Solid State Communications, Vo1.39, pp.371-374. Pergamon Press Ltd. 1981. Printed in Great Britain.

003%lO98/81/263371-04$02.00/O

PHONON ANOMALIES AND SUPERCONDUCTIVITY IN THE hcp METALS, Tc, Re, AND Ru*

H. G. Smith and N. l*lakahayashi Solid State Division, Oak Ridge National Laboratory

Oak Ridge, Tennessee 37830

(Received 24th April 1981 by H. Suhl)

The phonon dispersion curves have been measured for the hcp metals, Tc, Re, and Pu in the [OOl] direction at room temperature. A pronounced phonon anomaly has been observed for the LD mode in Tc and Re which is absent in Ru. A low temperature study of Tc revealed a strong tempera- ture dependence of the anomaly. It is suggested that the magnitude of the phonon anomaly is correlated with the strength of the electron-phonon interaction in these metals.

Technetium, an hcp metal, has a surprising- ly high superconducting transition temperature' (T, = 7.35 K), for the hcp system is not gener- ally regarded as favorable for high-T, supercon- ductivity. 4mong the elements its T, is second highest to that of bee Nb (T, = 9.25 K) and

increases T, dramatic lly, higher than even in the bee Nh-Zr alloys. B As with other moderate- to-high-T, superconducting materials, anoma- lies536 in the phonon spectra are to he expected in certain regions of the Brillouin Zone (BZ). Although the hand struct re and Fermi surface of

? Tc have been calculated, not enough is known ahout the electron-phonon interaction to he able to predict the location and magnitude of the anomalies. For the transition metals Matthias8 discovered the empirical rule that the super- conducting transition temperature of a metal could be correlated with the number of valence electrons per atom with maxima in T, occurring at e/a = 4.7 and at e/a = 6.6. Most of the reported phonon studies have been concerned with superconducting materials with an e/a near the first maximum, whereas, the results presented here are some of the first phonon studies of materials associated with the second maximum. Inelastic neutron scattering (INS) is a very valuable and almost unique technique for study- ing phonon anomalies. This communication reports the observation by INS of a pronounced phonon anomaly in Tcg in the LO[OOl] branch and its strong temperature dependence. A similar though somewhat reduced anomaly is also reported for Re at room temperature, which has the same e/a ratio. In contrast, vastly different behav- ior is observed for the same branch for Ru6 an element in the VIIIb column with a very low Tr of 0.49 K. The dispersion curves presented h&e are only for the [OOl] direction, although a complete set of dispersion curves for the Cl001 and Cl101 directions has also been collected for

*Research sponsored by the Division of Materials Sciences, U.S. Department of Energy under contract W-7405-eng-26 with the Union Carbide Corporation.

Tc at room temperature. These results and their Tnodel analvsis will be reoortedl" in a full paper with-other hcp metals in the near future.

The crystal of Tc was grown by S. Mihailovich of the Argonne National Lahora- tory from technetium metal obtained from the Oak Ridge National Laboratory. The metal was puri- fied by repeated outgassing at elevated tempera- tures during the crystal growing process. The single crystal of Re was grown at DRNL by H. Harmon of the Solid State Division and the crystal of Ru was obtained through commercial sources. The phonon measurements were made on the HR-3 triole-axis soectrometer at the HFIR. For the low temperature measurements on Tc the crystal was cooled with a Displex CS-202 closed cycle refrigerator. The constant-Q method was employed for most of the phonon scans although a limited number of phonons were determined by the constant-E method. However, in all cases the outgoing neutron energy was held fixed.

The room temperature dispersion curves in the c-direction for Tc, Re, and Ru are shown in Fig. 1. They are plotted in an extended-zone scheme for clarity; the BZ boundary in this direction is indicated by the dotted line at A (5 = 0.5, 5 = cq/2n). The acoustic modes extend from < = 0 to 0.5 and the optic modes from 5 = 0.5 to 1.0. The transverse modes in this direction are doubly degenerate due to the symmetry of the crystal.. Particular attention is drawn to the behavior of the LO branch in Tc as compared to that in Ru. This branch in Tc exhihits a tremendous dip between A and T, unlike those ohserved in most hcp metals. This dip is similar to, but more pronounced than those obser ed in-other good'superconductors, such as Nb. Yl Pb.12 and TaC.13 etc. It has been the gen ral expedience with-several theoretical modelsIt- of the lattice dynamics of high-T, superconductors with large electron-phonon interactions that in certain regions of the BZ the electronic contributions to the dynamical matrix (and hence, the phonon frequencies) are large and negative, producing the observed anomalies. In the case of Ru, the dispersion of the branches appears normal for an hcp metal, except for the small inflection in the LO mode at r, = 0.6. It is not known at this time whether

371

PHONON ANOMALlES AND SUPERCONDUCTIVITY IN THE hcp METALS, Tc, Re, AND Ru Vol. 39, No. 2

0 0.2 0.4 0.6 0.8 f.0

s=cq/zrr

Fig. 1. Phonon dispersion curves in the c- direction for Tc, Re, and Ru at room temperature.

this inflection is a consequence of a weak electron-phonon interaction as indicated by its low T, or is merely an ordinary Kohn anomaly reflecting the geometry of the Fermi surface. The slight inflection in the TO mode in Tc may well, indeed, he a true Kohn anomaly associated with its Fermi surface.7

The dispersion curves of Re are similar in appearence to those of Tc. This is not supris- ing since they are in the same column of the periodic table. Since Re is almost twice as heavy as Tc one expects the phonon frequencies to be lower, and they are for small and inter- mediate values of 5. However, the lower T, of Re suggests a somewhat weaker electron-phonon interaction and, hence, a smaller phonon anomaly than in Tc and this is born out in the phonon measurements near 5 = 1.0.

The apparent degeneracy of the LO and TO modes at r for Tc and Re is accidental for this is not required by symmetry, as is evidenced by the Ru data. In fact, the frequency of the LO mode at r decreases substantially in Tc as the temperature is lowered while there is a slight hardening of the TO mode. The LA mode (5 = 0 to 0.5) shows essenti,ally no temperature dependence and the LO mode (5 = 0.5 to 1.0)

;;ries with temperature only for c > 0.7 (Fig. . Similar results are expected for Re. As

one increases the temperature ahove room tem- perature the Ln mode at r is expected to increase and the anomaly disappear, as was obsg;ved for Lr, / 8

he low-Tc superconductors Ti,*I and t'f. .3 These last three Imetals are

ohserved to transform from the hcp structure to the hcc structure at elevated temperatures; how- ever, as far as the authors are aware Tc does not.

I I I I I

02 04 06 08 10

s=cq/2Tr

Fig. ?. Temperature dependence of the longitu- dinal phonon in the c-direction for Tc. The solid lines are the model calcula- tions.IO

The temperature dependence of the square of the soft optic mode frequency at I in Tc is shown in Fig. 3. The softening is finally arrested at 2.4 THz at about 30 K. This is a stronger temperature dependence than has been observed in other superconductors except for the A-15 compounds Nb3Sn and V3Si. There was also an apparent temperature dependence in the width of this mode indicating some degree of anhar- monicity helow room temperature. However, mea- surements were made under conditions of low resolution to maximize the intensity and it wi 1 be necessarv to make phonon width measurements under conditions of much better resolution in

;;zecra:; ;T;@ them wi h theory as was done and MO. $5

As mentioned above a successful analysis hased on the theory of charge fluctuations16s1 has been made on a more complete set of Tc dis persion curves which includes other symmetry directions and a detailed description will appear in a forthcoming paper.IO A decomposi- tion of the dynamical matrix clearly shows the parameters which are responsible for the dips i Tc. It is observed that the magnitude of the

vol. 39, No. 2 PHONON ANOMALIES AND SUPERCONDUCTIVITY IN THE hcp METALS, Tc, Re, AND Ru

TECHNETIUM

LO [OO!] AT l-

T (K)

Fig. 3. Temperature dependence of the square of the soft optic mode frequency at r in Tc.

anomaly is particularly sensitive to the mode in these alloys to . . _ . _ _. _ examine whether this

373

dlpolar-dinolar coupling hetween nearest neigh- hors, indicating the tendency toward an insta- bility in the electronic system of technetium.

4110ying of Tc with Mo3 and Nb2 in the hcp

soft mode is, indeed, associated with the lat- tice instability which triggers the onset of the o-phase and a concomitant decrease in the super- conducting temperature.

phase increases the observed T, to 14.3 K for Mon.25TcO.75 and to 12.6 K for NbO.16TcO.84, Acknowledgment - The authors wish to thank before the phase becomes unstable. It would be G. Yostorz for initiating the growth of the Tc very desirable to study the behavior of the soft crystals.

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