Martienssen W., Warlimont H. (Eds.). Handbook of Condensed Matter and Materials Data
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842 Part 4 Functional Materials
Table 4.4-8 Hexagonal, point group 6mm (C
6v
) materials, cont.
General Static dielectric Elastic stiffness Piezoelectric Elastooptic
tensor tensor tensor tensor
Material
g/cm
3
ε
S
11
c
11
d
31
p
11
Mohs hardness ε
S
33
c
33
d
33
p
12
κ ⊥ c ε
T
11
c
44
d
15
p
13
κ c ε
T
33
c
12
d
h
p
31
(W/mK) c
13
(10
−12
C/N) p
33
(10
9
Pa) p
44
α-Zinc sulfide, α-ZnS 4.09 8.58 122.0 −1.1(0) −0.115
(wurtzite, zinc blende) – 8.52 140.2 +3.2(1) 0.017
27 [4.45] 8.60(5) 28.5 −2.8(1) 0.025
− 8.57(7) 58.0 +1.0 [4.237, 238] 0.0271
[4.239,240] 46.8 −0.13
[4.239,240]
b
−0.0627 [4.241]
a
These values for ε
ij
are neither at constant stress nor at constant strain.
b
The elastic stiffness constant were measured at constant electric field
c
E
.
Table 4.4-9 Hexagonal, point group 6 (C
6
) materials
General Static dielectric Elastic stiffness Piezoelectric Elastooptic
tensor tensor strain tensor tensor
Material
g/cm
3
ε
S
11
c
11
d
31
p
11
Mohs hardness ε
S
33
c
33
d
33
p
12
κ ⊥ c ε
T
11
c
44
d
14
p
13
κ c ε
T
33
c
12
d
15
p
16
(W/mK) c
13
(10
−12
C/N) p
31
(10
9
Pa) p
33
p
44
p
45
Barium nitrite 3.179 – 54.2 −1.73(17)
monohydrate, − – 29.9 +3.27(16)
Ba(NO
2
)
2
·H
2
O − 7.56(8) 11.2 +0.47(9)
− 6.78(7) 27.5 −1.03(10)
− [4.242] 17.8 [4.242]
[4.242]
b
α-Lithium iodate, LiIO
3
4.490 7.9(4) (−20
◦
C) 82.5(8) 3.5 [4.8,243, 244] |0.32|
4 [4.245] 55.9(23) 48.5 –
1.27 (⊥ c) 5.9(3) (−20
◦
C) 18.0(3) [4.8, 243,244] |0.24|
0.65 ( c) [4.245] 31.9(8) 73(7) [4.246] |0.03|
[4.247,248] 8.25
a
(0
◦
C) 20.8(87) 55.5 [4.8, 243, 244] |0.41|
[4.246] [4.7, 249]
b
|0.23| [4.250]
6.53
a
(0
◦
C) −
[4.246] −
a
The values for ε
ij
are neither at constant stress nor at constant strain.
b
The elastic stiffness constants were measured at constant electric field
c
E
.
Part 4 4.4
Dielectrics and Electrooptics 4.4 Tables of Numerical Data for Dielectrics and Electrooptics 843
Table 4.4-8 Hexagonal, point group 6mm (C
6v
) materials, cont.
Electrooptic General Refractive index Nonlinear dielectric
tensor optical properties susceptibility
r
T
13
Transparency range n
o
n
e
d
31
r
T
33
(µm) A A d
33
r
T
51
dn
o
/dT (10
−5
K
−1
) B B d
15
(10
−12
m/V) dn
e
/dT (10
−5
K
−1
) C C (10
−12
m/V)
at λ = 633 nm D D
E E
0.92 0.35–23 [4.122] 2.213 (10.6 µm) 2.219 (10.6 µm) −18.9 ±6.3
1.85 [4.234,235] − 3.4175 3.4264 +37.3 ±12.6
− − 1.7396 1.7491 21.4 ±8.4
0.07166 0.07150 (all at 10.6 µm)
0 [4.222]
e
0 [4.222]
e
[4.109,251]
− −
cde
Dispersion relations (λ (mm), T =20
◦
C):
c
n
2
= A +
Bλ
2
λ
2
−C
+
Dλ
2
λ
2
−E
.
d
n
2
= A +
B
λ
2
−C
−Dλ
2
.
e
n
2
= A +
Bλ
2
λ
2
−C
−Dλ
2
.
Table 4.4-9 Hexagonal, point group 6 (C
6
) materials, cont.
Electrooptic General Refractive index Nonlinear dielectric
tensor optical properties susceptibility
r
T
13
Transparency range (µm) n
o
n
e
d
31
r
T
33
dn
o
/dT (10
−5
K
−1
) A A d
33
r
T
41
dn
e
/dT (10
−5
K
−1
) B B (10
−12
m/V)
r
T
51
C C
(10
−12
m/V) D D
at λ =633 nm
+3.47(10) 0.4–2 [4.252] 1.6266 (0.5 µm) 1.5238 (0.5 µm) 1.14 [4.252]
+3.31(13) − 1.99885 1.48610 −
−0.85(21) − 0.542910 0.775625
−0.41(10) 0.04128 0.01830
[4.242] 0.01012 [4.252]
c
0.00090 [4.252]
c
6.4 0.3–6.0 [4.253,254] 1.8571 1.7165 4.4
4.2 −9.38 [4.255] 3.415716 2.918692 4.5 [4.12,14]
3.1 −8.25 [4.255] 0.047031 0.035145
7.9
r
S
51
0.035306 0.028224
[4.256,257] 0.008801 [4.258]
c
0.003641 [4.258]
c
c
Dispersion relation (λ (mm), T =20
◦
C):
n
2
= A +
B
λ
2
−C
−Dλ
2
.
Part 4 4.4
844 Part 4 Functional Materials
Table 4.4-10 Trigonal, point group 3m (D
3d
) materials
General Static Dissipation Elastic Elastic Elastooptic
dielectric tensor factor stiffness tensor compliance tensor tensor
Material
g/cm
3
ε
S
11
tan δ
1
c
11
s
11
p
11
Mohs hardness ε
S
33
tan δ
3
c
33
s
33
p
12
κ ⊥ c ε
T
11
c
44
s
44
p
13
κ c ε
T
33
c
12
s
12
p
14
(W/mK) c
13
s
13
p
31
c
14
s
14
p
33
(10
9
Pa)
10
−12
Pa
−1
p
41
p
44
α-Aluminium oxide, 3.98 9.4 0.0001 496(3) 2.35 −0.23
Al
2
O
3
(sapphire) 9 11.5 [4.48]
a
[4.48] 499(4) 2.17 −0.03
33 (⊥ c) − 146(3) 6.95 0.02
35 ( c) 159(10) −0.70 0.00
[4.259] 114(3) −0.38 0.04
−23(1) 0.46 −0.20
[4.7,260] [4.260] 0.01
−0.10 (644 nm) [4.261]
Calcite, CaCO
3
2.71 8.0
ab
144(3) 11.4(2) 0.062
(calcspar, Iceland spar) 3 [4.26] 84.3(26) 17.3(5) 0.147
3.00 (⊥ c) 33.5(7) 41.4(12) 0.186
3.40 ( c) 54.2(47) −4.0(4) −0.011
(50
◦
C) 51.2(34) 4.5(4) 0.241
[4.262] −20.5(2) 9.5(5) 0.139
[4.7,263] [4.7] −0.036
−0.058 (514 nm) [4.264]
a
These values for ε
11
are neither at constant stress nor at constant strain.
b
It is not clear which relative dielectric constant ε
ij
is specified.
Table 4.4-11 Trigonal, point group 32 (D
3
) materials
General Static Elastic Piezoelectric Elastooptic
dielectric tensor stiffness tensor tensor tensor
Material
g/cm
3
ε
S
11
c
11
d
11
p
11
Mohs hardness ε
S
33
c
33
d
14
p
12
κ ⊥ c ε
T
11
c
44
(10
−12
C/N) p
13
κ c ε
T
33
c
12
p
14
(W/mK) c
13
p
31
c
14
p
33
(10
9
Pa) p
41
p
44
Aluminium phosphate, 2.620 5.88 67.0(26) −3.0
AlPO
4
(berlinite) 6.5 [4.8, 265] 87.2(10) 1.3
≈6 [4.45] – 42.9(4) [4.266,267]
− 4.73 9.3(14)
4.62 13.1(21)
[4.268,269] −12.7(5)
[4.7,270]
a
Part 4 4.4
Dielectrics and Electrooptics 4.4 Tables of Numerical Data for Dielectrics and Electrooptics 845
Table 4.4-10 Trigonal, point group 3m (D
3d
) materials, cont.
General Refractive index
optical properties
Transparency range (µm) n
o
n
e
dn
o
/dT (10
−5
K
−1
) A A
dn
e
/dT (10
−5
K
−1
) B B
C C
D D
E E
F F
0.147–5.2 [4.87] 1.7655 (0.7 µm) 1.7573 (0.7 µm)
− 1.077 1.041
− 0.0033 0.0004
1.025 1.030
0.0114 0.0141
5.04 3.55
151.2 [4.271]
cd
123.8 [4.271]
cd
0.2–2.3 1.6428 (1.042 µm) [4.272] 1.4799 (1.042 µm) [4.272]
0.21 (0.633 µm)
1.19 (0.633 µm) [4.22]
c
Dispersion relation (λ (µm), T = 20
◦
C):
n
2
= 1 +
Aλ
2
λ
2
−B
+
Cλ
2
λ
2
−D
+
Eλ
2
λ
2
−F
.
d
For crystals grown by heat exchanger method (HEM).
Table 4.4-11 Trigonal, point group 32 (D
3
) materials, cont.
Electrooptic General Refractive index Nonlinear dielectric
tensor optical properties susceptibility
r
T
11
Transparency range (µm) n
o
n
e
d
11
r
T
41
dn
o
/dT (10
−5
K
−1
) A A (10
−12
m/V)
(10
−12
m/V) dn
e
/dT (10
−5
K
−1
) B B
at λ = 633 nm C C
D D
E E
1.5161 (1 µm) [4.273] 1.5285 (1 µm) [4.273] 0.53 [4.228]
d
14
= 0.013 [4.228]
Part 4 4.4
846 Part 4 Functional Materials
Table 4.4-11 Trigonal, point group 32 (D
3
) materials, cont.
General Static Elastic Piezoelectric Elastooptic
dielectric tensor stiffness tensor tensor tensor
Material
g/cm
3
ε
S
11
c
11
d
11
p
11
Mohs hardness ε
S
33
c
33
d
14
p
12
κ ⊥ c ε
T
11
c
44
(10
−12
C/N) p
13
κ c ε
T
33
c
12
p
14
(W/mK) c
13
p
31
c
14
p
33
(10
9
Pa) p
41
p
44
α-Mercuric sulfide, 8.05 14.0(3) 35.36 19.1 –
HgS (cinnabar) 2–2.5 25.5(5) 50.92 ≈|1.7| –
− 15.0(3) 21.40 [4.8,274] |0.445|
− 25.5(5) 7.02 –
[4.275] 8.66 –
11.3 |0.115| [4.276]
[4.277]
b
−
−
Potassium
fluoroboratoberyllate,
KBe
2
BO
3
F
2
(KBBF)
α-Silicon dioxide, 2.6485 4.435 86.6(3) +2.3 0.16
SiO
2
(quartz) 7 4.640 106.4(12) −0.67 0.27
6.5 (⊥ c) 4.520 58.0(7) [4.278, 279] 0.27
11.7 ( c) 4.640 [4.280] 6.7(9) −0.030
[4.200] 12.4(16) 0.29
17.8(3) [4.7]
a
0.10
−0.047
−0.079 (589 nm)
[4.281]
Tellurium, Te 6.25 33 [4.282] 33(1) +55 0.164
2–2.5 53 [4.282] 71(3) +50 [4.283] 0.138
2.0 (⊥ c) – 31.8(25) 0.146
3.4 ( c) 37 [4.284] 9.1(7) −0.04
[4.285] 24.5(15) −0.086
(−)12.4(15) 0.038
[4.7] 0.28
0.14 (10.6 µm) [4.286]
a
These values are approximately the constant-field values c
E
.
b
c
E
at constant electric field.
cde
Dispersion relations (λ (µm), T =20
◦
C):
c
n
2
= A +
Bλ
2
λ
2
−C
+
Dλ
2
λ
2
−E
.
Part 4 4.4
Dielectrics and Electrooptics 4.4 Tables of Numerical Data for Dielectrics and Electrooptics 847
Table 4.4-11 Trigonal, point group 32 (D
3
) materials, cont.
Electrooptic General Refractive index Nonlinear dielectric
tensor optical properties susceptibility
r
T
11
Transparency range (µm) n
o
n
e
d
11
r
T
41
dn
o
/dT (10
−5
K
−1
) A A (10
−12
m/V)
(10
−12
m/V) dn
e
/dT (10
−5
K
−1
) B B
at λ =633 nm C C
D D
E E
3.1 0.63–13.5 [4.287] 2.7041 2.9909 50 (10.6 µm) [4.288]
1.55 [4.289] − 4.1506 4.0101
− 2.7896 4.3736
0.1328 0.1284
1.1378 1.5604
705 [4.227]
c
705 [4.227]
c
0.155–3.5 [4.290] 1.487 (0.4 µm) 1.410 (0.4 µm) 0.76 [4.290]
− 1 1
− 1.169725 0.956611
0.00624 0.0061926
0.009904 [4.290]
d
0.027849 [4.290]
d
− −
−0.445(10) 0.15–4.5 [4.262] 1.5350 (1 µm) 1.5438 (1 µm) 0.30
+0.1904(50) −0.62 (546 nm) For dispersion relation, For dispersion relation, [4.12–14, 128, 291, 292]
[4.293] −0.7 (546 nm) [4.68] see [4.68]
e
see [4.68]
e
3.8–32 [4.85] 4.7979 (10.6 µm) 6.2483 (10.6 µm) 598 (10.6 µm) [4.294]
− 18.5346 29.5222
− 4.3289 9.3068
3.9810 2.5766
3.78 9.235
11.813 [4.227]
c
13.521 [4.227]
c
d
n
2
= A +
Bλ
2
λ
2
−C
−Dλ
2
.
e
n
2
o
= 1 +
0.663044λ
2
λ
2
−0.0036
+
0.517852λ
2
λ
2
−0.0112
+
0.175912λ
2
λ
2
−0.0142
+
0.565380λ
2
λ
2
−78.216
+
1.675299λ
2
λ
2
−430.23
;
n
2
e
= 1 +
0.665721λ
2
λ
2
−0.0036
+
0.503511λ
2
λ
2
−0.0112
+
0.214792λ
2
λ
2
−0.0142
+
0.539173λ
2
λ
2
−77.30
+
1.807613λ
2
λ
2
−390.85
.
Part 4 4.4
848 Part 4 Functional Materials
Table 4.4-12 Trigonal, point group 3m (C
3v
) materials
General Static Dissipation Elastic Piezoelectric Elastooptic
dielectric tensor factor stiffness tensor tensor tensor
Material
g/cm
3
ε
S
11
tan δ
1
c
11
d
22
p
11
Mohs hardness ε
S
33
tan δ
3
c
33
d
31
p
12
κ ⊥ c ε
T
11
c
44
d
33
p
13
κ c ε
T
33
( f (kHz)) c
12
d
15
p
14
(W/mK) c
13
d
h
p
31
c
14
(10
−12
C/N) p
33
(10
9
Pa) p
41
p
44
β-Barium borate, 3.849 – < 10
−3
123.8
BaB
2
O
4
(BBO) 4 – < 10
−3
53.3
1.2 (⊥ c) 6.7 (10–50
◦
C, 7.8
1.6 ( c) 8.1 [4.295] 1–100 kHz) 60.3
[4.200] [4.295] 49.4
12.3 [4.295]
Lithium niobate, 4.628 43.9(22) [4.296] 0.0015(4) 202(2) 20.7(1) [4.297] −0.031(9)
LiNbO
3
5–5.5 23.7(12) [4.296] 0.0011(3) 244(5) −0.86(2) [4.297] 0.082(9)
4.6 [4.137] 85.2 [4.298] (1 GHz) 60.2(6) +16.2(1) [4.297] 0.135(7)
28.7 [4.298] [4.296] 55(2) 74.0(3) [4.297] −0.076(15)
72(5) 6.310(14) [4.299] 0.170(14)
8.5(7) [4.7]
a
0.069(5)
−0.150(10)
0.147(100) [4.11]
b
Lithium niobate
(5% MgO-doped)
MgO:LiNbO
3
Lithium tantalate, 7.45 42.6 0.0013(4) 230(2) 8.5 [4.300] −0.081
LiTaO
3
5.5 42.8 0.0007(3) 276(6) −3.0 [4.300] 0.081
53.6 (1 GHz) 96(1) 9.2 [4.300] 0.093
43.4 [4.298] [4.296] 42(6) 26 [4.300] −0.026
79(4) 2.000(12) [4.299] 0.089
−11(1) −0.044
[4.7,301,302] −0.085
0.028 [4.303,304]
Part 4 4.4
Dielectrics and Electrooptics 4.4 Tables of Numerical Data for Dielectrics and Electrooptics 849
Table 4.4-12 Trigonal, point group 3m (C
3v
) materials, cont.
Electrooptic General Refractive index Nonlinear dielectric
tensor optical properties susceptibility
r
T
13
Transparency range (µm) n
o
n
e
d
31
r
T
22
dn
o
/dT (10
−5
K
−1
) A A d
33
r
T
33
dn
e
/dT (10
−5
K
−1
) B B d
22
r
T
51
C C d
15
(10
−12
m/V) D D (10
−12
m/V)
at λ = 633 nm E E
F F
β-Barium borate, +0.27(2) 0.189–3.5 1.6551 1.5426 2.16±0.08 (d
22
)
BaB
2
O
4
(BBO) −2.41(3) [4.295,305–308] 2.7359 2.3753 [4.12, 14, 309]
+0.29(3) −1.66 [4.295] 0.01878 0.01224
+1.7(1) [4.310] −0.93 [4.295] 0.01822 0.01667
0.01471 0.01627
0.0006081 0.0005716
0.0000674 [4.311]
h
0.00006305 [4.311]
h
Lithium niobate, +9.6 0.33–5.5 [4.312] 2.2340 2.1554 −4.6
LiNbO
3
+6.8 dn
o
/dT = 0.141 [4.313]
f
4.91296 4.54528 −25 [4.13, 14]
+30.9 dn
o
/dT = 2.0 [4.314]
g
0.116275 0.091649 −
+32.6 dn
e
/dT = 3.85 [4.313]
f
0.048398 0.046079 −
[4.315,316] dn
e
/dT = 7.6 [4.314]
g
0.0273 [4.313]
i
0.0303 [4.313]
i
− −
− −
Lithium niobate 11.2(5) 0.4–5 [4.317–319] 2.2272 2.1463 −4.69 [4.309]
(5% MgO-doped) − − 4.9017 4.5583 |25| [4.13]
MgO:LiNbO
3
36.0(5) − 0.112280 0.091806 −
− 0.049656 0.048086 −
(for 10.7% MgO) 0.039636 [4.317, 318]
i
0.032068 [4.317,318]
i
[4.320] − −
− −
Lithium tantalate, 4.5 0.4–5.5 2.1366 (1.058 µm) 2.1406 (1.058 µm) −1.0±0.2
LiTaO
3
0.3 − [4.321] [4.321] −16±2
27 − +1.7±0.2 [4.156,322]
15 −
(all for r
S
at
3.39 µm) [4.323]
Part 4 4.4
850 Part 4 Functional Materials
Table 4.4-12 Trigonal, point group 3m (C
3v
) materials, cont.
General Static Dissipation Elastic Piezoelectric Elastooptic
dielectric tensor factor stiffness tensor tensor tensor
Material
g/cm
3
ε
S
11
tan δ
1
c
11
d
22
p
11
Mohs hardness ε
S
33
tan δ
3
c
33
d
31
p
12
κ ⊥ c ε
T
11
c
44
d
33
p
13
κ c ε
T
33
( f (kHz)) c
12
d
15
p
14
(W/mK) c
13
d
h
p
31
c
14
(10
−12
C/N) p
33
(10
9
Pa) p
41
p
44
Silver antimony sulfide, 5.83 – 52.7 16.2
Ag
3
SbS
3
(pyrargyrite) 2–2.5 – 35.6 −19.5
− 21.7(7) 11.6 62.2
− 24.7(7) 26.3 31.6
[4.324] 28.0 −
−0.4 [4.325, 326]
[4.324,327]
c
Silver arsenic sulfide, 5.63 20.2(2) 56.76 12.1 |0.056|
Ag
3
AsS
3
(proustite) 2–2.5 20.2(2) 37.0 −13.8 |0.082|
− 21.5 9.12 30 |0.068|
− 22.0 [4.324] 30.4 −20 [4.324] –
30.4 − |0.103|
−0.16 [4.324] |0.100|
|≈0.01| (1150 nm)
−
[4.328,329]
Thallium arsenic selenide, 7.83 See [4.330] See [4.330]
Tl
3
AsSe
3
(TAS) 2–3
−
−
Tourmaline, 3.0–3.2 6.3
e
[4.278] 277(19) −0.3 [4.331]
(Na, Ca)(Mg, Fe)
3
B
3
Al
6
7–7.5 7.1
e
[4.278] 163(11) −0.34 [4.331]
Si
6
(O, OH, F)
31
3.03 (⊥ c) 8.2 [4.331] 64(3) −1.8 [4.331]
2.92 ( c) 7.5 [4.331] 65(24) −3.6 [4.331]
(125
◦
C) 32(20) 4.00(6)
[4.332]
d
−6.9(25) [4.333, 334]
[4.7] [4.333,334]
a
These values are approximately the constant-field values c
E
.
b
p
E
at constant electric field.
c
c
E
at constant electric field.
d
The thermal conductivities have been interpolated from κ(⊥ c) = 0.108 × T
0.556
and κ( c) = 0.492 × T
0.297
,
valid for temperature ranges of 398.2–723.2 K and 393.2–729.2 K, respectively [4.332].
e
These values for ε
ij
are neither at constant stress nor at constant strain.
f
Fabricated by vapor transport equilibration (VTE).
g
Stoichiometric melt.
Part 4 4.4
Dielectrics and Electrooptics 4.4 Tables of Numerical Data for Dielectrics and Electrooptics 851
Table 4.4-12 Trigonal, point group 3m (C
3v
) materials, cont.
Electrooptic General Refractive index Nonlinear dielectric
tensor optical properties susceptibility
r
T
13
Transparency range (µm) n
o
n
e
d
31
r
T
22
dn
o
/dT (10
−5
K
−1
) A A d
33
r
T
33
dn
e
/dT (10
−5
K
−1
) B B d
22
r
T
51
C C d
15
(10
−12
m/V) D D (10
−12
m/V)
at λ = 633 nm E E
F F
0.7–14 [4.335] 2.9458 2.7956 7.8 (10.6 µm)
− 1 1 −
− 6.585 5.845 8.2 (10.6 µm)
0.16 0.16 −
0.1133 0.0202 [4.3, 4,294,336]
225 [4.335]
j
225 [4.335]
j
− −
2.0 [4.337,338] 0.6–13 [4.339] 2.8163 2.5822 10.4 (10.6 µm)
1.05(4) [4.340] − 9.220 7.007 –
0.22 [4.337,338] − 0.4454 0.3230 16.6 (10.6 µm)
3.4(5) [4.340] 0.1264 0.1192
1733 660 10.8 (10.6 µm)
1000 [4.341]
k
1000 [4.341]
k
[4.339,342]
− −
1.28–17 [4.343] 3.331 (11 µm) 3.152 (11 µm) d
eff
SHG 10.6 µm:
−4.52 [4.344] 1 1 67.5 [4.342, 343]
+3.55 [4.344] 10.210 8.993 36.5 [4.294, 343]
0.197136 0.197136 29 [4.345]
0.522 0.308 20 [4.346]
625 [4.344]
j
625 [4.344]
j
− −
r
S
13
= 1.7 [4.347] 1.6274 1.6088 0.13(3)
r
T
22
= 0.3 (589 nm) 1 1 0.47(6)
[4.348] 1.6346 1.57256 0.07(1)
r
S
33
= 1.7 [4.347] 0.010734 0.011346 0.23(4) [4.321]
0 [4.349]
j
0 [4.349]
j
− −
− −
hijk
Dispersion relations (λ (µm), T =20
◦
C):
h
n
2
= A +
B
λ
2
−C
−Dλ
2
+Eλ
4
−Fλ
6
.
i
n
2
= A +
B
λ
2
−C
−Dλ
2
.
j
n
2
= A +
Bλ
2
λ
2
−C
+
Dλ
2
λ
2
−E
.
k
n
2
= A +
B
λ
2
−C
+
D
λ
2
−E
.
Part 4 4.4