Friction as energy dissipation process associated with superlubricity of solids

Bo ZHANG

doi:10.1007/s40544-024-0875-6

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Research Article | Open Access

Friction as energy dissipation process associated with superlubricity of solids

Bo ZHANG()

Saga University, Saga-shi 840-8502, Japan

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Abstract

The paper shows that work in a quantum system is quantized with energy; the quantum work is equivalent to the highest eigenenergy (the Debye energy) of the system and the superlubricity of solids is derived from the quantum work. The prerequisite for the superlubricity is that the lateral force at contact surfaces in sliding is less than the Debye force so that the phonon of the solids is not excited.

Keywords

superlubricity phonon friction Plank law Debye frequency

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Friction

Volume 12 Issue 9,
September 2024

Pages 2083-2088

DOI: 10.1007/s40544-024-0875-6

Cite this article:

ZHANG B. Friction as energy dissipation process associated with superlubricity of solids. Friction, 2024, 12(9): 2083-2088. https://doi.org/10.1007/s40544-024-0875-6

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Table 1Infimum tangential stresses from the stiffness of cubic crystals.

Crystal	Stiffness at 300 K [8] (10¹² dyn/cm²)			$ρ$ (g/cm³)	a (Å)	$ω_{mx}$ (10¹⁴ rad/s)	$τ_{in}$ (10⁹ dyn/cm²)
Crystal	$k_{11}$	$k_{12}$	$k_{44}$	$ρ$ (g/cm³)	a (Å)	$ω_{mx}$ (10¹⁴ rad/s)	$τ_{in}$ (10⁹ dyn/cm²)
W	5.233	2.045	1.607	19.317	3.16	0.5181	1.7320
Cu	1.684	1.214	0.754	9.018	3.61	0.4301	0.9641
Ni	2.508	1.500	1.235	8.968	3.52	0.5364	1.2970
Diamond	10.760	1.250	5.760	3.516	3.57	1.6111	3.7440
Ge	1.285	0.483	0.680	5.320	5.66	0.3011	0.1753
Si	1.660	0.639	0.796	2.330	5.43	0.5287	0.3483

Table 2Debye stresses of solids.

Solid	$θ_{D}$ (K) [8]	$ω_{D}$ (10¹⁴ rad/s)	$τ_{D}$ (10⁹ dyn/cm²)	H_V (10⁹ dyn/cm²) [9]
W	400	0.5237	1.750	34.3
Cu	343	0.4490	1.007	3.69
Ni	450	0.5891	1.424	6.38
Diamond	2230	2.9194	6.784	>130
Graphite [10]	1560	2.0423	15.580 (a = 2.4 Å)	—
Ge	374	0.4896	0.285	—
Si	645	0.8444	0.556	—

Table 3Debye stresses of compounds.

Material	$θ_{D}$ (K)	a (Å)	$ω_{D}$ (10¹⁴ rad/s)	$τ_{D}$ (10⁹ dyn/cm²)	Ref.
Si₃N₄	955	2.91	1.2502	5.351	[11]
AlN	940	3.11	1.2306	4.314	[11]
AlN	971	3.11	1.2712	4.457	[12]
cBN	1620	3.60	2.1208	4.794	[10]
SiC	1195	4.30	1.5644	2.075	[13]
MoS₂	600	3.10	0.7855	2.781	[14]

Table 4Debye temperatures of surface and bulk [15].

Material	Surface $θ_{D}$ (K)	Bulk $θ_{D}$ (K)
Si	340	645
Ge (001)	215	290
Al (001)	189	370
Ag (111)	155	225
Cu (001)	210	322