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 ?(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. Title 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.: 277497 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.
debye model equation of state thermodynamic properties phase equilibrium