The specific heat of actinide compounds

14 Pages·2016·1.3 MB·English

by  A. Blaise

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￿
HAL Id: jpa-00218813
https://hal.science/jpa-00218813
Submitted on 1 Jan 1979
HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est
archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents
entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non,
lished or not. The documents may come from émanant des établissements d’enseignement et de
teaching and research institutions in France or recherche français ou étrangers, des laboratoires
abroad, or from public or private research centers. publics ou privés.
JOURNAL DE PHYSIQUE Colloque C4, suppl6ment au no 4, Tome 40, avril 1979, page C4-49
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- One can write :
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 C,,,, : lattice contribution
heat while the magnetic properties for instance, have CCon:d c ontribution of the conduction electrons
been extensively studied ? In the first part I will C,, : magnetic contribution (cooperative transition)
discuss the experimental difficulties associated with C,,,,, : contribution from the excited electronic
specific heat measurements, and also the difficulties states
involved in interpreting those results. In the second C,,,, : nuclear contribution
part of this work, I will give a review of the most C, : heat capacity at constant volume.
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- If we disregard C,,,,, a contribution which is
rements : the study of the critical phenomena in the generally negligible, above 1 K we see from eq. (1)
magnetically ordered actinides. that the specific heat can be an important source of
information on the electronic structure of a speci-
1. The measurements : difficulties of the ex- men provided that the resolution of the total heat
periments and of their interpretation. - Everybo- capacity into its separate components can be made.
dy knows the experimental difficulty of the specific
heat measurements whatever method is used : ther- 1.1 (C, - C, ) TERM. - The lattice contribution to
mometry accurate to 0.01 K, perfect screening of the heat capacity is always assumed to come from
the calorimeter to avoid radiation losses, sample harmonic forces. The anharmonic forces introduce a
holder heat capacities which are often of the same difference between C, and C, :
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 to work at temperatures below 6-10 K.
Then, the extreme toxicity of these materials (a! : thermal expansivity, K : isothermal compressi-
compels the use of a glove box, or the enclosure of bility, V,,, : molar volume).
-
the specimen in a container a procedure which As a and K are not always available, neglecting
makes worse the problems of addenda correction C, is a first source of uncertainty especially at high
and bad thermal contacts. temperature where Cd may reach several % of C,,,.
The interpretation itself of the measured heat
capacity (which is C, : heat capacity at constant 1.2 C,,,, TERM. - It is normally the most impor-
pressure) is another very difficult problem. 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
C4-50 A. BLAISE
most difficult to determine. Its theoretical expres- 1.3 C,, TERM. - The conduction electrons give
sion is : rise to a contribution :
no
3 kZ -ddko (3) C,,,, = YT (6)
y (0) being related to the density of state at the Fermi
level, can, in principle, been deduced from a plot of
C, /T(T2) extrapolated at T = 0 : C,,,, being propor-
and involves the knowledge of the phonon disper-
tional to T3, the ordinate at the origin gives y(0).
sion relation k(o). -
But, C,,,, T3i s only valid at very low temperature
In principle, the best way of getting C,,,, is to
and many experiments don't allow the correct deter-
derive k(w) from an experiment, namely neutron
mination of y(0). In the free electron model y is
inelastic scattering. If one does not have the phonon
essentially independent of T and could thus be
spectrum then one can use more or less good appro-
determined even from high temperature measure-
ximations (Einstein function : o = constant = w, ;
ment but this is an oversimplification and frequently
Debye function : o = v, k ; or a combination of
is not in agreement with the experimental results : y,
both) which, in term, leads to more or less exact
actually often decreases when T increases, and
results for C,,,, with errors reaching some 10 % or
y (300) may be 50 % of y (0).
more.
Attempts are sometimes made to get an experi-
1.4 C,, TERM. - This is the term associated with
mental estimate of C,,, by measuring an isostructural
the magnetic ordering of the Sf electrons in the
compound with no magnetic component to the speci-
actinides and the associated entropy has been the
fic heat (typically a thorium compound). The sim-
principal information sought in specific heat experi-
plest assumption in that respect is the corresponding
ments. The problem in the actinides is that one is
state approximation :
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-
where k is a constant experimentally deduced.
tion and the contributions C,,,, and C,, cannot be
Another useful relationship for isostructural
distinguished.
compounds of neighbouring molecular weights M
and M' where the Debye approximation is valid for
1.5 C,,,, TERM. - This term comes from the
the Th compound is : 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
or the more refined Lindeman's relation using the
case, it is difficult to resolve the electronic situation
melting points T,,, and molar volumes V :
without additional information.
v213
M 6 g(0)
constant = 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.
C,(298,15) S (298,15)
Crystal Latt. par. TN.~ AS(Tt) y (0) J/mole.K J/mole.K
Compound structure A K J/mole (K) m.J/mole.~~/A n atom /An atom Ref.
- -
uoz f.c.c. CaFz-type
NpO2
Puoz
u409
UaO, a tetragonal
P deformation
of uoz
orthorhombic
THE SPECIFIC HEAT OF ACTINIDE COMPOUNDS : ARE THOSE MEASUREMENTS USEFUL ? C4-51
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 U-30, : Exists under at least two different phases (a
listed in table I. and p), both of which having been measured
by [9] who give in [14] an excellent review of
UO, : The definitive work and the most precise of all
the specific heat of all the uranium oxides.
- the specific heat analysis referred to in that
paper has been given by Huntzicker and, -U,O, : Has been investigated by Westrum et al. [15]
in the low temperature range and by [16, 171
Westrum [I]. UO, is a simple type 1 antiferro-
above room temperature. A A -type anomaly
magnet with a A -type anomaly at 30.44 in
presumably of magnetic origin occurs at
agreement with the magnetic results. The latti-
25.3 K while another peak at 483 K is attri-
ce heat capacity has been estimated'by diffe-
buted to a very slight structural change [17].
rent methods [I-31 and an excess found in the
Two other anomalies at 568 and 860 K are
temperature region 30 to 120 K is attributed to
reported [I71 to be due to some order-disorder
a Jahn-Teller effect [I]. The spin-wave low
process.
temperature predictions fit the experimental
C, at low temperature with reasonable U-O, : The very old data of Jones et al. [18] show no
anomaly between 15 and 300 K.
agreement [I]. The position of excited crystal
field levels above the triplet ground state for 2.2 THE HALIDES. - Of interest for the chemists
an assumed U4' ion don't coincide with the
as potential process gas in the isotope separation,
calculations of Rahman and Runciman [4].
the halides of the first actinides with the valencies 3,
NpO, : This compound is still a challenge for the
4 and 5 have been known for a long time. Few
theorists : magnetic susceptibility and specific thermodynamic data are yet available : they are
heat [5] show a peak at 25 K, but neither
reported in table 11. We mention below the only
neutron diffraction nor Mossbauer experi-
compounds presenting specific heat anomalies or
ments give evidence of a magnetic ordering.
peculiarities.
The very old measurements of Westrum et
al. [5] propose a value of the magnetic entro-
Table I1
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 Compound Structure Ref.
- - -
Tho,. These differences illustrate clearly the
ThF, Monoclinic C2Ol
need of a rigorous evaluation for C,,, to advan-
ZrFnt ype
ce serious figures for the ionization state and UF, Monoclinic C221
fundamental multiplet of the Np atom. Ques- ZrF, type
UF6 Orthorhombic ~191
tionable is also the chemical purity of the
NpF, Orthorhombic r231
sample studied 24 years ago. PuF, Hexagonal C81
P-uO, : The old measurements of Sandenaw [6] LaF, type
between 13 and 325 K agree with those of PuF4 Monoclinic C8l
ZrFa type
Kruger et al. [7] from 200 to 1 400 K and show UCl, Hexagonal ~241
a peakfree heat capacity in accordance with LaCl, type
the magnetic results. More recently, Flotow et UCL Tetragonal ~241
UCl, type
al. [8J worked on a 244pU02s ample between 4 UCla Hexagonal ~241
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- U-F, : The most extensively studied of all the
de dioxides. Many phases exist for the ura- halides [19-221, it is also the one where an
nium oxides from UO, to UO,. The X-ray data interesting theoretical situation is reported.
for most of them have been collected by UF, has a Schottky anomaly at 6.4. It is
Westrum et al. [9] and, as potential reactor monoclinic with two inequivalent U sites. The
fuels, their specific heats have been measured U atom are thought to have a configuration
3 ~ 4
by several investigators. The data may be split by crystal field interactions with a triply
found in table I. degenerate I-, ground state. This triplet would
U-40, : Studied by Flotow et al. [lo] from 1.6 to 24 K be in term, split in 2 different schemes ac-
and by Osborne et al. [ll] from 5 to 310 K, cording to the U site.
this compound shows no evidence for a transi- P-uF, : In spite of the use of the 2 4 2is~o tope, Flotow
tion around 6.4 K where a susceptibility maxi- et al. [8] could only cool their sample down to
mum was found. Above 300 K, several 10 K which did not allow them to observe the
investigators [2, 12, 131 find a A -type anoma- antiferromagnetic transition at 9 K. They re-
C4-52 A. BLAISE
port an anomaly at 119 K, presumably of have led Danan [31] propose that the 5f elec-
structural origin. trons here are fully delocalized. The form of
U-Cl, : The tables of thermochemical data given by the narrow f band and the high density of
observers of the National Bureau of states at the Fermi level have been inferred by
Standards [24] do not mention any anomaly [28] from a careful study of UC-ThC solid
down to 15 K, though an antiferromagnetic solutions.
transition is reported at 22 K. Several papers give results which don't
U-I, : The magnetic and thermal properties of this fully agree [32-341 above room temperature.
compound have been measured from 1.2 to -NpC : The compound NpC, occurs over the range
4.2 K by Roberts et al. [25] : they attribute a 0.82 < x < 0.96 and two magnetic transitions
h -type peak in the specific heat at 2.61 K to an are reported : below 225 K, NpC is ferroma-
antiferromagnetic transition with T, = 3.4 K. gnetic, then becomes antiferromagnetic type I
The associated entropy at 4.2 K is only up to 280-310 K. The only heat capacity re-
0.5 R Ln(2) indicating that an extensive short sults are due to Sandenaw et al. [35] on a
range order persists at temperatures well abo- compound with x = 0.91. They find a A-type
ve T,. All these data could indicate the presen- anomaly corresponding to the Curie point and
ce of a 2 dimensional Ising ordering process in two irreproducible peaks between 260 and
this orthorhombic compound. 310 K. Other measurements are clearly
needed.
2.3 AN X COMPOUNDS. - All of these compounds
-Puc :: Again a substoichiometry in carbon with
have the NaCl type crystallographic structure and
0.78 < x < 0.90. There is only an antiferroma-
their magnetic properties have been extensively stu-
gnetic ordering at temperatures ranging from
died though not fully understood. In addition, the
20 to 100 K according to the stoichiometry.
binary compounds often form complete series of
The specific heat curves of [36] and [37] do not
solid solutions with one another or with lanthanide
show any peak for samples with x = 0.81,0.87
monocompounds. There are as yet no thermodyna-
and 0.97 whereas [38] and [39] observe clear
mic data on these latter compounds and such measu-
anomalies for samples in the same compositio-
rements could constitute an interesting subject of
nal range. The latter authors even observe a
investigation for the next few years. All data are
maximum in the curve Cp(298) versus x. A
summarized in table 111.
very recent study by R. Hall [40] from 10 to
2.3.1 The carbides. - Both neptunium and pluto- 300 K on a wider range of composition and on
nium nonocarbides undergo magnetic ordering and better defined samples with a more accurate
their magnetic properties are complicated by the analysis of C, (T)g ives what is likely to be the
existence of a large number of vacancies in the answer to the problem of the C, variation with
the composition. Some of these data are re-
carbon sublattice. The stoichiometry affects mainly
the transition temperatures. ported in table 111.
In the single-phase region of PuC, the maxi-
C-U : Many studies have been devoted to its low mum of Cp( 298) corresponds to a maximum of
temperature specific heat [26-291. UC has a the apparent y and corresponds to x = 0.89. A
temperature-independent susceptibility, no lo- similar maximum has been found in the
-
calized moment and a high y(0) value temperature-independent contribution to the
.
20 mJ/mole K2 [26, 281. All these properties susceptibility. The high temperature data of
Table 111.
Latt. par. S(298,lS)
Compound S~NC~. A J/mole . K Ref.
- - - - -
UC f.c.c. NaCl 4.951 59.75 [291,C 261 (Y)
type
NpCo 91 >> 4.995
4.972 3
hc0.89 >> 4.968 2
PUUCNa so >>,> 44..985889 9
PUN 4.895
UP >> 5.589
PUP 5.664
UAs >> 5.779
us >> 5.473
Use 5.739
THE SPECIFIC HEAT OF ACTINIDE COMPOUNDS : ARE THOSE MEASUREMENTS USEFUL ? C4-53
Kruger et al. [41] extrapolated at 298 K are in fic heat measurements of Mortimer [54] show
fair agreement with the low temperature re- the two A-type associated peaks. The same
sults. localized model as for UP holds for UAs with
experimental evidence for the transition
2.3.2 The pnictides. between the two lowest lying crystal field
UN : Going from UC to UN a certain stabilization of levels.
the 5f electron appears. UN is antiferromagne-
2.3.3 The chalcogenides.
tic below 52 K with
: This compound is a simple ferromagnet
para = 0.75 pBa nd = 3.1 pB.
(T, = 180 K) with a metallic conductivity and a
high melting point. The low-temperature speci-
However, its electrical conductivity is still
fic heat has been investigated by Westrum et
metallic and the specific heat measurements
give a very high y (0) value : 50 mJ/mole . KZ at. [55], the high temperature data are given by
[33] and [56]. The results have been analysed
together with a A-type anomaly at TN [42-441.
by Flotow et al. [57] in a careful study of ThS
The magnetic entropy estimated either by
and by Danan [31]. The proposed model is a
substraction of a Debye term [43] or by
localized one with a configuration 5fZ( U4') and
comparison with ThC [45] is far below
crystal field splitting whose energy gap is
R Ln (2). The first interpretations of these
deduced from the magnetic entropy in [58].
contradictory results had been by an ionic
This model is now rejected by [59] who assume
model but this has been objected by Danan and
a certain delocalization.
de Novion [3 1, 45, 461. The very interesting
& : With magnetic properties quite similar to US,
paper of Oetting et al. [47] gives a review of
the magnetic constants vary according to the
the high temperature results.
authors, probably due to the difficulty in obtai-
&N : Becomes antiferromagnetic below 13 K and
ning pure single phase specimens. The specific
displays an anomaly at 120 K in resistivity and
heat curve given by Takahashi et a1. [60]
thermoelectric power measurements. How-
between 5 and 350 K exhibits a transition
ever the specific heat measured from 10 to
corresponding to the Curie point. The magne-
300 K by Martin et al. [48] shows only an
tic entropy is rather low but no serious analysis
anomaly at 17.8 K with a small associated
of C,,,, is given. y(0) has the highest value of
entropy. The y value is very high as in UN. A
all the UX compounds.
table of thermodynamic functions in the range
300-3 000 K has been given by Alexander et
al. [49]. 2.3.4 Pseudo -binary compounds. - A number of
pseudo-binary uranium compounds has been stu-
EP : The increase in lattice parameter going from
died. The aim is the observation of the amount of 5f
UN to UP favours again the localization of the
electron localization with respect to :
5f electrons : TN= 125 K, p,, = 1.9 pB. But
there is a moment jump at 23 K : neutron The nature of the ligand (UCl-,N,).
diffraction and susceptibility show a decrease The number of 5f electrons available (Ul-, Th, P,
of podt o 1.72 pBw hen T is lowered without ul-,Th, S...).
any structural change. Both anomalies have In the localized systems, the authors have studied
been observed by Counsel1 et al. [50] in speci- UP,-,S,, for instance, to follow the change in
fic heat measurements from 10 to 320 K. At strength and sign of the exchange constant when a
higher temperatures, the works of Yokohama chalcogen ion is replaced by a pnictogen.
et al. [51] from 80 to 1080 K and Ono et
al. [52] from 400 to 900 K are reliable and in UCl-, N, : De Novion and Costa [61,62] have mea-
good agreement with each other. UP is a sured the thermal, electrical and ma-g netic pro-
semi-metal with a high y (0) value. Its proper- perties of a series of solid solutions. Long
ties are reasonably accounted for by a loca- distance order is observed only for 0.9 < x < 1
lized model with crystal field splitting. and short range order may exist for
-PUP : Again a semi-metal, its thermal conductivity
and heat capacity have been studied from 20 to
-
650 "C by Moser and Kruger [53]. At x 0.9 there is a maximum in y (0) as well
-UAs : Two magnetic anomalies are observed : one at as in ~ (K4).
127 K corresponding to a type I antiferroma- U, Th,-, S : Danan et al. [59] have studied magneti-
gnetic ordering and one at 64 K corresponding zation, neutron diffraction and specific heat in
to a transition to type IA antiferromagnetism the temperature range 1.5-300 K of solid solu-
associated with a moment jump from 2.24 to tions with x 0.20. Long range ferromagnetic
1.92 pBw hen T decreases. The recent speci- order occurs for x > 0.43. The electronic spe-
C4-54 A. BLAISE
cific heat is again a maximum at ,,x = 0.43. no thorium analog was available, this discre-
The proposed interpretation is a 5f virtual pancy reflects the different estimates of C,,,,
bound state model for the dilute alloys and a made in both publications. A third and proba-
narrow 5f-6d hybrid band model for the ura- bly more accurate approximation made by
nium rich alloys. Measurements not yet pu- Alles et a1. [65]l eads to a third value of S,, all
blished on U, Th,-, Se confirm this interpreta- of them being lower than R Ln (2) the ground
[a].
tion and show a tendency towards localization doublet level assumed by The magnetic
replacing the sulphur atoms by selenium. susceptibility measurements are well explain-
US,P,-, : Counsell et al. [63] have measured the ed by a localized model with crystal field
specific heat of alloys with x = 0.25, 0.5 and splitting and a pseudo-doublet as ground state.
0.75. As P is progressively substituted for S in The high temperature heat capacity values of
US the temperature of the anomaly and the Ono et al. [52] don't fit particularly well the
entropy increment become smaller. From the- data of [64] and [50].
se and other experiments it is concluded that U3As4, U3Sb, : Both compounds have been consi-
ferromagnetic interactions predominate over dered in the recent careful study of Alles et
the antiferromagnetic ones in this system. A al. [65]f rom 5 to 950 K and their specific heat
maximum of the y values is found for x = 0.5 curves are very close except for the Curie
.
( y= 58.6 mJ/mole K2) but the y values are anomalies. A surprising fact is then the diffe-
extrapolated from the temperature range Ilk rence between the data for these 2 compounds
20 K. The T, values of [63] don't agree ver; and those for U3P4. The y values are much
-
well with values drawn from the magnetic lower and the AS, much higher ( R Ln 3)
measurements. than for U3P4.T he former data were thought
better defined in [65] than in [50]b ecause [65]
worked down to 5 K but the recent low tempe-
2.4 An,X4 COMPOUNDS. - A number of An3X4
rature data of [54]t end to confirm the value of
compounds are formed with the elements from the
[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-types tructure. 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]a nd 2.3 1 for [50].A s thought to be a spin fluctuation system.
Table IV.
AS(T,) Y (0)
Latt. par. TN, 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.
10.690 0.50(94) 49.4 332 108.36 130.04 [42]
or(UN1") ' MnZ03ty pe
(UNI4 2 >> 10.644 0.21(33) 79.9 361 115.23 131.71 [42]
90 82.8
orthorhombic -
UzS, 50 54 75 141.7 199.12 1541
SbS3t ype
25 30.5
THE SPECIFIC HEAT OF ACTINIDE COMPOUNDS : ARE THOSE MEASUREMENTS USEFUL ? C4-55
Pu,C3 : Non magnetic and conductor. The first spe- U-P, : The NBel temperature is reported to be 203 K
cific heat results of Danan [67] were refined and is confirmed in the heat capacity measure-
by [38] and the best data are now those of [39]. ments of Stalinsky et al. [7l] from 22 to 350 K
aU,N3 : Two allotropic varieties of this compound and of 1541 and [72] from 1.5 to 300 K. The
have been reported, the a phase being b.c.c. results are in good agreement except for the
Mq03t ype and existing over a range of stoi- magnetic entropy which again is due to diffe-
chiometry ((UN, ), with 1.55 s x s 1.80). This rent estimates of C,,,. The interpretation has
phase is ferromagnetic at low temperatures, T, been that of a localized model [71] or a virtual
and 8 depending strongly on the stoichiome- bound state [72] which accounts better for the
try. Two samples with x = 1.59 and 1.73 have electrical properties and high y (0) value.
been studied by Counsel1 et al. [42] who find
UAs,, USb, : Similar properties to UP,. The ordered
A-type anomalies corresponding to the ferro-
and effective magnetic moments increase with
magnetic transitions.
the lattice parameter but the exchange is
U,S3, U,Se3 : Recent magnetic measurements reveal lowered (T, = 283 and 206 K for UAs, and
very complicated magnetic properties for the-
USb,) : Specific heat measurements are due to
se two compounds with up to three anomalies
Westrum et al. [73] from 5 to 700 K and Blaise
for the former [68]. The specific heat has been
et al. [72] b \tw een 1.5 and 300 K. The results
measured [54] for U,S3 and [69] for U,Se3 with
are in better agreement for USb, than for UAs,
A -type peaks corresponding to the above ano- as regards C, (T). There are still discrepancies
malies. No data table is available in [69] but the
for the AS, values and mainly for the y(0)
very high room temperature values of C, for
values which are definitely much higher than
both compounds reveal surprisingly high y
given by [73] and point out to the same model
values.
as that for UP,.
2.6 AnX, COMPOUNDS. - The results are given in ~ -
2.6.3 The dichalcogenides. - There is no structu-
table V for the general compounds and the discus-
ral identity among the dichalcogenides and the crys-
sion of the most important group : the Laves phases,
will be given in chapter 3. tal structure itself is very sensitive to the stoichiome-
try for a given compound.
2.6.1 UC,. - Specific heat measurements in hy-
postoichiometric compounds have been made by a, PUS, : The uranium disulphides US, crystallize
three groups [27, 29, 661 who find very similar in the a phase (tetragonal) for 1.80 S x S 1.93
results in the low temperature range while the results and in the P phase (orthorhombic) for x = 2.
Westrum et al. [74] have measured the specific
of Mukaibo et al. [32] from 100 to 400 OC are 10 %
lower. No magnetic anomaly is reported for this non heat of a compound with x = 1.9 between 5
and 350 K. With a rather rough estimate of the
magnetic compound and ThC, [70] is not isostructu-
ral to UC,. lattice component, they see a Schottky peak at
25 K corresponding to an excited state at 56 K
2.6.2 The dipnictides. - All of them are tetrago- above the ground state. A specimen corres-
nal, anti-Fe,As type and undergo antiferromagnetic ponding to the fl phase has been studied by
ordering at low temperature but their electrical Gronvold et al. [75] with results very similar to
conductivity is that of a metal or semi-metal. 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 16.7 304 60.75 68.32 [66]
94 CaC2 type
Tetragonal a = 3.800 5.48(203) 80.00 101.84 [71]
UP2 anti-Fe,As c = 7.762 TN= 207 1.65(202) 21.0 368 77.50 99.60 [72]
a=4.272 TN=206 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
us,
9 a-USzt ype c = 6.33
'
Orthorhombic
P ~ Cty-I p- ~e
Tetragonal a = 10.73
TN= 11 0.79(13.1)
aUSe2 a-USzt ype c = 6.59
A. BLAISE
Table VI.
Latt. par. TN,~ AS(T,) Y (0) YP e,(o) C, (298~5) ~(298~5)
Compound Struct. A K J/mole (K) mJ/mole.~m~J /mole.~~ K J/mole.K J/rnole.K Ref.
- - - - - - - - - - -
Cubic
PUH3 w30type
$1 {M onoclinic
ZrSe3 type
Cubic
lJRh3 AuCu3-type
CY Use, : This compound has the CY -US, type of of magnetic susceptibility at 19.5 K and a
crystal structure and a susceptibility maximum A -type peak of C, at 11.5 K whose origin is
at 11 K. Westrum et al. [74] find a A-type still not clear [54].
anomaly in C, at 13.1 K with a very low Cubic AuCu,-type compounds : The results of very
associated entropy. As in US,, there are two low temperature specific heat measurements
inequivalent U sites and they assume that only for 8 uranium and 2 neptunium compounds
one type of U undergoes the cooperative tran- are given in table VI together with the referen-
sition. ces. Nearly all these compounds show a tem-
perature independent susceptibility, a resistivi-
2.7 AnX, COMPOUNDS. - The most extensively ty increase proportional to T2a t low tempera-
studied compounds of this group are the AuCu,-type ture and high y(0) values. These and other
compounds. Although the An-An spacing is much data have been reviewed by Brodsky [82] who
larger here than the critical value set by Hill's attempts to explain these physical properties in
criterion, their electronic properties are often better terms of a localized spin fluctuation (1.s.f.)
interpreted in terms of spin-fluctuating systems than model. NpSn,, on the other hand, would be an
of crystal field theory. The results are given in itinerant-electron antif erromagnet [83, 841
table VI. with T, = 9.5 K. Quite apart from the magne-
tic evidence for this assumption, the specific
p UH, : This allotropic variety (cubic) is the usually
heat curve gives some additional proof : a
formed phase by direct reaction. Its conducti- -
AS, 0, a y (T) variation with a sharp peak at
vity is metallic but it undergoes a ferromagne-
T, and a y(0) value much lower than yp
tic ordering below 168 K. Flotow et al. studied
(paramagnetic state).
its specific heat from 5 to 350 K in [76] and
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.
d
Latt. par An-An e~(o)
Compound Struct. A A mJ/moYPl e . K' K Ref.
- - - - - - -
Orthorhombic
URe,
URe2t ype
Cubic
UIr, 7.509 3.25
MgCu, type
UAl, >> 7.795 3.38
NpRu, >> 7.446 3.22
NpOsz >> 7.528 3.26
NpIr2 >> 7.509 3.25
PuAl, >> 7.833 3.39
THE SPECIFIC HEAT OF ACTINIDE COMPOUNDS : ARE THOSE MEASUREMENTS USEFUL ? C4-57
in the Laves phases for the last five years because, 159.7 K and a low associated magnetic entropy
in these compounds, the An-An spacing is close to (possibly due to an incomplete definition of C,,tt).
the critical distance for localization of the 5f elec-
trons and the apparition of magnetism. For most of 4.2 COMPOUNDS UAsY (Y = S, Se, Te). - All
them, this results in an interpretation of their physi- being single uniaxial ferromagnets, the first two
cal properties by 1.s.f. or itinerant magnetism mo- compounds crystallize in the subgroup anti Fe,As-
dels. The specific heat experiments, although still type to which belong the dipnictides. UAsTe has the
very scarce, help to define the appropriate model : slightly distorted structure (space group I4mmm)
the 1.s.f. is characterized by an upturn of C/ T versus called UGeTe-type.
TZb elow the so-called spin fluctuation temperature.
UAsS, UAsSe : Their respective Curie points of 125
The y(0) values are extremely high (and the ASm(Tt)
and 113 K are reflected in the recent specific
are extremely low whenever a cooperative transition
heat measurements of Blaise et al. [90] in the
occurs). In table VII, we give the heat capacity
temperature range 1.5-300 K. As in UOTe, the
results and references.
magnetic entropies are low and as in the di-
URe,, UIr,, UAl,, NpRu, : These compounds are pnictides the y(0) values are high, making
proposed as ferromagnetic 1.s.f. systems. The likely a certain amount of delocalization
most carefully studied is UAI, [78,84,86] with among the 5f electrons.
a Ts, = 30 K. UAsTe : The increase in the c parameter and the
PuAl, : Several properties seem to exclude ferroma- reduction in the coordination number for the
gnetic excitations in this compound and Trai- U atom is accompanied by a decrease of
nor et al. [86] propose an antiferromagnetic T, = 66 K. The specific heat data of [90] show
spin fluctuation model. however an associated magnetic entropy and
NpOs, : Ferromagnetic below 7.5 K with a very mainly a y(0) value higher than those of UAsS
small ordered moment (0.25-0.44 p,) and a and UAsSe.
high y(O), Brodsky et al. [87,84] interprete the
results in terms of a weak itinerant ferroma-
5. The critical phenomena in the actinide
gnetism model.
compounds. - A recent synthesis has been given by
NpIr, : In a paper presented to LT 15, Brodsky et
Blaise [91] of the main theories of the critical beha-
al. [88] give specific heat and magnetic sus-
viour in magnetically ordering systems, the empha-
ceptibility results for this compound which has
sis is on the specific heat and magnetic properties in
a NCel temperature of 7.5 K. Their model is an
localized moment models. Some experimental exam-
itinerant antiferromagnet.
ples are given in [91] but none of them refer to
members of the actinide family. Of course this and
4. Ternary compounds. - Few such compounds other papers at this Conference emphasize the
have been studied up to now and all of them belong extent of our present knowledge on the actinide
to the general tetragonal structure group : P4nmm compounds.
already characteristic of the dipnictides. The speci- The contribution of the actinide compounds to the
fic heat data are listed in table VIII. study of the critical phenomena could be of impor-
tance : a number of these compounds are fairly good
4.1 UOTe. - This compound belongs to the sub- examples of localized systems. The exchange
group of PbFCl type and is reported as antiferroma- constants of these compounds can be altered by
gnetic type I below 162 K. Its specific heat has been replacement of either the cation or the anion without
measured from 21 to 362 K by Stalinsky et al. [89] any crystallographic modification. Many com-
who report the corresponding A-type peak at pounds display a magnetic transition in a temperatu-
Table VIII.
Latt. par. TN,= 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
TN = 162 4.48
UOTe PbFCl type c = 7.501
Tetrag.
a = 3.878
UAsS anti-Fe2As T, = 125 1.53(126) 23.5 288 80.90 114.48 [90]
c = 8.164
type
Tetrag.
UAsSe anti-Fe,As a = 3.981 T, = 113 0.63(110) 39 231 83.48 131.71 [90]
tvve
~it;a~. a =4.150
UAsTe T, = 66 2.75(63) 57 217 81.32 139.80 1901
UGeTe-type c = 17.270