The growth of seed crystals in supersaturated solutions of
calcium phosphate at 25° C is discussed. In the pH range 5-6, the
crystallization of dicalcium phosphate follows a second order rate
equation in a process which is surface reaction rather than· diffusion
controlled. Under physiological pH conditions, the growth
of hydroxyapatite seed crystals proceeds through the formation
of a precursor phase which has a calcium : phosphate ratio of
1.45 ± 0.05 and which attains the HAP composition after slow
interaction with the medium; the process again appears to be
interface controlled

G. H. Nancollas

English

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CR 0 AT IC A CHEMIC A ACT A 43 (1971) 261 CCA-674 548.5:546.41.185 Conference Paper The Nucleation and Growth of Calcium Phosphate Crystals* G. H. Nancollas Chemistry Department, State University of New York at Buffalo, Buffalo, New York, U.S.A. Received July 12, 1971 The growth of seed crystals in supersaturated solutions of calcium phosphate at 25° C is discussed. In the pH range 5-6, the crystallization of dicalcium phosphate follows a second order rate equation in a process which is surface reaction rather than· dif-fusion controlled. Under physiological pH conditions, the growth of hydroxyapatite seed crystals proceeds through the formation of a precursor phase which has a calcium : phosphate ratio of 1.45 ± 0.05 and which attains the HAP composition after slow interaction with the medium; the process again appears to be interface controlled. The control of supersaturation and the nucleatLon and ,growth of crystals in calcium phosphate systems are important in relation to the physiological deposition of bone and tooth mineral. The pathological deposition of calcium salts ·in abnormal or unusual locations from supersaturated tissue fluids will also be significantly dependent upon such processes. Numerous studies of spontaneous precipitation of calcium phosphates have been made in an attempt to determine the mechanism .of the process. In almost all experiments made at approximately the physiological pH, the stoichiometry of the initially formed phase does •not correspond to that of hydroxyapatite [HAP, Ca10(P04) 6 (OH)2]; the calcium : phosphate ratiio being invariably less than the re-quired 1.67. After prolonged periods of •ageing, the ratio rises and eventually reaches that for the pure HAP phase. In an attempt to explain this pheno-menon, several theories have been put forward. Francis1 proposed a surface oomplex of calcium hydrogen phosphate (DCP, CaHP04 ) to acoount for the solubility behaviour of HAP under moderately acidic conditions ranging from pH 3.5 to 6. At higher pH's (6.3 to 7.5) the <assumption of a surface complex of the ,general formula Ca2(HPO, ) (OH) 2 by Rootare, Dietz and Carpenter2 yielded ionic products which were reasonably consistent. Neuman and Neuman3, on the other hand, proposed an exchange of ·surface ions to account for the observed variation of composition of precipitated HAP. More recently, a number of physical methods have been used in an attempt to determine foe nature of the amorphous precursor in HAP precipitation. The results -of Posner and his co-workers4 indicate an appro-ximate composition of this phase corresponding to tricalcium phosphate * Based on a lecture presented at the II International Summer Conference on the Chemistry of Solid/Liquid Interfaces, »Rudjer Boskovic« Institute, Rovinj Yugoslavia, September 1970. 262 G.H.NANCOLLAS (TCP, Ca3(P04 ) 2). Subsequent changes to the more crystalline HAP phase, followed :by an x-ray diffraction method, were found to be autocatalytic in nature. Brown5 has made extensive x-ray studies ·Of calcium .phosphate phases and has determined the crystal structure {)f another phase, octacalcium phosphate (OCP, Ca8H 2(P04) 0 • 5 H 20) which is prec1pitated at physiological pH's. The close epitaxial similarity of OCP to HAP led to the suggestion that the fol'mer phase was a precursor in the process of calcification5• Previous studies of calcium phosphate precipitation have usually been concerned with the spontaneous format~on of solid phase in supersaturated sol!utions. The supersaturated solutions are made by the slow mixing of sol!utions containing the lattice i·ons and it is assumed that the initial sohd phases are formed by homogeneous nucleation. However, it is doubtful whether heterogeneous nucleation can be avoided im any practical medium and in any event, biol!ogical calcification almost certainly results from a heterogeneous rather than a homogeneous nucleahon. In addi·tion, in spon-taneous iprecipitation experiments, both :nucleation and the subsequent gr.owth of the nuclei occur s1multaneously and the results are markedly dependent upon the fluid dynamics of the systems and Uipon the rates .of mi~ing of the reagents. The difficulty of repmducing the results of such ex;perirnents renders them unattractive as a means 10f studying the mechanism ·Of formation of crystals or for assessing the effectiveness of additives in inhibiting the rate of crystal growth. The existence of well-defined metastable Emits for the spontaneous crystallization of most sparingly soluble electrolytes makes it possible, ·by careful control of experimental conditions, to prepare supersaturated solutions which are stable for considerable periods&,7• The kinetics .of growth of well -characterized seed crystals may then be studied, under reproducible condi:ti·ons, by inoculation of these supersa1Jurated solutions and by fo11owing the con-centrations of lattice i:ons as a function of time7- 9• In this paper, we discuss two calcium phosphate crystal growth systems, DCP and HAP, for whrich this method has been applied . . Dicalcium phosphate dihydrate There is considerable interest in the mechanism of growth of DCP crystals from supersaturated solutions of the salt since this phase may play an important part in the production of dental caries10• Studies have been made in calcium phosphate solutions within the pH range 5 to 6 in which the equilibria H2PO~ !::;: H+ + HPO!- k2 (1) Ca2+ + H2PO~ :;o:: CaH2Po: K+ (2) and Ca2+ + HPO~ :;o:: CaHP04 K• (3) must be .taken int<0 account. The concentrations of ionic species in the super-saturated calcium phosphate solutions at any instant were calculated from mass balance and ·electroneutrality C·onditions and the known values for the equilibrium constants11 by successhre approximation of the ionic strength12• As stated ,previously, the seeded growth experiments yield highly repr.o-duci:ble results and in Fig. 1 are shown typical plots of total calcium and NUCLEATION OF CALCIUM PHOSPHATE 263 4 . 40 ~ . -4 . 20 g 4 . 00 40 (.• Minutes Fig. 1: ·Plots of total calcium and total phosphate concentrations as a function of time. Initial conditions: pH= 5.939, Tea= 4.808 X 10-s M, Tro• = 1.185 X 10-2 M total phosphate concentrations as a fanction of time. It is seen that growth commences immediately upon the additton of DCP seed crystals to the supersaturated solutions prepared by the careful mixing of calcium chlo-ride, disodiurm hydrogen phosphate and potassium dihydrogen phosphate solutions. After a brief initial fast period the growth process, represented by the smooth curv.es in Fig. 1, follows equation (4)10 (4) in which the rate .of growth, dT/dt, is expressed as a change in either total calcium ·or total phosphate concentrations, K sp is the thermodynamic solubility product, f 2 the activity coefficient of divalent ions, k the rate constant and s, the surface area. The correction factor (w/ w)"I• is introduced to correct the rate of growth at ·time t to that corresponding to the initial surface area of the seed crystals. wi is the weight of seed crystals at time zero and w, the weight present at time t. Adherence to the second order kinetic equation (4) indicates that the growth of DCP crystals is surface rather than diffusion con-trolled10. It is interesting to note that similar oonclusions have been reached for the gr.owth of crystals of several other sparingly soluble electrplytes. The rate of growth is independent of the rate of stirring within the crystallization cells. For DCP, the kinetic plots in Fig. 2 .confirm the second order dependence of equation 4. The striking effect of additives in reducing the rate .of crystallization has been desc6bed for a number of systems7• If it is assumed that the additive is adsorbed at growth sites ·on the crystal · surface and effectively 1prevents :flurther deposition, the retarding action can be described in terms of a Langmuir adsorption is-otherm. The excellent reproducibility ·Of the experi-mental results for DCP crystal growth has enabled such a study of the effect of sodium pyrophosphate upon the growth rate. Pyrophosphate has been 264 G.H.NANCOLLAS {{Ca2+J [HPO! - ) - ,Ksp/f~) 'x 10 6 Fig. 2. Plots of -(Wi/ W)' !• dT/ dt (="slope" ) against ([Ca'+] [HPo,2-1 - K si,/f 2'). Initial conditions : (0) PH = 5.595, T ea = 1.211 X 10-2 M, T ro< = 1.131 X 10-2 M; (0) pH= 5.59, 'l;'ca = 1.171 X 10-2 M , T ro• = 1.083 X 10-2 M. invoked as a substance which is effective ,in preventing pathological calcifi-cation in the 1body13• Its action in inhibiting the growth of DCP crystals is striking, a concentration as low as 5 X 10-5 M being sufficient to prevent almost entirely the crystal growth process. The reduction in rate constant k (equation 4) is satisfactorily descrrbed in terms of a Langmuir adsorption isotherm10• Hydroxyapatite The existence of a precursor in the predpitation of HAP from super-saturated solutions of caldum phosphate has already been discussed. Our own studies have concerned the growth .of well characterized HAP preparations in supersaturated solutions in which the pH was maintained constant at a value of 7.4 by means of pH-stat-controlled additions of alkali. Under such conditions, in addition to equilibria 1-3, it is necessary to take into account the following reactions14 HPO :- :;:::: H + + PO!-c a2+ +PO!- :;:::: CaPO~ ka (5) (6) The additional species and known values for the equilibrium constants are introduced 'into the computational procedure described previously. After the addit1on 'Of HAP seed crystals to the supersaturated solutions the concen-trations of calcium and phosphate and the alkali uptake were monitored as a £unction of time14• The tyipical rate plots in Fig. 3 indicate that crystal griowth takes place immediately upon inocula·tion with crystals and the overall growth curves consist of two main regions. In the first , of 60-90 min duration, growth proceeds rapidly with the precipitation of a calcium phosphate phase having a calcium : phosphate ratio of 1.45 ± 0.05. Thereafter, this p recursor phase undergoes a slow interaction with the medium and the ratio of cal-cium : phosphate taken up from the supersaturated solution increases to a val:ue NUCLEATION OF CALCIUM PHOSPHATE 265 Fig. 3. Plots of total calcium (0) and total phosphate (0) concentrations as a function of time at a constant pH = 7.4. Initial conditions: T ea = 1.244 X 10-s M, Tpo• = 0.782 X 10-s M. a1pproaching 2.0. Equilibrium is attained after 6-7 days at the end of which time, the overall calcium: phosphate ratio of the material deposited is close to the 1.67 required for HAP. The stoichiometry of the precursor phase is close to that, 1.5, for TCP. It is interesting to note, however,15 that the caldum: phosphate ratio is con-sistently 3-50/o lower than that required for pure TCP and thus it is not possible to rule out other phases, such as DCP or OCP which may participate in the early stages of the crystall .growth process. As was found with DCP, the rates •of change of concentrations with time and hence the rate of crystal gl'\owth are independent of t he rates of stirring. This evidence strongly suggests that the seeded growth ·of HAP is also controlled by a reaction at the surface of the crystals rather than by a diffusion prncess. Acknowledgements. We acknowledge the present support for this work through a grant from the National Institutes of Health. REFERENCES 1. M. D. Francis, N. Y. Acad. Sci. 131 (1965) 694. 2. H. M. Root are, V. R. Deitz, and F. G. Carpenter, J . . Colloid Sci. 17 (1962) 179. 3. W. F. Neuman and M. W. Neuman, Chem. Rev. 53 (1953) 1. 4. E. D. Eanes, I. H. G i 11 es sen, and A. S. Posner, Proc. Int. Conj. on Crystal Growth, Boston, (1966) 373. Pergamon Press, Oxford. 5. W. E. Brown, Clin. Orthop. 44 (1966) 5318. 6. C. W. D av i es and G. H. Nan co 11 as, Trans. Faraday Soc. 51 (1955) 818. 7. G. H. Nan co 11 as and N. Purdie, Quart. Rev. 18 (1964) 1. 8. J. R. Cam be 11, and G. H. Nan co 11 as, J. Phys. Chem. 73 (1969) 1735. 9. H. T. Liu and G. H. Nan co 11 as, J. Cryst. Growth 6 (1970) 281. 10. R. W. Marsh a 11 and G. H. Nan co 11 as, J. Phys. Chem. 73 (1969) 3838. 266 G.H. NANCOLLAS 11. A. Chug ht a i, R. W. Marsh a 11, and G. H. Nan co 11 as, J. Phys. Chem. 72 (1968) 208. 12. G. H . Nan co 11 as, Interactions in Electrolyte Solutions, 1966. 13. H. F 1 e is ch, Clin. Orthop. 32 (1964) 170. 14. G. H. Nan co 11 as and M. S. Moh an, Arch. Oral Biol. 15 (1970) 731. 15. A. G. W a 1 ton, W. J. B o din, H. F tire di, and A. Schwartz, Canad. J. Chem. 45 (1967) 2695. IZVOD Nukleacija i rast kristala kalcium-fosfata G. H. Nancollas Opisan je rast kristala kalcium-fosfata iz zasiCenih vodenih otopina kod 25°. Proces rasta dikalcium-fosfata u otopinama fizioloskog pH 5 do 6 slijedi kineticku jednadzbu za reakciju drugog reda. Proces je kontroliran povrsinskim pojavama, a ne difuzijom iz otopine. Rast kristala hidroksiapatita ukljueuje fazu predstanja (pre-kurzora) s odnosom kalciuma prema fosfatu od 1.45 ± 0.05. Tek iz tog predstanja sporom interakcijom s medijem dolazi do stvaranja hidroksiapatita. I ovaj proces kontroliran je stanjem na povrsini. STATE UNIVERSITY OF NEW YORK CHEMISTRY DEPARTMENT BUFFALO, N . Y. U.S. A. Primljeno 12. srpnja 1971. 

The Nucleation and Growth of Calcium Phosphate Crystals

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