PHYSICAL REVIEW 8 VOLUME 25, NUMBER 10

Addendum to the lattice dynamics of y-Ce

15 MAY 1982

C. Stassis, C. -K. I.oong, and O. D. McMastersAmes Laboratory U.—S. Department of Energy and Department of Physics, Iowa State University,

Ames, Iowa 50011

R. M. NicklowSolid State Division, Oak Ridge National Laboratory, Oak Ridge„Tennessee 37830

(Received 21 December 1981; revised manuscript received 22 February 1982)

Inelastic neutron scattering techniques have been used to study the temperature depen-dence of the dispersion curves of y-Ce. We find that the frequencies of all but theT [111]branches exhibit normal temperature dependence. Close to the zone boundary thefrequencies of the T [111]branch, on the other hand, decrease with decreasing tempera-ture, and at room temperature this branch exhibits a dip at the zone boundary. Thisanomalous behavior may be related to the fcc~dhcp phase transition.

I. INTRODUCTION

The properties of cerium metal have been thesubject of many experimental and theoretical inves-tigations. ' Of particular interest are the physicalproperties of the fcc phase (y) which is stable atroom temperature and atmospheric pressure. They phase of cerium transforms under moderate pres-sure (-8 kbar at 300 K) or upon cooling to lowtemperatures ( & 100 K at 1 atm) to the fcc aphase in which the cerium ions are in a mixed-valence state. Furthermore, y-Ce transforms to thedhcp phase below approximately 260 K at 1 atm.

In a previous paper (hereafter referred to as I),published previously in this journal, we have re-ported the results of an inelastic neutron scatteringstudy of the phonon dispersion curves of y-Cealong the [100], [110],[111],and [Ogl] symmetrydirections. Comparison of the measured dispersioncurves with those of Th has indicated that the y-Ce phonon frequencies are lower than one wouldexpect, this relative softening being more pro-nounced for the T [111]branch. We therefore feltthat a study of the temperature dependence of thephonon frequencies of y-Ce may provide additionalinformation regarding the lattice dynamics of thisphase and in this paper we present the results ofthese experiments.

II. EXPERIMENTAL DETAILS

In the present experiment a single crystal of y-Ce grown at the Ames Laboratory (for details see I

and Ref. 3) was mounted in a high-temperaturevacuum furnace positioned on the sample goniome-ter of a triple-axis neutron spectrometer. At 87SK the temperature was controlled to within a fewdegrees and the vacuum was approximately 10Torr.

The measurements were performed using atriple-axis spectrometer at the 100-MW high fluxisotope reactor of the Dak Ridge National Labora-tory. All data were collected using the constant Q(where Q is the neutron scattering vector) mode ofoperation and a fixed scattered-neutron energy of3.6 THz. Pyrolytic graphite [reflecting from the(002) planes] was used as both monochromator andanalyzer, and a pyrolytic graphite filter was placedin the scattered beam to attenuate higher-ordercontaminations. The collimation of the neutronbeam before and after the sample was 40' of arc.

III. EXPERIMENTAL RESULTSAND DISCUSSION

The T [111]branch of y-Ce has been studied inconsiderable detail at room temperature and 875K. The frequencies of a selected number of pho-nons of the L[111],L[110],L[100], T [100],andTz[110]branches were also determined both atroom temperature and 875 K. In all cases theroom- and high-temperature data were collectedunder identical experimental conditions. The mea-sured phonon frequencies are listed in Table I andthe temperature dependence of the T [111]disper-

25 64S5 1982 The American Physical Society

6486 BRIEF REPORTS 25

TABLE I. Measured frequencies (THz) at 295 and 875 K of y-Ce.

Branch v (295) v (875) Branch v (295) % (875)

T [111]

L[111]

0.1

0.150.20.250.30.350.40.450.50.1

0.30.5

0.46+0.020.63+0.020.80+0.030.94+0.031.05+0.041.01+0.040.92+0.040.86+0.040.82+0.040.95+0.052.40+0.052.86+0.05

0.41+0.020.60+0.020.70+0.030.84+0.030.90+0.030.96+0.030.97+0.040,98+0.030.94+0.030.90+0.072.40+0.082.80+0.06

T [110] 0.150.40.8

L[110] 0.30.8

T [100] 0.40.81.0

L[100] 0.40.81.0

0.70+0.021.80+0.032.83+0,041.80+0.062.19+0.051.27+0.032.10+0.042.10+0.051.50+0.062.73+0.083.20+0.08

0.67+0.021.65+0.032.70+0.041.80+0.062.17+0.061.17+0.031.94+0.042.00+0.061.44+0.062.65+0.073.03+0.08

I

I.2-TA [I I I]

I.O-

N

0.8-

z 06-LIJ

C3

0.4

y- Ce

0295 K

~ 875 K

0.2-

I I I I

0 O. I 0.2 0.3 0.4 0.5REDUCED WAVE VECTOR

FIG. 1. Temperature dependence of the TA[111]branch of y-Ce. Some phonon frequencies (Ref. 5) forfcc La at 660 K are also shown (triangles).

sion curve is shown in Fig. 1. The room-temperature data are in good agreement with themeasurements reported in I.

It can be seen (see Table I) that the frequenciesof all but the T [111]branch of y-Ce decrease withincreasing temperature. This behavior is what onewould normally expect from the effect on the vi-

brational frequencies of the thermal expansion ofthe lattice. The temperature dependence of the fre-quencies of the T [111]branch of y-Ce is, on theother hand, anomalous (see Fig. 1). Close to thezone boundary the frequencies of this branch de-

crease with decreasing temperature and at roomtemperature the T [111]branch exhibits a dip atthe zone boundary.

It is unlikely that the anomalous dispersion andtemperature dependence of the frequencies of theT [111]branch of y-Ce are related to the mixed-valence transition to the a phase. In fact, the

T [111]branch of fcc La, which does not undergoa transition to a mixed-valence state, was found toalso exhibit similar dispersion (see Fig. 1) and tem-perature dependence as the corresponding branchof y-Ce. This is not surprising since La and Cehave comparable masses and similar (Sd 6s ) outerelectronic configurations (of course La, unlike Ce,does not have any 4f electrons); actually one wouldexpect nearly identical dispersion curves for thesetwo metals in the absence of any mixed-valence ef-fects on the dispersion curves of Ce or pronouncedelectron-phonon effects on those of superconduct-ing La. Thus the anomalous dispersion and tem-perature dependence exhibited by the T [111]branch must be related to the common electronicstructure of these metals.

It is important to recall at this point that fcc Ceand fcc La both undergo a transformation to thedhcp phase (y-Ce at -260 K and P-La at -583K); actually below the transformation temperaturethe fcc and dhcp phases coexist in these metals.The fcc—+dhcp phase transformation involves fourtransverse waves propagating along the [111]direc-

1 1 1tion with reduced wave vectors q of —,, —,, and —,.It is natural therefore to assume that the anoma-lous dispersion and temperature dependence of theT [111]branch of y-Ce (and P-La) is related to thefcc~dhcp phase transformation in this metal. Asimilar conclusion has been reached by Pickett,Freeman, and Koelling in their detailed theoreticalstudy of the eltx:tronic band structure of y-Ce andp-La. In particular, Pickett, Freeman, and Koel-ling found that the calculated generalized suscepti-bility X(q) of La is remarkably large along the[111]symmetry direction and exhibits peaks nearthe wave vectors which are involved in the fcc

BRIEF REPORTS

dhcp phase transformation. A more fundamentalunderstanding of the relationship between theanomalous dispersion and temperature dependenceof the T [111]branch of y-Ce, the electronic struc-ture and the fcc~dhcp phase transformation canonly be obtained within the framework of the mi-croscopic theories7 of lattice dynamics. Only re-

cently, calculations at finite temperatures using

these theories have been attempted. '

The Ames Laboratory is operated for the U. S.Department of Energy by Iowa State Universityunder Contract No. 7405-Eng-82. This researchwas supported by the Director for EnergyResearch, Office of Basic Energy Sciences.

~For a comprehensive review of the properties of Ce, seeD. C. Koskenmaki and K. A. Gschneidner, Jr., inHandbook on the Physics and Chemistry of RareEarths, edited by K. A. Gschneidner, Jr. and L. Eyr-ing (North-Holland, Amsterdam, 1978), .Vol. 1, Chap.4.

C. Stassis, T. Gould, O. D. McMasters, K. A.Gschneidner, Jr., and R. M. Nicklow, Phys. Rev. 819, 5746 (1979).

3D. C. Koskinmaki, K. A. Gschneidner, Jr., and N. J.Panousis, J. Cryst. Growth 22, 225 (1974).

4The frequencies determined in the present experimentwere found to be slightly higher than those reported

in I. This was expected, since most of the frequenciesreported in I were obtained with better instrumentalresolution (using a Be crystal as monochromator).For further details see Sec. II of I.

5C. Stassis, J. Zarestky, C.-K. Loong, and O. D.McMasters (unpublished).

6W. E. Pickett, A. J. Freeman, and D. D. Koelling,Phys. Rev. 8 23, 1266 (1981);22, 2695 (1980).

7C. M. Varma and %. %'cher, Phys. Rev. 8 19 6142(1979), and references therein.

K. Motizuki, N. Suzuki, Y. Yoshida, and Y. Takaoka(unpublished).