## Mechanical properties, elastic constants, lattice vibrations

Basic Parameter
Elastic constants
Acoustic Wave Speeds
Phonon frequencies

### Basic Parameter

 Bulk modulus (7.1+1.7x)·1011 dyn/cm2 Density 4.81-0.67x g/cm3 Hardness ~5 on the Mohs scale Surface microhardness (using Knoop's pyramid test) x=0   460 kg/mm2 x=1   850 kg/mm2 Piezoelectric constant e14= -(0.035+0.065x) C m-2

### Elastic constants

C11 = (10.11 + 3.94x)·1011 dyn/cm2
C12 = (5.61 + 0.59)·1011 dyn/cm2
C44 = (4.56 + 2.47)·1011 dyn/cm2
 Bulk modulus (compressibility-1) Bs = (7.11+1.71x)·1011 dyn/cm2 Shear modulus C' = (2.25+1.67x)·1011 dyn/cm2 [100] Young's modulus Yo= (6.11+4.19x)·1011 dyn/cm2 [100] Poisson ratio σo = 0.36-0.05x

### Acoustic Wave Speeds

 Wave propagation Direction Wave character Expression for wave speed Wave speed (in units of 105 cm/s) [100] VL (C11/ρ)1/2 4.58+1.25x VT (C44/ρ)1/2 3.08+1.04x [100] Vl [(C11+Cl2+2C44)/2ρ]1/2 5.08+1.35x Vt|| Vt||=VT=(C44/ρ)1/2 3.08+1.04x Vt⊥ [(C11-C12)/2ρ]1/2 2.16+0.92x [111] Vl' [(C11+2C12+4C44)/3ρ]1/2 5.23+1.40x Vt' [(C11-C12+C44)/3ρ]1/2 2.51+0.95x

 Compositional dependences of longitudinal (dashed lines) and transverse (solid lines) phonon frequencies (Jahne and Ulrici [1980]).

### Phonon frequencies

 ωLO(GaP - like) 404.99-38.97x-18.18x2 cm-1 ωLO(InP - like) 394.59-80.36x+30.26x2 cm-1 ωTO(M) 368-88.95x+26.04x2 cm-1 ωTO(m) 3.95.02-54.26x+6.72x2 cm-1
(Lee et al. [1994])