Abstracts Book - IMRC 2018

• SD1-O019
CONFIGURATIONAL ENERGY LANDSCAPE OF ALLOYS
Juan Miguel Sanchez 1
1 University of Texas at Austin, Institute for Computationa Science and Engineering, United
States.
A widely used approach to describe the configurational energy of alloys consists of
fitting the energies of a set of compounds, typically calculated using some
implementation of the Kohn-Sham equations in Density Functional Theory (DFT), to
a generalized Ising-like energy model. The Ising-like model itself is characterized by
a set of constant Effective Cluster Interactions (ECI). The approach is known as the
Connolly-Williams (CW) method and its implementation to real alloy systems is
usually justified by invoking the Cluster Expansion (CE) formalism introduced by
Sanchez et al. 1 , and by the assumption that the ECIs decay sufficiently fast so that
the CE can be truncated for clusters larger than a judiciously chosen maximum
cluster. In this talk, we show that truncation of the CE and/or structural relaxations
in the alloy invalidate the commonly used Ising-like representation of the
configurational energy of alloys. In particular, we show that truncating the cluster
expansion of the energy of alloys gives rise to renormalized effective cluster
interactions that are explicit functions of the configurational variables that
characterize the state of short- and long-range order of the system. The
dependence of the renormalized cluster interactions on the configurational
variables is in addition to their dependence on the alloys volume and on other
structural parameters. A new physical picture emerges in which the sum of the
interactions, which are projections of the energy onto the basis functions in
configurational space, contribute over long distances but the expected “near -
sightedness of the energy is preserved by the renormalized interactions. The latter
are configuration dependent and decay rapidly with both cluster size and distances.
In order to illustrate our results and observations, we revisit the cluster expansion
of the energy of the Cu-Au system.
1
J.M. Sanchez, F. Ducastelle, and D. Gratias, Physica A 128, 334 (1984).
Acknowledgment: The author acknowledges the computational support
provided by the Texas Advanced Computing Center (TACC) at the University of
Texas at Austin
Keywords: Cluster Expansion, Configurational Energy, Alloys
Presenting authors email: jsanchez@austin.utexas.edu