Phasego: A toolkit for automatic calculation and plot of phase diagram

The Phasego package extracts the Helmholtz free energy from the phonon density of states obtained by the first-principles calculations. With the help of equation of states fitting, it reduces the Gibbs free energy as a function of pressure/temperature at fixed temperature/pressure. Based on the quasi-harmonic approximation (QHA), it calculates the possible phase boundaries among all the structures of interest and finally plots the phase diagram automatically. For the single phase analysis, Phasego can numerically derive many properties, such as the thermal expansion coefficients, the bulk moduli, the heat capacities, the thermal pressures, the Hugoniot pressure–volume–temperature relations, the Grüneisen parameters, and the Debye temperatures. In order to check its ability of phase transition analysis, I present here two examples: semiconductor GaN and metallic Fe. In the case of GaN, Phasego automatically determined and plotted the phase boundaries among the provided zinc blende (ZB), wurtzite (WZ) and rocksalt (RS) structures. In the case of Fe, the results indicate that at high temperature the electronic thermal excitation free energy corrections considerably alter the phase boundaries among the body-centered cubic (bcc), face-centered cubic (fcc) and hexagonal close-packed (hcp) structures.Program summaryProgram title: PhasegoCatalogue identifier: AEVQ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEVQ_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 837140No. of bytes in distributed program, including test data, etc.: 8816053Distribution format: tar.gzProgramming language: Python (versions 2.4 and later).Computer: Any computer that can run Python (versions 2.4 and later).Operating system: Any operating system that can run Python.RAM: 10 M bytesClassification: 7.8.External routines: Numpy [1], Scipy [2], Matplotlib [3]Nature of problem:Materials usually undergo structural phase transitions when the environmental pressure and temperature are elevated to high enough values. The phase transition process obeys the principle of lowest Gibbs free energy. In addition to the static energy, current density functional theory (DFT) calculations can easily give the phonon density of states of lattice vibrations, from which the Helmholtz free energy of phonons are reduced. Then Gibbs free energy can be achieved for the analysis of phase stability and phase transition at high pressure and temperature within the framework of QHA. The problem is to extract the Gibbs free energies from the DFT calculations and automatically analyze the high pressure and temperature phase boundaries among a number of structures.Solution method:With the help of numerical interpolation techniques, the Gibbs free energy as a function of pressure/temperature at fixed temperature/pressure can be obtained. Then the QHA based phase boundaries can be automatically determined and plotted by scanning the pressure/temperature at fixed temperature/pressure according to the principle of lowest Gibbs free energy.Restrictions:The restriction is from the QHA which takes partially into account the anharmonic effects.Unusual features:The phase boundaries among a number of structures can be automatically determined and plotted, which largely improve the efficiency of phase transition analysis. In addition to some basic thermodynamic properties of each single structure, the Hugoniot pressure–volume–temperature relations are also automatically reduced.Additional comments:This package can treat the phonon density of states data from many packages, such as PHON [4], PHONOPY [5], Quantum ESPRESSO [6], and ABINIT [7].Running time:The examples provided in the distribution take less than a minute to run.References:[1]www.numpy.org.[2]www.scipy.org.[3]www.matplotlib.org.[4]D. Alfè, Comput. Phys. Comm. 180 (2009) 2622, www.homepages.ucl.ac.uk/~ucfbdxa/.[5]www.phonopy.sourceforge.net.[6]P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G.L. Chiarotti, M. Cococcioni, I. Dabo, A.D. Corso, S.D. Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A.P. Seitsonen, A. Smogunov, P. Umari, R.M. Wentzcovitch, J. Phys. Condens. Matter 21 (2009) 395502, www.quantum-espresso.org.[7]X. Gonze, B. Amadon, P.-M. Anglade, J.-M. Beuken, F. Bottin, P. Boulanger, F. Bruneval, D. Caliste, R. Caracas, M. Ct, T. Deutsch, L. Genovese, P. Ghosez, M. Giantomassi, S. Goedecker, D. Hamann, P. Hermet, F. Jollet, G. Jomard, S. Leroux, M. Mancini, S. Mazevet, M. Oliveira, G. Onida, Y. Pouillon, T. Rangel, G.-M. Rignanese, D. Sangalli, R. Shaltaf, M. Torrent, M. Verstraete, G. Zerah, J. Zwanziger, Comput. Phys. Comm. 180 (2009) 2582, www.abinit.org.