NSM Archive - Diamond (C) - Mechanical properties, elastic constants, lattice vibrations

C - Diamond

Mechanical Properties, Elastic Constants, Lattice Vibrations

Basic Parameters
Elastic Constants
Acoustic Wave Speeds
Phonon Frequencies

Basic Parameters

Density 3.515 g cm-3
Bulk modulus 44.2·1011 dyn cm-2
Hardness on the Mohs scale 10
Surface microhardness (using Knoop's pyramid test) (8 ÷ 10)·103 kg mm-2
Cleavage plane {111}

Elastic constants

at 300 K (McSkimin and Andreatch, Jr. [1972]). C11= 107.9·1011 dyn cm-2
C12= 12.4·1011 dyn cm-2
C44= 57.8·1011 dyn cm-2 
Ratio of modulus at temperature T to modulus at 25°C
(McSkimin and Andreatch, Jr. [1972]).


Bulk modulus (compressibility-1) For T = 300 K
Bs=(C11+2C12)/3 Bs = 44.2·1011 dyn cm-2
Shear modulus  
C'=(C11-C12)/2 C' = 47.8·1011 dyn cm-2
[100] Young's modulus  
Yo=(C11+2C12)·(C11-C12)/(C11+C12) Yo= 105·1011 dyn cm-2
[100] Poisson ratio  
σo=C12/(C11+C12) σo = 0.1

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 17.52
VT (C44/ρ )1/2 12.82
[110] Vl [(C11+Cl2+2C44)/2ρ ]1/2 18.32
Vt|| Vt||=VT= (C44/ρ )1/2 12.82
Vt⊥ [(C11-C12)/2ρ ]1/2 11.66
[111] Vl' [(C11+2C12+4C44)/3ρ ]1/2 18.58
Vt' [(C11-C12+C44)/3ρ ]1/2 12.06

Phonon frequencies (in units of 1012 Hz)

(Solin and Ramdas [1970]).
vLTO(Γ25') 39.9 vLA (L1) 30.2
vLAO(X1) 35.5 vLO (L2') 37.6
vTA (X3) 24.2 vTO(L3') 36.2
vTO(X4) 32.1 vTA(L3) 16.9