Vibrational entropy of disorder in Cu3Au with different degrees of short-range order.

A Benisek,E Dachs,M Grodzicki

doi:10.1039/c8cp01656a

Abstract

L12 ordered Cu3Au and fcc-disordered samples with different degrees of short-range order were synthesised by annealing and/or quenching experiments. Low-temperature heat capacities were determined by relaxation calorimetry. From these data the vibrational entropy of disorder was derived. The calorimetric results show that the vibrational entropy does not depend on the degree of short-range order. The calorimetric investigations were complemented by density functional calculations with different functionals simulating various atomic configurations by super cells of different size. Using super cells containing 32 atoms, the computed entropies show only small variations with the change of short-range order in good agreement with the calorimetric results. Using, however, super cells with only 8 atoms, the results depend strongly on the chosen atomic configuration at variance with the calorimetric data. This result is important for investigating substances with larger molecules (e.g., silicate solid solutions) because such investigations are typically limited on super cells containing only a few sites on which substitution takes place.

Highlights

The atomic distribution of Au and Cu in Cu3Au changes as a function of temperature
Of a single thermodynamically averaged crystallographic site. These results are at variance with a recent study[14] on Cu3Au, which proposed large differences in the vibrational entropy with regard to different degrees of short-range order (SRO) (DSdviibs ranged from 0.03–0.16 R)
Calculated DSdviibs values increase with temperature in the low temperature regime and reaches the high temperature limit asymptotically at room temperature as shown in Fig. 2, where local density approximation (LDA) calculated DSdviibs values using cells with 32 atoms are plotted against temperature and compared to the calorimetric ones

Summary

Introduction

The atomic distribution of Au and Cu in Cu3Au changes as a function of temperature. At low temperatures a L12 ordered phase (with Pm3%m symmetry) is stable with Au occupying the corner and Cu the face centres of the cubic unit cell.[1]. The difference in heat capacity between the ordered and the disordered structure below room temperature is of vibrational origin and yields the vibrational enthalpy and entropy of disorder approaching the high temperature limit asymptotically at about 300 K. Density functional calculations using ordered Pm3%m and various disordered Cu3Au super cells were performed and the results were compared to the calorimetric ones.

Results

Conclusion