J. Chem. SOC., Faraday Trans. I, 1984, 80, 1617-1629 Kinetics of the Crystallisation of Calcium Oxalate Monohydrate BY EMIL N. RIZKALLA* AND MONA M. MOAWAD Faculty of Science, Ain Shams University, Abbassia, Cairo, Egypt Received 5th October. 1983 The kinetics of precipitation of calcium oxalate monohydrate have been studied conducto- metrically at 298 K for both spontaneous and seeded growth systems. The rate of growth follows a quadratic dependence upon the relative supersaturation, which suggests a surface- controlled growth mechanism. This rate equation holds fairly well for the various solid/solution ratios used in the range of 2.35-10.18 relative supersaturation and for seed concentrations of 0-200 mg dmP3. The effect of sodium tripolyphosphate and phosphonate additives on the precipitation kinetics of calcium oxalate in the absence and presence of well characterised seeds has been investigated at various levels of additive concentration.The inhibiting activity of these additives is discussed in relation to the surface characteristics of the inoculated seeds and structural features of the additive molecules. The fit of experimental data to the Langmuir adsorption isotherm supports a mechanism of inhibition through molecular adsorption of the foreign ions on the surface of the growing crystals. Numerous studies have been reported on the kinetics of crystal growth and dissolution of alkaline-earth oxalates. 1-4 Crystallisation of calcium oxalate is of particular interest, not only from the point of view of analytical chemistry, but also because of its biological importance as one of the main constituents of pathological deposits in the urinary tract.5 Earlier studies on the mechanism of renal stone formation have been concerned with the role of the organic matrix,6 the degree of urine supersaturation with respect to theconstituent ofinterest’ and theinfluence ofurinaryin- hibitors.8 At one stage the uncontrollable deposition of stone minerals was attributed to the role played by the organic matrix;6 however, Vermeulen et aL9 suggested that this mucoid organic matrix is a non-essential phase resulting from protein adsorption on the developing crystalline surface and can act only as a heterogeneous nucleation site for the precipitation of calcium oxalate.1° Previous studies of the precipitation of calcium oxalate have demonstrated the importance of kinetic factors in determining the phase formed during the crystallisation process.11-14 The observed stabilisation of the thermodynamically less stable dihydrate species over the more stable monohydrate phase was attributed to adsorption effects caused by polyphosphate anions on the calculus surface.15-16 On the other hand, Gardner17 claimed that the rate of crystal growth of calcium oxalate in the presence of low-molecular-weight additives such as pyrophosphate and organic phosphonates is independent of additive concentration, and only the induction period preceding growth was found to increase with increasing pyrophosphate concentration. Apparently, these results are in direct disagreement with the results of Robertson et aZ.,18 Sarig et al.19 and Crawford et a1.,20 who demonstrated the in vitro inhibitive effects of 1 -hydroxyethane- 1,l -diphosphonate (HEDP), pyrophosphate anions and polyelectrolytes, as well as the polyanions of heparin and condroitin sulphate.10171618 CRYSTALLISATION OF CALCIUM OXALATE MONOHYDRATE This paper presents a more detailed systematic investigation of the precipitation kinetics of calcium oxalate over a wide range of supersaturation ratios for both spontaneous and seeded growth systems using surface-characterised calcium oxalate seeds. The inhibitory effects of sodium tripolyphosphate and polyphosphonate anions have been studied at various levels of additive concentrations. EXPERIMENTAL REAGENTS AND SOLUTIONS Calcium chloride and potassium oxalate of AnalaR grade were supplied by B.D.H.Commercial-grade sodium tripolyphosphate (STP) was purified by recrystallisation four times from methanol + water mixtures.,l The purity of the final product (Na,P,O,, . 6H20) was checked by elemental analysis. The organic phosphonates (shown below), namely those of ethylenediaminetetra(methy1enephosphonic acid) (ENTMP), hexamethylenediaminetetra- (methylenephosphonic acid) (TENTMP) and 1 -hydroxyethane- 1,l -diphosphonic acid (HEDP), were kindly donated by Monsanto Industrial Chemicals, Louvain-La-Neuve, Belgium, and were used as such except for ENTMP, which was recrystallised as the tetrasodium salt following the procedure described before.22 Elemental analysis of the solid ENTMP and TENTMP and pH titration with standard sodium hydroxide solution (carbonate-free) indicated a purity > 99 % .The active acid content of HEDP was similarly determined by titrating a suitable aliquot of the reagent with NaOH solution, and its purity was calculated on the basis of the amount of base consumed per acid equivalent. CH,-N(CH,PO,H,), I OH CH,-N(CH,PO,H,), HEDP ENTMP TENTMP Stock solutions of the lattice ions and the additives were freshly prepared in conductivity water (doubly distilled, deionised water; conductivity < a) and diluted as required. The exact molarity of the calcium and oxalate ions was then checked using standard analytical methods. 23 Calcium oxalate seeds were prepared by three different methods: seed A was obtained as the spontaneously precipitated so!id formed upon the drop-wise addition of calcium chloride solution (0.01 mol drn-,) to a well stirred potassium oxalate solution (0.01 mol dm-9.The solid was filtered at once, washed well, dried overnight at 383 K and stored. Seed B was prepared essentially as described above, but in this case the precipitate was allowed to age with the mother-liquor for one month. Seed C was prepared by adding urea to an acidic solution of an equimolar mixture of calcium and oxalate ions. The mixture was allowed to stand for one week and the resultant oxalate salt was filtered, washed, dried at 383 K and stored. NITROGEN ADSORPTION MEASUREMENTS The surface areas of the solid materials were measured using a typical volumetric apparatus for nitrogen adsorption.The dead space of the sample bulb and its connecting tubes were calibrated using 99.9% pure helium. The adsorption isotherms were obtained by introducing known volumes of N, gas into the sample bulb and measuring the equilibrium pressures. The amount of adsorbed gas was then calculated assuming ideal behaviour. The saturated vapour pressure of the nitrogen gas was determined periodically during the adsorption run by measuring directly the pressure in equilibrium with liquid nitrogen. The area was calculated by using a value of 16.2 w2 per N, molecule. Table 1 summarises the relevant parameters calculated from the isotherms of the three solids. KINETIC MEASUREMENTS Details of the kinetic procedure are essentially the same as described in an earlier comrn~nication.~~ Supersaturated solutions of calcium oxalate were prepared by adding smallE.N. RIZKALLA AND M. M. MOAWAD 1619 Table 1. Relevant parameters calculated from the isotherms of solids A, B and C affinity constant, surface area average pore seed C /m2 g-' radius, s;/A A B C 3.0 1 .o 3.7 90.2 137.3 133.4 39.3 38.5 28.0 volumes of a pre-thermostatted potassium oxalate solution to the calcium chloride solution so as to make the final concentration of both reactants the same. The rate of growth was then monitored conductometrically. Phosphonate additives and/or calcium oxalate seeds were always added to the calcium solution and the volume of the reacting mixtures was kept constant at 250 cm3. The delivery time of the oxalate solution was determined to be 30 s or less.The temperature in all experiments was maintained constant at 298.00+0.01 K by means of a circulating constant-temperature bath. During mixing of the reactants stirring was achieved mechanically, then the mixture was left static. RESULTS In the absence of additives the following equilibria may be considered: Hf + C20i- HC,O, ; K? (1) Caf&) + C20i~q) * CaC204(aq) ; P I (2) CaC204(aq) + C20i~q) * c(c204)t~q) ; P 2 (3) Ca!zq) + C2Oiraq) CaC20,* H,O,,) ; Ksp. (4) Under the working experimental conditions (pH > 6.5; Ca2+/C20i- = 1 .OO) equilibria (1) and (3) may be n e g l e ~ t e d . ~ ~ . ~ ~ Concentrations of the ionic species in the supersaturated solutions were calculated from the changes in the specific conductance and from the expressions for the total metal and total ligand and the mass-balance equations.Details of the calculations are given by Nancollas and Gardner. l1 Computer-assisted iterative algebraic methods were used which involve successive approximations to the ionic strength, I . The activity coefficients for a z-valent ion, yz, were obtained using the extended Debye- Huckel equation proposed by Davies -log yz = 0.51 15 z2[h/(1 + P ) - 0 . 3 I]. ( 5 ) By analogy with the results of previous crystallisation studiesll the rate of crystal growth, R, in the absence and the presence of seeds and/or additives were analysed using the following relationship : R = - d[Ca2+]/dt = - d[C20,2-]/dt (6) = kobs{([Ca2+t]t [C2042-1t)' - ( g p / , i ) a ) 2 = kobsA2 where K& is the thermodynamic solubility product, [XI, is the ionic concentration of species X at time t and kobs is the observed rate constant.For all calculations the value of K& was taken as 2.00 x The results of crystal-growth experiments from pure solutions are summarised in mo12 dm-6.281620 CRYSTALLISATION OF CALCIUM OXALATE MONOHYDRATE Table 2. Crystallisation of calcium oxalate from supersaturated solutions at 298 K in the absence of additivesa (A) spontaneous growth expt. &a(= Tox) kobsl lo2 no. / mol dm-3 S dm3 mol-1 min-' 1 2.50 2 3.00 3 3.50 4 4.00 5 5.00 4.59 5.71 6.83 7.94 10.18 1.15 1.95 2.69 4.02 6.07 (B) seeded growth k / 102 expt. Tea( = Tax) seed seed dm6 mol-l no. /lo-* mol dm-3 S type conc./mg dm-3 min-l m-2 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 1 S O 2.00 2.50 1 S O 2.50 1 S O 2.00 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.35 3.47 4.59 2.35 4.59 2.35 3.47 4.59 4.59 4.59 4.59 4.59 4.59 4.59 4.59 4.59 4.59 A A A B B C C C A A A B B B C C C 200 200 200 200 200 200 200 200 80 120 160 80 120 160 80 120 1 60 0.30 0.70 1.04 0.78 1.07 0.58 1.20 1.80 1.10 1.05 1.12 1.07 0.98 1.08 1.70 1.71 1.81 a Tc, and To, represent the initial calcium and oxalate concentrations, respectively, and S is the relative supersaturation given by s = Wa2+l, [C2o:-I,Y - (Gp/YW(g!p/Y3+.table 2, and typical crystallisation rate curves are shown in fig. 1. At all seed concentrations and in the range of supersaturation ratio, S, used in these experiments for spontaneous growth, precipitation commenced immediately, with no evidence of an induction period. The integrated form of eqn (6) A;' - AT' = kobs t (7) where At1 and A;' represent the concentration functions at time t and t = 0, respectively, is plotted in fig.2 and clearly shows an initial slow growth surge, the duration of which is a function of the supersaturation ratio and which is undetectable for solutions with S 2 10 or in the presence of seeds. The effect of additives on the kinetics of growth was studied at S = 10.18 forE. N. RIZKALLA AND M. M. MOAWAD 50 100 3 3t 1621 10 20 t/min Fig. 1. Growth curves for calcium oxalate monohydrate in the absence of additives for spontaneous-growth systems (0, expt. I ) and seeded-growth systems (0, expt. 19; A, expt. 16; 0 ; expt. 22). 4 8 12 I I I I I I 20 40 60 t/min Fig. 2. Plots of the integrated form of eqn (6) for the growth of calcium oxalate at different supersaturation ratios in the absence and in the presence of different seeds: A, expt.1 ; ., expt. 2; A, expt. 3; 0, expt. 4; 0, expt. 16; x , expt. 19; 0, expt. 21. spontaneous-growth experiments and at S = 4.59 and in the presence of 200 mg dm-3 for seeded-growth runs. The results obtained are listed in table 3. Plots of calcium concentration as a function of time in the presence of STP or other phosphonate additives are illustrated in fig. 3-6. DISCUSSION Agreement of the growth-rate data with a parabolic rate law [eqn (7)] over the range of supersaturation ratios and solid/solution ratios used (as seen in fig. 2) rules out bulk diffusion of electrolyte to the crystal surface as the rate-determining step and is indicative of a surface-controlled growth mechanism.1622 CRYSTALLISATION OF CALCIUM OXALATE MONOHYDRATE Table 3.Effect of additives on the rate of growth of calcium oxalate at 298 K (A) spontaneous growth: (Tea = To, = 5.00 x mol dm-3) exp t . additive conc. kobs no. additive / 1 OPs mol dm-3 / 1 O2 dm3 mol-1 min-I 24 25 26 27 28 29 30 31 32 33 34 STP STP STP TENTMP TENTMP ENTMP ENTMP ENTMP ENTMP HEDP HEDP 4.0 10.0 20.0 2.0 4.0 0.8 4.0 10.0 20.0 2.0 4.0 1.18 0.59 0.20 0.94 0.58 2.92 1.29 0.88 0.30 0.86 0.68 (B) seeded growth: (Tea = To, = 2.50 x mol dm-3; seed conc. = 200 mg dmP3) expt. additive conc. k'/ 1 O2 no. seed additive / lop6 mol dm-3 dm6 mol-l rnin-' m-2 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 A A A A A A A A A A A A A A B B B B B B B B B B B B B C C C C C C STP STP STP TENTMP TENTMP TENTMP ENTMP ENTMP ENTMP ENTMP HEDP HEDP HEDP HEDP STP STP STP TENTMP TENTMP TENTMP ENTMP ENTMP ENTMP ENTMP HEDP HEDP HEDP STP STP STP STP TENTMP TENTMP 2.0 4.0 10.0 0.4 2.0 4.0 0.4 2.0 4.0 10.0 0.4 2.0 4.0 10.0 2.0 4.0 10.0 0.4 2.0 4.0 0.4 2.0 4.0 10.0 0.4 2.0 4.0 0.4 2.0 4.0 10.0 0.4 1.2 0.26 0.12 0.02 0.60 0.38 0.20 0.61 0.1 1 0.05 0.02 1.23 0.99 0.56 0.54 0.28 0.16 0.02 0.46 0.18 0.15 0.50 0.11 0.04 0.02 0.75 0.38 0.32 1.20 0.35 0.16 0.03 0.59 0.27E. N.RIZKALLA AND M. M. MOAWAD 1623 10 20 t/min Fig. 3. Effect of STP on the crystal growth of calcium oxalate: 0, expt. 24; 0, expt. 36; A, expt. 50; 0, expt. 64. I I I 1 I i 10 20 tlmin Fig.4. Effect of TENTMP on the crystal growth of calcium oxalate: 0, expt. 27; A, expt. 39; 0, expt. 53; 0, expt. 68. Attempts to use Nielsen's chronomal analysis29 to interpret the kinetic results were successful only over a limited range of 0, where 0 is the degree of reaction. Thus for a diffusion-controlled or surface-controlled reaction of order P, the growth rate can be expressed by the following integrals: ID=K,t=j~~e-I(l-e)-'de (8 4 Ip = KPt = j:B-$(l -B)-PdB (8 b) where K,, and K p are constants related to the final particle size and the initial concentrations of the reactants. Plots of I (obtained through 0) against time are expected to be linear for a particular mechanism. The results obtained here are1624 CRYSTALLISATION OF CALCIUM OXALATE MONOHYDRATE 10 20 t/min Fig.5. Effect of ENTMP on the crystal growth of calcium oxalate: 0, expt. 30; 0, expt. 43; 0, expt. 57. 1 I I I I 10 20 t/min Fig. 6. Effect of HEDP on the crystal growth of calcium oxalate: 0, expt. 34; x , expt. 47; 0, expt. 61. illustrated in fig. 7(A) and (B) for spontaneous-growth [run (l), S = 4.591 and seeded-growth [run (15), S = 4.59, concentration of seed A = 80 mg dmP3] experi- ments, respectively. The linearity conditions appear to be limited to the late stages of growth (6 = 0.3-0.8) in both cases. Also, it is quite difficult to distinguish between I, and I3 operating mechanisms. Nielsen4 concluded from his results on spontaneous precipitation measurements that the growth reaction is controlled by an interphase process for the concentration range 0.3-1 .O mmol dm-3 and is diffusion-limited at higher concentrations.It was also shown that the value of P is apparently constant, 2 < P < 4, in limited concentration ranges. P reaches the limiting value of 4 as the solution becomes infinitely dilute. Reported plots of I, and I4 chronomals for solutions of initial concentration ca. 0.8-1.5 mmol dm-3 show a discontinuity below 6 = 0.25-0.35 with either positive or negative intercepts at t = 0.30 The fractional- order behaviour was attributed to the incompleteness of dissociation of calciumE. N . RIZKALLA AND M. M. MOAWAD 1625 1 tlmin 24 l6 tlmin 8 Fig. 7. Plots of ID and I , ( P = 1-4) chronomals as a function of time for calcium oxalate precipitation; (a) in the absence of seed (expt.1) and (b) in the presence of seed A (expt. 15). oxalate and the true order of reaction was believed to be 4. On the other hand Gardner,13 applying seeded-growth conditions ([Ca] = [Ox] = 0.5 mmol dmP3, seed concentration = 50 mg dm-3) and correcting for the incomplete dissociation of the complex species, concluded that the growth reaction over the range (8 z 0.2-0.9) is controlled by an I, mechanism. In the latter case a negative intercept was also observed. This non-zero intercept might suggest a different operating mechanism for growth in the low-8 range. Such compound-growth mechanisms have been proposed for many other Other factors which might lead to the discontinuity of the Ip against t plots are (1) the precipitation of different hydrate forms and (2) the hypothesis behind the chronomal analysis which presumes (a) homogeneous nucleation and (b) the formation of uniformly spherical particles.29 The first two possibilities are ruled out, since in the first case the discontinuity should be reflected in the plots of (Arl-A~l) against t , whereas in the second case plots for seeded and unseeded conditions are expected to be different. Recent electron-microscopy meas~rements~~1626 CRYSTALLISATION OF CALCIUM OXALATE MONOHYDRATE d 40 20 60 40 20 ~ ~~ " 0 0.2 0.4 0.6 0.8 1.0 PIP O Fig.8. Nitrogen adsorption isotherms for solids A (O), B (0) and C (a). revealed that calcium oxalate can be precipitated in any of the forms monoclinic monohydrate, tetragonal dihydrate or triclinic trihydrate, which are not spherical in shape as chronomal analysis presumes.Increasing the supersaturation ratio corresponds to an increase in the observed rate constants. The logarithmic relationship between S and kobs is satisfactorily linear with slope equal to 2.0-2.2, which is consistent with the former rate equation. For any particular supersaturation the observed rate constant when solutions are inoculated with seeds is two orders of magnitude higher than that observed for a spontaneous-growth experiment, and the extent of this enhancement is a function of the seed weight in solution. According to classical nucleation theories, in pure solutions a fraction of the lattice ions is consumed in forming the embryos which are used as a base for the actual growth stage, whereas in seeded systems the added solid presents suitable sites for direct growth.This also accounts for the slow surge observed in the integrated rate plots in the case of spontaneous growth which disappears upon impregnation with seeds or with increasing S. Accordingly, eqn (7) may be rewritten in the form (9) A t 1 - A71 = k'st where s is a parameter related to the surface area of the solid matrix. At low supersaturation ratios the value of k' was found to be an increasing function of the surface area of the solid (cf. table 1); however, at higher supersaturations solid B behaved in an opposite manner to that expected relative to seed C . This may be assessed by investigating the adsorption isotherms of the three solids. As is seen in fig. 8, solid B shows a type-3 isotherm with a hysteresis loop, indicating that it has high affinity towards capillary condensation.The low value of the constant C for this solid also suggests that the solid has low affinity towards nitrogen adsorption. On the other hand, solids A and C showed an intermediate type of isotherm between 2 and 3, with solid C much closer to type 2. With solid B a decondensation process is expected to take place at low ionic concentrations. Accordingly, more active sites will be obtained, aiding the acceleration of the rate of precipitation.E. N. RIZKALLA AND M. M. MOAWAD 1627 4 8 12 1.8 51 4 b -u" .y W \ 1.4 1.0 1 I I I I 2 4 6 [Add] -'/I O5 mol dm-3 Fig. 9. Langmuir adsorption isotherms in the presence of STP (-) and ENTMP (---): 0, 0, unseeded growth; x , A, in the presence of seed A; 0, in the presence of seed C.Experimental results obtained for calcium oxalate precipitation in the presence of STP and phosphonate additives shown in table 3 for spontaneous- and seeded-growth systems clearly indicate a marked inhibitory effect on the overall precipitation process. The term 'inhibitory activity' will be referred to in this context to describe the reduction in the rate of nucleation of new crystals of calcium oxalate and/or the rate of growth of new or added seed crystals of the salt. If we assume that the retarding action of the additive anions is a result of their adsorption at growth sites on crystal surfaces32 or that prevents their further growth, then the Langmuir adsorption treatment should be valid. If the adsorbed additive of concentration [Add] covers a fraction a of the total available surface, then the rate of adsorption may be expressed as kA[Add] (1 -a) and the rate of desorption as kda, where kA and k, are the corresponding rate constants.At equilibrium, it can be shown that where ko and kAdd are the growth rate constants in the absence and presence of additive, respectively. Plots of eqn (10) are illustrated in fig. 9 for STP and ENTMP additives. The inhibitory action of STP in unseeded systems was attributed to a dynamic adsorption mechanism based on the probability of collision between embryos and STP ions33 which leads to the former's disintegration before reaching a critical size. G l a ~ s n e r , ~ ~ on the other hand, suggested that the active minor component acts as a nucleator either in the form of a complex or a polymeric species,35 leading to the stabilisation of the supersaturated solution.The other class of additives which has proved to be most effective in inhibiting calcification is the organic polypho~phonates.~~ These compounds are characterised1628 CRYSTALLISATION OF CALCIUM OXALATE MONOHYDRATE by the relatively inert P-C-P and P-C-N-C-P linkages which are substituted for the hydrolysable P-0-P bond of the polyphosphates. The relative abilities of the additives in retarding the precipitation process vary with varying experimental conditions and the texture of the inoculated seed. Thus at a level of 4 pmol dm-3 additive concentration, the orders TENTMP > HEDP > ENTMP and ENTMP > TENTMP > HEDP hold for spontaneous and seeGed growth, respectively. In the light of the foregoing discussion, it is reasonable to interpret the observed results in terms of both adsorption and complexation phenomena. Adsorption-rate measurements of 32P-labelled tripolyphosphate on 3-5 pm particles of strontium sulphate precipitated from ‘pure ’ solutions showed that adsorption of STP takes place soon after the birth of 17 A nuclei in a solution containing p~lyphosphate.~~ If we extend these conclusions to other phosphonate systems, it would be expected that adsorption of the larger molecules ENTMP and TENTMP is likely to take place after the birth of larger aggregates of the host lattice, whereas with the HEDP molecule nuclei of smaller dimensions would fulfil the adsorption re- quirements.This sequence holds fairly well for the spontaneous-growth results except for TENTMP. The enhanced reactivity of TENTMP is ascribed to other structural factors. It is generally accepted that one molecule of ENTMP, HEDP or STP is capable of interaction with one active metal site, whereas with TENTMP it is quite difficult to group the four phosphonate ligands simultaneously around one metal site; most probably each -N(CH,PO,H,), group will interact independently. This might suggest that at the same molar concentration TENTMP is capable of inhibiting a greater number of small embryos in comparison with ENTMP. In the presence of seeds, other structural factors such as surface area, affinity towards adsorption of polar molecules, pore sizes and their distribution, rate of adsorption and desorption of the additives from the solid matrix, and cross-sectional areas of the additive molecules are equally important.For one and the same batch of seeds the rate of adsorption is related to the number of binding groups, and the inhibiting activity would be expected to follow the order ENTMP > TENTMP 2 HEDP. A comparison of the k’ values obtained at a constant additive concentration and in the presence of various seeds shows that the degree of inhibition decreases in the order C > B > A with TENTMP, ENTMP and HEDP and A 2 B > C with STP. If the surface area of the solid is the dominant factor, the sequence A 2 C x B should hold. Apparently, the pore radius is an equally important controlling factor. Large molecules such as TENTMP (cross-sectional area estimated to be 55 A2) are expected to block small capillaries, as is the case with solid C.Increasing the pore radius of the solid matrix will allow some calcium and/or oxalate ions to diffuse inside the pores and allow growth to proceed. Introduction of a second molecule of TENTMP will be sterically hindered by the presence of the first. Using smaller molecules such as STP (cross-sectional area ca. 37 A2) an interesting sequence of inhi- bition is displayed. Solid C behaves as the least inhibited seed, whereas solids A and B are retarded almost to the same extent. Following the same argument, surfaces of wide pores are capable of accepting more than one molecule of STP, resulting in a higher degree of retardation, whereas surfaces of narrow pores are not sufficiently blocked by these small molecules in spite of the differences in surface area.We thank Prof. S. A. Selim for her help with the nitrogen-adsorption measurements.E. N. RIZKALLA AND M. M. MOAWAD 1629 G. L. Gardner and G. H. Nancollas, J. Znorg. Nucl. Chem., 1976, 38, 523. S. T. Liu and G. H. Nancollas, J. Znorg. Nucl. Chem., 1976, 38, 515. G. H. Nancollas and N. Purdie, Trans. Faraday Soc., 1961, 57, 2272. A. E. Nielsen, Acta Chem. Scand., 1960, 14, 1654. (a) E. L. Prien and C. Fondel, J. Urol., 1947, 57, 949; (b) C. Langren, Acta Radiol. Suppl., 1956, 1, 133; (c) W. H. Boyce, Am. J. Med., 1968, 45, 673. (a) J. S. King and W. H. Boyce, Ann. N. Y. Acad. Sci., 1963,104,579; (b) B. 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