Equilibrium vacancies and thermophysical properties of metals

Yaakov Kraftmakher

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218 Scopus citations


Despite a significant progress in studies of point defects, some important problems have not received unambiguous solutions. One of the most practically important questions relates to equilibrium concentrations of point defects. It is indeed surprising that this fundamental problem is still under debate. There exist two opposite viewpoints on equilibrium point defects in metals: (1)Defect contributions to the physical properties of metals at high temperatures are small and cannot be separated from the effects of anharmonicity. The only suitable methods are the positron-annihilation spectroscopy providing enthalpies of the vacancy formation and the differential dilatometry yielding equilibrium vacancy concentrations. The equilibrium vacancy concentrations at the melting points are in the range 10-4 to 10-3. Reasonable values of the formation enthalpies deduced from the nonlinear increase in the high-temperature specific heat of metals are accidental and the derived defect concentrations are improbably large, so that this approach is generally erroneous. (2)In many cases, defect contributions to the specific heat of metals are much larger than nonlinear effects of the anharmonicity and can be separated without crucial errors. This approach is quite adequate for determination of the defect parameters, especially, the equilibrium vacancy concentrations. The equilibrium concentrations at the melting points are of the order of 10-3 in low-melting-point metals and of 10-2 in high-melting-point metals. The strong nonlinear effects in the specific heat and thermal expansivity of metals at high temperatures can be explained by the formation of point defects. Examination of these effects rules out the anharmonicity as a possible origin of this phenomenon. Important arguments supporting this viewpoint have appeared in the last decade. It may turn out that just calorimetric determinations provide most reliable values of equilibrium vacancy concentrations in metals. The aim of the review is to discuss the experimental results and theoretical considerations favoring both claims. At present, the first point of view is shared by the majority of the scientific community. Regrettably, the data supporting the second viewpoint were never displayed and discussed together, and the criticism of this viewpoint never included a detailed analysis. In this review, the main attention is paid to equilibrium vacancies in metals and their relation to thermophysical properties of metals. Along with a discussion of experimental data and theoretical estimates now available, some approaches are proposed that seem to be most suitable to solve the question.

Original languageEnglish
Pages (from-to)79-188
Number of pages110
JournalPhysics Reports
Issue number2-3
StatePublished - 1 Jun 1998

Bibliographical note

Funding Information:
The author gratefully acknowledges the support by the Ministry of Science and Technology of Israel and by the Dr. Irving and Cherna Moskowitz Program for the Absorption of Scientists. Many thanks to the referee for useful comments.


  • 61.72.Ji, 61.72.Cc, 65.40.+g
  • High temperatures
  • Metals
  • Point defects
  • Thermophysical properties
  • Vacancy formation


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