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

  1. aReference 26
  2. bReference 50
  3. cNote that α1 = α1*(T − T0)