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Master's Dissertation
DOI
10.11606/D.3.2003.tde-21102003-094851
Document
Author
Full name
Luiz Tadeu Fernandes Eleno
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2003
Supervisor
Committee
Schon, Claudio Geraldo (President)
Castro, Tania Tome Martins de
Goldenstein, Helio
Title in Portuguese
Incorporação do volume ao método variacional de clusters.
Keywords in Portuguese
Diagramas de Fases
Entropia Vibracional
Método Variacional de Clusters
Termodinâmica Computacional
Abstract in Portuguese
O CVM - Cluster Variation Method, ou Método Variacional de Clusters é um método para cálculos termodinâmicos, baseado na aproximação de campo médio para a energia livre. Em sua concepção original, o CVM dispõe apenas de contribuições configuracionais. A proposta do presente trabalho é neste sentido aprimorar o método com a incorporação de outras componentes à energia livre. Acreditamos que as contribuições volumétricas, tanto dilatacionais quanto vibracionais, são de grande importância, e estas contribuições à energia livre foram aqui adicionadas ao método. Outro objetivo do presente trabalho foi verificar se esta abordagem solucionaria o problema da escala de temperaturas de cálculos ab initio aliados ao CVM. Nestes cálculos, a escala de temperaturas dos diagramas de fases geralmente é duas a três vezes maior que o verificado experimentalmente ou, equivalentemente, que os resultados CVM a partir de dados experimentais. Um novo algoritmo de minimização foi deste modo proposto para levar em conta os efeitos vibracionais e a inclusão do volume como variável. O algoritmo é baseado no NIM (Natural Iteration Method), que é utilizado para a minimização no caso configuracional. Um método para os cálculos vibracionais foi elaborado a partir do modelo de Debye-Grüneisen, com considerações adicionais elásticas, adaptado para sistemas multicomponentes (isto é, ligas). O modelo é baseado naquele desenvolvido por Anderson, quando existem dados ab initio de constantes elásticas, ou Moruzzi-Janak-Schwarz caso contrário. Em cálculos ab initio é possível determinar as constantes elásticas de cada estrutura considerada. Com estes dados, a temperatura de Debye e o módulo de volume a 0K são determinados com maior precisão. Dados de primeiros princípios relativos a energias de coesão/formação em função do volume para o sistema prototípico Fe-Al CCC (ferro-alumínio cúbico de corpo centrado) foram utilizados como exemplo para a obtenção de parâmetros para o modelo.
Title in English
The volume as a variable in the Cluster Variation Method.
Keywords in English
Cluster Variation Method
Computational Thermodynamics
Phase Diagrams
Vibrational Entropy
Abstract in English
The Cluster Variation Method (CVM), used in thermodynamical calculations, is based in the mean-field approximation to the free energy. The CVM was originally devised to treat configurational-only cases. The scope of the present work is to enhance the method's capabilities, introducing other free energy components. The volumetric contributions, either dilatacional or vibrational, are believed to be of great importance, and are therefore incorporated here in the method. Another aim is to verify whether this approach would solve the temperature range calculated with CVM using ab initio data. In this kind of calculation, the phase diagram temperature range is usually twice or three times as large as experimentally verified or, equivalently, as the ones obtained in CVM calculations using experimental data. Therefore, a new minimisation algorithm was proposed to handle with the vibrational effects and the volume as a variable. The algorithm is based on the NIM (Natural Iteration Method), which is used for the minimization in the configurational case. The Debye-Grüneisen approximation has been adapted, with elastical considerations, for multicomponent systems (i.e., alloys). The method is based on Anderson model, when ab initio elastic constants are available, or on Moruzzi-Janak-Schwarz model otherwise. In ab initio calculations it is possible to determine the elastic constants for each structure considered. Using these data, Debye temperature and bulk modulus at 0K are determined with greater accuracy. First-principles cohesion/formation energies in function of volume for the b.c.c. Fe-Al (body-centered cubic iron-aluminum) system were used as an example to derive parameters to the model.
 
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mestrado.pdf (1.06 Mbytes)
Publishing Date
2003-10-30
 
WARNING: The material described below relates to works resulting from this thesis or dissertation. The contents of these works are the author's responsibility.
  • ELENO, L. T. F., et al. Prototype calculations of B2 miscibility gaps in ternary bcc systems with strong ordering tendencies [doi:10.1016/s0966-9795(03)00165-1]. Intermetallics (Barking) [online], 2003, vol. 11, nº 11-12, p. 1245-1252.
  • ELENO, L. T. F., et al. Experimental study and Cluster Variation modelling of the A2/B2 equilibria at the titanium-rich side of the Ti-Fe system. Zeitschrift für Metallkunde [online], 2004, vol. 95, nº 6, p. 464-468. Available from: http://www.ijmr.de/directlink.asp?MK017978.
  • ELENO, L. T. F., et al. Phase equilibria in the Fe-Rh-Ti system II. CVM Calculations [doi:10.1016/j.intermet.2007.03.008]. Intermetallics (Barking) [online], 2007, vol. 15, p. 1248-1256.
  • ELENO, L. T. F., and SCHON, Claudio Geraldo. CVM calculation of the b.c.c. Co-Cr-Al phase diagram [doi:10.1016/j.calphad.2003.11.003]. Calphad (New York) [online], 2003, vol. 27, nº 3, p. 335-342.
  • SCHON, Claudio Geraldo, INDEN, G., and ELENO, L. T. F. Comparison between Monte Carlo and Cluster Variation Method calculations in the BCC Fe-Al system including tetrahedron interactions. Zeitschrift für Metallkunde (Cessou em 2006. Cont. ISSN 1862-5282 International Journal of Materials Research) [online], 2004, vol. 95, nº 6, p. 459-463. Available from: http://www.ijmr.de/directlink.asp?mk17979.
  • ELENO, L. T. F., e SCHON, Claudio Geraldo. Deformação de vidros metálicos. Boletim Técnico da Escola Politécnica da USP. BT/PMT, 2003, vol. MT0303, nº BT/PMT/030, p. 1-21.
  • ELENO, L. T. F., et al. Prototype calculations of B2 miscibility gaps in ternary bcc systems with strong ordering tendencies. In Discussion Meeting on Thermodynamics of Alloys - TOFA2002, Roma, 2002. Discussion meeting on thermodynamics of alloys - TOFA2002., 2002. Abstract.
  • ELENO, L. T. F., and SCHON, C. G. The volume as a new variable in the cluster variation method (CVM). In CALPHAD XXXIX, Ilha de Jeju, Coréia do Sul, 2010. Program and Abstract.Seoul, Coréia do Sul : Korean Institute of Metals and Materials, 2011. Abstract.
  • ELENO, L. T. F., and SCHON, Claudio Geraldo. CVM calculation of the phase diagram of the BCC Co-Cr-Al system. In CALPHAD XXX, York, 2001. CALPHAD XXX - Technical programme and Abstracts.York : Calphad Inc., 2001. Abstract.
  • BALUN, J., et al. Phase equilibria in the ternary Fe-Rh-Ti system. In 2003 TMS Annual Meeting/ International Symposium on Intermetallics and Advanced Metallic Systems - A symposium dedicated to Dr. C. T. Liu, San Diego/ EUA, 2003. 132nd Annual International Meeting & Exhibition - Technical Program., 2003. Abstract. Available from: http://www.tms.org.
  • ELENO, L. T. F., et al. CVM calculations of the bcc Fe-Rh-Ti system. In CALPHAD XXXIV, Maastricht, 2005. Abstracts.Utrecht : University of Utrecht, 2005. Abstract.
  • ELENO, L. T. F., e SCHON, Claudio Geraldo. Modelamento por CVM do diagramam de fases do sistema cobalto - cromo - alumínio cúbico de corpo centrado. In 57o Congresso Anual da ABM Internacional, São Paulo, 2002. Anais do 57o Congresso Anual da ABM Internacional.São Paulo : Associação Brasileira de Metalurgia e de Materiais, 2002.
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