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

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Calcium orthophosphates: crystallization and dissolution.

The basal slip systems of biotite and their mechanical expressions have been investigated by shortening single crystals oriented to maximize and minimize shear stresses on (001). Samples loaded at 45° to (001) exhibit gentle external rotations associated with dislocation glide. High-angle kink bands in these samples, unlike those developed in micas loaded parallel to (001), are limited to sample corners. Samples shortened perpendicular to (001) show no evidence of nonbasal slip and fail by fracture over all conditions tested. The mechanical response of biotite shortened at 45° to (001) is nearly perfectly elastic-plastic; stress-strain curves are characterized by a steep elastic slope, a sharply defined yield point, and continued deformation at low (mostly 1%. Stresses measured beyond the yield point are insensitive to confining pressure over the range 200 to 500 MPa and exhibit weak dependencies upon strain rate and temperature. Assuming an exponential relationship between differential stress σd and strain rate e˙ of the form e˙=Cexp(ασd)exp(−Q/RT), the data collected over strain rates and temperatures of 10−7 to 10−4 s−1 and 20° to 400°C, respectively, are best fit by an exponential constant α of 0.41±0.08 MPa-1 and an activation energy Q of 82±13 kJ/mol. A power law fits the data equally well with n = 18±4 and Q = 51±9 kJ/mol. Samples oriented favorably for slip in directions [100] and [110] are measurably weaker than those shortened at 45° to [010] and [310], consistent with the reported Burgers vectors 〈100〉, 1/2 〈110〉, and 1/2 〈110〉. The anisotropy of biotite is further revealed by contrasting these plastic strengths with results of samples deformed parallel and perpendicular to (001). Previous studies have shown that biotite loaded in the (001) plane is strong prior to the nucleation of kink bands. The strength of biotite shortened perpendicular to (001) exceeds that measured parallel to (001) and is pressure dependent. Application of the results to deformation within the continental crust suggests that biotite oriented favorably for slip is much weaker than most other silicates over a wide range of geologic conditions. Its presence within foliated rocks and shear zones may limit locally the stresses that can be supported.

Basal slip and mechanical anisotropy of biotite

Step dynamics and spiral growth on calcite

The magnetization of some rare-earth orthoferrites and related compounds, and of some iron-group cyanides, has been investigated at temperatures between room temperature and 1.3\ifmmode^\circ\else\textdegree\fi{}K. Some are ferromagnetic, some antiferromagnetic, and some paramagnetic following the Curie-Weiss law.The compounds GdV${\mathrm{O}}_{3}$, GdFe${\mathrm{O}}_{3}$, and ErFe${\mathrm{O}}_{3}$ are apparently antiferromagnetic with N\'eel points of 7.5\ifmmode^\circ\else\textdegree\fi{}, 2.5\ifmmode^\circ\else\textdegree\fi{}, and 4.5\ifmmode^\circ\else\textdegree\fi{}K, respectively. Ordering of the Gd and Er ions at low temperatures is indicated. The compounds NdFe${\mathrm{O}}_{3}$, SmFe${\mathrm{O}}_{3}$, YFe${\mathrm{O}}_{3}$, NdV${\mathrm{O}}_{3}$, PrV${\mathrm{O}}_{3}$, and SmV${\mathrm{O}}_{3}$ show a rapid rise in ferromagnetic moment as the temperature is lowered below about 15\ifmmode^\circ\else\textdegree\fi{}K. GdTi${\mathrm{O}}_{3}$ is ferromagnetic with 0.54 Bohr magneton per molecule.Many of the cyanides of type $A(B{\mathrm{C}}_{6}{\mathrm{N}}_{6})$ are ferromagnetic with magnetic moments of 1 to 4 Bohr magnetons per molecule and Curie points of 3 to 50\ifmmode^\circ\else\textdegree\fi{}K.A null method of measurement is used. Movement of a pendulum in a field gradient is detected with strain gauges and balanced with a coil. In the space containing the specimen and the balancing coil the gradient varies linearly with distance.

Magnetic Properties of Some Orthoferrites and Cyanides at Low Temperatures

The theory of the growth of perfect crystals deriving from Gibbs and Volmer, shows that new crystal layers cannot be nucleated at an appreciable rate at low supersaturation. The essential truth of this theory is confirmed by the growth of crystals in polyhedra, which would otherwise be incomprehensible. But on this theory, by itself, the growth rate of such crystals would be virtually zero. This is not usually the case (though the necessary conditions have apparently been realized in Hawards experiments). The discrepancy is removed by considering that a real crystal contains dislocations and may therefore consist of only one layer of atoms perpetually overlapping itself. Such a crystal can grow to an unlimited size without any nucleation of new layers. The rate of growth of such a crystal can be calculated; it is proportional to the square of the supersaturation for low values and to the first power of the supersaturation for higher values in satisfactory quantitative agreement with the experimental results of Volmer and Schultze. The theory indicates that an almost flat crystal surface will show spiral growth steps, ending on dislocations. These are observed in many different cristals, confirming that this mode of growth is very common. Finally, some discussion is given to the way in which dislocations are produced in the growth process.

Crystal growth and dislocations

The theory of crystal growth based on dislocation theory as formulated by F. C. Frank1 predicts the presence of growth features in the form of very flat, spirally terraced hills on the crystal face which is perpendicular to a screw dislocation line. Microscopic spirals often appear on the surfaces of solids grown slowly from solution. In 1949, F. C. Frank proposed an explanation, suggesting that crystal growth could lead to screw dislocations — linear defects oriented normally to the growing surface and forming the core of a lattice structure locally akin to a spiral staircase. In Nature, four years later, Ajit Ram Verma and S. Amelinckx offered experimental support for the idea. Photos of a solid forming on a surface revealed a growth front spiralling outward around a central point. Measurements confirmed the height of the growing layer as a single unit cell.

Spiral Growth on Carborundum Crystal Faces

DIRECT evidence for the existence of dislocations has so far been confined to known examples of spiral growth: beryl1, an n-paraffin2, silicon carbide3,4 and cadmium iodide5. We have now experimental evidence for the existence of screw dislocations in mica (muscovite).

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Screw Dislocations in Mica

GROWTH spirals, as predicted by F. C. Frank's theory1 on crystal growth, have been observed on the c (0001) faces of carborundum by Ajit Ram Verma2 and by S. Amelinckx3. The steps between successive turns, as stated by Frank, are exactly one unit cell high. This seems, in fact, to be true in many cases, although of several unit cells high are not exceptions.

Growth Mechanism of Carborundum Crystals

RECENTLY, observations of the growth spirals suggested by Frank's theory1 have been reported on crystals of beryl2, n-paraffin3, silicon carbide4, cadmium iodide5 and gold6; for mica7 experimental evidence has been put forward to support the hypothesis that here, too, the same mechanism is responsible for the growth of the crystals.

Spiral Growth Patterns on Apatite Crystals

THE observation of growth spirals, as predicted by the theory of Burton, Cabrera and Frank1, on prism faces (10&1bar;0) of apatite crystals, has been reported earlier2. We have now observed completely differently shaped growth spiral patterns on tabular colourless apatite crystals from Sulzbachtal (Austria), which have probably grown from solution. The accompanying photograph (Fig. 1) shows one of the observed patterns. The direction of the c-axis is vertical. The shape and orientation of the spiral are the same in all cases. The dominating system consists of two co-operating spirals, which dominate several other dislocations of equal and of different strengths. In the latter case the formation of residual steps is noticed. Interlacing occurs in one direction. The main growth-fronts have a step-height of 140 ±.20 A.

S. Amelinckx

Papers

Spiral Growth on Carborundum Crystal Faces

Screw Dislocations in Mica

Growth Mechanism of Carborundum Crystals

Spiral Growth Patterns on Apatite Crystals

Growth Spirals and their Relation to Crystal Habit as Illustrated by Apatite