含义Meaning
判断 ABX₃ 化合物能否形成钙钛矿结构：t ≈ 0.8–1.0 时可形成，t = 1 为理想立方钙钛矿；t < 1 常发生八面体倾斜（正交、四方）。
Predicts perovskite formation for ABX₃: about 0.8–1.0 works, t = 1 is ideal cubic; t < 1 brings octahedral tilting.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(r_\mathrm{A}\) | A 位（12 配位）大阳离子半径radius of the 12-coordinate A cation | pm |
| \(r_\mathrm{B}\) | B 位（6 配位）阳离子半径radius of the octahedral B cation | pm |
| \(r_\mathrm{X}\) | 阴离子半径anion radius | pm |
推导Derivation
理想立方钙钛矿中，B–X 沿棱：\(a = 2(r_\mathrm{B} + r_\mathrm{X})\)。
In ideal cubic perovskite, B–X lies along the edge: \(a = 2(r_\mathrm{B} + r_\mathrm{X})\).
A–X 沿面对角线一半：\(\sqrt2 a = 2(r_\mathrm{A} + r_\mathrm{X})\)。
A–X spans half a face diagonal: \(\sqrt2 a = 2(r_\mathrm{A} + r_\mathrm{X})\).
二者同时满足时比值为 1，定义 t 衡量失配程度。
Both hold when t = 1; t measures the mismatch.
适用条件与局限Assumptions & limitations
硬球几何判据，还需配合八面体因子 \(\mu = r_\mathrm{B}/r_\mathrm{X}\)（约 0.41–0.90）；卤化物钙钛矿（光伏材料）预测准确率有限。
A geometric criterion; combine with the octahedral factor \(\mu = r_\mathrm{B}/r_\mathrm{X}\); limited accuracy for halide perovskites.
例题Worked example
SrTiO₃：r(Sr²⁺) = 144，r(Ti⁴⁺) = 60.5，r(O²⁻) = 140 pm → t = 1.00，立方钙钛矿。
SrTiO₃: t = 1.00, cubic perovskite.