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Phonon softening in UO2
Physica B 180 & 181 (1992) North-Holland
PHYSICA El
321-322
Phonon softening in UO, P. de V. du Plessis”, G.H.
Landerb,
A.M.
Strydom’
and B. Ftikd
“Department of Physics, Rand Afrikaans University, PO Box 524, Johannesburg, South Africa hCommission of the European Communities, JRC Karlsruhe, Postfach 2340, W-7500 Karlsruhe, ilEC of South Africa Ltd., PO Box 582, Pretoria, South Africa ‘lnstitut Laue-Langevin, 156X, 38042 Grenoble Cedex, France
Inelastic neutron scattering approximately 20% on cooling
and ultrasonic measurements both indicate a softening of the from room temperature to the N&e1 temperature at 31 K.
Uranium dioxide which crystallizes in the cubic fluoride structure, undergoes a sharp first order transition to an antiferromagnetic structure below T, = 31 K [l]. Allen [2] explained the first order transition in terms of a Jahn-Teller effect and predicted the existence of an internal strain as the dominant distortion mode for the spin-lattice coupling. Ultrasonic measurements [3] indicate a large softening of the C,, elastic constant. This renormalization sets in continuously from room temperature on cooling to T, and originates from the coupling between uranium quadrupoles and oxygen atom displacements [2]. Elastic neutron scattering cross-section measurements [4] indicate that rather than the homogeneous deformation considered by Allen, the internal distortion concept must be extended to include inhomogeneous deformations corresponding to a zone boundary q = (2~rla) (l,O,O) phonon of symmetry M, [l]. A theoretical analysis is given by Cooper [5] and critically extended by Solt and Erdiis [6]. A study of the temperature dependencies of the frequencies of Mpoint phonon modes (M, and Ml) indicates no significant change in the paramagnetic region and only a 2-3% change of frequencies below TN [l]. Furthermore, the frequency of the acoustic A, branch at a reduced wave vector of 0.2 shows no significant temperature dependence between 300 and 4 K [l]. This mode corresponds to the shear elastic constant C,,, thus indicating a difference in the temperature dependence found for ultrasonic results compared to the neutron data. In this contribution we compare C,, data measured for UO, at different temperatures respectively using the inelastic neutron scattering technique and ultrasonics. Measurements were performed on a crystal obtained from Battelle Northwest. A slab 6.1 mm thick was cut from the one end of the crystal for the ultrasonic measurements and the large remaining part of volume 8.9 cm’ was used for the neutron measurements. Phonon dispersion curves were measured using the IN 14 triple-axis crystal spectrometer at ILL, Gre0921-4526/92/$05.00
0
1992
Elsevier
Science
Publishers
Germany
elastic
constant
C,,
of
noble. Pyrolytic graphite (0 0 2) was used both for the monochromator and the analyser. Constant energy (E) scans (E=0.75, 1.0, 1.5, 2.0 and 3SmeV) were employed to obtain the (0 0 <) TA phonons (A, branch) measured from the (22 0) reciprocal lattice point. Representative neutron groups are given in fig. 1. Figure l(a) illustrates that for an energy of 3.5 meV the sum of two Gaussian functions is adequate to represent the peaks at reduced wave vector positions (0, 0, * 6). For E G 2 meV there appeared a contribu-
01 .-’
-,15
.-
-.lO
__
-.05
REDUCED
_
0
,05
.lO
WAVEVECTOR
.15 <
Fig. 1. Neutron groups observed for UO, at 200 K in constant energy (E) scans. The lines represents the sum of two gaussian functions
B.V. All rights
functions in (a) for E = 3.5 meV, and three in (b) for E = 1.5 meV. reserved
gaussian
P. de V. du Plessis et al.
322
tion of scattering centred at the origin in fig. l(b) and the sum of three gaussian functions is needed to represent the data. Dispersion curves are given in fig. 2 for 200 and 50 K and the softening of the acoustic branch at low temperature is evident at all wave vectors. The dispersion curves are linear for E 4 2 meV. The slopes in this region have been used to determine the transverse velocity v,. for the (00 1) direction and hence C,, = pv; (p = 10.96gcmm3). These neutron deduced values of C,, are depicted by squares in fig. 3. Also indicated by circles are the results of ultrasonic velocity measurements using the pulse-echo-overlap technique (Matec equipment). Ultrasonic measurements were made during a cooling run and temperature were controlled to within 20.02 K before data were taken. It is clear that our measurements confirm the C,, softening (31 between room temperature and T, as observed from the results of both ultrasonics and from neutron scattering. It is noted that in the paramagnetic region our ultrasonic values are approximately 14% lower than the neutron derived values. but the difference is smaller in the ordered region. Previous ultrasonic measurements of C,, at room temperature give values of 6.41 X lo-“‘N m -’ [7] and 5.97 x lO_“‘Nm-’ [8]. Our ultrasonic results are in good agreement with the latter. These differences do not change the conclusion that the softening of C,, seen in ultrasonic measurements is also observed in the neutron determination. A large step in C,, is evident at T, and could be
softening in UO,
Phonon
.
. .
...........
0 2
4.6’
.
F
0
ii
100
3. 30
’ 50
’
200
TEMPERATURE
1
1 70
300 IK)
Fig. 3. The temperature dependence of the C,, elastic constant as determined by inelastic neutron scattering (squares) and ultrasonic velocity measurements (circles).
followed in cooling through T, in spite of an increase in attenuation. This is in contrast with the results in ref. [3] where attenuation excluded measurements near T,. The results indicate that C,, does not return near absolute zero to the unrenormalized values one would expect from its phonon behaviour. However. interpretation of such a difference, as well as the complete modelhng [2] of the softening in C,, in the paramagnetic region, should await the extension of ultrasonic measurements to above room temperature in order to accurately assess the phonon contribution. Acknowledgement
,
8
P. de V. du P. acknowledges support by the Foundation for Research Development. Work performed by A.M.S. is in partial fulfilment of the requirements of a Ph.D. study for Rand Afrikaans University. References
REDUCED
WAVEVECTOR
<
Fig. 2. Dispersion curves for UOz at different temperatures for phonons propagating in the [0 0 [] direction.
W.J.L. Buyers and T.M. Holden, in: Handbook on the Physics and Chemistry of the Actinides, Vol. 2. eds. A.J. Freeman and G.H. Lander (North-Holland, Amsterdam. 1985) p. 246. PI S.J. Allen. Phys. Rev. 166 (1968) 530; Phys. Rev. 167 ( 1968) 492. [31 O.G. Brandt and C.T. Walker, Phys. Rev. 170 (1968) 528. [41 J. Faber and G.H. Lander, Phys. Rev. B I4 (1976) 1151. [51 R. Siemann and B.R. Cooper, Phys. Rev. B 20 (1979) 2869, and refs. therein. [61 G. Solt and P. Erdiis, Phys. Rev. B 22 (lY80) 471X. M.L. Wheat, H.J. Anderson and J.L. [71 J.B. Wachtman, Bates, J. Nucl. Mater. 16 (1965) 39. 181 I.J. Fritz. J. Appl. Phys. 47 (1976) 4353.
PHYSICA El
321-322
Phonon softening in UO, P. de V. du Plessis”, G.H.
Landerb,
A.M.
Strydom’
and B. Ftikd
“Department of Physics, Rand Afrikaans University, PO Box 524, Johannesburg, South Africa hCommission of the European Communities, JRC Karlsruhe, Postfach 2340, W-7500 Karlsruhe, ilEC of South Africa Ltd., PO Box 582, Pretoria, South Africa ‘lnstitut Laue-Langevin, 156X, 38042 Grenoble Cedex, France
Inelastic neutron scattering approximately 20% on cooling
and ultrasonic measurements both indicate a softening of the from room temperature to the N&e1 temperature at 31 K.
Uranium dioxide which crystallizes in the cubic fluoride structure, undergoes a sharp first order transition to an antiferromagnetic structure below T, = 31 K [l]. Allen [2] explained the first order transition in terms of a Jahn-Teller effect and predicted the existence of an internal strain as the dominant distortion mode for the spin-lattice coupling. Ultrasonic measurements [3] indicate a large softening of the C,, elastic constant. This renormalization sets in continuously from room temperature on cooling to T, and originates from the coupling between uranium quadrupoles and oxygen atom displacements [2]. Elastic neutron scattering cross-section measurements [4] indicate that rather than the homogeneous deformation considered by Allen, the internal distortion concept must be extended to include inhomogeneous deformations corresponding to a zone boundary q = (2~rla) (l,O,O) phonon of symmetry M, [l]. A theoretical analysis is given by Cooper [5] and critically extended by Solt and Erdiis [6]. A study of the temperature dependencies of the frequencies of Mpoint phonon modes (M, and Ml) indicates no significant change in the paramagnetic region and only a 2-3% change of frequencies below TN [l]. Furthermore, the frequency of the acoustic A, branch at a reduced wave vector of 0.2 shows no significant temperature dependence between 300 and 4 K [l]. This mode corresponds to the shear elastic constant C,,, thus indicating a difference in the temperature dependence found for ultrasonic results compared to the neutron data. In this contribution we compare C,, data measured for UO, at different temperatures respectively using the inelastic neutron scattering technique and ultrasonics. Measurements were performed on a crystal obtained from Battelle Northwest. A slab 6.1 mm thick was cut from the one end of the crystal for the ultrasonic measurements and the large remaining part of volume 8.9 cm’ was used for the neutron measurements. Phonon dispersion curves were measured using the IN 14 triple-axis crystal spectrometer at ILL, Gre0921-4526/92/$05.00
0
1992
Elsevier
Science
Publishers
Germany
elastic
constant
C,,
of
noble. Pyrolytic graphite (0 0 2) was used both for the monochromator and the analyser. Constant energy (E) scans (E=0.75, 1.0, 1.5, 2.0 and 3SmeV) were employed to obtain the (0 0 <) TA phonons (A, branch) measured from the (22 0) reciprocal lattice point. Representative neutron groups are given in fig. 1. Figure l(a) illustrates that for an energy of 3.5 meV the sum of two Gaussian functions is adequate to represent the peaks at reduced wave vector positions (0, 0, * 6). For E G 2 meV there appeared a contribu-
01 .-’
-,15
.-
-.lO
__
-.05
REDUCED
_
0
,05
.lO
WAVEVECTOR
.15 <
Fig. 1. Neutron groups observed for UO, at 200 K in constant energy (E) scans. The lines represents the sum of two gaussian functions
B.V. All rights
functions in (a) for E = 3.5 meV, and three in (b) for E = 1.5 meV. reserved
gaussian
P. de V. du Plessis et al.
322
tion of scattering centred at the origin in fig. l(b) and the sum of three gaussian functions is needed to represent the data. Dispersion curves are given in fig. 2 for 200 and 50 K and the softening of the acoustic branch at low temperature is evident at all wave vectors. The dispersion curves are linear for E 4 2 meV. The slopes in this region have been used to determine the transverse velocity v,. for the (00 1) direction and hence C,, = pv; (p = 10.96gcmm3). These neutron deduced values of C,, are depicted by squares in fig. 3. Also indicated by circles are the results of ultrasonic velocity measurements using the pulse-echo-overlap technique (Matec equipment). Ultrasonic measurements were made during a cooling run and temperature were controlled to within 20.02 K before data were taken. It is clear that our measurements confirm the C,, softening (31 between room temperature and T, as observed from the results of both ultrasonics and from neutron scattering. It is noted that in the paramagnetic region our ultrasonic values are approximately 14% lower than the neutron derived values. but the difference is smaller in the ordered region. Previous ultrasonic measurements of C,, at room temperature give values of 6.41 X lo-“‘N m -’ [7] and 5.97 x lO_“‘Nm-’ [8]. Our ultrasonic results are in good agreement with the latter. These differences do not change the conclusion that the softening of C,, seen in ultrasonic measurements is also observed in the neutron determination. A large step in C,, is evident at T, and could be
softening in UO,
Phonon
.
. .
...........
0 2
4.6’
.
F
0
ii
100
3. 30
’ 50
’
200
TEMPERATURE
1
1 70
300 IK)
Fig. 3. The temperature dependence of the C,, elastic constant as determined by inelastic neutron scattering (squares) and ultrasonic velocity measurements (circles).
followed in cooling through T, in spite of an increase in attenuation. This is in contrast with the results in ref. [3] where attenuation excluded measurements near T,. The results indicate that C,, does not return near absolute zero to the unrenormalized values one would expect from its phonon behaviour. However. interpretation of such a difference, as well as the complete modelhng [2] of the softening in C,, in the paramagnetic region, should await the extension of ultrasonic measurements to above room temperature in order to accurately assess the phonon contribution. Acknowledgement
,
8
P. de V. du P. acknowledges support by the Foundation for Research Development. Work performed by A.M.S. is in partial fulfilment of the requirements of a Ph.D. study for Rand Afrikaans University. References
REDUCED
WAVEVECTOR
<
Fig. 2. Dispersion curves for UOz at different temperatures for phonons propagating in the [0 0 [] direction.
W.J.L. Buyers and T.M. Holden, in: Handbook on the Physics and Chemistry of the Actinides, Vol. 2. eds. A.J. Freeman and G.H. Lander (North-Holland, Amsterdam. 1985) p. 246. PI S.J. Allen. Phys. Rev. 166 (1968) 530; Phys. Rev. 167 ( 1968) 492. [31 O.G. Brandt and C.T. Walker, Phys. Rev. 170 (1968) 528. [41 J. Faber and G.H. Lander, Phys. Rev. B I4 (1976) 1151. [51 R. Siemann and B.R. Cooper, Phys. Rev. B 20 (1979) 2869, and refs. therein. [61 G. Solt and P. Erdiis, Phys. Rev. B 22 (lY80) 471X. M.L. Wheat, H.J. Anderson and J.L. [71 J.B. Wachtman, Bates, J. Nucl. Mater. 16 (1965) 39. 181 I.J. Fritz. J. Appl. Phys. 47 (1976) 4353.