Journal of Magnetism and Magnetic Materials 37 (1983) L7-LI0 L7 North-Holland Publishing Company

LETTER TO THE EDITOR

STUDY OF POSITRON LIFETIMES IN ct, [~ AND "t CERIUM AT HIGH PRESSURES

A.M. BORING, C.-Y. H U A N G

Los Alamos National Laboratory, Los Alamos, NM 87545, USA

K.A. GSCHNEIDNER, Jr.

Ames Laboratory, Iowa State University, Ames, 1.4 50011, USA

J.D. McGERVEY, M. PANIGRAHI and S.G. USMAR

Case Western Reserve University, Cleveland, OH 44106, USA

Received 28 January 1983

The positron lifetimes in the a, fl and y phases of Ce have been measured by applying hydrostatic pressure (up to 1.4 GPa) and by reducing the temperature (to 80 K). Two-component fitting programs showed that the main component ( ~ 90%) had virtually the same mean lifetime ( = 233 ps) in all three phases. The uncertainty in each lifetime was 4-_ 2 ps. With this high precision, our results are in agreement with those of band calculations which give the same number of 4f electrons ( = 1.2) in all phases.

1. Introduction

In the past few years a great deal of research has been done on lanthanide metals and com- pounds which exhibit non-integral valences [1-3]. The lanthanide ion in these materials undergoes a change of valence in response to temperature, pressure or alloying variation. Historically, Ce was the first material suspected of having a valence change. X-ray studies indicated that when Ce was compressed to modest pressure (> 0.8 GPa at = 300 K) [4] or cooled to low temperature (< 100 K at 1 arm) [5] a large (> 12%) volume con- traction ( t h e ) , - ~ ct transformation) takes place while the crystal structure remains fcc. Zacharia- sen [6] and Pauling [7] independently suggested that this volume contraction corresponds to a va- lence change from 3 for y Ce (the 4f l{ds)a config- uration) to 4 for a Ce (the 4f °{ds) 4 configuration), that is, the 4f electron of y Ce is promoted to the valence band, leaving the 4f level of t~ Ce empty. As a result of this valence change, there exists a first-order transition line between the a and y

phases in the pressure-temperature (P-T) dia- gram terminating in a critical point (fig. 1), in complete analogy to the gas-liquid condensation [8]. At low pressure the fl-phase appears when temperature is lowered. This double hexagonal closed-packed fl-allotrope of Ce is antiferromag- netic below 12.5 K and exhibits the Kondo effect [8,91.

Kmetko [10], on the basis of APW band calcu- lations, reported the 4f electron in both , /and a Ce are somewhat itinerant, in contradiction to the simple promotional model described above. In agreement with this observation, Johansson pro- posed the Mott transition in the 4f shell to explain the y ~ a transition. In addition, other experimen- tal observations, such as positron annihilation [ 12], Compton scattering [13], neutron scattering [14] and photoemission [15], also refute the simple promotional model. To further examine the et, fl and 3' phases, we have chosen the positron annihi- lation technique, because the positron result de- pends on the nature of electronic wavefunctions a n d in o t h e r cases [16] ( S m S a n d

0304-8853/83/0000-0000/$03.00 © 1983 North-Holland

Lg A.M. Boring et al. / Positron lifetimes in cq fl and y cerium

6 5 0 - - - • - T

6 0 0 [

550F I I

500'*

450~ y

~ 4 0 0 F . Ld

350"

o~ i' / LJ 300~-~ "

J\ / 2509 ~,

V -+7" r

CP

/ ! / ~

/

/ /

/ / /

i I

5% i

0 '4 0 8 112 1.6 2L.O PRESSURE, GPo (tOkb)

24

Fig. 1. Low-pressure, low-temperature region of phase diagram of c~,/3 and y Ce. The letters C.P. mean critical point (from ref.

[81).

program EXFIT, which includes the width of the resolution function as an adjustable parameter [17]. Improvements in our lifetime spectrometer [18] allowed us to use 40% energy windows and rela- tively large ( - -20 cm 3) scintillators (thereby com- pensating for gamma-ray attenuation in the walls of the pressure cell), while still achieving a time resolution of about 250 ps fwhm. Our self-clamped pressure cell (fig. 2), designed by Chu and de- scribed previously [19], maintains a hydrostatic pressure of up to 2.0 GPa, using a 50-50 mixture of n-pentane and isoamyl alcohol as the pressure transmitting medium. Use of hydrostatic pressure minimizes the probability that stress-induced de- fects will affect the positron lifetime and mask effects that could be caused by the phase transi- tions. The source (22Na) is glued between two thin Ce plates ( -- 0.5 mm thick).

The cerium samples used in this study were cut using a low speed diamond saw from the same stock material (see table 1 for the chemical analy- sis). After cutting each sample was cleaned by electropolishing, sealed in a tantalum crucible, heat treated by annealing at 700°C for three hours, and then air cooled. At this point all samples were in

[Sm0jGdo.2]S - whose 4f electrons are even not as extended as those in Ce) substantial changes in positron lifetimes have been produced by valence transitions.

2. Experimental technique

As pointed out above, the positron annihilation technique was first applied to Ce by Gustafson et al. [12]. They used the centroid shift method, which measures only the average lifetime of all positrons observed. Their data show slightly different life- times in the two phases, but the uncertainties were large (_+ 20 ps, or about 8%, in some cases), and their results could be influenced by changes in the percentage of positron annihilating in the source material. In contrast, our method separates the source component from the annihilations in the sample, by fitting the entire lifetime spectrum to a sum of two exponentials using the fitting program P O S I T R O N F I T E X T E N D E D as well as our own

ThREAOEC CuBe CAP

CuBe DISC. ,i" - - CuBe BOD~

TUNGSTEN CARBIDE PIN

TEELON STOPPER

CuBe BUSHES ~ ~ AN: . . . . ENTANE

" \ \ \ ~ TEFLON CJP

TUNGSTEN ~ SANDWICN CARBIDE PIN

CuBe OISE THREADED

Fig. 2. High-pressure clamp.

A.M. Boring et aL / Positron lifetimes in a, /3 and )" cerium L9

Table 1 Chemical analyses of cerium. All impurity levels are in ppm atomic (elements not listed were found to be present at an impurity level of less than l ppm)

Impurity Concentration Impurity Concentration

H 556 Cu < 2 B < 8 Y 1 C 222 Nb < 5 N 300 Ba < 2 O 394 La < 4 F 96 Pr 13 Si 2.6 Nd 4 CI 2 Gd 4 Cr 1 Tb < 3 Ni 2 Ta 20

the y Ce polymorphic form. The a Ce form was obtained by pressurizing the y Ce samples using the technique described above. The fl Ce form was obtained by using the cooling-warming cycle (298

4.2 ~ 298 K) plus annealing (348 K) process described by Koskimaki et al. [20]. This procedure was repeated six times to insure complete conver- sion of the y form to fl Ce.

3. Re su l t s and d i s c u s s i o n

Fig. 3 shows some typical positron lifetime spectra in a, fl and y Ce at 1.4, 0 and 0 GPa, respectively. (The pressure uncertainty is estimated to be about 0.05 GPa; the pressure was rechecked at the end of each run.) Two-component fits were o b t a i n e d fo r e a c h c u r v e u s i n g b o t h f i t t i ng p ro -

g r a m s . T h e e s t i m a t e d s t a n d a r d d e v i a t i o n in e a c h

r e s u l t is a b o u t 2 ps, a n d t he a g r e e m e n t b e t w e e n

t he r e su l t s of t he tw o f i t t i ng p r o c e d u r e s is c o n -

s i s t e n t w i t h t h a t e s t i m a t e . T h e s o u r c e c o m p o n e n t

was la rge ( - - - 1 0 % ) a n d was o b s e r v e d to c h a n g e

c o n s i d e r a b l y as t h e p r e s s u r e w as a p p l i e d ; s u c h a

c h a n g e w o u l d h a v e a m o r e se r ious e f fec t o n p rev i -

o u s r e su l t s in w h i c h o n l y t he c e n t r o i d sh i f t was

m e a s u r e d [ 12].

T a b l e 2 s h o w s t he r e s u l t s o b t a i n e d a t p r e s s u r e s

o f 0, 0.9 a n d 1.4 G P a a t r o o m t e m p e r a t u r e a n d at

80 K. T h e f i rs t f o u r r e s u l t s a re f r o m o n e s a m p l e

o r i g i n a l l y in the y p h a s e (a t r o o m t e m p e r a t u r e a n d

,o 5

d

F-

,#

"04 ~ O O

A & 0 °

5 ~ o - oo~ o

0 A 0 0 A 0

O°O0~I~L~C ~ 0 o A

o & O

0 0 f I I I I ~ I 0

)O 200

CHANNEL NUMBER

Fig. 3. Positron lifetime spectra in (O:), Ce, 1.4 GPa; r,: /3 Ce, 0 GPa; circles: 7 Ce, 0 GPa). Each point gives the average count in several channels. Same vertical scale applies to all three curves. Horizontal scale is 12.5 ps/channel.

ambient pressure), and the last two results are from a second sample originally in the fl phase. As shown, the variation in lifetime is remarkably small, even smaller than changes that have been observed in other metals as pressure and tempera- ture are varied and no phase transition occurs [21 ].

Table 2 Positron lifetimes in cerium

Phase a Mean lifetime (ps)

),(293 K, 0 GPa) 235 + 1 a(293 K, 0.9 GPa) 232 + 2 a(293 K, 1.4 GPa) 230 + 2

a(80 K, 1.4 GPa) b 233 + 2

fl(293 K, 0 GPa) 236+2 a(293 K, 1.4 GPa) 236 + 2

a First four results are from one sample originally in the V phase. Last two are from a second sample originally in the/3 phase.

b Pressure is less certain for this run, but the sample had to be in the a phase at this temperature.

LI0 A.M. Boring et aL / Pos'itron lifetimes" in a, [~ and y cerium

The argument from band calculations has been that no change in the lifetimes is in agreement with no change in f electron count. Most of the band calculations (relativistic, either spin-polarized [22] or non-spin-polarized [23]) give about 1.2 f electrons in both the c~ and "/ phases. Boring has performed an LMTO calculation [24] in which the 4f-electron is localized (or in a resonant orbital) as would be more appropriate to the y phase. In this calculation, it was found that 0.2 f electrons are in the band states (plus 1.0 localized 4f) giving again a total of 1.2 4f electrons. Therefore all these band calculations given give about 2.8 non-f electrons in the conduction band ( = 0.3 s, = 0.7 p and = 1.9 d electrons) in both phases. This fixed electron charge indicates a similar response to charged particles (positrons) in both c~ and ~, Ce. A detailed consid- eration of this point must await a proper calcula- tion of the y phase in which the electron correla- tion is included [25]. The recently proposed many-electron Kondo model by Allen and Martin [26] is also consistent with the same electron charge distribution in both phases with the "collapse" being due to increased coupling between the "4f" electrons and the conduction band electrons as pressure is applied. Again, this many-body theory is also in agreement with our results.

Acknowledgements

We would like to thank A.J. Freeman for many discussions and C.W. Chu for providing us with the pressure cell. Some of us (Boring, Huang and Gschneidner ) are supported by the US Depart- ment of Energy. The rest were supported by NSF grant number DMR79-06726.

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