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Thermodynamic calculation of self-diffusion in sodium chloride

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Abstract

Using the available pressure–volume–temperature equation of state of sodium chloride, we show that the self-diffusion coefficients of sodium and chloride in sodium chloride as a function of temperature and pressure can be successfully reproduced in terms of bulk elastic and expansivity data. We use a thermodynamic model that interconnects point-defect parameters with bulk properties. Our calculated diffusion coefficients and point-defect parameters, including activation enthalpy, activation entropy, and activation volume, well agree with reported experimental results when uncertainties are considered. Furthermore, the ionic conductivity of sodium chloride inferred from our predicted diffusivities of sodium through the Nernst–Einstein equation is compared with previous experimental data.

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References

  • Alexopoulos KD, Varotsos PA (1981) Calculation of diffusion coefficients at any temperature and pressure from a single measurement: II. Heterodiffusion. Phys Rev B 24:3606–3609

    Article  Google Scholar 

  • Birch F (1986) Equation of state and thermodynamic parameters of NaCl to 300 kbar in the high-temperature domain. J Geophys Res 91(B5):4949–4954

    Article  Google Scholar 

  • Brown JM (1999) The NaCl pressure standard. J Appl Phys 86(10):5801–5808

    Article  Google Scholar 

  • Chroneos A, Vovk RV (2015a) Modeling indium diffusion in germanium by connecting point defect parameters with bulk properties. J Mater Sci Mater Electron 26(4):2113–2116

    Article  Google Scholar 

  • Chroneos A, Vovk RV (2015b) Connecting bulk properties of germanium with the behavior of self- and dopant diffusion. Mater Sci Semicond Proc 180:277–283

    Google Scholar 

  • Chroneos A, Vovk RV (2015c) Modeling self-diffusion in UO2 and ThO2 by connecting point defect parameters with bulk properties. Solid State Ion 274:1–3

    Article  Google Scholar 

  • Cooper MWD, Grimes RW, Fitzpatrick ME, Chroneos A (2015) Modeling oxygen self-diffusion in UO2 under pressure. Solid State Ion 286:26–30

    Article  Google Scholar 

  • Decker DL (1971) High-pressure equation of state for NaCl, KCl, and CsCl. J Appl Phys 42:3239–3244

    Article  Google Scholar 

  • Etzel HW, Maurer RJ (1950) The concentration and mobility of vacancies in sodium chloride. J Chem Phys 18(8):1003–1007

    Article  Google Scholar 

  • Ganniari-Papageorgiou E, Fitzpatrick ME, Chroneos A (2015) Germanium diffusion in aluminium: connection between point defect parameters with bulk properties. J Mater Sci: Mater Electron 26(11):8421–8424

    Google Scholar 

  • Harrison LG, Morrison JA, Rudham R (1958) Chloride ion diffusion in sodium chloride. Trans Faraday Soc 54:106–115

    Article  Google Scholar 

  • Laurance N (1960) Self-diffusion of the chloride ion in sodium chloride. Phys Rev 120(1):57–62

    Article  Google Scholar 

  • Mapother D, Crooks HN, Maurer R (1950) Self-diffusion of sodium in sodium chloride and sodium bromide. J Chem Phys 18(9):1231–1236

    Article  Google Scholar 

  • Martin G, Lazarus D, Mitchell JL (1973) Pressure dependence of self-diffusion of Na22 in NaCl. Phys Rev B 8(4):1726–1731

    Article  Google Scholar 

  • Matsui M (2009) Temperature–pressure–volume equation of state of the B1 phase of sodium chloride. Phys Earth Planet Inter 174:93–97

    Article  Google Scholar 

  • Matsui M, Higo Y, Okamoto Y, Irifune T, Funakoshi K (2012) Simultaneous sound velocity and density measurements of NaCl at high temperatures and pressures: Application as a primary pressure standard. Am Miner 97:1670–1675

    Article  Google Scholar 

  • Papathanassiou AN, Sakellis I (2010) Correlation of the scaling exponent γ of the diffusivity-density function in viscous liquids with their elastic properties. J Chem Phys 132(15):154503

    Article  Google Scholar 

  • Philibert J (2006) Some thoughts and/or questions about activation energy and pre-exponential factor. Defect Diffus Forum 249:61–72

    Google Scholar 

  • Saltas V, Vallianatos F (2015) Thermodynamic calculations of self- and hetero-diffusion parameters in germanium. Mater Chem Phys 163:507–511

    Article  Google Scholar 

  • Shewmon PG (1963) Diffusion in Solids. McGraw-Hill, New York

    Google Scholar 

  • Song T, Sun XW, Liu ZJ, Li JF, Tian JH (2012) Isothermal bulk modulus and its first pressure derivative of NaCl at high pressure and high temperature. Chin Phys B 21(3):037103

    Article  Google Scholar 

  • Tilley RJD (2008) Defects in solids. Wiley, New Jersey, pp 231–232

    Book  Google Scholar 

  • Vallianatos F (1998) Analysis of self- and heterodiffusion data in ferromagnetic and paramagnetic α-iron. Geol Carpath 49(1):51–55

    Google Scholar 

  • Vallianatos F, Eftaxias K (1992) The application of the cBΩ model for the calculation of the variation of the activation volume for creep with depth in the Earth’s lower mantle. Phys Earth Planet Inter 71:141–146

    Article  Google Scholar 

  • Vallianatos F, Eftaxias K (1994) Some aspects on estimation methods for activation volume. Acta Geophys Pol XLII(1):13–22

    Google Scholar 

  • Vallianatos F, Saltas V (2014) Application of the cBΩ model to the calculation of diffusion parameters of He in olivine. Phys Chem Miner 41:181–188

    Article  Google Scholar 

  • Vallianatos F, Eftaxias K, Vasilikou-Dova A (1995) A material science approach for the evaluation of the rheological state into the Earth’s lower mantle. Radiat Eff Defects Solids 137:217–221

    Article  Google Scholar 

  • Varotsos PA (2007a) Comparison of models that interconnect point defect parameters in solids with bulk properties. J Appl Phys 101(12):123503

    Article  Google Scholar 

  • Varotsos PA (2007b) Defect volumes and the equation of state in α-PbF2. Phys Rev B 76(9):092106

    Article  Google Scholar 

  • Varotsos PA (2007c) Calculation of point defect parameters in diamond. Phys Rev B 75(17):172107

    Article  Google Scholar 

  • Varotsos PA (2008) Point defect parameters in β-PbF2 revisited. Solid State Ion 179(11–12):438–441

    Article  Google Scholar 

  • Varotsos PA, Alexopoulos KD (1980) Calculation of diffusion coefficients at any temperature and pressure from a single measurement: I. Self-diffusion. Phys Rev B 22(6):3130–3134

    Article  Google Scholar 

  • Varotsos PA, Alexopoulos KD (1986) Thermodynamics of point defects and their relation with bulk properties. North Holland, Amsterdam

    Google Scholar 

  • Varotsos PA, Ludwig W, Alexopoulos KD (1978) Calculation of the formation volume of vacancies in solids. Phys Rev B 18(6):2683–2691

    Article  Google Scholar 

  • Wert C, Zener C (1949) Interstitial atomic diffusion coefficients. Phys Rev 76(8):1169–1175

    Article  Google Scholar 

  • Zener C (1951) Theory of Do for atomic diffusion in metals. J Appl Phys 22:372–375

    Article  Google Scholar 

  • Zhang BH (2012) Diffusion of hydrogen in (Mg, Fe)2SiO4 and high pressure polymorphs refined by the cBΩ model. J Asian Earth Sci 54–55:9–17

    Article  Google Scholar 

  • Zhang BH (2014) Calculation of self-diffusion coefficients in iron. AIP Adv 4(1):017128

    Article  Google Scholar 

  • Zhang BH, Shan SM (2015a) Application of the cBΩ model to the calculation of diffusion parameters of Si in silicates. Geochem Geophys Geosyst 16:705–718

    Article  Google Scholar 

  • Zhang BH, Shan SM (2015b) Thermodynamic calculations of Fe–Mg interdiffusion in (Mg, Fe)2SiO4 polymorphs and perovskite. J Appl Phys 117(5):054906

    Article  Google Scholar 

  • Zhang BH, Wu XP (2012) Calculation of self-diffusion coefficients in diamond. Appl Phys Lett 100(5):051901

    Article  Google Scholar 

  • Zhang BH, Wu XP (2013) Diffusion of aluminum in MgO: a thermodynamic approach. Chin Phys B 22(5):056601

    Article  Google Scholar 

  • Zhang BH, Wu XP, Xu JS, Zhou RL (2010) Application of the cBΩ model for the calculation of oxygen self-diffusion coefficients in minerals. J Appl Phys 108(5):053505

    Article  Google Scholar 

  • Zhang BH, Wu XP, Zhou RL (2011) Calculation of oxygen self-diffusion coefficients in Mg2SiO4 polymorphs and MgSiO3 perovskite based on the compensation law. Solid State Ionics 186(1):20–28

    Article  Google Scholar 

  • Zhang BH, Shan SM, Wu XP (2015) Modeling H, Na, and K diffusion in plagioclase feldspar by relating point defect parameters to bulk properties. Phys Chem Miner. doi:10.1007/s00269-015-0782-5

    Google Scholar 

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Acknowledgments

This study was supported by the 1000Plan Program for Young Talents, Hundred Talent Program of CAS and NSF of China (41303048) to B.Z., and NSF of China (41472048) to S.S.

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Authors and Affiliations

  1. Key Laboratory for High-Temperature and High-Pressure Study of the Earth’s Interior, Institute of Geochemistry, Chinese Academy of Sciences, Guiyang, 550081, Guizhou, People’s Republic of China

    Baohua Zhang & Shuangming Shan

  2. School of Mathematics and Physics, Anyang Institute of Technology, Anyang, 455000, People’s Republic of China

    Chengbo Li

Authors
  1. Baohua Zhang
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  2. Chengbo Li
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  3. Shuangming Shan
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Correspondence to Baohua Zhang.

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Zhang, B., Li, C. & Shan, S. Thermodynamic calculation of self-diffusion in sodium chloride. Phys Chem Minerals 43, 371–376 (2016). https://doi.org/10.1007/s00269-016-0801-1

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  • DOI: https://doi.org/10.1007/s00269-016-0801-1

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