Si - Silicon

Mechanical properties, elastic constants, lattice vibrations

Basic Parameter
Elastic constants
Acoustic Wave Speeds
Phonon frequencies

Basic Parameter

Bulk moduluss 9.8·1011 dyn/cm2
Density 2.329 g/cm3
Hardness 7 on the Mohs scale
Surface microhardness (using Knoop's pyramid test) 1150 kg/mm2
Cleavage plane { 111 }

Elastic constants

C11 = 16.60·1011 dyn/cm2
C12 = 6.40·1011 dyn/cm2
C44 = 7.96·1011 dyn/cm2
Temperature dependences of elastic constants.
Dashed lines - (Mc. Skimin [1953]).
Circles - (Nikanorov et al. [1971]).

For 400 K < T < 873 K (in units of 1011 dyn/cm2)

C11 ≈16.38 - 1.28·10-3T;
C12 ≈5.92 - 0.48·10-3T
C44 ≈8.17 - 0.59·10-3T

For 300 K

Bulk modulus (compressibility-1) Bs = 9.8·1011 dyn/cm2
Shear modulus C' = 5.2·1011 dyn/cm2
[111] Young's modulus Y111 = 18.5·1011 dyn/cm2
[110] Young's modulus Y110 = 17.0·1011 dyn/cm2
[100] Young's modulus Y100 = 13.0·1011 dyn/cm2
[100] Poisson ratio σ100 = 0.28
[111] Poisson ratio σ111 = 0.26

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 8.43
VT (C44/ρ)1/2 5.84
[100] Vl [(C11+Cl2+2C44)/2ρ]1/2 9.13
Vt|| Vt||=VT=(C44/ρ)1/2 5.84
Vt⊥ [(C11-C12)/2ρ]1/2 4.67
[111] Vl' [(C11+2C12+4C44)/3ρ]1/2 9.36
Vt' [(C11-C12+C44)/3ρ]1/2 5.10

Phonon frequencies (in units of 1012 Hz)

νLTO(Γ25') 15.5 νTA (l3) 3.45
νTA(X3) 4.5 νLA(L2') 11.3
νLAO(X1) 12.3 νLO(L1) 12.6
νTO(X4 ) 13.9 νTO(L3') 14.7