The damping of lattice vibrations in solid compounds is treated using kinetic theory analogous to damping in gases. It is based on the collision frequency of atoms, taking into consideration the atomic coordination due to the crystalline structure, the cross section of collision, the radius ratio of the component atoms (atomic size factor), as well as an anharmonic factor which is an expression for the anharmonicity of lattice vibrations. A semiempirical formulation is derived without need for constants fitted to experimental data. This formulation of damping is shown valid for more than eighty solids, mostly binary compounds, also some ternary compounds and elements. They may have either ionic or covalent or metallic binding. They cover ten different structures and valencies from one through four. In addition, a close relationship is shown between damping and thermal expansion as a function of temperatures. Based on this relationship, the temperature dependence is empirically expressed by an exponential function of the coefficient of thermal expansion. This function agrees with the variation of ir energy absorption vs temperatures. The complete damping formulation is shown valid for the entire temperature range of solids, from absolute zero to the melting point, for a variety of solids for which all pertinent data were on hand.
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Here ν0, in general, means νTO, except for ZnS, ZnSe, ZnTe, and CdS, where it stands for νLO.
Pertinent literature supporting the experimental data of Δν/ν0 may be found in Refs. 3 and 4.
Characteristic parameter CN/Cstr = 4/π = 1.27.
Reference 9.
Table IV
Damping Data for TO and LO Modes for Selected Dielectrics
TO Mode
LO Mode
Substance
ν0 (cm−1)
Δν/ν0
ν0 (cm−1)
Δν/ν0
Spectrum
NaCl
166.5
0.14
245
0.15
ir energy absorption
LiF
306
0.23
525
0.17
ir energy absorption
NaI
122
0.19
170
0.20
cold neutron scattering
Table V
Damping Data for the Mean T Mode of Five Metallic Elements, as Experimentally Determined from Cold Neutron Spectra3,4 and Calculated for Metallic Binding in Elements
Here ν0, in general, means νTO, except for ZnS, ZnSe, ZnTe, and CdS, where it stands for νLO.
Pertinent literature supporting the experimental data of Δν/ν0 may be found in Refs. 3 and 4.
Characteristic parameter CN/Cstr = 4/π = 1.27.
Reference 9.
Table IV
Damping Data for TO and LO Modes for Selected Dielectrics
TO Mode
LO Mode
Substance
ν0 (cm−1)
Δν/ν0
ν0 (cm−1)
Δν/ν0
Spectrum
NaCl
166.5
0.14
245
0.15
ir energy absorption
LiF
306
0.23
525
0.17
ir energy absorption
NaI
122
0.19
170
0.20
cold neutron scattering
Table V
Damping Data for the Mean T Mode of Five Metallic Elements, as Experimentally Determined from Cold Neutron Spectra3,4 and Calculated for Metallic Binding in Elements
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