The specific heat of actinide compounds : are those measurements useful ?

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The specific heat of actinide compounds : are those measurements useful ?

A. Blaise

To cite this version:

A. Blaise. The specific heat of actinide compounds : are those measurements useful ?. Journal de

Physique Colloques, 1979, 40 (C4), pp.C4-49-C4-61. �10.1051/jphyscol:1979417�. �jpa-00218813�

The specific heat of actinide compounds : are those measurements useful ?

A. Blaise

Centre &Etudes NuclCaires de Grenobie, DLpartement de Recherche Fondamentale, Section de Physique du Solide, 85X, 38041 Grenoble Cedex, France

Rhsumh. - On rappelle bribvement les difficult& exp6rimentales et les problbmes posks par la separation de la chaleur spkcifique en ses diffkrentes contributions. On fait ensuite une revue des principaux rksultats connus sur les composks binaires et ternaires d'actinides. Ces resultats sont utilis6s pour discuter les modbles de structure Blectronique. On attire enfin I'attention sur 1'intCrCt des phknomknes critiques dans les composes d'actinides. Quelques exemples et suggestions sont donnts partir des systkmes citks prtcidemment.

Abstract.

-

The experimental difficulties and the problem of the separation of heat capacity data in its different components are briefly recalled. Then a review is given of the specific heat measurements made on the principal binary and ternary actinide compounds. In each case, the results are used to discuss the electronic structure models. Attention is drawn on the interest of studying the critical phenomena in the actinide compounds. Some examples and suggestions are issued from the systems above mentioned.

Introduction.

-

As will be shown below, relative- ly few results have been obtained on the specific heat of the An compounds. Some of those we do have date from a time when the chemistry of the actinides was still uncertain and others are contra- dictory. Why is there such a situation for the specific heat while the magnetic properties for instance, have been extensively studied ? In the first part I will discuss the experimental difficulties associated with specific heat measurements, and also the difficulties involved in interpreting those results. In the second part of this work, I will give a review of the most recent specific heat data for the actinide compounds. In a third part, I will draw attention to another possible interest of the specific heat measu- rements : the study of the critical phenomena in the magnetically ordered actinides.

1. The measurements : difficulties of the ex- periments and of their interpretation. - Everybo- dy knows the experimental difficulty of the specific heat measurements whatever method is used : ther- mometry accurate to 0.01 K, perfect screening of the calorimeter to avoid radiation losses, sample holder heat capacities which are often of the same order of magnitude as the specimen heat capacity.

For the actinides, the situation is worse : the self heating of the transuranium elements makes extre- mely difficult t o work at temperatures below 6-10 K.

Then, the extreme toxicity of these materials compels the use of a glove box, or the enclosure of the specimen in a container

-

a procedure which makes worse the problems of addenda correction and bad thermal contacts.

The interpretation itself of the measured heat capacity (which is C, : heat capacity at constant pressure) is another very difficult problem.

One can write :

C,,,, : lattice contribution

CCond : contribution of the conduction electrons C,, : magnetic contribution (cooperative transition) C,,,,, : contribution from the excited electronic states

C,,,, : nuclear contribution

C, : heat capacity at constant volume.

If we disregard C,,,,, a contribution which is generally negligible, above 1 K we see from eq. (1) that the specific heat can be an important source of information on the electronic structure of a speci- men provided that the resolution of the total heat capacity into its separate components can be made.

1.1 (C, - C, ) TERM.

-

The lattice contribution to the heat capacity is always assumed to come from harmonic forces. The anharmonic forces introduce a difference between C, and C, :

(a! : thermal expansivity, K : isothermal compressi- bility, V,,, : molar volume).

As a and K are not always available, neglecting C, is a first source of uncertainty especially at high temperature where Cd may reach several % of C,,,.

1.2 C,,,, TERM.

-

It is normally the most impor- tant term in (1) for T > 10 K and this term is also the

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979417

most difficult to determine. Its theoretical expres- 1.3 C,, TERM.

-

The conduction electrons give

sion is : rise to a contribution :

no

3 k Z dk

- d o (3) C,,,, = Y T (6)

y (0) being related to the density of state at the Fermi level, can, in principle, been deduced from a plot of and involves the knowledge of the phonon disper-

sion relation k(o).

In principle, the best way of getting C,,,, is to derive k(w) from an experiment, namely neutron inelastic scattering. If one does not have the phonon spectrum then one can use more or less good appro- ximations (Einstein function : o = constant = w , ; Debye function : o = v, k ; or a combination of both) which, in term, leads to more or less exact results for C,,,, with errors reaching some 10 % or more.

Attempts are sometimes made to get an experi- mental estimate of C,,, by measuring an isostructural compound with no magnetic component to the speci- fic heat (typically a thorium compound). The sim- plest assumption in that respect is the corresponding state approximation :

where k is a constant experimentally deduced.

Another useful relationship for isostructural compounds of neighbouring molecular weights M and M' where the Debye approximation is valid for the Th compound is :

or the more refined Lindeman's relation using the melting points T,,, and molar volumes V :

C, /T(T2) extrapolated at T = 0 : C,,,, being propor- tional to T3, the ordinate at the origin gives y(0).

But, C,,,,

-

T 3 is only valid at very low temperature and many experiments don't allow the correct deter- mination of y(0). In the free electron model y is essentially independent of T and could thus be determined even from high temperature measure- ment but this is an oversimplification and frequently is not in agreement with the experimental results : y, actually often decreases when T increases, and y (300) may be 50 % of y (0).

1.4 C,, TERM. - This is the term associated with the magnetic ordering of the Sf electrons in the actinides and the associated entropy has been the principal information sought in specific heat experi- ments. The problem in the actinides is that one is generally not sure at all of what is the electronic ground state of the Sf electrons and what is its multiplicity (because of similarity of the Coulombic, spin-orbit and crystal field interactions). Moreover, some Sf electrons very often take part to the conduc- tion and the contributions C,,,, and C,, cannot be distinguished.

1.5 C,,,, TERM. - This term comes from the excitation of the higher lying multiplets issued from the Sf electrons coupling. These levels don't pose any problems when their contributions to the speci- fic heat are well separated from each other and from any magnetic anomaly. Clearly, if this is not the case, it is difficult to resolve the electronic situation without additional information.

constant = M

v213

^{6 g(0)} _{2 . The} binary compounds.

-

As there is still no Tm comprehensive review paper for the specific heat of

the actinides, we will try to list all the known data for Typically, C,,, which may amounts for up to 95 % the main binary and ternary compounds. Some of the measured heat capacity at room temperature comments will be made on the most extensively is the main source of uncertainty in the interpreta- studied systems but this paper is seen only as an tion of the measurements. easy handling compendium to refer at.

Table I .

Compound -

uoz

NpO2 Puoz u409 UaO, a

P

Crystal structure

- f.c.c. CaFz-type

tetragonal deformation

of u o z orthorhombic

Latt. par.

A

C,(298,15)

T N . ~ AS(Tt) y (0) J/mole.K

K J/mole (K) m . J / m o l e . ~ ~ /An atom

S (298,15) J/mole.K /An atom Ref.

2.1 THE OXIDES.

-

All of the dioxides order in ly around 348 K tentatively ascribed to an the cubic CaF, structure. The other cited uranium order-disorder process involving the oxygen oxides crystallize in structures derived from CaF, by atoms.

more or less pronounced distortions. The data are U30,

-

: Exists under at least two different phases (a listed in table I. and p ) , both of which having been measured UO, : The definitive work and the most precise of all

-

the specific heat analysis referred to in that paper has been given by Huntzicker and, Westrum [I]. UO, is a simple type 1 antiferro- magnet with a A -type anomaly at 30.44 in agreement with the magnetic results. The latti- ce heat capacity has been estimated'by diffe- rent methods [I-31 and an excess found in the temperature region 30 to 120 K is attributed to a Jahn-Teller effect [I]. The spin-wave low temperature predictions fit the experimental C, at low temperature with reasonable agreement [I]. The position of excited crystal field levels above the triplet ground state for an assumed U4' ion don't coincide with the calculations of Rahman and Runciman [4].

NpO, : This compound is still a challenge for the theorists : magnetic susceptibility and specific heat [5] show a peak at 25 K, but neither neutron diffraction nor Mossbauer experi- ments give evidence of a magnetic ordering.

The very old measurements of Westrum et al. [5] propose a value of the magnetic entro- py of 7.11 taking C,,,, as a Debye function whereas [3] announce the value 15.06 (J/mole

.

K) taking C,,,, as the specific heat of Tho,. These differences illustrate clearly the need of a rigorous evaluation for C,,, to advan- ce serious figures for the ionization state and fundamental multiplet of the Np atom. Ques- tionable is also the chemical purity of the sample studied 24 years ago.

PuO,

-

: The old measurements of Sandenaw [6]

between 13 and 325 K agree with those of Kruger et al. [7] from 200 to 1 400 K and show a peakfree heat capacity in accordance with the magnetic results. More recently, Flotow et al. [8J worked on a 244pU02 sample between 4 and 25 K to get rid of the self-heating problem and find C, values lower than [6].

No other results are available for the actini- de dioxides. Many phases exist for the ura- nium oxides from UO, to UO,. The X-ray data for most of them have been collected by Westrum et al. [9] and, as potential reactor fuels, their specific heats have been measured by several investigators. The data may be found in table I.

U40,

-

: Studied by Flotow et al. [lo] from 1.6 to 24 K and by Osborne et al. [ l l ] from 5 to 310 K, this compound shows no evidence for a transi- tion around 6.4 K where a susceptibility maxi- mum was found. Above 300 K, several investigators [2, 12, 131 find a A -type anoma-

by [9] who give in [14] an excellent review of the specific heat of all the uranium oxides.

U,O, : Has been investigated by Westrum et al. [15]

-

in the low temperature range and by [16, 171 above room temperature. A A -type anomaly presumably of magnetic origin occurs at 25.3 K while another peak at 483 K is attri- buted to a very slight structural change [17].

Two other anomalies at 568 and 860 K are reported [I71 to be due to some order-disorder process.

UO,

-

: The very old data of Jones et al. [18] show no anomaly between 15 and 300 K .

2.2 T H E HALIDES.

-

Of interest for the chemists as potential process gas in the isotope separation, the halides of the first actinides with the valencies 3, 4 and 5 have been known for a long time. Few thermodynamic data are yet available : they are reported in table 11. We mention below the only compounds presenting specific heat anomalies or peculiarities.

Table I1

Compound Structure

- -

ThF, Monoclinic ZrFn type UF, Monoclinic

ZrF, type UF6 Orthorhombic NpF, Orthorhombic PuF, Hexagonal

LaF, type PuF4 Monoclinic

ZrFa type UCl, Hexagonal LaCl, type UCL Tetragonal UCl, type UCla Hexagonal

Ref.

- C2Ol C221

~ 1 9 1 r231

C81 C8l

~ 2 4 1

~ 2 4 1

~ 2 4 1

UF, : The most extensively studied of all the

-

halides [19-221, it is also the one where an interesting theoretical situation is reported.

UF, has a Schottky anomaly at 6.4. It is monoclinic with two inequivalent U sites. The U atom are thought to have a 3 ~configuration 4

split by crystal field interactions with a triply degenerate I-, ground state. This triplet would be in term, split in 2 different schemes ac- cording to the U site.

PuF,

-

: In spite of the use of the 2 4 2isotope, Flotow ~

et al. [8] could only cool their sample down to 10 K which did not allow them to observe the antiferromagnetic transition at 9 K. They re-

port an anomaly at 119 K, presumably of structural origin.

UCl,

-

: The tables of thermochemical data given by observers of the National Bureau of Standards [24] do not mention any anomaly down to 15 K, though an antiferromagnetic transition is reported at 22 K.

UI,

- : The magnetic and thermal properties of this compound have been measured from 1.2 to 4.2 K by Roberts et al. [25] : they attribute a h -type peak in the specific heat at 2.61 K to an antiferromagnetic transition with T , = 3.4 K . The associated entropy at 4.2 K is only 0.5 R Ln(2) indicating that an extensive short range order persists at temperatures well abo- ve T,. All these data could indicate the presen- ce of a 2 dimensional Ising ordering process in this orthorhombic compound.

have led Danan [31] propose that the 5f elec- trons here are fully delocalized. The form of the narrow f band and the high density of states at the Fermi level have been inferred by [28] from a careful study of UC-ThC solid solutions.

Several papers give results which don't fully agree [32-341 above room temperature.

NpC : The compound NpC, occurs over the range

-

0.82 < x < 0.96 and two magnetic transitions are reported : below 225 K, NpC is ferroma- gnetic, then becomes antiferromagnetic type I up to 280-310 K. The only heat capacity re- sults are due to Sandenaw et al. [35] on a compound with x = 0.91. They find a A-type anomaly corresponding to the Curie point and two irreproducible peaks between 260 and 310 K . Other measurements are clearly 2.3 AN X COMPOUNDS.

-

All of these compounds

P u c : have the NaCl type crystallographic structure and

-

their magnetic properties have been extensively stu- died though not fully understood. In addition, the binary compounds often form complete series of solid solutions with one another or with lanthanide monocompounds. There are as yet no thermodyna- mic data on these latter compounds and such measu- rements could constitute an interesting subject of investigation for the next few years. All data are summarized in table 111.

2.3.1 The carbides. - Both neptunium and pluto- nium nonocarbides undergo magnetic ordering and their magnetic properties are complicated by the existence of a large number of vacancies in the carbon sublattice. The stoichiometry affects mainly the transition temperatures.

U -

C : Many studies have been devoted to its low temperature specific heat [26-291. UC has a temperature-independent susceptibility, no lo- calized moment and a high y(0) value

-

20 mJ/mole

.

K 2 [26, 281. All these properties

Table 111.

Compound - UC NpCo 91

hc0.89 PUCa so

UN PUN UP PUP UAs

us

U s e

S ~ N C ~ . - f.c.c. NaCl

type

>>

>>

>>

>,

>>

>>

>>

Latt. par.

- A

4.951 4.995 4.972 3 4.968 2 4.958 9 4.889 4.895 5.589 5.664 5.779 5.473 5.739

needed.

: Again a substoichiometry in carbon with 0.78 < x < 0.90. There is only an antiferroma- gnetic ordering at temperatures ranging from 20 to 100 K according to the stoichiometry.

The specific heat curves of [36] and [37] do not show any peak for samples with x = 0.81,0.87 and 0.97 whereas [38] and [39] observe clear anomalies for samples in the same compositio- nal range. The latter authors even observe a maximum in the curve Cp(298) versus x. A very recent study by R. Hall [40] from 10 to 300 K on a wider range of composition and on better defined samples with a more accurate analysis of C, ( T ) gives what is likely to be the answer to the problem of the C, variation with the composition. Some of these data are re- ported in table 111.

In the single-phase region of PuC, the maxi- mum of Cp (298) corresponds to a maximum of the apparent y and corresponds to x = 0.89. A similar maximum has been found in the temperature-independent contribution to the susceptibility. The high temperature data of

S(298,lS)

J/mole

.

^{K Ref.}

- -

59.75 [291, C261 (Y)

Kruger et al. [41] extrapolated at 298 K are in fair agreement with the low temperature re- sults.

2.3.2 The pnictides.

UN : Going from UC to UN a certain stabilization of the 5f electron appears. UN is antiferromagne- tic below 52 K with

para = 0.75 pB and = 3.1 pB.

However, its electrical conductivity is still metallic and the specific heat measurements give a very high y (0) value : 50 mJ/mole

.

^KZ

together with a A-type anomaly at TN [42-441.

The magnetic entropy estimated either by substraction of a Debye term [43] or by comparison with ThC [45] is far below R Ln (2). The first interpretations of these contradictory results had been by an ionic model but this has been objected by Danan and de Novion [3 1, 45, 461. The very interesting paper of Oetting et al. [47] gives a review of the high temperature results.

&

N : Becomes antiferromagnetic below 13 K and displays an anomaly at 120 K in resistivity and thermoelectric power measurements. How- ever the specific heat measured from 10 to 300 K by Martin et al. [48] shows only an anomaly at 17.8 K with a small associated entropy. The y value is very high as in UN. A table of thermodynamic functions in the range 300-3 000 K has been given by Alexander et al. [49].

EP : The increase in lattice parameter going from UN to UP favours again the localization of the 5f electrons : TN = 125 K, p,, = 1.9 pB. But there is a moment jump at 23 K : neutron diffraction and susceptibility show a decrease of pod to 1.72 pB when T is lowered without any structural change. Both anomalies have been observed by Counsel1 et al. [50] in speci- fic heat measurements from 10 to 320 K. At higher temperatures, the works of Yokohama et al. [51] from 80 to 1080 K and Ono et al. [52] from 400 to 900 K are reliable and in good agreement with each other. UP is a semi-metal with a high y (0) value. Its proper- ties are reasonably accounted for by a loca- lized model with crystal field splitting.

PUP : Again a semi-metal, its thermal conductivity

-

and heat capacity have been studied from 20 to 650 "C by Moser and Kruger [53].

UAs : Two magnetic anomalies are observed : one at

-

127 K corresponding to a type I antiferroma- gnetic ordering and one at 64 K corresponding to a transition to type IA antiferromagnetism associated with a moment jump from 2.24 to 1.92 pB when T decreases. The recent speci-

fic heat measurements of Mortimer [54] show the two A-type associated peaks. The same localized model as for UP holds for UAs with experimental evidence for the transition between the two lowest lying crystal field levels.

2.3.3 The chalcogenides.

: This compound is a simple ferromagnet (T, = 180 K) with a metallic conductivity and a high melting point. The low-temperature speci- fic heat has been investigated by Westrum et at. [55], the high temperature data are given by [33] and [56]. The results have been analysed by Flotow et al. [57] in a careful study of ThS and by Danan [31]. The proposed model is a localized one with a configuration 5fZ (U4') and crystal field splitting whose energy gap is deduced from the magnetic entropy in [58].

This model is now rejected by [59] who assume a certain delocalization.

&

: With magnetic properties quite similar to US, the magnetic constants vary according to the authors, probably due to the difficulty in obtai- ning pure single phase specimens. The specific heat curve given by Takahashi et a1. [60]

between 5 and 350 K exhibits a transition corresponding to the Curie point. The magne- tic entropy is rather low but no serious analysis of C,,,, is given. y(0) has the highest value of all the UX compounds.

2.3.4 Pseudo -binary compounds. - A number of pseudo-binary uranium compounds has been stu- died. The aim is the observation of the amount of 5f electron localization with respect to :

The nature of the ligand (UCl-,N,).

The number of 5f electrons available (Ul-, Th, P, ul-,Th, S...).

In the localized systems, the authors have studied UP,-,S,, for instance, to follow the change in strength and sign of the exchange constant when a chalcogen ion is replaced by a pnictogen.

UCl-, N, : De Novion and Costa [61,62] have mea- sured the thermal, electrical and magnetic pro- -

perties of a series of solid solutions. Long distance order is observed only for 0.9 < x < 1 and short range order may exist for

At x

-

0.9 there is a maximum in y (0) as well as in ~ ( 4 K).

U, Th,-, S : Danan et al. [59] have studied magneti- zation, neutron diffraction and specific heat in the temperature range 1.5-300 K of solid solu- tions with x 0.20. Long range ferromagnetic order occurs for x > 0.43. The electronic spe-

cific heat is again a maximum at ,,x = 0.43.

The proposed interpretation is a 5f virtual bound state model for the dilute alloys and a narrow 5f-6d hybrid band model for the ura- nium rich alloys. Measurements not yet pu- blished on U, Th,-, Se confirm this interpreta- tion and show a tendency towards localization replacing the sulphur atoms by selenium.

US,P,-, : Counsell et al. [63] have measured the specific heat of alloys with x = 0.25, 0.5 and 0.75. As P is progressively substituted for S in US the temperature of the anomaly and the entropy increment become smaller. From the- se and other experiments it is concluded that ferromagnetic interactions predominate over the antiferromagnetic ones in this system. A maximum of the y values is found for x = 0.5 ( y = 58.6 mJ/mole

.

K2) but the y values are extrapolated from the temperature range Ilk 20 K . The T , values of [63] don't agree ver;

well with values drawn from the magnetic measurements.

no thorium analog was available, this discre- pancy reflects the different estimates of C,,,, made in both publications. A third and proba- bly more accurate approximation made by Alles et a1. [65] leads to a third value of S,, all of them being lower than R Ln (2) the ground doublet level assumed by

[a].

The magnetic susceptibility measurements are well explain- ed by a localized model with crystal field splitting and a pseudo-doublet as ground state.

The high temperature heat capacity values of Ono et al. [52] don't fit particularly well the data of [64] and [50].

U3As4, U3Sb, : Both compounds have been consi- dered in the recent careful study of Alles et al. [65] from 5 to 950 K and their specific heat curves are very close except for the Curie anomalies. A surprising fact is then the diffe- rence between the data for these 2 compounds and those for U3P4. The y values are much lower and the AS, much higher (

-

^{R Ln 3)}

than for U3P4. The former data were thought better defined in [65] than in [50] because [65]

worked down to 5 K but the recent low tempe- 2.4 An,X4 COMPOUNDS.

-

A number of An3X4

compounds are formed with the elements from the rature data of [54] tend to confirm the value of [50]. [65] assume a triplet ground state as the Groups IVA and VA and crystallize in the cubic

responsible of the cooperative transition and Th3P4-type structure. Up to now, thermal measure-

two higher lying levels giving rise to a Schottky ments have been made only on the U-pnictogens. All

anomaly at high temperature, but here again, of them are ferromagnetic with an easy axis

C,,, is only a theoretical estimate.

along [lll] but the direction of the magnetic mo- - -

ments is open to doubt for crystal symmetry consi- 2.5 A~,x, COMPOUNDS.

-

These oc- derations lead to an assumption that the moments cur over a range of stoichiometry and present a great are aligned with [loo]. The results are listed in variety of crystal and magnetic proper-

table IV. ties. Their specific heat data are listed in table IV.

U,P4 : The data of Stalinsky et al. [64] from 22.5 to U,C3 : An anomaly at 59 K in the magnetic and

- -

349 K and of Counsel1 et al. [50] from 11 to electrical properties does not appear in the 320 K generally agree well except for the specific heat curves of Andon et al. [27] or entropy of the magnetic transition : Farr et al. [66]. This compound is actually 4.3 1 J/mole U at for [64] and 2.3 1 for [50]. As thought to be a spin fluctuation system.

Table IV.

AS(T,) Y (0)

Latt. par. T N , J/mole (K) mJ/mole.KZ OD C, (298,15) S(298,15)

Compound Struct. A K /U at. /U at. K J/mole.K J/mole.K Ref.

-

-

- -

-

- -

-

-

-

b.c.c.

or(UN1 ")' MnZ03 type 10.690 0.50(94) 49.4 332 108.36 130.04 [42]

(UNI ^{4 2} >> 10.644 0.21(33) 79.9 361 115.23 131.71 [42]

90 82.8 orthorhombic

UzS, _{S b S 3 type} 50 54

-

^{75 141.7 199.12 1541}

25 30.5

Pu,C3 : Non magnetic and conductor. The first spe- cific heat results of Danan [67] were refined by [38] and the best data are now those of [39].

aU,N3 : Two allotropic varieties of this compound have been reported, the a phase being b.c.c.

M q 0 3 type and existing over a range of stoi- chiometry ((UN, ), with 1.55 s x

s

1.80). This phase is ferromagnetic at low temperatures, T , and 8 depending strongly on the stoichiome- try. Two samples with x = 1.59 and 1.73 have been studied by Counsel1 et al. [42] who find A-type anomalies corresponding to the ferro- magnetic transitions.

U,S3, U,Se3 : Recent magnetic measurements reveal very complicated magnetic properties for the- se two compounds with up to three anomalies for the former [68]. The specific heat has been measured [54] for U,S3 and [69] for U,Se3 with A -type peaks corresponding to the above ano- malies. No data table is available in [69] but the very high room temperature values of C, for both compounds reveal surprisingly high y values.

2.6 AnX, COMPOUNDS.

-

The results are given in table V for the general compounds and the discus- sion of the most important group : the Laves phases, will be given in chapter 3.

2.6.1 UC,.

-

Specific heat measurements in hy- postoichiometric compounds have been made by three groups [27, 29, 661 who find very similar results in the low temperature range while the results of Mukaibo et al. [32] from 100 to 400 OC are 10 % lower. No magnetic anomaly is reported for this non magnetic compound and ThC, [70] is not isostructu- ral to UC,.

2.6.2 The dipnictides.

-

All of them are tetrago- nal, anti-Fe,As type and undergo antiferromagnetic ordering at low temperature but their electrical conductivity is that of a metal or semi-metal.

UP,

-

: The NBel temperature is reported to be 203 K and is confirmed in the heat capacity measure- ments of Stalinsky et al. [7l] from 22 to 350 K and of 1541 and [72] from 1.5 to 300 K. The results are in good agreement except for the magnetic entropy which again is due to diffe- rent estimates of C,,,. The interpretation has been that of a localized model [71] or a virtual bound state [72] which accounts better for the electrical properties and high y (0) value.

UAs,, USb, : Similar properties to UP,. The ordered and effective magnetic moments increase with the lattice parameter but the exchange is lowered (T, = 283 and 206 K for UAs, and USb,) : Specific heat measurements are due to Westrum et al. [73] from 5 to 700 K and Blaise et al. [72] b tween 1.5 and 300 K. The results are in better agreement for USb, than for UAs,

\

as regards C, (T). There are still discrepancies for the AS, values and mainly for the y(0) values which are definitely much higher than given by [73] and point out to the same model as that for UP,.

~ -

2.6.3 The dichalcogenides.

-

There is no structu- ral identity among the dichalcogenides and the crys- tal structure itself is very sensitive to the stoichiome- try for a given compound.

a , PUS, : The uranium disulphides US, crystallize in the a phase (tetragonal) for 1.80 S x S 1.93 and in the

P

phase (orthorhombic) for x = 2.

Westrum et al. [74] have measured the specific heat of a compound with x = 1.9 between 5 and 350 K. With a rather rough estimate of the lattice component, they see a Schottky peak at 25 K corresponding to an excited state at 56 K above the ground state. A specimen corres- ponding to the fl phase has been studied by Gronvold et al. [75] with results very similar to the a sample.

Table V.

Latt. par. TN.c AS(T,) y ( 0 ) OD(0) C, (298,15) S(298,15) Compound Struct.

A

K J/mole ( K ) mJ/mole.K2 K J/mole.K J/mole.K Ref.

Tetragonal

UCI ⁹⁴ CaC2 type 16.7 304 60.75 68.32 [66]

Tetragonal a = 3.800 5.48(203) 80.00 101.84 [71]

UP2 T N = 207

1.65(202) 21.0

anti-Fe,As c = 7.762 368 77.50 99.60 [72]

a = 4 . 2 7 2 T N = 2 0 6 7.11(202.5) 12.5 80.16 141.46 [73]

USbz >>

c = 8.741 212 4.65(201.5) 30.5 201 80.87 144.10 [72]

Tetragonal a = 10.28 u s , ⁹ a-USz type c = 6.33

Orthorhombic

'

P ~ C I ~ type - -

Tetragonal a = 10.73

aUSe2 a-USz type c = 6.59 T N = 1 1 0.79(13.1)

Table VI.

Latt. par. T N , ~ AS(T,) Y (0) YP e,(o) C, ( 2 9 8 ~ 5 ) ~ ( 2 9 8 ~ 5 ) Compound Struct. A K J/mole (K) m J / m o l e . ~ ~ m J / m o l e . ~ ~ K J/mole.K J/rnole.K Ref.

- - - - - - - - - - -

Cubic

PUH3 w 3 0 t y p e

$1 ^{

Monoclinic ZrSe3 type

Cubic lJRh3 AuCu3-type

CY Use, : This compound has the ^CY -US, type of crystal structure and a susceptibility maximum at 11 K. Westrum et al. [74] find a A-type anomaly in C, at 13.1 K with a very low associated entropy. As in US,, there are two inequivalent U sites and they assume that only one type of U undergoes the cooperative tran- sition.

2.7 AnX, COMPOUNDS.

-

The most extensively studied compounds of this group are the AuCu,-type compounds. Although the An-An spacing is much larger here than the critical value set by Hill's criterion, their electronic properties are often better interpreted in terms of spin-fluctuating systems than of crystal field theory. The results are given in table VI.

p UH, : This allotropic variety (cubic) is the usually formed phase by direct reaction. Its conducti- vity is metallic but it undergoes a ferromagne- tic ordering below 168 K. Flotow et al. studied its specific heat from 5 to 350 K in [76] and

of magnetic susceptibility at 19.5 K and a A -type peak of C, at 11.5 K whose origin is still not clear [54].

Cubic AuCu,-type compounds : The results of very low temperature specific heat measurements for 8 uranium and 2 neptunium compounds are given in table VI together with the referen- ces. Nearly all these compounds show a tem- perature independent susceptibility, a resistivi- ty increase proportional to

T 2

at low tempera- ture and high y(0) values. These and other data have been reviewed by Brodsky [82] who attempts to explain these physical properties in terms of a localized spin fluctuation (1.s.f.) model. NpSn,, on the other hand, would be an itinerant-electron antif erromagnet [83, 841 with T , = 9.5 K. Quite apart from the magne- tic evidence for this assumption, the specific heat curve gives some additional proof : a AS,

-

^{0, a y (T)} variation with a sharp peak at T , and a y(0) value much lower than yp (paramagnetic state).

from 1.4 to 23 K in [77]. They found a A-type

anomaly at 170.7 K with a rather low AS, and 3. The Laves phases.

-

Nearly all the compounds a high y (0). of this group crystallize in the cubic MgCu, type US,, UTe, : Both monoclinic of the same ZrSe,- structure. The X partner atoms are, either transition type, US, measured by Gronvold et al. [75] is elements, or members of the IIA column in the non magnetic, while UTe, exhibits a maximum periodic table. There has been an increasing interest Table VII.

Compound -

URe, UIr, UAl, NpRu, NpOsz NpIr2 PuAl,

Struct.

- Orthorhombic

URe2 type Cubic MgCu, type

>>

>>

>>

>>

>>

Latt. par -

A

7.509 7.795 7.446 7.528 7.509 7.833

d An-An

-

A

3.25 3.38 3.22 3.26 3.25 3.39

YP e ~ ( o ) mJ/mole . K' K Ref.

-

-

-

in the Laves phases for the last five years because, in these compounds, the An-An spacing is close to the critical distance for localization of the 5f elec- trons and the apparition of magnetism. For most of them, this results in an interpretation of their physi- cal properties by 1.s.f. or itinerant magnetism mo- dels. The specific heat experiments, although still very scarce, help to define the appropriate model : the 1.s.f. is characterized by an upturn of C / T versus

T Z below the so-called spin fluctuation temperature.

The y(0) values are extremely high (and the ASm(Tt) are extremely low whenever a cooperative transition occurs). In table VII, we give the heat capacity results and references.

URe,, UIr,, UAl,, NpRu, : These compounds are proposed as ferromagnetic 1.s.f. systems. The most carefully studied is UAI, [78,84,86] with a Ts, = 30 K.

PuAl, : Several properties seem to exclude ferroma- gnetic excitations in this compound and Trai- nor et al. [86] propose an antiferromagnetic spin fluctuation model.

NpOs, : Ferromagnetic below 7.5 K with a very small ordered moment (0.25-0.44 p,) and a high y(O), Brodsky et al. [87,84] interprete the results in terms of a weak itinerant ferroma- gnetism model.

NpIr, : In a paper presented to LT 15, Brodsky et al. [88] give specific heat and magnetic sus- ceptibility results for this compound which has a NCel temperature of 7.5 K. Their model is an itinerant antiferromagnet.

4. Ternary compounds.

-

Few such compounds have been studied up t o now and all of them belong to the general tetragonal structure group : P4nmm already characteristic of the dipnictides. The speci- fic heat data are listed in table VIII.

4.1 UOTe. - This compound belongs t o the sub- group of PbFCl type and is reported as antiferroma- gnetic type I below 162 K. Its specific heat has been measured from 21 to 362 K by Stalinsky et al. [89]

who report the corresponding A-type peak at

159.7 K and a low associated magnetic entropy (possibly due to an incomplete definition of C,,tt).

4.2 COMPOUNDS UAsY (Y = S , Se, Te).

-

All being single uniaxial ferromagnets, the first two compounds crystallize in the subgroup anti Fe,As- type to which belong the dipnictides. UAsTe has the slightly distorted structure (space group I4mmm) called UGeTe-type.

UAsS, UAsSe : Their respective Curie points of 125 and 113 K are reflected in the recent specific heat measurements of Blaise et al. [90] in the temperature range 1.5-300 K. As in UOTe, the magnetic entropies are low and as in the di- pnictides the y(0) values are high, making likely a certain amount of delocalization among the 5f electrons.

UAsTe : The increase in the c parameter and the reduction in the coordination number for the U atom is accompanied by a decrease of

T, = 66 K. The specific heat data of [90] show however an associated magnetic entropy and mainly a y(0) value higher than those of UAsS and UAsSe.

5. The critical phenomena in the actinide compounds. - A recent synthesis has been given by Blaise [91] of the main theories of the critical beha- viour in magnetically ordering systems, the empha- sis is on the specific heat and magnetic properties in localized moment models. Some experimental exam- ples are given in [91] but none of them refer to members of the actinide family. Of course this and other papers at this Conference emphasize the extent of our present knowledge on the actinide compounds.

The contribution of the actinide compounds to the study of the critical phenomena could be of impor- tance : a number of these compounds are fairly good examples of localized systems. The exchange constants of these compounds can be altered by replacement of either the cation or the anion without any crystallographic modification. Many com- pounds display a magnetic transition in a temperatu- Table VIII.

Latt. par. T N , = Smq(Tt) y ( 0 ) O0(O) C,(298,15) S(198,15) Compound Struct. A K S/mole (K) mJ/mole.KZ K J/mole.K J/mole.K Ref.

- - -

- - - - - - - Tetrag. a = 4.012

UOTe PbFCl type c = 7.501 TN = 162 4.48 Tetrag.

UAsS a = 3.878

anti-Fe2As

c = 8.164 T, = 125 1.53(126) 23.5 288 80.90 114.48 [90]

type Tetrag.

UAsSe anti-Fe,As a = 3.981 T , = 113 0.63(110) 39 231 83.48 131.71 [90]

tvve

~ i t ; a ~ .

UAsTe a =4.150

T , = 66 2.75(63)

UGeTe-type c = 17.270 57 217 81.32 139.80 1901

re range very convenient to achieve a great precision in the critical exponent problem. Lastly, in several cases, the lattice component of Cp may be deduced with reasonable accuracy from the study of an isomorphous thorium compound.

Unfortunately, few authors have been attracted by these happy auspices and nearly all is still to be done in this respect. Being primarily interested in the specific heat, we will restrict ourselves to the compounds listed above and mainly to the 3 dimensional problem as there is still no examples of true mono- or bi-dimensional actinide compounds except possibly UI,.

Typical candidates for this study could be the three families : the simple f.c.c. monocompounds and the b.c.c. An3X4 compounds because of the highly symmetrical cation environment, then the tetragonal compounds (P4mmm-type) because of their numerical importance and of their special ma- gnetic pseudo-bi-dimensional structure.

The next very important parameter to consider is the magnetic anisotropy in comparison to the ex- change forces which will make the difference between an Ising or Heisenberg model. All the U compounds have very high anisotropies and one is tempted to consider them as good examples of Ising compounds, although the experimental evidence is not so conclusive.

5.1 AnX GROUP.

-

A very careful study of the magnetic properties of US has been made by Till- wick et al. [92]. Results are given for the critical exponents of

x

above Tc : y, and of M, below T : P.

They find

For comparison :

Landau theory Ising Heisenberg

- - -

Y 1 1.40 1.25

P

0.5 0.312 0.333

Which does not allow a definite answer. To be noted however is the fact that their coefficients y,

p

and 8 ( a (H, T,)

-

^{H 'IS)} satisfy the scaling relations and general homogeneous equation of state.

The specific heat data of [57] are well represented by a magnetic low-temperature contribution in T3/, which is the spin-wave result for a Heisenberg system. On the other hand, the shape of their C,(T) curve with its low temperature tail much higher than the high temperature one is more typical of an Ising model than of an Heisenberg. Not enough data are available from [57] to allow a critical exponent calculation.

5.2 An3X4 GROUP. - No one has been interested by the critical phenomena and the experimental situation is not an easy one. First of all, these compounds have a large metallic conductivity and are not good localized models. There is a very high magnetocrystalline anisotropy but the directions of the moments are still uncertain. No Th isomorphous compound is available for U3As4 and U3Sb4 where moreover the additional Schottky levels would make the separation of the cooperative transition in Cp rather difficult.

5.3 THE TETRAGONAL COMPOUNDS.

-

The preci- sion of the magnetic measurements is not yet suffi- cient to make an estimate of the critical exponents of any interest but such measurements are now under way.

The specific heat measurements on the dipnictides and ternary uranium compounds made by [90] allow a first estimate of the critical exponents of C , and of the ratio of the enthalpies E above and below T,.

up2 U As, USb, UAsS U AsSe UAsTe

The values of a and a' agree rather with an Heisenberg model while the values of the ratios of the enthalpies correspond to an Ising model.

There are preliminary results and more extensive studies of C, around the critical points are now being made by Gordon [93].

6. Conclusion. - If we return to the title of this talk, we must admit that no definitive answer can be

given to the question of the usefulness of specific heat measurements on the actinide compounds.

Where the various contributions to the heat capacity give rise to anomalies widely separated in tempefa- ture , fairly unambiguous information can be obtain- ed from the thermal data. Where this is not the case, the specific heat results must be used in conjunction with other data if they are to provide useful insights into the complicated behaviour of the actinide compounds.