Solid State Communications, Vol.54,No.9, pp.771-774, ]985. 0038-I098/85 $3.00 + .00 Printed in Great Britain. Pergamon Press Ltd. ON THE CONCENTRATION DEPENDENCE OF TRANSPORT COEFFICIENTS IN AMORPHOUS TRANSITION METAL ALLOYS Davor PAVlrNA Laboratolre d'Etudes des Propri~t~s Electronlques des Solldes CNRS - BP 166 - 38042 Grenoble-Cedex - France (Received 21 February 1985 by E.F. Bertaut) We discuss the concentration dependence of resistivity of CuTM (TM E Ti, Zr, Hf) amorphous alloys within a framework of a two-band mo- del in which the s-states dominate conduction at the Cu end while the conduction of the d-states becomes increasingly important at TM rich end. We present a simple empirical relation that well describes the concentration dependence of the Hall coefficient and its sign reversal. While the overal understanding of the elec- tron transport in "dirty" metallic regime has been greatly enhanced since the development of the scaling theory of locallzatlonl, 2, the un- derstanding of the effects of alloying and its consequences for electronic structure and trans- port is still relatively poor. Moreover, on me- tallic glasses most experimental studies in re- cent years were concentrating on the temperatu- re3,4 and magnetic fleldS, 6 dependence of resis- tivity and there were few truly systematic stu- dies of the concentration dependence of transport coefficients, despite the fact that the variation of concentration is one of the attractive featu- res of these solids. In order to somewhat fill that gap, we have systematically studied the concentration, tempe- rature and field dependence of resistivity of Cu-TM (TM E Ti, Zr, Hf) glassy alloys. In this communication, we discuss the variation of the transport coefficients with concentration of TM in Cu. In particular, we concentrate our atten- tion to the region below ~ 30 at. % TM where all three alloy systems seem to show no sign of su- perconductivity (at least down to ~ 20mK) but where the temperature coefficient of resistivity (TCR), ~ the Hall coefficient, RH, and possibly the thermopower, S, reverse their sign. We have deliberately chosen Cu-TM glasses for our studies because they were already extensively studied so the wealth of important published results facili- tates the discussion of the physics of electron transport. First we sunnnarize the essential features of a two-band model which we use to discuss the con- centration dependence of resistivity, 0(x). We proceed with a discussion of a simple empirical relation that gives a surprisingly good fit of RH(X) data. We conclude the paper with a brief conunent on the change of sign of TCR, ~, and the thermopower. All our samples were produced by melt- spinning in helium atmosphere and were charac- terized to be fully amorphous by means of x ray diffraction. The resistivity was measured by a standard four probe DC technique ; its magnitude has been estimated with an accuracy of ~ ± 3 % by using the results of measured densities. The de- 771 tails of preparation, characterization, experimen- tal techniques and or a~ing/oxldisatlon problems are presented elsewhere I. The relevant results for our discussion of the concentration dependence of transport coeffi- cients are presented in Figures 1 and 2. In Fi- gure 1 we compare the concentration dependence of resistivity of CuTi and CuZr alloys. At the edges of the alloy diagram, we use the values published for pure liquid metalsS. We note that the results on 0290(x) are very similar to the ones we measured at 4 K which are typically ~ 5~cm higher in magnitude 9. To facilitate the subsequent discussion, we have also included in Figure I the bare density of states (DOS) at the Fermi level, EF,for CuTi and CuZr : these values were estimated from the specific heat datal0, II. For Cu-Zr alloys, we also use the results of recent calculation of electronic structure 12 which yield th~respective contribution of s,p- and d-states to the total DOS. That enables us better estimate of the va- riation of the d-DOS with concentration than the one we presented in an earlier publlcatlonl3. As one can see in Figure I, the contribution of the s,p states is roughly constant accross the phase diagram and these states account for about 30 % of the total DOS. The d-DOS rises sharply up to about ~ 50 at. % Zr and then remains practically constant. The total DOS in CuTi is some 30 % hi- gher than total DOS of CuZr - it seems reasonable to propose that the difference is almost entirely due to the d-DOS : in what follows we assume that d-DOS in CuTi is ~ 30 % higher than that of CuZr. This is fully in accordance with calculated va- lues for pure Ti and Zr : 1.59 and 1.28 states/eV atom respectively 12 . For our discussion of the concentration de- pendence of resistivity, p(x), we invoke a simple two-band model 13. The central idea is that at the copper rich end the conduction is dominated by the s-states that are being scattered into d-sta- tes, while at TM-rlch end the conduction by the d-states becomes an increasingly important contri- bution. Two bands conduct in parallel, hence, = o s + Od, and the corresponding conductlvities compete accross the compositional range 13. The alloy diagram can be divided into three regions