NSM Archive - Gallium Nitride (GaN) - Mechanical Properties, Elastic Constants, Lattice Vibrations
Mechanical Properties, Elastic Constants, Lattice Vibrations
Basic ParametersElastic Constants
Acoustic Wave Speeds
Phonon Frequencies
Frequencies and Symmetries of the Strongest Modes
Basic Parameters
| Remarks | Referens | ||
| Density | 6.15 g cm-3 | 300 K | Bougrov et al. (2001) |
| Surface microhardness | 1200 - 1700 kg mm-2 | 300 K, using Knoop's pyramid test | Nikolaev et al. (1998) see also Drory et al. (1996) |
Elastic constants at 300 K.
Wurtzite GaN. Elastic constants at 300 K.| C11 | 390 ±15 GPa | Polian et al. (1996)
see also Wright (1997) |
| C12 | 145 ± 20 GPa | |
| C13 | 106 ± 20 GPa | |
| C33 | 398 ± 20 GPa | |
| C44 | 105 ± 10 GPa |
| C11 | 29.6(1.8) 1011 dyncm -2 | calculated from the mean square displacement of the lattice atoms measured by X-ray diffraction |
Madelung (1991) |
| C12 | 13.0(1.1) 1011 dyncm -2 | ||
| C13 | 15.8(0.6) 1011 dyncm -2 | ||
| C33 | 26.7(1.8) 1011 dyncm -2 | ||
| C44 | 2.41 (20) 1011 dyncm -2 |
| C11 | 293 GPa | Wright (1997) |
| C12 | 159GPa | |
| C44 | 155 GPa |
| Wurtzite GaN. Bulk modulus (compressibility-1) | For T = 300 K |
| Bs = [ C33(C11 + C11) - 2(C13)2] x [C11+ C12-4C13+ 2C33 ]-1 | Bs = 210 ± 10 GPa |
| Zinc Blende GaN. Bulk modulus (compressibility-1) | For T = 300 K |
| Bs=(C11+2C12)/3 | Bs = 204 GPa |
| Anisotropy factor | |
| C'=(C11-C12)/2 | A = 0.43 |
| Shear modulus | |
| C'=(C11-C12)/2 | C' = 67GPa |
| [100] Young's modulus | |
| Y0=(C11+2C12)·(C11-C12)/(C11+C12) | Y0= 181 GPa |
| [100] Poisson ratio | |
| σo=C12/(C11+C12) | σo = 0.352 |
Acoustic Wave Speeds
Zinc Blende crystal structure
| Wave propagation direction | Wave character | Expression for wave speed | Wave speed (in units of 105 cm/s) |
| [100] | VL (longitudinal) | (C11/ρ )1/2 | 6.9 |
| VT (transverse) | (C44/ρ )1/2 | 5.02 | |
| [110] | Vl | [(C11+Cl2+2C44)/2ρ ]1/2 | 7.87 |
| Vt|| | Vt||=VT= (C44/ρ)1/2 | 5.02 | |
Vt |
[(C11-C12)/2ρ]1/2 | 3.3 | |
| [111] | Vl' | [(C11+2C12+4C44)/3ρ ]1/2 | 8.17 |
| Vt' | [(C11-C12+C44)/3ρ ]1/2 | 3.96 |
Wurtzite crystal structure
| Wave propagation direction | Wave character | Expression for wave speed | Wave speed (in units of 105 cm/s) |
| [100] | VL (longitudinal) | (C11/ρ )1/2 | 7.96 |
| VT (transverse, polarization along [001]) | (C44/ρ )1/2 | 4.13 | |
| VT (transverse, polarization along [010]) | ((C11-C12)/2ρ )1/2 | 6.31 | |
| [001] | VL (longitudinal) | (C33/ρ )1/2 | 8.04 |
| VT (transverse ) | (C44/ρ )1/2 | 4.13 |
For details see Truell R. et al. (1969)
Phonon frequencies
Wurtzite crystal structure
| A1 - LO | 710-735 cm-1 | Siegle et al. (1997);
Akasaki & Amano (1994); Karch et al. (1998); Zi et al. (1996) |
| A1 - TO | 533-534 cm-1 | |
| E1 - LO | 741-742 cm-1 | |
| E1 - TO | 556-559 cm-1 | |
| E2 (low) | 143-146 cm-1 | |
| E2 (high) | 560-579 cm-1 |
| phonon wavenumbers: |
Remarks | Referens | |
| νA1(TO||) | 533 cm-1 | T=300K; Raman spectroscopy | Manchon et al.(1970) |
| νE1(TO)
|
559 cm-1 | T=300K; Raman spectroscopy | Lemos et al.(1972) |
| νE1(LO)
|
746 cm-1 | T=300K; Kramers-Kronig analysis of infrared reflectivity |
Barker & Ilegems (1973) |
| νA1(LO) | 744 cm-1 | T=300K; Kramers-Kronig analysis of infrared reflectivity |
Barker & Ilegems (1973) |
 |
GaN, Wurtzite. Calculated dispersion curves for acoustic and
optical branch phonons. Siegle et al. (1997), |
Zinc Blende crystal structure
| LO (G) | 748 cm-1 | LO (L) | 675 cm-1 | Zi et al. (1996) | |
| TO (G) | 562 cm-1 | TO (L) | 554 cm-1 | ||
| LO (X) | 639 cm-1 | LA (L) | 296 cm-1 | ||
| TO (X) | 558 cm-1 | TA (L) | 144 cm-1 | ||
| LA (X) | 286 cm-1 | ||||
| TA (X) | 207 cm-1 |
 |
GaN, Zinc Blende (cubic). Calculated dispersion curves for
acoustic and optical branch phonons. Zi et al. (1996), |
Frequencies and Symmetries of the Strongest Modes
Frequencies and Symmetries of the Strongest Modes Found in the Second-Order Raman Spectra of Hexagonal GaN and Their Assignments [Siegle et al. (1997)].| Frequency (cm-1) |
Symmetry | Process | Point in the BZ |
| 317 cm-1 | A1 | Acoustic, overtone | H |
| 410 cm-1 | A1 | Acoustic, overtone | A,K |
| 420 cm-1 | A1, E2 | Acoustic, overtone | M |
| 533 cm-1 | A1 | First-order process | Γ = A1(TO) |
| 560 cm-1 | E1 | First-order process | Γ = E1(TO) |
| 569 cm-1 | E2 | First-order process | Γ = E2(high) |
| 640 cm-1 | A1 | Overtone | Γ = [B]2, L |
| 735 cm-1 | A1 | First-order process | Γ = A1(LO) |
| 742 cm-1 | E1 | First-order process | Γ = E1(LO) |
| 855 cm-1 | A1, E1, E2 | Acoustic-optical combination | |
| 915 cm-1 | A1 | Acoustic-optical combination | |
| 1000 cm-1 | A1, (E2) | Acoustic-optical combination | |
| 1150 cm-1 | A1 | Optical overtone | |
| 1280 cm-1 | A1, (E1) | Optical combination | |
| 1289 cm-1 | E2 | Optical combination | |
| 1313 cm-1 | A1, (E1, E2) | Optical combination | |
| 1385 cm-1 | A1 | Optical overtone | A,K |
| 1465 cm-1 | A1 | Optical overtone | Γ =A1(LO)2 |
| Cutoff 1495 cm-1 | A1 , E2 | Optical overtone | Γ = E1(LO)2 |