Specific heats of actinide metals

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Specific heats of actinide metals

M. Mortimer

To cite this version:

M. Mortimer. Specific heats of actinide metals. Journal de Physique Colloques, 1979, 40 (C4), pp.C4-

124-C4-129. �10.1051/jphyscol:1979438�. �jpa-00218834�

JOURNAL DE PHYSIQUE Colloque C4, supplément au n° 4, Tome 40, avril 1979, page C4-124

Specific heats of actinide metals

M . J. M o r t i m e r

Chemistry Division, AERE Harwell, Didcot, Oxon, OX11 ORA, G.B.

Résumé. — Nous discutons les méthodes qui permettent, à partir des paramètres de la chaleur spécifique, de déterminer le coefficient électronique y et la température de Debye 0D. Nous étudions l'évolution de ces grandeurs ainsi que celle de la chaleur spécifique le long de la série des actinides. Les valeurs inattendues obtenues pour le protactinium sont comparées à celles de la résistivité électrique. Nous discutons l'importance du coefficient de dilatation pour la chaleur spécifique et pour les propriétés électroniques. Finalement nous comparons les anomalies observées pour a - U , Pu et Am.

Abstract. — After a brief discussion of the methods of extraction of the specific heat parameters, the electronic specific heat and the Debye temperature, an analysis is given of the trends in these, and in the measured specific heat, across the actinide series. The unexpected values obtained for protactinium are considered, with reference to the electrical resistivity. The importance of the expansion coefficient, both in the derivation of the specific heat parameters, and in any explanation of the electronic origins of their behaviour is discussed. Finally, the anomalies observed in ct-U, Pu and Am are compared.

1. Introduction. — Since t h e last r e v i e w of t h e specific h e a t s of t h e actinide metals [1] a d v a n c e s h a v e b e e n m a d e in a n u m b e r of d i r e c t i o n s . T h e first m e a s u r e m e n t s h a v e b e e n r e p o r t e d for t h e rarer a c t i n i d e s , p r o t a c t i n i u m a n d a m e r i c i u m , while mea- s u r e m e n t s on p l u t o n i u m h a v e b e e n m a d e at lower t e m p e r a t u r e s , using t h e less active i s o t o p e 242Pu.

F u r t h e r w o r k h a s b e e n d o n e on t h e low t e m p e r a t u r e a n o m a l i e s in a - u r a n i u m , a n d o n t h e variation in e l e c t r o n i c specific h e a t w i t h crystallinity.

I n this p a p e r I begin with a s u m m a r y of t h e m e t h o d s w e h a v e u s e d in analysing t h e available specific h e a t d a t a in v a r i o u s t e m p e r a t u r e r e g i o n s . T h e n t h e specific h e a t of e a c h actinide e l e m e n t is r e v i e w e d in t u r n , with a discussion of a b s o l u t e v a l u e s , of t h e n e w m e a s u r e m e n t s derived p a r a m e - t e r s , a n d of a n y a n o m a l o u s b e h a v i o u r . Finally, t h e variation in specific h e a t s a c r o s s t h e series is dis- c u s s e d a n d related t o o t h e r p r o p e r t i e s .

2. Analysis of specific heat data. — T h e specific h e a t s of real materials m a y b e d e s c r i b e d b y a D e b y e model in t w o t e m p e r a t u r e r a n g e s : b e l o w T = 0D/5O a n d a b o v e T = 6J2.

High t e m p e r a t u r e Cp data as m e a s u r e d a r e first c o r r e c t e d to C„, t h e dilation c o r r e c t i o n being given b y :

w h e r e a is t h e coefficient of linear t h e r m a l e x p a n - sion, V is t h e molar v o l u m e a n d K t h e compressibi- lity.

T h e lattice specific C, is calculated for a range of e l e c t r o n i c specific h e a t coefficients y, a n d t h e n u s e d

t o give t h e D e b y e t e m p e r a t u r e 6D at e a c h t e m p e r a t u r e

Cl=Cv-yT = f(6D, T) .

T h e best value of y is t a k e n as t h a t for w h i c h 6D is c o n s t a n t a s a function of t e m p e r a t u r e .

At low t e m p e r a t u r e s , t h e m e a s u r e d v a l u e s of Cp

a r e given b y

Cp = yT + pT3

h e r e /8 is related t o t h e D e b y e t e m p e r a t u r e 0D. T h e e q u a t i o n is valid u p t o s o m e m a x i m u m t e m p e r a t u r e

T .

max

E x a m p l e s of t h e s e d e r i v a t i o n s a r e given in figures 1 a n d 2 for 242Pu [2].

E a c h table given in this p a p e r is divided into t w o p a r t s . T h e u p p e r part s u m m a r i z e s results u p t o r o o m t e m p e r a t u r e , with a n a l y s i s , w h e r e given, a s detailed a b o v e . I call this high temperature data. T h e lower p a r t of e a c h t a b l e gives l o w t e m p e r a t u r e d a t a .

3. Results. — 3.1 THORIUM (Table I). — N o fur- t h e r high t e m p e r a t u r e m e a s u r e m e n t s h a v e b e e n r e - p o r t e d since t h o s e of Griff el a n d S k o c h d o p o l e [3], r e v i e w e d earlier [1]. A t l o w t e m p e r a t u r e s , a s p r e - viously r e v i e w e d [4, 5] G o r d o n et al. [5] f o u n d a y value of 4.31 ± 0 . 0 5 , for v a n A r k e l t h o r i u m , total metallic impurity level 20 p p m , a n d non-metallic level 230 p p m . N e w low t e m p e r a t u r e r e s u l t s r e - p o r t e d by L u e n g o et al. [6] s h o w a value of y of 4.08 ± 0.03 for 99.95 % p u r e t h o r i u m . T h e y s h o w t h a t alloying with u r a n i u m c a u s e s a rapid increase in

y of 4.85 ± 0.5 m J . m o l "1. KT2 (at % U ) "1. This is higher t h a n h a s b e e n o b s e r v e d in o t h e r s y s t e m s .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979438

SPECIFIC HEATS OF ACTINIDE METALS

Fig. 1. - Extraction of high temperature y and OD values for ='Pu.

' ^--L-LLJ -

situation.

T E H P E R ~ T U R E ~ I K ~ I The specific heat measurements show no effect at

103 K where both sets of resistivity measurements Fig. 2 . -Low temperature specific heat of w2pU. show a small change of slope.

I I I I I I I I I I I I ~

-

-

PLUTOYIUH-2L2 +ADDENDA

t 111 BRASS STRIP

r 2nd BRASS STRlP

-

-

-

-

-

(Fig. 3). Because of the small mass available, only 25 % of the sample was protactinium. A careful analysis of the two sets of data has failed to reveal.

any systematic error to account for the difference in y in the two temperature regions. It is worth noting, however, that while early rather imprecise electrical resistivity measurements [9] gave results between those of thorium and uranium, recent more precise measurements

[lo]

suggest a value for the electrical resistivity much lower than that for thorium, per- haps supporting a low y value. Specific heat measu- rements on more massive samples will clarify the

,

,.. .

confuse the picture, the low temperature

measurements [8] indicate a value close to zero Fig. 3. - Low temperature specific heat of protactinium metal.

3.2 PROTACTINIUM (Table I).

-

The first results 120-

of specific heat measurements on protactinium me-

tal present a confusing picture. A single sample, ^{% IOO-} prepared by the van Arkel process (typical impuri- a

Ole 5 8 0 -

-

-

ties < 400 ppm metallic : 900 ppm 0, 40 ppm N,

. .

50 ppm C) was measured from 10 to 300 K [7] _{6 0 -}

and below 20 K [8]. The room temperature C,, ^Pa

33 +- 1 J

.

mol-'

.

K-' was higher than expected, ^{o Hagh k} s t r t p r Low k s t r l p

being much higher than that of either of its neighbours. In turn, the derived y value, 30 mJ

.

mol-'

.

K-' is the highest of any of the actini-

de elements for which results are available. To ^{0 100} 7 2 , u 2 , ^{200 300 LOO}

C4-126 Table I.

M. J. MORTIMER

Year of Pub.

Temperature range of measurements

Electronic coefficient y mJ

.

^{mol-' . K-2}

-

Debye

temperature T max for OD linear C,,/ T

- -

Refs.

-

a Griffel and Skochdopole 131 Smith and Wolcott

8

Gordon, Montgomery et a/.

Luengo et al.

$ Brown, Hall et al.

5 .a

$, Hall, Mortimer, Blaise et al.

Jones, Gordon and Long Clusius and Piesbergen Flotow and Lohr

Lee, Mendelssohn and Sut- cliffe

Sandenaw Smith and Wolcott

.z

Goodman, Hilliard et al.

Dempesey, Gordon et al.

'

Flotow and Osborne Gordon, Montgomery et al.

Ho, Phillips and Smith Crangle and Temporal Bader, Phillips and Fisher Hall and Mortimer Hall

27.48 not given

27.66

(*) 10 kbar.

(*) Depends on crystallinity = single crystal -+ polycrystal.

3.3 URANIUM (Table I).

-

Previously reviewed high temperature results 111-141 give a coherent picture with (C,),,, about 27.5 J

.

mol-'

.

^{K-' and}

derived y of about 8 to 8.8 mJ

.

^mol-'

.

^{K-,. The one}

new paper [IS] does not give y or Cp values, but looks instead at various specific heat irregularities and consequent entropy changes as a function of cold work and annealing.

Earlier low temperature results [4, 5, 16, 17, 181 were mostly consistent with a y value of about 10.0, although there was some variation in the derived 0,. More recent measurements have looked at the effect of pressure [19] and of variations in crystallinity [20, 211 on y and at the various low temperature anomalies in a-uranium [20, 22, 231.

The measurements of Ho, Phillips and Smith [I91 at zero pressure gave a y value of

10.3 mJ

.

^mol-'

.

K-', while at a pressure of 10 kbar this rose to 12.2 mJ

.

^mol-'

.

K-'. Furthermore, whi- le the zero pressure measurements showed no ma- gnetic field dependence, and no anomaly characte- ristic of a superconducting transition down to 0.35 K, the high pressure measurements indicated that bulk superconductivity occurred at about 2 K, and was destroyed by the application of a field of 2 000 Oe. Later measurements [21] did show the existence of bulk superconductivity in a -uranium, but only below 0.3 K in a single crystal or, smeared out at slightly higher temperatures, in polycrystalline uranium. Thus both y and

T,

rise with pressure.

Another property affecting y is the crystallinity.

Crangle and Temporal [20] measured a single crys-

tal, a polycrystalline sample with large grains, and a polycrystal, and showed that y rose from 9.14 mJ

.

^mol-'

.

K-2 through 9.46 mJ

.

^mol-'

.

^{K-' to}

10 mJ

.

^mol-'

.

K-Z while 0, fell from 210 to 195.

This rise was confirmed by Bader et al. [21] who found a rise in y from 9.14 to 9.90 mJ

.

mol-'

.

^{K-2 in}

a similar series. Since polycrystals also show an enhanced T , it is apparent that the inhomogeneous strains in the crystal affect y and

T,

in the same way as hydrostatic pressure. The question of whether this is mainly electronic in origin [24] or is accounted for by the effect of pressure on the phonon spectrum [21] is not yet clear.

Following the early results of Steinitz et al. [25]

which showed 2 f i s t order (at 22 K and 37 K) and 1 2nd order transition (at 43 K) in expansion measure- ments on a-uranium single crystals, specific heat measurements [20] confirmed presence of the asso- ciated latent heats in single crystals. Having con- firmed earlier measurements on a single crystal [20], Hall [23] heat treated the sample to convert it to a large grained polycrystal, then progressively de- creased the grain size, showing that the 2 first order transitions were progressively suppressed and the second order smeared out. This effectively disposed of the idea that these low temperature anomalies might not be intrinsic to pure uranium, but be produced by impurities left in during the crystal growing process [IS, 221.

The specific heat of uranium in this temperature range is now fairly well defined. The origin of the anomalies is not clear. If magnetic in origin it must

SPECIFIC HEATS OF ACTINIDE METALS C4-127 presumably be some form of spin density wave, not yet linear ; if a high temperature fit is made, giving a magnetic structure below 43 K which under- as outlined in section 2, a y value of goes minor atomic re-arrangement at 22 K and 15.5 d

.

mol-'

.

KT2 is found. Apart therefore from 37 K [26,20]. If this is the case the magnetism must some thermal cycling effects these are in good be below the detection limit in neutron diffraction agreement with previous measurements on 2 3 9 P ~ . measurements [27]. The second of the measurements [2] on 242Pu gives a

3.4 NEPTUNIUM (Table 11).

-

Previously discus- sed measurements [28, 29, 301 at high temperatures showed neptunium to have a normal specific heat- temperature dependence, with no anomalies. The y value derived from high temperature data was 14.2 and 8, 187 K. These measurements taken down to 7.5 K [29, 301 permitted low temperature parame- ters to be determined. They proved not very diffe- rent.

Two further measurements at low tem- peratures [2, 311 confirmed this y value, al- though a much higher value of 8, was found, 240 K.

The materials used were of quite different origins.

Since the temperature region of the latter measure- ments covered more of the linear C, T region, this value of 8, is preferred.

lower (C, ),,, of 3 1.19 J

.

mol-'

.

K-', hence a lower y of 10.5 mJ

.

mol-'

.

K-2. Following various tests [2]

no systematic error was found, and this result is believed genuine, even though low. The sample was also measured at low temperature [2] when a much higher y value of 22 was found. There was good agreement between the two sets of measurements in the region of overlap. Other measurements of Gordon [37] also support a higher low temperature y value.

Whether or not the y value derived from the 242pU high temperature data is accepted, the measure- ments contrast with those on neptunium results taken at the same time, where high and low tempera- ture regions gave y values to within about 4 %. In the case of plutonium the high temperature y is 50 % or 100 % lower than the low temperature y depend- ing on which high temperature y value is taken.

Differences in anharmonicity are unlikely to be significant, so one is forced to conclude that the electronic specific heat is different in the high and low temperature regions. It is tempting to associate this with the decrease in electrical resistivity above 100 K, not directly as a change in the density of states, but perhaps on a spin fluctuation model, which has been invoked to explain the resistivity (Ref. [2] and references therein).

The small anomaly at 60 K seen in several sam- ples of 2 3 9 P ~ [29,30] was not seen in '"'Pu. The point 3.5 PLUTONIUM (Table 11).

-

The high temperatu-

re data 129-351 (all taken on '"Pu) mostly gave (C, ), values between 3 1.97 and 32.82 J

.

^mol-'

.

^{K-', y}

values between 11.9 and 15.9 mJ

.

^mol-'

.

K-2 and 8, of about 160 K. Since this earlier data two reports giving high temperature data for '"Pu have been published [36, 21. In the first of these, Sandenaw reported some dependence on thermal cycling, but gave (C, ),,, = 32.9 J

.

mol-'

.

^{K - ' ,} though with a ve- ry high y = 44 mJ

.

^mol-'

.

K-'. This latter was cal- culated for the region near 15 K, where C,

/

T is

Table 11.

Year of pub. Refs.

-

- (1965) [28]

(1968, [29, 1970) 301

Temperature range of measurements

-

8-320 7.5-300

Electronic coefficient y mJ . mol-' . K-2

-

- ^13.8 14.2 ^C 0.5

Debye temperature

-

e,

-

¹⁹⁰

185 c 5

T max for linear CdT

- - - Sandenaw

Lee, Mendelssohn and Sut- c l i e

.-

3

Lee, Mendelssohn and Sut- cliife

Gordon, Hall et al.

(1968, [29, 1970) 301 (1976) C21 unpub. [31]

Blaise, Mortimer et al.

Sandenaw, Olsen and Gibney Sandenaw

Lee, Mendelssohn and Sut- cliffe

g

Taylor, Loasby, Dean et a[.

.- Lee, Mendelssohn and Sut- cliffe

Sandenaw, Gibney (Pu242) Gordon, Hall et al. (Pu242) Gordon, Hall et al. (Pu242) Gordon, Hall et al. (Pu239) Gordon (Pu242)

(1976) 121 (1976) E21 unpub. [37]

Miiller, Schenkel et al.

'G Smith, Stewart, Huang and

.- (1978) this

c o d .

(*) Recalculated from high temperature data.

C4-128 M. J. MORTIMER is fully discussed in reference [ 2 ] . Its non-

observance is not due to poorer precision in the latter case. The suggestion that its presence or absence depends on the purity of the sample warrants closer investigation ; a difference between the '"'Pu and z3h samples is the higher americium content of the latter. Magnetic susceptibility studies of low concentrations of Am in Z42Pu might be worth examining.

3 . 6 AMERICIUM (Table 11). - The first reported specific heat measurements on americium [38] show a break with results for earlier elements. The room temperature specific heat (C, ,,) has fallen to 28 J

.

mol-'

.

K-I, not much above those for uranium and thorium, and y to 3 mJ

.

mol-'

.

K-', well below earlier values. While the precision of these measure- ments is necessarily reduced, in view of the high self-heat of americium, these results show that the intervention of the 5f electrons in conduction is much reduced, a conclusion supported also by elec- trical resistivity measurements [2] ( I ) .

Both specific heat and electrical resistivity show a pronounced anomaly at 6 0 K (Fig. 4). That in the specific heat is much more pronounced than in any other actinide metal. It is evidently not magnetic in origin, but seems rather spread out to be the latent heat associated with a structure change. Measure- ments of other properties, for example, lattice para- meters, are required to give further information.

given to measuring such highly active materials. The specific heat of protactinium is not at all clear. Here samples of a greater mass are required to give more precision.

The derived specific heat y and 8, values may be compared with other selected parameters :

exp. coeff.

a x lo6 11.6 10.3 14.9 27.7 53.7 - 7.07 XRT 0.41 1.16 1.6 2.28 2.15

-

2.8 (*) At time t = 0, normalized for self-heat.

While the y values (apart from that for protactinium) change regularly across the series, the 8, values do not follow any trend. There is no clear correlation between the measured magnetic suscep- tibility values, which peak a t americium with a dip at plutonium, and either the y values or the resistivity behaviour. This, and the lack of temperature depen- dence of the susceptibility is the problem which has occupied many people attempting to reconcile strong resistivity ,temperature dependence with essentially temperature independent susceptibilities (see Ref. [39] and references therein).

T E M P E R A T U R E I K )

Fig. 4. -Specific heat anomalies in the actinide elements.

4. Discussion. - For the well-known actinides, thorium, uranium, neptunium and plutonium, the specific heats are fairly well defined. More measure- ments can be expected to refine the data, and to define further the anomalous behaviour. In the case of americium, the general picture is clear, with a drop in C, compared with earlier elements. The thermodynamic functions are not well-known, and

+-+ f Specif~c Heat

+

^{x-.-.-x P J D 0}

0 - - - 4 a Expansion

before they can be defined, further thought must be

I I

0

I I I I 1 I

I

Th Pa U Np Pu Am

(') Low temperature measurements by Smith et al. (this

conference) indicate a y value of 2 mJ . mol-' . K-'. Fig. 5. - Selected results normalized for Pu = 1.

1 - - -

'./ .

^{N~ /' ::}

L-- -v-

,.

^{x ;. ..:}

v.

+

P 3 ~ 0 -./' .o. i:

,.' ...- l n ~ t ~ a l Self o... Damage

-

^{r a t e}

-

-

-

-

- -+ -

- - -

-

- - - - - - -

-

-

-

.

SPECIFIC HEATS OF ACTINIDE METALS C4-129 The expansion coefficients, on the other hand, are

not often discussed. To make the trend more clear, the high temperature y values, the resistivity data and the expansion coefficients have been norma- lized to Pu ⁼ l (Fig. 5) and it is clear that each shows similar variations across the series. The correlation is even closer with low temperature y values.

A correlation also exists between expansion coef- ficients of high temperature phases of plutonium and their electrical resistivity coefficient. Even where the expansion coefficients are negative, the coeffi- cients are in every phase inversely related in sign [40].

However the reason for a correlation between measured expansion coefficients and the electronic properties is not evident. The expansion coefficient may be expressed as the sum of a lattice component and an electronic component. The separation of these terms has been performed at low temperatures [41,24] using an equation analogous to that in section 2 for specific heat. The correlation between a and y suggests a very important electro- nic component in the expansion coefficient. This would merit future study and calculation to separate these components, as well as careful expansion coefficient measurements.

References

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[41] WHITE, G. K., Philos. Mag. 6 (1961) 815.

COMMENT

Pr. A. J. FREEMAN.

-

The higher y-value for a - U under pressure appears to be due to the sup- pression of the low temperature transitions. There- fore, it appears to be correct to assign the higher

y -value (12.2) as the true y -value of a -U.