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Magnetic properties of the pseudo-binaries Np1−xPuxB2, extension of the Curie-Weiss model for di-magnetic solid solutions
Journal
132
of Magnetism
and Magnetic
Materials
84 (1990) 132-142 North-Holland
MAGNETIC PROPERTIES OF THE PSEUDO-BINARIES Np,_ ,Pu,B2, EXTENSION OF THE CURIE-WEISS MODEL FOR DI-MAGNETIC SOLID SOLUTIONS R. CHIPAUX
’
DMECN/DECPu/SEFCA,
A. BLAISE DRF/SPh Received
CEN Cadarache, BP 1, 13108 Saint-Paul-lez-Durance cedex, France
and J.M. FOURNIER
/MDN,
CEN Grenoble, 85X, 38041 Grenoble cedex, France
12 May 1989
are reported, and confirm the previously Magnetic susceptibility measurements on NpB,, PUB, and their solid-solutions published Mossbauer spectroscopy investigations. Results on NpB, and PUB, are tentatively interpreted within a crystal field scheme. An extension of the Curie-Weiss model is proposed for the interpretation of results in the solid-solutions. A strong dependence of magnetic exchange interactions with interactinide smallest distances is observed, in good agreement with the general results on neptunium or plutonium compounds.
1. Introduction The diborides of neptunium and plutonium belong to the AlB,-type diborides, which form the most numerous series of binary metal-boron compounds. Their crystal structure is hexagonal, space group P6/mmm, composed of hexagonal boron networks alternating along the c-axis with hexagonal centered metal layers [l] (see fig. 1). They are reported to have an opposite magnetic behavior [2]. The published measurements on samples containing secondary phases indicate an approximately constant paramagnetism at all temperatures for Pub, and a ferromagnetism below 100 K for NpB,. The very low ordered moment of NpB, (0.14~~ at 2K) was attributed to itinerant magnetism. Synthesis of NpB,, PUB, and pseudo-binaries in good purity condition, and NP,-,Pu,B,, Mijssbauer spectroscopy results have recently been reported [3-51. The lattice parameters follow Vegard’s law, and the Mossbauer parameters only show a very slight evolution from NpB, to PUB,, ’ Present
address: Switzerland.
0304-8853/90/$03.50 (North-Holland)
CERN,
division
EF,
1211
Geneve
denoting a strong similarity of the compounds, from the point of view of ion environment. The isomer shift is almost constant among the series, and suggests a 4 + valency state for the neptunium ions. An extended quadrupolar splitting is observed, related to the crystal structure. It decreases slowly (less than 10%) when x varies from 0 to 0.83. In the three compounds ordered at low temperature (x = 0, 0.1, 0.3), the ordered magnetic moments on the neptunium ions are almost identical, (0.58 + O.O2)p,, and perpendicular to the caxis. In the middle range concentrations (0.3 I x I 0.67), magnetic relaxation seems to appear. The high plutonium concentrate compounds (x 2 0.67) do not show magnetic order down to 1.6 K, ap-
0
B.V.
(GO)
l boron(z=l/.Z)
23, Fig. 1. A&-type
0 Elsevier Science Publishers
metal
crystal
structure:
projection
along the c-axis.
R. Chipaux et al. / Properties of the pseudo-binaries
parently confirming the permanent paramagnetism of Pub. In this article we present magnetic measurements on Np&, PUB, and several Np,_,Pu,B2 solid-solutions. Results on the binary compounds are tentatively analyzed within a crystal field scheme, while an extension of the modified Curie-Weiss model is proposed for the analysis of the solid-solutions results.
2. Experimental The binary borides NpB,, PUB, and their solid-solutions were synthesized in vacuum by liquid-solid reaction between the stoichiometric quantities of actinides and boron [3,5]. The homogeneity of the solid-solution was ensured by a two step process: formation of a solid-solution between the two metals; reaction of the alloy (powdered by hydridation) with boron. After characterization, the powder samples were separated in two parts, one for the previously reported Mijssbauer experiments, the other for these magnetic measurements. These last samples, of mass about 300 mg, were encapsulated in pure aluminium containers, sealed under helium and carefully decontaminated. The susceptibilities in the paramagnetic range and the magnetizations in the ferromagnetic range were measured by the classical Faraday method, on our automated balance, between 2 and 300 K, in fields up to 1.7 T. Owing to the opposite magnetic behavior of NpB, and Pub, the whole range of sensibility of the apparatus has been used. The NpB, sample has reached the saturation limit, and at the other end the PUB, sample was not far from the sensibility limit, leading to some irregularities on the curves, especially at low temperatures where the container signal correction becomes important. In all samples, slight spontaneous magnetizations have been detected, indicating small contaminations by ferromagnetic impurities. In relation with their high Curie temperatures (> 600 K), we attribute them to traces of iron or nickel compounds. These magnetizations have been subtracted from the experimental data.
133
Np, _ x Pu, B,
3. Binary compounds 3.1. NpB, The inverse molar susceptibility, measured in a magnetic field of 0.82 T, is plotted in fig. 2 versus temperature. A strong curvature is observed and the data may be fitted by a modified Curie-Weiss law:
x=x0*+
c* T_(jp
with 8,, = 103 K and p,tf * = 1.31(2)pL,. If we assume that expression (1) may be renormalized in the molecular field approximation [6], this leads to p,rr = 0.75~~. All the parameters are reported in table 4. At low temperature a ferromagnetic order is observed, in agreement with ref. [2]. Due to the saturation of the Faraday balance, magnetization curves o(H) have not been obtained at low temperature. The Curie temperature, extrapolated from the u2 vs. T curve is T, = (103 +_2) K.
6oo*
100
Temperature
200
(K)
Fig. 2. Inverse of the molar susceptibilities versus temperature for Np&, solid line: MCW fit; dotted line: calculated curve, LS-RS model; dashed line: calculated curve, F-RS model; dash-dotted line: calculated curve, F-IC model.
134
R. Chipaux et al. / Properties of the pseudo-binaries
F
1600
-3 s
r
800
7 x
I
f
1200
s E
I
PUB,
tI-
400
I
__-;_-- _---./
_______*5i-‘--.
01
0
__-.-z_
I
I
100
200
Temperature
_ -2:
-2:
-I
300
(K)
Fig. 3. Inverse of the molar susceptibilities versus temperature for PUB,, solid line: MCW fit; dashed line: calculated curve, F-RS model; dash-dotted line: calculated curve, F-IC model.
3.2.PUB, PUB, is found to be a weak paramagnet. The inverse susceptibility, measured in 0.82 T, is plotted in fig. 3 versus temperature. The apparent anomaly observed around 77 K is an artifact due to the weakness of the signal. The data may be fitted by (l), leading to pLe*fr = 0.32~~ and 0, = - 30 K. Renormalization leads to Peff
=
O-75!-%
3.3. Crystal field calculations
Np, _ x Pu, B,
take the same 4 + valency for the plutonium ions. In a true ionic model, the neutrality of charges would lead to a 2 - valency for the boron ions. However, as remarked in ref. [4], the anions are more likely B’ - and the two extra electrons per formula unit must contribute a uniform negative charge along the metal layers. The B,"coefficients can be calculated using the computer program developed by Amoretti in the frame of either a purely ionic model extended to the whole lattice (LS) surrounding the metal ion [7] or of a so-called “layer” (F) model [8]. In the latter case, the most important contribution to the CF is considered as due to the ions in the layers next to the metallic one plus the metal ions and the conduction electrons in the metal layer. The relativistic values of (r”) given in ref. [9] have been used .for the metal ions. For Np4+, we take a Sternheimer shielding factor a, = 0.88, as suggested in ref. [lo], while a4 and a, are neglected as they are already very close to zero for U3+ and U4+ [ll]. In absence of any calculation for Pu4+, we assume the same shielding factors as for Np4+. In the Russell-Saunders (RS) coupling scheme, the ground multiplets are 4I9,2 (5f 3 configuration) and ‘I, (5f4 configuration) for Np4+ and Pu4+, respectively. In the intermediate coupling (IC) scheme, the corresponding J values are still good quantum numbers and we take for the Stevens factors (Y, j? and y the values calculated in ref. [12]. At last, in this scheme, the crystal-field parameters (CFP) for n = 2, 4 and 6 have to be multiplied by factors given in ref. [12] too.
The crystal-field (CF) Hamiltonian for the Dhh hexagonal symmetry is, in the point-charge model (PCM):
(2) where the B," are the CF-parameters and the &” the Stevens operator equivalents. In the present calculation, we shall restrict ourselves to the terminal compositions of the solid-solutions, i.e. to NpB, and PUB, which are representative of the results given by the PCM in this class of compounds. We assume a 4 + valency for the neptunium ion and, owing to the close crystallographic and chemical similarity between NpB, and PUB,, we
Table 1 Crystal field parameters (cm-‘) for the Np and Pu diborides. Reference frame rotated 7r/4 around c with respect to the a-axis, Stemheimer coefficient o, included
B20
840
B,oX104
NpB, (F-RS) NPB, (F-IC) NpBl (LS-IC)
- 18.33 - 12.47 - 11.71
0.1413 0.1018 0.2177
0.1720 0.1152 6.740
PUB, (F-RS) PUB, (F-IC) PUB, (LS-IC)
19.83 23.40 14.67
- 0.1685 - 0.1904 - 0.2961
- 0.1310 -0.1113 - 6.989
B,6x102 - 1.452 - 0.9727 - 1.672 1.799 1.529 1.779
135
R. Chipaux et al. / Properties of the pseudo-binaries Np, _ x Pu, B,
The final CFP have been computed in the RS and IC schemes for the LS and F models and only the most significant results are listed in table 1. To obtain the energy levels and eigenfunctions we must use these values and diagonalize the energy matrix in formula (2). In NpB,, the CF effect is to split the ten-fold degeneracy of the ground term for the neptunium ion into five Kramers doublets. The position of these five energy levels is given in table 2. The main difference between the LS and the F models is the presence in the latter of a level at about 70 K which should rise to a Schottky anomaly in the heat capacity if we were not in the ordered state. In hexagonal symmetry, the hexagonal CFP couple the matrix elements with AM = 6. The new ground eigenstate is of the type: ]‘k)=cr*]+:)+p*]G)
(3)
and the ordered moments values along the two axis x and z are reported in table 2 too. It is clear that, along z, the ordered moment values do not correspond to the experimental result of ref. [4], whereas along x the calculated values are in better agreement with the experiment. In PUB,, the CF splits the nine-fold degenerate ground multiplet into three singlets and three doublets. The position of these six energy levels with their multiplicity is given in table 3. The new ground state is a singlet (built from the axial CFP on the ) 0) matrix element) and thus bears no magnetic moment in agreement with the experiment. The next excited state is a doublet located around 250 K. There is hardly any difference in
Table 2 CF energy level (in K) and ordered moment (in pa) of the ground state in the PCM for NpB,
Energy levels
pz pLx
F-RS
F-IC
LS-RS
LS-IC
0 67 601 1244 1652
0 12 411 862 1150
0 590 731 1284 1700
0 404 538 898 1197
2.41 0.51
2.55 0.53
2.35 0.60
2.49 0.62
Table 3 CF energy level (in K) and multiplicity of the levels in PCM for PUB, Multiplicity
F-RS
F-IC
LS-IC
Multiplicity
1 2 2 1 1 2
0 216 159 1272 1402 1431
0 248 877 1494 1605 1683
0 261 926 1100 1498 1627
1 2 2 2 1 1
the
the level scheme between the LS and the F models, except for the multiplicity of the two highest levels. In the paramagnetic region, the knowledge of the energy levels allows to calculate the Van Vleck susceptibilities xZW and xX&, in the z and x direction, respectively, for both diborides. Assuming, in a first approximation, that the average calculated powder susceptibility is: XV” = :x=w + :xX&, we have plotted in figs. 2 and 3 the temperature variation of l/Xvv compared with the experimental data for NpB, and PUB,, respectively. It is clear that neither the slopes nor the absolute values of the calculated results agree with the experiments. - For the neptunium diboride, the RS calculation seems in better agreement because of the greater CF-splitting. But, if we take into account the exchange interaction by the corresponding translation of the Van Vleck curve, we find nearly an order of magnitude difference between calculated and observed susceptibilities at 300 K. This could be due in part to the core diamagnetism of the compound but essentially, this proves that the localized ionic model is unable to explain the overall results. _ For the plutonium diboride, the experimental curve can be decomposed in two parts. Below 100 K, the low temperature tail could be due to a paramagnetic impurity, whereas above 100 K, the temperature variation bears a similarity with that of the calculated curve in the IC. Again, however, the difference in magnitude between the two curves excludes an interpretation by diamagnetic contri-
R. Chipaux et al. / Properties of the pseudo-binaries Np, _ x Pu, B,
136
bution, and the PCM is no more adequate in that circumstance too. For this compound, there is no difference as regards the calculated susceptibility between the F and LS models. The quadrupolar interaction can readily be estimated by our PCM in the paramagnetic state of NpB,. The value of e2qQ reported in ref. [4] is 92.8 mm s-t, as observed at T = 110 K. This corresponds to an electric field gradient (EFG): ( eq 1 = 45 x 10” V cm-2, with a quasi-axial symmetry along the c-axis. The EFG in the paramagnetic state can be written as the sum of three terms:
+eq1’(1-
&)
1
(41
z being the CF-symmetry axis of the single paramagnetic ion. The first term in (4) represents the contribution of the lattice, the second term the contribution of the conduction electrons with non-s character and the third term the contribution of the 5f electronic cloud. Each term is multiplied by the corresponding screening coefficient. According to ref. [13], we have: - 4Bz” eqk = ___ ecx(r2) ’ eqlf =
-e4r-3>(QZ)Ty
(5)
where (Y is the Stevens factor for n = 2, (QZ)r is the thermal average of the operator (3t - j2) on the CF-states and Bi the CFP of order 2. The average values (r’) and (r-‘) are given in ref. [9]. All calculations done, one finds the following orders of magnitude: 1.5 X 10” V cmm2 for the 5f contribution, 250 X 10” V cmp2 for the lattice contribution (taking the Bt of table 1 before multiplication by ~~2). This result tends to demonstrate the importance of the lattice contribution, as evidenced in ref. [4]. But it also emphasizes the need of a high conduction electron contribution acting as a reduction factor [14] to yield the experimental EFG. This would suggest the interest of electrical resistivity measurements, especially of the anisotropy in the transport properties for single crystals, in
order to check the previously model.
assumed “layer”
4. Solid-solutions 4.1. Results The inverse molar susceptibilities, measured in a magnetic field of 0.82 T, are plotted in fig. 4 versus temperature. All the data may be fitted by a modified Curie-Weiss law. The fitted parameters, as well as the parameters renormalized following [6] are reported in table 4. We show in the next paragraph how these parameters can be related to each type of magnetic ion. The paramagnetic Curie temperature f$ is almost constant for x I 0.2. At higher plutonium concentration, it decreases slowly, approximately linearly, to reach zero for x = 0.83, and is negative in PUB,. At low temperatures, the ferromagnetic order is maintained for x I 0.5. The plots of versus T/l&, shown in fig. 5, indicate (+%+0)2 that the transition temperature T, decreases faster than 6, for x 2 0.3. No transition is observed in NPo.33PU 0,67B2, although 19, equals 21 K in this compound. In the same range of concentration
1600
-0
100
Temperature
300
200
(K)
Fig. 4. Inverse of the molar susceptibilities versus temperature for Np,_,F’u,B,. (a) x =O; (b) x = 0.1; (c) x =0.3; (d) x = 0.5; (e) x = 0.67; (f) x = 0.83; (g) x = 1. The solid lines represent the MCW fits.
137
R. Chipaux et al. / Properties of the pseudo-binaries Np, _ x Pu,B, Table 4 Fitting parameters Experimental X
of the magnetic
susceptibilities
parameters * ;lb
for Np, _,Pu,B,
C* (emu K/mol)
emu/mol)
&)
Peff
T,
(na)
(K)
0.00 0.10
878(49) 1222(37)
0.214 0.166
103.4(0.5) 102.3(0.5)
1.31(0.02) l.X(O.02)
103(2) 105(l)
0.30 0.50 0.67 0.83 1.00
1171(35) 1061(46) 730(19) 720(13) 576(11)
0.108 0.082 0.075 0.037 0.013
80.6(0.6) 60.2(1.5) 20.6(1.0) 0.6(1.6) - 29.7(7.3)
0.93(0.02) 0.81(0.02) 0.77(0.01) 0.55(0.01) 0.32(0.01)
77(l) 36(4)
renormalized X
parameters
0.00 0.10 0.30 0.50 0.67 0.83 1.00
x0 (10m6 emu/mol)
kff
hn
(pa)
(mol/emu)
504 303 149 236 584 712 1323
0.75 0.29 0.12 0.18 0.62 0.54 0.75
846 2480 5860 3300 344 15 -982
(0.3 I x I 0.67) and for T, < T < 19, the magnetization versus field curves are not linear but do not show spontaneous magnetization except for the small one of the aforesaid impurity. This can be due to magnetic relaxation phenomena, as also observed in the Mijssbauer spectroscopy experiments [3,4]. The ordered magnetic moments are reported in table 5. Contrary to the Mossbauer experiments, which give the local ordered magnetic moment p,,, the magnetization measurements, on powder samples, lead to a bulk moment /.L,,~~,, averaged over all crystallite orientations present in the sample. In anisotropic compounds like these diborides, ppowd can be notably inferior to pFlo.On the con-
Table 5 Ordered magnetic moments field) for Np, _XPu,B, x
CO
0.0 0.1 0.3 0.5
f&w/d
(PB)
(Mossbauer 0.57(l) 0.59(l) 0.57(l) 0.42(3)
at 4.2 K (extrapolated
[3,4])
(PB)
(Magnetization) not measured 0.56 0.53 0.16
at zero
trary, the closeness of the values observed in the x = 0.1 and 0.3 compounds suggests that mechanical reorientations of the crystallites by the magnetic field may occur during measurements in ferromagnetic regions. 4.2. Extension of the Curie- Weiss model and application to Np, _ x Pu, B, As shown in the appendix, in compounds containing two types of magnetic ions, the assumption of a Curie-Weiss behavior for the local magnetic susceptibilities (eq. (A.l)) leads strictly speaking to a global magnetic susceptibility law related, but different, to the modified Curie-Weiss law (MCW) (eq. (A.8)). However, in solid solutions, we can assume eqs. (A.14). The MCW is therefore recovered, but all the physical parameters can not be calculated from the experimental data (eqs. (A.15) to (A.17)). Nevertheless, the crystallographical and in Np,_,Pu,B,, Mossbauer spectroscopy results lead to a weak or null dependence of the physical quantities with x: small variation of the lattice distances and electric field gradient, constancy of the isomer shift and of the ordered magnetic moment. Thus, in a first
R. Chipaux et al. / Properties of the pseudo-binaries
138
0.8 N -
0 0.6
< b V
N -
0.4
0 0.6
< b V
0.4
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Np, _ x Pu, B,
$&?,2(1 -x) ( averaged smallest distance in volume, a and c being the lattice parameters) for the small neptunium concentrations, and to u//m (averaged smallest distance in the basal plane) for the high ones. The smallest quantity should be chosen. The same formula apply for the plutonium ions, changing (1 - x) into x.) The main results are, for the neptunium a pronounced maximum at d,,_,, = 0.37 nm, and for the plutonium an inversion of the sign of the magnetic interactions: antiferromagnetic below 0.35 nm and ferromagnetic above, with a maximum between 0.4 and 0.5 nm. It is interesting to compare these results with the general magnetic data for neptunium or plutonium compounds, summarized classically on the so-called Hill plot, [15]. As shown on fig. 7, the magnetic transition temperatures in neptunium compounds reach a maximum for d,,_ ,,+, - 0.36 nm, and in plutonium compounds, two separate domains can be distinguished: antiferromagnetism for dPu_Pu I 0.35 nm, and ferromagnetism for dPu_Pu > 0.35 nm. (Compounds containing magnetic ligands (e.g. iron, cobalt, nickel, . . . ) are obviously not included in this comparison.) Although our results on Np,_,Pu,B, apply only to a rough average of the magnetic interac-
5% Fig. 5. (a/~~_~)
’ vs. T/l?, curves for Np, _,P,B,.
11
5000
approximation, the magnetic parameters xONp, C, can be considered as constants, XOP”, Gl,, and be determined from the measurements on the pure binary compounds. Only X,, and X,, are concentration dependent, and their evolution with x is representative of the variation of the magnetic interactions with the concentration or, on another point of view, with the average of the interactinides smallest distances. The molecular field constants X,, and h,, are calculated as a function of x using eq. (A.20) and eq. (A.18) or (A.19), which are now redundant. The results are similar, as reported in table 6. Fig. 6 represents the variation of the calculated molecular field constants with the averaged smallest distance between the corresponding actinide. (For the neptunium ions, this distance is equal to
11
I(
I
I
I
:"b
4000 -
:
o NP
1 1
d 5
2
t 1000
t
-
c; ,
0
-.
\\
I
‘;,-;:;:zq
, b-c___,
,,‘o 1’
-lOOO-
-2000
d'
I’ 0.3
*
’
0.4
’
’
0.5
’
’
0.6
’
I
0.7
dAAn+,(nm) Fig. 6. Molecular field constants A,, averaged distances in Np, _,Pu,B,. guidelines.
and A,, vs. intermetallic The dashed lines are
R. Chipaux et al. / Properties of the pseudo-binaries
Table 6 Molecularfield constants X
0.00 0.10 0.30
x
x
NP
NP
d NP-NP (nm)
A
(mol/ emu)
(1)
(2)
(mol/ emu)
(1)
(2)
846 2240 4150
846 2290 4600
0.3162 0.3336 0.3788
0 238 1710
0 189 1250
cc 0.7009 0.4863
1900
0.4104
1600
1390
0.4104
128
122
0.4717
261
222
0.3883
0.83
16
21
0.5887
-1
-6
0.3493
0
(1) Calculated (2) calculated
0
CC
- 982
compounds,
with the general magnetic
their
data is re-
markable.
5. Conclusion
0.67
1.00
139
x Pu, B,
in these pseudo-binary
coherence
d Pu-P” (nm)
APIA
PU
(mol/ emu)
(mol/ emu)
0.50 1690
tions
for Np and Pu in Np, _XPu,B,
Np,
-982
Measurements of the magnetic properties of are in good agreement with several Np,_,Pu,B2 Mijssbauer spectroscopy results.
A tentative
0.3187
interpretation
of
these measure-
ments, within a crystal field model
of localized
ions shows that this hypothesis is inadequate to explain the paramagnetic susceptibility. However,
from x0 and A,; from C, and A,.
600
I
I I 8
I
a
:.-An
Intermclrlllcs b c d c f g h i j k I
:
:
AnNi, : AnCo, AnFc, : AnMn, : Anlr, : AnAl, :AnRh, AnAI, :AnSn, : AnPt : AI&,,
:
:
Carbides : m : AK n : An&, Doridcs :
I
600
‘.
I
o p q r
I
I
I
I
: : : :
An& AnD, AnB. AnD,,
Pnictides : I 2 3 4 5
: : : :
:
AnN AnP AnAs AnSb AnDi
Cbnlcogenida 6 I 8 9
:
: AnS :AnSe : AnTc : AnO,
(An = Np, Pu)
#
I
I
I
I
0.3
0.4
0.5
0.6
oLAn
W 0 A
: fewmagnetic
(nm)
Fig. 7. Hill plot for neptunium
and plutonium
trmnsttien transition
: dtr~tdb89gnctk : “0 transition
compounds.
140
R. Chipaux et al. / Properties of the pseudo-binaries Np, _ x Pu, B,
it gives the correct value of the magnetic moment of the ground state. Thus, the Sf electrons are probably not well localized in the diborides (UB, is in fact a weak Pauli paramagnet). In this context, heat capacity and electrical resistivity results on NpB, and PUB, would be most interesting, these compounds being candidates for heavyfermion behavior. An extension of the Curie-Weiss model for di-magnetic solid-solutions is proposed, which implies as a consequence that the molecular field constant - i.e. the exchange interaction - is
Appendix. Extension of the Curie-Weiss
strongly dependent upon the average smallest distance between the corresponding actinides atoms. The results are in good agreement with the socalled Hill plot.
Acknowledgements We are grateful to G. Amoretti for the use of his computer programs. We are also indebted to J. Chiapusio for encapsulation and decontamination of the a-radioactive samples.
model: calculations
In some compounds, particularly in actinide systems, system, or local susceptibility, should be written as:
the magnetic
susceptibility
of the non-interacting
(A.1)
xp = xo + C/T,
where C is the Curie-Weiss constant, equal to &/8 in molar units, and x0 a constant term due for instance to Van Vleck or Pauli contributions. In that case, assuming the molecular field approximation with a molecular field constant A, the macroscopic magnetic susceptibility follows the modified x0, C and A are Curie-Weiss law (MCW) (eq. (l)), and, as shown in ref. [6], the physical parameters connected to the experimental parameters by the following relations: xo=xo*(C*-~~xo*)/C*~
(A.2)
c=
(A.3)
(C” -e&,*)*/c*,
x = e&c*
- e,x,*).
(A.4)
In systems containing two different types of magnetic ions (a and b in the following equations), this molecular field treatment should be extended to take the crossed magnetic interactions into account. The effective field is written on each type of ion as a sum of the external field Hext, and of the contribution of the magnetization of each type of ion: Kffa
Assuming M=
=
Hext
+
X,,K
+
Kffh
h,bMb,
a molar proportion
=
Kx,
+
hb,Ma
+
(A.51
XbbMb.
(1 - x, x), for a and b, respectively,
the total magnetization
(1 -x)M,+xM,.
(A.6)
If the local susceptibility
follows in both types the expression
Xpa = Xoa + C,/T, the global magnetic
Xpb
=
susceptibility
C,* +
is:
C:/T
x=xo*+ T-l$,+8,,/T’
XOb
+
cb/T,
(A.l),
which reads: (A.7)
takes the form:
(‘4.8)
141
R. Chipnux et al. / Properties of the pseudo-binaries Np, _ x Pu,B,
with: (1 -x)x&$
- (A,, - L&)Xllb)
x0* =
c;
(1 - &J&)(1
=
((I
-
x)[ca(l
+x[Cb(l
-
xl/[(l
c:
=
-
-
[(l
-
=
x..ca
+
xbbcb
(I
-
=
(l
-
-
xaa)
+
xaaxOa)(l -
XaaXOa)(l
-
(l
-
+
-
haaXOa)(Xba
-
(A.91 ’
+
CbXabXOa(l
CaXbaXOb(l
-
-
(hbb
(‘aa -
-
XbZhO~)~
hba)xOb)l
-
-
-
‘bb))
‘a,))]
(A.ll)
XbaXabXOaXOb]2~ +
CbXOa)
(A.12) ’
XbaXabXOaXOb
xabxba)cacb
XbbXOb)
>
(A.10)
XbbXOb)(Xab
habhba)(CaXOb
XbbXOb)
- &-JX0a)
XbaXabXOaXOb]2,
XbbXOb)
-
-
(l
AbbXOb)
&,XOa)
-
+
-
&aXbb
xaaxOa)(l (‘hdbb
“I
hbbxOb)
- (L
hbaXabXOaXOb
-
-
hb)
-
-
&,b)XOb)(l
hba)XOa)(l
-
X)(XabXOa(hba
xcacb/[(l
PO
-
XaaXOa)(l
+X(hbaXOb(hab
6
- hbbX~b) +
(‘bb
(xaa
+ XXI&
(A.13)
-
‘baXabXOaXOb~
The eight physical parameters (xOa, xOb, C,, Cb, h,,, Aat,, Xba, X,,) cannot be entirely determined from the five experimental parameters (x$, C,,*, CT, op,,, et,,). Moreover, this model is formally exact but inapplicable in this form owing to the large number of parameters and to the weak specificity of eq. (A.8). Nevertheless, in solid solutions such as Np, _XP~XB2, where the two types of ions are very close in terms of size and physico-chemical behavior, we can assume that the molecular field seen on one site does not strictly depend on the type of the considered ion. This implies: (A.14)
Xab=Xbb.
&=&a, Thus the terms parameters:
tipI become
CT and
equal
to 0, and
the MCW
is recovered,
(l - x)xO~+ XxOb ‘O*
=
1
-
(l
c,* =
XuoXOa
-
-
x)Ca
+
’
+
(CbXOa
(1 caxaa epo =
1-
+
‘a&Oa
-
XbbXOb
c=
1 +
(CbXOa
x)xbb
-
xhaa)
(A.16)
1
xbbxOb)2
we can extract
-
CaXOb)[(l
-
X)XOa
+
xxOb
x)xbb
-
Xhaa]/[(l
the global physical
parameters: (A.I~)
-x)Ca
+
xcb]
’
(1 -x)c,+xc,
1+
(CbXOa
CaAaa x=
-
-
(A.17)
(l=
CaXOb)((l
.
Using eqs. (A.2), (A.3) and (A.4)
X0
-
cbxbb
XaaXOa
(1
+
-x)c,+xc,’
cbxbb
the experimental
(A.15)
XbbXOb
xcb
with
caxOb)[(l
-
x)xbb
-
(A.19) xhaa]/[(l
-x)Ca
+
xcb]
’
(A.20)
142
R. Chipaux et al. / Properties of
thepseudo-binaries
References [l] N.N. Greenwood, The Chemistry of Boron (Pergamon Press, Oxford, 1973) p. 697. [2] J.L. Smith and H.H. Hill, AIP Conf. Proc. 24 (1975) 382. [3] R. Chipaux, Thesis, UniversitC d’Aix-Marseille II, France (1987). [4] R. Chipaux, D. Bormisseau, M. Bog& and J. Larroque, J. Magn. Magn. Mat. 74 (1988) 67. [5] R. Chipaw, J. Larroque and M. Beauty, J. Less-Common Met. 153 (1989) 1. [6] G. Amoretti and J.M. Foumier, J. Magn. Magn. Mat. 43 (1984) L217. [7] G. Amoretti, A. Blaise, J.M. Collard, R.O.A. Hall, M.J. Mortimer and R. Trot. J. Magn. Magn. Mat. 46 (1984) 57. [S] G. Amoretti, A. Blaise, M. Bonnet, J.X. Boucherle, A.
[9] (lo] [ll] [12] [13]
[14] 1151
Np, _ x Pu, B,
Delapalme, J.M. Fournier and F. Vigneron, J. de Phys. C7 (1982) 293. J.P. Desclaux and A.J. Freeman, J. Magn. Magn. Mat. 8 (1978) 119. D. Sengupta and J.O. Artman, Phys. Rev. B 1 (1970) 2986. P. Erdiis and H.A. Razafimandimby, J. de Phys. 40 (1979) c4-171. G. Amoretti, J. de Phys. 45 (1984) 1067. S. Ofer, I. Nowik and S.G. Cohen, in: Chemical Applications of Mossbauer Spectroscopy, eds. V.I. Goldanskii and R.H. Herbes (Academic Press, New York, 1968) p. 426. R.S. Raghavan, E.N. Kaufmann and P. Raghavan, Phys. Rev. Lett. 34 (1975) 1280. H.H. Hill, in: Plutonium 1970 and other Actinides, ed. W.N. Miner (Metal Sot., AIME, New York, 1974) p. 52.
132
of Magnetism
and Magnetic
Materials
84 (1990) 132-142 North-Holland
MAGNETIC PROPERTIES OF THE PSEUDO-BINARIES Np,_ ,Pu,B2, EXTENSION OF THE CURIE-WEISS MODEL FOR DI-MAGNETIC SOLID SOLUTIONS R. CHIPAUX
’
DMECN/DECPu/SEFCA,
A. BLAISE DRF/SPh Received
CEN Cadarache, BP 1, 13108 Saint-Paul-lez-Durance cedex, France
and J.M. FOURNIER
/MDN,
CEN Grenoble, 85X, 38041 Grenoble cedex, France
12 May 1989
are reported, and confirm the previously Magnetic susceptibility measurements on NpB,, PUB, and their solid-solutions published Mossbauer spectroscopy investigations. Results on NpB, and PUB, are tentatively interpreted within a crystal field scheme. An extension of the Curie-Weiss model is proposed for the interpretation of results in the solid-solutions. A strong dependence of magnetic exchange interactions with interactinide smallest distances is observed, in good agreement with the general results on neptunium or plutonium compounds.
1. Introduction The diborides of neptunium and plutonium belong to the AlB,-type diborides, which form the most numerous series of binary metal-boron compounds. Their crystal structure is hexagonal, space group P6/mmm, composed of hexagonal boron networks alternating along the c-axis with hexagonal centered metal layers [l] (see fig. 1). They are reported to have an opposite magnetic behavior [2]. The published measurements on samples containing secondary phases indicate an approximately constant paramagnetism at all temperatures for Pub, and a ferromagnetism below 100 K for NpB,. The very low ordered moment of NpB, (0.14~~ at 2K) was attributed to itinerant magnetism. Synthesis of NpB,, PUB, and pseudo-binaries in good purity condition, and NP,-,Pu,B,, Mijssbauer spectroscopy results have recently been reported [3-51. The lattice parameters follow Vegard’s law, and the Mossbauer parameters only show a very slight evolution from NpB, to PUB,, ’ Present
address: Switzerland.
0304-8853/90/$03.50 (North-Holland)
CERN,
division
EF,
1211
Geneve
denoting a strong similarity of the compounds, from the point of view of ion environment. The isomer shift is almost constant among the series, and suggests a 4 + valency state for the neptunium ions. An extended quadrupolar splitting is observed, related to the crystal structure. It decreases slowly (less than 10%) when x varies from 0 to 0.83. In the three compounds ordered at low temperature (x = 0, 0.1, 0.3), the ordered magnetic moments on the neptunium ions are almost identical, (0.58 + O.O2)p,, and perpendicular to the caxis. In the middle range concentrations (0.3 I x I 0.67), magnetic relaxation seems to appear. The high plutonium concentrate compounds (x 2 0.67) do not show magnetic order down to 1.6 K, ap-
0
B.V.
(GO)
l boron(z=l/.Z)
23, Fig. 1. A&-type
0 Elsevier Science Publishers
metal
crystal
structure:
projection
along the c-axis.
R. Chipaux et al. / Properties of the pseudo-binaries
parently confirming the permanent paramagnetism of Pub. In this article we present magnetic measurements on Np&, PUB, and several Np,_,Pu,B2 solid-solutions. Results on the binary compounds are tentatively analyzed within a crystal field scheme, while an extension of the modified Curie-Weiss model is proposed for the analysis of the solid-solutions results.
2. Experimental The binary borides NpB,, PUB, and their solid-solutions were synthesized in vacuum by liquid-solid reaction between the stoichiometric quantities of actinides and boron [3,5]. The homogeneity of the solid-solution was ensured by a two step process: formation of a solid-solution between the two metals; reaction of the alloy (powdered by hydridation) with boron. After characterization, the powder samples were separated in two parts, one for the previously reported Mijssbauer experiments, the other for these magnetic measurements. These last samples, of mass about 300 mg, were encapsulated in pure aluminium containers, sealed under helium and carefully decontaminated. The susceptibilities in the paramagnetic range and the magnetizations in the ferromagnetic range were measured by the classical Faraday method, on our automated balance, between 2 and 300 K, in fields up to 1.7 T. Owing to the opposite magnetic behavior of NpB, and Pub, the whole range of sensibility of the apparatus has been used. The NpB, sample has reached the saturation limit, and at the other end the PUB, sample was not far from the sensibility limit, leading to some irregularities on the curves, especially at low temperatures where the container signal correction becomes important. In all samples, slight spontaneous magnetizations have been detected, indicating small contaminations by ferromagnetic impurities. In relation with their high Curie temperatures (> 600 K), we attribute them to traces of iron or nickel compounds. These magnetizations have been subtracted from the experimental data.
133
Np, _ x Pu, B,
3. Binary compounds 3.1. NpB, The inverse molar susceptibility, measured in a magnetic field of 0.82 T, is plotted in fig. 2 versus temperature. A strong curvature is observed and the data may be fitted by a modified Curie-Weiss law:
x=x0*+
c* T_(jp
with 8,, = 103 K and p,tf * = 1.31(2)pL,. If we assume that expression (1) may be renormalized in the molecular field approximation [6], this leads to p,rr = 0.75~~. All the parameters are reported in table 4. At low temperature a ferromagnetic order is observed, in agreement with ref. [2]. Due to the saturation of the Faraday balance, magnetization curves o(H) have not been obtained at low temperature. The Curie temperature, extrapolated from the u2 vs. T curve is T, = (103 +_2) K.
6oo*
100
Temperature
200
(K)
Fig. 2. Inverse of the molar susceptibilities versus temperature for Np&, solid line: MCW fit; dotted line: calculated curve, LS-RS model; dashed line: calculated curve, F-RS model; dash-dotted line: calculated curve, F-IC model.
134
R. Chipaux et al. / Properties of the pseudo-binaries
F
1600
-3 s
r
800
7 x
I
f
1200
s E
I
PUB,
tI-
400
I
__-;_-- _---./
_______*5i-‘--.
01
0
__-.-z_
I
I
100
200
Temperature
_ -2:
-2:
-I
300
(K)
Fig. 3. Inverse of the molar susceptibilities versus temperature for PUB,, solid line: MCW fit; dashed line: calculated curve, F-RS model; dash-dotted line: calculated curve, F-IC model.
3.2.PUB, PUB, is found to be a weak paramagnet. The inverse susceptibility, measured in 0.82 T, is plotted in fig. 3 versus temperature. The apparent anomaly observed around 77 K is an artifact due to the weakness of the signal. The data may be fitted by (l), leading to pLe*fr = 0.32~~ and 0, = - 30 K. Renormalization leads to Peff
=
O-75!-%
3.3. Crystal field calculations
Np, _ x Pu, B,
take the same 4 + valency for the plutonium ions. In a true ionic model, the neutrality of charges would lead to a 2 - valency for the boron ions. However, as remarked in ref. [4], the anions are more likely B’ - and the two extra electrons per formula unit must contribute a uniform negative charge along the metal layers. The B,"coefficients can be calculated using the computer program developed by Amoretti in the frame of either a purely ionic model extended to the whole lattice (LS) surrounding the metal ion [7] or of a so-called “layer” (F) model [8]. In the latter case, the most important contribution to the CF is considered as due to the ions in the layers next to the metallic one plus the metal ions and the conduction electrons in the metal layer. The relativistic values of (r”) given in ref. [9] have been used .for the metal ions. For Np4+, we take a Sternheimer shielding factor a, = 0.88, as suggested in ref. [lo], while a4 and a, are neglected as they are already very close to zero for U3+ and U4+ [ll]. In absence of any calculation for Pu4+, we assume the same shielding factors as for Np4+. In the Russell-Saunders (RS) coupling scheme, the ground multiplets are 4I9,2 (5f 3 configuration) and ‘I, (5f4 configuration) for Np4+ and Pu4+, respectively. In the intermediate coupling (IC) scheme, the corresponding J values are still good quantum numbers and we take for the Stevens factors (Y, j? and y the values calculated in ref. [12]. At last, in this scheme, the crystal-field parameters (CFP) for n = 2, 4 and 6 have to be multiplied by factors given in ref. [12] too.
The crystal-field (CF) Hamiltonian for the Dhh hexagonal symmetry is, in the point-charge model (PCM):
(2) where the B," are the CF-parameters and the &” the Stevens operator equivalents. In the present calculation, we shall restrict ourselves to the terminal compositions of the solid-solutions, i.e. to NpB, and PUB, which are representative of the results given by the PCM in this class of compounds. We assume a 4 + valency for the neptunium ion and, owing to the close crystallographic and chemical similarity between NpB, and PUB,, we
Table 1 Crystal field parameters (cm-‘) for the Np and Pu diborides. Reference frame rotated 7r/4 around c with respect to the a-axis, Stemheimer coefficient o, included
B20
840
B,oX104
NpB, (F-RS) NPB, (F-IC) NpBl (LS-IC)
- 18.33 - 12.47 - 11.71
0.1413 0.1018 0.2177
0.1720 0.1152 6.740
PUB, (F-RS) PUB, (F-IC) PUB, (LS-IC)
19.83 23.40 14.67
- 0.1685 - 0.1904 - 0.2961
- 0.1310 -0.1113 - 6.989
B,6x102 - 1.452 - 0.9727 - 1.672 1.799 1.529 1.779
135
R. Chipaux et al. / Properties of the pseudo-binaries Np, _ x Pu, B,
The final CFP have been computed in the RS and IC schemes for the LS and F models and only the most significant results are listed in table 1. To obtain the energy levels and eigenfunctions we must use these values and diagonalize the energy matrix in formula (2). In NpB,, the CF effect is to split the ten-fold degeneracy of the ground term for the neptunium ion into five Kramers doublets. The position of these five energy levels is given in table 2. The main difference between the LS and the F models is the presence in the latter of a level at about 70 K which should rise to a Schottky anomaly in the heat capacity if we were not in the ordered state. In hexagonal symmetry, the hexagonal CFP couple the matrix elements with AM = 6. The new ground eigenstate is of the type: ]‘k)=cr*]+:)+p*]G)
(3)
and the ordered moments values along the two axis x and z are reported in table 2 too. It is clear that, along z, the ordered moment values do not correspond to the experimental result of ref. [4], whereas along x the calculated values are in better agreement with the experiment. In PUB,, the CF splits the nine-fold degenerate ground multiplet into three singlets and three doublets. The position of these six energy levels with their multiplicity is given in table 3. The new ground state is a singlet (built from the axial CFP on the ) 0) matrix element) and thus bears no magnetic moment in agreement with the experiment. The next excited state is a doublet located around 250 K. There is hardly any difference in
Table 2 CF energy level (in K) and ordered moment (in pa) of the ground state in the PCM for NpB,
Energy levels
pz pLx
F-RS
F-IC
LS-RS
LS-IC
0 67 601 1244 1652
0 12 411 862 1150
0 590 731 1284 1700
0 404 538 898 1197
2.41 0.51
2.55 0.53
2.35 0.60
2.49 0.62
Table 3 CF energy level (in K) and multiplicity of the levels in PCM for PUB, Multiplicity
F-RS
F-IC
LS-IC
Multiplicity
1 2 2 1 1 2
0 216 159 1272 1402 1431
0 248 877 1494 1605 1683
0 261 926 1100 1498 1627
1 2 2 2 1 1
the
the level scheme between the LS and the F models, except for the multiplicity of the two highest levels. In the paramagnetic region, the knowledge of the energy levels allows to calculate the Van Vleck susceptibilities xZW and xX&, in the z and x direction, respectively, for both diborides. Assuming, in a first approximation, that the average calculated powder susceptibility is: XV” = :x=w + :xX&, we have plotted in figs. 2 and 3 the temperature variation of l/Xvv compared with the experimental data for NpB, and PUB,, respectively. It is clear that neither the slopes nor the absolute values of the calculated results agree with the experiments. - For the neptunium diboride, the RS calculation seems in better agreement because of the greater CF-splitting. But, if we take into account the exchange interaction by the corresponding translation of the Van Vleck curve, we find nearly an order of magnitude difference between calculated and observed susceptibilities at 300 K. This could be due in part to the core diamagnetism of the compound but essentially, this proves that the localized ionic model is unable to explain the overall results. _ For the plutonium diboride, the experimental curve can be decomposed in two parts. Below 100 K, the low temperature tail could be due to a paramagnetic impurity, whereas above 100 K, the temperature variation bears a similarity with that of the calculated curve in the IC. Again, however, the difference in magnitude between the two curves excludes an interpretation by diamagnetic contri-
R. Chipaux et al. / Properties of the pseudo-binaries Np, _ x Pu, B,
136
bution, and the PCM is no more adequate in that circumstance too. For this compound, there is no difference as regards the calculated susceptibility between the F and LS models. The quadrupolar interaction can readily be estimated by our PCM in the paramagnetic state of NpB,. The value of e2qQ reported in ref. [4] is 92.8 mm s-t, as observed at T = 110 K. This corresponds to an electric field gradient (EFG): ( eq 1 = 45 x 10” V cm-2, with a quasi-axial symmetry along the c-axis. The EFG in the paramagnetic state can be written as the sum of three terms:
+eq1’(1-
&)
1
(41
z being the CF-symmetry axis of the single paramagnetic ion. The first term in (4) represents the contribution of the lattice, the second term the contribution of the conduction electrons with non-s character and the third term the contribution of the 5f electronic cloud. Each term is multiplied by the corresponding screening coefficient. According to ref. [13], we have: - 4Bz” eqk = ___ ecx(r2) ’ eqlf =
-e4r-3>(QZ)Ty
(5)
where (Y is the Stevens factor for n = 2, (QZ)r is the thermal average of the operator (3t - j2) on the CF-states and Bi the CFP of order 2. The average values (r’) and (r-‘) are given in ref. [9]. All calculations done, one finds the following orders of magnitude: 1.5 X 10” V cmm2 for the 5f contribution, 250 X 10” V cmp2 for the lattice contribution (taking the Bt of table 1 before multiplication by ~~2). This result tends to demonstrate the importance of the lattice contribution, as evidenced in ref. [4]. But it also emphasizes the need of a high conduction electron contribution acting as a reduction factor [14] to yield the experimental EFG. This would suggest the interest of electrical resistivity measurements, especially of the anisotropy in the transport properties for single crystals, in
order to check the previously model.
assumed “layer”
4. Solid-solutions 4.1. Results The inverse molar susceptibilities, measured in a magnetic field of 0.82 T, are plotted in fig. 4 versus temperature. All the data may be fitted by a modified Curie-Weiss law. The fitted parameters, as well as the parameters renormalized following [6] are reported in table 4. We show in the next paragraph how these parameters can be related to each type of magnetic ion. The paramagnetic Curie temperature f$ is almost constant for x I 0.2. At higher plutonium concentration, it decreases slowly, approximately linearly, to reach zero for x = 0.83, and is negative in PUB,. At low temperatures, the ferromagnetic order is maintained for x I 0.5. The plots of versus T/l&, shown in fig. 5, indicate (+%+0)2 that the transition temperature T, decreases faster than 6, for x 2 0.3. No transition is observed in NPo.33PU 0,67B2, although 19, equals 21 K in this compound. In the same range of concentration
1600
-0
100
Temperature
300
200
(K)
Fig. 4. Inverse of the molar susceptibilities versus temperature for Np,_,F’u,B,. (a) x =O; (b) x = 0.1; (c) x =0.3; (d) x = 0.5; (e) x = 0.67; (f) x = 0.83; (g) x = 1. The solid lines represent the MCW fits.
137
R. Chipaux et al. / Properties of the pseudo-binaries Np, _ x Pu,B, Table 4 Fitting parameters Experimental X
of the magnetic
susceptibilities
parameters * ;lb
for Np, _,Pu,B,
C* (emu K/mol)
emu/mol)
&)
Peff
T,
(na)
(K)
0.00 0.10
878(49) 1222(37)
0.214 0.166
103.4(0.5) 102.3(0.5)
1.31(0.02) l.X(O.02)
103(2) 105(l)
0.30 0.50 0.67 0.83 1.00
1171(35) 1061(46) 730(19) 720(13) 576(11)
0.108 0.082 0.075 0.037 0.013
80.6(0.6) 60.2(1.5) 20.6(1.0) 0.6(1.6) - 29.7(7.3)
0.93(0.02) 0.81(0.02) 0.77(0.01) 0.55(0.01) 0.32(0.01)
77(l) 36(4)
renormalized X
parameters
0.00 0.10 0.30 0.50 0.67 0.83 1.00
x0 (10m6 emu/mol)
kff
hn
(pa)
(mol/emu)
504 303 149 236 584 712 1323
0.75 0.29 0.12 0.18 0.62 0.54 0.75
846 2480 5860 3300 344 15 -982
(0.3 I x I 0.67) and for T, < T < 19, the magnetization versus field curves are not linear but do not show spontaneous magnetization except for the small one of the aforesaid impurity. This can be due to magnetic relaxation phenomena, as also observed in the Mijssbauer spectroscopy experiments [3,4]. The ordered magnetic moments are reported in table 5. Contrary to the Mossbauer experiments, which give the local ordered magnetic moment p,,, the magnetization measurements, on powder samples, lead to a bulk moment /.L,,~~,, averaged over all crystallite orientations present in the sample. In anisotropic compounds like these diborides, ppowd can be notably inferior to pFlo.On the con-
Table 5 Ordered magnetic moments field) for Np, _XPu,B, x
CO
0.0 0.1 0.3 0.5
f&w/d
(PB)
(Mossbauer 0.57(l) 0.59(l) 0.57(l) 0.42(3)
at 4.2 K (extrapolated
[3,4])
(PB)
(Magnetization) not measured 0.56 0.53 0.16
at zero
trary, the closeness of the values observed in the x = 0.1 and 0.3 compounds suggests that mechanical reorientations of the crystallites by the magnetic field may occur during measurements in ferromagnetic regions. 4.2. Extension of the Curie- Weiss model and application to Np, _ x Pu, B, As shown in the appendix, in compounds containing two types of magnetic ions, the assumption of a Curie-Weiss behavior for the local magnetic susceptibilities (eq. (A.l)) leads strictly speaking to a global magnetic susceptibility law related, but different, to the modified Curie-Weiss law (MCW) (eq. (A.8)). However, in solid solutions, we can assume eqs. (A.14). The MCW is therefore recovered, but all the physical parameters can not be calculated from the experimental data (eqs. (A.15) to (A.17)). Nevertheless, the crystallographical and in Np,_,Pu,B,, Mossbauer spectroscopy results lead to a weak or null dependence of the physical quantities with x: small variation of the lattice distances and electric field gradient, constancy of the isomer shift and of the ordered magnetic moment. Thus, in a first
R. Chipaux et al. / Properties of the pseudo-binaries
138
0.8 N -
0 0.6
< b V
N -
0.4
0 0.6
< b V
0.4
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Np, _ x Pu, B,
$&?,2(1 -x) ( averaged smallest distance in volume, a and c being the lattice parameters) for the small neptunium concentrations, and to u//m (averaged smallest distance in the basal plane) for the high ones. The smallest quantity should be chosen. The same formula apply for the plutonium ions, changing (1 - x) into x.) The main results are, for the neptunium a pronounced maximum at d,,_,, = 0.37 nm, and for the plutonium an inversion of the sign of the magnetic interactions: antiferromagnetic below 0.35 nm and ferromagnetic above, with a maximum between 0.4 and 0.5 nm. It is interesting to compare these results with the general magnetic data for neptunium or plutonium compounds, summarized classically on the so-called Hill plot, [15]. As shown on fig. 7, the magnetic transition temperatures in neptunium compounds reach a maximum for d,,_ ,,+, - 0.36 nm, and in plutonium compounds, two separate domains can be distinguished: antiferromagnetism for dPu_Pu I 0.35 nm, and ferromagnetism for dPu_Pu > 0.35 nm. (Compounds containing magnetic ligands (e.g. iron, cobalt, nickel, . . . ) are obviously not included in this comparison.) Although our results on Np,_,Pu,B, apply only to a rough average of the magnetic interac-
5% Fig. 5. (a/~~_~)
’ vs. T/l?, curves for Np, _,P,B,.
11
5000
approximation, the magnetic parameters xONp, C, can be considered as constants, XOP”, Gl,, and be determined from the measurements on the pure binary compounds. Only X,, and X,, are concentration dependent, and their evolution with x is representative of the variation of the magnetic interactions with the concentration or, on another point of view, with the average of the interactinides smallest distances. The molecular field constants X,, and h,, are calculated as a function of x using eq. (A.20) and eq. (A.18) or (A.19), which are now redundant. The results are similar, as reported in table 6. Fig. 6 represents the variation of the calculated molecular field constants with the averaged smallest distance between the corresponding actinide. (For the neptunium ions, this distance is equal to
11
I(
I
I
I
:"b
4000 -
:
o NP
1 1
d 5
2
t 1000
t
-
c; ,
0
-.
\\
I
‘;,-;:;:zq
, b-c___,
,,‘o 1’
-lOOO-
-2000
d'
I’ 0.3
*
’
0.4
’
’
0.5
’
’
0.6
’
I
0.7
dAAn+,(nm) Fig. 6. Molecular field constants A,, averaged distances in Np, _,Pu,B,. guidelines.
and A,, vs. intermetallic The dashed lines are
R. Chipaux et al. / Properties of the pseudo-binaries
Table 6 Molecularfield constants X
0.00 0.10 0.30
x
x
NP
NP
d NP-NP (nm)
A
(mol/ emu)
(1)
(2)
(mol/ emu)
(1)
(2)
846 2240 4150
846 2290 4600
0.3162 0.3336 0.3788
0 238 1710
0 189 1250
cc 0.7009 0.4863
1900
0.4104
1600
1390
0.4104
128
122
0.4717
261
222
0.3883
0.83
16
21
0.5887
-1
-6
0.3493
0
(1) Calculated (2) calculated
0
CC
- 982
compounds,
with the general magnetic
their
data is re-
markable.
5. Conclusion
0.67
1.00
139
x Pu, B,
in these pseudo-binary
coherence
d Pu-P” (nm)
APIA
PU
(mol/ emu)
(mol/ emu)
0.50 1690
tions
for Np and Pu in Np, _XPu,B,
Np,
-982
Measurements of the magnetic properties of are in good agreement with several Np,_,Pu,B2 Mijssbauer spectroscopy results.
A tentative
0.3187
interpretation
of
these measure-
ments, within a crystal field model
of localized
ions shows that this hypothesis is inadequate to explain the paramagnetic susceptibility. However,
from x0 and A,; from C, and A,.
600
I
I I 8
I
a
:.-An
Intermclrlllcs b c d c f g h i j k I
:
:
AnNi, : AnCo, AnFc, : AnMn, : Anlr, : AnAl, :AnRh, AnAI, :AnSn, : AnPt : AI&,,
:
:
Carbides : m : AK n : An&, Doridcs :
I
600
‘.
I
o p q r
I
I
I
I
: : : :
An& AnD, AnB. AnD,,
Pnictides : I 2 3 4 5
: : : :
:
AnN AnP AnAs AnSb AnDi
Cbnlcogenida 6 I 8 9
:
: AnS :AnSe : AnTc : AnO,
(An = Np, Pu)
#
I
I
I
I
0.3
0.4
0.5
0.6
oLAn
W 0 A
: fewmagnetic
(nm)
Fig. 7. Hill plot for neptunium
and plutonium
trmnsttien transition
: dtr~tdb89gnctk : “0 transition
compounds.
140
R. Chipaux et al. / Properties of the pseudo-binaries Np, _ x Pu, B,
it gives the correct value of the magnetic moment of the ground state. Thus, the Sf electrons are probably not well localized in the diborides (UB, is in fact a weak Pauli paramagnet). In this context, heat capacity and electrical resistivity results on NpB, and PUB, would be most interesting, these compounds being candidates for heavyfermion behavior. An extension of the Curie-Weiss model for di-magnetic solid-solutions is proposed, which implies as a consequence that the molecular field constant - i.e. the exchange interaction - is
Appendix. Extension of the Curie-Weiss
strongly dependent upon the average smallest distance between the corresponding actinides atoms. The results are in good agreement with the socalled Hill plot.
Acknowledgements We are grateful to G. Amoretti for the use of his computer programs. We are also indebted to J. Chiapusio for encapsulation and decontamination of the a-radioactive samples.
model: calculations
In some compounds, particularly in actinide systems, system, or local susceptibility, should be written as:
the magnetic
susceptibility
of the non-interacting
(A.1)
xp = xo + C/T,
where C is the Curie-Weiss constant, equal to &/8 in molar units, and x0 a constant term due for instance to Van Vleck or Pauli contributions. In that case, assuming the molecular field approximation with a molecular field constant A, the macroscopic magnetic susceptibility follows the modified x0, C and A are Curie-Weiss law (MCW) (eq. (l)), and, as shown in ref. [6], the physical parameters connected to the experimental parameters by the following relations: xo=xo*(C*-~~xo*)/C*~
(A.2)
c=
(A.3)
(C” -e&,*)*/c*,
x = e&c*
- e,x,*).
(A.4)
In systems containing two different types of magnetic ions (a and b in the following equations), this molecular field treatment should be extended to take the crossed magnetic interactions into account. The effective field is written on each type of ion as a sum of the external field Hext, and of the contribution of the magnetization of each type of ion: Kffa
Assuming M=
=
Hext
+
X,,K
+
Kffh
h,bMb,
a molar proportion
=
Kx,
+
hb,Ma
+
(A.51
XbbMb.
(1 - x, x), for a and b, respectively,
the total magnetization
(1 -x)M,+xM,.
(A.6)
If the local susceptibility
follows in both types the expression
Xpa = Xoa + C,/T, the global magnetic
Xpb
=
susceptibility
C,* +
is:
C:/T
x=xo*+ T-l$,+8,,/T’
XOb
+
cb/T,
(A.l),
which reads: (A.7)
takes the form:
(‘4.8)
141
R. Chipnux et al. / Properties of the pseudo-binaries Np, _ x Pu,B,
with: (1 -x)x&$
- (A,, - L&)Xllb)
x0* =
c;
(1 - &J&)(1
=
((I
-
x)[ca(l
+x[Cb(l
-
xl/[(l
c:
=
-
-
[(l
-
=
x..ca
+
xbbcb
(I
-
=
(l
-
-
xaa)
+
xaaxOa)(l -
XaaXOa)(l
-
(l
-
+
-
haaXOa)(Xba
-
(A.91 ’
+
CbXabXOa(l
CaXbaXOb(l
-
-
(hbb
(‘aa -
-
XbZhO~)~
hba)xOb)l
-
-
-
‘bb))
‘a,))]
(A.ll)
XbaXabXOaXOb]2~ +
CbXOa)
(A.12) ’
XbaXabXOaXOb
xabxba)cacb
XbbXOb)
>
(A.10)
XbbXOb)(Xab
habhba)(CaXOb
XbbXOb)
- &-JX0a)
XbaXabXOaXOb]2,
XbbXOb)
-
-
(l
AbbXOb)
&,XOa)
-
+
-
&aXbb
xaaxOa)(l (‘hdbb
“I
hbbxOb)
- (L
hbaXabXOaXOb
-
-
hb)
-
-
&,b)XOb)(l
hba)XOa)(l
-
X)(XabXOa(hba
xcacb/[(l
PO
-
XaaXOa)(l
+X(hbaXOb(hab
6
- hbbX~b) +
(‘bb
(xaa
+ XXI&
(A.13)
-
‘baXabXOaXOb~
The eight physical parameters (xOa, xOb, C,, Cb, h,,, Aat,, Xba, X,,) cannot be entirely determined from the five experimental parameters (x$, C,,*, CT, op,,, et,,). Moreover, this model is formally exact but inapplicable in this form owing to the large number of parameters and to the weak specificity of eq. (A.8). Nevertheless, in solid solutions such as Np, _XP~XB2, where the two types of ions are very close in terms of size and physico-chemical behavior, we can assume that the molecular field seen on one site does not strictly depend on the type of the considered ion. This implies: (A.14)
Xab=Xbb.
&=&a, Thus the terms parameters:
tipI become
CT and
equal
to 0, and
the MCW
is recovered,
(l - x)xO~+ XxOb ‘O*
=
1
-
(l
c,* =
XuoXOa
-
-
x)Ca
+
’
+
(CbXOa
(1 caxaa epo =
1-
+
‘a&Oa
-
XbbXOb
c=
1 +
(CbXOa
x)xbb
-
xhaa)
(A.16)
1
xbbxOb)2
we can extract
-
CaXOb)[(l
-
X)XOa
+
xxOb
x)xbb
-
Xhaa]/[(l
the global physical
parameters: (A.I~)
-x)Ca
+
xcb]
’
(1 -x)c,+xc,
1+
(CbXOa
CaAaa x=
-
-
(A.17)
(l=
CaXOb)((l
.
Using eqs. (A.2), (A.3) and (A.4)
X0
-
cbxbb
XaaXOa
(1
+
-x)c,+xc,’
cbxbb
the experimental
(A.15)
XbbXOb
xcb
with
caxOb)[(l
-
x)xbb
-
(A.19) xhaa]/[(l
-x)Ca
+
xcb]
’
(A.20)
142
R. Chipaux et al. / Properties of
thepseudo-binaries
References [l] N.N. Greenwood, The Chemistry of Boron (Pergamon Press, Oxford, 1973) p. 697. [2] J.L. Smith and H.H. Hill, AIP Conf. Proc. 24 (1975) 382. [3] R. Chipaux, Thesis, UniversitC d’Aix-Marseille II, France (1987). [4] R. Chipaux, D. Bormisseau, M. Bog& and J. Larroque, J. Magn. Magn. Mat. 74 (1988) 67. [5] R. Chipaw, J. Larroque and M. Beauty, J. Less-Common Met. 153 (1989) 1. [6] G. Amoretti and J.M. Foumier, J. Magn. Magn. Mat. 43 (1984) L217. [7] G. Amoretti, A. Blaise, J.M. Collard, R.O.A. Hall, M.J. Mortimer and R. Trot. J. Magn. Magn. Mat. 46 (1984) 57. [S] G. Amoretti, A. Blaise, M. Bonnet, J.X. Boucherle, A.
[9] (lo] [ll] [12] [13]
[14] 1151
Np, _ x Pu, B,
Delapalme, J.M. Fournier and F. Vigneron, J. de Phys. C7 (1982) 293. J.P. Desclaux and A.J. Freeman, J. Magn. Magn. Mat. 8 (1978) 119. D. Sengupta and J.O. Artman, Phys. Rev. B 1 (1970) 2986. P. Erdiis and H.A. Razafimandimby, J. de Phys. 40 (1979) c4-171. G. Amoretti, J. de Phys. 45 (1984) 1067. S. Ofer, I. Nowik and S.G. Cohen, in: Chemical Applications of Mossbauer Spectroscopy, eds. V.I. Goldanskii and R.H. Herbes (Academic Press, New York, 1968) p. 426. R.S. Raghavan, E.N. Kaufmann and P. Raghavan, Phys. Rev. Lett. 34 (1975) 1280. H.H. Hill, in: Plutonium 1970 and other Actinides, ed. W.N. Miner (Metal Sot., AIME, New York, 1974) p. 52.