Dicalcium Phosphate Dihydrate Precipitation

Dicalcium Phosphate Dihydrate Precipitation

DICALCIUM PHOSPHATE DIHYDRATE PRECIPITATION Characterization and Crystal Growth C. Oliveira, A. Ferreira and F. Rocha Department of Chemical Engineer...

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DICALCIUM PHOSPHATE DIHYDRATE PRECIPITATION Characterization and Crystal Growth C. Oliveira, A. Ferreira and F. Rocha Department of Chemical Engineering, Faculty of Engineering, University of Porto, Porto, Portugal.

Abstract: The precipitation of dicalcium phosphate dihydrate, brushite, by mixing a calcium hydroxide suspension and an orthophosphoric acid solution in equimolar quantities, has been investigated in a batch system at 258C. The concentration of calcium hydroxide and orthophosphoric acid, before mixing, ranged from 50 to 400 mmol dm23. The precipitation process occurs in five stages, being the hydroxyapatite, Ca10(OH)2(PO4)6, the first phase to be precipitated, as shown in a previous work. This present work deals with the phenomena occurring during the last stage, according to the model presented: brushite grows due to direct consumption of calcium in solution, and due to the transformation of HAP into brushite. An equilibrium and mass balance equations system is formulated describing the chemical species present in solution and the change of their concentrations along each run. This system was validated through conductivity measurements. From this system, the type and composition of precipitate is determined, and the evolution of particle size is estimated and compared with experimental results. The kinetics of brushite growth due to calcium consumption (determined from the decrease of calcium concentration) was studied. The results obtained in these studies allow validating the proposed model concerning the transformation of HAP and brushite growth. Keywords: precipitation; crystal growth; brushite; hydroxyapatite.

INTRODUCTION



Correspondence to: Professor F. Rocha, Department of Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal. E-mail: [email protected] DOI: 10.1205/cherd06237 0263–8762/07/ $30.00 þ 0.00 Chemical Engineering Research and Design Trans IChemE, Part A, December 2007 # 2007 Institution of Chemical Engineers

(5) transformation of HAP into brushite and growth of brushite.

The precipitation of calcium phosphate is an operation of great importance to the industry as well as in physiological processes (Hohl et al., 1982; Marshall and Nancollas, 1969; Tsuge et al., 1996). For that, many authors have been devoting their effort to its study. Different compounds can be obtained, depending on the precipitation conditions (Hohl et al., 1982; Heughebaert and Nancollas, 1984; De Rooij et al., 1984; Abbona et al., 1986; Heughebaert et al., 1986). One of them is the dicalcium phosphate dihydrate (CaHPO4 . 2H2O) henceforth named DCPD or brushite. By mixing a calcium hydroxide suspension and an orthophosphoric acid solution, the precipitation of brushite occurs after the initial precipitation of hydroxyapatite (HAP) and through a very complex process (Ferreira et al., 2003). Five stages were identified:

The present work studies the growth of the brushite crystals, so formed, during the last stage of the process. In this stage, a slow increase in pH and a decrease in calcium concentration were observed. SEM and X-ray diffraction analyses showed a gradual reduction of HAP crystals simultaneously with the growth of brushite crystals, until the complete HAP disappearance. This happens because HAP is in low crystallinity-state and in metastable equilibrium with brushite. Further, as the crystallization rate of brushite is much higher than that for HAP, the kinetic factors can assume a decisive role, implying the disappearing of HAP and the formation of brushite. Figure 1 (Ferreira et al., 2003) refers to three different moments of this stage. The HAP disappearance and the consequent increase in brushite crystallinity are clearly visible. The experiments suggest, then, that the brushite particles grow due to direct consumption of calcium in the solution and due to the transformation of HAP into brushite. The growth of brushite crystals through the calcium consumption was studied by following the change of calcium concentration, whereas

(1) spontaneous precipitation of hydroxyapatite, Ca10 (OH)2 (PO4)6; (2) complete dissolution of calcium hydroxide and HAP growth; (3) formation of the first nuclei of brushite; (4) brushite and HAP coexist in solution; 1655

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Figure 1. Time evolution of crystallinity in the last stage: (a) initial, (b) middle, (c) final (Ferreira et al., 2003).

the transformation of HAP into brushite was determined by identifying the several chemical species present in solution, and evaluating the change of their concentrations with time. The transformation of HAP into brushite implies, also, an increase of the size of the crystals due to the difference in density of the two compounds: HAP density is higher than that of brushite. A model is present to explain and quantify the process leading to the formation and growth of brushite crystals, during the last stage of calcium phosphate precipitation. Due to the complexity of the system a study was made to characterize and quantify the chemical species present in the solution along the process. This was tested and validated by conductivity measurements. The experiments were performed in a batch reactor at 258C. The precipitation was carried out by mixing equimolar quantities of calcium hydroxide and orthophosphoric acid. The size of the crystals was measured by laser diffraction. To the best of our knowledge there are no previous works treating the growth of brushite crystals in the conditions of this study. There are several publications regarding the growth of brushite but at different conditions, as for example the works of Marshall and Nancollas (1969), Hohl et al. (1982) and Heughebaert et al. (1986) where the crystals grow in stable and seeded solutions.

EXPERIMENTAL Experiments were performed in an apparatus already described in a previous work (Ferreira et al., 2003). The precipitation cell consists of a batch reactive crystallization

cylindrical tank made of glass, with 100 mm in diameter and 250 mm in height, and a glass stirrer operated at 270 rpm. Temperature was regulated by a water jacket and a thermostatic bath maintained at 258C. The reactive crystallization of brushite began by quickly adding 0.5 dm3 of a calcium hydroxide (Riedel-de Hae¨n, 96%) aqueous suspension to an orthophosphoric acid (Pronalab, 85%) aqueous solution with the same volume and molar concentration. The volume fraction of Ca(OH)2 particles in solution at the beginning of the experiments was always lower than 0.7%, and the mass average size about 5 mm. The calcium concentration, pH, temperature and conductivity were continuously measured (inoLab pH/Cond Level 3, WTW) and recorded by a computer. Different initial reagent concentrations were used (from 50 to 400 mmol dm23 before mixing), and the duration of the run varied according to the final conditions pretended. The maximum duration was about 3 h. At the end of each experiment, to determine the type of precipitate suspension samples were withdrawn, filtered and dried, and the crystals were analysed by scanning electron microscopy (SEM) and characterized by X-ray diffraction using a Philips PW1830 diffractometer with Co Ka radiation (lCoKa ¼ 0.1789 nm). The size distribution of the crystals was determined using a laser sizer (Coulter LS 230). For that, because of the aggregation problem caused by the filtration and drying steps, solution sample was withdrawn and directly analysed in the laser sizer. In each experiment one only sample was analysed. Experiments with different durations were performed in order to have results covering the last stage under study. Calcium was analysed using

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CHARACTERIZATION AND CRYSTAL GROWTH Table 1. Chemical reactions for the Ca(OH)2/H3PO4/H2O system. H2O  Hþ þ OH2

(A1)

H3PO4  Hþ þ H2PO2 4

(A2)

þ 22 H2PO2 4  H þ HPO4

(A3)

32 þ HPO22 4  H þ PO4

(A4)

CaHPO4  Ca2þ þ HPO22 4

(A5)

2þ þ PO32 CaPO2 4  Ca 4 2þ þ H2PO2 CaH2POþ 4  Ca 4

(A6) (A7)

CaOHþ  Ca2þ þ OH2

(A8)

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The Ca(OH)2/H3PO4/H2O system (A) is very complex, and was represented by the set of chemical reactions shown in Table 1 (Tsuge et al., 1996). The concentrations of the different chemical species were determined using the system of equilibrium equations and mass balance equations presented in Table 2. The activity coefficients were calculated using the Debye–Hu¨ckel equation. The values used for the equilibrium constants are presented in Table 3 (Tsuge et al., 1996; Lundager Madsen and Thorvardarson, 1984). Measured values of temperature, pH and calcium concentration were used to solve the system of equations. After mixing of reagents, and for a short period, an increase of temperature occurred. This increase depends on initial concentration of reagents. This effect was considered in the calculations made. So, the brushite solubility was determined as a function of pH and taking into account the temperature effect, as f1 –f2 [equations (A19) and (A20), respectively]. To evaluate if the system of equations represents correctly the reality, the solution conductivity was measured and compared with the conductivity, k (S cm21), calculated using the estimated concentration of the chemical species, by the formula

a selective electrode (WTW-D 82362 Weitheim) and pH was measured by an electrode WTW Sentix 6. The different electrodes were calibrated using buffer solutions at 258C. In some runs, the density of the solids was measured using helium pycnometry and mercury porosimetry (Quantachrome, Poremaster 60).

DESCRIPTION OF THE SYSTEM In order to identify the composition of the precipitate and its evolution with time, the concentration of all chemical species presented in solution must be determined.



X Ci li 1000 i

(1)

Table 2. Equilibrium and mass balance equations. K1 ¼ K2 ¼

y12 ½H þ  ½OH   y12 ½H þ  ½H2 PO 4 ½H3 PO4 

(A9) (A10)

K3 ¼

y2 ½H þ  ½HPO2 4  ½H2 PO4 

(A11)

K4 ¼

y1 y3 H PO3 4 y2 HPO2 4

(A12)

½ ½  ½  y22 ½Ca2þ  ½HPO2 4  þ

K5 ¼ K6 ¼ K7 ¼

(A13)

½CaHPO4  y2 y3 ½Ca2þ  ½PO3 4  y1 ½CaPO 4 2þ

½



y2 Ca H2 PO 4 CaH2 POþ 4

½

(A14)



(A15)





y ½Ca  ½OH K8 ¼ 2 ½CaOHþ  rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi y 2 ½Ca2þ ½HPO2 4  S¼ 2 Ksp





(A16) (A17)

½Ca2þ   1000  40:082

(A18)

f1 f2 4

3

2

f1 ¼ 9:1083pH  246:5800pH þ 2521:1000pH  11562pH þ 20138 4:1187pH 4 þ 100:4689pH 3  891:8019pH 2 þ 3373:7539pH  4479:3947 f2 ¼ 5=ðt(8C)  25Þ       þ þ TCA ¼ Ca2þ þ ½CaHPO4  þ CaPO 4 þ CaH2 PO4 þ ½CaOH         2 3 TPO ¼ ½H3 PO4  þ H2 PO4 þ HPO4 þ PO4 þ ½CaHPO4 þ     þ þ CaPO 4 þ CaH2 PO4        þ   1 2 I¼ ½OH   þ H2 PO þ 9 PO3 þ H þ 4 Ca2þ þ 4 þ 4 HPO4 4 2        þ þ þ CaPO  4pffiþ CaOH þ CaH2 PO4  0:51pffiI y1 ¼ 10 1þ I   pffi pffi I  40:51 1þ I y2 ¼ 10   pffi pffi I  90:51 1þ I y3 ¼ 10 þ

pH ¼  logðy1 ½H Þ

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(A19) (A20) (A21) (A22)

(A23)

(A24) (A25) (A26) (A27)

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Table 3. Equilibrium constants for the chemical reactions shown in Table 1 and solubility product for brushite at 258C. K1 ¼ 1  10214 K2 ¼ 7.11  1023 K3 ¼ 6.31  1028 K4 ¼ 4.52  10213 K5 ¼ 1/264 K6 ¼ 1/(2.9  106) K7 ¼ 1/8.48 K8 ¼ 1/20 8403:5 KSP ¼ e( T þ41:8630:09678T)

where Ci is the concentration of each species (mol dm23) and li the correspondent molar ionic conductivity (S cm2 mol21). The values of li used (Lide, 2006) are presented in Table 4. These values are for 258C that is the temperature occurring (or very close) in the last stage. It was not possible to find þ the ionic conductivity for some species (CaPO2 4 , CaH2PO4 and CaOHþ). The concentration of these ions is very small, so the error in the calculation of the conductivity will be not very relevant. The ionic conductivities used are at infinite dilution. This fact may have a significant effect on the estimated conductivities and so, the calculated conductivities will be higher than the measured ones, as we can find in Figure 2. Even so, a good agreement between the two conductivities occurs, as it is shown in the example presented in this figure. The deviations are small, increasing with reagent concentration. Considering the last stage, the average deviation ranges from 0.22% for 0.05 M to 3.3% for 0.4 M. The ionic strength was always adjusted by the addition of KCl 4 M. For all initial reagent concentrations the results obtained show the same behaviour, proving that the system of equations represents well the real system mainly in the last stage. KCl contributes with about 90% to the total conductivity. But, as its contribution is considered constant, the variation of the conductivities will be due to the variation of the concentrations of the chemical species of the defined system. So, one can conclude that the system represents satisfactorily the solution composition. The agreement in the first stages, when HAP is forming and growing is not so good, implying that the system proposed does not apply correctly to this situation. As, in this work, we are concerned with what is happening in the last stage, this question is irrelevant.

Table 4. Equivalent ionic conductivities at 258C. Ion Hþ OH2 H2PO2 4 1/2HPO22 4 1/3PO32 4 CaPO2 4 CaH2POþ 4 CaOHþ 2þ 1/2Ca Kþ Cl2

l8 (S cm2 mol21) 349.65 198 36 57 92.8 — — — 59.47 73.48 76.31

Figure 2. Measured and estimated solution conductivity for the experiment at initial reagents’ concentration of 0.1 M.

RESULTS AND DISCUSSION Desupersaturation curves of calcium are represented in Figure 3 and the average size in mass L43 of the crystals in Figure 4 as functions of time. In all cases the average size L43 increases rapidly, reaching soon a maximum value practically constant with time. The final size of crystals was in the range 30 –35 mm. The influence of the initial concentration is small, but it seems that the higher the initial concentration, the bigger the crystals. The results present a significant scattering, acceptable given the small range of size change. The last stage of the precipitation process begins approximately as calcium concentration starts to decrease. This happens after a period of almost constant calcium concentration (the fourth period of precipitation process) occurring the sooner, the higher the calcium concentration. This period is well perceptible for the concentrations of 0.05 and 0.1 M. As already explained, the first phase to be precipitated is hidroxyapatite. Nevertheless, the rapid decrease of HAP supersaturation during the second stage of the process, the low reached pH, and the low crystallinity of HAP (Ferreira et al., 2003) will thermodynamically have an unfavourable impact on the precipitation and growth of HAP. In these conditions, brushite can exist in metastable equilibrium with HAP, rendering possible the occurrence of brushite crystals. The kinetic factors assume, then, a decisive role (crystallization rate of brushite is much higher than that for HAP; at 378C and pH 6 the ratio is about 1000) leading to the gradual disappearing of HAP and the consequent formation of brushite. HAP transforms into brushite, according to the following equation: Ca10 (OH)2 (PO4 )6 þ 4 H3 PO4 þ 18 H2 O ! 10 CaHPO4  2H2 O

(2)

We can follow the transformation of HAP into brushite by calculating the calcium to phosphate molar ratio (R ¼ Ca/P) in the precipitate, through the system of equations already presented. In any instant, R is determined knowing the initial

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CHARACTERIZATION AND CRYSTAL GROWTH

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Figure 3. Desupersaturation curve against time at different initial reagents’ concentrations.

concentrations of calcium and phosphorous, and from their concentrations in solution given by equation system [equations (A21) and (A22)], respectively. The transformation of HAP into brushite along the time can, then, be quantified from the knowledge of the amount of Ca and P in the precipitate and the stoichiometric relations involving those compounds and their elements. This ratio is 1.67 for HAP and 1 for brushite. Along the time, and as HAP transforms into brushite this ratio, beginning at 1.67, decreases until reaching the value 1. The number of particles was estimated by knowing the mass of precipitate and the size distribution given by laser diffraction, and it was found practically constant along the last stage. For each run, and along the time, the mass of HAP and brushite present in the precipitate, and the ratio R were calculated. From the results obtained, it was found that the transformation of HAP is well fitted by an equation of type: dmHAP ¼ kHAP (mHAP )2 dt

(3)

Further, the solution is supersaturated relatively to brushite, and calcium concentration decreases with the time. So, the mass of brushite crystals will increase through two mechanisms: by HAP transformation into brushite [equation (2)], and by crystal growth from solution, defined by JB ¼ Ac  Rg ¼ a

dmC dt

(4)

where a ¼ (MB =MC ). In short, the variation of the mass of brushite with time can be represented by: dmB dmHAP ¼ JB þ b dt dt

(5)

being b ¼ 10(MB =MHAP ) the transformation factor (¼1.71). It must be taken into account the difference in density of HAP and brushite, 3155 and 2310kg m23, respectively (Lide, 2006). In some runs, samples were withdrawn and

Figure 4. Average particle size (experimental and estimated) as a function of time at different initial reagents’ concentrations: (a) 0.05 M, (b) 0.1 M, (c) 0.2 M, (d) 0.3 M, (e) 0.4 M.

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the density measured by helium pycnometry and mercury porosimetry. The results obtained show that the density of precipitate decreased along the last stage, confirming, also by this way, the transformation of HAP into brushite. Due to this fact, when HAP transforms into brushite there is an increase on the volume of the particle. The enlargement of the particle size can be easily quantified through the equations relating the mass, the volume, and the size of the particle: LB ¼ kL LHAP

(6)

where kL ¼ ½(rHAP kvHAP )=(rB kvB )1=3 . As the number of particles was found to be practically unchanged along the time, one can estimate the size of the particles taking into account the transformation of HAP into brushite, the effect of the different densities on the size of particles, and the variation of calcium concentration. The model above formulated was the basis for the estimate of the size of the particles along each run. The calculation begins at a time where R is 1.67, indicating that we have, at this point, essentially HAP. This initial R value agrees very well, for all reagent initial concentrations, with the beginning of last stage as determined by an independent way (referred already in this section). The particle experimental size L43 at these conditions was taken as initial value of particle size. The particles were considered spherical in such way that the estimates could be compared with the experimental data L43 given by laser diffraction. The estimates obtained are presented in Figure 4. Disregarding the scattering of the experimental results, the agreement between the calculated and the experimental results is good, showing that the model proposed for the formation and growth of brushite represents well the phenomena occurring in the precipitation process. The deposition of brushite from solution is measured by the decrease of calcium concentration, and can be represented by Rg ¼ K s n

(7)

The total crystal area in contact with solution increases with time. This area was calculated from the crystal size calculated from the system of equations and knowing the total number of crystals in solution (considered constant as already mentioned). The relative supersaturation, s(¼[Ca2þ]/ [Ca2þ] 2 1), was determined from the same system of equations. So, the previous equation represents the brushite growth rate corresponding to the calcium consumption. The results obtained, Rg versus s, are shown in Figure 5, and the kinetic parameters K and n presented in Table 5. For the initial reagents’ concentrations of 0.1, 0.2 and 0.3 M the exponent n is near of 2, for 0.4 M the exponent is 3.60, while for 0.05 M, as the fourth stage is very long, there is no data in significant amount to take a safe conclusion. Data on brushite growth found in literature are not comparable with the data of this work. It was found (Hohl et al., 1982) that brushite growth rate in seeded solutions depends on pH. In this work pH is not constant. In the last stage, it increases slowly with the time, the change range depending on the initial reagents’ concentration.

Figure 5. DCPD growth rate from solution at different initial reagents’ concentrations: (a) 0.1 M, (b) 0.2 M, (c) 0.3 M, (d) 0.4 M.

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CHARACTERIZATION AND CRYSTAL GROWTH Table 5. Kinetic parameters of equation (7). Concentration (M) 0.1 0.2 0.3 0.4

K

n

1.77  1026 1.34  1026 3.18  1026 3.42  1026

2.15 1.90 2.25 3.60

CONCLUSIONS A model is presented to represent the phenomena occurring in the last stage of the dicalcium phosphate dihydrate precipitation, namely the transformation of HAP into brushite and the growth of brushite. The chemical species in solution are described and quantified along each run from a system of equilibrium and mass balance equations. This system was validated comparing conductivity measurements with estimated ones from the system of equations. Using this system, the particle size was estimated and compared with experimental results. Disregarding the scattering of experimental results, the calculated results agree well with the experimental ones. The kinetics of brushite growth due to calcium consumption in solution was studied. This process seems to be of second order. Globally, the results obtained allow concluding that the proposed model represents well the phenomena occurring in the last stage of brushite precipitation.

NOMENCLATURE Ac C f1 f2 I JB K Ki Ksp k kL kHAP kvB, kvHAP LB, LHAP L43 M MB, MC, MHAP

surface area of crystals, m2 concentration, mol dm23 brushite solubility as function of pH at 258C (data taken from Gregory et al., 1974) correction of brushite solubility taking into account temperature change (Ferreira et al., 2003) ionic strength, mol dm23 precipitation rate, kg s21 overall growth constant [equation (7)], kg m22 s21 equilibrium constant in Table 3, mol dm23 solubility product conductivity, S cm21 constant in equation (6) (kL ¼ (rHAP kvHAP )=(rB kvB )1=3 ) constant of equation (3) volume shape factor of brushite, HAP crystal size of brushite, HAP, m average mass crystal size, m molarity, mol dm23 molecular weight of brushite, calcium, HAP, kg mol21

mB, mHAP mC n R Rg S T TCA TPO t t(8C) yz

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mass of brushite, HAP, kg mass of calcium in solution, kg overall growth order calcium to phosphate molar ratio overall growth rate, kg m22 s21 supersaturation temperature (K) total calcium concentration, mol dm23 total phosphate concentration, mol dm23 time, s temperature (8C) activity coefficient of an ion with charge z

Greek symbols a b l rB, rHAP s

constant in equation (4) (a ¼ MB/MC) constant in equation (5) (b ¼ 10MB/MHAP) ionic conductivity, S cm2 mol21 density of brushite, HAP, kg m23 relative supersaturation

REFERENCES Abbona, F., Lundager Madsen, H.E. and Boistelle, R., 1986, The initial phases of calcium and magnesium phosphates precipitated from solutions of high to medium concentrations, J Crystal Growth, 74: 581– 590. De Rooij, J.F., Heughebaert, J.C. and Nancollas, G.H., 1984, A pH study of calcium phosphate seeded precipitation, J Colloid Interface Sci., 100: 350–358. Ferreira, A., Oliveira, C. and Rocha, F., 2003, The different phases in the precipitation of dicalcium phosphate dihydrate, J Crystal Growth 252: 599–611. Gregory, T.M., Moreno, E.C., Patel, J.M. and Brown, W.E., 1974, Solubility of b-Ca3(PO4)2 in the system Ca(OH)2-H3PO4-H2O at 5, 15, 25 and 378C, J Res Natl Bur Stand-A Phys Chem, 78A(6): 667– 674. Heughebaert, J.C., De Rooij, J.F. and Nancollas, G.H., 1986, The growth of dicalcium phosphate dehydrate on octacalcium phosphate at 258C, J Crystal Growth, 77: 192– 198. Heughebaert, J.C. and Nancollas, G.H., 1984, Mineralization kinetics: the role of octacalcium phosphate in the precipitation of calcium phosphates, Colloids Surf, 9: 89–93. Hohl, H., Koutsoukos, P.G. and Nancollas, G.H., 1982, The crystallization of hydroxyapatite and dicalcium phosphate dehydrate; representation of growth curves, J Crystal Growth, 57: 325–335. Lide, D.R. (ed) 2006, CRC, Handbook of Chemistry and Physics, 87th edition (Taylor and Francis, Boca Raton, FL, USA). Lundager Madsen, H.E. and Thorvardarson, G., 1984, Precipitation of calcium phosphate from moderately acid solution, J Crystal Growth, 66: 369– 376. Marshall, R.W. and Nancollas, G.H., 1969, The kinetics of crystal growth of dicalcium phosphate dehydrate, J Phys Chem, 73(14): 3838–3844. Tsuge, H., Yoshizawa, S. and Tsuzuki, M., 1996, Reactive crystallization of calcium phosphate, Trans Ind Chem Eng, 74(A): 797– 802. The manuscript was received 5 December 2006 and accepted for publication after revision 11 August 2007.

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