Renormalized Interactions in the Cluster Expansion Method

Speaker: Dr. Juan M. Sanchez, Provost, American University of Sharjah

Abstract:

For the last 30 years or so, the Cluster Expansion (CE) method has been used with some degree of success to describe the configurational energy of alloys with arbitrary degree of short-range. The technique addresses a central problem in alloy theory, namely, that of describing the energy of configurationally disordered systems from first principles. However, most applications to date cast the cluster expansion of the energy in the form of simple Ising-like model with constant Effective Cluster Interactions.

Here we show that truncating the cluster expansion gives rise to renormalized effective cluster interactions that are explicit functions of the configurational variables.  Such a dependence of the renormalized cluster interactions is in addition to their dependence on the volume of the alloy and on other structural parameters. The physical picture that emerges is different from the commonly used representation of the configurational energy by means of a generalized Ising-like model, which follows from the assumption that the contributions of the effective cluster interactions can be neglected beyond a relatively small cluster size. The new physical picture is one in which the sum of the effective interactions contribute over long distances but the expected "near-sightedness" of the energy is preserved by the renormalized interactions. Furthermore, the cluster expansion is implemented by simultaneously fitting the volume and configuration dependent energy function to the zero pressure values of the energies of formation, volumes, bulk moduli and pressure derivatives of the bulk modulus of a set of ordered compounds. As an example of the new formulation of the cluster expansion, we apply the methodology to the Cu-Au system for different types of cell-internal and cell-external relaxations.

Speaker: Dr. Juan M. Sanchez

As Provost and Chief Academic Officer, Dr. Juan Sanchez sets AUS’ overall academic priorities and has management responsibilities for academic affairs at the university, colleges and school. In his role of Chief Academic Officer, he works with the deans and the faculty to sustain and advance the highest standards of scholarly achievements at AUS, and to ensure the success of our students through the delivery of high-quality academic programs.

Prior to joining AUS in January 2019, Dr. Sanchez served as Vice President for Research at the University of Texas at Austin for more than 16 years, where he was also appointed as a Temple Foundation Endowed Professor in the Department of Mechanical Engineering. Before joining the University of Texas at Austin, he served as Assistant, Associate and Full Professor at Columbia University in New York. As an educator, he has supervised 17 PhD and 7 MS students at both Columbia University and at the University of Texas at Austin.

Dr. Sanchez’s research interests and expertise are in computational materials science and engineering, with a focus on alloy theory and on the modeling and simulation of materials properties from first principles. He has contributed extensively to the scientific and engineering literature in materials science and engineering. He holds a PhD and Master of Science in Materials Science and Engineering from the University of California, Los Angeles, and a Bachelor of Science in Physics from the National University of Córdoba, Argentina.

For more information, contact nabdulmaati@aus.edu.