Electronic transport properties of liquid zinc and zinc–germanium alloys: Theory versus experiment A. Makradi b , J.G. Gasser a, * , S. Belouettar b a Laboratoire de Physique des Milieux Denses, Université Paul-Verlaine – Metz, 1 B d Arago, 57078 Metz cedex 03, France b AMS, Centre de Recherche Henri Tudor, 29 Avenue John F. Kennedy, L-1855 Luxembourg, Luxembourg article info Article history: Received 16 September 2008 Available online 8 January 2010 Keywords: Liquid alloys and liquid metals Conductivity Thermopower Density functional theory abstract The electrical resistivity and the absolute thermoelectric power of liquid zinc, germanium, and zinc–ger- manium alloys have been measured as a function of temperature by 10 at.% steps between pure zinc and 70 at.% of germanium. The electronic transport properties of the pure liquid metals and alloys are eval- uated in the framework of the extended Faber–Ziman theory using a single-site t-matrix. Different muf- fin-tin potentials are constructed using Hartree Fock and density functional theory (LDA and GGA), to interpret the electron–ion interaction. This formalism explains the anomalous temperature dependence of both the resistivity and the positive absolute thermoelectric power (ATP) of liquid zinc. Concerning the experimental first peak asymmetry of germanium and zinc, the static structure factors cannot be repro- duced with hard spheres. They are better described for both pure metals and alloys by a square well pair potential. Ó 2009 Elsevier B.V. All rights reserved. 0. Introduction Relative to the melting point of germanium (T m = 937 °C), the low boiling point of zinc (T b = 906 °C), make the experimental study of the transport properties of liquid germanium–zinc (Ge– Zn) alloys difficult to realize using standard techniques. Such experiment could be achieved by using a new experimental tech- nique [1]. Regarding the calculation of the resistivity (q) and the absolute thermoelectric power (ATP) of liquid Ge–Zn, new possibil- ities have been offered by using the density functional theory [2–4] to interpret the electron–ion interaction (form factor), while the atom–atom interaction (structure factor) is expressed by the square well potential [5–8]. The resistivity and the absolute ther- moelectric power of pure germanium have been interpreted by Makradi et al. [9] and their temperature coefficient by Bestandji et al. [10]. The aim of this paper is to present our experimental re- sults of the resistivity and the absolute thermoelectric power of Ge–Zn alloys, and to adopt the formalism used for pure metals [9,10] to calculate the transport properties of the Ge–Zn alloys. In Section 1, we present briefly our experimental technique for measuring the transport properties of high vapor pressure alloys. In Section 2, we recall the Faber–Ziman expression of the resistiv- ity and absolute thermoelectric power. In Section 3, we describe briefly the construction of the muffin-tin potential and of energy dependent phase-shifts by taking into account recent density func- tional formalism developments. In Section 4, we discuss the meth- od used to determine the Fermi energy. In Section 5, we present an analytical improvement on the determination of partial hard sphere structure of alloys by the so-called Silbert–Young [5] poten- tial. Finally, in Section 6 we present our experimental results and compare them to our ab initio calculations. 1. Experimental method The experimental study of liquid germanium–zinc alloys is dif- ficult because of the high vapor pressure of the pure zinc at the melting point of the pure germanium (germanium melts at 31 °C above the boiling point of zinc!). The measurement of the electrical properties of this system is made possible by a new fused silica cell [1] (Fig. 1), which allows for all manipulations of the liquid metal and alloys to be under pressure. With this new cell, the fact that the temperature is above the boiling point of zinc does not repre- sent a major problem. The boiling temperature is the value of the temperature where the vapor pressure is 1 bar. If the experiment is conducted in a closed cell, the alloy remains liquid; there is sim- ply a high vapor pressure above the liquid. If the cell is open (as in our case) we have to play on the kinetics of evaporation by apply- ing a ‘as high as possible’ pressure of argon which hinders the dis- tillation process. If the distillation occurs, we observe a layer of distillated metal in the cold part of the cell. This cell avoids using the vacuum to fill the measurement capillary and to eliminate 0022-3093/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2009.11.027 * Corresponding author. Address: Laboratoire de Physique des Milieux Denses (L.P.M.D.), 1 B d Dominique François, Arago, 57078 Metz cedex 03, France. Tel.: +33 3 87 31 58 59; fax: +33 3 87 31 58 84. E-mail address: gasser@univ-metz.fr (J.G. Gasser). Journal of Non-Crystalline Solids 356 (2010) 400–406 Contents lists available at ScienceDirect Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol