Thermal behavior of the Debye-Waller factor and the specific heat of anharmonic crystals

1980 ◽  
Vol 21 (2) ◽  
pp. 458-466 ◽  
Author(s):  
Raimundo Alexandre Tavares Lima ◽  
Constantino Tsallis
Keyword(s):  
Thermal Behavior ◽  
Specific Heat ◽  
Waller Factor ◽  
Debye Waller Factor ◽  
Anharmonic Crystals

COMPUTATION OF THE NORMAL AND ANOMALOUS TERMS IN THE LOWEST ORDER ANHARMONIC CONTRIBUTIONS TO THE DEBYE-WALLER FACTOR FOR SODIUM METAL

1994 ◽  
Vol 05 (02) ◽  
pp. 303-309
Author(s):  
Sajalendu Dey
Keyword(s):  
Wave Vector ◽  
Waller Factor ◽  
Sodium Metal ◽  
Debye Waller Factor ◽  
Scattering Wave ◽  
Anharmonic Crystals

It has been shown by Maradudin and Flinn1 (1963) that, in weak anharmonic crystals, the lowest order anharmonic contributions to the Debye-Waller factor are of 0(λ2), where λ is the Van Hove2 (1961) ordering parameter. There are four such terms, two of them are of [Formula: see text] (where [Formula: see text] is the scattering wave-vector) and are known as the normal terms. Other two terms are of [Formula: see text] and are known as the anomalous terms. These four terms are of significant complexity. In this present work, a computation of these four terms will be reported for sodium metal and the results will be compared with experimentally determined values.

Lattice Dynamical Properties of Nickel

1973 ◽  
Vol 51 (17) ◽  
pp. 1869-1873 ◽  
Author(s):  
Satya Pal
Keyword(s):  
Experimental Data ◽  
Specific Heat ◽  
Frequency Spectrum ◽  
Reasonable Agreement ◽  
Sampling Technique ◽  
Waller Factor ◽  
Characteristic Temperatures ◽  
Debye Waller Factor ◽  
Root Sampling ◽  
Theoretical Results

The frequency spectrum of nickel has been calculated on the basis of the lattice dynamical model of Sharma and Joshi. The frequency spectrum has been computed with the help of Blackman's root sampling technique for a discrete subdivision in the reciprocal space. The computed frequency distribution has been employed for the calculation of the specific heat and the temperature variation of the Debye–Waller factor of nickel. The theoretically computed values of specific heat are compared with the experimental data in terms of the Debye characteristic temperatures. The theoretical results are in reasonable agreement with the experimental data.

The effect of temperature on high-resolution TEM image contrast

1995 ◽  
Vol 53 ◽  
pp. 640-641
Author(s):  
T. Geipel ◽  
W. Mader ◽  
P. Pirouz
Keyword(s):  
Form Factor ◽  
Inelastic Scattering ◽  
Accurate Method ◽  
Waller Factor ◽  
Effect Of Temperature ◽  
Specimen Thickness ◽  
Influence Of Temperature ◽  
Debye Waller Factor ◽  
Influence Of Temperature On ◽  
Atomic Form Factor

Temperature affects both elastic and inelastic scattering of electrons in a crystal. The Debye-Waller factor, B, describes the influence of temperature on the elastic scattering of electrons, whereas the imaginary part of the (complex) atomic form factor, fc = fr + ifi, describes the influence of temperature on the inelastic scattering of electrons (i.e. absorption). In HRTEM simulations, two possible ways to include absorption are: (i) an approximate method in which absorption is described by a phenomenological constant, μ, i.e. fi; - μfr, with the real part of the atomic form factor, fr, obtained from Hartree-Fock calculations, (ii) a more accurate method in which the absorptive components, fi of the atomic form factor are explicitly calculated. In this contribution, the inclusion of both the Debye-Waller factor and absorption on HRTEM images of a (Oll)-oriented GaAs crystal are presented (using the EMS software.Fig. 1 shows the the amplitudes and phases of the dominant 111 beams as a function of the specimen thickness, t, for the cases when μ = 0 (i.e. no absorption, solid line) and μ = 0.1 (with absorption, dashed line).

Anharmonic contributions to the Debye-Waller factor of aluminium

1989 ◽  
Vol 72 (11) ◽  
pp. 1135-1140 ◽  
Author(s):  
R.C. Shukla ◽  
H. Hübschle
Keyword(s):  
Waller Factor ◽  
Debye Waller Factor

On the Debye-Waller factor in atom-surface scattering

1982 ◽  
Vol 45 (2) ◽  
pp. 287-298 ◽  
Author(s):  
N. Garcia ◽  
A. A. Maradudin ◽  
V. Celli
Keyword(s):  
Waller Factor ◽  
Surface Scattering ◽  
Debye Waller Factor
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