- Email: [email protected]
Kinetic study of the carbothermic synthesis of uranium monocarbide microspheres
Journal of Nuclear North-Holland
Materials
172 (1990) 37-46
37
KINETIC STUDY OF THE CARBOTHERMIC MONOCARBIDE MICROSPHERES
SK. MUKERJEE,
J.V. DEHADRAYA,
SYNTHESIS
OF URANIUM
V.N. VAIDYA and D.D. SOOD
Fuel Chemistry Division, Bhabha Atomic Research Centre, Trombay, Bombay-4000085, Received
20 November
1989; accepted
8 February
India
1990
Uranium monocarbide microspheres were synthesized by carbothermic reduction of porous uranium oxide microspheres with uniformly dispersed carbon black. Kinetics of the reduction was studied under vacuum and flowing inert gas from 1250 to 1550 o C. The carbon monoxide gas concentration in the effluent stream during reduction was used to determine the rate of
carbide formation. Under vacuum, reduction was found to be controlled by reaction at the reactant-product interface whereas under flowinggas conditions, the diffusion of carbon monoxide gas through the carbide layer was the rate controlling process. The activation energy was 335.1+ 8.6 and 363.7 + 7.6 kJ/mol for reduction under vacuum and flowing gas, respectively.
1. Introduction The present trend of fast reactors towards higher operational temperature, higher linear power rating and higher breeding, points towards the possible use of carbides as nuclear fuel for future systems. Presently, carbothermic reduction of UOz + PuO, powders followed by grinding and pelletization of carbide powders is the established route for mixed carbide fuel fabrication. The sol-gel method of carbide preparation has several advantages over the conventional pellet route, as it uses a minimum number of steps with carbothermic reduction itself leading to dense particles, and no grinding or milling of reactive and pyrophoric powders is required. Several reports [l-4] have been written concerning the carbothermic reduction of carbon-containing oxide gel particles to carbide. All these reports deal with the reduction carried out in two steps: firstly the reduction of UO, to UO, by hydrogen, followed by carbothetmic reduction. This was necessary as the C/M ratio of approximately 3.5, required for direct carbothermic reduction of the particles, could not be obtained because of difficulties in the dispersion of large amounts of carbon. The hydrogen reduction of UO, is complicated due to side reaction of hydrogen and moisture with carbon [5], and thus fixing of the carbide stoichiometry becomes difficult. In the present study, the Internal Gelation Technique [6] was used for the preparation of carbon-con0022-3115/90/$03.50
0 1990 - Elsevier Science Publishers
taining uranium oxide microspheres. The problem of carbon stoichiometry could be overcome as a sufficient quantity of carbon could be dispersed in the microspheres using the proper metal ion concentration by the use of the gelation field diagram proposed by Vaidya et al. [7], and a C/M ratio of about 3.5 could be obtained easily in the microspheres. Heating of these gel particles to 650 o C under vacuum reduces UO, to UO, according to the following overall reaction: UO,(s)
+ iC(s)
+ UO,(s)
+ $0,(g).
(1)
At this temperature, the gaseous reaction product is mainly CO, [5,8], which facilitates fixing of the carbon stoichiometry for further reaction. Carbothermic reduction of these UOz microspheres has been studied with an emphasis on the reaction kinetics.
2. Theory Several models have been suggested for solid state reactions in sphere [9]. The important modes by which the reaction can take place are given in fig. 1. Stinton et al. [lo] have postulated that for the carbothermic reduction of (UO, + C) microspheres, surface nucleation is extremely fast (mode B), and the reacting particle is instantaneously covered by a thin layer of the product and the rate determining process becomes the propagation of the reacting interface into the centre of the particle, controlled by either diffusion, reaction at the
B.V. (North-Holland)
S.K. Mukerjee
38
INITIAL
et al. / Carbothermic
PARTICLE
P SOLID
PRODUCTS
NUCLEATED
A
B
C
D
-MODE
Fig. 1. Classification of solid-stateprocess.
synthesis of UC microspheres
surface or reaction at the interface. In the case of two initial reacting species (both solids), the relative sizes of the particles are important for reaction under mode B. For the purpose of evaluation, the species with larger particle size is taken as the homogeneous phase in which the particles of the second species are uniformly dispersed. In the case of (UO* + C) microspheres obtained by the sol-gel process, UO, is expected to be the continuous phase. Mode B is main reaction path for the carbothermic reduction of UOz powder. The other modes are not dominant in the present study and therefore not discussed in detail. The details of mode B are best understood from the work of Lindemer et al. [ll], who investigated the preparation of UC/UC, by the reaction of UO, microspheres (400 pm diameter) dispersed in a graphite matrix. The authors have proposed a sequence of steps which lead to the conversion of UO, to UCz. These are as follows: Step 1 C + [C]UC, at the surface. Step 2 [C]UC, diffusion from the surface to the UO,UC, interface. Step 3 The reaction [C]UC, + UO, -+ UC, + 2[O]UC, at the interface. Step 4 [O]UC, diffusion to the surface of the sphere. Step 5 [O]UC, + C --f CO(g) at the surface of the individual particles.
CONVERSION
MAIRIK
CARSON
-
CARBON
MATRIX
AREiON Fig. 2. Mechanistic model for the conversion of UO, to UC.
39
S.K. Mukerjee et al. / Carbothermic synthesis of UC microspheres [C] and [0] denotes species C and 0 in solid solution. Reaction steps 1 and 5 come under the category of surface controlled reactions, step 3 under interface controlled reactions and steps 2 and 4 come under the category of diffusion controlled processes. Similar steps are expected in the carbothermic reduction of UO, to UC when microspheres of (UO, + C) prepared by solgel process are used. For all future discussions in this paper, UC, is replaced by UC in the reaction steps 1 to 5. In this case, however, the dissolution of carbon in UC (step 1) and reaction of [O]UC with carbon (step 5) takes place not only at the surface of the particle UO,, but at the reactant-product interface within the (UO, + C) microsphere. Step 5 leads to the formation of CO within the microsphere and its diffusion through the product layer is an additional step to be considered in the present study. This step is called step number 6 for this process. Step 6 CO(g) diffusion to surface of the microsphere through the UC layer. Fig. 2 gives a mechanistic model for the carbothermic reduction of UO, to UC based on the model proposed by Stinton et al. for the carbothermic reduction of UO, to UC, [lo], which is applicable to the present study. It can be seen that for the present study the process steps are either interface reactions or diffusion reactions. The rate equations for such reactions are discussed briefly in the following section. 2.1. Interface controlled reactions When diffusion through the product layer is so rapid that the reactants cannot combine fast enough at the reaction interface to establish equilibrium, the process becomes interface controlled. Assuming that the nucleation step occurs virtually instantaneously and that the reaction rate is proportional to the surface area of the fraction of unreacted material, the rate equation can be given as follows: da/dt
= kS,/VO,
where the reaction equation, a=(%-
ratio
BMW,-
(2) (Y is given by the following
w,>.
(3) We, y, and W, are the initial weight, weight at time t, and final weight of the sample respectively, k is the rate constant, S, is the instantaneous surface area of yet unreacted particle core and V, is the original volume of the particle. After various mathematical operations, eq. (2) is reduced to the form given by Spencer and Topley [12]: 1 - (1 - 0~)~‘~ = kt/r,,,
(4)
where r, is the radius of the particle. In this type of reaction the rate decreases with decreasing radius of the reacting spherical particle. 2.2. Diffusion controlled reactions When the penetration of one of the reactants through the product layer dividing two reacting phases is the rate controlling process, then the time dependence of a gradual build up of the planar product layer is inversely proportional to its thickness: dy/dt
= k/y,
(5)
where y is the thickness of the product layer. Integration of eq. (5) gives the parabolic relation of the form y* = 2kt.
(6)
In terms of (Y,eq. (6) is written
as [13]
a*=kt.
(7)
Jander powdered equation:
[14] applied the parabolic compacts and derived
(1 - (1 - o)i”)‘=
2KDt/rz,
rate law, eq. (6) to the following rate
(8)
where K is a proportionality constant. Eq. (6) is valid under the following simplifying assumptions, namely: (i) instantaneous surface nucleation (a coherent product layer is already present), (ii) omnidirectional bulk diffusion, (iii) the immiscibility of the product phase with any of the reactant phases, (iv) the reacting particles are spheres of uniform radii and (v) the diffusion coefficient and reactant activity as well as the particle volume are constant during the process [14]. Zhuravlev, Lesokhin and Tempelman [15] modified the Jander relation by assuming that the activity of the reacting substance was proportional to the fraction of unreacted material, (1 - a), and arrived at the expression:
[(l/(1
- r~)i’~) - I]* = 2kDt/r:.
(9)
Ginstling and Brounshtein [16] discarded the parabolic law in favour of an equation relating the growth of the product layer to the decrease in interface area using Barrer’s equation [17] for steady-state heat transfer across a spherical shell, and obtained the following equation: 1 - (2a/3)
- (1 - (u)~” = 2kDt/ri.
(10)
Carter [18] and Valensi [19] accounted for differences in the volume of the product layer with respect to the volume of the reactant consumed in their equation.
S.K. Mukerjee
40
et al. / Carbothermic
They also assumed that diffusion takes place through layer of constant composition, the equation relating to t being given by
a (Y
(F/(F-1))-(1-a)2’3 - (l/(F-
l))(l
+ (Y(F-
1))“’
= 2DHM,t/d,r:, (11)
where H is the difference in concentrations of the diffusing species at the two boundaries of the product layer, and F is the ratio M,d,/M,d,, where M and d are the formula weights and densities of the reactant and product species. Although eq. (11) appears complex, it can be shown that on rearrangement it approximates to a first order relationship of the type shown below. ln( 1 - a) = - kt/rz,
(12)
where k is the rate constant. The experimental data have been analysed using eqs. (4), (7), (8)-(10) and (12) to arrive at the reaction mechanism.
3. Experimental 3. I. Sample preparation The internal gelation process and gelation assembly used for the preparation of (UO, + C) microspheres has been described elsewhere [20]. Uranyl nitrate solution was prepared by dissolving nuclear grade U,Os powder in analytical grade nitric acid. Hexamethylenetetramine (HMTA) and urea of analytical grade were used. Carbon black of “united HAF” grade, with average particle size 0.03 pm and surface area 120 m2/g was used. The maximum C/M ratio obtainable with standard feed composition, uranium molarity of 1.25M and a (HMTA, urea)/uranium mole ratio of 1.4, is 3.3. Thus in the present investigation the uranium molarity in the feed solutions was lowered to achieve a higher C/M ratio. Uranyl nitrate solution (3M) was mixed with a solution of HMTA and urea containing finely dispersed carbon powder in cold condition (0 o C) to obtain a feed solution l.lM in uranium and having a (HMTA, urea)/uranium mole ratio of 1.5. Droplets of this solution were contacted with hot silicone oil (90” C) to obtain UO, microspheres (- 2200 pm) with homogeneously dispersed carbon. In total, 10 batches were prepared and the C/M mole ratio in the feed was varied between 3.45 to 3.60. The gel particles were washed, dried and heated in argon up to 300” C to remove moisture, ammonia and residual gelation agents.
synthesis
of UC microspheres
For kinetic studies, gel particles having C/U = 3.5 were used. The specific surface area of the gel particles was determined by the BET method using an instrument supplied by Quantachrome Pvt. Ltd. For the determination of true densities, a stereo pycnometer (Quantachrome make) was used. Helium was used for the volume measurements. The specific surface area of these (UO, + C) microspheres heated at 300’ C was 55 m’/g and the true density was 4.3 g/cm3. Heating of these particles up to 650°C in a vacuum leaves behind porous (UO, + C) microspheres with a specific surface area of 22 m2/g and a true density of 6.7 g/cm3 [21]. The presence of the UO, phase was confirmed by XRD and thermogravimetric analysis. The average size of UO, or UO, particles in the (UO, + C) or (UO, + C) microspheres was calculated from the values of the specific surface area of UOs/UO, and their respective true densities. It was assumed that UO, and UO, particles are spherical in shape. The specific surface areas of UO,/UO, were obtained from the specific surface area values of their respective mixtures with carbon, by subtracting the surface area contribution of carbon. UO, particle size in (UO, + C) microspheres heated up to 300°C was 3-4 pm and the particle size of UOZ in (UO, + C) microspheres heated up to 650 o C was - 10 pm. 3.2. Apparatus Heat treatment experiments were performed with 50 g per batch in a 5 cm diameter tantalum carbide crucible. Heating was carried out in a high-temperature high-vacuum tungsten heater furnace. Carbothermic reduction of UO, takes place according to the following reaction, UO,(s)
+ 3C(s) --) UC(s)
+ 2CO(g).
(13)
Isothermal experiments to determine the rate constants were carried out at temperatures between 1250 and 1550’ C, and the soak time at various temperatures was varied between 2 and 20 h under vacuum and flowing gas conditions. The gas flow rate was varied between 50 and 80 ml/(min g) of sample. Argon gas was purified by passing over the reduced form of a copper based catalyst for removal of oxygen, and for moisture removal it was passed through 4A molecular sieves. A gas inlet made of $ inch tantalum tube was placed very near (2 cm) the sample for efficient flushing of CO gas produced. Sample temperature was measured by keeping a W-58 Re/W-26% Re thermocouple at the centre of the crucible almost touching the sample. To determine the temperature gradient across the sample, the
41
S. K. Mukerjee et al. / Carbothermic synthesis of UC microspheres temperature was also measured just outside the crucible. The temperature gradient was around 10 o C. Progress of the reaction was followed by monitoring the amount of CO gas evolved. For the experiments carried out under vacuum, total gas pressure was measured assuming that the gas was mainly composed of CO as shown by eq. (13). For the reaction carried out under flowing gas, CO was oxidised to CO2 by passing through the oxidised form of a copper based catalyst at 140 o C and subsequently trapped in NaOH solution for estimation.
4. Results
3.3. Procedure
4.1. Reaction rate
3.3.1. Reaction rate measurements 3.3.1.1. Vacuum The furnace was evacuated with the help of a Roots blower backed up by a rotary pump. At 1150° C the furnace was thoroughly degassed, so that during reduction, pressure in the furnace was mainly due to CO. The samples were heated to reaction temperatures within lo-15 min. The pumping speed (S) of the system at various pressure was determined by running the system with a constant known amount of nitrogen gas leak and noting the equilibrium pressure. It was found that the pumping speed was nearly constant during the experiments. The rate of CO release from the sample, Q(t), can be related to the pressure P(t) by the following equation:
Q(r) = SP(t),
3.3.2. Preparation of carbide Based on these studies, a procedure for the preparation of carbide microspheres by continuously heating UOz + C microspheres at a predetermined rate was established. After completion of the carbothermic reaction the microspheres were sintered at 1700°C for 2 h in high purity argon gas. The product was analysed for C, 0 and U content. X-ray diffraction analysis was used to identify the phases present. The density of the product was determined by stereo pycnometer.
(14)
where t is the reaction time. The reaction ratio a was calculated by integrating Q(t) with respect to t. Data below a = 0.2 could not be used because of the delay in attaining the reaction temperature. To check the effectiveness of the method, the samples were quenched at various reaction stages and the total carbon content was chemically analysed. The carbon content agreed well with the expected value calculated on the basis of the original carbon content and carbon lost during experiment. 3.3.1.2. Flowing gas Purified argon gas was used to flush out CO gas from the sytem, which was oxidised to CO, and quantitatively absorbed in NaOH solution. The weight gain of NaOH solution and titrimetric estimation were used to determine the amount of CO released. A correction was applied for the loss of weight of NaOH solution caused by the saturation of dry gas.
4.1.1. Vacuum The Rate of evolution of CO is shown in fig. 3, and the reaction ratio was calculated from the area integration of these curves. Typical data for the reduction carried out at 1450° C is given in table 1. At 1450° C 98% of the reaction could be completed in 100 min. Beyond a = 0.98 reaction was very slow. The reaction ratio a is plotted against time t in fig. 4. At lower temperatures, the time required for the completion of more than 95% of the reaction was over 4 h (up to 20 h). Complete data for lower temperatures is not shown in
-
15OO'C ro-SOo(UO,
lc)
MICROSPHERES
Fig. 3. Evolution of CO gas during carbothermic (UO, + C) microspheres in vacuum as a function
reaction in of time.
S. K. Mukerjee
42
et al. / Carbothermic
synthesis of UC microspheres
Table 1 Carbothermic reduction of (UO, + C) microspheres under vacuum at 1450 o C. C/U = 3.5 (C = 12.48% and U = 70.72%). Pumping speed of the system =1250 l/min, sample weight = 41.45 g Time (in) -11 -6 0 c, 12 23 27 30 38 42 50 63 80
Q(t) a)
P(r) (X102 mbar)
(X103 mol/min)
0.65 10.0 20.0 15.0 10.0 8.5 7.0 4.5 3.5 2.0 1.0 0.6
0.36 5.58 11.16 8.37 5.58 4.74 3.90 2.51 1.95 1.11 0.55 0.36
- 0.9
Amount of CO evolved b, (mol)
(y
_
_
0.023 0.037 0.120 0.177 0.188 0.202 0.225 0.234 0.251 0.271 0.276
0.08 0.13 0.42 0.62 0.66 0.71 0.79 0.82 0.88 0.95 0.97
=) Q(l) = P(~)x10-3/l.013)(1250/22.4). b, From integration of the Q(t) versus ‘) Temperature 1450 o C.
- 0.95 06
c -e Y a
- 0.8
0.4
Y - 0.7 - 0.6 - 0.5
0.2
-
0.3
- 0.1 0.0 0
40
120
00 TIME
160
(min.)
Fig. 5. Plot of (1 - (1 - CY)“~) against time for carbothermic reaction in (UO, + C) microspheres carried out under vacuum. Symbols are same as in fig. 4.
t curve. the plot in order to highlight data at higher temperatures. Also two experiments were carried out at each temperature, but data of only one is plotted in the figure. Results were fitted in the various rate equations mentioned in section 2 (eqs. (4), (7), (8)-(10) and (12)). The best linear fit was obtained with eq. (4), indicating that the reaction at the reactant-product interface is the rate controlling step. The quantity (1 - (1 - a)‘j3) is plotted against t in fig. 5. Temperature dependence of the reaction rate constant is given by the expression:
0.8
0.4
k [s-l]
= 1.82 X lo6 exp( -40185
f 451/T).
(15)
Ii
Variation of the rate constant with temperature is given in table 3. Ink values are plotted against l/T in fig. 7. From eq. (15), the value of the activation energy for reaction (13) is 335.1 k 8.6 kJ/mol for reaction under vacuum.
0.4
0.2
0.0
0
50
TIME
200
I50
100 (min
250
I
Fig. 4. Variation of reaction ratio with time for carbothermic reaction in (UOz +C) microspheres, carried out under flowing gas and vacuum. Gas flow rate = 60 ml/min/g of gel particle. Temperature Flowing gas:
Vacuum:
(“C):
1550 x
1500 n .
1450 q
.
1400 D .
1350
1300
4.1.2. Flowing gas The reaction ratio cu was calculated from the weight of CO, trapped. Typical data for the reduction carried out at 1450 o C is given in table 2. In fig. 4, a is plotted against time for a gas flow rate of 60 ml/(min g) of sample. As seen from the data given in table 2, the reaction rate in flowing gas is much slower than that in vacuum. At all temperatures the rate of reaction increased with increase of the gas flow rate. The data could be fitted to eq. (12) indicating a diffusion controlled kinetics. A plot of -ln(l - a) against t is given in fig. 6. The temperature dependence of the reaction
S. K. Mukerjee ei al. / C~~the~~c
43
synthesis of UC microspheres
Table 2 Carbothermic reduction of (UO* + C) microspheres under flowing gas at 1450°C. C/U = 3.5 (C =12.48% and U = 70.72%). Gas flow rate 60 ml/(m.in g) of sample, sample weight = 40.90 g Time (mm) 0 50
a)
100 150
200 250 300 350 400 450 SO0 550 600 650 700 750 800
Amount of COa trapped (mof)
a
0.017 0.050 0.093 0.124 0.152 0.175 0.192 0.208 0.220 0.228 0.240 0.248 0.254 0.257 0.262 0.268 0.271
0.06 0.18 0.33 0.44 0.54 0.62 0.68 0.74 0.78 0.81 0.85 0.88 0.90 0.91 0.93 0.95 0.96
- 0.1 - 0.3
-c.s -0.1 -0.8 kl - 0.9
- 0 9s
3
- 0.97
L
*
0
, 200
1
L
400 TIME
I
I
600
800
I
I min.)
Fig. 6. First order type plot for carbothermic reaction in (UO, +C) microspheres under flowing gas. Symbols are the same as in fig. 4.
af Temperature 1450 o C.
rate constant
is shown in fig. 7 and is given by the
expression: kfs-‘]
= 2.02 X 10’ exp( -43614
f 396/T).
(16) The activation energy was found to be 363.7 rf 7.6 kJ/mol for this reaction under flowing gas conditions. The values of the activation energy are less than the 385 kJ/mol reported for carbothermic reduction of
Table 3 Variation of reaction rate constant, k, with temperature for the carbothermic reaction of (UO, + C) microspheres under vacuum and flowing gas Temperature (“C) 1300 1350 1400 1450 1500 1550
a>
Reaction rate constant (10W5s-‘) vacuum af
flowing gas b,
1.51 3.34 6.13 13.60 27.50
0.46 1.35 2.80 6.36 12.30 27.10
k = (l,'t)(l - (I- L+‘~. b, k = (l/f) In(l- o).
UO, powder and pellets obtained by conventional methods [22]. This may be attributed to homogeneity of carbon dispersion in the gel, the small size of UOz particles (10 pm diameter) and its highly porous structure. 4.2. Preparation
of UC
The preparation of UC microspheres was carried out under vacuum. The results are summarised in table 4. Reduction carried out at lower temperatures (batch no. 5 and 6) resulted in a high oxygen content. This could be because of the slow rate of reaction, leading to entrapment of the reactant core inside the sintered product layer. At higher temperatures (batch no. 1, 2, 3 and 4) the rate of reaction is fast, but a good fraction of the product is cracked because of the high rate of evolution of CO gas. A compromise was made between entrapment of the reactant core and cracking of the microspheres by increasing the temperature from 1300 to 15OO’C at a constant rate of about 1°C/min. This helped the reaction to proceed at a steady rate and the product contained around 1000 ppm of oxygen. Sintering at 1700°C in purified argon gas at a pressure of 20 mbar for two hours yielded UC microspheres of - 97%
44
S.K. Mukerjee
et al. / Carbothermic
synthesis of UC microspheres
TD. Silvery shining crack-free UC microspheres be readily obtained by this procedure.
could
5. Discussion 9-
10
-
II
-
12
-
-* 5
0.58
0.54
Fig.
7. Arrhenius carbothermic
Table 4 Preparation Batch
K
plot of reaction rate constant k for the reaction in (UO, + C) microspheres.
of UC microspheres C/U
0.66
0.62 IOOOlT
in
gel
from (UO, + C) microspheres Temp. (“C)
Reaction time
Ainsley et al. carried out the reaction in vacuum, and reported solid state diffusion as the rate controlling step for carbothermic reduction of UO, + C powder and pellet [22]. They are of the opinion that carbon diffusion is rate controlling, because diffusion of oxygen as the rate controlling step would have resulted in the formation of sesquicarbide or dicarbide under vacuum, as carbon must diffuse relatively rapidly in the opposite direction. Holmes et al. [23] studied the conversion of 1.5 to 2 mm agglomerates (made from submicron carbon and UO,) to UC in a fluidised bed. Lindemer [24] analysed their data and compared the total reaction time with the value theoretically calculated on the basis of a reaction governed by steps 2 and 4 or step 6 (section 2). He reported that the reaction appeared to be controlled by the solid state diffusion process (steps 2 and 4). From the data of Ainsley et al. [22] on the variation of the reaction rate constant with CO partial pressure, Lindemer [ll] concluded that oxygen diffusion through the product layer (step 4) should be rate controlling, since an increase of CO pressure decreases the oxygen activity gradient leading to a decrease in the reaction rate. Stinton et al. [lo] investigated the conversion of (UO, + C) microspheres to (UC, + C) under fluidised bed conditions. Finely dispersed UO, in a porous carbon matrix was obtained by controlled heating of uranium loaded ion exchange resin in the absence of air. They
by carbothermic Product
reduction
under
vacuum
(wt%)
Phase
U
0
C
94.8 94.5 94.3 94.8 91.9 92.9 95.0 94.9 94.9 95.0
0.12 0.18 0.21 0.16 1.20 0.68 0.11 0.10 0.06 0.15
4.90 5.12 5.01 4.88 7.04 6.49 4.83 4.81 5.10 4.83
(h) 1
2 3 4 5 6 7 8 9 10
3.51 3.56 3.54 3.51 3.51 3.51 3.49 3.50 3.56 3.45
‘) UC is the main phase.
1500 1450 1450 1450 1300 1300 1300-1500 1300-1500 1300-1500 1300-1500
0.9 2.0 2.0 2.0 6.0 10.0 in 4 in 4 in 4 in 4
h h h h
UC, UC, UC, UC, UC2 UC 4 2 UC 2 UC, uq UC, uq UC a) UC a) UC, UC, UC a)
UC;
S.K. Mukerjee et al. / Carbothermic synthesis of UC microspheres
reported that the conversion rate was controlled by reaction at the outer surface of the microsphere. The actual surface reaction was not identified. They also reported that decreased partial pressures of CO accelerated the rate of reaction. In the present investigation with a porous UO, matrix with uniformly dispersed carbon black, carbothermic reaction is interface controlled when carried out under vacuum with reaction steps 1, 3 or 5 as rate controlling. Under a flowing gas, the reaction follows diffusion governed kinetics (steps 2, 4 or 6). The possibility of steps 2 and 4 (solid state diffusion) as rate controlling appears less likely in the light of the following three facts: (1) For a solid state diffusion controlled reaction, the mechanism will not change to interface controlled with the change of reaction conditions from flowing gas to a vacuum. (2) The extent of diffusion that CO gas has to undergo (UO, + C microsphere radius) is much more than that for carbon and oxygen (UO, particle radius). (3) The reaction rate decreases with an increase in CO partial pressure. Hence, diffusion of CO gas through the product layer appears to be rate controlling for the reaction carried out under flowing gas. Our results in a flowing gas agree with the mechanism suggested by Namba et al. 1251 for compacted (ThO, + UO, + C) specimens reduced under vacuum, but the rate equations are different. They reported Jander’s equation for diffusion limited kinetics as the best fit, whereas the present results fit the first order type relationship. The mechanism for the reduction of UO, by carbon greatly depends upon the nature of the specimen and the conditions during reaction. In fact, all three mechanisms mentioned in section 2 have been observed for specimens with different histories (method of preparation and properties such as surface area, particle size, etc.). In compacted specimens, CO diffusion through the product layer is slow and hence rate controlling. In the case of porous microspheres (present work) CO diffusion is fast under vacuum, and hence the interface reaction is rate controlling. For the same specimen reacted in flowing gas conditions, the rate is diffusion controlled because of the slow removal of CO through the product layer. Further, in the case of the specimen having finely dispersed UOZ (submicron size) in a very porous carbon matrix, when reacted under fluidised conditions, the reaction was surface controlled. 6. Conclusion The main conclusions summarised as follows.
of the present
study
can be
45
(1) The carbothermic
reduction of (UO, + C) microspheres, under vacuum, appears to be controlled by reaction at the reactant-product interface. Under flowing gas conditions the reaction is con(2) trolled by diffusion of CO gas through the product layer. (3) Activation energies for reduction carried out under vacuum and flowing gas are 335.1 + 8.6 kJ/mol and 363.7 f 7.6 kJ/mol respectively. for this reaction greatly (4) The reaction mechanism depends upon the nature of the specimen and experimental conditions. by the Internal (5) The production of UC microspheres Gelation Process, using direct carbothermic reduction of UO, microspheres without resorting to a hydrogen reduction step, is possible.
References [l] J.I. Federer and V.J. Tennery, ORNL/TM-6089 (1978). [2] K. Bischoff, V. Scherer and H. Schumacher, in: Symp. on Sol-Gel Processes and Reactor Fuel Cycle, CONF-700502 (1970) p. 164. [3] K. Bischoff, M.H. Lloyd and H. Schumacher, in: Sol-Gel Processes for Fuel Fabrication, IAEA-161 (International Atomic Energy Agency, Vienna, 1974) p. 95. [4] A. Facchini and P. Gerontopulos, in: Sol-Gel Processes for Fuel Fabrication, IAEA-161 (International Atomic Energy Agency, Vienna, 1974) p. 227. [5] G.H.B. Lovell, in: Proc. on New Nuclear Materials Including Nonmetallic Fuels, Prague, 1-5 July 1963, p. 507. [6] J.B.W. Kanij, A.J. Noothout, and 0. Votocik, Sol-Gel Processes for Fuel Fabrication, IAEA-161 (IAEA, Vienna, 1974) p. 185. [7] V.N. Vaidya, S.K. Mukerjee, J.K. Joshi, R.V. Kamat and D.D. Sood, J. Nucl. Mater. 148 (1987) 324. [8] J.J. Lawrance and D.J.O. Connor, J. Nucl. Mater. 4 (1961) 79. [9] J. Sestak, V. Satava and W.W. Wendlandt, Thermochimica Acta 7 (1973) 333. [lo] D.P. Stinton, S.M. Tiegs, W.J. Lackey and T.B. Lindemer, J. Am. Ceram. Sot. 62 (11-12) (1979) 596. [ll] T.B. Lindemer, M.D. Allen, and J.M. Leitnaker, J. Am. Ceram. Sot. 52 (1969) 233. [12] W.D. Spencer and B. Topley, J. Chem. Sot. (1929) 2633. [13] J. Sestak, in: Thermal Analysis, Vol. 3, Proc. 3rd ICTA, Davos, 1971. [14] W. Jander, Z. Anorg. Allg. Chem. 163 (1) (1927). [15] V.F. Zhuravlev, I.G. Lesokhin and R.G. Tempelman, J. Appl. Chem. USSR 21 (1948) 887. [16] A.M. Gistling and B.I. Brounshtein, J. Appl. Chem. USSR, 23 (1950) 1327. [17] R.M. Barrer, Philos. Mag. 35 (1944) 802. [18] R.E. Carter, J. Chem. Phys. 34 (1961) 2010; 35 (1961) 1137.
46
S.K. Mukerjee et al. / Carbothermic synthesis of UC microspheres
[19] M.G. Valensi, C.R. Acad. Sci. 202 (1936) 309. [20] V.N. Vaidya, R.V. Kamat and D.D. Sood, Radiochemistry Division Annual Progress Report for 1978, BARC1114 (1981). [21] S.K. Mukerjee, J.V. Dehadraya, Y.R. Bamankar, V.N. Vaidya and D.D. Sood, in: Proc. Nat. Symp. on Thermal Analysis, Kbaragpur, India, 1985. [22] R. Ainsley, B.R. Harder, N. Hodge, R.G. Sowden, D.B. White and D.C. Wood, in: Proc. on New Nuclear Materi-
als Including Nonmetallic Fuels, Prague, 1-5 July 1963, p. 349. [23] J.T. Holmes, J.R. Pavlik, P.A. Nelson and J.E.A. Graae, USAEC Report ANL-7482, Argonne National laboratory, 1968. [24] T.B. Lindemer, Nucl. Appl. Technol. 9 (1970) 711. [25] T. Namba, T. Koyama, G. Imada, A. Kanno and M. Yamawaki, J. Nucl. Mater. 150 (1987) 226.
Materials
172 (1990) 37-46
37
KINETIC STUDY OF THE CARBOTHERMIC MONOCARBIDE MICROSPHERES
SK. MUKERJEE,
J.V. DEHADRAYA,
SYNTHESIS
OF URANIUM
V.N. VAIDYA and D.D. SOOD
Fuel Chemistry Division, Bhabha Atomic Research Centre, Trombay, Bombay-4000085, Received
20 November
1989; accepted
8 February
India
1990
Uranium monocarbide microspheres were synthesized by carbothermic reduction of porous uranium oxide microspheres with uniformly dispersed carbon black. Kinetics of the reduction was studied under vacuum and flowing inert gas from 1250 to 1550 o C. The carbon monoxide gas concentration in the effluent stream during reduction was used to determine the rate of
carbide formation. Under vacuum, reduction was found to be controlled by reaction at the reactant-product interface whereas under flowinggas conditions, the diffusion of carbon monoxide gas through the carbide layer was the rate controlling process. The activation energy was 335.1+ 8.6 and 363.7 + 7.6 kJ/mol for reduction under vacuum and flowing gas, respectively.
1. Introduction The present trend of fast reactors towards higher operational temperature, higher linear power rating and higher breeding, points towards the possible use of carbides as nuclear fuel for future systems. Presently, carbothermic reduction of UOz + PuO, powders followed by grinding and pelletization of carbide powders is the established route for mixed carbide fuel fabrication. The sol-gel method of carbide preparation has several advantages over the conventional pellet route, as it uses a minimum number of steps with carbothermic reduction itself leading to dense particles, and no grinding or milling of reactive and pyrophoric powders is required. Several reports [l-4] have been written concerning the carbothermic reduction of carbon-containing oxide gel particles to carbide. All these reports deal with the reduction carried out in two steps: firstly the reduction of UO, to UO, by hydrogen, followed by carbothetmic reduction. This was necessary as the C/M ratio of approximately 3.5, required for direct carbothermic reduction of the particles, could not be obtained because of difficulties in the dispersion of large amounts of carbon. The hydrogen reduction of UO, is complicated due to side reaction of hydrogen and moisture with carbon [5], and thus fixing of the carbide stoichiometry becomes difficult. In the present study, the Internal Gelation Technique [6] was used for the preparation of carbon-con0022-3115/90/$03.50
0 1990 - Elsevier Science Publishers
taining uranium oxide microspheres. The problem of carbon stoichiometry could be overcome as a sufficient quantity of carbon could be dispersed in the microspheres using the proper metal ion concentration by the use of the gelation field diagram proposed by Vaidya et al. [7], and a C/M ratio of about 3.5 could be obtained easily in the microspheres. Heating of these gel particles to 650 o C under vacuum reduces UO, to UO, according to the following overall reaction: UO,(s)
+ iC(s)
+ UO,(s)
+ $0,(g).
(1)
At this temperature, the gaseous reaction product is mainly CO, [5,8], which facilitates fixing of the carbon stoichiometry for further reaction. Carbothermic reduction of these UOz microspheres has been studied with an emphasis on the reaction kinetics.
2. Theory Several models have been suggested for solid state reactions in sphere [9]. The important modes by which the reaction can take place are given in fig. 1. Stinton et al. [lo] have postulated that for the carbothermic reduction of (UO, + C) microspheres, surface nucleation is extremely fast (mode B), and the reacting particle is instantaneously covered by a thin layer of the product and the rate determining process becomes the propagation of the reacting interface into the centre of the particle, controlled by either diffusion, reaction at the
B.V. (North-Holland)
S.K. Mukerjee
38
INITIAL
et al. / Carbothermic
PARTICLE
P SOLID
PRODUCTS
NUCLEATED
A
B
C
D
-MODE
Fig. 1. Classification of solid-stateprocess.
synthesis of UC microspheres
surface or reaction at the interface. In the case of two initial reacting species (both solids), the relative sizes of the particles are important for reaction under mode B. For the purpose of evaluation, the species with larger particle size is taken as the homogeneous phase in which the particles of the second species are uniformly dispersed. In the case of (UO* + C) microspheres obtained by the sol-gel process, UO, is expected to be the continuous phase. Mode B is main reaction path for the carbothermic reduction of UOz powder. The other modes are not dominant in the present study and therefore not discussed in detail. The details of mode B are best understood from the work of Lindemer et al. [ll], who investigated the preparation of UC/UC, by the reaction of UO, microspheres (400 pm diameter) dispersed in a graphite matrix. The authors have proposed a sequence of steps which lead to the conversion of UO, to UCz. These are as follows: Step 1 C + [C]UC, at the surface. Step 2 [C]UC, diffusion from the surface to the UO,UC, interface. Step 3 The reaction [C]UC, + UO, -+ UC, + 2[O]UC, at the interface. Step 4 [O]UC, diffusion to the surface of the sphere. Step 5 [O]UC, + C --f CO(g) at the surface of the individual particles.
CONVERSION
MAIRIK
CARSON
-
CARBON
MATRIX
AREiON Fig. 2. Mechanistic model for the conversion of UO, to UC.
39
S.K. Mukerjee et al. / Carbothermic synthesis of UC microspheres [C] and [0] denotes species C and 0 in solid solution. Reaction steps 1 and 5 come under the category of surface controlled reactions, step 3 under interface controlled reactions and steps 2 and 4 come under the category of diffusion controlled processes. Similar steps are expected in the carbothermic reduction of UO, to UC when microspheres of (UO, + C) prepared by solgel process are used. For all future discussions in this paper, UC, is replaced by UC in the reaction steps 1 to 5. In this case, however, the dissolution of carbon in UC (step 1) and reaction of [O]UC with carbon (step 5) takes place not only at the surface of the particle UO,, but at the reactant-product interface within the (UO, + C) microsphere. Step 5 leads to the formation of CO within the microsphere and its diffusion through the product layer is an additional step to be considered in the present study. This step is called step number 6 for this process. Step 6 CO(g) diffusion to surface of the microsphere through the UC layer. Fig. 2 gives a mechanistic model for the carbothermic reduction of UO, to UC based on the model proposed by Stinton et al. for the carbothermic reduction of UO, to UC, [lo], which is applicable to the present study. It can be seen that for the present study the process steps are either interface reactions or diffusion reactions. The rate equations for such reactions are discussed briefly in the following section. 2.1. Interface controlled reactions When diffusion through the product layer is so rapid that the reactants cannot combine fast enough at the reaction interface to establish equilibrium, the process becomes interface controlled. Assuming that the nucleation step occurs virtually instantaneously and that the reaction rate is proportional to the surface area of the fraction of unreacted material, the rate equation can be given as follows: da/dt
= kS,/VO,
where the reaction equation, a=(%-
ratio
BMW,-
(2) (Y is given by the following
w,>.
(3) We, y, and W, are the initial weight, weight at time t, and final weight of the sample respectively, k is the rate constant, S, is the instantaneous surface area of yet unreacted particle core and V, is the original volume of the particle. After various mathematical operations, eq. (2) is reduced to the form given by Spencer and Topley [12]: 1 - (1 - 0~)~‘~ = kt/r,,,
(4)
where r, is the radius of the particle. In this type of reaction the rate decreases with decreasing radius of the reacting spherical particle. 2.2. Diffusion controlled reactions When the penetration of one of the reactants through the product layer dividing two reacting phases is the rate controlling process, then the time dependence of a gradual build up of the planar product layer is inversely proportional to its thickness: dy/dt
= k/y,
(5)
where y is the thickness of the product layer. Integration of eq. (5) gives the parabolic relation of the form y* = 2kt.
(6)
In terms of (Y,eq. (6) is written
as [13]
a*=kt.
(7)
Jander powdered equation:
[14] applied the parabolic compacts and derived
(1 - (1 - o)i”)‘=
2KDt/rz,
rate law, eq. (6) to the following rate
(8)
where K is a proportionality constant. Eq. (6) is valid under the following simplifying assumptions, namely: (i) instantaneous surface nucleation (a coherent product layer is already present), (ii) omnidirectional bulk diffusion, (iii) the immiscibility of the product phase with any of the reactant phases, (iv) the reacting particles are spheres of uniform radii and (v) the diffusion coefficient and reactant activity as well as the particle volume are constant during the process [14]. Zhuravlev, Lesokhin and Tempelman [15] modified the Jander relation by assuming that the activity of the reacting substance was proportional to the fraction of unreacted material, (1 - a), and arrived at the expression:
[(l/(1
- r~)i’~) - I]* = 2kDt/r:.
(9)
Ginstling and Brounshtein [16] discarded the parabolic law in favour of an equation relating the growth of the product layer to the decrease in interface area using Barrer’s equation [17] for steady-state heat transfer across a spherical shell, and obtained the following equation: 1 - (2a/3)
- (1 - (u)~” = 2kDt/ri.
(10)
Carter [18] and Valensi [19] accounted for differences in the volume of the product layer with respect to the volume of the reactant consumed in their equation.
S.K. Mukerjee
40
et al. / Carbothermic
They also assumed that diffusion takes place through layer of constant composition, the equation relating to t being given by
a (Y
(F/(F-1))-(1-a)2’3 - (l/(F-
l))(l
+ (Y(F-
1))“’
= 2DHM,t/d,r:, (11)
where H is the difference in concentrations of the diffusing species at the two boundaries of the product layer, and F is the ratio M,d,/M,d,, where M and d are the formula weights and densities of the reactant and product species. Although eq. (11) appears complex, it can be shown that on rearrangement it approximates to a first order relationship of the type shown below. ln( 1 - a) = - kt/rz,
(12)
where k is the rate constant. The experimental data have been analysed using eqs. (4), (7), (8)-(10) and (12) to arrive at the reaction mechanism.
3. Experimental 3. I. Sample preparation The internal gelation process and gelation assembly used for the preparation of (UO, + C) microspheres has been described elsewhere [20]. Uranyl nitrate solution was prepared by dissolving nuclear grade U,Os powder in analytical grade nitric acid. Hexamethylenetetramine (HMTA) and urea of analytical grade were used. Carbon black of “united HAF” grade, with average particle size 0.03 pm and surface area 120 m2/g was used. The maximum C/M ratio obtainable with standard feed composition, uranium molarity of 1.25M and a (HMTA, urea)/uranium mole ratio of 1.4, is 3.3. Thus in the present investigation the uranium molarity in the feed solutions was lowered to achieve a higher C/M ratio. Uranyl nitrate solution (3M) was mixed with a solution of HMTA and urea containing finely dispersed carbon powder in cold condition (0 o C) to obtain a feed solution l.lM in uranium and having a (HMTA, urea)/uranium mole ratio of 1.5. Droplets of this solution were contacted with hot silicone oil (90” C) to obtain UO, microspheres (- 2200 pm) with homogeneously dispersed carbon. In total, 10 batches were prepared and the C/M mole ratio in the feed was varied between 3.45 to 3.60. The gel particles were washed, dried and heated in argon up to 300” C to remove moisture, ammonia and residual gelation agents.
synthesis
of UC microspheres
For kinetic studies, gel particles having C/U = 3.5 were used. The specific surface area of the gel particles was determined by the BET method using an instrument supplied by Quantachrome Pvt. Ltd. For the determination of true densities, a stereo pycnometer (Quantachrome make) was used. Helium was used for the volume measurements. The specific surface area of these (UO, + C) microspheres heated at 300’ C was 55 m’/g and the true density was 4.3 g/cm3. Heating of these particles up to 650°C in a vacuum leaves behind porous (UO, + C) microspheres with a specific surface area of 22 m2/g and a true density of 6.7 g/cm3 [21]. The presence of the UO, phase was confirmed by XRD and thermogravimetric analysis. The average size of UO, or UO, particles in the (UO, + C) or (UO, + C) microspheres was calculated from the values of the specific surface area of UOs/UO, and their respective true densities. It was assumed that UO, and UO, particles are spherical in shape. The specific surface areas of UO,/UO, were obtained from the specific surface area values of their respective mixtures with carbon, by subtracting the surface area contribution of carbon. UO, particle size in (UO, + C) microspheres heated up to 300°C was 3-4 pm and the particle size of UOZ in (UO, + C) microspheres heated up to 650 o C was - 10 pm. 3.2. Apparatus Heat treatment experiments were performed with 50 g per batch in a 5 cm diameter tantalum carbide crucible. Heating was carried out in a high-temperature high-vacuum tungsten heater furnace. Carbothermic reduction of UO, takes place according to the following reaction, UO,(s)
+ 3C(s) --) UC(s)
+ 2CO(g).
(13)
Isothermal experiments to determine the rate constants were carried out at temperatures between 1250 and 1550’ C, and the soak time at various temperatures was varied between 2 and 20 h under vacuum and flowing gas conditions. The gas flow rate was varied between 50 and 80 ml/(min g) of sample. Argon gas was purified by passing over the reduced form of a copper based catalyst for removal of oxygen, and for moisture removal it was passed through 4A molecular sieves. A gas inlet made of $ inch tantalum tube was placed very near (2 cm) the sample for efficient flushing of CO gas produced. Sample temperature was measured by keeping a W-58 Re/W-26% Re thermocouple at the centre of the crucible almost touching the sample. To determine the temperature gradient across the sample, the
41
S. K. Mukerjee et al. / Carbothermic synthesis of UC microspheres temperature was also measured just outside the crucible. The temperature gradient was around 10 o C. Progress of the reaction was followed by monitoring the amount of CO gas evolved. For the experiments carried out under vacuum, total gas pressure was measured assuming that the gas was mainly composed of CO as shown by eq. (13). For the reaction carried out under flowing gas, CO was oxidised to CO2 by passing through the oxidised form of a copper based catalyst at 140 o C and subsequently trapped in NaOH solution for estimation.
4. Results
3.3. Procedure
4.1. Reaction rate
3.3.1. Reaction rate measurements 3.3.1.1. Vacuum The furnace was evacuated with the help of a Roots blower backed up by a rotary pump. At 1150° C the furnace was thoroughly degassed, so that during reduction, pressure in the furnace was mainly due to CO. The samples were heated to reaction temperatures within lo-15 min. The pumping speed (S) of the system at various pressure was determined by running the system with a constant known amount of nitrogen gas leak and noting the equilibrium pressure. It was found that the pumping speed was nearly constant during the experiments. The rate of CO release from the sample, Q(t), can be related to the pressure P(t) by the following equation:
Q(r) = SP(t),
3.3.2. Preparation of carbide Based on these studies, a procedure for the preparation of carbide microspheres by continuously heating UOz + C microspheres at a predetermined rate was established. After completion of the carbothermic reaction the microspheres were sintered at 1700°C for 2 h in high purity argon gas. The product was analysed for C, 0 and U content. X-ray diffraction analysis was used to identify the phases present. The density of the product was determined by stereo pycnometer.
(14)
where t is the reaction time. The reaction ratio a was calculated by integrating Q(t) with respect to t. Data below a = 0.2 could not be used because of the delay in attaining the reaction temperature. To check the effectiveness of the method, the samples were quenched at various reaction stages and the total carbon content was chemically analysed. The carbon content agreed well with the expected value calculated on the basis of the original carbon content and carbon lost during experiment. 3.3.1.2. Flowing gas Purified argon gas was used to flush out CO gas from the sytem, which was oxidised to CO, and quantitatively absorbed in NaOH solution. The weight gain of NaOH solution and titrimetric estimation were used to determine the amount of CO released. A correction was applied for the loss of weight of NaOH solution caused by the saturation of dry gas.
4.1.1. Vacuum The Rate of evolution of CO is shown in fig. 3, and the reaction ratio was calculated from the area integration of these curves. Typical data for the reduction carried out at 1450° C is given in table 1. At 1450° C 98% of the reaction could be completed in 100 min. Beyond a = 0.98 reaction was very slow. The reaction ratio a is plotted against time t in fig. 4. At lower temperatures, the time required for the completion of more than 95% of the reaction was over 4 h (up to 20 h). Complete data for lower temperatures is not shown in
-
15OO'C ro-SOo(UO,
lc)
MICROSPHERES
Fig. 3. Evolution of CO gas during carbothermic (UO, + C) microspheres in vacuum as a function
reaction in of time.
S. K. Mukerjee
42
et al. / Carbothermic
synthesis of UC microspheres
Table 1 Carbothermic reduction of (UO, + C) microspheres under vacuum at 1450 o C. C/U = 3.5 (C = 12.48% and U = 70.72%). Pumping speed of the system =1250 l/min, sample weight = 41.45 g Time (in) -11 -6 0 c, 12 23 27 30 38 42 50 63 80
Q(t) a)
P(r) (X102 mbar)
(X103 mol/min)
0.65 10.0 20.0 15.0 10.0 8.5 7.0 4.5 3.5 2.0 1.0 0.6
0.36 5.58 11.16 8.37 5.58 4.74 3.90 2.51 1.95 1.11 0.55 0.36
- 0.9
Amount of CO evolved b, (mol)
(y
_
_
0.023 0.037 0.120 0.177 0.188 0.202 0.225 0.234 0.251 0.271 0.276
0.08 0.13 0.42 0.62 0.66 0.71 0.79 0.82 0.88 0.95 0.97
=) Q(l) = P(~)x10-3/l.013)(1250/22.4). b, From integration of the Q(t) versus ‘) Temperature 1450 o C.
- 0.95 06
c -e Y a
- 0.8
0.4
Y - 0.7 - 0.6 - 0.5
0.2
-
0.3
- 0.1 0.0 0
40
120
00 TIME
160
(min.)
Fig. 5. Plot of (1 - (1 - CY)“~) against time for carbothermic reaction in (UO, + C) microspheres carried out under vacuum. Symbols are same as in fig. 4.
t curve. the plot in order to highlight data at higher temperatures. Also two experiments were carried out at each temperature, but data of only one is plotted in the figure. Results were fitted in the various rate equations mentioned in section 2 (eqs. (4), (7), (8)-(10) and (12)). The best linear fit was obtained with eq. (4), indicating that the reaction at the reactant-product interface is the rate controlling step. The quantity (1 - (1 - a)‘j3) is plotted against t in fig. 5. Temperature dependence of the reaction rate constant is given by the expression:
0.8
0.4
k [s-l]
= 1.82 X lo6 exp( -40185
f 451/T).
(15)
Ii
Variation of the rate constant with temperature is given in table 3. Ink values are plotted against l/T in fig. 7. From eq. (15), the value of the activation energy for reaction (13) is 335.1 k 8.6 kJ/mol for reaction under vacuum.
0.4
0.2
0.0
0
50
TIME
200
I50
100 (min
250
I
Fig. 4. Variation of reaction ratio with time for carbothermic reaction in (UOz +C) microspheres, carried out under flowing gas and vacuum. Gas flow rate = 60 ml/min/g of gel particle. Temperature Flowing gas:
Vacuum:
(“C):
1550 x
1500 n .
1450 q
.
1400 D .
1350
1300
4.1.2. Flowing gas The reaction ratio cu was calculated from the weight of CO, trapped. Typical data for the reduction carried out at 1450 o C is given in table 2. In fig. 4, a is plotted against time for a gas flow rate of 60 ml/(min g) of sample. As seen from the data given in table 2, the reaction rate in flowing gas is much slower than that in vacuum. At all temperatures the rate of reaction increased with increase of the gas flow rate. The data could be fitted to eq. (12) indicating a diffusion controlled kinetics. A plot of -ln(l - a) against t is given in fig. 6. The temperature dependence of the reaction
S. K. Mukerjee ei al. / C~~the~~c
43
synthesis of UC microspheres
Table 2 Carbothermic reduction of (UO* + C) microspheres under flowing gas at 1450°C. C/U = 3.5 (C =12.48% and U = 70.72%). Gas flow rate 60 ml/(m.in g) of sample, sample weight = 40.90 g Time (mm) 0 50
a)
100 150
200 250 300 350 400 450 SO0 550 600 650 700 750 800
Amount of COa trapped (mof)
a
0.017 0.050 0.093 0.124 0.152 0.175 0.192 0.208 0.220 0.228 0.240 0.248 0.254 0.257 0.262 0.268 0.271
0.06 0.18 0.33 0.44 0.54 0.62 0.68 0.74 0.78 0.81 0.85 0.88 0.90 0.91 0.93 0.95 0.96
- 0.1 - 0.3
-c.s -0.1 -0.8 kl - 0.9
- 0 9s
3
- 0.97
L
*
0
, 200
1
L
400 TIME
I
I
600
800
I
I min.)
Fig. 6. First order type plot for carbothermic reaction in (UO, +C) microspheres under flowing gas. Symbols are the same as in fig. 4.
af Temperature 1450 o C.
rate constant
is shown in fig. 7 and is given by the
expression: kfs-‘]
= 2.02 X 10’ exp( -43614
f 396/T).
(16) The activation energy was found to be 363.7 rf 7.6 kJ/mol for this reaction under flowing gas conditions. The values of the activation energy are less than the 385 kJ/mol reported for carbothermic reduction of
Table 3 Variation of reaction rate constant, k, with temperature for the carbothermic reaction of (UO, + C) microspheres under vacuum and flowing gas Temperature (“C) 1300 1350 1400 1450 1500 1550
a>
Reaction rate constant (10W5s-‘) vacuum af
flowing gas b,
1.51 3.34 6.13 13.60 27.50
0.46 1.35 2.80 6.36 12.30 27.10
k = (l,'t)(l - (I- L+‘~. b, k = (l/f) In(l- o).
UO, powder and pellets obtained by conventional methods [22]. This may be attributed to homogeneity of carbon dispersion in the gel, the small size of UOz particles (10 pm diameter) and its highly porous structure. 4.2. Preparation
of UC
The preparation of UC microspheres was carried out under vacuum. The results are summarised in table 4. Reduction carried out at lower temperatures (batch no. 5 and 6) resulted in a high oxygen content. This could be because of the slow rate of reaction, leading to entrapment of the reactant core inside the sintered product layer. At higher temperatures (batch no. 1, 2, 3 and 4) the rate of reaction is fast, but a good fraction of the product is cracked because of the high rate of evolution of CO gas. A compromise was made between entrapment of the reactant core and cracking of the microspheres by increasing the temperature from 1300 to 15OO’C at a constant rate of about 1°C/min. This helped the reaction to proceed at a steady rate and the product contained around 1000 ppm of oxygen. Sintering at 1700°C in purified argon gas at a pressure of 20 mbar for two hours yielded UC microspheres of - 97%
44
S.K. Mukerjee
et al. / Carbothermic
synthesis of UC microspheres
TD. Silvery shining crack-free UC microspheres be readily obtained by this procedure.
could
5. Discussion 9-
10
-
II
-
12
-
-* 5
0.58
0.54
Fig.
7. Arrhenius carbothermic
Table 4 Preparation Batch
K
plot of reaction rate constant k for the reaction in (UO, + C) microspheres.
of UC microspheres C/U
0.66
0.62 IOOOlT
in
gel
from (UO, + C) microspheres Temp. (“C)
Reaction time
Ainsley et al. carried out the reaction in vacuum, and reported solid state diffusion as the rate controlling step for carbothermic reduction of UO, + C powder and pellet [22]. They are of the opinion that carbon diffusion is rate controlling, because diffusion of oxygen as the rate controlling step would have resulted in the formation of sesquicarbide or dicarbide under vacuum, as carbon must diffuse relatively rapidly in the opposite direction. Holmes et al. [23] studied the conversion of 1.5 to 2 mm agglomerates (made from submicron carbon and UO,) to UC in a fluidised bed. Lindemer [24] analysed their data and compared the total reaction time with the value theoretically calculated on the basis of a reaction governed by steps 2 and 4 or step 6 (section 2). He reported that the reaction appeared to be controlled by the solid state diffusion process (steps 2 and 4). From the data of Ainsley et al. [22] on the variation of the reaction rate constant with CO partial pressure, Lindemer [ll] concluded that oxygen diffusion through the product layer (step 4) should be rate controlling, since an increase of CO pressure decreases the oxygen activity gradient leading to a decrease in the reaction rate. Stinton et al. [lo] investigated the conversion of (UO, + C) microspheres to (UC, + C) under fluidised bed conditions. Finely dispersed UO, in a porous carbon matrix was obtained by controlled heating of uranium loaded ion exchange resin in the absence of air. They
by carbothermic Product
reduction
under
vacuum
(wt%)
Phase
U
0
C
94.8 94.5 94.3 94.8 91.9 92.9 95.0 94.9 94.9 95.0
0.12 0.18 0.21 0.16 1.20 0.68 0.11 0.10 0.06 0.15
4.90 5.12 5.01 4.88 7.04 6.49 4.83 4.81 5.10 4.83
(h) 1
2 3 4 5 6 7 8 9 10
3.51 3.56 3.54 3.51 3.51 3.51 3.49 3.50 3.56 3.45
‘) UC is the main phase.
1500 1450 1450 1450 1300 1300 1300-1500 1300-1500 1300-1500 1300-1500
0.9 2.0 2.0 2.0 6.0 10.0 in 4 in 4 in 4 in 4
h h h h
UC, UC, UC, UC, UC2 UC 4 2 UC 2 UC, uq UC, uq UC a) UC a) UC, UC, UC a)
UC;
S.K. Mukerjee et al. / Carbothermic synthesis of UC microspheres
reported that the conversion rate was controlled by reaction at the outer surface of the microsphere. The actual surface reaction was not identified. They also reported that decreased partial pressures of CO accelerated the rate of reaction. In the present investigation with a porous UO, matrix with uniformly dispersed carbon black, carbothermic reaction is interface controlled when carried out under vacuum with reaction steps 1, 3 or 5 as rate controlling. Under a flowing gas, the reaction follows diffusion governed kinetics (steps 2, 4 or 6). The possibility of steps 2 and 4 (solid state diffusion) as rate controlling appears less likely in the light of the following three facts: (1) For a solid state diffusion controlled reaction, the mechanism will not change to interface controlled with the change of reaction conditions from flowing gas to a vacuum. (2) The extent of diffusion that CO gas has to undergo (UO, + C microsphere radius) is much more than that for carbon and oxygen (UO, particle radius). (3) The reaction rate decreases with an increase in CO partial pressure. Hence, diffusion of CO gas through the product layer appears to be rate controlling for the reaction carried out under flowing gas. Our results in a flowing gas agree with the mechanism suggested by Namba et al. 1251 for compacted (ThO, + UO, + C) specimens reduced under vacuum, but the rate equations are different. They reported Jander’s equation for diffusion limited kinetics as the best fit, whereas the present results fit the first order type relationship. The mechanism for the reduction of UO, by carbon greatly depends upon the nature of the specimen and the conditions during reaction. In fact, all three mechanisms mentioned in section 2 have been observed for specimens with different histories (method of preparation and properties such as surface area, particle size, etc.). In compacted specimens, CO diffusion through the product layer is slow and hence rate controlling. In the case of porous microspheres (present work) CO diffusion is fast under vacuum, and hence the interface reaction is rate controlling. For the same specimen reacted in flowing gas conditions, the rate is diffusion controlled because of the slow removal of CO through the product layer. Further, in the case of the specimen having finely dispersed UOZ (submicron size) in a very porous carbon matrix, when reacted under fluidised conditions, the reaction was surface controlled. 6. Conclusion The main conclusions summarised as follows.
of the present
study
can be
45
(1) The carbothermic
reduction of (UO, + C) microspheres, under vacuum, appears to be controlled by reaction at the reactant-product interface. Under flowing gas conditions the reaction is con(2) trolled by diffusion of CO gas through the product layer. (3) Activation energies for reduction carried out under vacuum and flowing gas are 335.1 + 8.6 kJ/mol and 363.7 f 7.6 kJ/mol respectively. for this reaction greatly (4) The reaction mechanism depends upon the nature of the specimen and experimental conditions. by the Internal (5) The production of UC microspheres Gelation Process, using direct carbothermic reduction of UO, microspheres without resorting to a hydrogen reduction step, is possible.
References [l] J.I. Federer and V.J. Tennery, ORNL/TM-6089 (1978). [2] K. Bischoff, V. Scherer and H. Schumacher, in: Symp. on Sol-Gel Processes and Reactor Fuel Cycle, CONF-700502 (1970) p. 164. [3] K. Bischoff, M.H. Lloyd and H. Schumacher, in: Sol-Gel Processes for Fuel Fabrication, IAEA-161 (International Atomic Energy Agency, Vienna, 1974) p. 95. [4] A. Facchini and P. Gerontopulos, in: Sol-Gel Processes for Fuel Fabrication, IAEA-161 (International Atomic Energy Agency, Vienna, 1974) p. 227. [5] G.H.B. Lovell, in: Proc. on New Nuclear Materials Including Nonmetallic Fuels, Prague, 1-5 July 1963, p. 507. [6] J.B.W. Kanij, A.J. Noothout, and 0. Votocik, Sol-Gel Processes for Fuel Fabrication, IAEA-161 (IAEA, Vienna, 1974) p. 185. [7] V.N. Vaidya, S.K. Mukerjee, J.K. Joshi, R.V. Kamat and D.D. Sood, J. Nucl. Mater. 148 (1987) 324. [8] J.J. Lawrance and D.J.O. Connor, J. Nucl. Mater. 4 (1961) 79. [9] J. Sestak, V. Satava and W.W. Wendlandt, Thermochimica Acta 7 (1973) 333. [lo] D.P. Stinton, S.M. Tiegs, W.J. Lackey and T.B. Lindemer, J. Am. Ceram. Sot. 62 (11-12) (1979) 596. [ll] T.B. Lindemer, M.D. Allen, and J.M. Leitnaker, J. Am. Ceram. Sot. 52 (1969) 233. [12] W.D. Spencer and B. Topley, J. Chem. Sot. (1929) 2633. [13] J. Sestak, in: Thermal Analysis, Vol. 3, Proc. 3rd ICTA, Davos, 1971. [14] W. Jander, Z. Anorg. Allg. Chem. 163 (1) (1927). [15] V.F. Zhuravlev, I.G. Lesokhin and R.G. Tempelman, J. Appl. Chem. USSR 21 (1948) 887. [16] A.M. Gistling and B.I. Brounshtein, J. Appl. Chem. USSR, 23 (1950) 1327. [17] R.M. Barrer, Philos. Mag. 35 (1944) 802. [18] R.E. Carter, J. Chem. Phys. 34 (1961) 2010; 35 (1961) 1137.
46
S.K. Mukerjee et al. / Carbothermic synthesis of UC microspheres
[19] M.G. Valensi, C.R. Acad. Sci. 202 (1936) 309. [20] V.N. Vaidya, R.V. Kamat and D.D. Sood, Radiochemistry Division Annual Progress Report for 1978, BARC1114 (1981). [21] S.K. Mukerjee, J.V. Dehadraya, Y.R. Bamankar, V.N. Vaidya and D.D. Sood, in: Proc. Nat. Symp. on Thermal Analysis, Kbaragpur, India, 1985. [22] R. Ainsley, B.R. Harder, N. Hodge, R.G. Sowden, D.B. White and D.C. Wood, in: Proc. on New Nuclear Materi-
als Including Nonmetallic Fuels, Prague, 1-5 July 1963, p. 349. [23] J.T. Holmes, J.R. Pavlik, P.A. Nelson and J.E.A. Graae, USAEC Report ANL-7482, Argonne National laboratory, 1968. [24] T.B. Lindemer, Nucl. Appl. Technol. 9 (1970) 711. [25] T. Namba, T. Koyama, G. Imada, A. Kanno and M. Yamawaki, J. Nucl. Mater. 150 (1987) 226.