New Semiconductor Materials. Biology systems.
Characteristics and Properties

NSM Archive - Silicon Carbide (SiC) - Mechanical Properties, Elastic Constants, Lattice Vibrations

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       σ_o=C₁₂/(C₁₁+C₁₂) σ_o = 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 Velosity	1.26 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)

 

Statistics