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10.1 Introduction

The crystallization of calcium phosphates has fascinated researchers for many decades, especially because of the role of apatites in the biomineralization of bone and teeth but also due to its relevance for geochemistry (Hughes and Rakovan 2015). There is an enormous body of work on calcium phosphates in the literature (Wang and Nancollas 2008; Dorozhkin 2009; Elliott 1994). Several calcium phosphates can be obtained from precipitation experiments, including hydroxyapatite (Ca10(PO4)6(OH)2, HAP), octacalcium phosphate (Ca8H2(PO4)6 · 5(H2O), OCP), brushite (CaHPO4 · 2(H2O)), and monetite (CaHPO4). Herein, we will mostly cover aspects related to the mechanisms of crystallization and almost exclusively focus on pathways leading to apatite formation.

Crystallization research has undergone a renaissance over the last decade or two. While attempts have been made to establish a unifying picture of inorganic crystallization processes based on the numerous recent findings (De Yoreo etal. 2015; De Yoreo et al. 2017, Chap. 1), many important fundamental questions remain unanswered, particularly in systems like the calcium phosphates. These questions pertain both to idealized laboratory conditions (Delgado-Lopez and Guagliardi 2017, Chap. 11) and to the formation of biogenic calcium phosphate minerals in vivo (Falini and Fermani 2017, Chap. 9). In the latter context, several new perspectives have emerged recently, including the idea that citrate ions constitute an integral part of nanoparticle aggregates in bone, forming organic bridges between minute inorganic crystals (Davies et al. 2014).

Hydroxyapatite (HAP) has an ideal composition of Ca10(PO4)6(OH)2. However, there is a wide range of possible substitutions; for example, carbonate ions can substitute on either the phosphate or hydroxide position (Fig. 10.1a), with the former occurring almost exclusively at low temperature and in biogenic apatites. HAP is typically hexagonal with disordered hydroxide ion orientations, as shown in Fig. 10.1a. The ordered monoclinic form is usually not observed in apatite obtained from syntheses giving nanocrystals.

Fig. 10.1
figure 1

(a) Hexagonal apatite crystal structure with disordered hydroxyl ion orientations. (b)pH dependence of the speciation of phosphate in aqueous solution

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In aqueous solution, phosphate speciation is strongly dependent on pH as shown in Fig. 10.1b. This means that the free phosphate concentration at pH values below about 9 is negligible. It should be recalled, however, that coordination to metal ions such as calcium changes the effective acidity constant and can strongly influence acid/base equilibria.

In the following, various aspects of calcium phosphate formation will be discussed, starting with a brief account of amorphous calcium phosphates (ACPs) and progressing via prenucleation phenomena to a presentation of recent results from our laboratory on the crystallization of HAP from ACP, to end with a recapitulation of current works on the importance of confinement for calcium phosphate crystallization.

10.2 Amorphous Calcium Phosphates

Amorphous calcium phosphate forms easily from aqueous solution, where it subsequently transforms into, e.g., HAP. There are several excellent reviews on this subject (Combes and Rey 2010; Dorozhkin 2010) and the present discussion will therefore be kept brief. Today it is clear that there are many ways to stabilize ACPs, for example, by the addition of organic additives or foreign ions such as carbonate or pyrophosphate. However, the “true” structure of ACPs is still a matter of debate. Posner and Betts used X-ray diffraction to derive a structural model for the basic building block of ACP in the form typically obtained under basic conditions (Posner and Betts 1975). Through pair-distribution function (PDF) analysis, they proposed that ACP is built from Ca9(PO4)6 clusters that are interspersed with water to form the larger spheroids observed experimentally in electron microscopy. These so-called Posner clusters have been central to most discussions about ACP and apatite crystallization ever since. Meanwhile it is known that there are several different structural forms of ACP (Combes and Rey 2010; Dorozhkin 2010), depending on the way in which they are prepared – much like in the case of calcium carbonate (Fernandez-Martinez et al. 2017, Chap. 4, this volume). It is also clear that while Posner clusters certainly explain part of the phenomena observed, they are not able to account for all features observed for ACPs. Thus there is an urgent need for improved models of the structure and composition of ACPs, especially because their importance as precursor species in HAP and biogenic apatite formation increases, as discussed below and elsewhere in this book (Delgado-Lopez and Guagliardi 2017, Chap. 11, this volume). Recent improvements in PDF analysis methods, including the ability to perform in situ experiments, promise deeper insights into the structure of ACPs (Tyrsted et al. 2014), especially when combined with advanced NMR (Davies et al. 2014) and TEM (Dey et al. 2010; Nudelman et al. 2010; Nielsen and De Yoreo 2017, Chap. 18) techniques.

10.3 Prenucleation Phenomena

At concentrations below saturation, ion pairs have been known to form for a long time (Berry et al. 2000). In 2008, however, it was suggested that somewhat larger clusters, termed prenucleation clusters, occur in the CaCO3 system (Gebauer et al. 2008; Gebauer et al. 2014). They have also been reported for silica (Tobler et al. 2017, Chap. 15) and iron oxyhydroxide (Reichel and Faivre 2017, Chap. 12 and Penn et al. 2017, Chap. 13) and some other systems (Gebauer et al. 2014). In solutions of zirconium acetate, from which zirconia forms upon heating, metastable polymeric states were observed (Bremholm et al. 2015) and have been shown to be directly involved in crystallization through a series of structural rearrangements (Tyrsted et al. 2014).

For calcium phosphates, there were early suggestions by Posner and Betts that such clusters should exist in solution, even though this was based exclusively on indirect evidence from their work on solid ACP (Posner and Betts 1975). Using light scattering and other techniques, Onuma and Ito (1998) detected calcium phosphate clusters in simulated body fluid (SBF) at pH 7.4, but also in acidified SBF solutions at pH 5.3, which are only supersaturated with respect to HAP but undersaturated with respect to octacalcium phosphate and ACP. These clusters were 0.7–1.1 nm in diameter, consistent with the size of Posner clusters. Moreover, the authors suggested a cluster aggregation model for crystal growth of HAP. More recently, Dey et al. (2010) used cryo-TEM to study the early stages of the formation of apatite from SBF at 37 °C at the surface of a Langmuir monolayer of arachidic acid in a “frozen-snapshot” manner, where selected stages of the growth process could be resolved by stabilizing them through vitrification. Clusters were observed in solution also in this study, as shown in Fig. 10.2a, b. Their sizes were consistent with those of Posner clusters, although their chemical composition again remained undetermined. Upon contact with the arachidic acid monolayer, the clusters accumulated at the interface forming fractal aggregates (Fig 10.2c, d), which condensed further over time (Fig. 10.2e, f) to form dense ACP globules (Fig. 10.2g, h), shown to be amorphous by electron diffraction (inset of Fig. 10.2g), that ultimately crystallized to yield HAP. It should be stressed that the identification of the observed nanometric species as Posner clusters is based mostly on size. Secondly, in both works cited above, the investigated solutions were supersaturated with respect to HAP. Thus these clusters are not necessarily prenucleation clusters per se (Gebauer et al. 2014), but rather they should be considered as strong indications that prenucleation phenomena are also at play in calcium phosphate systems.

Fig. 10.2
figure 2

Cryo-TEM studies of prenucleation clusters and the early stages of ACP formation from SBF solution in contact with a monolayer of arachidic acid. Panels a, c, e, and g are 2D projected TEM images with scale bars of 50 nm. Panels b, d, f, and h are corresponding 3D computer renderings of cryo-TEM tomograms with the monolayer shown in gray and the calcium phosphate in purple. The inset in panel g is a selected-area electron diffraction image showing that the particles are amorphous. Adapted and reprinted with permission from Macmillan Publishers Ltd: Nature Materials (Dey et al. 2010), copyright 2010

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In another recent study, Habraken et al. (2013) conducted experiments where TRIS buffer solutions of calcium and phosphate salts were mixed at an initial pH of 7.4 and a Ca:P molar ratio of 1.43. Subsequently, the authors followed the progress of the reaction by ion-selective electrodes and pH measurements. Based on the data, a model was proposed in which the initially formed clusters are assumed to be highly charged with the composition [Ca(HPO4)3]4−, while 57 % of these species are protonated ([Ca(HPO4)2(H2PO4)]3−) under the given conditions. With time, these charged complexes were suggested to take up a calcium ion, and the resulting clusters (i.e., [Ca2(HPO4)3]2−) would then form the basis of ACP by building up a fractal network. This speciation model has been criticized in particular due to the fact that it is based on ion association constants from the literature, which were obtained without accounting for cluster formation, and by the question of how such highly charged ion complexes would aggregate without an additional charge-compensating step (Gebauer et al. 2014). Again the work of Habraken et al. took place under supersaturated conditions with respect to all crystalline phases.

Thus there are strong – almost “smoking gun” – indications that prenucleation clusters may occur in the calcium phosphate system, but still complete and conclusive evidence in particular for undersaturated conditions is missing. In addition, most studies were performed at pH levels very close to 7.4, even though HAP is known to form much more readily at high pH. This choice has presumably been based on the use of SBF as a biologically relevant fluid. However, in actual body fluid, crystallization is suppressed by a range of mechanisms to avoid mineralization, and hence one is left to wonder how particularly biologically relevant these conditions are (see also below).

10.4 Crystallization of HAP

The formation of HAP crystals demands either a transformation from preformed ACP or the agglomeration/association of prenucleation clusters and/or ions. Which particular pathway is followed must depend on several factors, including concentration and pH (Delgado-Lopez and Guagliardi 2017, Chap. 11).

To understand the crystallization process, it is essential to be able to study it as it happens, i.e., using in situ techniques. The amorphous phase is supposed to have spherical morphology, whereas apatite crystals are strongly anisotropic in shape. From the hexagonal symmetry, a needlelike morphology can be expected, which is indeed observed in synthetic and geological apatites (Hughes and Rakovan 2015). In teeth, the crystals are needle-shaped, while in bone, they are predominantly nanoplates (Mann 2001; Weiner and Wagner 1998). However, it has been an open question at what point during crystal growth the anisotropic morphology is attained, i.e., when one transitions from a sphere to an anisotropic shape. This question is related to the crystal surface energy, and thus it is tightly connected to phase stability and its dependence on nanocrystal size (Jensen et al. 2010). One suitable technique for studying crystallization kinetics is to use synchrotron in situ X-ray diffraction. This allows quantifying how much crystalline material is formed over time, but it can also yield the lattice constants of the forming crystals and, by analysis of the diffraction peak widths, the nanocrystal shape. We have reported several such studies based on a custom-designed stopped-flow apparatus (Ibsen and Birkedal 2010; Ibsen and Birkedal 2012; Jensen et al. 2015; Ibsen et al. 2016a; Ibsen etal. 2016b). We mixed calcium- and phosphate-containing solutions to induce the formation of ACP under the desired temperature and pH conditions. The ACP phase was formed directly in the X-ray diffraction cell, thus allowing its crystallization to be monitored in situ with excellent time resolution. We precipitated ACP both with (Ibsen and Birkedal 2010; Ibsen and Birkedal 2012) and without additives (Ibsen etal. 2016a; Ibsen et al. 2016b); herein we shall only discuss the latter case. Apatite was obtained by the following reaction sequence:

$$ 10{\mathrm{CaCl}}_2+6{\mathrm{M}}_3{\mathrm{PO}}_4+x\mathrm{M}\mathrm{O}\mathrm{H}\to \mathrm{A}\mathrm{C}\mathrm{P}\to \mathrm{H}\mathrm{A}\mathrm{P} $$
(10.1)

where M+ is either Na+ or K+ and the initial calcium concentration was 0.2 M, with x equaling either 2 or 0 to correspond to stoichiometric HAP (x = 2) or HPO4 2−-dominated conditions.

Due to the extensive substitution chemistry of apatites, it is essential to carefully consider which counterions to use. With sodium as phosphate counterion, carbonate (from dissolved atmospheric CO2) can substitute into the apatite lattice, while with potassium this does not happen as evidenced by FTIR spectroscopy (Ibsen et al. 2016b). For x = 2 in reaction (1), the initial solution is dominated by phosphate, while with x = 0, HPO4 2− is the main phosphate species (cf. Fig. 10.1b). In the phosphate-dominated case, the crystals had a small aspect ratio at early stages, suggesting that the initial nuclei were close to spherical in shape. They then rapidly grew along the c-axis and only much slower in the (a,b) plane, resulting in anisotropic particles. The nanocrystal size and formation kinetics depended on the choice of the counterion, i.e., sodium or potassium (Ibsen et al. 2016b), with potassium yielding more slender and longer needles than sodium.

Under HPO4 2−-dominated conditions and with potassium as counterion, the observed crystallization behavior was very different than in the phosphate-dominated case discussed above. Figure 10.3 displays some of the kinetic data obtained at 60 °C, which we will discuss in some more detail here to illustrate the large degree of information that can be obtained by high-quality in situ diffraction methods (Ibsen et al. 2016a). The raw diffraction data show strong scattering signal of the aqueous solvent (Fig. 10.3a), but it was nevertheless possible to extract high-quality diffraction data by subtracting the solvent scattering (Fig. 10.3b). Initially, only the scattering signal of ACP was observed as two broad diffuse maxima at 2θ ≈ 12° and 18°. After a while, diffraction peaks from HAP appeared, while no other crystalline phases could be observed. The data were treated by Rietveld refinement. The Rietveld scale factor is a measure of the amount of crystalline material present. As seen in Fig. 10.3c, it increased rapidly to a plateau after a short induction time and remained constant thereafter, showing that the amount of crystalline material did not change after this nucleation burst. The nanocrystal size and composition, however, evolved over longer periods of time. In stark contrast to the phosphate-dominated situation, the initially detected nanocrystals were highly anisotropic, only ∼3.5 nm wide, and almost ten times longer, as shown in Fig. 10.3e, 10.3f. The shape aspect ratio decreased in two stages, a rapid initial drop followed by a slower decay (Fig. 10.3e). During the early stage of growth, the chemistry of the crystals changes drastically. Initially, they were found to be highly Ca deficient as shown in Figure 10.3d, where the Ca occupation in the HAP unit cell is plotted as a function of time. There is first a rapid increase in the average calcium content of the nanocrystals followed by a stage of slower Ca uptake.

Fig. 10.3
figure 3

In situ X-ray diffraction data on apatite nanocrystal formation under HPO4 2−-dominated conditions (for explanations see text). Adapted from (Ibsen et al. 2016a) with permission from the publisher

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This behavior is also reflected in the time evolution of the unit cell parameters shown in Fig. 10.3g and was interpreted as follows: the initial Ca deficiency is most likely charge-compensated by hydrogen phosphate resulting in compositions of the general formula Ca10-y (HPO4)2y (PO4)6-2y(OH)2. The initial highly anisotropic nanocrystals had a composition close to y = 3, i.e., with all phosphates being hydrogenated. At later stages of growth, y approached 1. In a simple model, we assumed that stoichiometric HAP was added to a fully hydrogenated initial nanocrystal; this allowed predicting the Ca occupancy with the nanocrystal volumes as obtained from their measured sizes (Fig. 10.3f). A nearly perfect match to the experimentally determined time evolution of the Ca occupancy was found (Ibsen et al. 2016a). The presence of HPO4 2− was confirmed by FTIR, an example of which is shown in Fig. 10.4. As expected with potassium as counterion, no carbonate peaks are observed, but a clear hydrogen phosphate resonance occurs at ca. 871 cm−1.

Fig. 10.4
figure 4

FTIR spectrum of HAP nanocrystals obtained under HPO4 2−-dominated conditions with potassium as counterion (Adapted from (Ibsen et al. 2016a) with permission from the publisher)

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The observations described above can be explained as follows. The initial nanocrystals had a composition very similar to that of octacalcium phosphate (OCP), which has a layered structure comprising HAP-like layers interspersed by water-containing sheets. However, the layer-stacking diffraction peak was not observed at any time, indicating that 3D-ordered OCP did not form, presumably due to the extremely low thickness of the nanocrystals formed within the ACP. These nascent crystals were then overgrown by near-stoichiometric HAP, resulting in an acidification of the surrounding ACP and solution (cf. Eq. (10.1)) that eventually stops growth.

OCP has long been suggested to be a precursor phase in biological apatite formation (Brown and Chow 1976), and more recent Raman spectroscopic studies of in vitro mineralization experiments point in the same direction (Crane et al. 2006). However, other evidence indicates that ACP is the relevant precursor material in biogenic crystallization, as first shown in chiton teeth (Lowenstam and Weiner 1985) and more recently in the youngest tissue of continuously forming special bones of zebrafish fin rays (Mahamid et al. 2010) as well as in more common bone (Mahamid et al. 2011). There has thus been a controversy about whether the initial phase is indeed ACP/OCP or ACP/nonstoichiometric apatite crystals (Weiner 2006; Grynpas 2007).

The in situ diffraction experiments described above seem to reconcile these different points of view. From the initial HPO4 2−-rich ACP, OCP-like crystals form which, however, do not have the 3D-stacking order found in OCP minerals. During the later stages of growth, the average composition of the crystals approaches that of nonstoichiometric apatites seen in biomineralization. It should be stressed that these experiments were performed at high pH and without the many additives used in biology, e.g., pyro- and higher polyphosphates (Omelon et al. 2013) or citrate (Hu et al. 2010; Davies et al. 2014) as well as biomacromolecules. A major outstanding issue in the field of biogenic crystallization remains in fact the value of pH under which initial minerals form within compartments like matrix vesicles. Such vesicles are widely present especially in endochondral ossification (Anderson et al. 2005) and in osteoblasts, where ACP has been shown to form within intracellular vesicles (Boonrungsiman et al. 2012). The use of vesicles in biomineralization should serve to dispel the notion that biogenic crystallization necessarily occurs at pH 7.4, as assumed by a large number of materials scientists.

The results discussed in this section clearly illustrate that HAP formation is strongly dependent on initial solution composition (e.g., counterions and the possibility of substitution chemistry) and, even more so, that the pH alters the speciation of phosphate and thus strongly affects its crystallization behavior.

10.5 Confinement Effects

It has become clear that the physical environment plays a key role in deciding how crystallization proceeds, as documented in particular for the case of biogenic apatite formation (Weiner and Wagner 1998; Mann 2001; Olszta et al. 2007; Gower 2008). Rajasekharan and Andersson, for example, have recently reported the formation of crystalline calcium phosphates from amorphous calcium phosphate within the pores of polymerized liquid crystals and found that the pore size of aqueous domains influenced the outcome of crystallization (Rajasekharan and Andersson 2015). Polymerized liquid crystals were obtained by using functionalized Pluronic F127 (EO100PO70EO100, where EO is ethylene oxide and PO is propylene oxide), which was crystallized into a hexagonal mesoporous material and then polymerized to yield covalently cross-linked mesoporous networks with excellent mechanical stability (He et al. 2015). These structures were infiltrated with acidic calcium and phosphate solutions at high concentrations. Subsequent exposure to ammonia gas triggered crystallization through a pH increase, leading to ACP formation in the pores of the mesoporous scaffold. With pore sizes below ∼10 nm, nanocrystalline HAP was obtained, while a mixture of acidic polymorphs (monetite and brushite) were formed at larger pore sizes (Rajasekharan and Andersson 2015). This method gave purely artificial materials reminiscent of bone (He et al. 2015). Interestingly, confinement can also stabilize ACP and influence the alignment and morphology of the resulting crystals, as shown by Cantaert et al. (2013) using anodized alumina membranes. Likewise, growth of calcium phosphates on patterned, carboxylate-functionalized substrates with gelatin as growth modifier results in ultrahigh aspect ratio nanocrystals oriented perpendicular to the substrate (Tseng et al. 2013). It has also been proven possible to form apatites as chemical gardens using metal-loaded gelatin gels as metal reservoirs (Ibsen et al. 2014). All these findings illustrate how both physical and chemical factors can influence calcium phosphate mineralization.

10.6 Outlook

While great strides have been made in the understanding of calcium phosphate mineralization in general and ACP and HAP formation in particular, a range of open questions remain that need to be addressed in the coming years. As has been argued throughout this chapter, the strong pH dependence of phosphate speciation suggests that there is not one universal mechanism of calcium phosphate mineralization.

The nature of ACP remains a mystery and there is a strong need for improved structural models of ACPs formed under various conditions. With recent developments in, e.g., pair-distribution function analysis and NMR, it seems likely that this goal will be attained within a few years.

The prenucleation state and the steps leading to ACP formation remain contested, and much more work is needed before this part of the calcium phosphate picture is painted. This problem is challenging for several reasons. First and foremost, there is a technical challenge: the low solubility of HAP means that solutions undersaturated with respect to HAP have very low concentrations of the relevant species, which renders the range of applicable experimental techniques limited. Secondly, there is a need for establishing widely accepted methodologies for detecting these phenomena. In the view of the present author, the titration approach employed by Gebauer et al. (2008) is promising, even though it also suffers from drawbacks including a varying ionic strength. The next challenge is to identify which species are present in any detected clusters. As argued above, phosphate speciation changes drastically with pH. Even when taking into account the possible change in effective pKa due to coordination by, e.g., calcium, there is likely to be several types of cluster compositions that will change with pH. The situation is further complicated by the ability of phosphate to undergo self-oligomerization through condensation, leading to pyrophosphate and higher polyphosphates that are both potent inhibitors of crystallization (Omelon and Grynpas 2008; Omelon et al. 2013) and species that must be considered for a full description of solution composition. These challenges call for novel and above all systematic approaches employing several complementary techniques, both experimental and theoretical.

The crystallization process itself also deserves more attention. An exceedingly large number of additives that affect calcium phosphate crystallization have been identified. Many of these are of relevance to biomineralization, even though it remains unclear which species are the main actors in which type of biomineralization. As shown in this chapter, the crystallization kinetics are very diverse and studying them with in situ techniques provides extremely valuable information, which ultimately can afford very detailed insights into crystallization pathways and (with additional model input) shed light on the relative importance of terms contributing to surface energies (Jensen et al. 2010). Above all there is a need for systematic studies including variations of the Ca:P ratio, pH, temperature, and solution composition. This will pave the way for understanding the factors determining, e.g., nanocrystal morphology evolution.

Thus, while much has been learned about calcium phosphate crystallization in the past years, we have only scratched the surface to reveal that much more is yet to be understood.