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The crystal structure of UMn2
Journal
of the Less-Common Metals, 90 (1983) LB-L16
L13
Letter The crystal structure of UMn, A. C. LAWSON * Los Alamos National Laboratory, University of California, Los Alamos, NM 87545(U.S.A.) (Received December 2,1982)
Recently Marpoe and Lander [l] have investigated the crystal structure of the Cl5 compound UMn, at low temperatures. They found that this compound undergoes a large crystallographic distortion at 112 K and described this distortion in terms of a monoclinic unit cell. By making a specific assumption about the atomic parameters within this unit cell, fair agreement with a limited set of intensity data was obtained and a set of three distinct U-U nearest-neighbor distances was derived. A re-analysis of their data shows that at low temperatures UMn, has a more symmetric orthorhombic structure which is characterized by a single non-magnetic U-U nearest-neighbor distance. At room temperature UMn, has an f.c.c. lattice with the cubic lattice constant a, = 7.16s A. At 5 K, the peak positions can be indexed with a monoclinic unit cell with the monoclinic lattice constants a, = c, = 7.125 A, b, = 7.180 A and /I = 94.85”. For intensity calculations, Marpoe and Lander assumed that the only atomic motions were those of uranium atoms along one of the face diagonals so that “a pair of uranium atoms at (4,&i) and ( -4, -& -i) have new coordinates (i-&$,A-@ and@-4, -&, S-4)“. Suchanassumptionrequiresa twofold axis parallel to the [loll,,, direction which is inconsistent with the assumed cell for which the twofold axis is presumably parallel to the [OlO], direction. In view of this inconsistency, it is possible that the agreement of calculated and observed intensities is fortuitous. Because a,,, = c,,,,it is possible to re-index the observed reflections using a body-centered orthorhombic cell with (2~3’~ x (2b,)“2 x c, w a,. After reindexing, we obtain a, = 4.820 A, b, = 5.247 A and c, = 7.180 A. This cell can be interpreted either as orthorhombic, with three mutually perpendicular twofold axes, or as monoclinic, with the b axis as the unique twofold axis. For determination of the atomic positions the consequence of this choice is rather different in each case. In the orthorhombic case we assume the space group Immu, as it is a subgroup of Fd3m which is the space group of the cubic structure of UMn, observed * Present address: Department Beach, CA90840, U.S.A.
0022-5088/83/0000-0000/$03.00
of Mechanical
Engineering,
California
State University,
0 Elsevier Sequoia/Printed
Long
in The Netherlands
L14
at room temperature. We locate the atoms in the special positions b, d an_de as follows: uranium, 4e, (O,&&- E), (O,f, i+ E); manganese, 4d, (i,& a), f,i), 4b, (O,i,j), (O,O,i). With E= 0, this description is equivalent to the cubic Cl5 structure. The atomic motions of the uranium atoms are the only ones permitted in the space group Imma; they are not equivalent to those proposed by Marpoe and Lander Cl] but are instead equivalent to a motion along the [OlO], direction of their unit cell. The positions of the manganese atoms are fixed by symmetry. As a test of the proposed orthorhombic structure, we re-indexed those reflections for which observed intensities were available and calculated the appropriate structure factors as a function of E.The indexing is given in Table 1, the ratio I,,/mLP) FI 2 is plotted uersus Efor the X-ray case in Fig. 1 and the ratio I,/mL 1FJ 2 is plotted versus Efor the neutron case in Fig. 2. (I0 is the observed intensity, m is a multiplying factor, LP is the Lorentz-polarization factor for a flat powder sample, L is the Lorentz factor for a cylindrical powder sample and )8’12 is the square of the calculated structure factor.) In both cases the best agreement is obtained for E= 0.01 + 0.002.
TABLE 1 Line positions and intensities observed in X-ray and neutron diffraction spectra of UMn, at 80 K Neutron data
X-ray data
hkl Orthorhombic
Monoclinic
101 011
28 @xl
28 (de&
I0
ill 111
15.97 16.83
100 67
110 002
200 020
19.04 I 18.86
112 200 020 121
220 202 202 311
36.56 37.17 34.25 41.17
100 22 22 100
26.91 27.66 i 25.94 31.09
68
103 022 211 013 202
131 222 311 iii 222
42.13 42.75 43.07 41.49 46.20
49 26 103 43 8
31.80 32.26 32.50 31.33 I 34.07
18
I0
<2
16
The data are from ref. 1.
The body-centered cell can also be interpreted in terms of the unconventional space group Imma when it will accommodate the atomic positions proposed by Marpoe and Lander [l] in addition to those just considered. (Two distinct indexings with 6 and Kinterchanged must be considered since the identity of the unique axis is not known in advance.) In considering atomic motions of the type proposed by Marpoe and Lander, we find that the calculated structure factors are only weakly dependent on the parameter which is associated with the
600,-
I
I
1
IO
N ;;
7 09 E
‘;= 2
OS
07
Fig. 1. The ratio Z,/mLPlF)* n , 022; 0,103.
us. E for X-ray diffraction
reflections:
V, 202; 0,013;
0,121;
A, 211;
Fig. 2. The ratio Zo/mL\F12 us. E for neutron diffraction reflections (the change in scale should be noted): I, 121,013,103,022,211; 0,200,112,020; 0,101; 0,011; A, 022.
monoclinic distortion and that as a consequence an improvement of the constancy of scaled intensity values can be obtained. The orthorhombic model seems to be the most consistent with the available data. In the orthorhombic model there are only two crystallographically distinct U-U nearest-neighbor distances, and these turn out to be identical within experimental error. These distances are given by d, =
d2
{(;)l+c2(;+2c~~‘2
={(;)‘+e2(~-%~}“’
and we can substitute the values given previously as a,, = 4.820 A, b, = 5.247 A, c, = 7.180 A and E = 0.01 to obtain dl = 3.09 8, and d2 = 3.10 A. These distances are very close to the U-U distance in cubic UMn, at room temperature (3.102 A) and in hypothetical cubic UMn, at 78 K (3”‘(2 Vo)‘i3/4 = 3.089 A), and all of the U-U distances are well on the non-magnetic side of d = 3.5 A which was established by Hill [Z] as an empirical criterion for the occurrence of magnetic order in uranium compounds. Of course, the agreement d, = d2 may be fortuitous, and it would be interesting to see whether such an agreement holds at different temperatures and for other UX2 compounds which also undergo this transformation.
L16
I am pleased to thank A. C. Larson and G. H. Lander for several helpful discussions. The hospitality of R. N. R. Mulford, R. N. Silver and J. L. Smith is greatly appreciated. This work was performed under the auspices of the U.S. Department of Energy. 1 G. R. Marpoeand G. H. Lander,Solid StateCommun., 26(1978) 699. H. H. Hill, in W. N. Miner (ed.), Plutonium and Other Actinides, Metallurgical Society of the American Institute of Mechanical Engineers, New York, 1970,p. 2.
2
of the Less-Common Metals, 90 (1983) LB-L16
L13
Letter The crystal structure of UMn, A. C. LAWSON * Los Alamos National Laboratory, University of California, Los Alamos, NM 87545(U.S.A.) (Received December 2,1982)
Recently Marpoe and Lander [l] have investigated the crystal structure of the Cl5 compound UMn, at low temperatures. They found that this compound undergoes a large crystallographic distortion at 112 K and described this distortion in terms of a monoclinic unit cell. By making a specific assumption about the atomic parameters within this unit cell, fair agreement with a limited set of intensity data was obtained and a set of three distinct U-U nearest-neighbor distances was derived. A re-analysis of their data shows that at low temperatures UMn, has a more symmetric orthorhombic structure which is characterized by a single non-magnetic U-U nearest-neighbor distance. At room temperature UMn, has an f.c.c. lattice with the cubic lattice constant a, = 7.16s A. At 5 K, the peak positions can be indexed with a monoclinic unit cell with the monoclinic lattice constants a, = c, = 7.125 A, b, = 7.180 A and /I = 94.85”. For intensity calculations, Marpoe and Lander assumed that the only atomic motions were those of uranium atoms along one of the face diagonals so that “a pair of uranium atoms at (4,&i) and ( -4, -& -i) have new coordinates (i-&$,A-@ and@-4, -&, S-4)“. Suchanassumptionrequiresa twofold axis parallel to the [loll,,, direction which is inconsistent with the assumed cell for which the twofold axis is presumably parallel to the [OlO], direction. In view of this inconsistency, it is possible that the agreement of calculated and observed intensities is fortuitous. Because a,,, = c,,,,it is possible to re-index the observed reflections using a body-centered orthorhombic cell with (2~3’~ x (2b,)“2 x c, w a,. After reindexing, we obtain a, = 4.820 A, b, = 5.247 A and c, = 7.180 A. This cell can be interpreted either as orthorhombic, with three mutually perpendicular twofold axes, or as monoclinic, with the b axis as the unique twofold axis. For determination of the atomic positions the consequence of this choice is rather different in each case. In the orthorhombic case we assume the space group Immu, as it is a subgroup of Fd3m which is the space group of the cubic structure of UMn, observed * Present address: Department Beach, CA90840, U.S.A.
0022-5088/83/0000-0000/$03.00
of Mechanical
Engineering,
California
State University,
0 Elsevier Sequoia/Printed
Long
in The Netherlands
L14
at room temperature. We locate the atoms in the special positions b, d an_de as follows: uranium, 4e, (O,&&- E), (O,f, i+ E); manganese, 4d, (i,& a), f,i), 4b, (O,i,j), (O,O,i). With E= 0, this description is equivalent to the cubic Cl5 structure. The atomic motions of the uranium atoms are the only ones permitted in the space group Imma; they are not equivalent to those proposed by Marpoe and Lander Cl] but are instead equivalent to a motion along the [OlO], direction of their unit cell. The positions of the manganese atoms are fixed by symmetry. As a test of the proposed orthorhombic structure, we re-indexed those reflections for which observed intensities were available and calculated the appropriate structure factors as a function of E.The indexing is given in Table 1, the ratio I,,/mLP) FI 2 is plotted uersus Efor the X-ray case in Fig. 1 and the ratio I,/mL 1FJ 2 is plotted versus Efor the neutron case in Fig. 2. (I0 is the observed intensity, m is a multiplying factor, LP is the Lorentz-polarization factor for a flat powder sample, L is the Lorentz factor for a cylindrical powder sample and )8’12 is the square of the calculated structure factor.) In both cases the best agreement is obtained for E= 0.01 + 0.002.
TABLE 1 Line positions and intensities observed in X-ray and neutron diffraction spectra of UMn, at 80 K Neutron data
X-ray data
hkl Orthorhombic
Monoclinic
101 011
28 @xl
28 (de&
I0
ill 111
15.97 16.83
100 67
110 002
200 020
19.04 I 18.86
112 200 020 121
220 202 202 311
36.56 37.17 34.25 41.17
100 22 22 100
26.91 27.66 i 25.94 31.09
68
103 022 211 013 202
131 222 311 iii 222
42.13 42.75 43.07 41.49 46.20
49 26 103 43 8
31.80 32.26 32.50 31.33 I 34.07
18
I0
<2
16
The data are from ref. 1.
The body-centered cell can also be interpreted in terms of the unconventional space group Imma when it will accommodate the atomic positions proposed by Marpoe and Lander [l] in addition to those just considered. (Two distinct indexings with 6 and Kinterchanged must be considered since the identity of the unique axis is not known in advance.) In considering atomic motions of the type proposed by Marpoe and Lander, we find that the calculated structure factors are only weakly dependent on the parameter which is associated with the
600,-
I
I
1
IO
N ;;
7 09 E
‘;= 2
OS
07
Fig. 1. The ratio Z,/mLPlF)* n , 022; 0,103.
us. E for X-ray diffraction
reflections:
V, 202; 0,013;
0,121;
A, 211;
Fig. 2. The ratio Zo/mL\F12 us. E for neutron diffraction reflections (the change in scale should be noted): I, 121,013,103,022,211; 0,200,112,020; 0,101; 0,011; A, 022.
monoclinic distortion and that as a consequence an improvement of the constancy of scaled intensity values can be obtained. The orthorhombic model seems to be the most consistent with the available data. In the orthorhombic model there are only two crystallographically distinct U-U nearest-neighbor distances, and these turn out to be identical within experimental error. These distances are given by d, =
d2
{(;)l+c2(;+2c~~‘2
={(;)‘+e2(~-%~}“’
and we can substitute the values given previously as a,, = 4.820 A, b, = 5.247 A, c, = 7.180 A and E = 0.01 to obtain dl = 3.09 8, and d2 = 3.10 A. These distances are very close to the U-U distance in cubic UMn, at room temperature (3.102 A) and in hypothetical cubic UMn, at 78 K (3”‘(2 Vo)‘i3/4 = 3.089 A), and all of the U-U distances are well on the non-magnetic side of d = 3.5 A which was established by Hill [Z] as an empirical criterion for the occurrence of magnetic order in uranium compounds. Of course, the agreement d, = d2 may be fortuitous, and it would be interesting to see whether such an agreement holds at different temperatures and for other UX2 compounds which also undergo this transformation.
L16
I am pleased to thank A. C. Larson and G. H. Lander for several helpful discussions. The hospitality of R. N. R. Mulford, R. N. Silver and J. L. Smith is greatly appreciated. This work was performed under the auspices of the U.S. Department of Energy. 1 G. R. Marpoeand G. H. Lander,Solid StateCommun., 26(1978) 699. H. H. Hill, in W. N. Miner (ed.), Plutonium and Other Actinides, Metallurgical Society of the American Institute of Mechanical Engineers, New York, 1970,p. 2.
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