Site Occupation Reversal in the C14 Laves Phase Nb(Cr_1–xCo_x)₂

Abstract

The C14 phase Nb(Cr 1Ϫx Co x ) 2 forms within a broad homogeneity range of 0.127(3) Յ x Յ 0.937(8) at 1100°C. The distribution of chromium and cobalt atoms on the crystallographic positions 2a and 6h has been studied by single crystal structure analysis and a statistical mechanics approach using energies from 637 first-principles full potential electronic structure calculations. For the first time a preferential occupation of the minority component on the 2a site has been observed. The calculations support a preferential site occupation with a reversal close to equal chromium and cobalt content.

Laves phases: a review of their functional and structural applications and an improved fundamental understanding of stability and properties

“…1 and Table 1), which allow for preferential site substitution on the B or on the A sites, stabilize the C14/C36 polytypes with respect to the original C15 polytype. Energies from first-principles calculations confirm this stabilization for C14 with respect to C15 [183,184]. Assuming that only the simplest polytype is formed, which is necessary to allow for some energetically favorable preferred site occupation, explains why in case of mixed occupation of the B sites the C14 polytype develops whereas for mixed occupation of the A sites the more complicated C36 polytype forms.…”

“…Several of such systems were explored more recently in some detail, as Al-Cr-Nb [93,95] and Al-Co-Nb [182]. In systems ranging from C15 Laves phase to C15 Laves phase such as NbCr 2 -NbCo 2 [155,183,184] and ZrV 2 -ZrCo 2 [184], C14 Laves phase occurs at intermediate compositions with enrichment of the respective minority element on the 2a site; see Fig. 10.…”

“…10. 2 Energetics of such preferred site occupation was also supplemented by firstprinciples calculations [183]. In contrast to the effects upon alloying binary C15 Laves phases with a third element, alloying of binary C14 binary Laves phases (e.g., C14 TiFe 2 with Si) does not lead to a change of the polytype.…”

“…Beyond the above-mentioned investigations dealing experimentally and theoretically with polytypism, there are further first-principles-based calculations demonstrating the power of these methods to reveal the thermodynamics of polytypism of the Laves phases. For example, the relative stability of polytypes of stoichiometric binary Laves phases at T = 0 K can reliably be predicted for HfV 2 [202], [183,184] as determined on the basis of single-crystal-based X-ray diffraction data, revealing preferred occupation of the 2a sites by the minority B element being accompanied with an inversion of the occupancies at x & 0.5 (adapted with permission from [184]).…”

The Influence of the Valence Electron Concentration on the Structural Variation of the Laves Phases MgNi2–xGex

“…A comparably preferential site occupation, in which the third element primarily fills the positions of the 3 6 nets, is also observed for example in TiFe 2-x Al x [36] and in NbCr 2-x Co x . [37] In case of the title compound MgNi 1.3 Ge 0.7 , the question needs to be raised, whether another synthesis strategy might lead to a more pronounced ordering on the different positions. In Figure 5 the group-subgroup relationship between MgZn 2 and hP36-MgNi 1.3 Ge 0.7 is discussed: Starting from the MgZn 2 structure type, a klassengleiche transition of index 3 (k3) leads to the structure of MgNi 1.3 Ge 0.7 with space group P6 3 /mcm.…”