1.4.2 Elastic Moduli
The mechanical response of a material to an applied force is described by various moduli. Young’s modulus E (extension in tension) and the modulus of rigidity or shear G are related to Poisson’s ratio (ratio of lateral to longitudinal strain under unilateral stress) by = E/2G) – 1. The bulk modulus B (1/isothermal compressibility) is related to the above moduli by B = E/3(1 – ).
Elastic Moduli
|
|
|
Moduli |
|
|
Poisson’s |
Young’s |
Rigidity |
Bulk |
Material |
ratio |
E (GPa) |
G (GPa) |
B (GPa) |
Ag3AsS3 |
0.38 |
28 |
10 |
37 |
AgBr |
0.39 |
24.7 |
8.8 |
40.5 |
AgCl |
0.41 |
22.9 |
8.1 |
44.0 |
AgGaS2 |
0.37 |
52 |
19 |
67 |
β–AgI |
0.4 |
12 |
4.4 |
24 |
AlAs |
0.27 |
108 |
42.4 |
77.2 |
AlN |
0.26 |
294 |
117 |
202 |
Al2O3 |
0.23 |
400 |
162 |
250 |
ALON |
0.24 |
317 |
128 |
203 |
BaB2O4 |
0.41 |
30 |
11 |
60.6 |
BaF2 |
0.31 |
65.8 |
25.1 |
57.6 |
BaTiO3 |
0.36 |
145 |
53 |
174 |
BeAl2O4 |
— |
469 |
— |
— |
BeO |
0.23 |
395 |
162 |
240 |
Bi12GeO20 |
0.28 |
82 |
32 |
63.3 |
Bi12SiO20 |
0.28 |
84 |
33 |
63.1 |
BN |
0.11 |
833 |
375 |
358 |
BP |
0.19 |
324 |
136 |
172 |
C (diamond) |
0.10 |
1100 |
500 |
460 |
CaCO3 |
0.31 |
83 |
32 |
73.2 |
CaF2 |
0.29 |
110 |
42.5 |
85.7 |
CaLa2S4 |
0.25 |
96 |
38.4 |
64 |
CaMoO4 |
0.29 |
103 |
40 |
80 |
CaWO4 |
0.29 |
96 |
37 |
78 |
CdGeS2 |
0.32 |
74 |
28 |
70 |
CdS |
0.38 |
42 |
15 |
59 |
CdSe |
0.37 |
42 |
15.3 |
53 |
CdTe |
0.35 |
8.4 |
14.2 |
42.9 |
CsBr |
0.27 |
22 |
8.8 |
15.8 |
CsCl |
0.27 |
25 |
10.0 |
18.2 |
CsI |
0.26 |
18 |
7.3 |
12.6 |
CuCl |
0.30 |
24.8 |
8.9 |
39.3 |
GaAs |
0.24 |
116 |
46.6 |
75.0 |
GaN |
0.25 |
294 |
118 |
195 |
GaP |
0.24 |
140 |
56.5 |
89.3 |
© 2003 by CRC Press LLC
Elastic Moduli—continued
|
|
|
Moduli |
|
|
Poisson’s |
Young’s |
Rigidity |
Bulk |
Material |
ratio |
E (GPa) |
G (GPa) |
B (GPa) |
Ge |
0.20 |
132 |
54.8 |
75.0 |
InAs |
0.30 |
74 |
28 |
61 |
InP |
0.30 |
89 |
34 |
72.7 |
KBr |
0.30 |
18 |
7.2 |
15.2 |
KCl |
0.29 |
22 |
8.5 |
18.4 |
KF |
0.28 |
41 |
16 |
31.8 |
KH2PO4 |
0.26 |
38 |
15 |
28 |
KI |
0.30 |
14 |
5.5 |
11.9 |
KNbO3 |
0.22 |
250 |
71 |
95 |
KTaO3 |
0.27 |
316 |
124 |
230 |
LaF3 |
0.32 |
120 |
46 |
100 |
LiF |
0.22 |
110 |
45 |
65.0 |
LiIO3 |
0.23 |
55 |
22.4 |
33.5 |
LiNbO3 |
0.25 |
170 |
68 |
112 |
LiSrAlF6 |
0.3 |
109 |
— |
— |
LiYF4 |
0.32 |
85 |
32 |
81 |
MgAl2O4 |
0.26 |
276 |
109 |
198 |
MgF2 |
0.26 |
137 |
53.9 |
99.1 |
MgO |
0.18 |
310 |
131 |
163 |
NaBr |
0.26 |
29 |
11.6 |
19.9 |
NaCl |
0.26 |
37 |
14.5 |
25.3 |
NaF |
0.24 |
76 |
30.7 |
48.5 |
NaI |
0.28 |
22 |
8.4 |
16.1 |
[NH4] 2CO |
0.41 |
~9 |
~3 |
17 |
NH4H2PO4 |
0.32 |
29 |
11 |
27.9 |
PbF2 |
0.33 |
59.8 |
22.4 |
60.5 |
PbMoO4 |
0.35 |
66 |
24 |
72 |
PbS |
0.28 |
70.2 |
27.5 |
52.8 |
PbSe |
0.28 |
64.8 |
25.4 |
48.5 |
PbTe |
0.26 |
56.9 |
22.6 |
39.8 |
Se |
0.27 |
24 |
9 |
17 |
Si |
0.22 |
162 |
66.2 |
97.7 |
α–SiC |
0.16 |
455 |
197 |
221 |
β–SiC |
0.17 |
447 |
191 |
224 |
β–SiC (CVD) |
0.21 |
466 |
— |
— |
SiO2, α–quartz |
0.08 |
95 |
44 |
38 |
SrF2 |
0.29 |
89 |
34.6 |
71.3 |
SrMoO4 |
0.30 |
87 |
33 |
73 |
SrTiO3 |
0.23 |
283 |
115 |
174 |
Te |
0.25 |
35 |
14 |
24 |
TeO2 |
0.33 |
45 |
17 |
46 |
TiO2 |
0.27 |
293 |
115 |
215 |
© 2003 by CRC Press LLC
Elastic Moduli—continued
|
|
|
Moduli |
|
|
Poisson’s |
Young’s |
Rigidity |
Bulk |
Material |
ratio |
E (GPa) |
G (GPa) |
B (GPa) |
TlBr |
0.32 |
24 |
8.9 |
22.4 |
Tl[Br,I] KRS-5 |
0.34 |
19.6 |
7.3 |
20.4 |
TlCl |
0.33 |
25 |
9.3 |
23.8 |
Tl[Br,Cl], KRS-6 |
0.33 |
24 |
9.0 |
32.2 |
Y3Al5O12 |
0.24 |
280 |
113 |
180 |
Y3Fe5O12 |
0.29 |
200 |
— |
— |
Y2O3 |
0.30 |
173 |
67 |
145 |
ZnO |
0.35 |
127 |
47 |
144 |
α-ZnS |
0.30 |
87 |
33 |
74 |
β-ZnS |
0.32 |
82.5 |
31.2 |
76.6 |
β-ZnS (CVD) |
0.29 |
74.5 |
— |
— |
ZnSe |
0.30 |
75.4 |
29.1 |
61.8 |
ZnSe (CVD) |
0.28 |
70.3 |
|
|
ZnTe |
0.30 |
61.1 |
23.5 |
51.0 |
ZrO2: 12%Y2O3 |
0.31 |
233 |
88.6 |
205 |
The above table was adapted from Tropf, W. J., Thomas, M. F., and Harris, T. J., Properties of crystals and glasses, Handbook of Optics, Vol. II (McGraw-Hill, New York, 1995), p. 33.48.
1.4.3 Engineering Data
The following engineering properties can depend on the production method and exhibit sample–to–sample variations. Material strength may also depend on subsurface damage resulting from grinding and polishing. Therefore, the data should be considered only as a guide.
Engineering Data
|
Flexure |
Fracture |
Volume |
|
|
strength |
toughness |
compressibility |
|
Material |
(MPa) |
(MPa m1/2) |
(Tpa–1) |
Ref. |
AgCl |
26 |
|
|
1 |
AgSb |
|
|
57.1 |
4 |
Al2O3 |
1200 |
3 |
1.36 || c |
1 |
|
|
|
1.22 || a |
1 |
AlN |
225 |
3 |
|
1 |
Al23O27N5 |
310 |
1.4 |
|
1 |
α-AgI |
|
|
41 |
4 |
BaB2O4 |
|
1.5 |
|
1 |
BaF2 |
27 |
|
|
1 |
Be3Al2Si6O18 |
|
|
6.65 |
2 |
BeO |
275 |
|
|
1 |
C (diamond) |
2940 |
2.0 |
|
1 |
© 2003 by CRC Press LLC
Engineering Data—continued
|
Flexure |
Fracture |
Volume |
|
||
|
strength |
toughness |
compressibility |
|
||
Material |
(MPa) |
(MPa m1/2) |
(TPa–1) |
Ref. |
||
Ca5(PO4)3F |
|
|
|
13.2 |
|
2 |
CaF2 |
90 |
0.5 |
|
11.64 |
1,2 |
|
CaLa2S4 |
81 |
0.68 |
|
|
|
1 |
CaMoO4 |
|
|
|
12.5 |
|
2 |
CaWO4 |
|
|
|
13.3 |
|
2 |
CdS |
28 |
|
|
|
|
1 |
CdSe |
21 |
|
|
|
|
1 |
CdSiAs2S4 |
|
|
|
4.3 |
|
4 |
CdTe |
26 |
|
|
|
|
1 |
CsBr |
8.4 |
|
|
|
|
1 |
CsI |
5.6 |
|
|
|
|
1 |
GaAs |
55 |
|
|
77.1 |
|
1,4 |
GaN |
70 |
|
|
|
|
1 |
GaP |
100 |
0.9 |
|
11.0 |
|
1,4 |
GaSbs |
|
|
|
45.7 |
|
4 |
Gd2(MoO4)3 |
|
|
|
27.2 |
|
2 |
Gd3Ga5O12 |
|
|
|
5.88 |
2 |
|
Gd3Sc2Ga3O12 |
|
1.2 |
|
|
|
3 |
Ge |
100 |
0.66 |
|
|
|
1 |
InAs |
|
|
|
54.9 |
|
4 |
InP |
|
|
|
73.5 |
|
4 |
InSb |
|
|
|
44.2 |
|
4 |
KBr |
11 |
|
|
|
|
1 |
KCl |
10 |
|
|
|
|
1 |
KMgO3 |
|
|
|
14.4 |
|
2 |
LaB3O6 |
|
1.9 (111) |
|
|
|
|
|
|
0.38 (10–1) |
|
|
|
|
LaF3 |
33 |
|
|
|
|
1 |
LiB3O5 |
|
2.0 |
|
|
|
|
LiCaAlF6 |
|
0.18 || |
c |
|
|
3 |
|
|
0.37 c |
|
|
3 |
|
LiF |
27 |
|
|
15.05 |
1,2 |
|
LiNbO3 |
|
|
|
8.8 |
|
2 |
LiSrAlF6 |
|
0.40 || |
c |
|
|
3 |
LiYF4 |
35 |
|
|
|
|
1 |
Lu3Al5O12 |
|
1.1 |
|
|
|
3 |
MgAl2O4 |
170 |
1.5 |
|
|
|
1 |
MgF2 |
100 |
|
|
10.1 |
|
1 |
MgO |
130 |
1.0 |
|
6.2 |
|
1 |
MnF2 |
|
|
|
4.3 |
|| a |
2 |
|
|
|
|
2.0 |
c |
2 |
© 2003 by CRC Press LLC
Engineering Data—continued
|
Flexure |
Fracture |
Volume |
|
||
|
strength |
toughness |
compressibility |
|
||
Material |
(MPa) |
(MPa m1/2) |
(TPa–1) |
Ref. |
||
NaCl |
9.6 |
|
|
|
|
1 |
Si |
130 |
0.95 |
|
|
|
1 |
β-SiC |
250 |
|
|
|
|
1 |
β-SiC (CVD) |
|
3.3 |
|
|
|
|
Sr5(PO4)3F |
|
0.51 |
|
|
|
3 |
Sr5(VO4)3F |
|
0.36 |
|| |
c |
|
3 |
Te |
11 |
|
|
|
|
1 |
Tl[Br,Cl], KRS-6 |
21 |
|
|
|
|
1 |
Tl[Br,I] KRS-5 |
26 |
|
|
|
|
1 |
Y2.25Yb0.75Al5O12 |
|
1.3 |
|
|
|
3 |
Y2O3 |
150 |
0.7 |
|
|
|
1 |
Y2SiO5 |
|
0.54 |
|| |
a |
|
3 |
|
|
0.70 |
|| |
b |
|
3 |
|
|
0.78 |
|| |
c |
|
3 |
Y3Al5O12 |
|
1.0, 1.4 |
|
3 |
||
Y3Al5O12 |
|
|
|
|
5.34 |
2 |
Y3Fe5O12 |
|
|
|
|
6.15 |
2 |
Y3Ga5O12 |
|
|
|
|
5.73 |
2 |
α-ZnS |
69 |
|
|
|
|
1 |
β-ZnS (CVD) |
60 |
0.8 |
|
|
|
1 |
ZnSe |
55 |
0.32 |
|
|
|
1 |
ZnSe (CVD) |
52 |
≈ 1 |
|
|
|
|
ZnTe |
24 |
|
|
|
|
1 |
ZrO2: 12%Y2O3 |
200 |
2.0 |
|
|
|
1 |
|
|
|
|
|
|
|
References:
1.Tropf, W. J., Thomas, M. F., and Harris, T. J., Properties of crystals and glasses, Handbook of Optics, Vol. II 2 (McGraw–Hill, New York, 1995), p. 33.48.
2.DeShazer, L. G., Rand, S. C., and Wechsler, B. A., Laser crystals, Handbook of Laser Science and Technology,Vol. IV: Optical Materials, Part 3 (CRC Press, Boca Raton, FL, 1987), p. 595.
3.Wechsler, B. A. and Sumida, D. S., Laser crystals, Handbook of Laser Science and Technology, Suppl. 2: Optical Materials (CRC Press, Boca Raton, FL, 1995), p. 595.
4.Berger, L. I. and Pamplin, B. R., Properties of semiconductors, CRC Handbook of Chemistry and Physics, 82nd edition, Lide, D. R., Ed. (CRC Press, Boca Raton, FL, 2001), p. 12–87.
© 2003 by CRC Press LLC