DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**Richard Otis, Pennsylvania State University

**Title: ***
Global energy minimization of multi-component phases with internal degrees of freedom
*

**Abstract:**
In computational thermodynamics, miscibility gap detection is a crucial feature to accurately calculate
the energy of phases containing regions of instability, i.e., spinodals, and is commonly handled through
global minimization (GM) of the Gibbs energy. While many authors have outlined methods for either the
two-component or two-phase cases, few examples of multi-component GM methods exist in the
literature. Here we develop an approach that treats a phases internal degrees of freedom as its primary
variables. Composition space is quasi-randomly sampled using an N-dimensional Halton sequence and
the minimum energy surface is computed using the QuickHull convex hull algorithm. Tie hyperplanes
spanning miscibility gaps and/or multi-phase regions are identified by facet projection along each
composition axis. A software implementation, provided in the open-source Python library pycalphad, is
discussed within the broader context of interactive scientific computing.

**Time:** Friday, February 6, 2015, 1:30-2:30 p.m.

**Place:** Exploratory Hall, Room 4106

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491