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Superconductivity in Metallic Glasses W SUPERCONDUCTIVITY IN METALLIC GLASSES W. Johnson To cite this version: W. Johnson. SUPERCONDUCTIVITY IN METALLIC GLASSES. Journal de Physique Colloques, 1980, 41 (C8), pp.C8-731-C8-741. 10.1051/jphyscol:19808183. jpa-00220286 HAL Id: jpa-00220286 https://hal.archives-ouvertes.fr/jpa-00220286 Submitted on 1 Jan 1980 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. JOURNAL DE PHYSIQUE CoZZoque C8, suppZBment au n08, Tome 41, aoCt 1980, page ~8-731 SUPERCONDUCTIVITY IN METALLIC GLASSES W.L. Johnson W. M. Keck Laboratory of Engineering Materials, CaZifornia Institute of TechnoZogy, Pasadem, California 91125, U.S.A. I. INTRODUCTION The earliest studies of amorphous superconduc- tors were carried out twenty-five years ago on thin where D(0) = electron density pf states at fi lms of simple metals prepared by vapor deposition the Fermi level on a cryogenic substrate(''*). ~er~mann(~),and 2 <I > = average squared electron-ion the author(4) have surveyed some of the properties matrix element of such materials in recent reviews. In the past ten years, studies of amorphous superconductors M = ionic mass 2 have been extended to transition and <w > = mean square phonon frequency most recently to metal1 ic glasses (4,697). rhe (defined by FlcMi 11 an) latter materials are prepared by rapid quenching of liquid metal1 ic alloys using techni.ques originally Although the phonon spectrum and Eliashberg func- 2 developed by ~uwez(~). tion a (w)F(w) of amorphous metals may differ from It would be both difficult and repetitive to that used by IlcMillan to obtain eqn. (I), one would completely review this field in the limited space sti11 expect that the corresponding expression for available here. The interested reader is referred T, in amorphous alloys will have a similar to the above mentioned articles for a morecomplete form (4y10). Therefore, eqns. (1) and (2) still survey. In the present article, attention will be provide a convenient framework in which to analyze focused on recent developments. The main results the systematics of superconductivity in amorphous of earlier work will be summarized where conve- metals . nient. A. Simple Metals 11. ELECTRONIC STRUCTURE AND SUPERCONDUCTIVITY The occurrence of superconductivity in amor- ~c~i11 an(') has given a solution to the strong- phous simple metals can be understood by using an coupling equations of Eliashberg which he obtained extension of the nearly free electron model. using numerical techniques together with the mea- Ziman has applied this model to 1 iquid metals('' ) . sured phonon spectrum of niobium. Using his solu- ~er~mann'~)has given an extensive account of the tion, the superconducti ng transition temperature is experimental evidence which supports such a given by picture in the case of superconducting amorphous simple metals. In particular, the model correctly predicts the Hall coefficient(12) RH, electrical resistivity p(T), and temperature dependence of In this expression, eD is the Debye temperature p(T) for the majority of simple metals(13). Rainer and ~ergmann"~)have also discussed the (or suitably averaged phonon frequency), ].I* the 2 2 calculation of <I > and <w >. effective Coulomb coupling constant, and X the They argue that dimensionless electron phonon coupling constant. disorder results in an enhancement of low fre- quency contributions to electron-phonon scatter- I.lcbli 11 an expresses A in terms of other microscopic parameters as ing and consequently to enhanced values of X. They conclude that amorphous metal s should tend to be strong-coupling (A > 1) superconductors. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19808183 (28-732 JOURNAL DE PHYSIQUE Experimental evidence obtained from superconductive In crystalline metals, the influence of long tunneling indeed supports this con~lusion(~~~~~~~).range order on electronic band structure results in The author(4) has attempted to explain the large deviations of the electronic density of states systematics of superconductivity in simple amor- D(E) from the free electron model. These deviations phous metals by assuming that the strong disorder in turn influence electron-phonon scattering, and leads to a nearly spherical Fermi surface. A electron screening. The absence of long rangeorder simple jellium model was used to determine the in amorphous metals tends to eliminate these band variation of X with a few simple parameters such as structure effects and leads to a free electron-li ke valence Z, atomic volume va, and ionic mass M. In Fermi surface. As a result, the jellium model the jellium model, the ionic plasma frequency gives a much better description of amorphous as compared to crystalline simple metals which are not Q P = (*)'(where N = density of ions) is a we1 1 described by the jellium model(4). The micro- natural scale for phonon frequencies. A plot of scopic origin and systematics of superconductivity the dimensionless ratio [kBTc/#S2 1 for amorphous P are correspondingly easier to understand in amor- simple metals as a function of average valence Z phous metals . is shown in Fig. 1 and suggests remarkably system- atic relationship. Roughly speaking, this ratio is 6. Transition Metals a measure of the exponential factor on the right The superconducting properties of amorphous hand side of eqn. (1) ,. and thus a measure of A. transition metals are governed mainly by the Using Z, va, and b1 as input parameters in the partially occupied d-states. In contrast with the jellium model, together with the Heine-Abarenkov case of simple metals, one cannot use the free pseudopotential form factors for simple metals, a electron approach to understand these materials. simple model calculation of h was carried out (4) The d-electrons are perhaps best described as being It was found that X is determined mainly byvalence. tightly bound. Friedel(18), Cyrot-Lackmann (19) , These results are illustrated in Fig. 2. and others have discussed the tight-binding approx- imation TBA as it applied to liquid transition metals. Recently, Varma and ~ynes'~') have ana- - lyzed superconductivity in crystalline transition Amorphous Simple I metals using an extension of the TBA method to Metals Pb.9 Cu.~ - 1.2- *I: : include the nonorthogonal ity of atomic d-orbi tals ,J P?75B!25 - 1.0 - centered on neighboring atoms. They find that the II Te9Te.l d-band contribution D~(E,~)to D(E~)is the most 0.8 - GO*:*. .S%Cu., important microscopic parameter which determines X. / '?ES?z 2 2 0.6 - II Their argument shows that the ratio [<I >/<w >] in I I I eqn. (2) should be roughly constant within a given 0.4 - Be I/ 0 r d-band (i.e. the 4d or 5d band). .//*cd,9~e., 0.2 - Applying the Varma-Dynes analysis to the case ,'I f Mg., Z~II (melt-quenched) of amorphous transition metals requires information 0 ---:I L 0 2 4 regarding the behavior of Dd(c). Several experi- Valence Z mental techniques have been used to obtain such information. These include measurements of mag- Fig. 1. Variation with valence of the supercon- netic susceptibility, low temperature specific ducting transition temperature of simple heat, x-ray and ultraviolet photoemission spectra, amorphous metals. The values of Tc are and also indirect deduction of D(E~)from upper normalized to the characteristic bare critical field, Hc2(T), measurements. Magnetic phonon temperature ChS2 /K ] of each P susceptibility measurements on metal 1ic glasses of material. the series (Mol-xRux)80P20 have been reported(21 1, The temperature independent contribution to the susceptibility, G, was found to be large and to decrease with x as sb~wnin Fig. 3. If one Fig. 2. Values of the electron- phonon coupling constant A calcu- lated using a simple jelliummdel with Z, M, and v, as input para- meters. See ref. 4 for details. VALENCE Z assumes that the Paul i paramagnetic contribution have used XPS and UPS measurements to gain insight associated with D(E~)dominates x0, then this can into the variation of D(E) for E < cF. Typical be interpreted to indicate a smooth decrease of results are shown in Fig. 4 for the alloy D(cF) with increasing x as shown in the figure. (f.100~6R~0~4)80B20.The data suggest that a general Also shown in the figure is the variation of Tc loss of structure in D(E) Occurs on going from the with x for these metallic glasses and the varia- crystalline to the amorphous state. ' It also sug- tion of Tc vrith x for amorphous Mol-xRux thin gests that D(E) is characterized by a broad maxi- films pre ared by cryoquenching by, Coll ver and mum with the peak occurring somewhat below the Hamm~nd(~~.These results suggest a direct re1a- Fermi level of the alloy. In other words, Dd(~) tionship between D(E) and Tc. Recent low tempera- appears to vary rather smoothly with d-band ture specific heat meas~rements(~)on the same occupation exhibiting a maximum for a roughly half series of metallic glasses have confirmed the de- filled d-shell. The variatfon of Tc observed by crease of D(E) with x, The absolute values of Col 1ver and ~amnond'~)for cryoqueiched films of D(E) obtained from the coefficient of the linear transition metals and alloys ofaneighboring metals contribution to c are in remarkably good agree- of the 4d series is shown in Fig.
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