Mechanical properties, elastic constants, lattice vibrations of Germanium (Ge)
Mechanical properties, elastic constants, lattice vibrations
Basic ParametersElastic Constants
Acoustic Wave Speeds
Phonon Frequencies
Basic Parameters
| Bulk modulus | 7.5·1011dyn cm-2 |
| Density | 5.323 g cm-3 |
| Hardness on the Mohs scale | 6 |
| Surface microhardness (using Knoop's pyramid test) | 780 kg mm-2 |
| Cleavage plane | { 001 } |
Elastic Constants at 300 K
C11 = 12.60·1011 dyn cm-2C12 = 4.40·1011 dyn cm-2
C44 = 6.77·1011 dyn cm-2
 | Temperature
dependences of elastic constants. (Kardashev and Nikanorov [1985]). |
 | Elastic
constant C44 versus temperature for pure (curve 1) and doped (curve 2. Nd=3.5·1019cm-3) samples. (Bruner and Keyes [1961]). |
| For 300 K: | |
| Bulk modulus (compressibility-1) | Bs=7.13·1011 dyn cm-2 |
| Shear modulus | C'=4.1·1011 dyn cm-2 |
| [100] Young's modulus | Yo = 10.3·1011 dyn cm-2 |
| [100] Poisson ratio | σo= 0.26 |
 |
Si, Ge. Young's modulus vs. direction in the (001) plane. Wortman & Evans (1965) |
 |
Si, Ge. Poisson ratio vs. direction in the (001) plane. Wortman & Evans (1965) |
Acoustic Wave Speeds
| Wave propagation direction | Wave Character | Expression for wave speed | Wave speed |
| [100] | VL | [C11/ρ]1/2 | 4.87 ·105 cm/s |
| VT | [C44/ρ]1/2 | 3.57 ·105 cm/s | |
| [110] | Vl | [(C11+C12+2C44)/2ρ]1/2 | 5.36 ·105 cm/s |
| Vt|| | Vt|| = VT = (C44/ρ)1/2 | 3.57 ·105 cm/s | |
| Vt ort; | [(C11-C12)/2ρ]1/2 | 2.77 ·105 cm/s | |
| [111] | Vl' | [(C11+2C12+4C44)/3ρ]1/2 | 5.51 ·105 cm/s |
| Vt' | [(C11-C12+C44)/3ρ]1/2 | 3.06 ·105 cm/s |
Phonon Frequencies (in units of 1012 Hz)
| phonon wavenumbers: | Remarks | Referens | ||
| Ge | νLTO(Γ25') | 9.02 1012 Hz | T=300K | Nillsson & Nelin (1972) |
| νTA(X3) | 2.385 1012 Hz | |||
| νLAO(X1) | 7.14 1012 Hz | |||
| νTO(X4 ) | 8.17 1012 Hz | |||
| νTA (L3) | 1.87 1012 Hz | |||
| νLA(L2') | 6.63 1012 Hz | |||
| νLO(L1) | 7.27 1012 Hz | |||
| νTO(L3') | 8.55 1012 Hz | |||
 |
Ge. Dispersion curves for acoustic and optical phonons. Weber (1977) |