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Change of the dielectric constant at the phase transition in U4O9
Solid State Communications, Vol. 8, pp. 1043—1045, 1970. Pergamon Press.
Printed in Great Britain
CHANGE OF THE DIELECTRIC CONSTANT AT THE PHASE TRANSITION IN U4O9 Jun Tateno Japan Atomic Energy Research Institute, Tokai-mura, Naka.gun, Ibaraki-ken, Japan (Received 25 April 1970 by T. Nagamiya).
The dielectric constant of U4Og measured at 9.4 GHz changes at the phase transition point. ~ is 70 in the low temperature phase and 260 in the high temperature phase. This change is discussed on the basis of the electronic ordering of the phase transition.
A PHASE transition occurs in U409 at about 80°C. U409 is one of the mixed valence type 4~and U~,and oxides containing U to the ordering of this transition wascations, attributed the valence electrons.’ That is, in the high temperature phase the excess electrons at the cation sites for U5~are distributed at random, or delocalized as suggested by Verwey et al.2 It was also reported that there exists a lattice distortion accompanied with the transition.’ The dielectric properties of U 409 in a low frequency range was3studied connection with but no in anomaly was obthe phase served at the transition, transition point perhaps because of the layer structure of these kinds of materials as
0.3mm. Figure 1 shows the temperature dependence of the realconstant. and imarginary dielectric e’ is parts 70 in of thethe lowcomplex temperature phase, and 260 just above the phase transition temperature. The dielectric loss tan 3 is about 0.15 in both phases, but it increases up to 0.45 in the range of the phase transition.
200
dielectric suggested constant by Koops.4 of UIn the present work the 4O9was in the micro-wave frequency range, 9.3 GHz, measured, and we discuss the mechanism of the change in the dielectric constant at the phase transition,
150 100 so
~~o~Pr ° I
U4O9 crystals were prepared by specimens the method 3 The already described elsewhere, were cut in needle shape, the typical dimensions of which was 0.265cm x 0.000767cm2. The apparatus and the method of measurement at 9.4 GHz are the same as those for the study of the dielectric constant of U0 5 The skin depth of the specimen at 100°Cwas2.about 1 mm, which is larger than the diameter of the specimen,
Phase Transition
° I
I
I
40 2o
___________________________ I
-100
-50
Temperature
I
0
50
tOO
(t)
FIG. 1. Temperature dependence of real and imaginary parts of the dielectric constant of U 4O9 at 9.4 GHz. 1043
DIELECTRIC CONSTANT AT THE PHASE TRANSITION IN U
1044
409
The phase transition may affect the dielectric properties via three mechanism: (i) the change of the electronic part of the polarization, (ii) the change of force constants due to the distortion accompanied with the electronic ordering (this causes the change of the ionic part of the polarization) and (iii) other origins such as electron hopping. The first one is rejected because the reflectivity of U409 in the optical 6 As to region does by the transition, the third one,nota change simple estimate of the dipole moment due to the hopping of electrons which is based on the analogy with the re-orientation of a dipole over a potential barrier, shows that the contribution to the dielectric constant change is only a few per cent. Hence we shall discuss
Vol. 8, No, 13
for the high temperature phase, and 1 2
+
=
±TTN(a + a 3 e2
)
(ib)
for the low temperature phase. From the reason mentioned above a~ = a~2. (3) Subtracting equation (la) from equation (ib) and using equations (2) and (3) we obtain — _____
1
E
2
+
—
— ______
c~
1
6
2
+
=
4 _TrNe*2
3
/ 1
1 —
\1
2
(4)
where k
The 7 ionic part of the polarizability is expressed as 2 e*2 a (2) e* = = Mw~ k ‘
1 and k2 are the force constants in the high and low temperature phases, respectively, and N is the number of oscillators, We have ~ = 260 and ‘~ = 70 from the experimental results, but N and e* are unknown because we have no knowledge about lattice dynamics of U409. Here we use N = 2.2 x 10~. the number of the cations per unit volume in U409, 4~in and e* U0 = 82.4e, Alsothe we use the effective chargebetween of U U4~and 2, 02 in U0 force constant 2 for 5 cm-dyn’’. Using these values, we obtain k k1, that is, k1 = 2.1x10 2 = 2.2x 10~,from eq. (4) i.e. k 2 = 1.05k1 , It is not unreasonable that a change in the force constant occurs to this extent at the phase transition,
where e* is the effective charge of an ion, M the reduced mass of the ion, ~ the characteristic
Acknowledgement — The author wishes to thank Dr. K~Gesi for his help in dielectric constant
frequency of the lattice vibration, and k is the force constant, Equation (1) is written as
measurements and Dr. Y. Sasaki for his encouragement,
our experimental results on the F,asis of the lattice distortion, There is a following relation between the dielectric constant E’ and the electronic and ionic parts of the polarizability a~,a~: er’
— +
21
3‘I ‘rrN(a~+ a~.
=
e—1 _______
=
4 _7TN(aei
+
(1)
a~ 1)
(la)
3
REFERENCES
J.,
1.
TATENO
2.
VERWEY E.J.W. and HAAYMAN P.W., Physica 8, 979 (1941).
3.
TATENO
4,
KOOPS C.G., Phys. Rev. 83, 121 (1951)~
5.
GESI K. and TATENO
6.
TATENO
7,
FROHLICH H., Theory of Dielectrics, p. 156. Clarendon Press, Oxford (1958).
J.
J. Phys. Chem. Solids 30, 1321 (1969).
and NAITO K., Solid State Commun. 7, 807 (1969).
J., to
J.,
Japan. J. appi. Phys. 8, 1358 (1969).
be published.
8~ AXEJ.D. and PETTITG.D,, Phys. Rev. 151, 676 (1966).
Vol. 8, No. 13.
DIELECTRIC CONSTANT AT THE PHASE TRANSITION IN U
4 09
Die bei 9.4 GHz gemessene Dielektrizitätskonstante von U4O9 andert sich bairn Phasenubergangspunkt. ‘ ist 70 in der Hochtemperaturephase und 260 in der Tieftemperaturephase. Diese Anderung Mechanismus 1st auf der elektronischen bei dern PhaseniThergang der elektronischen Verordnung diskutiert.
1045
Printed in Great Britain
CHANGE OF THE DIELECTRIC CONSTANT AT THE PHASE TRANSITION IN U4O9 Jun Tateno Japan Atomic Energy Research Institute, Tokai-mura, Naka.gun, Ibaraki-ken, Japan (Received 25 April 1970 by T. Nagamiya).
The dielectric constant of U4Og measured at 9.4 GHz changes at the phase transition point. ~ is 70 in the low temperature phase and 260 in the high temperature phase. This change is discussed on the basis of the electronic ordering of the phase transition.
A PHASE transition occurs in U409 at about 80°C. U409 is one of the mixed valence type 4~and U~,and oxides containing U to the ordering of this transition wascations, attributed the valence electrons.’ That is, in the high temperature phase the excess electrons at the cation sites for U5~are distributed at random, or delocalized as suggested by Verwey et al.2 It was also reported that there exists a lattice distortion accompanied with the transition.’ The dielectric properties of U 409 in a low frequency range was3studied connection with but no in anomaly was obthe phase served at the transition, transition point perhaps because of the layer structure of these kinds of materials as
0.3mm. Figure 1 shows the temperature dependence of the realconstant. and imarginary dielectric e’ is parts 70 in of thethe lowcomplex temperature phase, and 260 just above the phase transition temperature. The dielectric loss tan 3 is about 0.15 in both phases, but it increases up to 0.45 in the range of the phase transition.
200
dielectric suggested constant by Koops.4 of UIn the present work the 4O9was in the micro-wave frequency range, 9.3 GHz, measured, and we discuss the mechanism of the change in the dielectric constant at the phase transition,
150 100 so
~~o~Pr ° I
U4O9 crystals were prepared by specimens the method 3 The already described elsewhere, were cut in needle shape, the typical dimensions of which was 0.265cm x 0.000767cm2. The apparatus and the method of measurement at 9.4 GHz are the same as those for the study of the dielectric constant of U0 5 The skin depth of the specimen at 100°Cwas2.about 1 mm, which is larger than the diameter of the specimen,
Phase Transition
° I
I
I
40 2o
___________________________ I
-100
-50
Temperature
I
0
50
tOO
(t)
FIG. 1. Temperature dependence of real and imaginary parts of the dielectric constant of U 4O9 at 9.4 GHz. 1043
DIELECTRIC CONSTANT AT THE PHASE TRANSITION IN U
1044
409
The phase transition may affect the dielectric properties via three mechanism: (i) the change of the electronic part of the polarization, (ii) the change of force constants due to the distortion accompanied with the electronic ordering (this causes the change of the ionic part of the polarization) and (iii) other origins such as electron hopping. The first one is rejected because the reflectivity of U409 in the optical 6 As to region does by the transition, the third one,nota change simple estimate of the dipole moment due to the hopping of electrons which is based on the analogy with the re-orientation of a dipole over a potential barrier, shows that the contribution to the dielectric constant change is only a few per cent. Hence we shall discuss
Vol. 8, No, 13
for the high temperature phase, and 1 2
+
=
±TTN(a + a 3 e2
)
(ib)
for the low temperature phase. From the reason mentioned above a~ = a~2. (3) Subtracting equation (la) from equation (ib) and using equations (2) and (3) we obtain — _____
1
E
2
+
—
— ______
c~
1
6
2
+
=
4 _TrNe*2
3
/ 1
1 —
\1
2
(4)
where k
The 7 ionic part of the polarizability is expressed as 2 e*2 a (2) e* = = Mw~ k ‘
1 and k2 are the force constants in the high and low temperature phases, respectively, and N is the number of oscillators, We have ~ = 260 and ‘~ = 70 from the experimental results, but N and e* are unknown because we have no knowledge about lattice dynamics of U409. Here we use N = 2.2 x 10~. the number of the cations per unit volume in U409, 4~in and e* U0 = 82.4e, Alsothe we use the effective chargebetween of U U4~and 2, 02 in U0 force constant 2 for 5 cm-dyn’’. Using these values, we obtain k k1, that is, k1 = 2.1x10 2 = 2.2x 10~,from eq. (4) i.e. k 2 = 1.05k1 , It is not unreasonable that a change in the force constant occurs to this extent at the phase transition,
where e* is the effective charge of an ion, M the reduced mass of the ion, ~ the characteristic
Acknowledgement — The author wishes to thank Dr. K~Gesi for his help in dielectric constant
frequency of the lattice vibration, and k is the force constant, Equation (1) is written as
measurements and Dr. Y. Sasaki for his encouragement,
our experimental results on the F,asis of the lattice distortion, There is a following relation between the dielectric constant E’ and the electronic and ionic parts of the polarizability a~,a~: er’
— +
21
3‘I ‘rrN(a~+ a~.
=
e—1 _______
=
4 _7TN(aei
+
(1)
a~ 1)
(la)
3
REFERENCES
J.,
1.
TATENO
2.
VERWEY E.J.W. and HAAYMAN P.W., Physica 8, 979 (1941).
3.
TATENO
4,
KOOPS C.G., Phys. Rev. 83, 121 (1951)~
5.
GESI K. and TATENO
6.
TATENO
7,
FROHLICH H., Theory of Dielectrics, p. 156. Clarendon Press, Oxford (1958).
J.
J. Phys. Chem. Solids 30, 1321 (1969).
and NAITO K., Solid State Commun. 7, 807 (1969).
J., to
J.,
Japan. J. appi. Phys. 8, 1358 (1969).
be published.
8~ AXEJ.D. and PETTITG.D,, Phys. Rev. 151, 676 (1966).
Vol. 8, No. 13.
DIELECTRIC CONSTANT AT THE PHASE TRANSITION IN U
4 09
Die bei 9.4 GHz gemessene Dielektrizitätskonstante von U4O9 andert sich bairn Phasenubergangspunkt. ‘ ist 70 in der Hochtemperaturephase und 260 in der Tieftemperaturephase. Diese Anderung Mechanismus 1st auf der elektronischen bei dern PhaseniThergang der elektronischen Verordnung diskutiert.
1045