Kinetics of the carbothermic synthesis of uranium mononitride microspheres

39

Journal of Nuclear Materials 185 (1991) 39-49

North-Holland

Kinetics of the carbothermic synthesis of uranium mononitride microspheres SK. Mukerjee, J.V. Dehadraya, V.N. Vaidya and D.D. Sood Fuel Chemistry Division, Bhabha Atomic Research Centre, Trombay, Bombay 400085, India

Received 20 March 1991; accepted 3 May 1991

The mononitride of uranium is an important nuclear fuel material. Kinetics of UN microspherespreparation by the reaction of carbon containing porous uranium oxide microsphereswith nitrogen was studied in the temperature range of 1573 to 1823 K. Carbon monoxide concentration in the nitrogen stream during the reaction was used to determine the rate of formation of the nitride. The results show that the carbothermic synthesis of the mononitride microspheres follows a first order rate equation and the value of the energy of activation for the reaction was found to be 365.7k14.9 kJ/mol. The diffusion of carbon monoxide through the product layer appears to be the rate controlling step.

1. Introduction

Mononitrides of uranium and plutonium are potential fast reactor fuel materials [l]. Presently the most important method for the preparation of these nitrides is the carbothermic conversion of metal oxides in nitrogen atmosphere followed by grinding of the nitride powders, pressing and sintering to obtain nitride pellets [2-81. This involves handling of radioactive and chemically active powders of the nitrides. Several investigations on the reaction of UO, with carbon and nitrogen have been reported [9-171. For use as fast reactor fuel, the nitride product should have very low carbon and oxygen contents [18]. Imoto and Stocker [19] have carried out a thermodynamic analysis of the phases during UO,-C-N, reaction. They predicted that uranium nitride having residual oxygen < 0.003 wt% could be prepared at temperatures between 1673 and 2473 K in an atmosphere of nitrogen and with CO partial pressure of less than 10.1 Pa. However, nothing has been mentioned about carbon content in the final product. Kinetics of the uranium nitride formation from oxide has been studied by several authors [20-251. In most of the investigations the formation of uranium carbonitride has been postulated as the first step in the reaction. Lindemer [21] studied the formation of uranium carbonitride, UN,_,C,, from the reaction between a UO, pellet and carbon pellet in nitrogen atmosphere ( pN, = 50.6 kPa) at 1973 K and reported that uranium 0022-3115/91/$03.50

oxynitride is formed as an intermediate species and the formation of the carbonitride is controlled by solid state diffusion across the carbonitride layer. Greenhalgh [22] measured the reaction rate between UOz and carbon powder in nitrogen atmosphere as a function of temperature and nitrogen flow rate. He reported that the reaction is governed by a first order rate equation and the activation energy is 359.5 kJ/mol. Muromura and Tagawa [23] studied the effect of C/UO, mole ratio and reacting atmosphere (N, + 8% H,, N, + 75% H, or NH,) on the rate of reaction. They reported that the rate of reaction increases with increase of carbon content in the starting material. They also reported diffusion (species not specified) as the rate governing process, fitting in first order rate equation, with an activation energy of 347 kJ/mol. Naoumidis and Stocker [24] reported that the value of x, in the intermediate UN, _,C,, has a strong influence on the reaction rate of the process. Recently Pautasso et al. [25] investigated the reaction thermogravimetrically by heating UO, +X + PuO, + C pellets in N2 atmosphere. They suggested the following sequence of steps that lead to the conversion of UO, + PuO, + C to (U, Pu)N: (1) Formation of a carbonitride, MN,_,C,, layer at the carbon-oxide interface, (2) Reaction of free carbon and MN, _,C, with oxygen and nitrogen until near-equilibrium composition is reached, (3) Reaction of nitrogen with free carbon and residual

0 1991 - Elsevier Science Publishers B.V. All rights reserved

S. K. Mukerjee et al. / Kinetics of UN microspheres synthesis

40

oxide present in MN,_.& (near equilibrium composition) to form nitride, if the initial carbon to oxide ratio was 2, or (near equilibrium composi(4) Reaction of MN,_&, tion) with nitrogen and hydrogen to form nitride if the initial carbon to oxide ratio was greater than 2. Their results also fit into a first order rate equation with an activation energy of 307 kJ/mol. They are of the opinion that carbon diffusion through the product layer is the rate controlling step. This paper describes a synthesis process for uranium nitride microspheres, based on the carbothermic reduction of carbon containing UO, gel particles prepared by a sol-gel process using internal gelation route. The sol-gel process has the advantage of total eli~nation of handling of powders thus avoiding the associated hazards. The preparation of nitride microspheres is a single step heat treatment process combining the reaction and sintering steps. Also muting of carbon in liquid gives homogeneous dispersion of carbon and UO, particles in gel microspheres, which is an essential condition for carrying out any solid state reaction effectively. The ratio C/UO, in the gel microspheres was varied between 2.5 to 2.7. Heating of these UO, + C microspheres at 923 K under vacuum reduces UOs to UOz according to the following overall reaction: UO3(s)

+ O.SC(s) + UOz(s)

+ OSCO*(g).

(1)

At this temperature the gaseous reaction product is mainly CO, [26,27], which facilitates the fixing of carbon stoichiometry for further reaction. The present work was carried out to study the kinetics and mechanism of uranium nitride microspheres formation and to suggest a rn~ha~sti~ model similar to the model proposed by Muketjee et al. 1281 for the UO, + C reaction.

2. Theory Sestak et al. [29] have proposed several generahsed models for the solid state reactions of spheres. They have also discussed these models along with the possible rate controlling processes and their analytical expressions. These models have been used in the present study for suggesting the mechanism for the UO, + C + N, reaction as discussed in section 5. Naoumidis and Stocker have suggested that this reaction proceeds by two different routes depending upon the temperature of the reaction [24]. At temperatures below about 1723 K and 101.3 kPa pressure of nitrogen, direct formation of UN occurs as given by reaction (2). Uq(s)

+ X(s)

+ 0.5N,(g)

-+ UN(s)

+ 2CO(g).

(2)

At temperatures above 1723 K the reaction proceeds via an intermediate product UN,_,C, at 101.3 kPa pressure of nitrogen. The value of x increases with the increase in temperature at a perticular nitrogen pressure and decreases with the increase of the nitrogen pressure at the same temperature as seen in fig. 1 [24]. The reaction is given by reaction (3). UO,(s)

+ (2 + x)C(s)

--$ UN,_,C,(s)

+ [(I - x)/2IN,(g)

+ 2CO(g).

(3)

Accordingly at temperatures greater than 1723 K when the starting sample contains stoichiometric amounts of carbon (C/UO, = 2.0), reaction (3) does not go to completion and leaves behind unreacted UOz core along with UN, _,C,. In nitrogen atmosphere, the carbonitride on further heating reacts according to reaction (4). UN,_,C,(s)

+ (x/2)N,(g)

--f UN(s)

+ xc(s).

(4)

This is a slow reaction [24] and proceeds if the liberated carbon is removed either by left over UOz core or by reaction with hydrogen. Even though reaction (2) is ideal for uranium nitride preparation, the constraint of maintaining reaction temperature below 1723 K is a handicap because of the low reaction rate. When higher temperatures are used the product UN,_,C, is formed at 101.3 kPa pressure of nitrogen. Formation of the ‘intermediate’ carbon&ride strongly influences the reaction rate of the process.

3. Experimental 3.1. Sam@

preparation

The internal gelation process and the gelation assembly used for the preparation of UO, + C gel microspheres has been described elsewhere [30]. Uranyl nitrate solution was prepared by dissolving nuclear grade UsOs powder in analytical grade nitric acid. Hexamethylenetetramine (HMTA) and urea of analytical grade were used. Carbon black powder of grade “United HAF was used. The average particle size of the carbon powder was 0.03 pm and the specific surface area 120 m2/g. A 3.OM uranyl nitrate solution was mixed at 273 K with a solution of HMTA and urea containing finely dispersed carbon powder, to obtain a feed solution l.lM in uranium and with (HMTA, ur~}/ur~um mole ratio of 1.5. Droplets of this solution were contacted with hot silicone oil (363 K) to obtain UO, + C gel microspheres (- 2200 pm diameter). The gel microspheres were washed, dried, and heated in argon up to 573 K to remove moisture, ammonia and residual gelation agents.

S. K. Mukerjee et al. / Kinetics of UN microspheres synthesis

4

IO2

_

’

4 ,” - IO’

,z-

4

0

0.2

0.4 x [in

0.6 UC,.,

0.8

1.0

Nx]

Fig. 1. Isotherms for dependence of the nitrogen equilibrium pressure on the composition of UC, _,NX in presence of excess carbon (241.

Ten such batches of 1 kg each were prepared and the C/UO, mole ratio in the feed was varied between 2.50 to 2.70. Specific surface area of the microspheres was determined by the BET method and the true densities were determined using stereo pycnometer with helium gas for volume measurement. The specific surface area of these UO, + C microspheres heated up to 573 K was found to be 48 m’/g and the true density was 4.8 g/cm3. Heating of these microspheres in vacuum up to 923 K produced porous UO, + C microspheres having a specific surface area of 19 m2/g and true density of 6.9 g/cm3. Complete conversion of the UO, to UO, phase was confirmed by XRD and thermogravimetric analysis [31]. By assuming that the UO,/UO, particles in the microspheres to be spherical, the average size of the particles was calculated from the values of the specific surface area and their respective true densities. The specific surface area of UOs and UO, were obtained from the specific surface area values of their respective mixtures with carbon, by subtracting the surface area contribution from carbon. The size of UO, particle in UO, + C microspheres heated upto 573 K was 3-4 pm and the particle size of UO, in UOz + C microspheres heated up to 923 K was approximately 10 pm. 3.2. Procedure Experiments on heat treatment were done on 50 g/batch scale in a 5 cm diameter carburised tantalum crucible. Heating was carried out in a high temperature high vacuum/controlled atmosphere tungsten heater furnace. The UO, + C microspheres were first heated in vacuum up to 923 K until a vacuum of 1 mPa was obtained in the system. This ensured complete conver-

41

sion of UO, + C microspheres into UO, + C microspheres. These UO, + C microspheres having a C/U02 mole ratio of 2.0, 2.1 and 2.2 were used as starting material for kinetic studies and UN preparation. A flow of high purity nitrogen over the microspheres placed in the tantalum crucible was started. The nitrogen gas was purified by passing over reduced copper based catalyts for the removal of oxygen and over molecular sieves 4A for the removal of moisture. A gas inlet made of 6 mm tantalum tube was taken very near (2 cm) the sample for efficient flushing of CO gas produced during the reaction. The nitrogen gas flow rate was varied between 40 to 80 ml/mm per gram of the sample. The material was then taken to the desired temperature, in about 20 min, to carry out the isothermal kinetic studies. The experiments to determine the rate constants were carried out at temperatures between 1573 to 1823 K, which cover temperatures below and above 1723 K (temperature around which change over from reaction (2) to (3) takes place). Period for the completion of a major fraction of the reaction varied between 2 to 24 h. The sample temperature was measured by keeping W-S% Re/W-26% Re thermocouple at the centre of the crucible, almost touching the sample. Progress of the reaction was followed by monitoring the amount of CO gas evolved. The effluent gas was passed through oxidised copper based catalyst heated at 413 K to oxidise CO to CO, and subsequently CO, was trapped in NaOH solution for estimation. 3.2.1. Reaction rate measurements Carbon dioxide in the effluent gas was absorbed in NaOH solution and was determined quantitatively by weight gain of the solution and by titrimetric estimation. Correction was applied for the loss of weight of NaOH solution caused by the saturation of the dry gas. 3.2.2. Preparation of nitride For the preparation of UN, UO, + C microspheres having C/U02 mole ratio of 2.0 and more were used. Isothermal reduction experiments were done at 1623, 1723 and 1823 K. In some experiments nitride microspheres were prepared by continuously heating U02 + C microspheres at a predetermined rate. In all the experiments the nitrogen gas flow rate was 60 ml/mm g, maintained at a pressure of 101.3 kPa. In cases where initial material had C/UOz greater than 2.0, the excess carbon after carbothermic reduction, which is present in the form of UN,_,C,, was removed as CH, gas by heating the product at 1673 K under N, + 8% Hz gas flow (60 ml/mm g) for 3 h. After completion of the reaction the microspheres were sintered in nitrogen

S.K. Mukerjee et al. / Kinetics of UN microspheressynthesis

42

Table 1 Carbothermic reaction of UOz + C microspheres under flowing nitrogen at 1723 K. C/UOz = 2.0 (C = 8.14 wt% and U = 80.9 wt%). Nitrogen flow rate 60 ml/min g of sample. Sample weight = 50.84 g Time (min) 0

a)

50 100 150 200 250 300 350 400 450 500 550 600 650 700 @. Temperature

Amount (trapped

0.017 0.083 0.138 0.183 0.217 0.245 0.265 0.283 0.296 0.307 0.317 0.324 0.327 0.331 0.335

of CO, moles)

I

d

0.05 0.24 0.40 0.53 0.63 0.71 0.77 0.82 0.86 0.89 0.92 0.94 0.95 0.96 0.97

0

0 ,O

200

400 Time

1723 K.

atmosphere at 1973 K for 3 h and cooled in vacuum to prevent the formation of U,N, phase. The product was chemically analysed for the N, C, 0 and U content. The precision for the estimation of N, C, 0 and U were + 5%, _t lo%%, + 10% and +0.05%, respectively. X-ray diffraction analysis was done to identify the phases present. The density of the product was determined by stereo pycnometer.

4. I. Reaction rate The reaction ratio a was calculated from the weight of CO2 trapped which was taken as a measure of CO liberated.

’

(5)

Typical data for the reduction carried out at 1723 K are given in table 1. In fig. 2, a is plotted against time for a gas flow rate of 60 ml/min g of the sample. At temperatures below 1723 K the time required for the completion of more than 95% of the reaction was more than 12 h. Complete data for lower temperatures is not shown in the figure in order to highlight the data at higher temperatures. Two experiments were carried out

600 (min.)

Fig. 2. Variation of the reaction ratio (I with time for the carbothermic reaction in UO, +C microspheres carried out under flowing nitrogen. Gas flow rate = 60 ml/min g of gel microspheres.(0) 1573 K, 0 1623 K, (v) 1673 K, (0) 1723 K, (A) 1773 K, (X)

1823 K.

at each temperature, but as the results were nearly identical, data of only one is plotted in the figure. At all temperatures the rate of reaction increased with increase of gas flow rate as shown in fig. 3. The data could be fitted to eq. (6): -ln(l

4. Results

Weight of CO liberated at time ‘t ’ a = Total CO expected as per reaction (2)/(3)

0

-a)

= kt,

(6)

where k is the reaction rate constant. A plot of -ln(l _ a) against time t is given in fig. 4. Eq. (6) indicates a diffusion controlled mechanism [32]. Variation of reaction rate constant with temperature is given in table 2, and its plot is shown in fig. 5. The data points for the sample having C/UOz mole ratio 2.2 fitted on a straight line which can be represented by the expression; k(s-‘)

= 1.0

x

10’ exp - (43749 + 810)/T.

(7)

However, the data points for samples having a C/UO, mole ratio of 2.0 did not fit in a single straight line. Data points below and above 1673 K fitted in the line represented by eq. (7) and (8), respectively. k(s-‘)

= 0.23 exp - (14278 k 1089)/T.

(8)

The energies of activation corresponding to eq. (7) and (8) are 365.7 + 14.9 kJ/mol and 119.4 + 16.2 kJ/mol,

S.K. Mukerjee et al. / Kinetics of UN mic~~spheres synthesis

43

Table 2 Variation of the reaction rate constant with temperature for the carbothermic reaction of UOz +C microspheres under flowing nitrogen Temperature (K)

k = - ln(1 - a)/? (10-s s-1)

= 2.0

1573 1623 I673 1723 1773 1823

1.02 (1.09) a> 2.75 (2.83) a) 5.54 9.61 (8.76) ‘) 14.34 (14.82) =) 23.86 (22.39) a)

C,A.JO~ = 2.2

1573 1723 1773

1.04 12.30 24.23

c/uo,

Twnperatura Nitrogen 0

1723

K

flow rak ;

80nl /min.g

of

mmph

cl 60-*A 40--“-

a)

Values obtained in the second set of experiments.

respectively. The values of the activation energy and the pre-exponential factors for the carbothermic reduction of U02 + C microspheres with a C/JO2 mole ratio of 2.0 to UN at higher temperatures are much lower than Fig. 3. Vacation of the reaction ratio a with nitrogen gas flow rate for the carbothermic reaction in UOz + C microsphere.

8

$: 9-

& 5 tot

P

I

0

200

I

I

400

12 600

800

Time (min.)

Fig. 4. First order type of plot fur the ~r~tbe~c reaction in UOz +C microspheres under flowing nitrogen gas. Gas flow rate = 60 ml/min g of gel microsphere. Symbols are the same as in fig. 2.

0.54

0.58

0.62

0.1

6

Fig. 5. Arrhenius plot of the reaction rate constant k for the carbothermic reaction in Uq +C microsphere under flowing nitrogen.

44

S.K. Mukerjee et ai. / Kinetics of UN microspheres qwtheris

the values reported in the literature. This variation in the slope of the Arrhenius plot at higher temperature points towards a change in the mechanism of the reaction. A probable mechanism is suggested in section 5. 4.2. preparation

or UC, U,N, phases. Further, the total non-metallic content (N + C f 0) of 5.74 wt% agrees with the expected value of 5.55 wt% within the precision of the analysis. It can therefore be inferred that the product is UN with dissolved C and 0. The carbothermic reaction with samples having C/UO, greater than 2.0 (batch nos. 7 and 8) could be completed in about 4 h at 1823 K. In these experiments the oxygen content of the product was 0.06 wt% but carbon content was 0.4 to 0.6 wt%. To reduce the carbon content the product after carbothermic reaction was heated under a flow of N, + 8% H, (60 ml/mm g) at 1673 K. This led to an increase in nitrogen content to 5.45 wt% and decrease of carbon content to 0.1 wt%.

of UN

Preparation of UN was carried out with UO, + C gel microspheres containing 2.0 to 2.2 moles of carbon per mole of UO,. The microspheres were heated as per the scheme mentioned in section 3.2.2. In all cases the product was sintered after the carbothermic reaction. Sintering was done at 1973 K at a nitrogen pressure of 2 kPa. The microspheres had a metallic lustre, were crack free and the density was 97% TD. The results are summarized in table 3. The C/UO, ratio in the first six experiments was kept at 2.0. At temperatures of 1623 K and 1723 K (batches 1 to 3) the nitride product had a high (> 0.5 wt%) oxygen content. This could be because of the slow rate of reaction accompanied by sintering leading to the entrapment of the reactant core inside the sintered product layer. At 1823 K (batch 4) the reaction could be completed in 5 h, but oxygen content was still close to 0.3 wt% and a separate oxide phase could be detected by XRD. The oxygen content could be decreased by gradual heating of microspheres above 1623 K and was brought down to 0.16 wt% by heating from 1623 to 1823 K at a rate of 20 K/h (batch no. 6). An X-ray diffraction pattern of the product from batch 6 did not indicate the presence of a separate UO, phase

5. Discussion Muromura and Tagawa [33] have observed that in the pellets of UO, + C the carbothermic reaction of UOz in the presence of nitrogen initiates at the surface of UO, pellet and proceeds towards the centre. Stinton et al. [34] have studied the carbothermic reaction of UOz + C microspheres for making UC and suggested that under flowing inert gas, surface nucleation is extremely fast and the reacting UO, particle is instantaneously covered by a thin layer of the product. Similar studies by Mukerjee et al. [28] also suggest that in the case of UO, + C microsphere, which is made up of numerous UO, particles (10 pm) dispersed in a carbon

Table 3 Preparation of UN microspheres from LJO: + C microspheres by carbothermic reduction under flowing nitrogen. rate 60 ml/min

Batch no.

1 2 3 4 5 6 7 8 9

Nitrogen

gas flow

g of sample

C/U%

Temp.

in sample

W

2.0 2.0 2.0 2.0 2.0 2.0 2.1 2.2 2.1

1623 1623 1723 1823 1623-1823 1623-1823 1823 1823 1623-1823 +1673”

Reaction time

PrccIuc1 U

(h) 10.0 14.0 10.0 5.0 in 8h in 10 h 4.1 3.3 in 7 h 3.0

” N, + 8% H, gas flow rate 60 nd/min g of sample. h1 Carbon is present as UN, _&/free carbon.

N

0

c h’

Phase

1.35 0.92 0.68 0.32 0.28 0.16 0.06 0.06 0.08 0.06

1.25 1.12 0.54 0.26 0.23 0.17 0.40 0.60 0.34 0.10

UN. UN. UN, UN. UN. UN UN UN UN UN

(wt%) 93.7 93.9 94.0 94.2 94.1 94.2 94.2 94.1 94.2 94.2

3.65 3.95 4.89 5.19 5.36 5.41 5.29 5.17 5.38 5.4s

UO, UO, UO, UO, UQ

S. K. Mukerjee et al. / Kinetics of UN microspheres synthesis

matrix, the reaction initiates at the surface of the UO, particles present at the surface of the UO, + C microsphere. In nitrogen atmosphere, an extrapolation of similar logic would suggest that the carbothermic reaction would result in instantaneous covering of the UO, + C microsphere by a thin layer of UN or UN, _$Z, depending upon the reaction temperature. Propagation of this reacting interface, into the centre of the microsphere, becomes the rate determining process, which is controlled either by diffusion or reaction at the interface (model C of ref. [29]). Analysis of fig. 5 indicates that with a C/UO, mole ratio of 2.2 an Arrhenius equation is followed for the conversion of UO, to UN or UO, to UN, _,C, in the temperature range of 1573 to 1673 K and 1673 to 1823 K, respectively. However, the same reaction with stoichiometric amounts of carbon (C/UO, = 2.0) deviates from linearity at temperatures greater than 1673 K. This could be due to the formation of an intermediate carbonitride at temperatures higher than 1673 K as suggested by Naoumidis et al. and Stocker [24]. However Naoumidis and Stocker reported a temperature higher than 1673 K (around 1723 K) at which carbonitride formation initiates. This difference in temperature could arise due to difference in marphology of the sample or experimental conditions. A mechanistic model has been proposed in this paper to explain this deviation. In cases where the Arrhenius equation is followed for the complete conversion of UO, to UN or UN, _,C, the mechanism is expected to be similar to the one suggested by Mukejee et al. for conversion of UO, + C microspheres to UC, as in these cases the reactant is directly converted to the product without the formation of an intermediate [28]. In case of the conversion of UO, to UN with stoichiometric amounts of carbon (C/UO, = 2.0) at temperatures higher than 1723 K, where conversion to UN proceeds via an intermediate a UN,_&,, mechanism is expected to be different. On the left side of fig. 6 the conversion of UO, + C to UN/UN,_,C, has been shown for a C/UOz mole ratio of 2.0 at temperatures above 1673 K. The right side of this figure shows the conversion to UN,_& at temperatures above 1673 K for samples with C/UOz mole ratio of > 2.0 when the amount of carbon is sufficient for the complete conversion of UO, to UN, _,C, without leaving any UO, core. With a C/UO, mole ratio of 2.0 the conversion of UO, + C microspheres to UN microsphere follows the route shown by fig. 6b. The reaction starts with an outer layer of UN, _,C, but at the intermediate stage we have an outer layer of UN, an intermediate layer of UN, _,C, and a core of UO, + C. As the reaction proceeds the thickness of the UN layer goes on increasing and that of

45

r

Fig. 6. Mechanistic model for conversion of UO, to UN at temperatures above 1673 K.

UO, + C core goes on decreasing and eventually UN microspheres with dissolved oxygen and carbon is formed. In order to understand the process steps involved in the carbothermic reduction process it is worthwhile to analyse the reactions occuring at various interfaces. When C/UOz = 2.0 there are two interfaces: UN-(UN, _,C,) and UN, _,C,-(UO, + C). Let us consider the particle at the latter interface. A magnified view of this particle is shown in fig. 6c. The sequence of reaction steps that may lead to the conversion of UOz + C to UN,_&, in analogy to reaction steps suggested by Mukejee et al. for the conversion of UO, + C to UC are detailed below: Step 1. Instantaneous formation of a thin UN,_& layer on the surface of each UO, particle present at the UN,_,C,-(UO, + C) interface. (This step is not depicted in fig. 6~). Step 2. Diffusion of N,(g) present at the surface of the reacting particle to the UN, _,C-(UO,) interface of the reacting UO, particle. Step 3. Dissolution of carbon present at the surface of reacting particle in the UN,_,C, layer. Step 4. Diffusion of dissolved carbon from the surface of the UN,_,C, layer into the UN,_&-(UOz) interface of the particle.

46

S.K. Mukerjee Edal. / Kinetrcs of UN mrcrmphere.~ synthesis

Step 5. The reaction of dissolved carbon with UO, and nitrogen at the interface of the particle as per the following reaction, where [C] and [0] denote species C and 0 in solid solution.

Step

UN, _$, UN,

Reaction of hydrogen, as per the following reaction

10.

.C,ts)

+ (x/2)N,(g)

+ UN(s) [c],N,

.c,+ uo,+[(l

-UN,-.C,

+ Z[O]un,_~c,.

(9)

The oxygen released gets dissolved in UN, _,C, layer. Step 6. Diffusion of dissolved oxygen to the outer surface of UN, _ .$, layer. Step 7. Reaction of this oxygen with carbon present outside the UN, _ .C, layer as follows: [o]LN,

,C.+ c -co(g).

+ xCH,(g).

-x)/2]&

(10)

Step 8. Diffusion of CO out of the microsphere (shown in fig. 6b). Fig. 6d depicts the situation when free carbon has been exhausted at the outer surface of the UN, _,C, layer leaving behind unreacted UO, core trapped in the intermediate product UN, _ $,. At this stage conversion of UN , ,C, to UN + C takes place as per the following step. Step 9. Precipitation of free carbon from UN, _ $, as per reaction (4) and the formation of UN. The precipitated carbon then diffuses towards UO, core and again the same sequence of steps 1 to 8 mentioned above is repeated leading to formation of UN, _,C,, except for the fact that this time CO gas formation takes place at the UN-(UN, _ ,C,) interface within the particle (step 7). Fig. 6e represents partial conversion of the UN, _,C, layer to UN as per reaction step 9 followed by steps 1 to 8. This process continues till UN, _ ,C, layer and UO, core merge together at the centre of the particle completing UN formation (fig. 6f). Because of the large number of transport and reaction steps involved the overall rate of reaction for the formation of UN is expected to be low when the reaction proceeds through the process steps described above. Similarly when the C/UO, mole ratio in the microsphere is > 2.0 the conversion of UO, + C micromicrosphere follows the route spheres to UN, _ $, shown by fig. 6g. As the reaction proceeds the layer of UN, _ .C, goes on becoming larger eventually leading to complete conversion of UO, + C to UN, _ .C,. To understand the process step let us consider a UO, particle at a UN, ,C, and a UO, + C interface. In this case also the reaction proceeds via process step 1 to 8 described above. Since the carbon content is sufficient to completely convert UO, to UN, _,C, without leaving any UO, core, and step 9 is not involved. The carbonitride is then converted to UN by step 10.

nitrogen and to give UN.

+ 2xH,(g) (II)

From fig. 6 it can be seen that although there are a number of process steps through which conversion of UO, to UN takes place the probable rate controlling mechanisms are only two: (1) A mechanism involving reactions at the interface: Reaction steps 3 to 7 as rate controlling will come under this catagory. These reactions are occuring at the UN, _,C,-(UO, + C) interface and the rate of the reaction will be proportional to the interface area. This would fit in the shrinking core model suggested by Spencer and Topley [35] and given by eq. (12): k = l/t(l

- (1 -#‘).

(12)

(2) A diffusion controlled mechanism: Reaction steps 2 and 8 would come under this category. Various analytical expressions for the diffusion controlled process are discussed elsewhere [28]. A survey of literature as discussed in section 1 indicates that reaction of UO, + C + N, is governed by diffusion controlled kinetics. Lindemer [21] reported solid state diffusion (step 4 or 6) as rate controlling for reaction between carbon and UO, pellet in the presence of nitrogen. In this case CO formation takes place outside the product layer and hence step 8, i.e. diffusion out of CO gas through product layer as rate controlling process, does not come into picture. Pautasso et al. [25] reported carbon diffusion as the slowest step. However, this appears unlikely because the formation of UN, _,C, intermediate, which takes place in presence of free carbon, points towards fast diffusion of carbon. Also carbon diffusion as rate controlling step should have fitted in an equation governed by an interface controlled reaction (eq. (12)) for the UO, + PuO, + C pellet, where reaction initiates at the surface and then propogates towards the centre. We are of the opinion that in the case of UO, + C microspheres diffusion of CO(g) through the product layer is the rate controlling step. Our study on variation of reaction rate with nitrogen gas flow rate, as shown in fig. 3, further confirms that CO gas diffusion through the product layer must be the rate controlling step, as decrease in nitrogen gas flow rate, i.e., increase in CO partial pressure results in decrease of reaction rate. Similar results were observed by Greenhalgh [22]. Reaction rate constants for the overall reaction are given in table 2. Plot of In k verses l/T given in fig. 5

S. K. Mukerjee

er al. / Kinetics o/ UN microspheres synrhesis

show deviation from linearity at temperatures higher than 1673 K for samples having stoichiometric amount of carbon. When the values of the reaction rate constants at higher temperature are compared with those at lower temperature, the increase in reaction rate at higher temperature is not as high as expected from the Arrhenius relationship (obtained on the basis of the data at lower temperature for samples with a C/UO, mole ratio of 2.0 or at any temperature for C/UO, > 2.0). This could be due to the formation of UN, _ ,C, with higher valued of x at higher temperature as shown in fig. 1. A high value of x will mean larger core of UO, left after the disappearance of free carbon, when the starting sample had stoichiometric amounts of carbon. The mechanistic model depicted in fig. 6, indicates that the lower the overall reaction rate will be, the larger is the size of unreacted UO, core left after the disappeared of free carbon. Naoumidis and Stocker [24] also experienced a strong influence of the value of x, in UN, _ $,, on the reaction rate of the process for powder samples containing stoichiometric amounts of carbon. They reported that the increase of temperature produces contradictory effects on the rate of reaction for this process. The rate of reaction increases with increase of temperatures as the diffusion rate is increased and CO equilibirium pressure is higher. On the other hand, at higher temperatures, the rate of reaction decreases because, the equilibirium solid solution U(N, C) contains more carbon than at lower temperatures. They carried out experiments with identical mixtures under similar conditions to study the effect of temperature on the rate of reaction. They observed that at higher temperatures the initial reaction rate was much higher but later decreased to a lower value, where as at lower temperatures the initial rate of reaction was lower but there was no sharp drop later and the reaction terminated much earlier than at higher temperature. Chemical analysis of carbon, coupled with metallographic examination and X-ray powder patterns of partially reacted samples showed that drop in reaction rate and disappearance of free carbon occurred simultaneously. Greenhalgh [22], who worked with powder samples, observed reduction in reaction rate around a = 0.75. In the present study with UO, + C microspheres. the above mentioned observation, namely (1) drop in reaction rate, at higher temperature, with disappearance of free carbon, and (2) early completion of reaction at lower temperatures, were not encountered. In our opinion the drop in reaction rate with disappearance of carbon would be observed only in the case of powder samples, where reaction takes place simultaneouly in all the UO, particles. This drop in reaction

47

rate essentially appears at a stage where formation of UN, _,C, from the reaction of free carbon with UO, is completed, leaving behind a UO, core (reaction (3)) and UN formation from UN,_,C, (a slow reaction) starts according to reaction (4). In the case of UO, + C microspheres, where the UO, particles react layer by layer from the surface to the core of UO, + C microsphere, the above mentioned reactions take place simultaneously, resulting in a decrease of the overall rate of reaction. Since disappearance of free carbon takes place only at the end of the reaction, sudden drop in reaction rate during the course of reaction is not observed. In our study increase in reaction rate with increase of temperature was not as high as expected from the increased diffusion rate and equilibirium CO pressure. This can be attributed to the formation of UN,_.C, with higher values of x. Neverthless the time required for the completion of reaction was always lower at higher temperatures. For the preparation of UN reaction (2) appears to be ideal, but in actual practice at temperatures below 1723 K where reaction (2) holds good, the rate of reaction is very low and the reaction does not go to completion because of accompanied sintering. At higher temperatures high initial reaction rates cause cracks in the microspheres. In this case also because of the accompanied sintering it is difficult to decrease the oxygen content below 0.3 wt% with the starting sample having stoichiometric amount of carbon. However, oxygen content can be decreased further by heating the sample from 1623 to 1823 K at a constant rate of 20 K/mm, which helps in maintaining a steady rate of reaction. For still lower contents of oxygen the starting sample should have more than stoichiometric amounts of carbon. Muromura and Tagawa [16] prepared UN containing a total amount of impurities (oxygen + carbon) in the range of a 0.05-0.1 wt% using more than stoichiometric amounts of carbon in the sample. The C/UO, mole ratio was varied from 2.01 to 3.59. Complete reaction was carried out in reaction a atmosphere of NH, or 758 Hz + 25% N, or 8% H, + 92% N,. They reported that there is a minimum mixing ratio of C/UO, depending upon the temperature of reaction and reaction atmosphere. The total reaction time for the preparation of UN varied between 2 to 21 h depending upon C/UO, mole ratio, reaction atmosphere and temperature. In this procedure carbothermic nitriding reaction and removal of carbon takes place simultaneously, which makes the control of temperature and percentage of hydrogen in the reaction atmosphere very important for obtaining a pure product. Matthews et al. [17] modified the process suggested by Muromura and

48

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et al. / Kinetics of UN microspheres synthesis

Tagawa [16]. They first subjected a UO, + C mixture to carbothermic reduction under vacuum at 1873 K. When the reaction was partially complete N, + 6% Hz gas was introduced into the furnace to prepare UN and remove carbon. They studied the reaction at 1773 and 1873 K for samples having C/UO, mole ratios between 2.0 and 3.11. They reported that a C/UO, mole ratio of less than 2.2 is needed to keep carbon levels low at 1773 K reaction temperature. However, because oxygen levels increase with decreasing carbon, a higher reaction temperature (1873 K) is required to remove residual oxygen. Their product contained less than 0.05% C and 0.02% residual oxygen but details regarding batch size, N, + 6% H, gas flow rate and total reaction time are not given. In the present study the total reaction time for the preparation of UN having < 0.1 wt% OZ and < 0.2 wt% C from UO, + C microspheres containing C/UO, = 2.0 and C/JO, > 2.0 was almost the same. In case of microspheres with C/UO, > 2.0, the additional time required for removal of residual carbon, present in the form of UN,_,C,, is compensated by the fast reaction of UN,_& formation. This procedure has the advantage of yielding a purer product.

6. Conclusion The following conclusions can be drawn from the present study on reaction of UO, + C microspheres in nitrogen atmosphere; (1) Reaction of UO, + C + N, is controlled by diffusion of CO(g) through the product layer. The energy of activation is 365.7 f 14.9 kJ/mol. (2) The rate of the reaction depends upon the value of x in the intermediate UN,_& and the value of x depends upon the reaction temperature and N, pressure. (3) Sol-gel material, being very porous, has the advantage of having high reaction rates (fast diffusion of CO(g)) at relatively lower temperatures. Since at low temperatures (< 1723 K), the value of x in intermediate UN, _,C, is small, it further facilitates fast completion of the reaction. (4) The rate of the reaction at a certain temperature > 1673 K increases with the increase of carbon content in the starting material as long as an unreacted UO, core is left behind with intermediate UN, _ $2,. (5) For the preparation of pure UN (0, = 0.05 wt% and C = 0.1 wt%), in a reasonably short time, it is recommended that the starting material should have enough carbon to complete the conversion of UO1

to UN, _,C,, followed by the reaction of UN, _,C, with N, + 8% H2/ NH, to obtain UN.

References PI Hj. Matzke, Advanced LMFBR Fuels (Elsevier, Amsterdam, 1986) p. 2. PI K.M. Taylor, C.H. McMurtry and J.C. Andersen, Carbides in Nuclear Energy, Vol. 2 (Macmillan, London, 1964) p. 668. [31 J.C. Andersen and A.A. Strasser, Chemical Engineering Progress, Symp. Series No. 80 (American Institute of Chemical Engineers, New York, 1964) p. 7. 141 J.M. Horspool, N.F. Rose and M.B. Finlayson, Proc. British Ceram. Sot. 7 (1963) 23. R.A. Smith, W.M. Pardue and D.E. Kizer, BMI-1809, A-l (1967). Fl M.U. Goodyear, R.A. Smith and W.M. Pardue, BMI-1826, A-l (1968). [71 J.D.L. Harrison, J.W. Isaac, W.G. Roberts and L.E. Russell, Carbides in Nuclear Energy, Vol. 2 (Macmillan, London, 1964) p. 629. PI C. Ganguly, Ph.D. Thesis, University of Calcutta, India (1979). 191 A. Naoumidis, ORNL-tr-1918 (1968). [W K.R. Hydem, D.A. Lansman, J.B. Morris, W.E. Seddon and H.J.C. Tulloch, AERE-R-4650 (1964). [Ill K. Richter, M. Coquerelle, J. Gabolde and P. Werner, Fuel and Fuel Elements for Fast Reactors, Vol. 1 (IAEA, Vienna, 1974) STI/PUB/346, p. 71. WI W.O. Greenhalgh and E.T. Weber, BNWL-SA-1866 (1968). [13] E.T. Weber, W.O. Greenhalgh and R.I. Ribby, Trans. Am. Nucl. Sot. 2 (1968) 104. [14] T. Sano, M. Katsura and H. Kai, Thermodynamics of Nuclear Materials (IAEA, Vienna, 1967) STI/PUB/162, p. 301. [15] J.R. Mclaren, R.J. Dicker, J.D.L. Harrison and L.E. Russel, Tech. Rept. AERE-5810 (1968). [16] T. Muromura and H. Tagawa, J. Nucl. Mater. 71 (1977) 65. [17] R.B. Matthews, K.M. Chidester, C.W. Hoth, R.E. Mason and R.L. Petty, J. Nucl. Mater. 151 (1988) 334. [18] Hj. Matzke, Advanced LMFBR Fuels (Elsevier, Amsterdam, 1986) Chapter II, p. 129. [19] S. Imoto and H.J. Stocker, Thermodynamics of Nuclear Materials, Vol. II (IAEA, Vienna, 1966) STI/PUB/109, p. 533. (201 M. Henke, Neue Hutte 15 (1970) 188. [21] T.B. Lindemer, J. Am. Ceram. Sot. 55 (1972) 601. [22] W.O. Greenhalgh, J. Am. Ceram.Soc. 56 (1973) 553. [23] T. Muromura and H. Tagawa, J. Nucl. Mater. 80 (1979) 330. [24] A. Naoumidis and H.J. Stocker, Thermodynamics of Nuclear Materials (IAEA, Vienna, 1967) STI/PUB/162, p. 287.

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