Crystallization Example Chemistry Assignment

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The large number of calcium phosphate phases that may form and their regions of stability, depending upon lattice ion concentrations and pH, make it possible that apatite formation in vivo involves more acidic calcium phosphate phases that later transform to HAP. In an attempt to understand these events in vivo, numerous spontaneous precipitation studies have been made in vitro. The stoichiometric molar ratio of calcium to phosphate calculated from changes in concentration during precipitation from solution is frequently in the range of 1.45 ± 0.05, which is considerably lower than the value 1.67 required for the thermodynamically favored HAP. In order to reach the approximate HAP composition, extended solid/solution equilibration is required. At relatively high supersaturations, as stated above, and at pH values greater than 7, an amorphous calcium phosphate phase is formed.56,57 It has been proposed that subsequent conversion to more stable calcium phosphate phases takes place by an autocatalytic solution-mediated crystallization process.7,5861 Formation of HAP without the initial precipitation of more acidic phases is achieved in solutions supersaturated only with respect to HAP (Figure 1). The transformation of the low-temperature (monoclinic, P21/b) to the high-temperature (hexagonal, P63/m) modification was investigated by means of molecular dynamics simulations. In the monoclinic phase, the orientation of the hydroxide ions is strictly ordered.62 Above the critical temperature of about 200 °C, orientational changes of the hydroxide ions were observed.62 In the course of each reorientation event, a hydroxide ion passes through the surrounding calcium triangle. From an Arrhenius fit, the related activation energy was calculated. In the high-temperature phase, the hydroxide ions are statistically disordered. Of the two possible concepts for the formation and structure of hexagonal HAP, the simulations clearly identified the disordering of hydroxide ion orientation that occurs in a nonconcerted manner as the more important; that is, collective reorientation of OH ion rows was not observed.62 General Considerations

In spontaneous precipitation studies at high supersaturation and pH, the initial highly hydrated cryptocrystalline ACP was detected by a gradual development of opalescence in the solution following induction periods63 that were dependent upon concentration, ionic strength, and pH.64,65 It was shown that the induction periods for the formation of ACP and the lifetimes of this phase were increased at lower supersaturations.21 As described in section 2.1.1, ACP2 has a more crystalline structure than ACP1.14,65 In neutral solution, hydrolysis of ACP2 to OCP or poorly crystalline apatite was observed. In more acidic solutions, a precipitate of DCPD was formed, but without involving ACP as an initial phase. Based on the analysis of the measured precipitate induction times and the structure of the developing solid phase, OCP was also proposed by Feenstra and de Bruyn66 as an intermediate in the conversion of ACP to apatitic calcium phosphate. Since OCP or apatite crystals were generally found in association with the ACP spherules, it is possible that ACP acts as a template for the growth of these crystal phases. Their formation, however, appears to take place by consuming ions largely supplied from the surrounding solution rather than from direct hydrolysis of the solid amorphous material. A study of ACP transformation under more alkaline conditions (pH = 10) was made by Harries et al.19 using extended X-ray absorption fine structure (EXAFS). This method is concerned with the variation in absorption coefficient of an element on the high-energy side of the X-ray absorption edge. This is the result of the interference between a primary photoelectron wave emitted by an atom on absorption of an X-ray photon and secondary waves backscattered from neighboring atoms. This interference is dependent on the precise geometry of the atomic environment around the emitting atom, thus providing information on the coordination distances of atoms from the excited atoms.19 EXAFS has the advantage of defining radial distribution functions with a specific atom type defined as the origin, in terms of coordination numbers, atom types, shell radii, and Debye–Waller factors, provided that spectra of related model compounds of known crystal structure are available. Transformation experiments of ACP at pH 10 showed that the formation of poorly crystalline HAP proceeds without change in the local calcium environment, but with the development of longer range order.19 For poorly crystalline HAP, it was necessary to invoke a regular structure out to 0.57 nm from the calcium atom, while spectra from ACP could be explained by order extending out to only about 0.31 nm. This corresponds with the first three shells, which have similar radii in ACP to those of poorly and fully crystalline HAP.19 The lack of order beyond these three shells in ACP may be ascribed to its structure, which is characteristic of an amorphous solid, exhibiting paracrystalline disorder of the second kind.67 The EXAFS results provide an alternative model to the suggestion, based on an analysis of X-ray (XRD) autocorrelation functions, that ACP consists of stereochemical clusters of TCP. 7,19 In the latter study, it was shown that the first two peaks in the reduced radial distribution function of ACP are similar in size and position to the corresponding peaks for HAP arising from spacings up to about 0.3 nm. This corresponds to the three shells that give rise to the features of the EXAFS spectrum, which shows no evidence for order beyond this distance from a calcium atom origin. The striking agreement between the results of these studies indicates that transformation of ACP to poorly crystalline apatite may proceed without changes in the local environment of the calcium ions and involves simply an increase in the long-range order in the structure. The influence of magnesium in the conversion of ACP to HAP and on the crystal structure and habit of HAP was interpreted in terms of its incorporation and surface adsorption.68

The participation of ACP as a precursor phase during apatite formation in vivo has been suggested.69,70 In a comparison of XRD data for synthetic HAP and biological apatite, it was found that the peak intensity of the latter was, in general, lower, suggesting that another phase lacking X-ray fine structure was present. The conclusion that this phase must be ACP was questioned by Glimcher et al.,71 who compared XRD spectra of stoichiometric HAP with those of nonstoichiometric and carbonate-containing samples. It was suggested that the lower peak intensities of the latter explained to some extent the missing fractions, which were attributed to ACP-like inclusions. Moreover, the small size of the apatite crystals, the presence of adsorbed impurities, and intergrown surface layers were also invoked as reasons to explain the differences between the XRD peak intensities of biological and synthetic apatites.71 In spite of these interpretations of the spectroscopic data without invoking ACP, the similarities in short-range order around the calcium ions indicate that the possibility of ACP, as a precursor of in vivo formed apatite, cannot be ruled out. The rapid transformation of ACP to more crystalline calcium phosphate phases makes it unlikely that large amounts would be maintained, even in the presence of the inhibitors found in serum. However, it is important to bear in mind that the rate of this transformation of ACP is normally very rapid in vitro, so that this phase may be transformed before it can be detected experimentally. Consequently, the lack of observed ACP in tissue cannot be used as evidence for ruling it out as an in vivo precursor. The similarities in the calcium ion environment, as revealed by EXAFS, indicate that local aggregates of ions from hydrolyzing ACP can be readily incorporated into a growing apatite lattice.71 Kazanci et al. employed Raman analysis of the chemical conversion of ACP to HAP. The precipitation began with ACP (ν1PO4 around 950 cm−1), and at the transition point (about 90 min at the nucleation stage), OCP at ν1PO4 955 cm−1 was observed. After 90 min, the structure completed its maturation and the band position shifted to ν1PO4 960 cm−1 (crystalline stage).72 When the structure evolved from ACP to OCP, the XRD lines became visible. Prior to this region, the precursor was completely amorphous.72 The formation of HAP from ACP was observed in situ in calcium-rich aqueous solutions with the Ca/P molar ratios 1.67, 1.83, and 2.0 by freeze-drying the precipitates withdrawn at selected time intervals during the reaction. As the amount of excess calcium ions increased in the solution, the HAP crystallization from ACP occurred more rapidly and the Ca/P molar ratio of the final precipitates increased to reach the stoichiometric value of 1.67. Acicular HAP nanocrystals grew from the interparticle phase between the spherical particles within the ACP aggregates in an initial stage of the phase transformation. This observation favors the view that an internal rearrangement process is responsible for the ACP–HAP transformation rather than a dissolution–reprecipitation process.73

The microstructural changes in the initial stage of conversion of α-TCP to HAP using the hydrolysis method were also investigated by TEM.74 At first, the surface of the α-TCP was covered by an ACP layer, resulting from hydration or dissolution of α-TCP. Subsequently, the nucleation of HAP occurred on the amorphous layer, after which dendritic structures appeared on the layer. Thereafter, the dendritic structures developed into needlelike fine HAP crystals. Under physiological conditions, the picture appears to be quite different; the transformation of ACP to HAP in aqueous medium has been described as an autocatalytic conversion process,58 and the results of a number of studies investigating the importance of solution environment75,76 were usually interpreted as a single event, without involving discrete intermediate phases. However, Tung and Brown57 used a titration method to study the conversion of ACP at high slurry concentrations, calculating the thermodynamic driving forces for each calcium phosphate phase to determine if the solution phase was in quasi-equilibrium with precipitated solids. A typical conversion kinetics experiment clearly indicated two processes: the first, consuming acid, and the second, consuming base, in order to maintain a constant pH of 7.4 (25 °C). In the first process, the calcium concentration increased by about 10%, reaching a maximum when the consumption of acid also reached its maximum. This implied that calcium and hydroxide ions were released simultaneously from the ACP, in accordance with the conversion of ACP to an OCP-like intermediate by reaction 2.2,3


Moreover, in the first acid-consuming step, the phosphate concentration decreased, ruling out the possibility that the increase in calcium and hydroxide ions was due to the simple dissolution of ACP. In the second step, requiring a consumption of base, the calcium concentration decreased and the phosphate concentration began to increase after about 100 min, indicating that the OCP-like intermediate, as well as ACP, converted to an apatite. Following 24 h of reaction, the final product was nonstoichiometric, with Ca/P = 1.56, and showed an apatitic X-ray diffraction spectrum. Clear evidence for the formation of OCP as an intermediate in the precipitation of HAP was obtained from studies of the transition stage in the spontaneous precipitation of calcium phosphate made under pH-stat conditions by titration with base.77 Typical plots of ΔGOCP show the existence of a secondary inflection during the amorphous to crystalline transformation. Moreover, the ionic activity product of the solution phase in contact with the first-formed crystalline material was invariant and close to the solubility value for OCP, indicating the formation of this phase. The hydrolysis of the OCP to more apatitic phases may occur either by the dissolution of OCP, followed by precipitation of HAP, or by a direct solid-state transformation25 by the hydrolysis of an OCP unit cell to a two-unit cell thick layer of HAP.78 Either the transformation of OCP or simultaneous growth of both phases would yield an eventual apatitic phase having calcium ion deficiencies. The transformation is probably never complete, leaving unhydrolyzed regions of OCP associated with the precipitated apatite. Moreover, other ions, adsorbed at surfaces having a relatively high specific surface area, may also change the experimental Ca/P ratio. Thus, if a half-unit cell of OCP covered a stoichiometric HAP crystal, the Ca/P ratio would be about 1.64.25 From a more detailed analysis of the experimental data,38 a typical biological apatite is formed by the initial precipitation of OCP, which hydrolyzes to an intermediate phase termed octacalcium phosphate hydrolyzate (OCPH). This phase was thought to be made up of layers of both OCP- and HAP-like structures and included impurity ions and ion vacancies. In support of this model, TEM studies of hydrolyzed OCP crystals indicate the intergrowth of both HAP and OCP crystallites, together with a mixture of both phases,78 which could very well be described in terms of an OCPH phase. Furthermore, crystal defects and impurity ions would be maintained in the apatitic structure, since the hydrolysis to the thermodynamically most stable phase is irreversible.79 Daculsi et al.80,81 compared the dissolution behavior of biological and synthetic apatites containing the central defects in the core. In all cases, dissolution occurred both at the crystal core and at the surface, with the biological apatite showing preferential core dissolution. Although this may be due to the presence of OCP in the crystal core, it could also be attributed to impurities such as carbonate in the biological apatite, with preferential dissolution of carbonated apatite.

Although many studies have favored the hypothesis that OCP is involved as an in vivo precursor during apatite formation, there appears to be no real evidence for the presence of this phase in nonpathological mineralization. At one stage, it was suggested that DCPD was formed in the early stages of development of embryonic bones in chicken,82 but this finding has since been disputed.3 There is little doubt, however, that OCP occurs as an initial phase in pathological deposits, such as calculus and kidney stones. At lower pH, DCPD may also be involved as a precursor phase, either in place of or together with OCP. Moreover, certain calcium positions in DCPD and HAP are closely aligned, opening the possibility of epitaxial intergrowth and transformation of DCPD to HAP, which has also been demonstrated using constant composition kinetics methods.83 The results of a typical experiment demonstrated the nucleation and growth of HAP at DCPD surfaces in these solutions that were supersaturated in HAP and saturated with respect to DCPD. In situ AFM studies of dissolution kinetics of the (010) face of DCPD and the transformation of DCPD to HAP showed that the precipitation of HAP occurred after the dissolution of DCPD, and no evidence of direct structural transformation from DCPD to HAP was observed. This indicates that DCPD acts as a heterogeneous growth center for HAP without requiring any structural modification.84

The Ca/P ratio of precipitated calcium-deficient apatite gradually increases with the age of the precipitate, probably due to in situ transformation.82 In general, the sequence of calcium phosphate precipitation has been observed by the relative solubility of the different solid phases at constant pH and temperature. Thus, van Kenemade and de Bruyn85 showed that the Ostwald rule86 was obeyed, regardless of solution conditions under which the relaxation experiments were made. Homogenous formation of HAP at low supersaturation was never observed but was always preceded by the growth of precursors. At pH 6.7, OCP was observed to form at intermediate supersaturation, largely due to the exclusion of other phases. The growth curves and relaxation times obtained under these conditions were analyzed in terms of classic nucleation and growth theories. The kinetics of formation of OCP was best described by a flashlike nucleation step in combination with surface nucleation and growth based on a mononuclear growth model. At intermediate supersaturations, the surfaces of the grown crystalline particles could be regarded as being relatively smooth, with growth proceeding by a layer mechanism, requiring the formation of a surface nucleus.85

In attempting to explain the preferential precipitation of one crystalline phase when compared with another, it can be argued that a lower interfacial tension or edge free energy is to be expected for a more soluble phase.87 This could result in a lower free energy for two-dimensional nucleation, in spite of the lower supersaturation. It is quite clear that the Ostwald rule of stages, which states that the least stable, most soluble phase forms preferentially in a sequential precipitation, is likely to be obeyed for the calcium phosphates. However, in these cases, the sequence is also influenced by another important parameter, pH. It would appear, therefore, that where the driving force for HAP is relatively high, at about pH 10, the participation of more acidic phases, such as DCPD and OCP, can be ruled out. It is interesting to note that a recent constant composition study of defect apatite crystal growth also pointed to stoichiometries approaching the HAP value at high pH.88 Stability and Transformation of ACP in the Presence of Macromolecules

The Ca9(PO4)6 cluster is an interesting HAP growth unit, and whether its structure is S6 or C3, it can be regarded as being essentially identical to the structure known as Posner’s cluster.9,11 These represent the minimum structural unit of ACP based on the results of small-angle X-ray scattering measurements. If the same structure is a constituent of HAP, it will provide important clues about the ACP–HAP phase transition mechanism by so-called solution-mediated transitions: one phase dissolves and then acts as a seed for the formation of a different phase, directing subsequent structural transformations by rearranging its internal structure. As yet, no conclusive evidence has been presented about the ACP–HAP phase transition. However, when the common aspects of growth units are considered, the phase transition mechanism is highly likely to involve a direct structural transformation.89 To analyze the phase transition process, it is necessary to track with high time resolution how the molecular weight, size, and internal structure of aggregates (formed by clusters) change. The most suitable method is static light scattering (SLS).89 By investigating how the intensity of light scattered from aggregates in a solution varies with the scattering angle (scattering vector), the mean molecular weight, Mw, and inertial radius, Rg, can be derived using eq 2.389


where ΔR(q) is the solution Rayleigh ratio, c is the concentration of the material being measured, and A2 is the second virial material coefficient.

When the Ca9(PO4)6 cluster size exceeds a certain threshold value, it becomes possible to define a fractal dimension, d, that represents the degree of coarseness of the internal structure of the aggregate, enabling semiquantitative verification of whether it is random or regular.89 By combining a high-speed CCD camera with an ellipsoidal mirror that encompasses a wide range of scattering angles, Onuma et al. have developed an SLS device to simultaneously measure the scattered light over scattering angles of 10°–170° with a time resolution of 0.1 s.90Figure 3 shows the results of using this new SLS device to determine how the molecular weight and gyration radius of the aggregates change over time in a simple CaCl2–H3PO4–H2O system under near-physiological pH, temperature, and concentration. XRD showed that ACP aggregates were present in the initial solution and the final product was low-crystalline HAP.90

Figure 3

Time-resolved SLS measurements for the transition from ACP to HAP. (a) Change in apparent molecular weight and gyration radius of aggregates. (b) Change in fractal dimension of aggregates. The molecular weight and the fractal dimension of the aggregates...

The molecular weight of the aggregates abruptly increased about 20 min following the start of the measurement and reached a plateau at about 40 min. Immediately thereafter, the formation of HAP deposits became visible.89 The change in the gyration radius of the aggregates exhibited a completely different pattern. The radius remained almost constant, increasing only slightly following the time when HAP had started to form and accumulate.89 As shown in Figure 3b, the fractal dimension changed in concert with the molecular weight—a sharp increase at about 20 min following the start of the measurement. As mentioned above, the fractal dimension represents the degree of coarseness and regularity of the internal structure of aggregates. Considering that the initial aggregates in the solution were ACP and that the finally deposited product was HAP, since the initial aggregates of ACP had a very loose structure, they grew by assimilating growth units (calcium phosphate “Posner’s” clusters Ca9(PO4)6,) as time progressed.89 The internal density of the aggregates increased during this process, and the molecular weight increased while the gyration radius stayed almost the same. When the density reached a critical value, the random arrangement of growth units became disadvantageous in terms of total free energy, resulting in a sudden ordering of the structure, which was then deposited as HAP with a rapid increase in the fractal dimension, and the phase transition proceeded by a process of direct structural transformation.89 With the increase in the number of particles in the aggregate, the internal structure changed to close packed to reduce the total free energy of the aggregate. Thus, (1) ACP directly transforms to HAP by rearrangement of each molecule, and (2) the internal bonds of ACP are partially broken (partial fusion) with the immediate formation of HAP.88 Both cases indicate that ACP has a structural resemblance to HAP and strongly support previous conclusions that the growth unit of HAP is Posner’s cluster, Ca9(PO4)6, since this cluster is also thought to be a component of ACP.10 This phenomenon occurred because the ACP growth units and HAP growth units were “identical”. If the growth units of both materials were different, the aggregates would have dissociated and re-formed by overcoming a very large energy barrier during the phase transition process.89

In nucleation studies on foreign substrates, the phase transition process was influenced by the additive molecules that were present. AFM observations showed that the nucleation of HAP on collagen was greatly enhanced when phosvitin was bound to the collagen surface.91 The nucleated crystals were rapidly and uniformly distributed on the collagen surface in the presence of phosvitin, while, in the absence of phosvitin, the crystals nucleated slowly and were observed only on specific areas.91 Time-resolved static light scattering measurements revealed that the transformation from ACP to HAP was inhibited when phosvitin was present in the calcium phosphate solutions.91 Soluble matrix proteins isolated from Lingula shells specifically promote FAP crystallization by the destabilization of ACP precursor.92 Interestingly, the ability of Lingula shell macromolecules to promote FAP crystallization showed a nonlinear bell-shaped dependence on protein concentration with a maximum effect at about 0.5 μg mL−1.92 The main factor influencing this behavior was a reduction in the time associated with the ACP to FAP transformation, which also showed a nonlinear dependence on protein concentration.92 The above results indicate that soluble macromolecules associated with the phosphatic shell of L. anatina can specifically promote the in vitro crystallization of FAP. This behavior is unusual and contrary to numerous previous studies in which a wide range of low- and high-molecular-weight additives have been shown to inhibit calcium-phosphate crystallization by stabilization of a hydrated ACP precursor.9396 A possible mechanism for in vitro promotion was postulated.92 In general, transformation of ACP involves the formation of crystalline nuclei on the surface of the precursor in association with a solution-mediated process and dissolution of the amorphous phase.97 Protons are released in the nucleation step but consumed during ACP dissolution, and this process gives rise to a transient steady state. Strong adsorption of additives such as polyaspartate onto the surface of primary ACP nanoparticles reduces their surface charge readily in a reduction of the rate of dissolution of the amorphous phase due to colloidal aggregation.92 Moreover, the adsorbed macromolecules block the surface nucleation sites for FAP crystallization. In contrast, addition of the Lingula shell proteins at low concentration appears to destabilize the ACP particles. One possibility is that the surface charge on the primary nanoparticles is increased at low levels of protein adsorption such that the extent of secondary aggregation is reduced and the rate of dissolution increased. Surface attachment of the Lingula proteins might also induce local ordering of FAP nuclei on the amorphous surface by facilitating structural relaxation through changes in surface dehydration and deprotonation.92 Finally, the adsorbed macromolecules could act as templates for FAP nucleation by inducing the clustering of aqueous ions at the ACP surface. This would occur for example if the proteins were anchored at low surface coverage such that appropriate functional groups remained exposed at the solution interface rather than being buried by strong surface–macromolecule interactions associated with higher binding capacities. Indeed, it seems feasible that such conformational changes are responsible for the observed nonlinear dependence of FAP promotion on protein concentration.92

Both full-length recombinant DMP1 and post-translationally modified native DMP1 were able to nucleate HAP in the presence of type I collagen. However, the N-terminal domain of DMP1 (amino acid residues 1-334) inhibited HAP formation and stabilized the ACP phase that was formed. During the nucleation and growth process, the initially formed metastable ACP phase transformed into thermodynamically stable crystalline HAP in a precisely controlled manner.98 Experiments were performed in the presence and absence of albumin (BSA) and fibrinogen (Fib) in solution as well as studying the effect of surface immobilized proteins on the biomineralization process; the results suggested that the major influence of these proteins on the CaP growth rate was their adsorption to the initially formed ACP, inhibiting the dissolution/reprecipitation of calcium phosphate. Hence, it was possible to distinguish between an amorphous layer and partly crystalline regions of different composition, possibly OCP and carbonated HAP.99

To facilitate understanding of the underlying mechanisms of calcium phosphate crystallization, Füredi-Milhofer et al. discussed the influence of polyelectrolytes (PEs) including polystyrene sulfonate (PSS), poly-L-lysine (PLL), and poly-L-glutamic acid (PGA) on the formation and properties of ACP and on the nucleation and growth morphology of the crystalline phase. pH vs time curves revealed three distinct precipitation events: (1) precipitation of ACP, (2) secondary precipitation of a crystalline phase upon the amorphous precursor, and (3) solution-mediated phase transformation and crystal growth. Finally, crystalline mixtures with low Ca/P molar ratios (1.39), consisting of octacalcium phosphate crystals and small amounts of apatite, were obtained.100 The dual role of the PEs in inducing and/or inhibiting crystal nucleation in the ACP–apatite transformation system was established as follows: at low concentrations, the PE molecules adsorb reversibly on the surfaces of ACP particles in a random conformation. As a consequence, a large number of small, highly charged particles are created, which concentrate oppositely charged Ca2+ or HPO42− ions and thus provide effective sites for secondary nucleation; at high concentrations, the flexible PE chains spread out into a flat position at the surface of ACP particles. This type of adsorption process is most probably irreversible and inhibits the transport of ions to the template surface, thus inhibiting secondary nucleation.100 Moreover, Peytcheva et al. used SAXS/WAXS to study calcium phosphate crystallization in the presence of polyaspartate and found that high supersaturation leads to the immediate formation of a polymer-stabilized ACP phase with globular shape and a radius of about 100 nm.101 Following this stage, a very slow recrystallization takes place and most of the new nuclei are bound to the previous polymer–ACP mixtures. Finally, a “hollow snowball” structure is formed, composed of single crystal platelets.101

Recently, Onuma et al. have studied the growth and phase transition mechanisms of HAP and its interaction with a growth factor protein in a simulated physiological environment.89 Using AFM and real-time phase shift interferometry, they performed in situ observations of growth in simulated human body fluid solutions seeded with millimetersized HAP single crystals produced by hydrothermal synthesis, and the normal growth rate was measured.89 The step kinetic coefficient (derived from the velocity of growth steps) and the edge free energy (calculated from the variation in the normal growth rate with the degree of supersaturation) both deviated greatly from the standard values for typical inorganic salt crystals and were found to be close to those of protein crystals.89 This suggests that the growth units of HAP crystals are clusters rather than simple ions and that growth proceeds through the accumulation of these clusters.89 Observations using dynamic light scattering confirmed the presence of clusters with a diameter of about 0.8–1.0 nm in simulated body fluids. Ab initio analysis of the cluster energy stability indicated that calcium phosphate clusters based on Ca3(PO4)2 units achieve an energy minimum for clusters of the form [Ca3(PO4)2]3. These clusters have S6 symmetry, and, when they are used to build a HAP crystal, their structure is likely to become slightly modified, resulting in the formation of C3 structures.89 Since these clusters would also be the building blocks of ACP, they provide vital clues to the phase transition from ACP to HAP. Using time-resolved static light scattering, the ACP–HAP phase transition process was tracked and the degree of coarseness inside a cluster aggregate changed abruptly within a specific time interval, and HAP was formed and deposited in the final stages. This suggests that an ACP aggregate transforms into HAP as its internal structure becomes regularized.89

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