Effect of lattice strain on the Debye-Waller factors of Mg, Zn and Cd

Abstract

Lattice strains in Mg, Zn and Cd powders produced by grinding have been analyzed by X-ray powder diffraction. The lattice strain (e) and Debye-Waller factor (B) are determined from the half-widths and integrated intensities of the Bragg reflections. In all three cases viz. Mg, Zn and Cd, the Debye-Waller factor is found to increase with the lattice strain. From the correlation between the strain and effective Debye-Waller factor, the Debye-Waller factors for zero strain have been estimated for Mg, Zn and Cd. The variation of energy of vacancy formation as a function of lattice strain has been studied.The Debye-Waller factor is an important lattice dynamical property. Although there is considerable X-ray work on the Debye-Waller factors of Mg, Zn and Cd [1][2][3][4]. It is interesting to study the effect of lattice strains on the Debye-Waller factors of these metals. Inagaki et al [5,6] showed that in several non-metallic powders, the strains produced during grinding have a significant effect on the Debye-Waller factors measured from X-ray diffraction intensities. Sirdeshmukh et al [7] observed the effect of lattice strains on the Debye-Waller factors in semiconductor powder materials. Gopi Krishna and Sirdeshmukh [8] studied the effect of lattice strains on the Debye-Waller factor of ytterbium metal. In the present investigation the results of a systematic study of the effect of lattice strains on the Debye-Waller factors of hexagonal Mg, Zn and Cd metals are reported.The powder samples were obtained by gently filing highly pure Mg, Zn and Cd Note

Debye–Waller coefficient of heavily deformed nanocrystalline iron

“…Quite differently, the literature data for B iso appear overestimated (Zhao et al, 2001;Azzaza et al, 2015), probably because of experimental or modelling errors. XRD measurements of B iso require a strict control of all factors -primarily absorptionaffecting the diffracted intensity; moreover, as pointed out by Vetelino et al (1972), accounting for the TDS in XRPD data modelling is important, and failing to do so could be a further reason for the quite high B iso values reported in the literature (Lu & Zhao, 1999;Zhao et al, 2001;Azzaza et al, 2015;Sirdeshmukh et al, 1993;Purushotham & Krishna, 2010).…”

“…The interpretation of such large increases in B is not always clear. Even if the role of surfaces and grain boundaries is well established (Van Hove et al, 1986), large B values in ball-milled nanocrystalline materials have frequently been ascribed to some local strain (microstrain), a measure of which is obtained from diffraction line broadening (Azzaza et al, 2015;Zhao, 2001;Sirdeshmukh et al, 1993;Purushotham & Krishna, 2010), with no further justification or proof of a real cause-effect linkage.…”