How to estimate isotropic distributions and mean values in crystalline solids

Abstract

Abstract:The concept of special directions in the Brillouin zone and the applicability of Houston's formula (or its extended versions) to both theoretical and experimental investigations are discussed. We propose some expressions to describe the isotropic component in systems having both cubic and non-cubic symmetry.This results presented have implications for both experimentalists who want to obtain average properties from a small number of measurements on single crystals, and for theoretical calculations which are to be compared with isotropic experimental measurements, for example coming from investigations of polycrystalline or powder samples.

Comment on “Magnetic Compton scattering study of Laves phase ZrFe2 and Sc doped ZrFe2: Experiment and Green function based relativistic calculations” by Bhatt et al.

“…In order to compare the results of these experiments with the predictions of ab initio density-functional theory calculations, it is essential that an isotropic momentum distribution can be computed. Recently, we described how isotropic distributions (and mean values) can be calculated using so-called "special directions" (SDs) [7]. The purpose of this comment is to show how the method should be correctly applied, using as an example the recent study by Bhatt et al [1].…”

“…Meanwhile, the isotropic distribution can be estimated much more precisely by using SDs, as proposed by Bansil [9]. We have set out this in great detail in a recent paper [7] in which we looked at cubic, hexagonal, tetragonal and trigonal structures, showing that HSDs are very inconvenient. The power of using SDs is beautifully illustrated in a paper by Prasad and Bansil [10], in which several sets (28, 36, 45, 55, and 66) of special directions for cubic lattices were proposed and discussed showing their accuracy in density-of-states and Fermi-energy evaluations in disordered alloys.…”

“…For the current calculations, we choose N -SDs (with N = 6, 10 [11] and N = 15 [12]) to check the correctness of calculating an isotropic magnetic Compton profile (J 0 (p)) for ZrFe 2 depending on the number of SDs. Such directions were also considered in our previous paper [7]. We also perform calculations for In the case of the six directions applied in Ref.…”

“…2(c)), which define the deviation of the approximated J 0 (p) from its true value (for more details, see Ref. [7]). As seen, such an effect is not unexpected.…”

“…As we emphasised in Ref. [7], the impact of experimental resolution needs to be carefully considered.…”