- Email: [email protected]
Heat capacities and electrical conductivities of (U1 − yEuy)O2 ( y = 0.044 and 0.090) from 300 to 1550 K
Journal of Nuclear
Materials
jOU~l of nuclear
186 (1992) 2.54-258
North-Holland
lnaterials
Heat capacities and electrical conductivities of (U, _,Eu,)02 ( y = 0.044 and 0.090) from 300 to 1550 K Tsuneo Mats&, Toshiaki Kawase and Keiji Naito Department of NucuclearEngineering, Faculty of Engineering, Nagoya Unit:ersity, Furo-cho, Chikusa-ku, Nagoya 464-01, Japan Received
24 May 1991; accepted
4 September
1991
Heat capacities and electrical ~ondu~tivities of (U, _,Eu,)O, ( y = 0.044 and 0.0~) were measured by means of direct heating pulse calorimetry over the temperature range from 300 to 1550 K. An anomalous increase in the heat capacity cuwe of each sample of W~,Eu,)OZ was observed similarly to the cases of (U, _yM,)Oz fM = Gd, La and SC) found previously by the authors. As the increase of the europium content in (U, _,Eu ,)O, from y = 0.044 to 0.090, the onset temperature of an anomalous increase in the heat capacity decreased from about 1150 to 950 K. The values of the enthalpy (AH,) and the entropy for defect formation (A.S,) in (U,~,Eu,)O, were calculated from the excess heat capacity assuming the presence of Frenkel pairs of oxygen, and were found to be similar to those of UOz doped with La, Gd and SC previously obtained by the authors. On the other hand, no anomaly was seen in the electrical conductivjty curve around the onset temperature of the anomalous increase in the heat capacity. It is conducted that the occurrence of the excess heat capacity of (U, _,Eu,)O, originates from the predominant contribution of the formation of Frenkel pair-like defects of oxygen similarly to the cases of UO, doped with other trivalent cations. The difference in the onset temperatures of (U, _,Eu,)O, from those of UO, doped with other trivalent cations was thought to be originated from that of the elastic strain induced by the lattice parameter change.
1. Introduction Europium-doped UO, is expected to be used as a burnable poison fuel for higher burnups as well as gadolin~um-doped UO, [ 11.The nonstoi~hiometric region of the fluorite-type solid solution (U, _vE~v)02ir has been determined from the variation of the lattice constant versus composition by some inverstigators [24]. The oxygen potentials of (U,_,Eu,)O,+, were recently measured as a function of x and y values by Fujino et al. [4]. The heat capacity of (UI_,,Euy)O,, which is one of the most important properties of fuel materials to evaluate their thermal stabilities, has not been measured yet. The heat capacities of @J_,M,)O, CM = Cd [5], La [6], SC [7], Ti [7] and Nb [7]) have been measured in the temperature range from 300 to 1500 K by the authors. An anomalous increase in the heat capacity of each sample of UO, doped with trivalent cations such as Gd, La and SC was observed at temperatures from about 700 to 1300 K depending on the kind of dopant and its concentration. This anomalous increase in the ~22-3llS/92/$05.00
0 1992 - Elsevier
Science
Publishers
heat capacity of doped UO, was interpreted as due to the formation of Frenkel pair-like defects of oxygen by the authors [S-S] similarly to the case of UO, [9-111. In this study, the heat capacities and the electrical conductivities of (U,_,Eu,)O, (y = 0.044 and 0.090) were measured simultaneously from 300 to 1550 K by means of direct heating pulse calorimetry to investigate the origin of excess heat capacity of (U,..,.Eu,)O, in comparison with the results of (U,_,GdY)02, W_,,,La,,)Oz and (U, _,Sc,)Oz.
2. Experimental The mixture of Eu,O, and UO, powder was shaped into a cylindrical rod of about 7 mm in diameter and about 50 mm in length, using an evacuated rubber press with a hydrostatic pressure of about 400 MPa. The cylindrical rod thus prepared was sintered and homogenized at 1573 K for 7 days in an Ar gas flow and then at 1273 K for 1 day in a hydrogen gas flow so as to obtain the stoichiometric composition (O/M =
B.V. All rights reserved
255
T. Matsui et al. / Heat capacities and electrical conductivities of (U, _ yEu,)O, 2.00&0.01, M = U + Eu) according to the thermogravimetric study on (U,_,EU,)O~+~ by Fujino et al. [4]. This sintering and homogenizing process was repeated several times. X-ray diffraction analysis indicated a single fluorite phase for each sample. The heat capacity and the electrical conductivity were measured simultaneously by a direct heating pulse calorimeter, of which details have been given elsewhere [12]. In this calorimeter, the temperature of the sample rod was varied from room temperature to 1550 K by an external Pt heater, and after getting a constant temperature, a current pulse was supplied to both the sample rod and the double cylindrical molybdenum thermal shields simultaneously so as to obtain the small temperature rise. The electric potential drop, the current and the temperature rise of the sample rod were measured to obtain the heat capacity and the electrical conductivity.
I
50’ I 300
500
700
1500
1300
EU O~Ow)Oz in this study; fUw,,Gd,.,,,
10,
CP
1 undoped
(01
UOz
[53;
bl; (-- - -_)(U,,,,LaO,uuoIO, 161; (-. wM,~c”.“Y”)oz [71. by the least-squares
RJ,,,, f-,
-)
. . .)
method as
mol-’ = 80.663 + 6.1730 x 10-3(7-/N) - 1.7623 x 10h(l”,‘K)-2
(300 5 Z-/K I 1150).
(1) anomalous increase in the heat capacity of (U~~.~,~EU~.~IO, is also seen above 950 K in fig. 2. The equation for the heat capacity of (U~~.~,~~Eu~.~~)O~ below 950 K is given by the least-squares method as eq. (2)
An
C,/J
K- ’ mol -’ = 80.942 + 4.8856 + IO-“(T/K) -1.9524x
106(T/K)-2
(300 I T/K I 950).
110
5oL 303
,
WI
r
m
,
f 9%
I
1
1 loo
1
I
1300
I
00
,
15co
T/K
Fig. 1. Heat capacity of (U0,956E~0,0,44)02. (0) (U,,, EU 0_044)02 in this study; (----) undoped UO, 151; (-.-I 10, [Sk f- - -) fU,,,,La,,,,)02 [61. (Uw&d,w
J
J/K
C,/J K’ The heat capacities measured on (U,,~,,EuO,,,,)O, and (U0.~&u0.090 10, are shown in figs. 1 and 2, respectively, together with the reference results of undoped UO, and UO, doped with Gd, La and SC previously reported by the authors [5-71. As seen in fig. 1, an anomalous increase in the heat capacity curve of W0.956E~0.044~02 similar to those of (U0,956Gd0,044)OZ and U0.Ys6La,m~,10, is observed above 1150 K. Below 1150 K the baseline heat capacity of (U,,,,,EU~&O~ is nearly equal to that of undoped UO, [5]. The equation for the heat capacity of (U,,,,,Eu,,,,,)O, below
I
1100
Fig. 2. Heat capacity of (U~.~~~Eu~.~)O~.
1150 K is determined eq. (1):
3. Results and discussion
900
(2) As seen in both figures, the onset temperature of the heat-capacity anomaly of UO, doped with various cations differs each other even with the same dopant content, whose reason will be discussed later in this paper. The excess heat capacity was evaluated by subtracting the smoothed base line of heat capacity from the experimental values above the onset temperature. The smoothed base line was determined by the extrapolation of eqs. (1) and (2). Assuming that the excess heat capacity is due to the formation of Frenkel pairs of oxygen, similarly to the cases of Gd-, La- and SC-doped UO, [5-71, the excess heat capacity AC can be expressed as [lo]: AC = (AHr)‘/( X
fiRT2)
exp( - AH,/2RT),
exp(ASr/2R) (3)
256
T. Matsui et al. / Heat capacities and electrical conductiuities
of (U,_ yEu v)O,
where R is gas constant, and AS, and AH, are the entropy and enthalpy for a Frenkel-pair formation, respectively. The enthalpy and entropy for a Frenkelpair formation in NJP,Eu,,)02 obtained in this study are shown in figs. 3 and 4, respectively, together with those of UO, [9,10,13-161, (U,_,Gd,)OZ [Sl, (U, _,,La,)O, bl and NJ,,,,,SC,,.,,~Q ]71 reported previously. The values of the enthalpy (2.3 f 0.9 eV and 1.7 k 0.2 eV) and entropy (69 & 26 Jmol-‘K-’ and 38 Jo:2 Jmol-’ Km’) for a Frenkel-pair formation in QJ~.&%.~M~)O~ and (U,.,,,,Eu,,.~,,,,)O2, respectively, are seen to be not so different from those of UO, doped with other cations, considering the large error in (U, _-vEu, )O,, especially y = 0.044, originated from the least-squares fitting using eq. (3) for the steep increase in the heat-capacity curve over a limited temperature range. This similarity of the AHf and AS, values suggests the presence of the similar origin for the heat-capacity anomaly among doped UOz. As is also seen in these figures, the extrapolation of the values for doped UO, to zero dopant content yields the estimated values for undoped UOz : AH, = 3 eV and AS f = 60 J mol-’ K-‘, which are in good agree-
I
,
Fig. 4. Entropy for defect formation. (0) (U, _,,Eu,fO, in this study with an error bar; (0) (U,_,Gd,)O, [5], (v) W_,La,)O* Ed: (x) KJ”,,,,, Sc,,.,,,,)O, [71: (0) [91, (0) [lOI and CM) [IS]: three values obtained from the excess heat capacity of UO,; (U) calculated value for the formation of an electron-hole pair from the electrical conductivity and Seebeck coefficient [16].
ment with the experimental values of undoped UO, reported so far [9,10,15], implying the same mechanism for the heat-capacity anomaly between doped UOZ and undoped UO,. The estimated value of AH, for undoped UO, in fig. 3 is higher than the enthalpy for an electron-hole pair formation calculated theoretically by Harding et al. (131, but lower than that for a Frenkel pair of oxygen calculated theoretically also by Harding et al. [13]. The estimated value of AS, of = 60 Jmol-’ K-’ for undoped UO, is higher than the value of AS, of an electron-hole pair estimated from the electrical conductivity and the thermoelectric Seebeck coefficient of undoped UO, by Hyland and Ralph [16]. It is noted that the excess heat capacity due to the formation of an electron-hole pair can be expressed as [16]: AC = ( AH;)“/(2Rr2) Fig. 3. Enthalpy for defect formation. (0) (U,_,Eu,)02 in this study with an error bar; (0) (U, _,Gd,)Oz [5]; (VI (71; (A 1 theoretical (U, _,La,)O, 161;(x) (U,.,,0 Sc,,,JO, value for the formation of a Frenkel pair [13]; (a) from neutron-scattering study [14]; (0) [9], (0) [lo] and Cm) [15]: three values obtained from the excess heat capacity of UO,:
xexp( -AH,‘/2RT),
exp(ASf/ZR) (4)
where R is the gas constant, and AH{ and ASi are the enthalpy and entropy for an electron-hole pair formation, respectively. We can see that the value of AH/ equals to AH, in eq. (3) and the value of ASi is 5.8 JK-’ mol-’ higher than AS, in eq. (3). Therefore even if eq. (4) is used instead of eq. (3) for the analysis of the excess heat capacity, the same conclusion above
T. Matsui et al. / Heat capacities and electrical conducticities
mentioned can be obtained, since the difference between the value of AS; and the value of the enthalpy for an electron-hole pair formation estimated by Hyland and Ralph [16] is larger than the case of AS,. The electrical conductivities of (UrP,,Eu,)02 (y = 0.044 and 0.090) were measured in order to detect the occurrence of the electron-hole pair formation. The results are shown in fig. 5 together with those for UO, doped with other cations [6,7] and undoped UO, [8], where the onset temperatures of the anomalous increase in heat capacity are shown by vertical arrows. A slight increase of the slope in the electrical conductivity curve is seen around 1100-1200 K in both samples of (U,_,Eu,)OZ (y = 0.044 and 0.090) similarly to the case of (UO.&c,,.O,O 10,. From the facts that (1) the temperature at which the slope of the conductivity changes is almost independent of the kind of dopant and the dopant content, and is close to that of undoped UO,, (2) the temperature at which the slope changes does not necessarily coincide with the onset temperature of the heat-capacity anomaly, and (3) the increase of the slope is also observed in (U,,,,,,Ti,,,,)O,
251
of (U, _ y Eu,)O,
1600)I
t
,O”0
1
2
3
4
IA31X103/knda/t
Fig. 6. Relation
between
the onset
temperature of the heatin the lattice parameter of doped UO, per mol% of dopant. (0) Eu this study; (0) Gd 151,(0) La 161, (A) SC 171, (*) undoped UO, estimated by the present authors [7].
capacity anomaly CT,) and the change
IO,, both of which showed no heatand(Uo.wJbo.o,o capacity anomaly, the slight increase of the slope is thought to be due to the gradual transition from the extrinsic to intrinsic conduction region. It is, therefore, not likely that the excess heat capacity of (U,_,Eu,)O, is due to the formation of electron-hole pairs. In fig. 6 the onset temperatures of the heat-capacity anomaly of UO, doped with various cations [S-8] are plotted against I Au /, where I Aa / is the lattice parameter change per mol% of dopant in doped UO, calculated from the experimental values of Gd-doped [17], Ladoped [18], SC-doped [19] and Eu-doped UO, [2,19] reported previously. The onset temperature of the heat-capacity anomaly of (U,,,,,Gd,,~,,,)O, was estimated by the present authors from those of
5
10 ' '!
I 20
1;
10&K/T
Fig.
5. Electrical
conductivity
of
UO,
and
doped
1JO,.
(0 -0) (UD.956E~0.04)02 in this study; (o -01 NJO,,,OEu,,,,,)O, in this study; () undoped UO, [S]; (--- - --) (U,l.9,0La0.0,0)02 [61; (-- --)Q,.,,,Sc,,,,,)O, [71; (-. -) (U,,,,,Gd, o73 )02 @I; (-. .-I (U,,,,,Ti,,w,)O, 171; (-. . -) W,,,,,Nb ~.010)02 [71. The arrow shows the onset temperature
of the heat-capacity
anomaly.
(UO.,,,GdO.,,,,)Gz and WO.sssGdO.lO,)G, El. It is seen in this figure that the onset temperature of doped UO, with constant dopant concentration increases with increasing I Au 1, indicating the smaller elastic strain renders the onset temperature of the heat-capacity anomaly lower. The fact that the ionic conductivity of doped fluorite-type oxides (such as (Ce, M)O,, M = Gd, Y and La), where oxygen ion is the predominant mobile species, decreases with increasing I Aha 1 as reviewed by Kim [20], also supports the dependence of the onset temperature upon I Aa I value, since the
258
T. ~ats~i et al. / Heat capacities and electrical coild~ctit?itiesof CC; _ )‘ErQO,
Frenkel pair or Frenkel pair-like defect of oxygen is formed more easily under the condition that makes oxygen ions more mobile. For UO, doped with the same cation, the onset temperature is seen to decrease with increasing dopant concentration in fig. 6. The lower onset temperatures of doped UO, with higher dopant concentrations are related to the lower enthalpy and entropy for defect formation shown in figs. 3 and 4. This may be due to the easiness of the formation of the large numbers of Frenkel pair-like defects by thermally activated motion under the presence of the large amount of trivalent dopants. It is concluded that the anomalous increase in the heat capacity of (U,_,Eu,,)C& observed at relatively low temperatures below 1150 K is thought to be originated from the same mechanisms as those of Cd-, Laand SC-doped UO, and undoped UO,, and that the predominant thermal activated process as the origin of the excess heat capacity is likely to be the formation of
[2] L.N. Grossman, [3] [4] [S] [6] [7] [8] [9] [lo] [ll] [12] [13]
the Frenkel pair-like defect of oxygen. The onset temperatures of the heat-capacity anomaly observed for
[14]
doped UO, increased with increasing the lattice parameter change, suggesting that the larger elastic strain suppress the formation of the Frenkel pair-like defect of oxygen, thus, increases the onset temperature.
[15] 1161 1171 [18]
References [l] U. Berndt, R. Tanamas Chem. 17 (1976) 113.
[19]
and C. Keller, J. Solid State
[20]
J.E. Lewis and D.M. Rooney, J. Nucl. Mater. 21 (1967) 302. T. Ohmichi, S. Fukushima, A. Maeda and H. Watanabe, J. Nucl. Mater. 102 (1981) 40. T. Fujino, K. Ouchi, Y. Mozumi, R. Ueda and H. Tagawa. J. Nucl. Mater. I74 (1990) 92. H. Inaba, K. Naito and M. Oguma, J. Nucl. Mater. 149 (1987) 341. T. Matsui, Y. Arita and K. Naito, J. Radioanal. and Nucl. Chem. 143 (1991) 149. T. Matsui, Y. Arita and K. Naito, Solid State lonics (1991) in print. T. Matsui and K. Naito, J. Nucl. Mater. 138 (19861 19. J.P. Kerrish and D.G. Clifton, Nucl. Technol. 16 (1972) 531. R. Szwarc, J. Phys. Chem. Solids 30 (1969) 705. K. Naito, J. Nucl. Mater. 167 (1989) 30. K. Naito, H. Inaba, M. lshida and K. Seta, J. Phys. El2 (f979) 712. J.H. Harding, P. Masri and A.M. Stoneham, J. Nucl. Mater. 92 (1980) 73. K. Clausen, W. Hayes, J.E. Macdonald and R. Osborn, Phys. Rev. L&t. 52 (1984) 1238. P. Browning, J. Nucl. Mater. 9X (1981) 345. G. Hyland and J. Ralph, High Temp.-High Press. 15 (19831 179. C, Miyake, H. Anada and S. Imoto, J. Nucl. Sci. Technol. 23 (1986) 326. W.B. Wilson, CA. Alexander and A.F. Gerds, J. Inorg. Nucl. Chem. 20 (1961) 242. Y. Hinatsu and T. Fujino, J. Solid State Chem. 62 (1986) 342. D.J. Kim, J. Am. Ceram. Sot. 72 (1989) 1415.
Materials
jOU~l of nuclear
186 (1992) 2.54-258
North-Holland
lnaterials
Heat capacities and electrical conductivities of (U, _,Eu,)02 ( y = 0.044 and 0.090) from 300 to 1550 K Tsuneo Mats&, Toshiaki Kawase and Keiji Naito Department of NucuclearEngineering, Faculty of Engineering, Nagoya Unit:ersity, Furo-cho, Chikusa-ku, Nagoya 464-01, Japan Received
24 May 1991; accepted
4 September
1991
Heat capacities and electrical ~ondu~tivities of (U, _,Eu,)O, ( y = 0.044 and 0.0~) were measured by means of direct heating pulse calorimetry over the temperature range from 300 to 1550 K. An anomalous increase in the heat capacity cuwe of each sample of W~,Eu,)OZ was observed similarly to the cases of (U, _yM,)Oz fM = Gd, La and SC) found previously by the authors. As the increase of the europium content in (U, _,Eu ,)O, from y = 0.044 to 0.090, the onset temperature of an anomalous increase in the heat capacity decreased from about 1150 to 950 K. The values of the enthalpy (AH,) and the entropy for defect formation (A.S,) in (U,~,Eu,)O, were calculated from the excess heat capacity assuming the presence of Frenkel pairs of oxygen, and were found to be similar to those of UOz doped with La, Gd and SC previously obtained by the authors. On the other hand, no anomaly was seen in the electrical conductivjty curve around the onset temperature of the anomalous increase in the heat capacity. It is conducted that the occurrence of the excess heat capacity of (U, _,Eu,)O, originates from the predominant contribution of the formation of Frenkel pair-like defects of oxygen similarly to the cases of UO, doped with other trivalent cations. The difference in the onset temperatures of (U, _,Eu,)O, from those of UO, doped with other trivalent cations was thought to be originated from that of the elastic strain induced by the lattice parameter change.
1. Introduction Europium-doped UO, is expected to be used as a burnable poison fuel for higher burnups as well as gadolin~um-doped UO, [ 11.The nonstoi~hiometric region of the fluorite-type solid solution (U, _vE~v)02ir has been determined from the variation of the lattice constant versus composition by some inverstigators [24]. The oxygen potentials of (U,_,Eu,)O,+, were recently measured as a function of x and y values by Fujino et al. [4]. The heat capacity of (UI_,,Euy)O,, which is one of the most important properties of fuel materials to evaluate their thermal stabilities, has not been measured yet. The heat capacities of @J_,M,)O, CM = Cd [5], La [6], SC [7], Ti [7] and Nb [7]) have been measured in the temperature range from 300 to 1500 K by the authors. An anomalous increase in the heat capacity of each sample of UO, doped with trivalent cations such as Gd, La and SC was observed at temperatures from about 700 to 1300 K depending on the kind of dopant and its concentration. This anomalous increase in the ~22-3llS/92/$05.00
0 1992 - Elsevier
Science
Publishers
heat capacity of doped UO, was interpreted as due to the formation of Frenkel pair-like defects of oxygen by the authors [S-S] similarly to the case of UO, [9-111. In this study, the heat capacities and the electrical conductivities of (U,_,Eu,)O, (y = 0.044 and 0.090) were measured simultaneously from 300 to 1550 K by means of direct heating pulse calorimetry to investigate the origin of excess heat capacity of (U,..,.Eu,)O, in comparison with the results of (U,_,GdY)02, W_,,,La,,)Oz and (U, _,Sc,)Oz.
2. Experimental The mixture of Eu,O, and UO, powder was shaped into a cylindrical rod of about 7 mm in diameter and about 50 mm in length, using an evacuated rubber press with a hydrostatic pressure of about 400 MPa. The cylindrical rod thus prepared was sintered and homogenized at 1573 K for 7 days in an Ar gas flow and then at 1273 K for 1 day in a hydrogen gas flow so as to obtain the stoichiometric composition (O/M =
B.V. All rights reserved
255
T. Matsui et al. / Heat capacities and electrical conductivities of (U, _ yEu,)O, 2.00&0.01, M = U + Eu) according to the thermogravimetric study on (U,_,EU,)O~+~ by Fujino et al. [4]. This sintering and homogenizing process was repeated several times. X-ray diffraction analysis indicated a single fluorite phase for each sample. The heat capacity and the electrical conductivity were measured simultaneously by a direct heating pulse calorimeter, of which details have been given elsewhere [12]. In this calorimeter, the temperature of the sample rod was varied from room temperature to 1550 K by an external Pt heater, and after getting a constant temperature, a current pulse was supplied to both the sample rod and the double cylindrical molybdenum thermal shields simultaneously so as to obtain the small temperature rise. The electric potential drop, the current and the temperature rise of the sample rod were measured to obtain the heat capacity and the electrical conductivity.
I
50’ I 300
500
700
1500
1300
EU O~Ow)Oz in this study; fUw,,Gd,.,,,
10,
CP
1 undoped
(01
UOz
[53;
bl; (-- - -_)(U,,,,LaO,uuoIO, 161; (-. wM,~c”.“Y”)oz [71. by the least-squares
RJ,,,, f-,
-)
. . .)
method as
mol-’ = 80.663 + 6.1730 x 10-3(7-/N) - 1.7623 x 10h(l”,‘K)-2
(300 5 Z-/K I 1150).
(1) anomalous increase in the heat capacity of (U~~.~,~EU~.~IO, is also seen above 950 K in fig. 2. The equation for the heat capacity of (U~~.~,~~Eu~.~~)O~ below 950 K is given by the least-squares method as eq. (2)
An
C,/J
K- ’ mol -’ = 80.942 + 4.8856 + IO-“(T/K) -1.9524x
106(T/K)-2
(300 I T/K I 950).
110
5oL 303
,
WI
r
m
,
f 9%
I
1
1 loo
1
I
1300
I
00
,
15co
T/K
Fig. 1. Heat capacity of (U0,956E~0,0,44)02. (0) (U,,, EU 0_044)02 in this study; (----) undoped UO, 151; (-.-I 10, [Sk f- - -) fU,,,,La,,,,)02 [61. (Uw&d,w
J
J/K
C,/J K’ The heat capacities measured on (U,,~,,EuO,,,,)O, and (U0.~&u0.090 10, are shown in figs. 1 and 2, respectively, together with the reference results of undoped UO, and UO, doped with Gd, La and SC previously reported by the authors [5-71. As seen in fig. 1, an anomalous increase in the heat capacity curve of W0.956E~0.044~02 similar to those of (U0,956Gd0,044)OZ and U0.Ys6La,m~,10, is observed above 1150 K. Below 1150 K the baseline heat capacity of (U,,,,,EU~&O~ is nearly equal to that of undoped UO, [5]. The equation for the heat capacity of (U,,,,,Eu,,,,,)O, below
I
1100
Fig. 2. Heat capacity of (U~.~~~Eu~.~)O~.
1150 K is determined eq. (1):
3. Results and discussion
900
(2) As seen in both figures, the onset temperature of the heat-capacity anomaly of UO, doped with various cations differs each other even with the same dopant content, whose reason will be discussed later in this paper. The excess heat capacity was evaluated by subtracting the smoothed base line of heat capacity from the experimental values above the onset temperature. The smoothed base line was determined by the extrapolation of eqs. (1) and (2). Assuming that the excess heat capacity is due to the formation of Frenkel pairs of oxygen, similarly to the cases of Gd-, La- and SC-doped UO, [5-71, the excess heat capacity AC can be expressed as [lo]: AC = (AHr)‘/( X
fiRT2)
exp( - AH,/2RT),
exp(ASr/2R) (3)
256
T. Matsui et al. / Heat capacities and electrical conductiuities
of (U,_ yEu v)O,
where R is gas constant, and AS, and AH, are the entropy and enthalpy for a Frenkel-pair formation, respectively. The enthalpy and entropy for a Frenkelpair formation in NJP,Eu,,)02 obtained in this study are shown in figs. 3 and 4, respectively, together with those of UO, [9,10,13-161, (U,_,Gd,)OZ [Sl, (U, _,,La,)O, bl and NJ,,,,,SC,,.,,~Q ]71 reported previously. The values of the enthalpy (2.3 f 0.9 eV and 1.7 k 0.2 eV) and entropy (69 & 26 Jmol-‘K-’ and 38 Jo:2 Jmol-’ Km’) for a Frenkel-pair formation in QJ~.&%.~M~)O~ and (U,.,,,,Eu,,.~,,,,)O2, respectively, are seen to be not so different from those of UO, doped with other cations, considering the large error in (U, _-vEu, )O,, especially y = 0.044, originated from the least-squares fitting using eq. (3) for the steep increase in the heat-capacity curve over a limited temperature range. This similarity of the AHf and AS, values suggests the presence of the similar origin for the heat-capacity anomaly among doped UOz. As is also seen in these figures, the extrapolation of the values for doped UO, to zero dopant content yields the estimated values for undoped UOz : AH, = 3 eV and AS f = 60 J mol-’ K-‘, which are in good agree-
I
,
Fig. 4. Entropy for defect formation. (0) (U, _,,Eu,fO, in this study with an error bar; (0) (U,_,Gd,)O, [5], (v) W_,La,)O* Ed: (x) KJ”,,,,, Sc,,.,,,,)O, [71: (0) [91, (0) [lOI and CM) [IS]: three values obtained from the excess heat capacity of UO,; (U) calculated value for the formation of an electron-hole pair from the electrical conductivity and Seebeck coefficient [16].
ment with the experimental values of undoped UO, reported so far [9,10,15], implying the same mechanism for the heat-capacity anomaly between doped UOZ and undoped UO,. The estimated value of AH, for undoped UO, in fig. 3 is higher than the enthalpy for an electron-hole pair formation calculated theoretically by Harding et al. (131, but lower than that for a Frenkel pair of oxygen calculated theoretically also by Harding et al. [13]. The estimated value of AS, of = 60 Jmol-’ K-’ for undoped UO, is higher than the value of AS, of an electron-hole pair estimated from the electrical conductivity and the thermoelectric Seebeck coefficient of undoped UO, by Hyland and Ralph [16]. It is noted that the excess heat capacity due to the formation of an electron-hole pair can be expressed as [16]: AC = ( AH;)“/(2Rr2) Fig. 3. Enthalpy for defect formation. (0) (U,_,Eu,)02 in this study with an error bar; (0) (U, _,Gd,)Oz [5]; (VI (71; (A 1 theoretical (U, _,La,)O, 161;(x) (U,.,,0 Sc,,,JO, value for the formation of a Frenkel pair [13]; (a) from neutron-scattering study [14]; (0) [9], (0) [lo] and Cm) [15]: three values obtained from the excess heat capacity of UO,:
xexp( -AH,‘/2RT),
exp(ASf/ZR) (4)
where R is the gas constant, and AH{ and ASi are the enthalpy and entropy for an electron-hole pair formation, respectively. We can see that the value of AH/ equals to AH, in eq. (3) and the value of ASi is 5.8 JK-’ mol-’ higher than AS, in eq. (3). Therefore even if eq. (4) is used instead of eq. (3) for the analysis of the excess heat capacity, the same conclusion above
T. Matsui et al. / Heat capacities and electrical conducticities
mentioned can be obtained, since the difference between the value of AS; and the value of the enthalpy for an electron-hole pair formation estimated by Hyland and Ralph [16] is larger than the case of AS,. The electrical conductivities of (UrP,,Eu,)02 (y = 0.044 and 0.090) were measured in order to detect the occurrence of the electron-hole pair formation. The results are shown in fig. 5 together with those for UO, doped with other cations [6,7] and undoped UO, [8], where the onset temperatures of the anomalous increase in heat capacity are shown by vertical arrows. A slight increase of the slope in the electrical conductivity curve is seen around 1100-1200 K in both samples of (U,_,Eu,)OZ (y = 0.044 and 0.090) similarly to the case of (UO.&c,,.O,O 10,. From the facts that (1) the temperature at which the slope of the conductivity changes is almost independent of the kind of dopant and the dopant content, and is close to that of undoped UO,, (2) the temperature at which the slope changes does not necessarily coincide with the onset temperature of the heat-capacity anomaly, and (3) the increase of the slope is also observed in (U,,,,,,Ti,,,,)O,
251
of (U, _ y Eu,)O,
1600)I
t
,O”0
1
2
3
4
IA31X103/knda/t
Fig. 6. Relation
between
the onset
temperature of the heatin the lattice parameter of doped UO, per mol% of dopant. (0) Eu this study; (0) Gd 151,(0) La 161, (A) SC 171, (*) undoped UO, estimated by the present authors [7].
capacity anomaly CT,) and the change
IO,, both of which showed no heatand(Uo.wJbo.o,o capacity anomaly, the slight increase of the slope is thought to be due to the gradual transition from the extrinsic to intrinsic conduction region. It is, therefore, not likely that the excess heat capacity of (U,_,Eu,)O, is due to the formation of electron-hole pairs. In fig. 6 the onset temperatures of the heat-capacity anomaly of UO, doped with various cations [S-8] are plotted against I Au /, where I Aa / is the lattice parameter change per mol% of dopant in doped UO, calculated from the experimental values of Gd-doped [17], Ladoped [18], SC-doped [19] and Eu-doped UO, [2,19] reported previously. The onset temperature of the heat-capacity anomaly of (U,,,,,Gd,,~,,,)O, was estimated by the present authors from those of
5
10 ' '!
I 20
1;
10&K/T
Fig.
5. Electrical
conductivity
of
UO,
and
doped
1JO,.
(0 -0) (UD.956E~0.04)02 in this study; (o -01 NJO,,,OEu,,,,,)O, in this study; () undoped UO, [S]; (--- - --) (U,l.9,0La0.0,0)02 [61; (-- --)Q,.,,,Sc,,,,,)O, [71; (-. -) (U,,,,,Gd, o73 )02 @I; (-. .-I (U,,,,,Ti,,w,)O, 171; (-. . -) W,,,,,Nb ~.010)02 [71. The arrow shows the onset temperature
of the heat-capacity
anomaly.
(UO.,,,GdO.,,,,)Gz and WO.sssGdO.lO,)G, El. It is seen in this figure that the onset temperature of doped UO, with constant dopant concentration increases with increasing I Au 1, indicating the smaller elastic strain renders the onset temperature of the heat-capacity anomaly lower. The fact that the ionic conductivity of doped fluorite-type oxides (such as (Ce, M)O,, M = Gd, Y and La), where oxygen ion is the predominant mobile species, decreases with increasing I Aha 1 as reviewed by Kim [20], also supports the dependence of the onset temperature upon I Aa I value, since the
258
T. ~ats~i et al. / Heat capacities and electrical coild~ctit?itiesof CC; _ )‘ErQO,
Frenkel pair or Frenkel pair-like defect of oxygen is formed more easily under the condition that makes oxygen ions more mobile. For UO, doped with the same cation, the onset temperature is seen to decrease with increasing dopant concentration in fig. 6. The lower onset temperatures of doped UO, with higher dopant concentrations are related to the lower enthalpy and entropy for defect formation shown in figs. 3 and 4. This may be due to the easiness of the formation of the large numbers of Frenkel pair-like defects by thermally activated motion under the presence of the large amount of trivalent dopants. It is concluded that the anomalous increase in the heat capacity of (U,_,Eu,,)C& observed at relatively low temperatures below 1150 K is thought to be originated from the same mechanisms as those of Cd-, Laand SC-doped UO, and undoped UO,, and that the predominant thermal activated process as the origin of the excess heat capacity is likely to be the formation of
[2] L.N. Grossman, [3] [4] [S] [6] [7] [8] [9] [lo] [ll] [12] [13]
the Frenkel pair-like defect of oxygen. The onset temperatures of the heat-capacity anomaly observed for
[14]
doped UO, increased with increasing the lattice parameter change, suggesting that the larger elastic strain suppress the formation of the Frenkel pair-like defect of oxygen, thus, increases the onset temperature.
[15] 1161 1171 [18]
References [l] U. Berndt, R. Tanamas Chem. 17 (1976) 113.
[19]
and C. Keller, J. Solid State
[20]
J.E. Lewis and D.M. Rooney, J. Nucl. Mater. 21 (1967) 302. T. Ohmichi, S. Fukushima, A. Maeda and H. Watanabe, J. Nucl. Mater. 102 (1981) 40. T. Fujino, K. Ouchi, Y. Mozumi, R. Ueda and H. Tagawa. J. Nucl. Mater. I74 (1990) 92. H. Inaba, K. Naito and M. Oguma, J. Nucl. Mater. 149 (1987) 341. T. Matsui, Y. Arita and K. Naito, J. Radioanal. and Nucl. Chem. 143 (1991) 149. T. Matsui, Y. Arita and K. Naito, Solid State lonics (1991) in print. T. Matsui and K. Naito, J. Nucl. Mater. 138 (19861 19. J.P. Kerrish and D.G. Clifton, Nucl. Technol. 16 (1972) 531. R. Szwarc, J. Phys. Chem. Solids 30 (1969) 705. K. Naito, J. Nucl. Mater. 167 (1989) 30. K. Naito, H. Inaba, M. lshida and K. Seta, J. Phys. El2 (f979) 712. J.H. Harding, P. Masri and A.M. Stoneham, J. Nucl. Mater. 92 (1980) 73. K. Clausen, W. Hayes, J.E. Macdonald and R. Osborn, Phys. Rev. L&t. 52 (1984) 1238. P. Browning, J. Nucl. Mater. 9X (1981) 345. G. Hyland and J. Ralph, High Temp.-High Press. 15 (19831 179. C, Miyake, H. Anada and S. Imoto, J. Nucl. Sci. Technol. 23 (1986) 326. W.B. Wilson, CA. Alexander and A.F. Gerds, J. Inorg. Nucl. Chem. 20 (1961) 242. Y. Hinatsu and T. Fujino, J. Solid State Chem. 62 (1986) 342. D.J. Kim, J. Am. Ceram. Sot. 72 (1989) 1415.