zbMATH — the first resource for mathematics

Gibbs2: A new version of the quasi-harmonic model code. I. Robust treatment of the static data. (English) Zbl 06145406
Summary: We describe in this article the techniques developed for the robust treatment of the static energy versus volume theoretical curve in the new version of the quasi-harmonic model code [M. A. Blanco et al., ibid. 158, No. 1, 57–72 (2004; Zbl 1221.82001)]. An average of strain polynomials is used to determine, as precisely as the input data allow it, the equilibrium properties and the derivatives of the static \(E(V)\) curve. The method provides a conservative estimation of the error bars associated to the fitting procedure. We have also developed the techniques required for detecting, and eventually removing, problematic data points and jumps in the \(E(V)\) curve. The fitting routines are offered as an independent octave package, called AsturFit, with an open source license.

74-04 Software, source code, etc. for problems pertaining to mechanics of deformable solids
Full Text: DOI
[1] Blanco, M.A.; Francisco, E.; Luaña, V., GIBBS: isothermal-isobaric thermodynamics of solids from energy curves using a quasi-harmonic Debye model, Comput. phys. comm., 158, 57-72, (2004), source code distributed by the CPC Program Library: · Zbl 1221.82001
[2] Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G.L.; Cococcioni, M.; Dabo, I.; Dal Corso, A.; de Gironcoli, S.; Fabris, S.; Fratesi, G.; Gebauer, R.; Gerstmann, U.; Gougoussis, C.; Kokalj, A.; Lazzeri, M.; Martin-Samos, L.; Marzari, N.; Mauri, F.; Mazzarello, R.; Paolini, S.; Pasquarello, A.; Paulatto, L.; Sbraccia, C.; Scandolo, S.; Sclauzero, G.; Seitsonen, A.P.; Smogunov, A.; Umari, P.; Wentzcovitch, R.M., QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials, J. phys.-condens. matter, 21, 39, 395502, (2009), 19 pp.
[3] Zharkov, V.N.; Kalinin, V.A., Equations of state for solids at high pressure and temperatures, (1971), Consultants Bureau New York
[4] Stacey, F.D.; Brennan, B.J.; Irvine, R.D., Finite strain theories and comparisons with seismological data, Surv. geophys., 4, 189-232, (1981)
[5] ()
[6] Anderson, O.L., Equations of state for solids in geophysics and ceramic science, (1995), Oxford Univ. Press Oxford, UK
[7] Holzapfel, W.B., Physics of solids under strong compression, Rep. progr. phys., 59, 29-90, (1996)
[8] Poirier, J.-P., Introduction to the physics of the earthʼs interior, (2000), Cambridge University Press Cambridge, UK
[9] Holzapfel, W.B., Equations of state for solids under strong compression, Z. kristall., 216, 473-488, (2001)
[10] Eliezer, S.; Ghatak, A.K.; Hora, H., Fundamentals of equations of state, (2002), World Sci. Singapore · Zbl 1029.81002
[11] Stacey, F.D., High pressure equations of state and planetary interiors, Rep. progr. phys., 68, 341-383, (2005)
[12] Peiris, S.M.; Gump, J.C., Equations of state and high-pressure phases of explosives, (), 99-126
[13] Murnaghan, F.D., The compressibility of media under extreme pressures, Proc. natl. acad. sci. USA, 30, 244-247, (1944) · Zbl 0060.42901
[14] Birch, F., Finite elastic strain of cubic crystals, Phys. rev., 71, 809-824, (1947) · Zbl 0032.37804
[15] Birch, F., Finite strain isotherm and velocities for single-crystal and polycrystalline nacl at high pressures and 300 K, J. geophys. res., 83, 1257-1268, (1978)
[16] Maxima, a computer algebra system, version 5.20.1, URL http://maxima.sourceforge.net/.
[17] Poirier, J.-P.; Tarantola, A., A logarithmic equation of state, Phys. Earth planet. int., 109, 1-8, (1998)
[18] Mie, G., Zurkinetischen theorie der einatomigen Köper, Ann. phys., 11, 657-697, (1903) · JFM 34.0983.01
[19] Vinet, P.; Ferrante, J.; Smith, J.R.; Rose, J.H., An universal equation of state for solids, J. phys. C: solid state phys., 19, L467-L473, (1986) · Zbl 0938.82026
[20] Vinet, P.; Rose, J.H.; Ferrante, J.; Smith, J.R., Universal features of the equation of state of solids, J. phys: condens. matter, 1, 1941-1963, (1989)
[21] Cohen, R.E.; Gülseren, O.; Hemley, R.J., Accuracy of equation-of-state formulations, Amer. mineralogist, 85, 2, 338-344, (2000)
[22] Holzapfel, W.B., Equation of state for solids under strong compression, High pressure res., 16, 81-126, (1998)
[23] García Baonza, V.; Cáceres, M.; Nuñez, J., Universal compressibility behavior of dense phases, Phys. rev. B, 51, 28-37, (1995)
[24] García Baonza, V.; Taravillo, M.; Cáceres, M.; Nuñez, J., Universal features of the equation of state of solids from a pseudospinodal hypothesis, Phys. rev. B, 53, 5252-5258, (1996)
[25] Taravillo, M.; García Baonza, V.; Nuñez, J.; Cáceres, M., Simple equation of state for solids under compression, Phys. rev. B, 54, 7034-7045, (1996)
[26] M. Álvarez Blanco, Métodos cuánticos locales para la simulación de materiales iónicos, Fundamentos, algoritmos y aplicaciones, Tesis doctoral, Universidad de Oviedo, Julio 1997.
[27] Anton, H.; Schmidt, P.C., Theoretical investigations of the elastic constants in laves phases, Intermetallics, 5, 449-465, (1997)
[28] Mayer, B.; Anton, H.; Bott, E.; Methfessel, M.; Sticht, J.; Harris, J.; Schmidt, P.C., Ab-initio calculation of the elastic constants and thermal expansion coefficients of laves phases, Intermetallics, 11, 23-32, (2003)
[29] Bard, Y., Nonlinear parameter estimation, (1974), Academic Press New York · Zbl 0345.62045
[30] Draper, N.R.; Smith, H., Applied regression analysis, (1998), Wiley New York, USA · Zbl 0158.17101
[31] Wilcox, R.R., Fundamentals of modern statistical methods, (2010), Springer New York, USA · Zbl 1211.62001
[32] Moré, J.J.; Sorensen, D.C.; Hillstrom, K.E.; Garbow, B.S., The MINPACK project, (), 88-111
[33] Trefethen, L.N.; Bau, D., Numerical linear algebra, (1997), SIAM Philadelphia, PA · Zbl 0874.65013
[34] Thomson, L., On the fourth order anharmonic equation of state of solids, J. phys. chem. solids, 31, 2003-2016, (1970)
[35] Bardeen, J., Compressibilities of the alkali metals, J. chem. phys., 6, 372-378, (1938)
[36] Akaike, H., A new look at the statistical model identification, IEEE trans. automat. control, 19, 716-723, (1974) · Zbl 0314.62039
[37] Maronna, R.A.; Martin, D.R.; Yohai, V.J., Robust statistics: theory and methods, (2006), Wiley Chichester, England · Zbl 1094.62040
[38] Otero-de-la Roza, A.; Luaña, V., Runwien: a text-based interface for the wien package, Comput. phys. comm., 180, 800-812, (2009), source code distributed by the CPC Program Library
[39] Schwarz, K.; Blaha, P.; Madsen, G.K.H., Electronic structure calculations of solids using the WIEN2k package for material sciences, Comput. phys. comm., 147, 71-76, (2002) · Zbl 1004.81583
[40] Schwarz, K.; Blaha, P., Solid state calculations using WIEN2k, Comput. mater. sci., 28, 259-273, (2003)
[41] Cynn, H.; Clepeis, J.E.; Yao, C.-S.; Young, D.A., Osmium has the lowest experimentally determined compressibility, Phys. rev. lett., 88, 135701, (2002)
[42] Kenichi, T., Bulk modulus of osmium: high-pressure powder X-ray diffraction experiments under quasihydrostatic conditions, Phys. rev. B, 70, 012101, (2004)
[43] Hebbache, M.; Zemzemi, M., Ab initio study of high-pressure behavior of a low compressibility metal and a hard material: osmium and diamond, Phys. rev. B, 70, 224107, (2004)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.