On the Enthalpy and Entropy of Point Defect Formation in Crystals
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S AND LIQUIDS
On the Enthalpy and Entropy of Point Defect Formation in Crystals1 N. P. Kobeleva and V. A. Khonikb,* a
Institute of Solid State Physics, Russian Academy of Sciences (ISSP RAS), Chernogolovka, Moscow oblast, 142432 Russia b Voronezh State Pedagogical University, Voronezh, 394043 Russia *e-mail: [email protected] Received October 25, 2017
Abstract—A standard way to determine the formation enthalpy H and entropy S of point defect formation in crystals consists in the application of the Arrhenius equation for the defect concentration. In this work, we show that a formal use of this method actually gives the effective (apparent) values of these quantities, which appear to be significantly overestimated. The underlying physical reason lies in temperature-dependent formation enthalpy of the defects, which is controlled by temperature dependence of the elastic moduli. We present an evaluation of the “true” H- and S-values for aluminum, which are derived on the basis of experimental data by taking into account temperature dependence of the formation enthalpy related to temperature dependence of the elastic moduli. The knowledge of the “true” activation parameters is needed for a correct calculation of the defect concentration constituting thus an issue of major importance for different fundamental and application issues of condensed matter physics and chemistry. DOI: 10.1134/S1063776118030032
1. INTRODUCTION Intrinsic equilibrium point defects—vacancies and interstitials—play an important role in physical properties of crystalline materials. In particular, this is related to the fundamental phenomenon of melting. The understanding that melting can be related to the thermoactivated generation of point defects of the crystalline lattice was achieved long ago [1–3]. Meanwhile, the detailed mechanism of this phenomenon remains a matter of numerous discussions and any commonly accepted opinion on the nature of defects involved into melting and their interactions is absent hitherto [4]. In 1992, Granato [5] proposed the Interstitialcy theory, which assumes that the defects responsible for melting are interstitials in the dumbbell (split) form. Although it was later found that this theory provides qualitative and quantitative explanations for quite a few important phenomena occurring in liquids and glasses [6–8], it did not accept any wide recognition. One of the reasons for this consists in the wide-spread belief that the concentration of equilibrium dumbbell interstitials (= interstitialcies) is negligibly small even near the melting temperature Tm [9]. However, recent experimental studies performed on single-crystalline aluminum [10] and polycrystalline indium [11] provide strong evidence that the interstitialcy concentration starts to rapidly increase upon approaching the melting point and becomes compara1 The article was translated by the authors.
ble with the vacancy concentration just near Tm, in accordance with Granato’s theory. It has been shown that this takes place due to the high formation entropy
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