0016.7037/90/$3.00
Geochimrco a Cosmochimica Acla Vol. 54, pp. 18791887 Copyright 0 1990 Pergamon Press pk. Printed in U.S.A.
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Leaching of uranium and thorium from monazite: II. Elemental leaching DONALD R. OLANDER’ and YEHUDA EYAL* ‘Materials and Chemical Sciences Division, Lawrence Berkeley Laboratory and Department of Nuclear Engineering, University of California, Berkeley, CA 94720, USA *Department of Chemistry and Department of Nuclear Engineering, TechnionIsrael Institute of Technology, Haifa 32000, Israel (Received May
9, 1989; accepted in revised form April 10, 1990)
AbstractData
on the leaching of U and Th from monazite are analyzed by a solidstate, movingboundary diffusion model with a surface reaction boundary condition. Nonstoichiometric leaching of the actinide elements with respect to each other and to the matrix is due to different transport properties of the former in the nearsurface layers of the mineral and to the interplay of the diffusion process with mineral dissolution, which causes surface motion. Surface chemical kinetics (i.e., the rate of actinide element detachment from the surface into the solution) is rapid compared to diffusion in the solid, except for Th in an annealed monazite specimen. Diffusion coefficients between 1O23 and lol9 cm2/s are deduced from comparison of the model to the data. These mobilities represent movement of the actinide elements along various highdiffusivity pathways rather than true lattice diffusion. INTRODUCTION
also observed in the leaching rates of isotopes of both U and Th. Incongruent leaching may arise from differences in the rates of one or more of the following solution/mineral processes:
MANY MINERALS,EITHEROVER long time periods exposed to natural conditions or in laboratory tests accelerated by use of chemically active leachants, exhibit complex timedependent leach rates of their constituents. The mechanisms of actinide removal from radioactive minerals or from synthetic nuclear wasteforms can be divided into two categories. In the first and most common situation, the mineral (or synthetic) matrix has a higher solubility in the aqueous phase than the actinides, and the latter precipitate on the surface of the solid as the matrix dissolves. The solubility of the actinide ion in the precipitate provides the driving force for mass transfer into the liquid, which is the ratelimiting process that determines the actinide removal rate. In the second, less common situation, the actinides are more soluble in the aqueous phase than the matrix. In this situation, actinide precipitates do not build up on the solid surface. Rather, the surface of the dissolving solid becomes depleted in the actinide ions. If these ions are not mobile in the solid, dissolution is congruent, and the actinidetomatrix ion flux ratio is equal to the concentration ratio in the bulk solid. If the actinide ions can diffuse in the solid, however, dissolution of the solid constituents is incongruent. This type of leaching mechanism may apply to actinide leaching from matrix solids that are particularly resistant to dissolution (e.g., natural monazite and synthetic analogs) and for leaching solutions that contain anions which strongly complex the actinide cations (e.g., aqueous solutions containing HCO; /CO:). Although current modeling of the performance of nuclear wasteforms in groundwater is based upon the solubilitylimited mass transfer mechanism, some combinations of groundwater chemistry and wasteform stability may result in actinide removal mechanisms of the second category described above. As shown in Part 1 of this series (EYAL and OLANDER, 1990), the dissolution of monazite constituents in a bicarbonatecarbonate leaching solution is incongruent (or nonstoichiometric); the fractional release rates of U, Th, and the matrix are not equal. Significant nonstoichiometry was
transport kinetics in the solid, which supplies the dissolving constituent to the surface from the interior; the kinetics of conversion of the species at the surface from the solid to dissolved state; Mass transfer of the dissolved species from the surface to the bulk liquid by diffusion; approach to saturation of the dissolving species in the bulk liquid. Each of the above steps is characterized by physicochemical parameters whose use allows these processes to be readily modeled. These parameters are the solidstate diffusivity (step 1), the leachrate constant (step 2), the external masstransfer diffusivity coefficient (step 3)) and the saturation concentration and the ratio of the solid surface to liquid volume (step 4). The model presented here considers the processes outlined above and is applied to measurements of longterm leaching of monazite, (Ce,La,Th,U)POd, described in detail in Part I of this series ( EYALand OLANDER,1990). The present paper concentrates on modeling the dissolution of the mineral over periods from 1 day to 6.8 years, and the leaching of U (represented by its primary isotope 238U) and Th (represented by its primary isotope 232Th) from the matrix during this time. The objectives of the analysis are first to demonstrate that the model accurately describes the experimental results and second to deduce the values of the transport and reaction parameters which quantitatively characterize the leaching process. The initial period of high leach rates that was treated in Part I ( EYALand OLANDER,1990) is considered here only insofar as it contributes to the total leach rate during the early stages of the experiment. Part III of this series (OLANDER and EYAL, 1990) treats the leaching characteristics of the radiogenic daughters of the primary U and Th isotopes. 1879
D. R. Olander and Y. Eyal
1880
MODEL DESCRIF’T’ION The mineral is assumed to be a homogeneous, singlephase body, with both major and minor cation types. Mineral mass loss associated with the dissolution of the major species causes regression of the mineral surface, whereas leaching of a minor species does not. While this distinction is not clearcut in a physical sense, it is a useful concept for quantitative modeling. The major elements in monazite are the rare earths (comprising the mineral matrix), while Th and U are the minor elements (the abundances of Th and U are  10 and 0.2 wt%, respectively). The Th and U are in solid solution in the matrix. Preferential leaching of the actinides alters their concentrations at the surface of the solid but does not change the crystal structure. The formation of surface layers that have compositions and structures different from the bulk mineral, as may occur during incongruent hydrolysis of feldspars ( HELGESONet al., 1984)) is not considered. Behavior of the Major Element AAGAARDand HELGESON( 1982) have provided a general rate equation for mineralsolution reaction. For the present analysis, the simpler flux equation proposed by GRAMBOW ( 1985) is adopted: ro = bNo( 1  polio,,),
(1)
where kdlr, is the forward rate constant of the mineral dissolution reaction, No is the metal atom density in the mineral, and b is the maximum dissolution velocity or the speed of recession of the mineral surface when the system is far from equilibrium. The quantity a0 is the solution activity of the dissolved majorelement species. In a closed system with a fixed volume of leachant, the value of & increases with leaching time from an initial value of zero and asymptotically approaches the saturation activity a~,~,. The kinetics of approach to saturation is governed by mass balance of the major element in the leach solution: v(dColdt)
= 3.0 = .%No(
1  ColCo,sat),
(2)
where u is the volume of the leachant contacting the mineral with surface area, S, and Co is the concentration of the major element in solution. The activity coefficient of this species in the liquid has been assumed constant, so the activity ratio in Eqn. ( 1) is replaced by the concentration ratio. Equation (2) can be solved to yield cot Co,,, = 1 
(3)
exp(tlTo),
where r. is the characteristic time for approach to majorelement saturation of the leachant, ro = nco,satl(skoNo).
(4)
The surface recession velocity, u = ro/ No, is given by combining Eqns. ( 1) and ( 3)) u = b exp( t/To).
(5)
The increment of the fraction of the mineral dissolved in a time 6t after exposure to fresh leachant is & = S/( VNo) 6” r,,dt = (S/V)
l6’ udt,
(6)
where V is the volume of the solid mineral. Small changes in mineral volume and surface area during dissolution are neglected. Using Eqn. (5) for u, the above equation yields %I =
(S/Ww0{1

exp(6tl70)}.
(7)
In a series of J leaching steps between which the solution is replenished with fresh leachant (see EYAL and OLANDER, 1990), the cumulative fraction of the mineral dissolved is f0 = (S/V)&0
i
{ 1  exP(6tj/70)}.
(8)
j=l
Here, matrix dissolution during the initial leaching stage (i.e., initial  1.5 h) of the mineral ( EYAL and OLANDER, 1990) is neglected. Behavior of the Minor Elements Uranium and Thorium Nonstoichiometric leaching of a minor element with respect to the major element causes an enrichment (or depletion) of the former at the surface of the mineral. Sustained incongruent leaching requires either the existence of a region of the mineral which is easily accessible to the leachant or transport of the minor elements from the interior of the mineral by diffusion. The former concept, the “storage zone” concept, was used to model the initial stages of leaching of monazite (EYAL and OLANDER, 1990). This concept was also incorporated in the dissolution model of MURPHY and SMITH ( 1988 ). The alternative concept, solidstate diffusive transport, was used by MATSUZURLJand MORIYAMA( 1982) to analyze data from leaching of glass. Parabolic leachingrate behavior of minerals is often attributed to solidstate diffusion mechanisms ( GRANDSTAFF, 1977). The storage zone concept suffers from the inability to specify a priori the size of the zone or to understand the physical basis that permits ready access of the leach solution to the interior of the mineral. On the other hand, solidstate diffusion is a wellestablished process at high temperatures. However, true lattice diffusion of cations in minerals is very slow at ambient temperature. For example, extrapolation of the measured diffusion coefficient of U4+ in U02 to 300 K gives a value of  IO+ cm 2/ s, which could not provide a flux sufficient to maintain the leaching observed of U in monazite ( EYAL and OLANDER, 1990), if lattice diffusion was the ratecontrolling process. Diffusion rates can, however, be enhanced by a number of processes. Fast diffusion paths that occur along dislocations or grain boundaries generally dominate lattice diffusion at low temperatures ( SHEWMON, 1963). In addition, the depth from which minor elements are leached from monazite is only a few tens of nanometers even after years of exposure of the mineral to the leach solution. Microcracking from specimen preparation could easily produce nearsurface regions which exhibit higher effective diffusion coefficients than the deep bulk of the particles. Finally, radiation damage sites due to cyrecoil atoms in minerals such as monazite which contain actinide elements enhances solidstate diffusion. The diffusion mechanism is adopted in the present model. AS described below, solidstate diffusion of the actinides in the mineral is coupled to the surface reaction and to mass
Leaching of U and Th from monazite (II) transfer in the liquid to provide a complete analytical description of the leaching process. As actinide cations diffuse towards the surface, electrical neutrality in the solid is maintained by cotransport of an appropriate number of anions ( OLANDER,1976; ANDERSON, 1981). In monazite, a crystalline orthophosphate mineral, oxygen and phosphorousion diffusion (at an atomic oxygentophosphorous ratio of 4) is expected to be many orders of magnitude faster than that of the actinide cations, so the mobility of the latter controls the migration rate. Similarly, as Ce3+, La3’, and actinide cations enter the solution, so must POi at a rate which maintains electrical neutrality. Because the behavior of anions from the solid does not influence the kinetics of mineral dissolution or leaching it need not be explicitly treated in the model. Diffusion in the solid Figure I shows the concentration distribution of a minor element adjacent to the mineral surface. The frame of reference is chosen with the surface fixed so that the mineral flows towards the surface with a convective velocity equal to the surface recession velocity during matrix dissolution. In this coordinate system, the flux J of minor element in the solid is given by J = D(an/az)
 un,
monazite, diffusion coefficients which decrease with time of exposure to the solution and eventually approach a nonzero final value are required to apply this model. This behavior is attributed to changes in the surface layers of the mineral that are caused by exposure to the leachant, a process analogous to natural weathering. The timedependent diffusion coefficient is represented by the empirical equation D = Df+
an/at = aJ/az,
(10)
with Eqn. (9), yields the diffusion
(11)
The experimentally observed leach fractions could not be fit with a constant diffusion coefficient. For U and Th in
r = Mi
n (0, 0 A
”
Solid Convective V6loCity
z
/C&,,, ..._
I
ElementLeachFlux
(ActualCow. in Solution 81 Surface)
.Q..... C (Bulk Cont. in Leachant)
FIG. 1. Nearsurface concentration distributions of an incongruently leaching minor element from a mineral contacting a leaching solution.
exp[(tl~d21,
(12)
(13)
Because the depth of penetration of the concentration disturbance is a small fraction of the particle radius, the semiinfinite medium boundary condition applies: n(m,t)=N,
(14)
where N is the concentration of the minor element in the bulk mineral. The boundary condition at the surface links the solidstate diffusion process to the kinetics of the surface leaching reaction. The minorelement flux at the surface is
D(an/az),,, + z.uz(~, t).
(15)
Surface reaction The rate of the surface leaching reaction is assumed to be proportional to the difference between the activity of the minor element in the solid at the surface and that in the liquid immediately adjacent to this solid (both relative to the same standard state). The leaching flux is r = Wa,,
..: 1 *....
Df)
n(z, 0) = n(z, St,_,).
r =
anfat = D(a2nfaz2)+ u(an/az).
(DO 
where DOand D/are the diffusion coefficients at the start and at the end of the experiment, respectively, and 7d is the characteristic time for the change in the value of D. For our experiments, Eqn. ( 11) is integrated for each sequential leach period (0 5 t 5 St,, where St, = tj  t,_l is the duration of thejth leaching step). Integration is not continuous in time because replenishment of the leachant between steps effectively resets the matrix dissolution velocity u to its maximum value. The matrix dissolution velocity subsequently decreases with time (measured from the start of the leach step) according to Eqn. (5). However, the minor element concentration distribution in the solid is not affected by replacement of the solution with fresh leachant. The initial condition for Eqn. ( 11) is given, therefore, by the concentration distribution at the end of the preceding leach step:
(9)
where z is the depth in the solid and n is the time and depthdependent concentration of the minor species in the mineral. The first term on the righthand side of Eqn. (9) represents Fickian diffusion of the minor element in the mineral, and the second term accounts for the convective flow induced by surface recession. The mass balance equation for the minor element in the solid is
which, when combined equation
1881

asurf) = k’7,(C,,

Csurf>
(16)
where k’ is the reaction rate constant, &t (C,,) is the activity (concentration) in a saturated solution, asurf (C&f) is the actual activity (concentration) in the solution near the mineral surface, and yaq is the activity coefficient of the dissolved form of the minor species. The activity of the minor element in the solid at the surface is (by definition) equal to its activity in the saturated solution contacting the solid (& . The value of &“,,,ris less than the saturation activity unless k’ is very large. This formulation of the surfacereaction rate is similar to the critical undersaturation model applied to interfacial kinetics of salt dissolution in brine (ANTHONY and CLINE, 1971; GEGUZIN et al., 1975; OLANDER et al., 1982).
In both
D. R. Olander and Y. Eyal
1882
cases, the liquid at the surface is undersaturated with respect to the solid because of slow interfacial kinetics. To obtain the second equality in Eqn. ( 16), the activity coefficient yss is assumed to be concentrationindependent, so that the activity driving force is proportional to the concentration driving force. Mass transfer in the liquid phase As described by DIBBLE and TILLER ( 198 1), surface reaction and fluid mass transfer can be treated as series resistances. The mass transfer process describes diffusion and convection in the aqueous phase. Transport of species occurs either in a porous surface filled with leachant or, as sketched in Fig. 1, in the concentration boundary layer adjacent to the mineral surface. The liquidphase masstransfer rate is given by r = k,t(C,,,c
 C),
(17)
where kmt is the mass transfer coefficient in the liquid, and C is the bulk concentration of the minor element in the leachant. Eliminating Csurf between Eqns. ( 16) and ( 17) yields r = k(C,,
 C),
U4+(solid soln) + 3CO:(aq)
+ HZ0 = U02(C0,)$(aq)
+ 2H+(aq),
(23)
where U4+( solid soln) represents a U ion in solid solution. The leaching solution was exposed to air, so it was saturated with oxygen. The aqueous 0.1 M NaHC03 + 0.1 M Na2C03 leachant had a pH of 9.5 which was expected to remain essentially unaltered even if the solution reached equilibrium with atmospheric CO*. According to LANGMUIR( 1982), the carbonate complex is the stable aqueous uranium species in groundwater that has typical CO1 pressures for pH > 9. Therefore, the experimental conditions specified above promote formation of the uranyl carbonate complex according to the equilibrium relation Keq =
a,t(a~)2/[a,~(ac)3(p0,)1/21,
(24)
where ass,, a,.,, and ac denote, respectively, the activity of the minor element in solid solution at the mineral surface, and the hydrogen and carbonate ion activities in the aqueous solution. The initial condition for the first leach step is n(z, 0) = N.
(18)
where
+ (1/2)02(g)
(25)
The activity of the actinide element in the solid is written as
k = [l/&t
+
ll(r&‘)l
(19)
is the overall transfer coefficient, which includes both contributions. The fluidphase mass transfer coefficient depends on the diffusion coefficient of the aqueous ions (typically  10m5 cm ‘/s) . Unless liquid diffusion is restricted to surface layers of very low porosity, fluid mass transfer is likely to be much more rapid than solidstate diffusion or surface reaction. Assuming this to be so, Eqn. ( 19) reduces to k = y,k’.
(20)
a,1 = yss+,
where yssl is the activity coefficient of the ion in the solid. Combining Eqns. (24) and (26)) and using asat = r,Ga,
In a continuously flowing system, the concentrations of the minor elements in the solution are generally zero. In lab oratory leaching tests, however, these elements accumulate in a fixed volume, V, of leachant. Conservation of the minor element in the leach solution is expressed by v(dC/dt)
= Sr = Sk(C,,
 C).
(21)
The initial condition at the start of each leach step reflects replacement of the solution with fresh leachant: C(0) = 0.
(22)
Solutionsolid equilibrium In order to couple the solidstate diffusion process to the surface reaction, fluid mass transfer, and solute accumulation in the liquid, the saturation concentration, C,,, must be related to the concentration in the solid at the surface, n( 0, t). In the laboratory tests with a basic bicarbonatecarbonate solution ( EYAL and OLANDER, 1990), the U dissolves by formation of a very stable uranyl carbonate complex:
(27)
yields C,, = Kh(O, t).
(28)
where K is the equilibrium distribution coefficient for U between the mineral and the leach solution at the surface: K =
Liquid phase balance
(26)
(r~(aC)3(p~,)“21[raq(a~)21)K,,.
(29)
Although the aqueous uranyl carbonate complex is well established, much less is known of the stability of the analogous aqueous complexes of Th. In nearneutral groundwaters, the principal form of soluble Th is the neutral species, Th( OH)*, and the solubility from most minerals (including thorianite) is quite low ( LANGMUIR and HERMAN, 1980). In strong alkaline carbonate solutions, however, the solubility appears to be much higher. Evidence for this is found in the high Th concentrations in the alkaline carbonate lakes in the western part of the US, which are orders of magnitude greater than the solubility of ThOz in water and the concentration of Th in seawater ( SIMFTONet al., 1982; ANDERSONet al., 1982). The solubility of Th is ascribed to formation of stable complexes of the form [Th(OH),(C03),,,]k, where 0 < n < 4, 1 < m < 5, and k = 4  n  2m (LAFLAMME and MURRAY, 1987). The solubility of Th in carbonate solutions has been exploited in the Amex process for extracting Th from ores (CROUSEand BROWN,1959). One step in the process involves stripping Th from an organic amine by a 0.6 M Na2C03 solution. The Th loading of the aqueous phase is I2 13 g/ 1.
Leaching of U and Th from monazite (II) Based upon the above evidence, the Th dissolution reaction analogous to Eqn. (23 ) is written as Th4+(solid soln) + mCO:(aq)
+ nHIO
P’h(oWn(CWmlk(W
=
+ nH+(wh
(30)
for which K = ~m,(ac)“/[r,(e1Y1jK.v
(31)
By substituting Eqn. (28) into Eqn. ( 18), a relationship is established between the leach rate and the minor element concentrations in the mineral surface and in the bulk leachant. Because of the high solubility of the actinides in the basic bicarbonatecarbonate leach solution, minorelement saturation of the leachant is neglected. This is equivalent to assuming C,, $ C, so that Eqns. (2 1) and (22) are unnecessary. The boundary condition for the diffusion equation is obtained by equating the righthand sides of Eqns. ( 15) and ( 18) and eliminating C,, by use of Eqn. (28), which yields D(&r/az),,,
+ bn(O, t) exp(t/To)
= kKn(0, t),
(32)
where u has been eliminated by using Eqn. (5).
1883
kK is very large (i.e., rapid surface reaction), the concentration of the minor element at the mineral surface is near zero, and integration of Eqn. (34) is less accurate. Equation (35) is then the preferred method for computing SJ. At the other extreme, when D is large (rapid diffusion in the solid), the integrand in Eqn. (35) is difficult to evaluate, and Eqn. (34) is more appropriate. The rapid initial leaching process analyzed in Part I ( EYAL and OLANDER, 1990)is not quite complete at the end of the first 1.5 h of leaching. The remaining portion of the readily leached material, which amounts to the fraction
&it = FA exp(ti.itlrl\),
(36)
appears in solution during the first longterm leach step. In Eqn. (36), FA and 7A are the initial fraction of the minor element in the damaged zone which supplies the initial rapid leaching and the characteristic leaching time of this inventory, respectively, and tinit is the duration of the measurements during the initial leaching period (see EYAL and OLANDER, 1990). The result from Eqn. (36) is added to the Sh value computed from Eqn. (34) or Eqn. (35) during the first leach step only to account for the residual contribution of initial leaching.
Minor element fractional leaching
Computational method and fitting of the model to the data
The rate of change of the fraction of the initial sample inventory of a minor element released to the solution is given by
Theoretical analysis of sequential leaching periods requires solving Eqn. ( 11) numerically for each leach step. Between steps, the time t is reset to zero to simulate the effect of leachant replenishment on the recession velocity of the mineral surface (Eqn. 5 ). The concentration distribution of the minor element in the solid is not affected by leachant replenishment. Model fitting was accomplished assuming infinite solubilities of U and Th in the leachant. The computations involve six parameters: ror b, kK, Do, Df, and rd. The first two parameters, TOand /Q,, control the rate of matrix dissolution and must be the same for U and Th. The remaining four parameters are usually different for each minor element. For each experiment, two calculations are performed, one for U and the other for Th. The quantities S&predicted with the model (Eqn. 34 or Eqn. 35) are compared to those observed. The set of parameters which produces the least squares error of the sum over all steps is selected as a best fit to the data.
df/dt
= Sr/(VN)
= [SkK/(VN)]n(O,
t).
(33)
The increment of fractional minorelement release during each leach step j, SJ, can be given by either of two equations. First, the release may be obtained by integrating Eqn. (33) over time t: SJ = (S/V)kK
6 s0
O(0, t)dt,
(34)
where 0 = n/N. An alternative equation for the incremental minorelement fraction released during a leach step is 6&=(S/V)lm
{Q(Z,at,,)O(Z,dt,)}dZ+~~,j.
(35)
Equation (35) can be obtained either by simple minorelement mass balance at the beginning and end of each leach step or by integrating Eqn. ( 11) twice, first with respect to z over 0 I z I cc, and then with respect to t over 0 5 t _i St,. The first term on the righthand side of Eqn. (35) is the contribution to the fractional release of the minor element due to solid state diffusion and surface reaction, and the second term is the portion of minorelement release due to matrix dissolution during the leach step [ Eqn. (7)]. If the latter were the only contribution, minorelement leaching would be congruent to matrix dissolution. Incongruency arises from the first term on the righthand side of Eqn. ( 35). Equations (34) and (35 ) are equivalent, and the choice between them depends on the accuracy of numerical computation required for calculating the fraction released, When
RESULTS AND DISCUSSION The data analyzed by the model consist of experiments Ml(l), M1(2), and Ml(A) in which monazite Ml was leached in sequential steps by a bicarbonatecarbonate solution ( EYAL and OLANDER, 1990). Experiment Ml ( 1) contained 14 leach steps (in addition to 5 very short initial steps) for a total duration of 6.8 years. Experiment M l(2) (a replicate experiment) had 24 leach steps (in addition to 5 very short initial steps) and lasted 6.7 years. The third experiment, Ml (A), utilized the 8OO”Cannealed sample (EYAL and OLANDER, 1990) and consisted of 13 leach steps (in addition to 6 very short initial steps) over a period of 6.8 years.
D. R. Olander and Y. Eyal
1884 Table 1.
Model parameters
from longlerm
leaching
Sample Ml(Z)
Sample Ml(l)
of monazile
MI
Sample Ml (A)
Matrix 0.080 0.5
COSZX (mW#
U Th Actinides m kK(n&day) D, (cm2/si 2X1o195Go21 Df (cm2/s) 5x1021 1x1022 Td (days)
120
6 0.023 0.14
3 0.13 0.4
6
r. (days) ko (nm/day)*
M)
U Co
Th M
1.4
,
,
,”
/
/
Tie
1
25
25
Th 1x104
1x1020 4x1023 7x1022 ~023 110
200
v = 10 ml and density of
reduce the solubility of the mineral in the bicarbonatecarbonate solution by a factor of 4. Because the durations of the leach steps were generally much longer than 1 week, saturation of the leachant with respect to the matrix is predicted to have occurred in most steps. The mineral dissolution velocity in the absence of leachant saturation effects (k,,) was determined to be 0.1 nm/day for the unannealed specimen. This value decreased by a factor of 4 in the annealed sample. The predicted percentage of matrix dissolved, computed from the above parameters and the su~acet~volume ratio of the powder, is  1.6%, which may be compared to an upper limit of 2% obtained from weighing the samples before and after the experiments (EYAL and OLANDER, 1990). The experimental value is an upper limit because of possible small losses of sample during handling at the end of each leaching step. For the annealed sample, evolution of  1% (upper limit) of the matrix was measured, while the model gives 0.4%. The agreement of this aspect of the model and the data is very satisfactory, provided that secondary solid phases associated with major cation species were not precipitated from the solution during leaching. For five of the six calculations repotted in Table 1, the constants representing the surface chemical reaction (kK) are much larger than the matrix dissolution velocity. The values of infinity in Table 1 simply mean that the leach rate of the minor elements is controlled by a combination of solidstate diffusion and the kinetics of mineral dissolution. A test of the validity of the model in amounting for renewal
I
(days)
FIG. 2. Uranium leaching from monazite sample Ml ( 1) into a bic~~nate~a~nate
=
7x1019 7x1020 6x1021 2x1022
* Calculated using S/V = 2.4~10~ cmt. # From Eq. (4) with No = 0.022 gatoms/cm3, 5.2 g/cm3 for monazite (CePOq)
Each of the longer leaching steps in the above experiments was followed by a short wash step (EYAL and OLANDER, 1990). The actinide radioactivity measured in the wash was added to that of the previous long leach step to ensure complete recovery. However, each wash step was analyzed separately in the model. The calculated releases during a long leach step and its associated wash step were later combined for the purpose of error computation and presentation. The model parameters that generate the best fit to the data for each of the three experiments are given in Table 1. Figures 24 show the agreement between the model fits and the data in the form of bar graphs, wherein each bar represents a single leach step. In general, the model is better able to fit the data when the minor element is preferentially leached relative to the matrix. For sample M 1 ( I), approximately 7% of the U is removed during the experiment, although only 2% of the mineral dissolves. Figure 2 shows the excellent agreement between the model and the data for U in this situation. At the other extreme, the Th data from experiment Ml (A), in which Th and matrix removals are 0.25 and 0.4%, respectively, are fit less well by the model (Fig. 4). In all cases, however, the model is able to reproduce most of the details of the experiments, including leach steps from 1 day to 2 years in duration. In all three model fits, the value of 7. that characterizes the approach to saturation of the leachant by the dissolved mineral was less than a week, which corresponds to solution saturation concentrations of 0.5 mM for the unannealed samples, M I( 1) and Ml (2). Heat treatment appeared to
U
solutioncomparison
of model and data.
FIG. 3. Thorium leaching from monazite sample MI ( 1f into a bicarbonatecarbonate solutioncomparison of model and data.
Leaching of U and Th from monazite f II)
Time (days)
FIG. 4. Thorium leaching from monazite sample M I (A) (anneaM in air for 6 h at 800°C prior to l~ching~ into a bi~nate~nate ~lu~oncorn~~~n
of model and data.
of mineral dissolution upon changing leach solution is available. The fractions of U and Th leached during the single 22day first longterm step of experiment M 1 ( 1) are, as predicted, smaller than those released during the 10 steps that occurred in the first 22 days of experiment M l(2 1. The model parameters used in both calculations are nearly equal. Annealing reduces the leach rate of Th by an order of magnitude. Leaching of Th from the annealed monazite, Ml (A), appeared to be controlled by both the surface reaction rate and s&idstate diffusion; both kKand De are much smaller than for the other five entries in Table 1. In this case, more matrix was removed than minor element, which caused a buildup of Th at the dissolving mineral surface. The rate constant of the U surface reaction and the solidstate diIIusivity of U appear to be less affected by annealing than those of Th. The model predicts that the matrix dissolution rate for annealed monazite is about three times slower than for untreated monazite. This is consistent with the lower uranium concentration measured in the leachate from the annealed sample. The solidstate diffusion coefficients shown in Table 1 range from ( 4 +: 3) X I Ol9 cm ‘/s for U in the unannealed samples to 2 X lO23 cm’/s for Th in the annealed monazite. Although these diffusion coefficients do not represent true lattice diffusion, they are reasonable values for the surface layers of the solid. For example, RUNDBERG( 1987) measured solidstate diffusivities of Cs*+, Sr*+, and Ba*+ cations in Yucca mountain tuff in the range 10‘61022 cm’/s. This rock contains minerals such as nordenite, which is porous on an atomic scale and thus would be expected to exhibit higher cation mobility than would dense monazite. Solidstate cation diffusivities in olivine have been measured over the temperature range lOOO1200°C (BUENING and BUSECK, 1973). The slope of the Arrhenius plot (In D vs. I /T) changes at about 1125°C. The apparent high mobility of the lowtemperature branch is ascribed to extrinsic point defects by BUENINGand BUSECK( 1973), but LASAGA( 198 1) suggests that shortcircuit diffusion along dislocations may be responsible for the high mobility. If the lowtemperature portion of the Arrhenius plot for 40 wt% Fe material is extrapolated to 25°C a cation diffusivity of 4 X 10m2’cm2/s is obtained. This value is well within the range ofactinideion diffusivities in monazite deduced from the leaching kinetics in the present study. As may be seen by comparing the values of Do and &in Table 1, the diffusion coefficients at the end of the leaching
I885
experiment are as much as two orders of magnitude lower than those at the start. This inference from the model indicates significant alteration of the surface region of the mineral by the leach solution. The period over which the most significant reduction in the value of D occurs is roughly 25 to 200 days from the start of the leaching experiment. Figure 5 shows the computed matrix surface positions and Th concentration profiles in the monazite calculated from the model for experiment M I( 1) with the parameters given in Table 1. Approximately 6 nm of the mineral surface was dissolved in 6.8 years (i.e., a total of  1.6% weight loss). The concentmtion ~~urbations extend about 4 nm into the solid. The reason for the relativeb constant ~~urbation profile for all times is that matrix dissolution moves the surface inwards and tends to compress the concentration distribution of the minor element. This effect opposes the spreading tendency of diffusion in the solid. For five of the six entries in Table 1, the calculated concentration distributions of the minor element in the mineral during leaching are similar to those shown in Fig. 5. However, the calculated concentration distributions of Th in the annealed specimen are very different from the other distributions, as shown in Fig. 6. First, because the mineral dissolution rate ka is greater than the minor~lement surface reactionrate constant kK ( see Table 1) , the surface becomes enriched in Th. With time, the concentration at the surface is reduced as Th diffuses back into the solid. Second, the depth of the concentration perturbation is very small; the calculated depth is less than 0.1 nm. Concentration variations over such a small distance have no meaning. Rather, the proper interpretation of the curves in Fig. 6 is qualitative. The matrix dissolution rate is sufficiently faster than Th dissolution so the surface becomes clogged with Th, and solidstate diffision is too slow to permit this surface buildup to be relieved by migration of Th to the interior of the solid. In analyzing the Th data in the annealed sample, a very strange effect was noted. If the rate constant for leaching of the minor element is less than the mineral dissolution velocity Surface at end of leach step no.
Depth from Original Surface (nm)
FIG. 5. Computed concentration distributions of Th in the mineral and computed matrix surface positions during leaching of monazite sample M I( 1) by a bicarbonatecarbonate solution. The sequence of leaching steps indicated consists of steps that lasted between 7 to 684 days each. The positions of the surface relative to the initial position are shown for each leach step by the tic marks on the upper abscissa ofthe figure. The four Th concentration distributions shown pertain to the end of the first, the last, and two intermediate leach steps.
D. R. Olander and Y. Eyal
1886
Specimen
Ml (A)
Time (d)
I18
rtace at ena or teacn step no. 1234567
I
OO
0.2
I
I
0.4
I
0.6
II
0.6
I
1.0
8 9
II
1.2
10 11
111 1.4
12 1.6
I .a
Depth from Original Surface (nm)
FIG. 6. Computed concentration distributions of Th in the mineral and computed matrix surface positions during leaching of monazite sample MI (A) by a bicarbonatecarbonate solution. The sample was annealed in air for 6 h at 800°C prior to leaching. The sequence of leaching steps indicated consists of steps that lasted between 7 to 690 days each. The positions of the surface relative to the initial position are shown for each leach step by the tic marks on the abscissa. The four Th concentration distributions shown pertain to the end of the
first, the last, and two intermediate leach steps.
(i.e., kK < b), the model predicts that an increase in the diffusion coefficient reduces the fraction of the minor element leached. This counterintuitive effect is, however, explainable, as the following argument demonstrates. The leach rate of the minor element is proportional to its concentration in the mineral at the surface (see Eqn. 33). With a low solidstate diffusion coefficient, the minorelement surface concentration builds up to high values, such as shown for the early leach steps in Fig. 6. Were the diffusion coefficient to be increased from the values shown in the last column of Table 1, the effect would be to move the minor element back into the interior of the solid, decreasing the surface concentration and hence reducing the leach rate below the observed rate. On the other hand, if surface reaction is fast compared to matrix dissolution (i.e., kK$ b), Eqn. (32) shows that the concentration gradient at the surface is positive, and an increase in diffusivity increases the minorelement flux at the surface. For example, in the simple case of a stationary surface (IQ, = 0) and kK + M, the flux varies as l/o (CARSLAW and
uration of the leachant were induced from fitting of the U and Th leaching data, these parameters a posteriori reproduce the observed matrix mass loss. Thermodynamic constraints on the leaching rates of the minor elements, due to approach to saturation of the leachant, are unimportant because actinides form stable carbonate complexes in the aqueous phase. However, saturation is quickly reached for the major elements in solution, relative to the duration of each leach step. Uranium and Th leach incongruently with respect to each other and to the host solid. The fractional release of U during the 6.8year experiments was 0.07, compared to 0.02 fractional removal of Th and mineral dissolution of less than 2%. Only solidstate diffusion allows for this observation, and the quality of the fit to the data is very sensitive to the U and Th diffusion coefficients in the solid. Uranium has greater mobility in monazite than Th. Except for the Th in an annealed monazite, the velocities of the surface chemical reactions by which the actinides are dissolved are much larger than the matrix dissolution velocity, implying no control on actinide release rate by the surface detachment reaction. Airannealing of monazite prior to leaching (800°C for 6 h) reduces both the fractions of U leached and mineral dissolved by a factor of 3 to 4. Thorium leach rates, on the other hand, are diminished by a factor of 10 by preannealing the mineral. The latter result is attributed to substantial reduction in the Th diffusivity in the mineral and in its rate constant for detachment from the surface. The diffusion coefficients found by the model fits to the data ( 10 23 10 I9 cm */s) are too large for true lattice diffusion and probably represent migration along highdiffusivity pathways in the nearsurface regions of the mineral. The penetration depth of the concentration perturbation due to these diffusion processes ranges from 5 nm to about 50 nm, except for Th in the annealed sample, in which essentially no penetration occurred. AcknowledgmentsWe thank Dr. Marilyn Buchholtz ten Brink and Dr. Celia Merzbacher for their thoughtful comments on this manuscript. This work was supported in part by the Director of the Office of Energy Research of the Office of Basic Energy Science, Material Science Division of the US Department of Energy under contract number DEAC0376stB0098. One of the authors (DRO) acknowledges with thanks a Lady Davis fellowship from the TechnionIsrael Institute of Technology. Editorial handling: E. J. Reardon
JAEGER, 1959). CONCLUSIONS
REFERENCES
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