Volume 64A, number 5
23 January 1978
POSSIBLE T~—XDIAGRAMS OF SUPERCONDUCTIVITY IN BINARY SYSTEMS A.F. PREKUL Institute of Metal Physics, Sverdlovsk, USSR Elementary dependences T~(X)whose superposition describes a number of complex experimental situations are shown to exist. The concept of superconductivity-state diagrams is introduced, nine main types of such diagrams are being presented.
Concentration-induced changes of the critical ternperature of superconductivity, Tc(X), for Ti- and Rebased alloys with cubic transition metals are the starting point of the study. It is generally accepted to describe experimental T~(X)data in these alloys by one smooth curve with a maximum. This “rigid approximation” underlies the well-known Matthias rules , which in their turn have defined the systematization principle for empirical data on Tc with the electron-per-atom ratio as a universal parameter. The present letter reports another way of describing T~data as well as another systematization principle. Reconsideration of data [2—6]showed that Tc does not begin to rise at X 0. The T~(X)curves have small minima near both pure-metal sides. Then, T~ rises rapidly with X but does not pass through a maxi mum. At some critical concentration X~,when the metal-covalent (MC) phase appears, w or a, Tc drops abruptly and symthetrically on both sides of X~,so that two high peaks are formed on the Tc(X) curve. Such considerable deviations from the rigid approximation can be explained in the simplest way by the fact that the change of electronic structure is not actually smooth even in alloying the neighbouring metals TiandV. According to ref.  a sharp decrease of Tc near Xcr is a characteristic property of non-equilibrium disordered alloys due to the fact that in their electronic band structure there is a gap or pseudo-gap. Thus, low T~of the w- and a-phases is not the primary cause for the drop in T~near X~. From what has been stated above one can see that the total picture of Tc is complex and consists of at least three parts: superconductivity of dilute solutions, superconductivity of MC phases and superconductivity
of intermediate non-equilibrium alloys. This is the main result of the analysis. That is why we suggest to describe Tc(X) data by a superposition of the three dependences of Tc(X) as illustrated in figs. 1.1—3. The mere possibility of such a description means that each of the above dependences is elementary and may be identified with definite electronic and structural states of the alloy. As far as the Tc-value may be a measure of the electronic density of states at the Fermi level, N~,it is possible that the curves 1.1—3 describe the simple band structuresat the same time. Dependence 1.1 is usually realized in binary systems having an unlimited range of solid solutions. In the above systems it is but partially conserved and describes the initial decrease of Tc on the pure-metal -________
‘~ - - -
X Fig. 1.
Volume 64A, number 5
sides until the solubility limit is reached in the solid state. Along curve 1.1 it is possible to change from metal to metal continuously, i.e. within the uniform state, Hence, curve 1.1 may be considered to be the feature of a typically metallic state. The two peaks on curve 1.2 are due to the twopeak behaviour of N6(X)  and are separated from one another by a pseudo-gap (arrow in fig. 1.2). Alloys in these concentration intervals are metastable and have two characteristic features non-metallic transport properties  and diffuse scattering of electron diffraction patterns . From now on we shall call this state the “dielectric” phase (DP), bearing in mind that, depending on X, metal—non-metal transition is possible here. Thus, there is every reason to believe that the DP is a particular state intermediate between metallic and metal-covalent states. Curve 1.3 shows the idealized behaviour of T~in the MC phase. Qualitatively this type of dependence corresponds to the original tendency to individualize superconductivity of the MC phases. Thus, experiment includes the data from different states both in equilibrium and non-equilibrium. Hence, in general, one should speak not of concentration depen dences of T~(X)in the interval 0
23 January 1978
in the DP (not in the equilibrium MC phase) on the edges of the pseudo-gap; one may be convinced of that by the above features of the DP. All in all, on the base of three dependences identifled, seven T~—Xdiagrams can be constructed, figs. 1.1 —7. Besides, for the DP one can foresee a “non-splitted” variant of the T~(X)curve, the curve shown in fig. 1.9. Along with this simple diagram one mixed diagram may be added, fig. 1.8. Supposedly, the present set of diagrams describe a great number of complex experimental situations. Very likely the leading singularities on T~versus X curves are the same for all binary systems. On the whole, the method of T~—Xdiagrams may become a useful technique in analyzing and systematizing empirical data on superconductivity. Unlike in the rigid approximation, the only necessary, but not universal parameter is the concentration X. Universality consists, after all, in maintaining each of the elementary dependences, wherever the electronic structure corresponding to them may appear. To avoid misunderstanding the author emphasizes that figs. 1.1—9 are but sketches and do not reflect the real scale. I should like to thank Professor N.y. Volkenshtein for useful discussion and critical remarks.
References  B.T. Matthias, Phys. Rev. 97 (1955) 74. [21 B.T. Matthias, J. Less Common Metals 12 (1967) 36.  A:F. Prekul, V.A. Rassokhin and NV. Volkenshtein, Fiz. Metal. Metalloved. 37 (1974) 671. [41 BR. Coles, Rev. Mod. Phys. 36 (1964) 149.  C.W. Chu, T.F. Smith and W.E. Gardner, Phys. Rev. Bi (1970) 214.  H.N. Ronami and V.P. Beresina, Fiz. Metal. Metalloved. 37 (1974) 872.  V.A. Rassokhin, N.y. Volkenshtein and A.F. Prekul, Proc. 19th Conf. Phys. low temperature (HT-l9) (Minsk, 1976) p. 471.
[81 A.F. Prekul, N.y. Volkenshtein and A.S. Scherbakov, Fiz. Nizkih Temp. 2 (1976) 1399.
[91~e1 V~A.RossokhinandN.V. Volkenshtein, [101 S.V. Sudareva, E.P. Romanov, A.F. Prekul and E.N. Juravleva, Fiz. Metall. Metalloved. 44 (1977) 357.