "d31",
            "d31",
            "d33",
            "0",
            "0",
            "0"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "d16 = -2 d22",
          "d21 = -d22",
          "d24 = d15",
          "d32 = d31"
        ]
      },
      "tensor": "piezo-strain-d",
      "unit": {
        "display": "pC/N",
        "ucum": "pC/N"
      },
      "variant": "cln",
      "variant_note": "SAW-grade congruent",
      "voigt": [
        [
          0.0,
          0.0,
          0.0,
          0.0,
          66.3805,
          -40.5958
        ],
        [
          -20.2979,
          20.2979,
          0.0,
          66.3805,
          0.0,
          0.0
        ],
        [
          -1.03662,
          -1.03662,
          8.68973,
          0.0,
          0.0,
          0.0
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "d_ijk = d_iJ x (1 if J<=3 else 1/2) (engineering shear strain)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "frame": {
        "convention": "IRE-1949",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "+c points out of the face that becomes negative on compression; equivalently it becomes positive on cooling (weis1985 pp. 192-193)"
      },
      "full": [
        [
          [
            0.0,
            -20.8,
            34.6
          ],
          [
            -20.8,
            0.0,
            0.0
          ],
          [
            34.6,
            0.0,
            0.0
          ]
        ],
        [
          [
            -20.8,
            0.0,
            0.0
          ],
          [
            0.0,
            20.8,
            34.6
          ],
          [
            0.0,
            34.6,
            0.0
          ]
        ],
        [
          [
            -0.85,
            0.0,
            0.0
          ],
          [
            0.0,
            -0.85,
            0.0
          ],
          [
            0.0,
            0.0,
            6.0
          ]
        ]
      ],
      "id": "piezo-strain-d/unspecified/weis1985-smithwelsh1971",
      "independent": {
        "d15": {
          "value": 69.2
        },
        "d22": {
          "value": 20.8
        },
        "d31": {
          "value": -0.85
        },
        "d33": {
          "value": 6.0
        }
      },
      "kind": "tensor",
      "name": "Piezoelectric strain constants",
      "notes": "cti1999 copies this set exactly. d33 = 6.0 is disfavoured by the hydrostatic d_h data.",
      "provenance": {
        "locator": "Table 3, p. 198 (unit 1.0e-11 C/N)",
        "original_reference": "Smith & Welsh, J. Appl. Phys. 42, 2219 (1971)",
        "source_id": "weis1985",
        "status": "P-comp",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 3,
      "scale": 1,
      "symbol": "d",
      "symmetry_form": {
        "form": [
          [
            "0",
            "0",
            "0",
            "0",
            "d15",
            "-2*d22"
          ],
          [
            "-d22",
            "d22",
            "0",
            "d15",
            "0",
            "0"
          ],
          [
            "d31",
            "d31",
            "d33",
            "0",
            "0",
            "0"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "d16 = -2 d22",
          "d21 = -d22",
          "d24 = d15",
          "d32 = d31"
        ]
      },
      "tensor": "piezo-strain-d",
      "unit": {
        "display": "pC/N",
        "ucum": "pC/N"
      },
      "variant": "unspecified",
      "voigt": [
        [
          0.0,
          0.0,
          0.0,
          0.0,
          69.2,
          -41.6
        ],
        [
          -20.8,
          20.8,
          0.0,
          69.2,
          0.0,
          0.0
        ],
        [
          -0.85,
          -0.85,
          6.0,
          0.0,
          0.0,
          0.0
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "d_ijk = d_iJ x (1 if J<=3 else 1/2) (engineering shear strain)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "frame": {
        "convention": "IRE-1949",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "+c points out of the face that becomes negative on compression; equivalently it becomes positive on cooling (weis1985 pp. 192-193)"
      },
      "full": [
        [
          [
            0.0,
            -21.0,
            34.0
          ],
          [
            -21.0,
            0.0,
            0.0
          ],
          [
            34.0,
            0.0,
            0.0
          ]
        ],
        [
          [
            -21.0,
            0.0,
            0.0
          ],
          [
            0.0,
            21.0,
            34.0
          ],
          [
            0.0,
            34.0,
            0.0
          ]
        ],
        [
          [
            -1.0,
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          "value": 68
        },
        "d22": {
          "value": 21
        },
        "d31": {
          "value": -1.0
        },
        "d33": {
          "value": 6
        }
      },
      "kind": "tensor",
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        "transcribed": "2026-10-25"
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      "public": true,
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      "variant": "unspecified",
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      "kind": "tensor",
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        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 3,
      "scale": 1,
      "symbol": "e",
      "symmetry_form": {
        "form": [
          [
            "0",
            "0",
            "0",
            "0",
            "e15",
            "-e22"
          ],
          [
            "-e22",
            "e22",
            "0",
            "e15",
            "0",
            "0"
          ],
          [
            "e31",
            "e31",
            "e33",
            "0",
            "0",
            "0"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "e16 = -e22",
          "e21 = -e22",
          "e24 = e15",
          "e32 = e31"
        ]
      },
      "tensor": "piezo-stress-e",
      "unit": {
        "display": "C/m^2",
        "qudt": "http://qudt.org/vocab/unit/C-PER-M2",
        "ucum": "C/m2"
      },
      "variant": "unspecified",
      "voigt": [
        [
          0.0,
          0.0,
          0.0,
          0.0,
          3.76,
          -2.43
        ],
        [
          -2.43,
          2.43,
          0.0,
          3.76,
          0.0,
          0.0
        ],
        [
          0.23,
          0.23,
          1.33,
          0.0,
          0.0,
          0.0
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "e_ijk = e_iJ, J = V(jk)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    },
    {
      "frame": {
        "convention": "unstated",
        "handedness": "right",
        "setting": "crystal-physics",
        "x": "a axis, perpendicular to a mirror plane",
        "y": "in a mirror plane",
        "z": "polar c axis",
        "z_sign_definition": "not stated in this record; tensor form matches this frame by symmetry"
      },
      "full": [
        [
          [
            0.0,
            -2.5,
            3.7
          ],
          [
            -2.5,
            0.0,
            0.0
          ],
          [
            3.7,
            0.0,
            0.0
          ]
        ],
        [
          [
            -2.5,
            0.0,
            0.0
          ],
          [
            0.0,
            2.5,
            3.7
          ],
          [
            0.0,
            3.7,
            0.0
          ]
        ],
        [
          [
            0.2,
            0.0,
            0.0
          ],
          [
            0.0,
            0.2,
            0.0
          ],
          [
            0.0,
            0.0,
            1.3
          ]
        ]
      ],
      "id": "piezo-stress-e/unspecified/ogi2002-warner1967",
      "independent": {
        "e15": {
          "value": 3.7
        },
        "e22": {
          "value": 2.5
        },
        "e31": {
          "value": 0.2
        },
        "e33": {
          "value": 1.3
        }
      },
      "kind": "tensor",
      "name": "Piezoelectric stress constants",
      "provenance": {
        "locator": "Table III",
        "original_reference": "Warner, Onoe, Coquin, JASA 42, 1223 (1967)",
        "source_id": "ogi2002",
        "status": "S",
        "transcribed": "2026-10-25"
      },
      "public": true,
      "rank": 3,
      "scale": 1,
      "symbol": "e",
      "symmetry_form": {
        "form": [
          [
            "0",
            "0",
            "0",
            "0",
            "e15",
            "-e22"
          ],
          [
            "-e22",
            "e22",
            "0",
            "e15",
            "0",
            "0"
          ],
          [
            "e31",
            "e31",
            "e33",
            "0",
            "0",
            "0"
          ]
        ],
        "mirror": "x = 0 plane (x perpendicular to the mirror, z polar)",
        "point_group": "3m",
        "relations": [
          "e16 = -e22",
          "e21 = -e22",
          "e24 = e15",
          "e32 = e31"
        ]
      },
      "tensor": "piezo-stress-e",
      "unit": {
        "display": "C/m^2",
        "qudt": "http://qudt.org/vocab/unit/C-PER-M2",
        "ucum": "C/m2"
      },
      "variant": "unspecified",
      "voigt": [
        [
          0.0,
          0.0,
          0.0,
          0.0,
          3.7,
          -2.5
        ],
        [
          -2.5,
          2.5,
          0.0,
          3.7,
          0.0,
          0.0
        ],
        [
          0.2,
          0.2,
          1.3,
          0.0,
          0.0,
          0.0
        ]
      ],
      "voigt_convention": {
        "full_from_voigt": "e_ijk = e_iJ, J = V(jk)",
        "order": [
          "xx",
          "yy",
          "zz",
          "yz",
          "xz",
          "xy"
        ],
        "shear_strain": "engineering"
      }
    }
  ]
}