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The Binary Alkali Nitrate and Chloride Phase Diagrams: NaNO3-KNO3, LiNO3-NaNO3, LiNO3-KNO3, and NaCl-KCl

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Abstract

LiNO3-NaNO3, LiNO3-KNO3, NaNO3-KNO3, and NaCl-KCl phase relations were formulated using the regular solution model to obtain desired compositions for their potential application as a heat transfer fluid. The simultaneous nonlinear equations formed were solved numerically using a contour plot technique in Matlab. An algorithm was developed to determine the real roots of the coupled nonlinear equations and subsequent phase diagrams were constructed. The phase diagrams were compared with those predicted using FactSage thermochemical package and literature data from experimental studies. The calculated NaNO3-KNO3 phase diagram shows that this system has a eutectic point at 0.5 mole fraction of KNO3 with a eutectic temperature of 220.85 °C, while the LiNO3-KNO3 system was found to have a eutectic point at 0.44 mole fraction LiNO3 at 137 °C. The LiNO3-NaNO3 system shows a eutectic at 0.524 mole fraction LiNO3 at 192.8 °C, and finally the NaCl-KCl system has a eutectic point at 0.48 mole fraction NaCl at 634 °C. The liquidus and solidus curves obtained fitted close against values obtained from the quasi-chemical model used in FactSage and experimental values from the literature. This study showed that the regular solution model combined with the contour plots approach can sufficiently describe the liquidus–solidus curves of the alkali binary nitrate and chloride systems and could be a useful method for predicting the phase diagrams for higher order alkali nitrates and chlorides.

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References

  1. R.W. Bradshaw, and C.E. Tyner: In 1988 Summer National Meeting, American Institute of Chemical Engineering (AIChE), Denver, Colorado, USA, 1988.

  2. F.S. Barnes, J.G. Levine: Large Energy Storage Systems Handbook. Taylor & Francis Group/CRC Press, Boca Raton, 2011

    Google Scholar 

  3. H Okamoto and TB Massalski, Journal of phase equilibria, 1993, vol. 14, pp. 316-335.

    CAS  Google Scholar 

  4. Ursula R Kattner, JOM, 1997, vol. 49, pp. 14-19.

    CAS  Google Scholar 

  5. Mats Hillert, Calphad, 1980, vol. 4, pp. 1-12.

    CAS  Google Scholar 

  6. K.-C. Chou, Y.A. Chang, Berichte der Bunsengesellschaft für physikalische Chemie, 1989, vol. 93, pp. 735-741.

    CAS  Google Scholar 

  7. Y.A. Chang, S. Chen, F. Zhang, X. Yan, F. Xie, R. Schmid-Fetzer, W.A. Oates, Progr. Mater. Sci., 2004, vol. 49, pp. 313-345.

    CAS  Google Scholar 

  8. James Sangster, Journal of phase equilibria, 2000, vol. 21, pp. 241-268.

    CAS  Google Scholar 

  9. Arthur D Pelton, Armand Gabriel and James Sangster, Journal of the Chemical Society, Faraday Transactions 1: Physical Chemistry in Condensed Phases, 1985, vol. 81, pp. 1167-1172.

    CAS  Google Scholar 

  10. K. H. Jürgen Buschow, R.W. Cahn, M.C. Flemings, B. Ilschner, E.J. Kramer, S. Mahajan, Encyclopedia of Materials: Science and Technology, Elsevier, London, 2001.

    Google Scholar 

  11. HG Wiedemann and G Bayer, Journal of Thermal Analysis and Calorimetry, 1985, vol. 30, pp. 1273-1281.

    CAS  Google Scholar 

  12. J.C. Zhao: Methods for Phase Diagram Determination. Elsevier Science, London, 2011.

    Google Scholar 

  13. H.L. Lukas, S. G Fries, B. Sundman: Computational Thermodynamics: The Calphad Method. Cambridge University Press. Cambridge, 2007.

    Google Scholar 

  14. D. S. Coleman and P. D. A. Lacy, Materials Research Bulletin, 1967, vol. 2, pp. 935-938.

    CAS  Google Scholar 

  15. A.P. Miodownik, N. Saunders, P. Nash, B. Sundman. Applications of Thermodynamics in the Synthesis and Processing of Materials. TMS, Warrendale, 1995.

    Google Scholar 

  16. Bo Sundman, Bo Jansson and Jan-Olof Andersson, Calphad, 1985, vol. 9, pp. 153-190.

    CAS  Google Scholar 

  17. H. L. Lukas, E. Th Henig and B. Zimmermann, Calphad, 1977, vol. 1, pp. 225-236.

    CAS  Google Scholar 

  18. H. L. Lukas, J. Weiss and E. Th Henig, Calphad, 1982, vol. 6, pp. 229-251.

    CAS  Google Scholar 

  19. Mats Hillert and Bo Sundman, Calphad, 2001, vol. 25, pp. 599-605.

    CAS  Google Scholar 

  20. E.M. Levin, and H.F. McMurdie: Phase Diagrams for Ceramists, 1975 Supplement, American Ceramic Society, Columbus, OH, 1975.

    Google Scholar 

  21. J.M. Prausnitz, R.N. Lichtenthaler, E.G. de Azevedo: Molecular Thermodynamics of Fluid-Phase Equilibria. Pearson Education, London, 1998.

    Google Scholar 

  22. Jan V Sengers: Applied Thermodynamics of Fluids. Royal Society of Chemistry, 2010.

    Google Scholar 

  23. Zahra Nickmand and Seyed Foad Aghamiri, Journal of Dispersion Science and Technology, 2010, vol. 31, pp. 1638-1647.

    CAS  Google Scholar 

  24. Evelyne Neau, Joan Escandell and Christophe Nicolas, Industrial & Engineering Chemistry Research, 2010, vol. 49, pp. 7580-7588.

    CAS  Google Scholar 

  25. WANG Yu, SHAO Guoquan, LI Shaobo, SUN Yimin and QIAO Zhiyu, Journal of Rare Earths, 2009, vol. 27, pp. 300-303.

    Google Scholar 

  26. Grant M Wilson, Journal of the American Chemical Society, 1964, vol. 86, pp. 127-130.

    CAS  Google Scholar 

  27. Koichiro Nakanishi, Industrial & Engineering Chemistry Fundamentals, 1970, vol. 9, pp. 449-453.

    CAS  Google Scholar 

  28. Milton Blander and SJ Yosim, The Journal of Chemical Physics, 1963, vol. 39, pp. 2610-2616.

    CAS  Google Scholar 

  29. ML Saboungi, H Schnyders, MS Foster and M Blander, The Journal of Physical Chemistry, 1974, vol. 78, pp. 1091-1096.

    CAS  Google Scholar 

  30. D. R. Waldbaum, Geochimica et Cosmochimica Acta, 1969, vol. 33, pp. 1415-1427.

    CAS  Google Scholar 

  31. P.D. Myers Jr., D.Y. Goswami, Applied Thermal Engineering, 2016, vol. 109, pp. 889-900.

    Google Scholar 

  32. C. M. McDonald and C. A. Floudas, Computers & Chemical Engineering, 1995, vol. 19, pp. 1111-1139.

    CAS  Google Scholar 

  33. J.M. Ortega, W.C. Rheinboldt: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York, 1970.

    Google Scholar 

  34. M. J. Maeso and J. Largo, Thermochimica Acta, 1993, vol. 223, pp. 145-156.

    CAS  Google Scholar 

  35. D. A. Nissen and B. H. Van Domelen, The Journal of Physical Chemistry, 1975, vol. 79, pp. 2003-2007.

    CAS  Google Scholar 

  36. Leroy S. Hersh and O. J. Kleppa, The Journal of Chemical Physics, 1965, vol. 42, pp. 1309-1322.

    CAS  Google Scholar 

  37. O. J. Kleppa, R. B. Clarke and L. S. Hersh, The Journal of Chemical Physics, 1961, vol. 35, pp. 175-180.

    CAS  Google Scholar 

  38. O. J. Kleppa and L. S. Hersh, The Journal of Chemical Physics, 1961, vol. 34, pp. 351-358.

    CAS  Google Scholar 

  39. O. J. Kleppa, The Journal of Physical Chemistry, 1960, vol. 64, pp. 1937-1940.

    CAS  Google Scholar 

  40. C. M. Kramer and C. J. Wilson, Thermochimica Acta, 1980, vol. 42, pp. 253-264.

    CAS  Google Scholar 

  41. Osami Abe, Taizo Utsunomiya and Yoshio Hoshino, Thermochimica Acta, 1984, vol. 78, pp. 251-260.

    CAS  Google Scholar 

  42. Xuejun Zhang, Jun Tian, Kangcheng Xu and Yici Gao, Journal of Phase Equilibria, 2003, vol. 24, pp. 441-446.

    CAS  Google Scholar 

  43. D Mantha, T Wang and RG Reddy, Journal of phase equilibria and diffusion, 2012, vol. 33, pp. 110-114.

    CAS  Google Scholar 

  44. Kevin Coscia, Tucker Elliott, Satish Mohapatra, Alparslan Oztekin and Sudhakar Neti, Journal of Solar Energy Engineering, 2013, vol. 135, p. 021011.

    Google Scholar 

  45. A.G. Bergman, S.I. Berul: Izv. Sekt., 1952, vol. 21, pp. 178–83.

    CAS  Google Scholar 

  46. W.M. Madgin, H.V.A. Briscoe, R.S. Hughesdon, H.G. Smith, J. Read, S. Glasstone, S. Biggs, F.G. Pope, J. Chem. Soc. Trans., 1923, vol. 123, pp. 2914-2916.

    CAS  Google Scholar 

  47. S.I. Berul, A.G. Bergman: Izv. Sekt, 1954, vol. 25, pp. 218-35.

    CAS  Google Scholar 

  48. AN Kirgintsev and VI Kosyakov, Izv. Akad. Nauk. SSSR, Ser. Khim, 1968, vol. 10, pp. 2208-13.

    Google Scholar 

  49. William Klement, Journal of Inorganic and Nuclear Chemistry, 1974, vol. 36, pp. 1916-1918.

    CAS  Google Scholar 

  50. D.J. Rogers and G.J. Janz, J. Chem. Eng. Data, 1982, vol. 27, pp. 424–428.

    CAS  Google Scholar 

  51. O. Greis, K. M. Bahamdan and B. M. Uwais, Thermochimica Acta, 1985, vol. 86, pp. 343-350.

    CAS  Google Scholar 

  52. D. Sergeev, D. Kobertz and M. Müller, Thermochimica Acta, 2015, vol. 606, pp. 25-33.

    CAS  Google Scholar 

  53. Markus Broström, Sonja Enestam, Rainer Backman and Kari Mäkelä, Fuel Processing Technology, 2013, vol. 105, pp. 142-148.

    Google Scholar 

  54. ER Van Artsdalen and IS Yaffe, The Journal of Physical Chemistry, 1955, vol. 59, pp. 118-127.

    Google Scholar 

  55. R. Benages-Vilau, T. Calvet, M.A. Cuevas-Diarte, H.A.J. Oonk, Phase Transit, 2015, 89, pp. 1-20.

    Google Scholar 

  56. HAJ Oonk, Pure and Applied Chemistry, 2001, vol. 73, pp. 807-823.

    CAS  Google Scholar 

  57. Fadi Awawdeh, Numerical Algorithms, 2010, vol. 54, pp. 395-409.

    Google Scholar 

  58. Ebrahim Pourjafari and Hamed Mojallali, Swarm and Evolutionary Computation, 2012, vol. 4, pp. 33-43.

    Google Scholar 

  59. C.R. Gwaltney, Y. Lin, L.D. Simoni, M.A. Stadtherr: Handbook of Granular Computing. Wiley, Chichester, 2008, pp. 81-96.

    Google Scholar 

  60. R.T. Rockafellar: Convex Analysis. Princeton University Press, Princeton, 2015.

    Google Scholar 

  61. S. Boyd, L. Vandenberghe: Convex Optimization. Cambridge University Press, Cambridge, 2004.

    Google Scholar 

  62. H. Tuy: Convex Analysis and Global Optimization. Springer US, 1998.

    Google Scholar 

  63. J.-B. Hiriart-Urruty, C. Lemaréchal: Convex Analysis and Minimization Algorithms I: Fundamentals. Springer Science & Business Media, New York, 2013.

    Google Scholar 

  64. J. Borwein, A.S. Lewis: Convex Analysis and Nonlinear Optimization: Theory and Examples. Springer Science & Business Media, New York, 2010.

    Google Scholar 

  65. I. Ekeland, R. Temam: Convex Analysis and Variational Problems. SIAM, Philadelphia, 1999.

    Google Scholar 

  66. Y. Nesterov: Introductory Lectures on Convex Optimization: A Basic Course. Springer Science & Business Media, New York, 2013.

    Google Scholar 

  67. I.K. Karpov, K.V. Chudnenko, D.A. Kulik, O.V. Avchenko, and V.A. Bychinskii: System, 2001, 3, 09.

    Google Scholar 

  68. M.B. Mohammad, G. Brooks, M.A. Rhamdhani: in Applications of Process Engineering Principles Materials Processing, Energy and Environmental Technologies: An EPD Symposium in Honor of Professor Ramana G. Reddy. S. Wang, M.L. Free, A. Shafiq, Z. Mingming, and P.R. Taylor, Springer International Publishing, Cham, 2017, pp 531–39.

  69. (CRCT-ThermFact Inc. & GTT-Technologies FACTSAGE©, 2014). http://www.factsage.com/, Accessed 6 August 2014.

  70. J. H. Hildebrand, The Journal of the American Chemical Society, 1929, vol. 51, pp. 66-80.

    CAS  Google Scholar 

  71. Bo Sundman and John Ågren, Journal of Physics and Chemistry of Solids, 1981, vol. 42, pp. 297-301.

    CAS  Google Scholar 

  72. J. H. Hildebrand, Journal of the American Chemical Society, 1916, vol. 38, pp. 1452-1473.

    CAS  Google Scholar 

  73. J. Vidal: Thermodynamics: Applications in Chemical Engineering and the Petroleum Industry, Editions Technip, Paris, 2003.

    Google Scholar 

  74. E.A. Guggenheim: Proceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences, 1935, vol. 148, pp. 304–12.

  75. C Vallet, The Journal of Chemical Thermodynamics, 1972, vol. 4, pp. 105-114.

    CAS  Google Scholar 

  76. S. Stølen, T. Grande: Chemical Thermodynamics of Materials: Macroscopic and Microscopic Aspects. Wiley, New York, 2004.

    Google Scholar 

  77. R. DeHoff: Thermodynamics in Materials Science, 2nd edn. Taylor & Francis, New York, 2006.

    Google Scholar 

  78. Vladimir Danek: Physico-chemical analysis of molten electrolytes. 1st ed. Elsevier Science, Amsterdam, Nehterlands, 2006.

    Google Scholar 

  79. I. Prigogine and R. Defay: Chemical Thermodynamics. Longmans, Green 1954.

    Google Scholar 

  80. W.D. Callister, D.G. Rethwisch: Fundamentals of Materials Science and Engineering: An Integrated Approach. Wiley, New York, 2012.

    Google Scholar 

  81. CW Bale, P Chartrand, SA Degterov, G Eriksson, K Hack, R Ben Mahfoud, J Melançon, AD Pelton and S Petersen, Calphad, 2002, vol. 26, pp. 189-228.

    CAS  Google Scholar 

  82. C. W. Bale, E. Bélisle, P. Chartrand, S. A. Decterov, G. Eriksson, A. E. Gheribi, K. Hack, I. H. Jung, Y. B. Kang, J. Melançon, A. D. Pelton, S. Petersen, C. Robelin, J. Sangster, P. Spencer and M. A. Van Ende, Calphad, 2016, vol. 54, pp. 35-53.

    CAS  Google Scholar 

  83. Xuejun Zhang, Kangcheng Xu and Yici Gao, Thermochimica Acta, 2002, vol. 385, pp. 81-84.

    CAS  Google Scholar 

  84. H. Ohtani, J. Mochinaga, K. Igarashi, Denki Journal, 1981, vol. 49, p. 19.

    Google Scholar 

  85. CW Bale, E Bélisle, P Chartrand, SA Decterov, G Eriksson, K Hack, I-H Jung, Y-B Kang, J Melançon and AD Pelton, Calphad, 2009, vol. 33, pp. 295-311.

    CAS  Google Scholar 

  86. K.E. Atkinson: An Introduction to Numerical Analysis. Wiley, New York, 2008.

    Google Scholar 

  87. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery: Numerical Recipes in C. Cambridge University Press, Cambridge, 1996.

    Google Scholar 

  88. É. Walter: Numerical Methods and Optimization. Springer, New York, 2014.

    Google Scholar 

  89. J.E. Dennis Jr., R.B. Schnabel: Numerical Methods for Unconstrained Optimization and Nonlinear Equations. SIAM, Philadelphia, 1996.

    Google Scholar 

  90. W.C. Rheinboldt: Methods for Solving Systems of Nonlinear Equations. SIAM, Philadelphia, 1998.

    Google Scholar 

  91. Charles G Broyden, Mathematics of computation, 1965, vol. 19, pp. 577-593.

    Google Scholar 

  92. J-F Tsai and M-H Lin, Engineering Optimization, 2007, vol. 39, pp. 649-659.

    Google Scholar 

  93. J-B Hiriart-Urruty and M Torki, Applied Mathematics and Optimization, 2002, vol. 45, pp. 169-184.

    Google Scholar 

  94. R.H. Hardaway: Proceedings of the December 9–11, 1968, Fall Joint Computer Conference, Part I, ACM. 1968. pp. 105–13.

  95. M.S. Petković, B. Neta, L.D. Petković, J. Džunić, Appl. Math. Comput., 2014, vol. 226, pp. 635-660.

    Google Scholar 

  96. A.R. Conn, N.I.M. Gould, P.L. Toint: Trust Region Methods. SIAM, Philadelphia, 2000.

    Google Scholar 

  97. W.H. Press: Numerical Recipes 3rd Edition: The Art of Scientific Computing. Cambridge University Press, Cambridge, 2007

    Google Scholar 

  98. L.C.W. Dixon, G.P. Szegö: Towards Global Optimisation 2. North-Holland Pub. Co., Amsterdam, 1978.

    Google Scholar 

  99. D.P. Bertsekas: Nonlinear programming. Athena Scientific, Belmont, 1999

    Google Scholar 

  100. MATLAB User’s Guide, Inc., Natick, 1998, vol. 5, p. 333.

  101. J.H. Mathews, K.D. Fink: Numerical Methods using MATLAB. Prentice Hall, Upper Saddle River, 1999.

    Google Scholar 

  102. W. Sun, Y.-X. Yuan: Optimization Theory and Methods: Nonlinear Programming. Springer Science & Business Media, New York, 2006.

    Google Scholar 

  103. J.W. Harris, H. Stöcker: Handbook of Mathematics and Computational Science. Springer Science & Business Media, New York, 1998.

    Google Scholar 

  104. Y Takahashi, R Sakamoto and M Kamimoto, International journal of thermophysics, 1988, vol. 9, pp. 1081-1090.

    CAS  Google Scholar 

  105. P.D. Myers, D.Y. Goswami, E. Stefanakos: J. Solar Energy Eng., 2015, vol. 137, p. 041002.

    Google Scholar 

  106. Q. Peng, X. Yang, X. Wei, J. Yang, and J. Ding, J. Lu: Proceedings of the Materials for Renewable Energy and Environment (ICMREE), 2013 International Conference on, IEEE, 2014, pp. 496–99.

  107. H.A.J. Oonk, M.T. Calvet: Equilibrium Between Phases of Matter: Phenomenology and Thermodynamics. Springer Science & Business Media, New York, 2007.

    Google Scholar 

  108. R. D. Weir, T.W. de Loos: Measurement of the Thermodynamic Properties of Multiple Phases. Gulf Professional Publishing, Houston, 2005.

    Google Scholar 

  109. Y Dessureault, J Sangster and AD Pelton, Journal de chimie physique, 1990, vol. 87, pp. 407-453.

    CAS  Google Scholar 

  110. H.V.A. Briscoe, W.M. Madgin, J. Chem. Soc. Trans., 1923, vol. 123, pp. 1608-1618.

    CAS  Google Scholar 

  111. Adelheid Kofler, Monatshefte für Chemie und verwandte Teile anderer Wissenschaften, 1955, vol. 86, pp. 643-652.

    CAS  Google Scholar 

  112. DJ Hussink, Z. Phys. Chem, 1900, vol. 32, pp. 536-40.

    Google Scholar 

  113. Kangcheng Xu, Journal of Physics and Chemistry of Solids, 1999, vol. 60, pp. 5-11.

    Google Scholar 

  114. SG Ingle and SR Ghadekar, Journal of Physics D: Applied Physics, 1978, vol. 11, p. 913.

    CAS  Google Scholar 

  115. M.B. Mohammad, G.A. Brooks, M.A. Rhamdhani, Metall. Mater. Trans. B, 2018, vol. 49, pp. 1482-1498.

    Google Scholar 

  116. M.B. Mohammad, G.A. Brooks, M. A. Rhamdhani, Renewable Energy, 2016, 104, pp. 76-87.

    Google Scholar 

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Acknowledgments

The authors want to thank Professor Peter Cadusch for his numerical solution approach and guidance. And thanks goes to Bapin Rout and Kamrul Hasan Rakib of MEPD, the Swinburne University of Technology for their valuable discussions on numerous times.

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The authors declare that there are no conflicts of interest.

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Manuscript submitted September 19, 2017.

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Mohammad, M.B., Cadusch, P., Brooks, G.A. et al. The Binary Alkali Nitrate and Chloride Phase Diagrams: NaNO3-KNO3, LiNO3-NaNO3, LiNO3-KNO3, and NaCl-KCl. Metall Mater Trans B 49, 3580–3593 (2018). https://doi.org/10.1007/s11663-018-1408-3

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