Table 1 Coefficients of thermodynamic potential, elastic compliance constants, and electrostrictive coefficients of Ba(ZrxTi1−x)O3 solid solutions
From: A thermodynamic potential for barium zirconate titanate solid solutions
Coefficient | Composition x in Ba(ZrxTi1−x)O3 | |||||||
---|---|---|---|---|---|---|---|---|
0a | 0.05 | 0.08b | 0.1 | 0.15 | 0.2 | 0.25 | 0.3 | |
T0 (◦C) | 115 | 107 | 100 | 84 | 64 | 32 | −10 | −52 |
α1*c [105m2N/(C2·◦C)] | 4.124 | 4.6 | 4.45 | 3.53 | 3.45 | 3.12 | 1.9 | 1.6 |
α11 (108m6N/C4) | −2.097 | −1.98 | −1.964 | −1.5 | −4.66 | −15.1 | −17.2 | −19.2 |
α12 (108m6N/C4) | 7.974 | 12.54 | 12.66 | 7.22 | 0.87 | 0.12 | 0.06 | 0.03 |
α111 (109m10N/C6) | 1.294 | 5.8 | 9.986 | 15.2 | 79 | 370 | 778 | 1153 |
α112 (109m10N/C6) | −1.95 | −9.85 | −19.42 | −18.5 | −13.28 | −5.28 | −2.88 | −2.38 |
α123 (109m10N/C6) | −2.5 | −5.72 | −2.132 | −1.8 | −1.2 | −0.75 | −0.35 | −0.15 |
α1111 (1010m14N/C8) | 3.863 | 9.65 | 15.08 | 14.3 | 9.1 | 0 | 0 | 0 |
α1112 (1010m14N/C8) | 2.529 | 4.421 | 6.333 | 9.4 | 12.5 | 0 | 0 | 0 |
α1122 (1010m14N/C8) | 1.637 | 4.821 | 8.005 | 10.5 | 12.6 | 0 | 0 | 0 |
α1123 (1010m14N/C8) | 1.367 | 1.422 | 11.15 | 16.2 | 10.38 | 0 | 0 | 0 |
S11 (10−12m2/N) | 8.3–4.87x | |||||||
S12 (10−12m2/N) | −2.7 + 2.025x | |||||||
S44 (10−12m2/N) | 9.24 + 5.05x | |||||||
Q11 (m4/C2) | 0.1–0.004x | |||||||
Q12 (m4/C2) | −0.034–0.005x | |||||||
Q44 (m4/C2) | 0.029 + 0.002x |