Study of EXAFS cumulants of crystals by the statistical moment method and anharmonic correlated Einstein model

Thermodynamic Properties and Anharmonic Effects in XAFS Based on Anharmonic Correlated Debye Model Debye–Waller Factors

“…[13,22,23,25] for Cu and [23] for Ni, as well as with those calculated using the ACEM [9]. Here, the present result is also compared to those calculated using the SMM [16], FCM [20], and LDA [21] for Cu and PIEP [18] for Ni, which are found to be in reasonable agreement with the experiment. Figure 5 shows good agreement of temperature dependence of third cumulant σ (3) (T) of Cu and Ni calculated using the present theory with the experimental values Expt.…”

“…But, the rst cumulant describing the net thermal expansion or lattice disorder and the third cumulant or MCRD describing the asymmetry of pair atomic distribution function are entirely anharmonic e ects. ese obtained quantities are evidently temperature-dependent where the rst and second cumulants are proportional to the temperature T and the [13,22,23,25] for Cu and [23] for Ni, as well as to those calculated using the ACEM [9], SMM [16], FCM [20], and LDA [21] for Cu and PIEP [18] for Ni. Expt.…”

“…Its simplicity and efficiency in XAFS studies is demonstrated by calculating and analyzing XAFS cumulants of fcc [9][10][11][12][13], hcp [14], and crystals and in studying pressure-dependent XAFS [15]. e statistical moment method [16,17] has been applied to calculate the mean square relative displacement (MSRD) including anharmonic contributions of some crystals. e derived pathintegral effective potential (PIEP) method [18] has the advantage for calculating XAFS DWFs presented in terms of cumulant expansion up to the fourth order based on quantum theory including three dimension, correlation, anharmonicity, and many-body effects.…”

“…is theory can be applied to any crystal structure including complex systems. Numerical results for Cu and Ni presented in Section 3 are compared to a large number of experimental data [13,[19][20][21][22][23][24][25][26] and to those calculated using several well-known methods such as ACEM [9], SMM [16], PIEP [18], PIMC [19], FCM [20], and LDA [21] at lowand high temperatures to show the advantage of the present theory. e conclusions on the obtained results are presented in Section 4 of the paper.…”

Study of Thermodynamic Properties of Zinc-Blende-Type Semiconductors: Temperature and Pressure Dependences

“…The lattice constant a h of the zinc-blende type semiconductor can be calculated easily by using the relation a h = r 1 (T )4/ √ 3. In the SMM method, [8][9][10][11][12] we have the relation between the first and second-order moment as…”