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Submitted on 1 Jan 1979
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Inelastic neutron scattering from liquid cerium
B. Rainford, V. Nguyen
To cite this version:
B. Rainford, V. Nguyen. Inelastic neutron scattering from liquid cerium. Journal de Physique Collo- ques, 1979, 40 (C5), pp.C5-262-C5-263. �10.1051/jphyscol:1979597�. �jpa-00219014�
JOURNAL DE PHYSIQUE Colloque C5, supple'rnent au no 5, Tome 40, Mai 1979, page C5-262
Inelastic neutron scattering from liquid cerium
B. D. Rainford (*) and V. T. Nguyen (**) (?)
(*) Biackett Laboratory, Imperial College, London SW7 2BZ, U.K.
(**) Physics Department, University of Leicester, U.K.
Resume. - Par des mesures de diffusion inklastique de neutrons, nous avons determine la dkpendance en tempk- rature de la susceptibilitk des Blectrons 4f du mktal cCrium jusqu'au-del8 de sa tempkrature de fusion. Les resul- tats confirment une d6localisation partielle des klectrons 4f dans 1'Ctat liquide. L'importance de cette dklocali- sation semble augmenter avec la tempkrature. Nos rksultats sont en dksaccord avec d'autres mesures antkrieures sur du ckrium liquide.
Abstract. - Inelastic neutron scattering measurements have allowed the temperature dependence of the 4f electron susceptibility to be determined through the melting temperature of cerium metal. The results confirm that there is a partial delocalisation of the 4f electron in the liquid state. The extent of the delocalisation appears to increase with temperature. Previous neutron diffraction data on liquid cerium are not compatible with our results.
1. Introduction. - Metallic cerium continues to attract considerable attention due to the unique features of its phase diagram [l]. These include the y-cc phase line which terminates in a critical point, and the fusion curve which has a negative slope as a function of pressure and a broad minimum above 30 kbar. The y-ct transition is thought to be associated with the promotion of the single 4f electron of y-Ce into the 5d conduction band. Recent inelastic neutron scattering data [2] are consistent with this hypothesis, since there is no evidence of paramagnetic scattering in the high pressure cr phase. The negative slope of the fusion curve was attributed by Jayaraman [l]
to a volume change resulting from a partial delo- calisation of the 4f electron in the liquid state. Sub- sequently Burr and Ehara [3] measured the magnetic susceptibility of cerium through the melting tempe- rature, but inferred that the small reduction in susceptibility on melting could be attributed to changes in the Pauli susceptibility and the effects of the structural changes on the f electron para- magnetism. They concluded that there was no delo- calisation in the liquid. More recently Enderby and Nguyen [4] claimed to show by neutron diffraction measurements that about 20
%
of the cerium ions were instantaneously magnetically inactive in the liquid state. However these authors compared their cross sections measured at 870 OC with those to be expected from the 2F,,, state, and ignored the significant population of the 'F,,, level. We estimate that when the population of the J = 712 level is taken into account the magnetic cross sections of reference [4]are consistent with a 34
%
delocalisation. We show below however that neutron diffraction data (i.e.total scattering measurements) are likely to be very misleading in this situation since the quasi-static
approximation, implicit in the analysis of the data, is not valid.
There have also been reports in the literature of well defined crystal field excitations in liquid cerium [5], with energies of 3.3 and 6.9 meV.
In an attempt to throw some light on this some- what confused situation we have carried out inelastic neutron scattering measurements on solid and liquid Ce and La at a number of temperatures.
2. Experimental procedure and results - Measure ments were made using the twin rotor time of flight spectrometer a t the Pluto reactor, A.E.R.E.. Harwell.
The incident neutron energy was 12.5 meV. and the flight path 1.8 m. Although data were collected for scattering angles between 110 and 700. only the low angle data (110-250) are presented here. These have elastic wave vector transfers well below the position of the first maximum in S ( Q ) of liquid Ce, hence the scattering is dominated by the magnetic cross section.
For the cerium sample time of flight spectra were measured at 950 and 840 OC (liquid state) and in the solid state at 650, 460 OC and room temperature.
Additionally a La sample was measured at 950 OC (liquid state) and at 650 0C (solid). Background measurements were made before loading the samples at each temperature. Typical runs were of 40 hours duration. Intensities were placed on a common scale by normalising spectra against the total incident neutron intensity, as measured by a monitor detector.
The intensities were also scaled to allow for the variation of the density with temperature. and for the difference in density between Ce and La. The time of flight spectra were corrected for the tempe- rature population factor. then the magnetic cross sections were obtained by subtracting the appropriate
(+) Present address : Shell Research Centre, Thomton, Chester CH13SH. U.K.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979597
INELASTIC NEUTRON SCATTERING FROM LIQUID CERIUM C5-263
La spectrum scaled by a factor M,, b&/Mct bf, where b is the nuclear coherent scattering ampl~tude, and M is the atomic weight. This should yield an accurate estimate of the nuclear contribution to the cerium spectra. The nuclear cross section was nowhere greater than 50
%
of the measured cross section, and for energy transfers greater than 25 meV it was less than 10 of the total. The time of flight cross sections were converted into the imaginary part of the generalised susceptibility Im x(Q. U). But rather than plot this function we prefer to display in figure 1 the function-
1 Im x(Q. U). which is an even functionW
of the energy transfer. This enables us to use the identity [6]
and the associated sum rule [6]
S-,
m doF(Q. U) = l.
(2)The magnetic scattering is seen in figure 1 to consist of a broad inelastic distribution whose width is markedly temperature dependent. The line shape is close to Lorentzian in form :
These results are in agreement with our earlier mea- surements on solid Ce [7]. We have previously attri- buted the large energy width to the rapid relaxation of the 4f electrons by the conduction electrons (Korringa process). The linewidths T. obtained by fitting a Lorentzian function (3) to the data in figure 1.
are seen in the inset in figure 1 to be roughly pro- portional to the absolute temperature Bt high tempe- ratures. The departure from linearity for the room temperature data is a consequence of ignoring the crystal field splitting which would modify the line- shape function [7] when the linewidth is comparable to the crystal field splitting. We note that the line- widths are very large (- 30 meV) in the liquid state.
These results invalidate the claim that well defined crystal field excitations exist in liquid cerium [5].
We may also infer that in neutron diffraction measure- ments on liquid Ce with 1
A
neutrons, like those described in reference [4], the quasi-static approxi- mation cannot be valid, since energy transfers of the order of the incident neutron energy are possible.Using the sum rule (2) we note that the area under the function l/w Im x(Q, U) gives a measure of the static susceptibility x,(Q) of the 4f electrons. Since the Refer [l] JAYARAMAN, A., Phys. Rev. 137 (1965) A 179.
[2] RAINFORD, B. D., BURAS, B. and LEBECH, B., Physica 86-88B (1977) 41.
[3] BURR, C. R. and EHARA, S., Phys. Rev. 149 (1966) 551.
[4] ENDERBY, J. E. apd NGUYEN, V. T., J. Phys. C 8 (1975) L 112.
[5] MILLHOUSE, A. H. and FURRW, A., Phys. Rev. Lett. 35 (1975) 1231.
E N E R G Y I m e V l
Fig. 1. - l/w Im x(Q, w) for solid Ce at 293, 733 and 923 K and for liquid Ce at 1 113 and 1 223 K. Inset : the variation of the half widths
r
(meV) (open circles), the areas (i.e. X,) (solid circles) and the bulk susceptibility X, (crosses) (arbitrary units) with tempe- rature.scattering is dominated by single ion phenomena (spin lattice, not spin spin relaxation) we may ignore the Q dependence of z,(Q). The areas under the experimental curves in figure 1 were calculated from the Lorentzian fitting and are displayed in the inset in figure l as solid circles. together with the bulk susceptibility X, [8] (crosses). The values of X, (areas) have been scaled by a constant to agree in magnitude with those of X,. to aid their comparison. It can be seen that the temperature variation of X, and X, is similar up to 650 OC. but that in the liquid state X, falls substantially below X,. This indicates that there is a partial delocalisation of the 4f electron in the liquid state amounting to 15
%
at 840 OC and 26%
at 950 oC. The effect of this delocalization on the bulk susceptibility is not very marked since a pro- motion of a 4f electron into the 5d conduction band, while reducing the 4f susceptibility will at the same time increase the Pauli susceptibility.
[6] MARSHALL, W. and LOVESEY, S. W., Theory of Thermal Neutron Scattering (OUP) Chap. 8.
[7] RAINFORD, B. D., in Crystal Field EBects in Metals and Alloys ed. A. Furrer (Plenum) 1977 p. 243.
RAINFORD, B. D., D. Phi1 Thesis (1969) Oxford University (unpublished).
[8] SCHLAPBACH, L., Phys. Cond. Matter 18 (1974) 189.
