Vibrational and magnetic properties of β-UD3

Journal of the Less-Common

267

Metals, 158 ( 1990) 267-274

VIBRATIONAL AND MAGNETIC PROPERTIES OF /?-UD3 A. C. LAWSON, A. WILLIAMS

A. SEVERING*,

Los Alamos National Laboratoq (Received

June

J. W. WARD,

C. E. OLSEN,

J. A. GOLDSTONE

and the late

Los Alamos, NM 87545 (U.S.A.)

17,1989)

Summary A neutron diffraction study of P-UD, has verified the previously reported ferromagnetic structure. The magnetic moments of the two crystallographically distinct uranium atoms are nearly identical at 1.5 ,~a. The cubic lattice constant has a minimum at the Curie point. The Debye temperature for the uranium atoms of 19= 238 K was obtained from a measurement of the Debye-Waller factors.

1. Introduction p-UD, crystallizes in a cubic structure with eight formula units per cell. As shown in Fig. 1, the metal atoms form a structure that is isomorphous with the Cr,Si-type structure. There are two types of uranium atom: U( 1) is analogous to silicon, and U(2) is analogous to chromium. In addition, there is a single type of deuterium atom that has no analog in the Cr,Si structure [ 13. The crystallization of an actinide compound in a structure usually characteristic of transiton metal intermetallics is not unique: PaD, -y has nearly the same structure, a-UD, has a different structure that is also related to Cr,Si, and PaD, +x has a structure that is related to the MgCu,-type structure [ 21. p-UD, was the first known actinide ferromagnet [4-61. The principal magnetic properties, which have been confirmed by many investigators, are a Curie temperature of 170 K and a paramagnetic moment of 2.26 ,uB [7-91. The magnetic properties of j3-UD, have previously been investigated by neutron diffraction on two different occasions [lo-l 11. In both cases it was found that the magnetic moments on the two inequivalent sites are the same within experimental error. The magnetic equivalence of the two uranium atoms is surprising in view of their very different crystalline environments. The U( 1) atoms have point symmetry rn3 with 12 U(2) near neighbors of distance 3.72 A and eight more distant U( 1) neighbors of distance 5.76 A. The U(2) atoms have point symmetry 4m2 with two U( 2) neighbors at 3.33 A, four U( 1) neighbors at 3.72 A and eight more distant U( 2) neighbors at 4.07 A. An empirical correlation proposed by Hill [ 121 suggests *Present

address:

0022-5088/90/$3.50

Institute

Laue-Langevin,

38042

Grenoble, 0 Elsevier

France. Sequoia/Printed

in The Netherlands

268

Fig. 1. Crystal structure of j3-UDI. Large dark circles represent U( 1) atoms at (0, 0 0) and (l/2, l/2, l/2). Smaller gray circles represent U(2) atoms at (l/4, 0, l/2) and symmetry-related positions. The small light circles represent deuterium atoms at (0,0.156,0.303) and symmetry-related positions. The square indicates the cubic unit cell that contains a total of 24 atoms.

that actinide materials with short bond lengths should be non-magnetic (and even superconducting), while those with longer bond lengths should exhibit magnetic order at low temperatures. The division between the two regimes occurs at a bond length of approximately 3.5( 1) A. The observed magnetic ordering of /CUD3 violates the Hill criterion, as the observed U( 1)-U( 2) and U( 2)-U( 2) distances are shorter than 3.5 A. If it were legitimate to apply the Hill criterion to the U( 1) and U( 2) atoms separately as was done in ref. 9, then magnetic order would be predicted for the U( 1) atoms alone. This prediction disagreed with the available neutron diffraction data [lo], and the present investigation was undertaken to resolve the dilemma. In the meantime, the diffraction study of Bartscher et al. [ 1 l] has verified that the magnetic moments of U( 1) and U( 2) are the same, and the magnetic results from the present experiments agree very closely with those reported previously. These now seem to be established beyond doubt, so that the discrepancy with the Hill criterion and with band-structure calculations [ 131 remains. We have also obtained information on the vibrational properties of p-UD, via diffraction measurements of the Debye-Waller factor. Presentation of this information is the principal contribution of this paper. The available information on the vibrational properties of /3-UD3 comes from heat capacity data [9, 14-151. At 350 K, the heat capacity [ 141 is not even close to saturation at the Dulong-Petit value of 12 R per mole that would be expected for complete equipartition. In the first attempt to determine the Debye temperature (0,) from low-temperature heat capacity data [ 151, a satisfactory analysis could not be made. A latter attempt was successful [9], and the value 8, = 338 K was reported.

269

2. Experimental procedure A 30 g sample of UD, was prepared in a Pyrex reaction vessel by slow reaction at 150 “C, starting with a billet of high-purity depleted uranium. The resultant finely divided powder was held at temperature under an overpressure of 1 bar for 48 h to ensure stoichiometry, then stored at room temperature under deuterium pressure. Time-of-flight neutron powder diffraction data were taken on a prototype of the high intensity powder diffractometer (HIPD) at the Manuel Lujan, Jr., Neutron Scattering Center (LANSCE) [16]. At the time of the measurement, the diffractometer constant for the 153” detector bank of this inst~ment was 3598.8 ys A~-‘. Powder diffraction measurements were made at five temperatures. Data collected in the 153”, 90” and 40” detector banks were analyzed using the Rietveld refinement codes in the generalized structure analysis system (GSAS) developed by Larson and Von Dreele [ 171. In order to separate nuclear and magnetic scattering, the d dependence of the magnetic form factor f( d) was exploited. f(d) decreases with decreasing d spacings, so that the high-angle detector banks (153” and 90”) that coliect data only at low d spacings are insensitive to magnetic scattering. The refinement of the high-angle data yields a description of the coherent nuclear scattering that contains all the structural parameters (lattice constants, atomic positions, anisotropic thermal parameters) resulting from the fit. The magnetic intensities are determined from the 40” detector banks by subtracting the calculated coherent nuclear intensities from the experimental data. A background refinement takes care of the incoherent nuclear and magnetic scattering, so that the difference between the observed and calculated (nuclear) diffraction patterns for this bank are due to coherent magnetic scattering. The method works because the magnetic and nuclear scattering of unpolarized neutrons are incoherent with respect to each other.

3. Results and discussion Some high-resolution di~action patterns are shown in Figs. 2 and 3. The quality of the refinements is good: the weighted profile agreement factors are about 5%. We were able to determine the lattice constants, atomic positions and anisotropic thermal displacements with high precision, and the refined values for these quantities are given in Tables 1 and 2. In the low-temperature data from the 40“ detector bank, which is shown in the lower panel of Fig. 3, there are obvious discrepancies in the fits for the 2 10 and 211 reflections, and to a lesser extent for the 200 reflection. These result from coherent magnetic scattering, which adds extra intensity to the nuclear Bragg peaks in the ferromagnetically ordered state that is not included in the Rietveld model. A slight error in the assumed peak shape gives rise to some error in the fit below d= 2 A. However, this error appears at all temperatures and is not indicative of magnetic order. The magnetic intensity of the (110) reflection, while barely

270

I

E

!

“‘4

28=153" T=307K

I+ '41 I!,

U”,

2e=40 T=307K

.' -

1,: *,

I

_

i

T=14K

_ __

tI

0.4

I

0.6

I

I

0.6

(

1.0

d-SPACING

I

I

1.2

I

I

1.4

11

____

~..______.---._..__~,

I

2.0

3.0

4.0

d-SPACING

(ii)

_

5.0

6.0

(ii)

Fig. 2. High-resolution time-of-flight neutron diffraction patterns of ,8-UDX at 307 and 14 K. The scattering angle is 153”. Crosses represent the measured data, the full line is the Bietveld fit, and the lower curve is the residual of the fit. The vertical tick marks indicate the possible d spacings for Bragg reflections. The intensity has been normalized by the measured incident spectrum, and the scale of the intensity axis is arbitrary. Fig. 3. High d-spacing diffraction patterns for p-UDI at 307 and 14 K. The scattering angle is 40”. Other details are the same as Fig. 2. As explained in the text, the magnetic scattering appears in the residual of the fit.

TABLE 1 UD, atomic positions in space group Pm3n Atom

X

Y

Z

Fractional occupancy

U(1)

0

0

0

U(2) D

114 0

0 0.15595(2)

l/2 0.30344(6)

1.026(S) 1.007(5) 1

observable in the plotted pattern, is zero within experimental error. No extra magnetic peaks that would indicate antiferromagnetism were observed. In agreement with previous reports, these observations show that UD, is a simple ferromagnet with a moment of 1.54( 7) ,+$ on both the U( 1) and U( 2) sites. The value for the moment comes from quantitative measurement of the magnetic intensities of the 200, 210 and 2 11 reflections. The equality of the moments follows from the vanishingly small 110 magnetic intensity. For cubic materials, it is

271

TABLE 2 UD, mean-square thermal displacements ui/ (A2) and Lattice Constant a (A) Temperature 307

(K) 185

160

150

14

U(1) = u,,).= uz;

3.1(2)

1.8(2)

1.4(2)

1.3(2)

0.4( 2)

1.3(3) 0.9(2)

0.5( 3) 0.0(2)

0.2( 3) -0.4(2)

O.O(3) - 0.6(2)

-0.8(3) - 1.6(2)

15.3(3) 8.9( 3) 11.9(3) - 1.2(2)

13.0(2) 8.7( 2) 10.7(2) - 1.0(2)

12.5(3) 8.8( 3) 10.3(3) -1.0(Z)

12.5( 3) 8.7( 3) 10.7( 3) - 1.0(2)

12.1(2) 8.7( 2) 10.7(2) - 1.2(2)

U (i.7 uxx u,., = uzz D u*x u.vy u:: u.v; a

6.6350(2)

6.6254(2)

6.6243(2)

6.6243(2)

6.6269(2)

not possible to determine the direction of the magnetic moments from powder diffraction data. Figure 4 shows the lattice constant of UD, plotted vs. temperature. These data show a pronounced minimum - but no discontinuity - at the Curie temperature. The precision of the lattice constants obtained with time-of-flight neutron diffraction is high enough to establish the general behavior even though only five temperatures are available. Figure 5 shows the mean-square atomic displacements (uiis) plotted vs. temperature. Altogether seven curves are shown, one for each of the independent components of the three unique atoms of UD,. In principle, the atomic displacements arise from thermal motion (temperature dependent) and from static displacements (temperature independent). The thermal displacements are finite even at T= 0,so that the static displacement may be regarded as an additional zeropoint motion. The components of these displacements are assumed to conform to the crystallographic point symmetry appropriate to each atom. However, it must be recognized that the values of the uiis are subject to considerable systematic experimental error. In particular, the numerical values that are actually obtained from the Rietveld method depend on the choice of background and peak shape functions that are used in the refinements. In addition, the uiis are highly correlated with absorption and extinction parameters. As a result, each of the ugs contains a systematic, temperature independent, error that behaves like a zero-point motion. This error term can be negative, so that an apparent unphysitally negative uii may result. However, this systematic error does not affect the temperature dependence of the uiis, so that the temperature dependence can be used for the inference of physical properties. Taking the simplest workable model, we can assume that each component of the displacement of each atom independently obeys the Debye-Waller formula

272

LATTICE CONSTANTS 6.636

I

I

UD3 I

I

I

I

MEAN-SQUARE

ATOMIC

DISPLACEMENT

UD3 6.634

~““““““““““““”

“““”

6.632

05

6.630

m 6.626

6.626

6.624

0’

100

200

TEMPERATURE

300

(K)

TEMPERATURE

(k)

Fig. 4. Lattice constants vs. temperature for /?-UDx, Fig. 5. Mean-square atomic displacements vs. temperature for p-UD3. The curves are fits to a Debye-Waller model modified by the addition of a constant offset.

TABLE 3 Debye temperatures

and offsets for UD, Observed oflrset

Thermal zero point

(1000 A)

(1000A)

Ratio

U(l) U($

=up=u,,

nxx un = uz,

238( 7)

-0.31(16)

0.65

- 0.48

258( 14) 228(7)

- 1.38(27) -2.30(17)

0.60 0.68

- 2.30 - 3.38

1493(28) 3651(583) 2118(91)

-0.21(40) 3.75(94) 1.94(53)

12.09 4.94 8.52

- 0.02 0.78 0.23

D uxx UYY

uz Average for Ds: 2421 K. Average for Us: 238 K.

[18] with an extra additive zero-point offset. Some justification for treating the atoms separately is provided by a modified Debye-Waller theory [ 191. The uij vs. temperature data were fit with a two-parameter formula to obtain the Debye temperature On, and the zero-point offset. The fitted values are given in Table 3. For the uranium atoms, the 6&s are isotropic: for U(l), this is required by crystal

213

symmetry, and isotropy is found experimentally (but not required) for U(2). The 8,,s for the uranium atoms are nearly the same, and the average is 238 K. The z+~(D) component is independent of temperature, and is taken as zero in consideration of the probable offset. Otherwise, the uVs for the deuterium atom are quite high, reflecting the large zero-point motion expected’for a light atom. The 8,, for the deuterium atom is highly anisotropic, and the average is 2400 K. The ratio of these temperatures, 10.1, is nearly the same as inverse square root of the ratio of the associated masses (238/2)“*= 10.9, in agreement with simple theory for an elastic continuum. Our value for uranium, f3,, is lower than the heat capacity value 8, = 338 K [9]. The discrepancy is the result of counting the deuterium atoms in the calculation of 0,. It is clear from the high temperature heat capacity data [14] that the optical vibrations of the deuterium atoms are not significantly excited at low temperatures. This means that the deuterium atoms should be regarded as part of the elastic continuum whose mechanical properties are dominated by uranium, rather than as independent entities. Accordingly, 8, should be reduced by a factor (4)“” = 1.59, so that the two measurements of the Debye temperature are in good agreement: 13, =338 K/1.59-213 K vs. en,= 238 K. The remaining discrepancy is probably not significant [20].

4. Conclusions In agreement with previous results, the magnetic moments on the two distinct uranium atoms of /?-UD3 are the sme, 1.5 ,u,. This result disagrees with expectations based on interatomic distances. The Rietveld profile refinement technique has been used to obtain precise values for the atomic Debye temperatures. At room temperature and below, B-UD3 behaves essentially as an elastic solid. However, a minimum in the lattice constant is observed at the Curie temperature.

Acknowledgments

This work was supported under the auspices of the United States Department of Energy. The Manuel Lujan, Jr., Neutron Scattering Center is a national user facility funded by the United States Department of Energy, Office of Basic Energy Sciences.

References 1 T. R. P. Gibb, Jr., Primary Solid Hydrides, in F. A. Cotton (ed.), Progress in Inorganic Chemistty, Vol. III, Interscience, New York, 1962, p. 388. 2 J. W. Ward, Properties and Comparative Trends in Actinide-Hydrogen Ssytems, in A. J. Freeman and C. Keller (eds.j, Handbook on the Physics and Chemistry of the Actinides, Vol. 3, Elsevier, Amsterdam, 1985, pp. 19-36.

274 3 W. Trzebiatowski, A. Sliwa and B. Stalinski, Rocz. Chem., 26 (1952) 110. 4 W. Trzebiatowski, A. Sliwa and B. Stalinski, Rocz. Chem., 28 (1954) 12. 5 W. Suski, Wlodzimierz Trzebiatowski: His Ltfe and Scientific Activity, in J. Rauluszkiewicz, H. Szymczak and H. K. Lachowicz (eds.), Physics of Magnetic Materials Jadwisin ‘84, Poland, Part 1,

World Scientific, Philadelphia, PA, 1988, p. 1. D. M. Gruen, J. Chem. Phys., 23 (1955) 1708. S. T. Lin and A. R. Kaufmann, Phys. Rev, 102 (1956) 640. W. H. Henry, Phys. Rev., 109(1958) 1976. J. W. Ward, L. E. Cox, J. L. Smith, G. R. Stewart and J. H. Wood, J. Phys. (Paris), C4 (1979) 15. 10 M. K. Wilkinson, C. G. Shull and R. E. Rundle, Phys. Rev., 99( 1955) 627. 11 W. Bartscher, A. Boeuf, R. Caciuffo, J. M. Fournier, W. F. Kuhs, J. Rebizant and F. Rustichelli, 6 7 8 9

SolidState Commun.,

53(1985)

423.

12 H. H. Hill, The Early “Actinides”: the Periodic System Sfelectron Transition Metal Series, in W. N. Miner (ed.), Plutonium and OtherActinides, 1970, Nucl. Met. Series, AIME, 17, 1970, p. 2. 13 A. C. Switendick, J. Less-Common Met., 88( 1982) 257. 14 B. M. Abraham and H. E. Flotow, J. Am. Chem. Sot., 77(1955) 1446. 15 H. E. Flotow and D. W. Osborne, Phys. Rev., I64 (1967) 755. 16 R. N. Silver, Physica B, 137 (1986) 359. 17 A. C. Larson and R. B. Van Dreele, Generalized Structure Analysis System, LAUR 86-748, Los Alamos National Laboratory, Los Alamos, NM, 1986. 18 B. T. M. Willis and A. W. Pryor, Thermal Vibrations in Crystallography, Cambridge University Press, Cambridge, 1975, p. 125. 19 R. D. Horning and J.-L. Staudemnann, Acta Crystallogr. Sect. A, 44 (1988) 136. 20 M. Born and K. Huang (Huang Kun), Dynamical Theory of Crystal Lattices, Oxford University Press, Oxford, 1954, pp. 6 l-66.