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Viscosity of liquid alloys: generalization of Andrade’s equation

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Abstract

The Andrade relation for the viscosity of liquid metals has been reformulated in terms of the Debye temperature for liquid metals. This semi-empirical relation has been extended to obtain a relation to calculate the composition and temperature dependence of the viscosity of liquid alloys using parameters which can be determined experimentally. The important inputs are the enthalpy of formation, ΔH, and the excess volume of mixing, ΔΩ. The composition dependence of the viscosity and its deviation from linear behavior could be positive or negative depending on the sign and magnitude of ΔH and ΔΩ. Several limiting cases of the semi-empirical relation for the viscosity of liquid alloys are compared and discussed. The results of the semi-empirical relation for viscosity isotherms for binary and ternary liquid alloys are mostly in reasonable agreement with available experimental results.

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References

  1. Brooks RF, Dinsdale AT, Quested PN (2005) Meas Sci Technol 16:354

    Article  CAS  Google Scholar 

  2. Battezzati L, Greer AL (1989) Acta Metall 37:1791

    Article  CAS  Google Scholar 

  3. Iida T, Guthrie RL (1988) The physical properties of liquid metals. Clarendon, Oxford

    Google Scholar 

  4. Chhabra RP, Seth DK (1990) Z Metallkd 81:264

    CAS  Google Scholar 

  5. Kaptay G (2005) Z Metallkd 96:24

    CAS  Google Scholar 

  6. Moelwyn-Hughes EA (1964) Physical chemistry. Pergamon, Oxford

    Google Scholar 

  7. Kozlov LYa, Romanov LM, Petrov NN (1983) Izv Vysch Uch Zav, Chernaya Metallurgica 7:7

  8. Kucharski M (1986) Z Metallkd 77:393

    CAS  Google Scholar 

  9. Seetharam S, Sichen D (1994) Metall Mater Trans 25B:589

    Google Scholar 

  10. Terzieff P (2009) Phys B 404:2039

    Article  CAS  Google Scholar 

  11. Hirai M (1993) Iron Steel Inst Jpn Int 33:251

    Article  CAS  Google Scholar 

  12. Kaptay G (2003) Proc of microCAD Inter Conf Section Metallurgy, Univ of Miskolc Hungary, p 23

  13. Gruner S, Hoyer W (2008) J Alloys Compd 460:496

    Article  CAS  Google Scholar 

  14. Gruner S, Marczinke J, Hoyer W (2009) J Non-Cryst Solids 355:880

    Article  CAS  Google Scholar 

  15. Wunderlich KR, Fecht H-J (2011) Int J Mater Res 102:1164

    Article  CAS  Google Scholar 

  16. Budai I, Benkö MZ, Kaptay G (2005) Mater Sci Forum 473–474:309

    Article  Google Scholar 

  17. Budai I, Benkö MZ, Kaptay G (2007) Mater Sci Forum 537–538:489

    Article  Google Scholar 

  18. Zivkovic D (2006) Z Metallkd 97:89

    CAS  Google Scholar 

  19. Zivkovic D (2009) Z Metallkd 99:748

    Google Scholar 

  20. Zivkovic D (2008) Metall Mater Trans 39B:395

    CAS  Google Scholar 

  21. Terzieff P (2010) Phys B 405:2668

    Article  CAS  Google Scholar 

  22. Knott S, Terzieff P (2010) Int J Mater Res 101:834

    Article  CAS  Google Scholar 

  23. Andrade ENC (1934) Phil Mag 17:497

    CAS  Google Scholar 

  24. Sommer F, Singh RN, Witusiewicz V (2001) J Alloys Comp 325:118

    Article  CAS  Google Scholar 

  25. Faber TF (1972) An introduction to the theory of liquid metals. Cambridge University Press, London

    Google Scholar 

  26. Singh RN, Sommer F (1998) Phys Chem Liq 36:17

    Article  CAS  Google Scholar 

  27. Iida I, Morita Z, Takeuchi S (1975) J Japan Inst Metals 39:1169

    CAS  Google Scholar 

  28. de Boer FR, Boom R, Mattens WC, Miedema AR, Viessen AK (1988) Cohesion in metals: transition metals alloys. North Holland, Amsterdam

    Google Scholar 

  29. Kohler F (1960) Monatsh Chem 91:738

    Article  CAS  Google Scholar 

  30. Tyrell HJ, Harris KR (1984) Diffusion in liquids. Butterworth, London

    Google Scholar 

  31. Ertl H, Ghai RK, Dullien FAL (1974) AIChE J 20:1

    Article  CAS  Google Scholar 

  32. Hiss TG, Cussler EL (1973) AIChE J 19:693

    Article  Google Scholar 

  33. Davies GA, Ponter AB, Craine K (1967) Can J Chem Eng 4:372

    Article  Google Scholar 

  34. Gebhard E, Becker M (1951) Z Metallkd 42:111

    Google Scholar 

  35. Predel B (1992–1998) Phase equilibria, crystallographic and thermodynamic data of binary alloys. Madelung O (ed) Landolt-Börnstein, Zahlenwerte und Funktionen aus Naturwissenschaften und Technik, Neue Serie, Band 5. Springer, Berlin

  36. Gebhard E, Wörwag G (1951) Z Metallkd 42:358

    Google Scholar 

  37. Sebo P, Galloiis B, Lupis CHP (1974) Metall Trans 8B:691

    Google Scholar 

  38. Nakajima H (1976) Trans Jpn Inst Met 17:403

    CAS  Google Scholar 

  39. Gebhard E, Becker EM, Dorner S (1954) Z Metallkd 45:83

    Google Scholar 

  40. Frohberg MG, Özbaji K (1981) Z Metallkd 72:630

    CAS  Google Scholar 

  41. Gomez M, Martin-Garin L, Ebert H, Bedon P, Desre P (1976) Z Metallkd 67:131

    CAS  Google Scholar 

  42. Vollmann J, Riedel D (1996) J Phys Condens Matter 8:6175

    Article  CAS  Google Scholar 

  43. Walsdorfer H, Arpshofen I, Predel B (1988) Z Metallkd 79:503

    CAS  Google Scholar 

  44. Predel B, Emmam A (1969) J Less-Common Met 18:385

    Article  CAS  Google Scholar 

  45. Walsdorfer H, Arpshofen I, Predel B (1988) Z Metallkd 79:654

    CAS  Google Scholar 

  46. Menz VW, Sauerwald F (1966) Z Phys Chem 232:134

    CAS  Google Scholar 

  47. Djmilli B, Martin-Garin L, Martin-Garin R, Desre P (1981) J Less-Common Met 79:29

    Article  Google Scholar 

  48. Crawly CF (1972) Metall Trans 3:971

    Article  Google Scholar 

  49. Gebhardt E, Becker M, Schäfer S (1952) Z Metallkd 43:292

    CAS  Google Scholar 

  50. Watanabe S, Saito T (1972) Trans Jpn Inst Met 13:186

    Google Scholar 

  51. Predel B, Arrpshofen I (1978) Forschungsberichte des Landes NRW, Nr 2714. Rau J (ed), Westdeutscher Verlag, Opladen

  52. Roeder A, Morawietz W (1956) Z Metallkd 47:734

    Google Scholar 

  53. Degenkolb J, Sauerwald F (1952) Z Anorg Chem 270:317

    Article  Google Scholar 

  54. Predel B, Arpshofen I (1974) Z Naturforsch 29a:1206

  55. Gebhardt E, Köstlin K (1957) Z Metallkd 48:636

    CAS  Google Scholar 

  56. Predel B, Emmam A (1969) Mater Sci Eng 4:287

    Article  CAS  Google Scholar 

  57. Berthou PE, Tougas R (1968) J Less-Common Met 16:465

    Article  CAS  Google Scholar 

  58. Gebhardt E, Wörwag G (1952) Z Metallkd 43:106

    CAS  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Physics, Sultan Quaboos University, Muscat, Oman

    Ram Nadan Singh

  2. Max Planck Institute for Intelligent Systems (formerly: Max Planck Institute for Metals Research), Heisenbergstr. 3, 70569, Stuttgart, Germany

    Ferdinand Sommer

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  1. Ram Nadan Singh
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  2. Ferdinand Sommer
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Correspondence to Ferdinand Sommer.

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Dedicated to Prof. Dr. Herbert Ipser on the occasion of his 65th birthday.

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Singh, R.N., Sommer, F. Viscosity of liquid alloys: generalization of Andrade’s equation. Monatsh Chem 143, 1235–1242 (2012). https://doi.org/10.1007/s00706-012-0728-2

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  • DOI: https://doi.org/10.1007/s00706-012-0728-2

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