Journal of Nuclear and Radiochemical Sciences, Vol. 10, No.1, pp. 19-26, 2009

Heat Capacity and Thermal Expansion of Uranium-Gadolinium Mixed Oxides
R. Venkata Krishnan, G. Panneerselvam, P. Manikandan, M.P. Antony, and K. Nagarajan*
Fuel Chemistry Division, Indira Gandhi Centre for Atomic Research, Kalpakkam-603 102, Tamil Nadu, India
Received: January 16, 2009; In Final Form: May 15, 2009
Uranium-gadolinium mixed oxides of four different compositions, (U1-y Gdy) O2±x (y = 0.1, 0.2, 0.5, and 0.8), weresynthesized. Single-phase fluorite structure was observed for the compositions (U1-y Gdy) O2±x (y = 0.1, 0.2, and0.5). The room temperature lattice constants measured for (U0.9 Gd0.1) O2.02, (U0.8 Gd0.2) O2.00, and (U0.5 Gd0.5) O1.98
are 0.5463, 0.5454, and 0.5433 nm, respectively. Heat capacity measurements in the temperature range 298 – 800
K were carried out using a differential scanning calorimetry. Considerable anomalous increases in the heat capacity values were observed for compositions (U1-y Gdy) O2±x with y = 0.1, 0.2, and 0.5. The heat capacity values of(U0.9 Gd0.1) O2.02, (U0.8 Gd0.2) O2.00, and (U0.5 Gd0.5) O1.98 at 298 K are 63.5, 61.1, and 65.7, respectively. Thermal
expansion characteristics of (U0.9 Gd0.1) O2.02, (U0.8 Gd0.2) O2.00, and (U0.5 Gd0.5) O1.98 were studied using a high temperature X-ray diffraction in the temperature range 298 – 1973 K.

1. Introduction
Gadolinium is one of the major fission products and its oxide
forms solid solutions with uranium. Thermodynamic properties, such as heat capacity, Gibbs free energy etc, of the (U, Gd)oxides are required for understanding the oxide fuel behaviour
during irradiation and also to understand the chemical state ofgadolinium in the fuel.
It has been observed1,2 that the heat capacity of UO2 increases
rapidly from about 1500 K and becomes more than twice theDulong-Petit value near the melting temperature. This anomalous behavior has been given various interpretation as due toformation of Frenkel pairs of oxygen,3 electronic excitation4-6
etc. It will be interesting to check whether (U, Gd) O2 solid
solution also shows anomalous increase in heat capacity like
UO2. Considerable discrepancy has been found in the literature
regarding the high temperature heat capacity anomalies
observed for Gd doped UO2. Inaba et al7 measured heat capacities of UO2 doped with GdO1.5 with Gd contents ranging from
4.4 to 14.2 mol% by direct heating pulse calorimetry andreported anomalous steep increase in the heat capacity withonset temperatures ranging from 800 to 1200 K. They also
reported that the onset temperature of heat capacity anomaly
decreases with increase in Gd content. Arita et al8 and Matsui
et al9-11 have also made similar observations on their measurements regarding the heat capacity of uranium oxide doped withoxides of lanthanides obtained by direct heating pulse calorimetry.
Amaya et al12,13 measured the heat capacity of (U, Gd) O2
with Gd contents ranging from 0 to 27% by differential scanning calorimetry in the temperature range 325 to 1673 K andreported no anomalous increase in the heat capacity in the temperature range of measurement. Takahashi et al14 measured theheat capacity of UO2 doped with Gd2O3 ranging from 7.5 mol%to 14.2 mol% using drop calorimetry in the temperature range
400 – 1500 K and reported that such thermal anomalies were
not found in the heat capacities. They also reported that theheat-capacity values are close to the ones computed using
Neumann-Kopp’s law, whereas the measured heat capacity values of Amaya et al are 3 – 4% lower than the values computed
using Neumann-Kopp’s additivity rule. The aim of the present*Corresponding author. E-mail: knag@igcar.gov.in Fax: (+91)
44-27480065

study is to investigate the existing discrepancy in the literaturedata. Measurements of heat capacities of (U1-y Gdy) O2±x (y =0.1, 0.2, and 0.5) were carried out using differential scanningcalorimeter in the temperature range 298 – 800 K.
To the best of our knowledge, high temperature X-ray diffraction (HTXRD) based lattice thermal expansion data for (U,Gd) mixed oxides are not available in the literature. Therefore,HTXRD based thermal expansion measurements were performed on (U1-y Gdy) O2±x (y = 0.1, 0.2, and 0.5) in the temperature range 298 to 1973 K. The results of the heat capacity andthermal expansion measurements are discussed in this paper.
2. Experimental
2.1. Sample preparation. UO2 of nuclear grade purity supplied by Nuclear Fuel Complex, Hyderabad and Gd 2 O3 of
99.9% purity supplied by M/s. Indian Rare Earths were used
for preparing the samples. Solid solutions of (U1-y Gdy) O2±x
were prepared by combustion synthesis using citric acid as fuel.
UO2 was heated in air at 873 K for 6 h to convert it to U3O8.
Gd2O3 was heated in air at 673 K to remove any adsorbed moisture. Stiochiometric amounts of U3O8 and Gd2O3 were taken
and dissolved in nitric acid by heating at around 353 K. Citricacid was then added to the nitrate solution and mixed to get aclear solution. The mixture was then heated on a hot plate at
673 K. Combustion of the mixture took place with a flame.
The resultant fine powder was calcined at 1073 K in air for 4 h
to remove carbonaceous material from the sample. The resultant fine powder was compacted into pellets of 5 mm diameterusing a hydraulic press. The pellets were heated at 1873 K in atungsten mesh furnace for 6 h. Before heating the samples, thefurnace was evacuated to 10 -3 mbar and filled with ultra highpure Ar+8% H 2 gas mixture three times. The heating of thesample pellets was done under flowing Ar+8% H2 gas mixture.
The samples prepared were stored in an argon atmosphereglove box containing less than 20 ppm of moisture and oxygento prevent oxidation of the sample.
2.2. Sample characterization.
2.2.1. Compositional characterization. The composition of
U and Gd in the samples was determined by high performanceliquid chromatography (HPLC) and inductively coupled plasma
atomic emission spectroscopy (ICP-AES) technique.
HPLC technique. A Jasco model HPLC system was used in
the present study. The instrument consists of a sample injector© 2009 The Japan Society of Nuclear and Radiochemical Sciences
Published on Web 06/30/2009

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Krishnan

J. Nucl. Radiochem. Sci., Vol. 10, No. 1, 2009

(Rheodyne, 20 µ L sample loop), reverse phase C18 column,
and a UV-visible spectrophotometric detector. The signal fromthe detector is processed using Borwin software for peak area,
peak height, and retention time measurements. U and Gd in
the samples were detected by a post-column derivitisation technique using arsenazo (III) as the post-column complexing agent
and the complexes were monitored at 665 nm. Solution of αhydroxy isobutyric acid (HIBA) in 7% methanol was used as
the eluent for the separation of metal ions. The pH of themobile phase was adjusted to 3 with dilute ammonia. Standard
samples of U and Gd was initially prepared by dissolving stoichiometric quantities of U3 O8 and Gd 2 O3 in nitric acid anddiluting to a concentration range of 5 – 100 ppm. Similarly
mixed oxide samples were also dissolved in nitric acid anddiluted. The concentration of U and Gd in the samples wasdetermined from the calibration plots of the standard samples.
ICP-AES technique. Standard samples of U and Gd in therange of 5 – 25 ppm were prepared as explained above. The
wavelengths used for U and Gd detection were 385.958 nm and342.247 nm, respectively. The concentration of U and Gd in
the samples was determined using calibration plots.
2.2.2. Structural Characterization. Pellets of (U0.9 Gd0.1),(U0.8 Gd0.2), (U0.5 Gd0.5), and (U0.2 Gd0.8) mixed oxides as well as
those of pure Gd 2O3 and UO2.00 from the same lot used for adifferential scanning calorimetry (DSC) measurements were
powdered and characterized by X-ray diffraction (XRD). The
XRD patterns were recorded in the range, 10°<2θ<80°. Peakpositions and the relative intensities were computed using apeak-fit program of the Philips X’pert Plus® software. The calibration of the diffractometer was carried out using silicon and
α-alumina standards. The XRD patterns of Gd2O3 and UO2.00
agree well with the literature data.15,16
The room temperature XRD patterns of UO2 , Gd 2O3, and(U1-y Gdy) O2±x (y = 0.1 – 0.8) are shown in Figure 1. The lattice parameter (a) in each case was estimated by considering
the eight major reflections of the CaF 2 structure. Finally aneffective high angle corrected lattice parameter at each temperature was obtained by the standard Nelson-Riley extrapolation
procedure. The solid solutions (U1-y Gdy) O2±x (y = 0.1, 0.2, and0.5) prepared have a well crystallized single phase fluorite
structure, whereas (U0.2 Gd 0.8 ) O1.71 showed in addition fainthexagonal Gadolinia lines (HGD).17 Beals et al18 also madesimilar observation and reported that in (U1-y Gdy) O2±x system,
single phase fluorite-type structure was observed until for y =0.54 but an additional monoclinic Gd2O3 phase was present insolid solution containing higher Gd. However, in the present
study the additional phase is hexagonal Gd2O3. In the reported
pseudo-binary phase diagram of UO2 – GdO1.5 by Aitken et al,19a hexagona l phase of composit ion cor respond i ng toUO2·3Gd2O3 has been reported. But in our samples and also inthe study of Beals et al,18 no such hexagonal phase wasobserved. The room temperature lattice parameter of UO 2 ,Gd2O3, (U0.9 Gd0.1) O2.02, (U0.8 Gd0.2) O2.00, and (U0.5 Gd0.5) O1.98
are given in Table 1.
2.2.3. Determination of O/M ratio. The O/M ratios of themixed oxides were determined by spectrophotometricmethod.20 The urania-gadolinia samples were dissolved inconcentrated phosphoric acid (2 – 3 mg/mL). U4+ was determined by absorbance at 540 nm and U6+ by absorption at 315
nm.14 Assuming that the Gd in the solid solution is present
only in +3 state and oxygen in –2 state, the O/U ratio wasdetermined as follows.
O/U = (3nU(VI) +2nU(IV)) / (nU(VI) +nU(IV) )(1)

where n U(VI) and n U(IV) are number of moles of U(VI) andU(IV), respectively. The O/M of (U1-y Gdy) O2±x is calculated
as follows

Figure 1. Room temperature XRD patterns of UO2, Gd2O3, and (U1-yGdy) O2±x.

TABLE 1: X-ray and chemical analysis of urania-gadolinia
solid solutions
Compound

O/U

O/M

Latticeparameter(nm)

Phasespresent

UO2.002.00

2.00

0.5468

FCC

Gd2O3

-

1.50

0.5396

FCC(U0.9 Gd0.1) O2.02

2.07

2.02

0.5463

FCC(U0.8 Gd0.2) O2.00

2.13

2.00

0.5454

FCC(U0.5 Gd0.5) O1.98

2.47

1.98

0.5433

FCC(U0.2 Gd0.8) O1.71

2.53

1.71

O/M = (1 - y)(O/U) + 1.5 y

FCC+
Hexagonal
Gadolinia
(HGD)

(2)

The estimated O/M, lattice parameter and the phases present
in the solid solution are listed in Table 1.
2.3. Calorimetric measurements. A heat flux type differential scanning calorimeter, model number DSC821e/700 of
M/s. Mettler Toledo GmbH, Switzerland was used in thisstudy. Temperature, heat, and τ-lag calibrations were carriedout as explained in our previous publication.21 Heat rate calibration was performed prior to each heat capacity measurementwith a disc of sapphire supplied by M/s. Mettler Toledo GmbHand using the heat capacity data of sapphire from NIST, USA.
Heat capacity measurements were carried out in the temperature range 298 – 800 K. To remove any adsorbed moisture on
the sample, the samples were heated to 573 K before starting
the experiment. About 100 – 150 mg of samples in the form ofpellet were weighed accurately and hermetically sealed in 40µL Al-pans. The flow rate of the purge gas (ultra high pureargon) was 50 mL min-1. A three segment-heating program, as
explained in our previous work,21 was used for heat capacity
measurements. Each heat capacity measurement consisted ofthree runs, namely, a blank run with empty pans on the sample
and the reference sides, a sapphire run with empty pan on thereference side and a pan with sapphire on the sample side, andfinally a sample run with empty pan on the reference side andthe pan with sample on the sample side.
2.4. Thermal expansion studies. The thermal expansion
characteristics of the samples were studied using HTXRD in
the temperature range 298 – 1973 K. The HTXRD studies

Heat Capacity and Thermal Expansion of Uranium-Gadolinium Mixed®

were performed in a Philips-X’pert MPD system equippedwith the Büehler® high vacuum heating stage. Typical instrument related parameters were: operating voltage of 40 kV; current of 45 mA for the X-ray tube; scan speed of 0.02° s-1 with acounting time of 6 s per step; an angular range (2θ) of 20 to80°. The heating stage consisted of a thin (~80 µm), heat-resistant tantalum foil, on top of which the sample was placed. The
temperature was measured by a W-Re thermocouple, which
was spot-welded to the bottom of the tantalum heater. The
temperature was controlled to an accuracy of about ± 1 K.
Diffraction studies were performed using CuKα radiation in
the Bragg-Brentano geometry in steps of 100 K up to 1973 K.
A heating rate of 1 K min-l and a holding time of 60 min ateach temperature of measurement were adopted. The specimen stage was purged with high purity helium three times
before the start of every experimental run and a vacuum levelof about 10 -5 mbar was maintained throughout the experiment.
Acquisition and preliminary analysis of data were performedby the Philips X’pert Plus® software, although at a latter stage,
an independent processing of the raw data for a precise determination of the peak position was resorted to. Room temperature XRD pattern was again taken after the completion ofthermal expansion measurements to confirm that no oxidationof the sample had taken place during measurement.

J. Nucl. Radiochem. Sci., Vol. 10, No. 1, 200921

tive standard deviations are given in Table 6. The measured
heat capacity values of the three different mixed oxide samples
were fitted to obtain the polynomial in temperature by a leastsquares method. The standard errors of the fits are also listed
in Table 6. The measured heat capacity of the mixed oxides
along with the fitting results is shown in Figures 3 – 5. The
heat capacity data estimated by Neumann-Kopp’s law using thepresent heat capacity data of Gd 2 O3 and the literature heat
capacity data24 of UO2 are also given in Figures 3 – 5. The corrections in the heat capacity values for non-stoichiometry weremade using the method described by Mills et al.25
Cp,m (UO2) = [(3 / (3 + x)] Cp,m (UO2+x)(4)

From the heat capacity data other thermodynamic functions
such as enthalpy, entropy, and Gibbs energy functions werecomputed and given in Table 3 – 5. The S298 data of (U1-y Gdy)

3. Results
3.1. Heat capacity of Gd 2O3 and UO2 . Heat capacity of
UO2 was measured and reported in our previous publication.21
Heat capacity values of Gd2O3 measured by DSC in the present
work and given in Table 2 are the mean of nine measurements.
The relative standard deviations are in the range of 1 – 3%.
The measured heat capacity data of Gd2O3 were fitted to obtainthe following polynomial in temperature by the least squares
method.
Cp,m (J K-1 mol-1) = 109.53 + 0.0259 T –734459.87 T -2 (298 – 820)

(3)

Figure 2. Heat capacity data of Gd2O3.

The standard error of the fit is 0.9 J K-1 mol-1. The measured
data along with the fit values are shown in Figure 2. The heat
capacity data of Gd 2 O3 reported in the literature22 are also
shown in Figure 2. As can be seen, the present data are 1 – 3%
higher than that of the recommended values of Pankratz. 22
Konings et al 23 measured low temperature (4 – 380 K) heat
capacity of monoclinic Gd2O3 using an adiabatic calorimeter.
The present value of Cp,m at 298 K of Gd2O3 (109.8 J K-1 mol-1)
is about 2% higher than that of Konings et al (108.1 J K-1
mol-1).23
3.2. Heat capacity of (U1-y Gdy) O2±x. Heat capacity of (U1-yGdy) O2±x (y = 0.1, 0.2, and 0.5) measured by DSC in the present work and given in Table 3 – 5 respectively are the mean ofnine measurements. The fitting equations along with the rela-

TABLE 3: Thermodynamic functions for (U0.9 Gd0.1) O2.02

TABLE 2: Heat capacity data of Gd2O3

TABLE 4: Thermodynamic functions for (U0.8 Gd0.2) O2.00

T (K)Cp,m (J K-1 mol-1)
22

MeasuredFit

Literature value

T(K)Cp,m (J K -1 mol-1) HT – H298
-1

GT – H298/T

ST
-1

-1

(J mol ) (J K mol ) (J K -1 mol-1)

Measured

Fit

298

63.5

63.2

0

78.5

-78.5

300

64.1

63.6

127

78.9

-78.5

400

72.5

73.1

7041

98.7

-81.1

500

76.3

76.7

14541

115.5

-86.4

600

79.2

79.3

22322

129.7

-92.5

700

82.6

82.4

30368

142.1

-98.7

800

85.4

86.7

38769

153.4

-104.9T(K)Cp,m (J K -1 mol-1) HT – H298
MeasuredFit-1

GT – H298/T

ST
-1

-1

(J mol ) (J K mol ) (J K -1 mol-1)

298

109.8

109.0

105.49

298

61.1

61.1

0

79.3

-79.3

300

110.0

109.1

105.75

300

61.9

61.3

122

79.8

-79.3

400

114.8

115.3

114.63

400

66.6

66.8

6566

98.3

-81.9

500

119.1

119.5

119.43

500

69.8

69.1

13350

113.5

-86.8

600

122.9

123.0

122.64

600

71.5

71.4

20341

126.3

-92.4

700

127.6

126.2

125.08

700

74.9

74.7

27594

137.5

-98.1

800

129.1

129.1

127.12

800

79.8

79.5

35237

147.8

-103.7

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J. Nucl. Radiochem. Sci., Vol. 10, No. 1, 2009

TABLE 5: Thermodynamic functions for (U0.5 Gd0.5) O1.98
T(K)Cp,m (J K -1 mol-1) HT – H298
MeasuredFit-1

GT – H298/T

ST
-1

-1

(J mol ) (J K mol ) (J K -1 mol -1)

298

65.7

65.7

0

82.2

-82.2

300

66.1

65.8

131

82.6

-82.2

400

69.1

69.5

6927

102.2

-84.9

500

69.6

70.3

13899

117.8

-90.0

600

70.0

71.3

20940

130.7

-95.8

700

72.0

73.4

28115

141.8

-101.7

800

75.1

77.0

35558

151.8

-107.4O2±x required for the computation of entropies were estimatedby Neumann-Kopp’s law using the literature data of S 0298 ofpure Gd2O322 and UO224 including the contribution of entropyof mixing.
3.3. Thermal expansion measurements.
3.3.1. Thermal expansion measurements of UO2 and Gd2O3.
Both UO2 and Gd2O3 have face centered cubic (fcc) lattice. Forfcc lattice, the lattice parameter a is related to the d-spacing by
the following equitationd=aFigure 3. Heat capacity data of (U0.9 Gd0.1) O2.02.

(5)

2

h + k2 + l2

where h, k, l are the Millar indices of the plane. The room
temperature cubic lattice parameter obtained for UO 2 andGd2O3 are 0.5470 and 0.5396 nm, respectively. The room temperature lattice parameters obtained in the present study are ingood agreement with the literature value.15,16 Room temperature XRD patterns for pure UO2 and Gd2O3 are given in Figure
1. The measured temperature dependence of the lattice parameter in the temperature range 298 – 1973 K for UO2 and Gd2O3
are presented in Figure 6. The variation of lattice parameter, a(nm) with temperature (K) for UO2 and Gd2O3 is fitted to a second order polynomial in the temperature interval (T-298) byleast squares and are given by the following expressiona(nm) (UO2) = 0.5458 + 3.0348 × 10 -6 (T − 298)
+ 1.4419 × 10 -10 (T – 298)2(6)a(nm) (Gd2O3) = 0.5391 + 1.3531 × 10 -6 (T − 298)
+ 1.1532 × 10 -10 (T – 298)2(7)

Figure 4. Heat capacity data of (U0.8 Gd0.2) O2.00.

Equations 6 and 7 are used to calculate the mean linear thermal
expansivities and are presented in Table 7. The percentage linear thermal expansions calculated from corrected lattice
parameters are fitted in to second order polynomial and theexpressions are presented below.
Thermal Expansion (%) (UO2) = – 0.20588 + 6.1209 × 10 -4 T +2.6361 × 10 -7 T 2 (298 – 1973)(8)
Figure 5. Heat capacity data of (U0.5 Gd0.5) O1.98.

TABLE 6: Fitting equations of the measured heat capacity data (298 ≤ T/K ≤800)
No.

CompoundFitting equation (J K-1 mol-1)

1(U0.9 Gd0.1) O2.02

124.364 – 0.1213 T – 3009415 T -2 + 0.0001 T 2

2
3(U0.8 Gd0.2) O2.00(U0.5 Gd0.5) O1.98

Standard deviation

Standard error J K-1 mol-1

1 – 2%

0.67

-2

2

1 – 2%

0.77

-2

2

1 – 2%

0.64

107.88 – 0.11156 T – 1992751 T + 0.0001 T
114.0413 – 0.12273 T – 1837744 T + 0.0001 T

Heat Capacity and Thermal Expansion of Uranium-Gadolinium Mixed

23

J. Nucl. Radiochem. Sci., Vol. 10, No. 1, 2009
TABLE 7: HTXRD data of UO2 and Gd2O3
UO2

Figure 6. Lattice parameter as function of temperature of UO 2 ,Gd2O3, and (U1-y Gdy) O2±x (y = 0.1, 0.2, and 0.5).

T(K)

a
(nm)

TE
(%)

298

0.54700.00

373

0.54730.06

473

0.54780.14

573

0.5482

0.23

Gd2O3
α
(10 -6 K-1)

α(10 -6 K-1)

a
(nm)

TE
(%)

7.69

0.5396

0.00

3.78

8.09

0.5397

0.03

4.10

8.61

0.5400

0.07

4.53

9.14

0.5402

0.12

4.96

673

0.54880.33

9.67

0.5405

0.17

5.38

773

0.5493

0.42

10.20

0.5408

0.23

5.81

873

0.5499

0.53

10.72

0.5411

0.29

6.24

973

0.5505

0.64

11.25

0.54150.35

6.67

1073 0.5511

0.75

11.78

0.54180.42

7.091173 0.5518

0.87

12.31

0.54220.49

7.52

1273 0.5524

1.00

12.83

0.54270.57

7.951373 0.5532

1.13

13.36

0.54310.65

8.38

1473 0.5539

1.27

13.89

0.54360.74

8.80

1573 0.5547

1.41

14.41

0.54410.83

9.23

1673 0.5555

1.56

14.94

0.54460.92

9.66

1773 0.5563

1.71

15.47

0.5451

1.02

10.09

1873 0.5572

1.87

16.00

0.5456

1.13

10.51

1973 0.5581

2.03

16.52

0.5462

1.23

10.94

a (nm) [(U0.9 Gd0.1) O2.02] = 0.54523 + 3.1149 × 10 -6 (T – 298)
+ 1.4154 × 10 -9 (T – 298)2 (298 – 1973)(10)

Figure 7. Thermal expansion data of UO2, Gd2O3, and (U1-y Gdy) O2±x(y = 0.1, 0.2, and 0.5).

Thermal Expansion (%) (Gd2O3) = – 0.09378 + 2.5077 × 10 -4 T
+ 2.1372 × 10 -7 T 2 (298 – 1973) (9)The percentage linear thermal expansion of UO2 and Gd 2O3computed from the above fitting equations are presented inTable 7 and are also shown in Figure 7. Good amount of work
regarding thermal expansion of urania have been carried out.2633
Based on them Belle and Berman 34 arrived at a recommended value of thermal expansion characteristics of UO 2 .
The percentage thermal expansion data of UO2 obtained in thepresent study as well as by Belle and Berman34 are illustrated
in Figure 7 as a function of temperature. The measured %thermal expansion is in good agreement with the values recommended by Belle and Berman 34 within ±1%. The % linear
thermal expansion value measured in the present study in thetemperature range from 298 to 1973 K is 2.03; this value compares with 2.04, the recommended values for UO2 by Belle andBerman.34
3.3.2. Thermal expansion measurements on (U1-y Gdy) O2±x.
The measured lattice parameters of (U0.9 Gd 0.1) O 2.02 , (U0.8
Gd0.2) O2.00, and (U0.5 Gd0.5) O1.98 as a function of temperature in
the temperature range 298 – 1973 K are shown in Figure 6 andare also listed in Table 8. The variation of lattice parameter, a(nm) with temperature (K) for (U0.9 Gd 0.1) O2.02 , (U0.8 Gd 0.2 )O2.00, and (U0.5 Gd0.5) O1.98 is fitted to a second order polynomialin the temperature interval (T-298) by a least squares method
and are given by the following expressions,a (nm) [(U0.8 Gd0.2) O2.00] = 0.54435 + 3.2626 × 10 -6 (T – 298)
+ 1.2673 × 10 -9 (T – 298)2 (298 – 1973)(11)a (nm) [(U0.5 Gd0.5) O1.98 ] = 0.54253 + 2.3244 × 10 -6 (T – 298)
+ 1.2917 × 10 -19 (T – 298)2 (298 – 1973).
(12)Equations 10, 11, and 12 are used to calculate the mean linear
thermal expansion of the respective mixed oxides and are presented in Table 8. From the variation of lattice parameters withtemperature, % linear thermal expansion was computed andfitted to the following polynomial in temperature by a leastsquares method,TE (%) [(U0.9 Gd0.1) O2.02] = – 0.1922 + 5.7020
× 10 -4 T + 2.5910 × 10 -7 T 2 (298 – 1973)(13)

TE (%) [(U0.8 Gd0.2) O2.00] = – 0.1985 + 5.9742
× 10 -4 T + 2.2519 × 10 -7 T 2 (298 – 1973)(14)TE (%) [(U0.5 Gd0.5) O1.98 ] = – 0.1985 + 4.2780
× 10 -4 T + 2.377 × 10 -7 T 2 (298 – 1973).

(15)

4. Discussion
As can be seen in Figure 3 representing the measured heat
capacity data of (U0.9 Gd0.1) O2.02, there is considerable anomalous increase in the heat capacity in the region above 550 – 600
K. Inaba et al7 observed the same phenomenon for (U0.899
Gd0.101) O2.001 in the region above 800 K, whereas Takahashi etal14 have found no appreciable anomaly in the heat capacity
curve up to 1500 K for nearly the same composition. Arita et
al8 have measured the heat capacities of UO2 doped with Pr, Zr,
and Ce, in which uranium predominantly exists as a tetravalent

24

Krishnan

J. Nucl. Radiochem. Sci., Vol. 10, No. 1, 2009

TABLE 8: HTXRD data of urania- gadolinia solid solution
T(K)(U0.9 Gd0.1) O2.02(U0.8 Gd0.2) O2.00(U0.5 Gd0.5) O1.98

a (nm)TE (%)α (10 -6 K-1)

a (nm)TE (%)α (10 -6 K-1)

a (nm)TE (%)α (10 -6 K-1)

298
373
473
573
673
773
873
973
1073
1173
1273
1373
1473
1573
1673
1773
1873

0.54630.54660.54700.54750.54800.54850.54900.54960.55020.55080.55150.55220.55290.5536
0.55440.55520.5560

0.00
0.06
0.14
0.22
0.31
0.40
0.50
0.61
0.72
0.83
0.95
1.08
1.21
1.35
1.49
1.63
1.78

7.25
7.63
8.15
8.67
9.19
9.71
10.23
10.74
11.26
11.78
12.30
12.82
13.34
13.85
14.37
14.89
15.41

0.54540.54570.54620.54660.54710.5476
0.5481
0.54870.54930.54990.55050.55110.55180.55250.55320.55400.5548

0.00
0.06
0.13
0.22
0.31
0.40
0.49
0.60
0.70
0.81
0.93
1.05
1.17
1.30
1.43
1.57
1.71

7.32
7.60
8.08
8.55
9.03
9.51
9.99
10.46
10.94
11.42
11.90
12.38
12.85
13.33
13.81
14.29
14.76

0.54330.5436
0.54390.54430.54470.54510.54550.54600.54650.54700.5476
0.5482
0.54880.54940.55000.55070.5514

0.00
0.04
0.11
0.17
0.25
0.32
0.41
0.49
0.58
0.68
0.78
0.89
1.00
1.11
1.23
1.36
1.49

5.70
6.05
6.53
7.00
7.48
7.95
8.43
8.91
9.38
9.86
10.33
10.81
11.28
11.76
12.23
12.71
13.19

1973

0.5563

1.94

15.93

0.5556

1.86

15.24

0.5521

1.62

13.66

state. They did not observe anomalous increase in the heat
capacity up to 1410 K. Also, in our previous work 21 on themeasurement of heat capacity of (U1-y Cey) O2, no such anomalous increase in the heat capacity was observed. Inaba et al7
and Matsui et al9,10 measured heat capacity of UO2 doped withtrivalent cations such as Gd, La, and Eu and observed that theonset temperature of the the heat capacity anomal decreases
with increase in the dopant concentration. Matsui et al10,11 alsomeasured the electrical conductivity of these mixed oxidematerials and observed, however, that the temperatures atwhich the slope of the conductivity curve changes is independent of the dopant and is close to the undoped UO2. Also, thetemperature at which the slope changes in the electrical conductivity curve did not coincide with the onset temperature of
the heat capacity anomaly. Therefore, Matsui et al ruled out
the formation of electron-hole pair being the cause for the heat
capacity anomaly. Instead, he attributed it to the formation of
Frenkel-pair like defects of oxygen. The present observed heat
capacity anomaly might also be due to predominant contribution of formation of Frenkel pairs of oxygen. This is because
the formation of large number of Frenkel-pair defects of oxygen is enabled when UO2 is doped with aliovalent cations (M 3+in this case).7-11 Arita et al8 suggested that doping of trivalentcations to UO2 produces greater complexity of oxygen arrangements, which in turn induces the formation of oxygen defects
resulting in the heat capacity anomaly. The lower onset temperature of the heat capacity anomaly in the present measurement for (U0.9 Gd0.1) O2.02 compared to that of Inaba et al7 fornearly the same composition ((U0.899 Gd0.101) O2.001 may be dueto the larger non-stoichiometry of the present sample comparedto that of Inaba et al.7 The baseline heat capacity of (U0.9 Gd0.1)
O2.02 was obtained from a least squares fitting for the data in
the low temperature region (298 to 500 K) and extrapolated up
to 800 K. The difference between the baseline heat capacity
and that of the measured data (∆Cp) is plotted against temperature for all the solid solution in Figure 8. As can be seen in
Figure 8, the onset of the heat capacity anomaly starts in theregion of 550 – 600 K for (U0.9 Gd0.1) O2.02.

Figure 8. Difference between the baseline and measured heat capacity data (∆Cp) vs T of (y = 0.1, 0.2, 0.5, and 0.8).

Heat capacity data of (U1-y Gdy) O2±x (y ≥ 0.2) available in
the literature are very less. The only measured heat capacity
data are from Amaya et al12,13 on (U0.792 Gd0.208) O2 and (U0.729
Gd0.271) O2. The present data is the first of the kind on the heat
capacity of (U1-y Gd y) O 2 ± x (y ≥ 0.271). As can be seen in
Figures 4 and 5 representing the measured heat capacity dataof (U0.8 Gd0.2) O2.00 and (U0.5 Gd0.5) O1.98 respectively there isconsiderable anomalous increase in the heat capacity values in
the region between 500 – 550 K. The heat capacity of (U0.792
Gd0.208) O2 measured by Amaya et al is also shown in Figure 4
for comparison. As can be seen in Figure 4, unlike the present
measurement on heat capacity of (U0.8 Gd0.2) O2.00, Amaya et al
did not observe any anomalous thermal effects for nearly thesame composition (U0.792 Gd0.208) O2. As observed by Inaba et
al7 and Matsui et al9,10 there is decrease in the onset temperature of the heat capacity anomaly with the increase in dopant
concentration. This observation is also shown in Figure 8.

Heat Capacity and Thermal Expansion of Uranium-Gadolinium Mixed

J. Nucl. Radiochem. Sci., Vol. 10, No. 1, 200925

However, the magnitude of the decrease in the onset temperature of the heat capacity anomaly as a function of dopant concentration is not as steep as that observed by Inaba et al. Also,in the present measurement it is observed that there is no
decrease in the onset temperature of the heat capacity anomal
for (U1-y Gdy) O2±x when y is increased from 0.2 to 0.5.
If E d is the energy needed to form a defect, the number ofdefects nd at any temperature T will be given by a Boltzmann
factornd = n0 exp (-Ed /kT)

(16)

and the specific heat of formation of such defects will be∆Cv = d/dT(nd Ed) = n0Ed2 /kT 2 exp (-Ed /kT)

(17)

Thus, a plot of ln(T 2∆Cv) against 1/T is a straight line with aslope of - Ed /k. Similarly, a plot of ln(T 2∆Cp) against 1/T is astraight line with a slope of -∆Hd /k, where ∆Hd is the enthalpy
of formation of the defect. The plot of ln(T 2∆Cp) against 1/T
for (U0.9 Gd0.1) O2.02, (U0.8 Gd0.2) O2.00, and (U0.5 Gd0.5) O1.98 in
the temperature range 600 – 800 K is given in Figure 9. The∆Hd determined from the slope of the plots for (U0.9 Gd0.1) O2.02,(U0.8 Gd0.2) O2.00, and (U0.5 Gd0.5) O1.98 are 78.5 kJ mol-1 (0.813
eV), 54.5 kJ mol-1 (0.565 eV), and 58.0 kJ mol-1 (0.601 eV),
respectively. The ∆Hd determined in the present study for (U0.9
Gd0.1) O2.02 is in the same range as that computed by Inaba et
al7 (71.2 kJ mol-1, 0.738 eV) for the nearly same composition(U0.899 Gd0.1.01)O2.001. Inaba et al7 also observed decrease in the∆Hd with increase in Gd content for their measurement on (U1-yGdy) O2±x upto y = 0.142. The ∆Hd for y = 0.142 of Inaba et al7
is 53.3 kJ mol-1 (0.552 eV). The determined ∆Hd from the present measurement on y = 0.2 and 0.5 are 0.565 eV and 0.601 eV.
Therefore, the present observation suggests that the decrease in
the ∆Hd with Gd content reaches plateau for Gd content greaterthan 15%. The slight increase in the ∆Hd values for y = 0.5
may be due to the extrapolation and fitting errors.
The heat capacity of (U1-y Gdy) O2±x decreases with increasein y from 0.1 to 0.2. Amaya et al13 attributed the phenomenon
due to the decrease in the contribution of U4+ to excess heat
capacity.13 However, we consider that, with the increase in theconcentration of trivalent dopant Gd, wherein heavier uranium
atoms is replaced by lighter Gd atoms in UO2 lattice as well as,
U4+ is getting oxidized to higher oxidation states such as U5+ or
U6+ to maintain electrical neutrality. Therefore, the phonon
frequencies of (U1-y Gdy) O2±x are expected to be higher thanthat of UO2 leading to lower heat capacity. But, the present
heat capacity value of (U1-y Gdy) O2±x with y = 0.5 is higher thanthat of y = 0.2 at temperatures below 400 K and lower than thatof y = 0.2 at temperatures above 400 K. Amaya et al13 observedthat the measured heat capacity data of (U1-y Gdy) O2±x tend to
decrease with increasing y up to y = 0.208 and increase for y =0.271. Amaya et al13 suggested that the excitation conditions of
the electrons might change with samples containing y > 0.2
compared to that of the samples having lower Gd concentrations because of the low concentration of U4+ ions (<50%).
However, in the present measurement the heat capacity valuesof (U1-y Gdy) O2±x with y = 0.5 are lower than that of y = 0.2 attemperatures above 400 K. This may be explained by the reason that the influence of oxidation of U4+ ions on the decreasein heat capacity overwhelms that of change in excitation conditions of the electrons suggested by Amaya et al13 at temperatures above 400 K.
As can be seen in Figure 10, the room temperature lattice
parameter (a) of (U1-y Gdy) O2±x decrease with increase in dopant concentration. The ionic radius of U4+ with eightfold coordination is 0.1001 nm and that of Gd3+ is 0.1053 nm.35 Though
the smaller U4 + is substituted with larger Gd 3+ ion there isdecrease in the room temperature lattice constant with increase

Figure 9. plot of ln(T 2∆Cp) vs 1/T in the temperature range 600 –800 K.

2±x

2±x

Figure 10. Variation of room temperature lattice constant as a function of Gd concentration.

in Gd content in the solid solution. This is because when U4+ issubstituted with Gd3+ in the UO2 lattice some of the U4+ is oxidized to either U5+ or U6+ in order to maintain electrical neutrality. The ionic radius of U5+ with eight fold co-ordination is
0.088 nm 36 and that of U6 + is 0.086 nm. 35 Therefore, theincrease in lattice constant expected by doping of cation withlarger ionic radius is overwhelmed by decrease in the average
ionic radius of uranium ions due to oxidation, assuming a random distribution of the cations in the cation sub lattice.
Therefore, a net negative change in the lattice constant on
increase in dopant concentration is observed. Ohmichi et al36
computed the da /dy of UO 2 doped with Gd based on theassumption that the U4 + oxidizes entirely to U5 + (da /dy =-0.0173 nm for Gd) or entirely to U6+ (da/dy = -0.0042 nm).
Omichi et al36 also measured room temperature lattice constantof UO2 doped with Gd up to 15 at. % and observed that themeasured da/dy (- 0.0173 nm) is close to that predicted with
U4+ oxidized entirely to U5+. The da/dy in the present measurement is -0.00743 nm, which suggests that U4+ may be oxidized
both to U5+ and U6+, but predominantly to U6+ on doping Gd3+.
5. Summary
1. Four solid solution of urania-gadolinia mixed oxides weresynthesized by combustion synthesis. Chemical compositions were determined by HPLC and ICP-AES. The structural characterization was done using XRD.

26

J. Nucl. Radiochem. Sci., Vol. 10, No. 1, 2009

2. Single phase fluorite structure was observed for (U1-y Gdy)
O2±x (y = 0.1 – 0.5) and for (U0.2 Gd0.8) O1.71 additional fainthexagonal gadolinia lines were observed.
3. The room temperature lattice constant (a) of (U1-y Gdy) O2±x(y = 0.1 – 0.5) decreases linearly with y. The slope da/dy
suggests that U4+ in the UO2 lattice is oxidized predominantly to U6+ on doping with Gd to maintain electrical neutrality.
4. Molar heat capacities were measured for (U1-y Gdy) O2±x (y= 0.1 – 0.5) by differential scanning calorimetry in thetemperature region 298 – 800 K.
5. Considerable anomalous increase in the heat capacity wereobserved for (U1-y Gdy) O2±x with y = 0.2 to 0.5. Also, it
was observed that the onset temperature of the anomalous
increase in the heat capacity decreases with the increase in
Gd content and the above behaviour is attributed to formation of Frenkel pair like defects of oxygen.
6. The enthalpy of defect formation ∆Hd determined from thepresent measurement for (U1-y Gdy) O2±x (y = 0.1) is in thesame range that determined by Inaba et al7 for nearly same
composition.
7. The ∆Hd values decrease with increase in Gd content for(U1-y Gdy) O2±x up to y = 0.15 and remains constant forhigher concentrations of Gd.
8. Thermal expansion measurements were carried out on (U1-yGdy) O2±x (y = 0.1 – 0.5) in the temperature range 298 –1973 K. There are no thermal expansion data of uraniagadolinia mixed oxide and the present data is the first of
the kind.
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