"1901

MASTERA RE-DETERMINATION AND RE-ASSESSMENT OF THE

THERMODYNAMICS OF SUBLIMATION OF URANIUM DIOXIDE

by

R, J, Ackermann and E. G. Rauh

any winaniy, expittl <ir implied.

or uwlulneu ut tny minin\»\inn. •ppiuiui, pto<\mt »i

Prepared for

International Symposium on

The Thermodynamics of Sublimation of Uranium Dioxide

Julich, Germany

January 29 - February 2, 1979

UofC-AUA-USDOEARGONNE NATIONAL LABORATORY, ARGONNE, ILLINOIS

Operated under Contract W-31-109-Eng-38 for the

U. S. DEPARTMENT OF ENERGY

1. Introduction

A reliable equation of state for U0? and other nuclear fuel

materials up to 6000 K is needed for the safety analysis of

hypothetical core-disruptive accidents in fast-breeder reactors.

The vapor pressure of the oxide fuel is an important parameter

in the energy release mechanism and requires either a long extra-

polation of the lower temperature data (T < 3000 K) or new

methods of measurement at the temperatures of interest. Both

options have certain limitations peculiar to the chemical

thermodynamic behavior of all materials at high temperatures.

The vapor pressure and enthalpy of sublimation of UO~ have

been reported by many investigators using the Knudsen (mass

effusion), Langmiur (surface evaporation), mass spectrometric,

and transpiration methods. The results of the most extensive

measurements to date are given in Table 1. The results of

Ackermann et at. [1] have been separated traditionally into low

and high temperature regions as a result of the observed

positive curvature in the plot of log p against 1/T. It is

necessary to re-examine these data in the light of new measurements

and to re-interpret the high and low extremities of the original

curve. Hence, in Table 1 are given the thermodynamic quantities

derived from the most reliable central region (1758-2378 K) of

the temperature range that is defined by no net statistical

deviation from linearity of log p vs 1/T. From Table 1 one

concludes that the variety of methods of measurement yield at

2150 K, a temperature common to nearely all of the studies,

values of the vapor pressure which agree within a factor of

approximately two except that calculated from the anomalously

high results of Gross [5]. Only the mass-spectrometric

results of Pattoret et al. [8] correspond explicitly to the

gaseous molecule, UO?(g); all of the other measurements

involve the total uranium transport as UO2(g) and losser

amounts of UO(g) and UO^(g). At temperatures near 2150 K,

the combined partial pressures of the latter two are relatively

small 18,10] so that p - .94 Pfcot- Hence, the respectively

derived enthalpies and entropies of sublimation should closely

approximate that of UO2(g) if the temperature range is centered

around this temperature.

A further inspection of Table I indicates a spread of

values for AH ranging from 140 to 152 kcal/mole. This variation

adds considerably to the uncertainty resulting from an extra-

polation of the vapor pressure to much higher temperatures.

Furthermore, the very recent measurements of the vaporization

rates of U0?(£) above 4000 K by laser irradiation and momentum

detection or mass transfer methods [11-13] correspond to total

vapor pressures of many atmospheres that appear to be significantly

4

higher than the values for UO-(g) calculated from many of the

results given in Table 1. The molecularity of vaporization

at these high temperatures has not been identified and therefore,

it will be elucidated from a more thorough assessment of the

results given in Table 1 supplemented by the present study.

Several of the previous measurements of the vapor pressure

of U02 cited in Table 1 (Ackermann et al. [1] and Okse [4]),

were carried out by extending the effusion method to pressures

approaching 10 atm. The upper pressure limit of the effusion

method must be more carefully examined in the light of some

recent studies [14-16], which clearly show a breakdown of

-4effusive flow for pressures exceeding 10 atm.

It is, therefore, the purpose of this study to improve the

reliability of the thermodynamic data for the vaporization of

uranium dioxide by 1) presenting precise mass spectrometric

measurements of the enthalpy of sublimation to UO-(g) over a

wide (^ 700°) temperature range, 2) calculating the thermodynamic

functions for UO_(s and g) from the critical assessment of

presently available data, and, 3) analyzing the departure from

molecular flow and the failure of the Knudsen effusion method

at vapor pressures of uranium dioxide in excess of approximately

10~4 atm.

2. Experimental methods and results

Seven series of measurements of the temperature dependence

of the partial pressure of UO_(g) over approximately stoichiometric

UO2(s) were made mass-spectrometrically by observing the U02 ion

current as a function of the effusion cell temperature. The

observations were obtained with a Bendix model 12-101 time-of-

flight mass spectrometer equipped with a tungsten effusion cell

heated by electron bombardment. Details of the cell assembly [17],

power regulator [18] and the pyrometric measurement of temperature

[19] have been reported elsewhere. Three different samples of UOp

(200-350 mg) were used and the overall instrumental sensitivity

was changed from one series to another in an attempt

to identify systematic instrumental errors that might involve a

non-linear response. The possibility of error due to temperature

gradients was investigated by altering the position of the cell

with respect to the filament. When the cell was raised sufficiently,

enough of a gradient could be introduced so that a deposit formed

within the orifice; at the other extreme the temperature measured

through the orifice began to appear "non-black". Within these

limits the position of the cell did not effect the reproducibility

of the results within the experimental uncertainties. The

possibility of temperature errors at the extremes of the pyrometer

scales was minimized by supporting readings through a calibrated

neutral density filter which shifted the readings down scale.

The linearity of the ion-detection system was established by

measurements of the neon isotopes at varying gas pressures.

Each of the seven series of measurements consisted of 17-30

random observations of the UO2 ion current-temperature relationship

over the range 1813-2463 K. All the data normalized to ci common

sensitivity at 2150 K are plotted in fig. 1. The maximum useful

temperature was limited by tha high rate of loss of sample and

the rapid formation of deposits in the collimating slits as well

as by the possibility of exceeding molecular flow where ion

currents are not simply proportional to partial pressures. The

combined results of all runs (140 data points) were expressed

as log I(UO2)T vs 1/T and treated by the linear least squares

method. The normalization of all runs to an arbitrary ion

current at 2150 K yields the linear equation, log I(UO2)T =

(18.388 + 0.026) - (30927 + 60)/T from which the average enthalpy

of sublimation is 141.5 +0.3 kcal mol" , a value in excellent

agreement with that, 141.2 + 1.1 kcal mol" , reported by Pattoret

et at. [8].

A careful examination of the residuals shown in the upper

plot of fig. 2 indicates a curvature in the data beyond the

experimental uncertainties and a lack of a good statistical fit

of a simple linear representation even though the standard deviations

in the slope and intercept are small. The results of each series

were then fitted to a three parameter least squares equation

of the form, log I(UO2)T = A + ^ + C £n T, and normalized to

a common sensitivity at 2150 K. The residual pattern resulting

from this treatment is shown by the lower plot in fig. 2. The

plots of the residuals clearly demonstrate that a linear least

squares representation of the data is not quite adequate and

shows a trend with temperature whereas the three parameter

equation removes the residual curvature and shows no trend with

temperature. All of the experimental precautions and variations

in the measurements of ion currents and temperatures did not

remove this curvature or reveal any readily identifiable systematic

errors. The solid line, fig. 1, through the results will

be identified and discussed in much greater detail later.

Attempts were made to extend the temperature range beyond 2460 K

into the region of non-effusive flow, but the measurements were

severely limited by the rapid loss of sample. However, at the

end of one of the series

range 2470-2580 K which showed increased U02 ion intensities

and a definite reversal of the downward curvature. These are

shown in fig. 1 at the higher temperature end of the curve and

will be discussed in terms of the departure from molecular flow

that follows.

3. Discussion

The constant C in three-parameter equation that has been used

to fit and to normalize the data shown in fig. 1 is equal to the

average value of the heat capacity change divided by the gas

constant, i.<>., (AC~ /R) . Hence, values of AC"n can be obtained

from each individual series and from the combined normalized

data; these values vary from extremes of -2.C. to -20 cal mol~

deg . This variation is too large to obtain a reliable average

value and nost certainly precludes the functional derivation

of the nature of the dependence of "AC upon temperature. Therefore,P

the experimental data alone are inadequate as a result of the gentle-

ness of the curvature compared with the existing random as well as

unknown systematic errors. However, the results strongly indicate

that AC cannot be regarded as zero but must be quite negative.

A small but insignificant systematic error is present at

the higher temperatures for the data plotted in fig. 1. The

UO2(s) phase does not remain exactly stoichiometric over the

large temperature range of this study. In fact, the congruently-

vaporizing-composition departs from the composition UO- »n

above 2000 K and becomes progressively substoichiometric reaching

a composition UO, o o near 2450 K [20j . The extend of this

departure reduces the partial pressure of UO-(g) by less than

1% up to 2450 K and, hence, is considered insignificant.

In order to represent the vapor pressure of UO2(g) sufficiently

accurately within the present temperature range and to permit

extrapolations much beyond this range of measurements, a knowledge

of the variation of AC with temperature is needed to complement

the present results.

Uranium dioxide exists as a crystalline solid with the

fluorite structure at all temperatures below the melting point.

Materials having this structure are known to possess excess

contributions to the enthalpy and heat capacity at high temperatures

due to the formation principally of Frenkel defects in the anion

sublattice [21,22]. This behavior is a cooperative process

resembling fusion and is often described as pre-melting of the

anion sub-lattice. Bredig [23] has analyzed and discussed the

excess enthalpy in UO2(s) and related its ? ̂ilarity with that

in other fluorite-structured materials and has concluded that

a lambda-type transition indeed may occur near 2670 K. Rand

et at. [24] have separated the five sets of experimental

measurements of enthalpy (675-3112 K) and the two sets of heat

capacity (298-1006 K) into two regions, below and above 2670 K,

and have shown that Bredig's astute prediction is borne out

statistically. As a numerical convenience only, the lambda

transiti near 2670 K is taken as first-order and amounts to

an enthalpy change of 436 cal/mol. The thermodynamic functions

derived by Rand et al. [24] are given in Table 2.

10

The heat capacity and other thermodynamic properties of UO^

have not been measured but can be calculated from known molecular

parameters and some numerically consistent estimates of the

electronic contribution to the partition function that can be

closely fitted to the measured vapor pressure and enthalpy of

sublimation over the large temperature range of this study.

The need to know or to estimate reliably the low-lying electronic

states and degeneracies in gaseous molecules is essential to any

third-law treatment of the data that can be used for extrapolative

purposes. At the present time, however, there exists no reliable

theoretical basis for predicting the term values and degeneracies

of electronic states particularly in a many-electron molecule

such as UO^(g). Brewer and co-workers [25,26] have attempted to

approximate the electronic contribution in a gaseous molecule

with that for the gaseous charged atom, e.g., a gaseous diatomic

oxide, MO(g), is taken the same as the electronic partition

+2function for M (g) or its isoelectronic equivalent. These

approximations in general are too large by several cal mol deg

in the entropy and free energy function in cases for which the

electronic states in both the molecule and gaseous ion are

known [27,28],

At the mid-temperature (2150 K) of the present study the

total vapor pressure of all uranium-bearing species from the

experimental measurements given in Table 1 is 1.36 x 10 atm.

11

The partial pressure of UO2(g) is about 94 ± 3% this values based

on the mass spectrometric measurements of Ackermann et al. [29]

and Pattoret et al. [8]. If this factor is applied to the total

pressure measurements (both effusion and transpiration), an

"international average", PT = 1.29 x 10~ atm,is obtained for

the partial pressure of UO2(g) in equilibrium with virtually

stoichiometric UO~(s) at 2150 K. The average enthalpy of

sublimation of UO2(g) at 2150 K measured mass spectrometrically

in the present study is 141.5 kcal mol which agrees closely

with that (141.2) reported by Pattoret et al. From these values

of the pressure and its temperature dependence an entropy of

sublimation of 38.9 cal mol" deg" at 2150 K is obtained. The

absolute entropy of UO2(s) at 2150 K is 57.0 cal mol" deg" ;

hence, the absolute entropy of UO-(g) is 95.9 cal mol deg at

2150 K. It is possible to account for 91.5 cal mol deg

calculated from the known molecular parameters of UO2(g). The

molecule is known to be linear in its ground state from matrix-

isolation spectroscopy from which the measured stretching

frequencies, v. = 765.4 cm and v, = 776.1 cm , were determined.

A doubly degenerate bending frequency, v2 = 190 cm" , calculated

from the valence force model applied to the uranyl ion, UO? ,

is consistent with the stretching frequencies. A previously

12

observed absorption band at 81 cm was tentatively assigned to

the bending mode in UO2(g) but has not been confirmed and appearso

to be abnormally small. A U-0 distance of 1.79 A has been used

in these calculations. The breakdown of the Born-Oppenheimer

approximation at high temperatures produces numerically significant

anharmonocity corrections which are included in these calculations.

Hence, the contribution to the entropy by unknown electronic

states in UO-fg) may be nominally as large as 4.4 cal mol" deg~ .

The spectra for u (g) are not known, but those for isoelectronic+2 +3

Th (g) and Pa (g) [30] give rise to electronic entropies of 7.1

and 6.2 cal mol deg , respectively, which clearly are too large.

Therefore, we have constructed somewhat arbitrarily an electronic

partition function for UO2(g) using as a guide that for ThO(g)

which is the only gaseous actinide oxide that has been so

characterized. Both molecules have two unbonded electrons but

any further similarity is lacking. However, the thermodynamic

functions can be constructed in a consistent fashion from these

electronic estimates and the known parameters and they are given

in Table 2. A plot of the heat capacities of the gas and solid

as well as AC is shown in fig. 3. The resultant AC is seen toP P

be strongly temperature-dependent and can be adequately approximated

by a parabolic dependence on temperature up to the transition

temperature, 2670 K.

13

An equation of the form:

2

log p U Q = A + BT + CT + D/T + E Jin T (1)

which incorporates the parabolic dependence of AC on temperature,

AC = 2.30>rf2BT + 6CT2 + E], (2)

has been fitted to the data of the present study. The constants

B, C, and E were fixed from the dependence of AC on temperatureP

seen in fig. 3 and the remaining constants A and D were obtained

by least-squares treatment of all the ion-current data shown in

fig. 1 normalized to the value of pn_ = 1.29 x 10~ atm at

2150 K. The values of the constants are as follows:A ~ 67.531 (p/atm)

B = 4.382 x 10"3

C = -4.411 x 10"7

D = -3.7094 x 104

E = -8.282

Equation (1) with these constants gives rise to the curve drawn

through the data shown in fig. 1. The enthalpy of sublimation

of UO2(g) obtained by differentiating eq. (1) with respect to

1/T varies from 143.0 kcal mol~ at 1800 K to 138.5 kcal mol~

14

at 2400 K. The change of the enthalpy of sublimation with

temperature is dominated by the excess heat capacity of the

solid phase as seen in fig. 3. The uncertainties in the estimates

of the bending vibrational constant and the electronic states in

UO_(g) have only a very minor influence on the change in ACf and

hence AH° with temperature. A third-law treatment of the data

according to the equation, hU° = -4.576T log p - A(G£-H°/T), and

the necessary quantities from eq. (1) and Table 2 yields a virtually

constant value, of AH2 = 147.5 kcal mol having an insignificant

trend of only 0.2 kcal mol across the temperature range,

1800-24 00 K. A plot of the residuals resulting from the least

squares treatment by means of eq. (1) of all the data shown in

fig. 1 yields a distribution pattern that is virtually identical

to that shown in the lower plot of fig. 2, and consequently,

demonstrates the absence of any significant systematic errors.

The partial pressure of UO~(g) above UO2(s) calculated from

eq. (1) is plotted against reciprocal temperature in fig. 4 and

is compared with the total pressure of uranium-bearing species

reported in some of the earlier studies. The results of

Ackermann et al. [1] and Tetenbaum and Hunt [9] are virtually

indistinguishable up to 2450 K. Above this temperature the

results of Ohse [4] are in close agreement with the higher

temperature mee jurements of Ackermann et al. It is immediately

15

clear that these latter two results are substantially higher than

the curve for UO2(g) that has been fixed at 2150 K as described

above. All previous mass spectrometric studies agree that UO2(g)

is the major species vaporizing from congrently vaporizing UO2(s);

the only other observed molecules of any importance, UO(g) and

UO3(g), occur at relatively smaller concentrations. Therefore,

the ostensibly higher pressures of Ackermann et at. and Ohse

above 24 50 K cannot be explained by unobserved gaseous species

of sufficiently large partial pressures or by any reasonable

variation of the value of AC for the vaporization of UO-tg)

that results from an arbitrary adjustment of C (U02 ).

The findings of Carlson et at. [14] describe quantitatively

the increased mass effusion rate of saturated mercury vapor that

occurs from a thin-edged orifice in the transition from molecular

to hydrodynamic flow. The departure from molecular (effusive)

flow begins when the mean-free-path in the vapor becomes

approximately equal to the diameter of the orifice. This condition

-4will prevail when the saturated vapor pressure exceeds ^ 10 atm.

At higher temperatures, and hence, for larger vapor pressures,

the mass effusion rate increased to a limiting hydrodynamic value

near 1.6 that expected for molecular flow. These results, shown

in fig. 5, show a marked increase in the ratio of the pressure

16

p calculated from the measured rate of mass transport of mercury

vapor via the effusion equation, p = m^ Jj.RT' , to the saturated

vapor pressure p plotted against log p . Similarly, the results

of Ackermann et al. and Ohse for UO- show a marked increase for

the same condition. The saturated vapor pressure of UO,(g), p ,

has been calculated from eq. (1). Inspection of the various

results in fig. 5 rather strongly indicates that the effusion

-4method cannot be extended to pressures exceeding 10 atm for

conventional size orifices, 0.05-0.1 cm diameter, and a

corresponding mean-free-path of comparable magnitude. The

deviation from molecular flow progressively increases with increasing

pressures shown in fig. 5 and hence, as seen in fig. 4, causes

the apparent enthalpy of sublimation to increase. Schulz and

Searcy [15] have also shown in a convincing manner that molecular-

flow conditions break down for CaF_(g) when the mean-free path

approaches the orifice diameter. However, Ewing and Stern [16],

in a study of the vaporization of alkali halides have proposed

the unsuspected result that the transition from molecular to

hydrodynamic flow depends on the mean-free-path and is independent

of the diameter of the orifice. Although there still exists some

lack of agreement among these investigations in the identification

of the parameters explicitly associated with the break-down of

17

-4molecular flow, it is clear that such occurs near 10 atm and

has undoubtedly contributed an appreciable systmatic error in

the vapor pressure of UO2 measured at the higher temperatures.

Therefore, the values thereof derived from the high temperature

data of Ackermann et at. [1] and those of Ohse [8] exceeding

150 kcal mol are not valid quantities and should not be used

to extrapolate the vapor pressure to higher temperatures [13,32]

even for comparative purposes.

The reasons for the breakdown of the effusion method at

higher pressures do not apply to the transpiration technique

employed by Tetenbaum and Hunt [9]. The small discrepancy

between the transpiration results and those of p u 0 in the present

study is explainable in terms of the concentrations of UO(g) and

UO., (g) in the vapor which increase relative to that of UO-(g)

with increasing temperature. Also seen in fig. 4 as ©-points

are the three highest temperature points of the present study

shown previously in fig. 1. These points very likely indicate

the departure from molecular flow for U02(g) observed mass

spectrometrically. The B-points are the effusion results

reported earlier by Cater [31].

3/24/78 cac

Table 1

Thermodynamics of Sublimation of Uranium Dioxide

Investigators

Ackermann et at.(1956) [1]

Ivanov et at.(1962) [2]

Voronov et at.(1962) [3]

Ohse(1966) [4]

Gross(1966) [5]

Alexander et at.(1967)** [6]

Gorban et at.(1967) [7]

Pattoret et at.(1968) [8]

Tetenbaum andHunt (1970) [9]

Method

mass effusion(total U)

mass effusion(total U)

Langmuir

mass effusion(total U)

mass effusion(total U)

transpiration

mass effusion(total U)

mass spect.UO2(g)

transpiration

Temp. Range(K)

1758-2378(1600-2809)

1930-2160

1723-2573

2200-2800

2021-2963

2090-2900

1873-2573

1890-2420

2080-2705

AH(kcai/mole)

142.5+1.4

150.0+4.0

140.5+1.4

151.8+3.3

108.1

140.9+1.9

147.5+0.5

141.2+1.1

143.1+3.0

AS(cal/mol/deg)

39.2+0.7

43.6+1.9

36.8+0.2

43.7+1.4

26.3

37.9+0.8

42.5+0.5

39.4+0.5

39.4+1.2

Vapor Pressureat 2150K (x 106 atm)

1.2,

1.9/

0.57?

1.32

*5.75

0.914

1.97

1.8,

1 J6

+A recalculation of the tabulated data yields the present values. av. = 1.36+ 0.1g

*Not included in the average

**Systematic temperature corrections obtained from C. A. Alexander were applied to the originally reported valuesand the lowest temperature point has been disregarded.

CO

19

References

[1] R. J. Ackermann, P. W. Gilles, and R. J. Thorn, J. Chem.

Phys., 2J5 (1956) 1089; see also R. J. Ackermann, Argonne

National Laboratory Report, ANL-5482, September, 1955.

[2] V. E. Ivanov, A. A. Krugl, V. S. Pavlov, G. P. Kovtin,

and V. M. Amonenko, in Thermo'dynamics of Nuclear1 Materials,

I.A.E.A., Vienna (1962) 735.

[3] N. M. Voronov, A. S. Danilin, and I. T. Kovalev, ibid.,

p. 789.

t'4] R. W. Ohse, J. Chem. Phys., £4 (1966) 1375.

[5] B. Gross, Institut fiir Kerntechnik der Technischen Universitat

Berlin Report, TUBIK-4, October, 1966.

[6] C. A. Alexander, J. S. Ogden, and G. C. Cunningham, Battelle

Memorial Institute Report, BMI-1789, January, 1967.

[7] Yu. A. Gorban, L. V. Pavlinov and V. N. Bykov, At. Energ. ^2

(1967) 465.

[8] A. Pattoret, J. Drowart and S. Smoes, in Thermodynamics of

Nuclear Materials, 1967, I.A.E.A., Vienna (1968) 613.

[9] M. Tetenbaum and P. D. Hunt, J. Nucl. Mater., 3£ (1970) 86.

[10] R. J. Ackermann, M. S. Chandrasckharaiah and E. G. Rauh,

Argonne National Laboratory Report, ANL-7048, July, 1965.

[11] M. Bober, W. Breitung, H. U. Karow and K. Schretzmann,

J. Nucl. Mater., 6£ (1976) 20.

20

[12] R. W. Ohse, J. F. Babelot, G. D. Brumme, and P. R. Kinsman,

Ber. der Buns. Gesell., 80 (1976) 780.

[13] N. Asami, M. Nishikawa, and M. Tagucki, in Thermodynamics of

Huclear Materials, 1974, I.A.E.A., Vienna (1975), Vol. 1,

p. 287.

[14] K. D. Carlson, P. W. Gilles and R. J. Thorn, J. Chem. Phys.,

3_8 (1963) 2725.

[15] D. A. Schulz and A. W. Searcy, J. Phys. Chem., 62 (1963) 103.

[16] C. T. Ewing and K. H. Stern, J. Phys. Chem., 7J3 (1974) 1998.

[17] E. G. Rauh, R. C. Sadler, and R. J. Thorn, Argonne National

Laboratory Report, ANL-6536, April, 1962.

[18] H. H. Cremer, Z. Instrumentenkd., 1_ (1964) 72.

[19] See for a description of the equipment and procedure,

R. J. Thorn and G. H. Winslow, Am. Soa. Meoh. Eng. Pap.,

63-WA, 244 (1963).

[20] R. J. Ackermann, unpublished work.

[21] B. F. Naylor, J. Am. Chem. Soc, 61_ (1945) 150.

[22] A. S. Dworkin and M. A. Bredig, J. Chem. Eng. Data, j} (1963)

41.

[23] M. A. Bredig in Colloq. Int. sur I'Etude des Trans. Cryst. a

Haute Temp, au-dessus de 2000°K, Odeillo, Septemhar 27-30, 1971,

C.N.R.S., Paris (1972) 183-191.

21

[24] M. H. Rand, R. J. Ackermann, F. Grtfnvold, F. L. Oetting,

and A. Pattoret, Rev. Int. Hautes Temp, et Refractaires,

to appear.

[25] L. Brewer and M. S. Chandrasekharaiah, University of

California, Radiation Laboratory Report, UCRL-8713 (Revised)

(1960)

[26] L. Brewer and G. M. Rosenblatt, in Advances in High Temperature

Chemistry, (L. Eyring, ed.) 2_, 1-83 (1969).

[27] R. P. Steiger and E. David Cater, High Temperature Science,

1 (1975) 288.

[28] R. J, Ackermann and E. G. Rauh, J. Pure and Appl. Chem., to

appear.

[29] R. J. Ackermann, E. G. Rauh and M. S. Chandrasekharaia,

Argonne National Laboratory Report, ANL-7048, July, 1965.

[30] Leo Brewer, J. Opt. Soc. America, §1 (1971) 1666.

[31] E. D. Cater, Argonne National Laboratory Report, ANL-6140,

March, 1960, page 86.

[32] E. A. Fischer, P. R. Kinsman and R. W. Ohse, J. Nucl. Mater.,

59 (1975) 125.

22

FIGURE CAPTIONS

Fig. 1. Mass-spectrometric measurement of temperature dependence

of p(UO2) over UO2(s), log I(UO2)T vs 104/T.

Fig. 2. Residuals from least squares analyses of mass-spectrometric

results of Fig. 1. Upper - from linear least squares,

log I(UO2)T = A + B/T. Lower - from three-parameter

least squares, log I(UO2)T = A + B/T + C en T.

Fig. 3. C (UO2,g), C (UO2#s) and AC vs T.

Fig, 4. Comparison of the partial pressure of UO2(g) over UO2(s)

from this study with total pressures of uranium bearing

species of other investigations. 0 Ackermann et al.,

Ref. 1, Series B-4 and B-8. • Ibid, Series H-l and H-2.

X , Ohse, Ref. 12. • Cater, Ref. 31. © This study.

Tetenbaum and Hunt, Ref. 9. p(UO2), equation

(1), this study.

Fig. 5. Departure from molecular flow at high temperatures.

• - Hg, Carlson, Ref. 14. © - U02, Ackermann et al.,

Ref. 1, Series B-4. A U02, Ohse, Ref. 12.

COro

3

y= !

oq I

(cal

c),

i

en"

3a

RES

II

+.05

, o

-.05

+.05

0

-.05

—o

o°

o

oo

©

o

0

o o

© 0

o

o

1

oo

° o

«

0

oo°© '

o

©

1

o

0

o

*

>

o

o°

1

o

»*©*<

0° °

1

1

» ° © •

• 1 ° •••©0 O

8© °et © ©

o •

o

8 ©o ©

o o o

o ••

1

0

f

©

>

8°

o

o

••v.0

0

°

1

1

©

o

o oo

o

O*©o oo

o

«

© o

° 00

o

« -8© o

0

© 00

1

©o

°© o

oo

o

oo

o ©

o

<

o

0

©

©

1

•

0 <o

0

o

o

1

—9

0

o

—

©o

©

1800 1900 2000 2100 2200T6K

2300 2400 2500

6ap/|Oiii/|DO(slZon)dO

6ap/|0Ui/|D3 (6*2o n) d0

HUD/ d 6o|

t?

2.0

1.5

1.0

O

b

0.0011

O A- Q O W-

1

PRESSURE (torr)0.01 O.I

1

X/c

i

* l

o

AA

r

& °o o

m mm

i I

11

o

o

JA

•

1-6.0 -5.0" -4.0

log ps/atm-3.0

- 2 . 0

1.5

0

-2.0