SiC - Silicon Carbide

Mechanical Properties, Elastic Constants, Lattice Vibrations

Basic Parameters
Elastic Constants
Acoustic Wave Speeds
Phonon Frequencies
Frequencies and Symmetries of the Strongest Modes

Basic Parameters

      Remarks Referens
Density 3C-SiC 3.166 g cm-3 293 K Kern et al. (1969)
  3.21 g cm-3 300 K Harris et al.(1995b)
  4H-SiC 3.211 g cm-3 300 K Gomes de Mesquita (1967)
  6H-SiC 3.21 g cm-3 300 K Harris et al.(1995b)
 
Hardness 3C-SiC,
4H-SiC
6H-SiC		 9.2-9.3 on the Mohs scale Goldberg et al.(2001)
 
Surface microhardness 3C-SiC,
4H-SiC
6H-SiC		 2900-3100 kg mm-2 300 K, using Knoop's pyramid test
see also Temperature dependence		 Kern et al. (1969), Shaffer (1965)
3C-SiC. Surface microhardness at elevated temperatures vs. temperature.
Using Knoop's pyramid test
Siegle et al. (1997),

Elastic constants at 300 K.

3C-SiC. Elastic constants at 300 K.
C11 290 GPa Gmelins Handbuch (1959)
3.523 10-12 dyn cm-2 Kunc et al. (1975)
C12 235 GPa Gmelins Handbuch (1959)
1.404 10-12 dyn cm-2 Kunc et al. (1975)
C44 55 GPa Gmelins Handbuch (1959)
2.329 10-12 dyn cm-2 Kunc et al. (1975)
4H-SiC & 6H-SiC elastic constants are the same whithin experimental uncertainties (Kamitani et al.(1997))
4H-SiC. 6H-SiC. Elastic constants at 300 K.
C11 501 GPa Kamitani et al.(1997)
5.00(20) 10-12 dyn cm-2 Arlt & Schodder (1965)
C12 111 GPa Kamitani et al.(1997)
0.92(28) 10-12 dyn cm-2 Arlt & Schodder (1965)
C13 52 GPa Kamitani et al.(1997)
see also Frantsevich et al.(1982)
C33 553 GPa Kamitani et al.(1997)
5.64(2) 10-12 dyn cm-2 Arlt & Schodder (1965)
C44 163 GPa Kamitani et al.(1997)
1.68(2) 10-12 dyn cm-2 Arlt & Schodder (1965)

3C-SiC Bulk modulus (compressibility-1) For T = 300 K  
  Bs=(C11+2C12)/3 Bs = 250 GPa Gmelins Handbuch (1959)
  Anisotropy factor    
  C'=(C11-C12)/2C44 A = 0.5 Gmelins Handbuch (1959)
  Shear modulus    
  C'=(C11-C12)/2 C' = 27.5 GPa Gmelins Handbuch (1959)
C' = 160 GPa Tairov & Tsvetkov (1995c)
  [100] Young's modulus    
  Y0=(C11+2C12)·(C11-C12)/(C11+C12) Y0 = 748 GPa Gmelins Handbuch (1959)
Y0 = 392-694 GPa Harris et al.(1995c)
Y0=(C11+2C12)·(C11-C12)/(C11+C12) Y0 = 748 GPa (Gmelins Handbuch (1959))
Y0 = 392-694 GPa (Harris et al.(1995c)		 Y0 = 748 GPa (Gmelins Handbuch (1959))
Y0 = 392-694 GPa (Harris et al.(1995c)
  [100] Poisson ratio       σo=C12/(C11+C12) σo = 0.45 Gmelins Handbuch (1959)
4H-SiC
6H-SiC 		Bulk modulus (compressibility-1) For T = 300 K  
  Bs=[C33(C11+C12)-2(C13)2]/(C11+C12-4C13+2C33 ) Bs = 220 GPa Kamitani et al. (1997); Kamitani et al. (1997)
    Bs = 97 GP Shaffer (1964)
Y0=(C11+2C12)·(C11-C12)/(C11+C12) Y0 = 748 GPa (Gmelins Handbuch (1959))
Y0 = 392-694 GPa (Harris et al.(1995c)		 Y0 = 748 GPa (Gmelins Handbuch (1959))
Y0 = 392-694 GPa (Harris et al.(1995c)

Acoustic Wave Speeds

3C-SiC
 Wave propagation direction Wave character Expression for wave speed Wave speed
  [100] VL (longitudinal) (C11/ρ )1/2 9.5 x 105 cm/s
VT (transverse) (C44/ρ )1/2 4.1 x 105 cm/s
  [110] Vl [(C11+Cl2+2C44)/2ρ ]1/2 9.95 x 105 cm/s
Vt|| Vt||=VT= (C44/ρ)1/2 4.1 x 105 cm/s
Vt⊥ [(C11-C12)/2ρ]1/2 2.9 x 105 cm/s
  [111] Vl' [(C11+2C12+4C44)/3ρ ]1/2 10.1 x 105 cm/s
Vt' [(C11-C12+C44)/3ρ ]1/2 3.4 x 105 cm/s
The cristalografic direction you can see part Band structure
      Remarks Referens
3C-SiC (polycrystal) Acoustic Velosity1.26 x 106 cm/s experimental result Chinone et al. (1989)
4H-SiC.
6H-SiC
 Wave propagation
 direction 		Wave character Expression for wave speed Wave speed
  [100] VL (longitudinal) (C11/ρ )1/2 12.5 x 105 cm/s
VT (transverse)
polarization along [001]		 (C44/ρ )1/2 7.1 x 105 cm/s
Vt(transverse)
polarization along [010]		 [(C11-C12)/2ρ]1/2 7.8 x 105 cm/s
  [001] VL (longitudinal) (C33/ρ )1/2 13.1 x 105 cm/s
VT (transverse) (C44/ρ )1/2 7.1 x 105 cm/s
Also see R. Truelet al. (1969)
The cristalografic direction you can see part Band structure.

Phonon frequencies

phonon wavenumbers:     Remarks Referens
3C-SiC   νTO(Γ) 796.2(3) cm-1     T=300K,
Raman spectroscopy		 Olego et al. (1982a)
  783-796 cm-1     T=300K Karch et al. (1994), Nakashima & Tahara (1989),
Feidman et al. (1968), Olego & Cardona (1982)
  νLO(Γ) 972.2(3) cm-1   T=300K,
Raman spectroscopy		 Olego et al. (1982a)
  829 cm-1   T=300K Karch et al. (1994), Nakashima & Tahara (1989),
Feidman et al. (1968), Olego & Cardona (1982)
  νTA(L) 266 cm-1   T=300K Olego et al. (1982b),
Karch et al. (1994),
Nakashima & Tahara (1989),
Feidman et al. (1968),
Olego & Cardona (1982)
  261-266 cm-1  
  νLA(L) 610 cm-1  
  νTO(L) 765-766 cm-1      
  νLO(L) 837-838 cm-1      
  νTA(X) 366-373 cm-1      
  νLA(X) 629-640 cm-1      
  νTO(X) 755-761 cm-1      
  νLO(X) 829 cm-1      
main phonon energies:     Remarks Referens
4H-SiC   TA1   46.7 meV       Freitas (1995)
  TA2   51.4 meV
53.4 meV  		     
  LA   76.9 meV
78.8 meV  		     
  TO1   95.0 meV        
  LO   104.0 meV
104.3 meV  		     
         
6H-SiC   TA   36.3 meV     discussion of free exciton replica
in wavelength modulated absorption 		Humphreys (1981)
  TA1   46.3 meV       Humphreys (1981) , Freitas (1995)
  TA2   53.5 meV       
  LA   53.3 meV      Humphreys et al. (1981)
  77.0 meV
     Humphreys et al. (1981), Freitas (1995)
  TO1   94.7 meV       Freitas (1995)
  TO2   95.6 meV       Humphreys et al. (1981), Freitas (1995)
  LO   104.2 meV
     Humphreys et al. (1981), Freitas (1995)
  104.7 meV
     Humphreys et al. (1981)
SiC, Wurtzite. Phonon dispersion curves of TO branches.
Nakashima & Tahara (1989)
SiC, Wurtzite. Phonon dispersion curves of TA branches.
The disorder-induced Raman spectrum obtained at 7 K for N+-implanted SiC.
Nakashima & Tahara (1989)
3C-SiC. Dispersion curves for acoustic and optical branch phonons.
Karch et al. (1994)
3C-SiC. Dispersion curves for acoustic and optical branch phonons.
Karch et al. (1994)