The Application of Computational Thermodynamics to the Cathode-Electrolyte in Solid Oxide Fuel Cells

  • Shadi Darvish
  • Mohammad Asadikiya
  • Mei Yang
  • Yu ZhongEmail author


The fundamentals of solid oxide fuel cell (SOFC) and computational thermodynamics, using the CALPHAD (CALculation of PHAse Diagrams) approach, are reviewed in this chapter. The thermodynamic database development for perovskites and fluorites is especially discussed. In addition, the application of computational thermodynamics to the cathode and electrolyte of SOFC is also discussed in detail including the defect chemistry and quantitative Brouwer diagrams, electronic and ionic conductivity, cathode-electrolyte triple phase boundary (TPB) stability, thermomechanical properties of perovskite cathode, the effect of gas impurities like CO2 to the phase stability of cathode, and phase diagram development for nano (n-)yttria-stabilized zirconia (YSZ) particles.


Solid oxide fuel cell (SOFC) CALPHAD modeling Computational thermodynamics Cathode Electrolyte Long-term degradation Phase stability 



This work is partially supported by the start-up funding from Florida International University for Dr. Yu Zhong and also the grant from the American Chemical Society Petroleum Research Fund (PRF#54190-DNI10). The Doctoral Evidence Acquisition (DEA) Fellowship from the graduate school of Florida International University is also appreciated for the financial support for Ms. Shadi Darvish and Mr. Mohammad Asadikiya. The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.


  1. 1.
    FCT – Fuel Cell Technologies – SOFC. 2017 [cited 2017]. Available from:
  2. 2.
    T. Ishihara, Perovskite Oxide for Solid Oxide Fuel Cells, Fuel Cells and Hydrogen Energy (Springer, Boston, 2009)Google Scholar
  3. 3.
    F.-P. Negal, Electricity from Wood through the Combination of Gasification and Solid Oxide Fuel Cells (ETH/PSI, Zurich, 2008)Google Scholar
  4. 4.
    N. Sammes, Y. Du, Intermediate-temperature SOFC electrolytes, in Fuel Cell Technologies: State and Perspectives, (Springer, Dordrecht, 2005), pp. 19–34Google Scholar
  5. 5.
    B.C. Steele, A. Heinzel, Materials for fuel-cell technologies. Nature 414(6861), 345–352 (2001)Google Scholar
  6. 6.
    T. Wolfram, S. Ellialtioglu, Electronic and Optical Properties of d-Band Perovskites (Cambridge University Press, Cambridge, UK, 2006)Google Scholar
  7. 7.
    D.M. Smyth, The Defect Chemistry of Metal Oxides (Oxford University Press, New York, 2000)Google Scholar
  8. 8.
    S. Darvish et al., Quantitative defect chemistry analysis and electronic conductivity prediction of La0.8Sr0.2MnO3±δ perovskite. J. Electrochem. Soc. 162(9), E134–E140 (2015)Google Scholar
  9. 9.
    S. Darvish, S.K. Saxena, Y. Zhong, Quantitative analysis of (La0. 8Sr0. 2) 0.98 MnO3±δ electronic conductivity using CALPHAD approach, in Developments in Strategic Ceramic Materials: A Collection of Papers Presented at the 39th International Conference on Advanced Ceramics and Composites, (Wiley Online Library, Hoboken, 2015)Google Scholar
  10. 10.
    Y. Yu et al., Effect of atmospheric CO2 on surface segregation and phase formation in La0.6Sr0.4Co0.2Fe0.8O3 thin films. Appl. Surf. Sci. 323, 71–77 (2014)Google Scholar
  11. 11.
    Y. Tanaka et al., Improvement of electrical efficiency of solid oxide fuel cells by anode gas recycle. ECS Trans. 30(1), 145–150 (2011)Google Scholar
  12. 12.
    S. Darvish et al., Thermodynamic prediction of the effect of CO2 to the stability of (La0.8Sr0.2)0.98MnO3±δ system. Int. J. Hydrog. Energy 41(24), 10239–10248 (2016)Google Scholar
  13. 13.
    S. Darvish, S. Gopalan, Y. Zhong, Thermodynamic stability maps for the La0.6Sr0.4Co0.2Fe0.8O3±δ–CO2–O2 system for application in solid oxide fuel cells. J. Power Sources 336, 351 (2016)Google Scholar
  14. 14.
    C. Wang et al., Effect of SO2 poisoning on the electrochemical activity of La0.6Sr0.4Co0.2Fe0.8O3-δ cathodes of solid oxide fuel cells. J. Electrochem. Soc. 164(6), F514–F524 (2016)Google Scholar
  15. 15.
    A. Arabacı, M.F. Öksüzömer, Preparation and characterization of 10 mol% Gd doped CeO2 (GDC) electrolyte for SOFC applications. Ceram. Int. 38(8), 6509–6515 (2012)Google Scholar
  16. 16.
    F.W. Poulsen, Defect chemistry modelling of oxygen-stoichiometry, vacancy concentrations, and conductivity of (La1−xSrx)yMnO3−δ. Solid State Ionics 129(1–4), 145–162 (2000)Google Scholar
  17. 17.
    X.D. Zhou, H. Anderson, A Global defect chemistry model or p-type mixed ionic and electronic conductors. ECS Trans. 25(2), 2807–2814 (2009)Google Scholar
  18. 18.
    J. Nowotny, M. Rekas, Defect chemistry of (La,Sr)MnO3. J. Am. Ceram. Soc. 80(191914), 67 (1998)Google Scholar
  19. 19.
    H. Kamata et al., High temperature electrical properties of the perovskite-type oxide La1−XSrXMnO3−d. J. Phys. Chem. Solids 87, 943–950 (1995)Google Scholar
  20. 20.
    J. Mizusaki et al., Electronic conductivity, Seebeck coefficient, defect and electronic structure of nonstoichiometric La1−xSrxMnO3. Solid State Ionics 132, 167–180 (2000)Google Scholar
  21. 21.
    G. Brouwer, A general asymptotic solution of reaction equations common in solid-state chemistry. Philips Res. Rep. 9(5), 366–376 (1954)Google Scholar
  22. 22.
    J.A.M. van Roosmalen, E.H.P. Cordfunke, A new defect model to describe the oxygen deficiency in perovskite-type oxides. J. Solid State Chem. 93(1), 212–219 (1991)Google Scholar
  23. 23.
    I. Yasuda, M. Hishinuma, Electrical conductivity and chemical diffusion coefficient of strontium-doped lanthanum manganites. J. Solid State Chem. 123(2), 382–390 (1996)Google Scholar
  24. 24.
    J. Mizusaki et al., Nonstoichiometry of the perovskite-type oxide La1−xSrxCrO3−δ. Solid State Ionics 12, 119–124 (1984)Google Scholar
  25. 25.
    I. Yasuda, T. Hikita, Precise determination of the chemical diffusion coefficient of calcium-doped lanthanum chromites by means of electrical conductivity relaxation. J. Electrochem. Soc. 141(5), 1268–1273 (1994)Google Scholar
  26. 26.
    B.F. Flandermeyer et al., High-temperature stability of magnesium-doped lanthanum chromite. High Temp. Sci. 20(259), 259–269 (1985)Google Scholar
  27. 27.
    J.H. Kuo, H.U. Anderson, D.M. Sparlin, Oxidation-reduction behavior of undoped and Sr-doped LaMnO3 nonstoichiometry and defect structure. J. Solid State Chem. 83(1), 52–60 (1989)Google Scholar
  28. 28.
    J. Mizusaki et al., Nonstoichiometry and defect structure of the perovskite-type oxides La1−XSrxFeO3−δ. J. Solid State Chem. 58(2), 257–266 (1985)Google Scholar
  29. 29.
    J.H. Kuo, H.U. Anderson, D.M. Sparlin, Oxidation-reduction behavior of undoped and Sr-doped LaMnO3: defect structure, electrical conductivity, and thermoelectric power. J. Solid State Chem. 87(1), 55–63 (1990)Google Scholar
  30. 30.
    Y.-L. Lee, D. Morgan, Ab initio and empirical defect modeling of LaMnO3±δ for solid oxide fuel cell cathodes. Phys. Chem. Chem. Phys. 14(1), 290–302 (2012)Google Scholar
  31. 31.
    B. Hu et al., Effect of CO2 on the stability of strontium doped lanthanum manganite cathode. J. Power Sources 268, 404–413 (2014)Google Scholar
  32. 32.
    B. Hu, M.K. Mahapatra, P. Singh, Performance regeneration in lanthanum strontium manganite cathode during exposure to H2O and CO2 containing ambient air atmospheres. J. Ceram. Soc. Jpn. 123(1436), 199–204 (2015)Google Scholar
  33. 33.
    D. Oh, D. Gostovica, E.D. Wachsman, Mechanism of La0.6Sr0.4Co0.2Fe0.8O3 cathode degradation. J. Mater. Res. 27(15), 1992–1999 (2012)Google Scholar
  34. 34.
    L. Zhao et al., Insight into surface segregation and chromium deposition on La0.6Sr0.4Co0.2Fe0.8O3−δ cathodes of solid oxide fuel cells. J. Mater. Chem. A 2(29), 11114–11123 (2014)Google Scholar
  35. 35.
    S.P. Simner et al., Degradation mechanisms of la-Sr-co-Fe-O3 SOFC cathodes. Electrochem. Solid-State Lett. 9(10), A478–A481 (2006)Google Scholar
  36. 36.
    M. Liu et al., Enhanced performance of LSCF cathode through surface modification. Int. J. Hydrog. Energy 37(10), 8613–8620 (2012)Google Scholar
  37. 37.
    F.S. Baumann et al., Strong performance improvement of La0.6Sr0.4Co0.8Fe0.2O3 − δ SOFC cathodes by electrochemical activation. J. Electrochem. Soc. 152(10), A2074–A2079 (2005)Google Scholar
  38. 38.
    Y. Yu, A.Y. Nikiforov, T.C. Kaspar, J.C. Woicik, K.F. Ludwig, S. Gopalan, U.B. Pal, S.N. Basu, Chemical characterization of surface precipitates in La0.7Sr0.3Co0.2Fe0.8O3−δ as cathode material for solid oxide fuel cells. J. Power Sources. 333, 247–253 (2016)Google Scholar
  39. 39.
    S. Lau, S. Singhal, Potential electrode/electrolyte interactions in solid oxide fuel cells, in Corrosion’85, (Boston, United States: National Association of Corrosion Engineers 1985)Google Scholar
  40. 40.
    O. Yamamoto et al., Stability of perovskite oxide electrode with stabilized zirconia, in Electrochemical Society 1989 Fall Meeting (Abstracts), (United States: The Electrochemical Society 1990)Google Scholar
  41. 41.
    G. Stochniol, E. Syskakis, A. Naoumidis, Chemical compatibility between strontium-doped lanthanum manganite and Yttria-stabilized zirconia. J. Am. Ceram. Soc. 78(4), 929–932 (1995)Google Scholar
  42. 42.
    A. Mitterdorfer, L. Gauckler, La2Zr2O7 formation and oxygen reduction kinetics of the La0.85Sr0.15MnyO3, O2(g)/YSZ system. Solid State Ionics 111(3), 185–218 (1998)Google Scholar
  43. 43.
    K. Wiik et al., Reactions between strontium-substituted lanthanum manganite and Yttria-stabilized zirconia: I, powder samples. J. Am. Ceram. Soc. 82(3), 721–728 (1999)Google Scholar
  44. 44.
    A. Grosjean et al., Reactivity and diffusion between La0.8 Sr0.2 MnO3 and ZrO2 at interfaces in SOFC cores by TEM analyses on FIB samples. Solid State Ionics 177(19), 1977–1980 (2006)Google Scholar
  45. 45.
    J. Labrincha, J. Frade, F. Marques, La2Zr2O7 formed at ceramic electrode/YSZ contacts. J. Mater. Sci. 28(14), 3809–3815 (1993)Google Scholar
  46. 46.
    C. Brugnoni, U. Ducati, M. Scagliotti, SOFC cathode/electrolyte interface. Part I: reactivity between La0.85Sr0.15MnO3 and ZrO2-Y2O3. Solid State Ionics 76(3–4), 177–182 (1995)Google Scholar
  47. 47.
    H.Y. Lee, S.M. Oh, Origin of cathodic degradation and new phase formation at the La0.9Sr0.1MnO3/YSZ interface. Solid State Ionics 90(1–4), 133–140 (1996)Google Scholar
  48. 48.
    N.Q. Minh, Solid oxide fuel cell technology – features and applications. Solid State Ionics 174, 271–277 (2004)Google Scholar
  49. 49.
    S. Jiang, Development of lanthanum strontium manganite perovskite cathode materials of solid oxide fuel cells: a review. J. Mater. Sci. 43(21), 6799–6833 (2008)Google Scholar
  50. 50.
    M. Mori et al., Thermal-expansion behaviors and mechanisms for Ca- or Sr-doped lanthanum manganite perovskites under oxidizing atmospheres. J. Electrochem. Soc. 147(4), 1295–1302 (2000)Google Scholar
  51. 51.
    A. Hammouche, E. Siebert, A. Hammou, Crystallographic, thermal and electrochemical properties of the system La1−xSrxMnO3 for high temperature solid electrolyte fuel cells. Mater. Res. Bull. 24(3), 367–380 (1989)Google Scholar
  52. 52.
    M. Mori, Effect of B-site doing on thermal cycle shrinkage for La0.8Sr0.2Mn1−xMxO3+δ perovskites (M=Mg, Al, Ti, Mn, Fe, Co, Ni; 0≤x≤0.1). Solid State Ionics 174(1–4), 1–8 (2004)Google Scholar
  53. 53.
    M. Mori, Mechanisms of thermal expansion and shrinkage of La0.8Sr0.2MnO3+δ perovskites with different densities during thermal cycling in air. J. Electrochem. Soc. 152(4), A732–A739 (2005)Google Scholar
  54. 54.
    B.P. McCarthy et al., Enhanced shrinkage of lanthanum strontium manganite (La0.90Sr0.10MnO3+δ) resulting from thermal and oxygen partial pressure cycling. J. Am. Ceram. Soc. 90(10), 3255–3262 (2007)Google Scholar
  55. 55.
    B.P. McCarthy et al., Low-temperature densification of lanthanum strontium manganite (La1−xSrxMnO3+δ), x=0.0–0.20. J. Am. Ceram. Soc. 92(8), 1672–1678 (2009)Google Scholar
  56. 56.
    T. Soma, et al., Porous lanthanum manganite sintered bodies and solid oxide fuel cells. U.S. Patent No. 5,432,024 (1995)Google Scholar
  57. 57.
    J. Chevalier et al., The tetragonal-monoclinic transformation in zirconia: Lessons learned and future trends. J. Am. Ceram. Soc. 92, 1901–1920 (2009)Google Scholar
  58. 58.
    J.R. Kelly, I. Denry, Stabilized zirconia as a structural ceramic: an overview. Dent. Mater. 24, 289–298 (2008)Google Scholar
  59. 59.
    C.H. Wang et al., Phase transformation and nanocrystallite growth behavior of 2 mol% yttria-partially stabilized zirconia (2Y-PSZ) powders. Ceram. Int. 39, 5165–5174 (2013)Google Scholar
  60. 60.
    Y. Li et al., Electrical conductivity of zirconia stabilized with yttria and calcia. J. Mater. Sci. Lett. 18, 443–444 (1999)Google Scholar
  61. 61.
    A. Nakamura, J.B. Wagner, Defect structure, ionic conductivity, and diffusion in yttria stabilized zirconia and related oxide electrolytes with fluorite structure. J. Electrochem. Soc. 133, 1542–1548 (1986)Google Scholar
  62. 62.
    W. Strickler, W.G. Carlson, Ionic conductivity of cubic solid solutions in the system CaO-Y2O3-ZrO2. J. Am. Ceram. Soc. 47, 122–127 (1963)Google Scholar
  63. 63.
    J. Goff et al., Defect structure of yttria-stabilized zirconia and its influence on the ionic conductivity at elevated temperatures. Phys. Rev. B 59(22), 14202 (1999)Google Scholar
  64. 64.
    R.C. Garvie, R.H. Hannink, R.T. Pascoe, Ceramic steel? Nature 258, 703–704 (1975)Google Scholar
  65. 65.
    O. Ruff, F. Ebert, Refractory ceramics: 1, the forms of zirconia dioxide. Z. Anorg. Allg. Chem. 180, 19–41 (1929)Google Scholar
  66. 66.
    C. Wagner, Über den Mechanismus der elektrischen Stromleitung im Nernststift. Naturwissenschaften 31(23–24), 265–268 (1943)Google Scholar
  67. 67.
    J.A. Krogstad et al., Effect of yttria content on the zirconia unit cell parameters. J. Am. Ceram. Soc. 94, 4548–4555 (2011)Google Scholar
  68. 68.
    A. Suresh, M.J. Mayo, W.D. Porter, Thermodynamics for Nanosystems: grain and particle-size dependent phase diagrams. Rev. Adv. Mater. Sci. 5, 100–109 (2003)Google Scholar
  69. 69.
    J.W. Drazin, R.H.R. Castro, Water adsorption microcalorimetry model: deciphering surface energies and water chemical potentials of nanocrystalline oxides. J. Phys. Chem. C 118, 10131–10142 (2014)Google Scholar
  70. 70.
    J.W. Drazin, R.H.R. Castro, Phase stability in nanocrystals: a predictive diagram for yttria-zirconia. J. Am. Ceram. Soc. 1384, 1377–1384 (2015)Google Scholar
  71. 71.
    M. Asadikiya et al., Phase diagram for a nano-yttria-stabilized zirconia system. RSC Adv. 6(21), 17438–17445 (2016)Google Scholar
  72. 72.
    L. Kaufman, H. Bernstein, Computer Calculation of Phase Diagrams with Special Reference to Refractory Metals (Academic, New York, 1970)Google Scholar
  73. 73.
    N. Saunders, A.P. Miodownik, CALPHAD (Calculation of Phase Diagrams): A Comprehensive Guide, vol xvi (Pergamon, Oxford, 1998), p. 479Google Scholar
  74. 74.
    M. Hillert, The compound energy formalism. J. Alloys Compd. 320(2), 161–176 (2001)Google Scholar
  75. 75.
    K. Hack (ed.), The SGTE Casebook : Thermodynamics at Work, Materials Modelling Series (Institute of Materials, London, 1996)Google Scholar
  76. 76.
    A.T. Dinsdale, SGTE data for pure elements. Calphad 15(4), 317–425 (1991)Google Scholar
  77. 77.
    B. Sundman, J. Agren, A regular solution model for phases with several components and sublattices, suitable for computer applications. J. Phys. Chem. Solids 42, 297–301 (1981)Google Scholar
  78. 78.
    J.O. Andersson et al., A compound-energy model of ordering in a phase with sites of different coordination numbers. Acta Metall. 34, 437–445 (1986)Google Scholar
  79. 79.
    A.N. Grundy et al., Calculation of defect chemistry using the CALPHAD approach. Calphad 30(1), 33–41 (2006)Google Scholar
  80. 80.
    M. Yang, Y. Zhong, Z.K. Liu, Defect Analysis and Thermodynamic Modeling of LaCoO3−δ. Solid State Ionics 178, 1072–1032 (2007)Google Scholar
  81. 81.
    S.H. Lee et al., Defect chemistry and phase equilibria of (La1−xCax)FeO3−δ thermodynamic modeling. J. Electrochem. Soc. 160(10), F1103–F1108 (2013)Google Scholar
  82. 82.
    M. Yang, Thermodynamic Modeling of La 1−x Sr x CoO 3−d . Diss. Master Thesis (The Pennsylvania State University, 2006)Google Scholar
  83. 83.
    J.E. Saal, Thermodynamic modeling of phase transformations and defects: From cobalt to doped cobaltate perovskites. Diss. The Pennsylvania State University, (The Pennsylvania State University, 2010), p. 268Google Scholar
  84. 84.
    W. Zhang, B. Rasmus, Investigation of degradation mechanisms of LSCF based SOFC cathodes – by CALPHAD modeling and experiments. Diss. Department of Energy Conversion and Storage, (Technical University of Denmark, 2012)Google Scholar
  85. 85.
    E.P. Karadeniz, Thermodynamic database of the La-Sr-Mn-Cr-O oxide system and applications to solid oxide fuel cells (Diss. ETH Zurich, 2008)Google Scholar
  86. 86.
    F.A. Kroeger, H.J. Vink, Solid State Ionics 3, 307 (1956)Google Scholar
  87. 87.
    M. Seppanen, M. Kyto, P. Taskinen, Defect structure and nonstoichiometry of LaCoO3. Scand. J. Metall. 9, 3–11 (1980)Google Scholar
  88. 88.
    M. Hillert, B. Jansson, B. Sundman, Application of the compound-energy model to oxide systems. Z. Met. 79(2), 81–87 (1988)Google Scholar
  89. 89.
    Scientific Group Thermodata Europe (SGTE), Thermodynamic properties of inorganic materials, in Landolt-Boernstein New Series, Group IV, (Springer, Berlin/Heidelberg, 1999)Google Scholar
  90. 90.
    A.N. Grundy et al., Assessment of the La-Mn-O system. J. Phase Equilib. Diffus. 26(2), 131–151 (2005)Google Scholar
  91. 91.
    O. Redlich, A.T. Kister, Algebraic representations of thermodynamic properties and the classification of solutions. Ind. Eng. Chem. 40(2), 345–348 (1948)Google Scholar
  92. 92.
    M. Asadikiya et al., Thermodynamic modeling and investigation of the oxygen effect on the sintering of B4C. J. Alloys Compd. 699, 1022–1029 (2017)Google Scholar
  93. 93.
    M. Asadikiya et al., The role of CALPHAD approach in the sintering of B4C with SiC as a sintering aid by spark plasma sintering technique. Additive manufacturing and strategic technologies in advanced ceramics. Ceram. Trans. 258, 185–191 (2016)Google Scholar
  94. 94.
    S. Gupta et al., Phase evolution and electrochemical performance of iron doped lanthanum strontium chromite in oxidizing and reducing atmosphere. Int. J. Hydrog. Energy 42, 6262 (2016)Google Scholar
  95. 95.
    H. Sabarou, Y. Zhong, Investigation on the phase stability of perovskite in La-Sr-Cr-Fe-O system. Advances in solid oxide fuel cells and electronic ceramics II. Ceram. Eng. Sci. Proc. 37(3), 127–135 (2017)Google Scholar
  96. 96.
    M. Asadikiya et al., The effect of sintering parameters on spark plasma sintering of B4C. Ceram. Int. 43(14), 11182–11188 (2017)Google Scholar
  97. 97.
    M. Chen, B. Hallstedt, L.J. Gauckler, Thermodynamic modeling of the ZrO2-YO1.5 system. Solid State Ionics 170, 255–274 (2004)Google Scholar
  98. 98.
    L. Kaufman, M. Cohen, Thermodynamics and kinetics of martensitic transformations. Prog. Met. Phys. 7, 165–246 (1958)Google Scholar
  99. 99.
    M. Chen et al., Thermodynamic modeling of the La-Mn-Y-Zr-O system. Calphad 30(4), 489–500 (2006)Google Scholar
  100. 100.
    S. Darvish, Y. Zhong, Quantitative defect chemistry analysis of (La1−xCax) yFeO3±δ perovskite. ECS Trans. 78(1), 565–572 (2017)Google Scholar
  101. 101.
    M. Barsoum, Fundamentals of Ceramics (Institute of Physics Publ, Bristol, 2003)Google Scholar
  102. 102.
    R. Casselton, Low field DC conduction in yttria-stabilized zirconia. Phys. Status Solidi A 2(3), 571–585 (1970)Google Scholar
  103. 103.
    C. Zhang et al., Ionic conductivity and its temperature dependence of atmospheric plasma-sprayed yttria stabilized zirconia electrolyte. Mater. Sci. Eng. B 137(1), 24–30 (2007)Google Scholar
  104. 104.
    R. Pornprasertsuk et al., Predicting ionic conductivity of solid oxide fuel cell electrolyte from first principles. J. Appl. Phys. 98(10), 103513 (2005)Google Scholar
  105. 105.
    A. Ioffe, D. Rutman, S. Karpachov, On the nature of the conductivity maximum in zirconia-based solid electrolytes. Electrochim. Acta 23(2), 141–142 (1978)Google Scholar
  106. 106.
    Z. Lu et al., SrZrO3 formation at the interlayer/electrolyte Interface during (La1−xSrx)1−δCo1−yFeyO3 cathode sintering. J. Electrochem. Soc. 164(10), F3097–F3103 (2017)Google Scholar
  107. 107.
    C. Levy et al., Thermodynamic stabilities of La2Zr2O7 and SrZrO3 in SOFC and their relationship with LSM synthesis processes. J. Electrochem. Soc. 157(11), B1597–B1601 (2010)Google Scholar
  108. 108.
    S. Darvish et al., Weight loss mechanism of (La0.8Sr0.2)0.98MnO3±δ during thermal cycles. Mechanical Properties and Performance of Engineering Ceramics and Composites X: A Collection of Papers Presented at the 39th International Conference on Advanced Ceramics and Composites. (John Wiley & Sons, Inc., 2015)Google Scholar
  109. 109.
    A.N. Grundy et al., Calculation of defect chemistry using the CALPHAD approach. Calphad Comput. Coupling Phase Diagrams Thermochem. 30(1), 33–41 (2006)Google Scholar
  110. 110.
    H. Yokokawa et al., Thermodynamic representation of nonstoichiometric lanthanum manganite. Solid State Ionics 86, 1161–1165 (1996)Google Scholar
  111. 111.
    J.O. Andersson et al., THERMO-CALC & DICTRA, computational tools for materials science. Calphad Comput. Coupling Phase Diagrams Thermochem. 26(2), 273–312 (2002)Google Scholar
  112. 112.
    S. Gupta, M.K. Mahapatra, P. Singh, Lanthanum chromite based perovskites for oxygen transport membrane. Mater. Sci. Eng. R. Rep. 90, 1–36 (2015)Google Scholar
  113. 113.
    T. Frolov, Y. Mishin, Temperature dependence of the surface free energy and surface stress: an atomistic calculation for Cu(110). Phys. Rev. B 79, 1–10 (2009)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Shadi Darvish
    • 1
    • 2
  • Mohammad Asadikiya
    • 1
    • 2
  • Mei Yang
    • 3
  • Yu Zhong
    • 1
    • 2
    • 4
    Email author
  1. 1.Department of Mechanical and Materials EngineeringFlorida International UniversityMiamiUSA
  2. 2.Center for the Study of Matter at Extreme Conditions (CeSMEC)Florida International UniversityMiamiUSA
  3. 3.H.C. Starck Inc.NewtonUSA
  4. 4.Mechanical Engineering DepartmentWorcester Polytechnic InstituteWorcesterUSA

Personalised recommendations