GIBBS: isothermal-isobaric thermodynamics of solids from energy curves using a quasi-harmonic Debye model

Given the energy of a solid ( E) as a function of the molecular volume ( V), the gibbs program uses a quasi-harmonic Debye model to generate the Debye temperature Θ( V), obtains the non-equilibrium Gibbs function G^★( V; p, T), and minimizes G^★ to derive the thermal equation of state (EOS) V( p, T) and the chemical potential G( p, T) of the corresponding phase. Other macroscopic properties are also derived as a function of p and T from standard thermodynamic relations. The program focuses in obtaining as much thermodynamical information as possible from a minimum set of ( E, V) data, making it suitable to analyse the output of costly electronic structure calculations, adding thermal effects at a low computational cost. Any of three analytical EOS widely used in the literature can be fitted to the p- V( p, T) data, giving an alternative set of isothermal bulk moduli and their pressure derivatives that can be fed to the Debye model machinery. Program summaryTitle of the program:gibbs Catalogue number: ADSY Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSY Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: Persons requesting the program must sign the standard CPC non-profit use license Computers on which the program has been tested: Intel Pentium, Alpha, Sun Sparc/Ultra/Blade Operating system under which the program has been tested: Unix, GNU/Linux Programming language used: Fortran 77 Memory required to execute with typical data: 700 KB No. of bits in a word: 32 No. of processors used: 1 No. of bytes in distributed program, including test data, etc.: 277 497 No. of lines in distributed program, including test data, etc.: 7390 Distribution format: tar gzip file Keywords: Quasi-harmonic Debye model, equation of state Nature of physical problem: Derivation of the static and thermal equation of state, chemical potential, and thermodynamic properties of a crystal from energy-volume data only. Method of solution: A quasi-harmonic Debye model is used to obtain the vibrational Helmholtz free energy as a function of temperature at the molecular volumes of input. The non-equilibrium Gibbs energy is then minimized at any temperature T and pressure p to obtain the EOS and the chemical potential. Several standard EOS parameters can be derived by fitting analytical forms to the pressure-volume data. Finally, some thermodynamic properties are computed for each ( p, T). Restrictions on the complexity of the problem: Thermal effects are assumed to be well represented by a quasi-harmonic Debye model, in which the temperature dependence of the internal parameters is embedded into the temperature dependence of the volume. Typical running time: less than 1 s (Pentium III, 800 MHz) for 25 ( E, V) pairs, 10 pressure and 10 temperature values.