Calcium orthophosphates are the main mineral constituents of bones and teeth, and there is great interest in understanding the physical mechanisms that underlie their growth, dissolution, and phase stability. By definition, all calcium orthophosphates consist of three major chemical elements: calcium (oxidation state +2), phosphorus (oxidation state +5), and oxygen (oxidation state −2).1 The orthophosphate group (PO43−) is structurally different from meta (PO3−), pyro (P2O74−), and poly (PO3)nn−. In this review, only calcium orthophosphates will be discussed. The chemical composition of many calcium orthophosphates includes hydrogen, either as an acidic orthophosphate anion such as HPO42− or H2PO4−, and/or incorporated water as in dicalcium phosphate dihydrate (CaHPO4 · 2H2O).1 Most calcium orthophosphates are sparingly soluble in water, but all dissolve in acids; the calcium to phosphate molar ratios (Ca/P) and the solubilities are important parameters to distinguish between the phases (Table 1) with crystallographic data summarized in Table 2. In general, the lower the Ca/P ratio, the more acidic and soluble the calcium phosphate phase.2 It is now generally recognized that the crystallization of many calcium phosphates involves the formation of metastable precursor phases that subsequently dissolve as the precipitation reactions proceed. Thus, complex intermediate phases can participate in the crystallization process. Moreover, the in vivo presence of small peptides, proteins, and inorganic additives other than calcium and phosphate has a considerable influence on crystallization, making it difficult to predict the possible phases that may form.3 Studies of apatite mineral formation are complicated by the possibility of forming several calcium phosphate phases. The least soluble, hydroxyapatite (HAP), is preferentially formed under neutral or basic conditions. In more acidic solutions, phases such as brushite (DCPD) and octacalcium phosphate (OCP) are often encountered. Even under ideal HAP precipitation conditions, the precipitates are generally nonstoichiometric, suggesting the formation of calcium-deficient apatites. Both DCPD and OCP have been implicated as possible precursors to the formation of apatite. This may occur by the initial precipitation of DCPD and/or OCP followed by transformation to a more apatitic phase. Although DCPD and OCP are often detected during in vitro crystallization, in vivo studies of bone formation rarely show the presence of these acidic calcium phosphate phases. In the latter case, the situation is more complicated, since a large number of ions and molecules are present that can be incorporated into the crystal lattice or adsorbed at the crystallite surfaces. In biological apatite, DCPD and OCP are usually detected only during pathological calcification, where the pH is often relatively low. In normal in vivo calcifications, these phases have not been found, suggesting the involvement of other precursors or the formation of an initial amorphous calcium phosphate phase (ACP) followed by transformation to apatite.



Table 1

Ca/P Molar Ratios, Chemical Formulas, and Solubilitiesa of Some Calcium Orthophosphate Minerals1,3,4





Table 2

Crystallographic Data of Calcium Orthophosphates1,4,5



In this review, we will discuss some important parameters related to crystal nucleation and growth/dissolution including the supersaturation/undersaturation, pH, ionic strength and the ratio of calcium to phosphate activities (Table 3). We then focus on the dynamics of crystallization/dissolution in the presence of additive molecules pertinent to biogenic calcium phosphate minerals.



Table 3

Crystal Growth Controls and Their Effect on the Bulk Solution and the Crystal Surfaces6




2. Biologically Related Calcium Phosphate Phases
2.1. Structure, Composition, and Phase Stability


2.1.1. Amorphous Calcium Phosphate (ACP) 
During the synthesis of HAP crystals through the interaction of calcium and phosphate ions in neutral to basic solution, a precursor amorphous phase is formed that is structurally and chemically distinct from HAP.7 However, calculations have shown that the phase consisted of individual or groups of HAP unit cells.8 Chemical analysis of the precursor phase indicated this noncrystalline phase to be a hydrated calcium phosphate (Ca3(PO4)2 · xH2O) with a Ca/P ratio 1.50,8 consisting of roughly spherical Ca9(PO4)6 “Posner’s clusters” (PC) close-packed to form larger spherical particles with water in the interstices.9 PCs appeared to be energetically favored in comparison to alternative candidates including Ca3(PO4)2 and Ca6(PO4)4 clusters.10 The structure of PCs in isolated form is notably different from that in a HAP environment.11 In particular, the chirality feature of PCs found in the HAP environment is suggested to disappear in an isolated form and in aqueous solution. The reconsideration of PCs as possible components in the actual structural model of ACP resulted from the cluster growth model of the HAP crystal.12 Ab initio calculations confirmed that stable isomers exist on the [Ca3(PO4)2]3 potential energy surface (PES).12,13 These isomers correspond to compact arrangements, i.e., arrangements in which the Ca and PO4 are disposed closely together. Their geometries are compatible with the terms “roughly spherical” used in Posner’s hypothesis. The calculations performed on the monomer and dimer PES revealed that the relative energies of the different isomers are governed by a specific bonding pattern in which a calcium atom interacts with two PO43− groups, forming four CaO bonds.12,13 The compact isomers on the trimer PES are energetically favored in comparison to monomer or dimer isomers. This is rationalized by the appearance of a specific bonding pattern for the trimer case in which a calcium forms six CaO bonds with six different PO4 groups. This type of bonding in encountered in HAP.13

It is now generally agreed that, both in vitro and in vivo, precipitation reactions at sufficiently high supersaturation and pH result in the initial formation of an amorphous calcium phosphate with a molar calcium/phosphate ratio of about 1.18–2.50. The chemical composition of ACP is strongly dependent on the solution pH: ACP phases with Ca/P ratios in the range of 1.18:1 precipitated at pH 6.6 to 1.53:1 at pH 11.7 and even as high as 2.5:1.4 Two amorphous calcium phosphates, ACP1 and ACP2, have been reported with the same composition, but differing in morphology and solubility.14,15 The formation of ACP precipitate with little long-range order tends to consist of aggregates of primary nuclei (roughly spherical clusters) with composition Ca9(PO4)65 dependent on the conditions of formation. It hydrolyzes almost instantaneously to more stable phases. These amorphous clusters served as seeds during HAP crystallization via a stepwise assembly process12 and were presumed to pack randomly with respect to each other,16 forming large 300–800 A spheres. Recent experimental studies found that ACP has definite local atomic microcrystalline order rather than a random network structure. NMR of thoroughly dried ACP suggests that the tightly held water resides in the interstices between clusters,17 but these are probably not of intrinsic importance in the structure of ACP. It is well-known that ACP contains 10–20% by weight of tightly bound water, which is removed by vacuum drying at elevated temperature.9 However, drying does not alter the calcium and phosphorus atomic arrangement. The side band intensities of dried ACP suggest that its chemical shift anisotropy is similar to or identical with that of normal ACP.17 ACP has an apatitic short-range structure, but with a crystal size so small that it appears to be amorphous by X-ray analysis. This is supported by extended X-ray absorption fine structure (EXAFS) on biogenic and synthetic ACP samples.18–20

The CaP amorphous phase transforms to HAP microcrystalline in the presence of water. The lifetime of the metastable amorphous precursor in aqueous solution was reported to be a function of the presence of additive molecules and ions, pH, ionic strength, and temperature.21 The transformation kinetics from ACP to HAP, which can be described by a ”first-order” rate law, is a function only of the pH of the mediating solution at constant temperature. The solution-mediated transformation depends upon the conditions which regulate both the dissolution of ACP and the formation of the early HAP nuclei.22 Tropp et al. used 31P NMR to demonstrate that the strength of ACP side bands is due to a characteristic structural distortion of unprotonated phosphate and not to a mixture of protonated and unprotonated phosphates,17 suggesting that ACP could contain substantial amounts of protonated phosphate not in the form of any known phase of calcium phosphate crystals. Yin and Stott suggested that, in the transformation from ACP to HAP, ACP need only dissociate into clusters rather than undergo complete ionic solvation. The cluster with C1 symmetry is the most stable isomer in vacuum. The interaction of Posner’s cluster with sodium ions and especially with protons leads to a considerable stability increase, and surprisingly, the cluster with six protons and six OH− recovers the C3 symmetry and similar atomic arrangement that it has as a structural unit in the HAP crystal. This may be a key factor in the transformation from ACP to HAP crystal.23

In general, ACP is a highly unstable phase that hydrolyzes almost instantaneously to more stable phases. In the presence of other ions and macromolecules or under in vivo conditions, ACP may persist for appreciable periods3 and retain the amporphous state under some specific experimental conditions.24

/pdf/calcium-orthophosphates-crystallization-and-dissolution-1c1riyx5dd.pdf

Calcium orthophosphates: crystallization and dissolution.

-- Part C: 1. The continuum approach to crystal interfaces: basics. I: Theoretical framework. 2. Operators for orientation-dependent parameters. 3. Mechanics and thermodynamics of interfaces. 4. Equilibrium structures of junctions, edges and vertices. 5. Growth: kinematic wave theory revisited. 6. Kinetic behaviour of junctions, edges and vertices. 7. Structural phase transitions of a crystal surface as a branch of soliton physics. 8. Miscellaneous topics. II: Growth rate functions. 9. Analytic representations of R(n,A) functions. 10. Nonlinear networks and the 'assembled function' notation. 11. Physical aspects of assembling operations. 12. The systematic construction of R(n,A) functions by a sequence of assembling steps. 13. Notes on sphere-growth experiments. 14. Summary: Conclusions and outstanding questions. References. List of symbols, abbreviations and notations.

Morphology of crystals

This paper briefly reviews hydrothermal synthesis of ceramic powders and shows how understanding the underlying physico-chemical processes occurring in the aqueous solution can be used for engineering hydrothermal crystallization processes Our overview covers the current status of hydrothermal technology for inorganic powders with respect to types of materials prepared, ability to control the process, and use in commercial manufacturing General discussion is supported with specific examples derived from our own research (hydroxyapatite, PZT, 􀄮-Al2O3, ZnO, carbon nanotubes) Hydrothermal crystallization processes afford excellent control of morphology (eg, spherical, cubic, fibrous, and plate-like) size (from a couple of nanometers to tens of microns), and degree of agglomeration These characteristics can be controlled in wide ranges using thermodynamic variables, such as reaction temperature, types and concentrations of the reactants, in addition to non-thermodynamic (kinetic) variables, such as stirring speed Moreover, the chemical composition of the powders can be easily controlled from the perspective of stoichiometry and formation of solid solutions Finally, hydrothermal technology affords the ability to achieve cost effective scale-up and commercial production

http://www.sawyerllc.com/images/content/hydrothermal_scp.pdf

Hydrothermal Synthesis of Advanced Ceramic Powders

Thermodynamics of magnesian calcite solid-solutions at 25°C and 1 atm total pressure

An optical interferometry system has been used to study the dynamics of the dissolution of anorthite (010) cleavage surfaces. With this technique, it is possible to measure directly the surface retreat of alumino-silicates as a function of time and thereby the dissolution rate using a new application of interferometry. The dissolution experiments are carried out in a flow-through cell system with a near endmember anorthite (An{sub 98}) from Miyake-Jima, Tokyo, Japan, Perchloric acid solutions (pH 3) were used at a constant temperature of 25 C. After having measured the topography of the original pristine anorthite surface, measurements of the surface normal retreat were taken after 48,84,120, and 168 hrs of run duration at 15 different regions on the surface. An internal-reference technique allows absolute measurements of the changes in surface height for the very first time. From these measurements, an average bulk rate for dissolution of the (010) anorthite surface is calculated to be 5.7 x 10{sup {minus}13} [moles/cm{sub 2}/sec]. Finally, their directly determined bulk rate for the (010) face is compared with the bulk rates calculated from the rate law obtained from powder experiments and using the BET or total surface area.

An interferometric study of the dissolution kinetics of anorthite; the role of reactive surface area

Activities of spiral growth hillocks on the (111) faces of barium nitrate crystals growing in an aqueous solution

Growth and perfection of crystals from aqueous solution: Case studies on barium nitrate and K-alum

Growth induced lattice defects in Ba(NO3)2 crystals

Observation of screw and mixed dislocations in barium nitrate crystals by means of birefringence and x-ray topography

The expressions for the intensity distribution in birefringence images and computer‐simulated images of a straight, pure screw dislocation with Burgers vector a[111] viewed end‐on in cubic crystals have been obtained for the first time by considering the anisotropy of both elastic and photoelastic properties of the material. The effect of elastic and photoelastic anisotropy on birefringence images of screw dislocation viewed end‐on has been discussed. And the computer‐simulated images have been compared with the experimental images observed in Ba(NO3)2 crystals grown from aqueous solution.

K. Maiwa

Papers

Activities of spiral growth hillocks on the (111) faces of barium nitrate crystals growing in an aqueous solution

Growth and perfection of crystals from aqueous solution: Case studies on barium nitrate and K-alum

Growth induced lattice defects in Ba(NO3)2 crystals

Observation of screw and mixed dislocations in barium nitrate crystals by means of birefringence and x-ray topography

Birefringence images of screw dislocations viewed end‐on in cubic crystals