Molecular mechanisms of crystallization impacting calcium phosphate cements

Abstract

The biomineral calcium hydrogen phosphate dihydrate (CaHPO₄·2H₂O), known as brushite, is a malleable material that both grows and dissolves faster than most other calcium minerals, including other calcium phosphate phases, calcium carbonates and calcium oxalates. Within the body, this ready formation and dissolution can play a role in certain diseases, such as kidney stone and plaque formation. However, these same properties, along with brushite’s excellent biocompatibility, can be used to great benefit in making resorbable biomedical cements. To optimize cements, additives are commonly used to control crystallization kinetics and phase transformation. This paper describes the use of in situ scanning probe microscopy to investigate the role of several solution parameters and additives in brushite atomic step motion. Surprisingly, this work demonstrates that the activation barrier for phosphate (rather than calcium) incorporation limits growth kinetics and that additives such as magnesium, citrate and bisphosphonates each influence step motion in distinctly different ways. Our findings provide details of how, and where, molecules inhibit or accelerate kinetics. These insights have the potential to aid in designing molecules to target specific steps and to guide synergistic combinations of additives.

1. Introduction

The biomineral calcium hydrogen phosphate dihydrate (CaHPO₄·2H₂O), commonly known as brushite and often denoted as DCPD, is a malleable material that both grows and dissolves readily. Compared with the other calcium phosphate (CaP) phases, it has a fast nucleation rate as a result of its low surface energy. It is also less stable than the other CaP phases at physiological pH. Within the body, these properties can play a role in certain diseases, most notably in kidney stone formation, where crystals form under mildly acidic conditions found in urine. However, these same properties, along with brushite’s excellent biocompatibility, can be used to great benefit in making resorbable biomedical cements. This paper describes findings from crystal growth experiments on brushite. To put these experiments in context, we use the synthesis of calcium phosphate cements as an example of how these kinetic data might be used to impact formulation and processing. We begin with a brief description of how CaP cements are made, pointing out desired processing goals and, in particular, describing which aspects of this problem might be aided by optimizing brushite crystallization conditions.

There are many processing challenges associated with optimizing calcium orthophosphate cements (Dorozhkin 2008). These begin with the formation of the cements themselves. Cements are either high- or low-viscosity pastes that can be moulded or injected into wound sites. They are synthesized by forming a viscous slurry from calcium phosphate powders mixed with a solvent. Typically two or more calcium phosphate species are reacted together to form either an apatite or brushite cement. The solvent is chosen such that the powders dissolve to form a supersaturated gel that eventually precipitates to form a solid composed of interlocked crystals. Brushite is of interest in both cement types—as an intermediate, in the formation of calcium-deficient hydroxyapatite (CDHA) cements, and as a product, in the formation of brushite (DCPD) cements.

During this precipitation process, it is important to control crystallization kinetics, the final crystal phase, the porosity and the microcrystalline structure (Bohner 2007). Together, these properties affect the performance of the implant by influencing the setting time, the mechanical characteristics and the resorption rate. For example, the setting time must be slow enough to allow a surgeon time to inject the material while it is still pliable, but fast enough to provide mechanical integrity to the wound. For this reason, it is important to control the nucleation and growth kinetics that initiate solidification. Similarly, the phase, the porosity and the microstructure all affect the mechanical strength and can be tuned to some degree to suit the application.

Once the implant has been formed, it must be resorbed into the body. Ideally, the resorption is balanced by bone growth to maintain mechanical strength at the wound site. Tuning the resorption rate is a complicated problem that depends both on the implant properties, such as phase and porosity, as well as the local biological processes. At the wound site, the local biochemistry is constantly evolving owing to the body’s inflammatory response and cellular activity. Proteins adsorb to the implant surface, altering its interfacial properties. In addition, transport in and out of the porous structure can be limited, which causes heterogeneities and concentration gradients throughout the structure. Within these temporally and spatially varying surroundings, the calcium phosphate material responds to its locale by dissolving or, in some cases, changing phase. While this process cannot yet be fully controlled, it is of general interest to be able to slow or speed the dissolution of the calcium phosphate material under a range of conditions.

The setting time and the resorption time are important time scales that dictate many of the desired goals associated with crystallization kinetics (figure 1). The setting time, which typically needs to be a few minutes, is the time that it takes to progress from a mixed paste to a solid, sufficiently rigid to hold its shape. This includes several stages from the dissolution of the starting materials to create a gel, the lag time before the onset of nucleation and the time needed to grow an interpenetrating network of crystals. For this reason, the setting time can be influenced by altering the dissolution rate of the reactants or by slowing the nucleation and growth of the products or intermediates. In both cement types, it is generally desirable to slow the nucleation and growth of DCPD crystals as this leads to the initial solidification of the gel and limits the surgeon’s working time. There are several strategies for achieving this including the use of different solvents, the use of additives that can either inhibit nucleation or alter growth rates and the variation of crystal growth parameters such as the supersaturation, the ionic strength or the ratio of calcium to phosphate.

Figure 1.

Goals and strategies for tuning brushite crystallization kinetics to improve, or better understand, calcium phosphate cement formation. A, B and C, various calcium phosphate phases; DCPD, brushite; CDHA, calcium-deficient hydroxyapatite.

The resorption time is dictated by both the biological and chemical environment as well as implant properties such as porosity, solubility and stability. Of these factors, the solubility and material stability can be modified by altering brushite’s inherent interfacial kinetics. Brushite is undersaturated in healthy physiological settings (Orme & Giocondi 2007). For this reason, brushite will either dissolve or be converted to apatite over time. The inherent dissolution of brushite can be influenced by both particle size (Tang et al. 2003) as well as additives. The conversion of brushite to less soluble apatite is an essential step in the formation of CDHA cements, but is typically undesirable for brushite cements because it slows the resorption rate. As hydrolysis is a step in this conversion, additives that influence the removal of water are of interest for DCPD cements. Magnesium ions (Lilley et al. 2005) and pyrophosphate (Grover et al. 2006) have been demonstrated to inhibit the hydrolysis reaction, thereby lessening CDHA formation and the associated decrease in resorption rate.

Recent reviews (Bohner 2007) have laid out a framework, summarized in figure 1, to connect molecular mechanisms of crystallization with aspects of process control. This paper continues along these lines, focusing on the interfacial physics at brushite surfaces that may impact the processing and evolution of calcium phosphate cement materials. Although dissolution is briefly discussed, the primary focus is on growth.

To address the questions of how solution parameters, solvents and impurities alter brushite kinetics, we have employed scanning probe microscopy (SPM) as a means of monitoring both the morphology and kinetics of atomic step motion. Brushite crystals are highly heterogeneous with multiple facets and several types of steps on each face. Unlike bulk studies, SPM results are not averaged over different step directions or different facets that may each interact with additives in unique ways. For this reason, SPM has been particularly useful in advancing the science of impurity interactions.

Because it is often interactions at step edges (as opposed to facets) that serve as the molecular docking sites for growth modifiers (Orme et al. 2001; Qiu et al. 2005), ascertaining step structure is fundamental to SPM studies. We use electron backscattered diffraction (EBSD) to provide positive identification of the step directions, which historically have been identified either by macroscopic morphology (Ohta et al. 1979) or by high-resolution atomic force microscopy (Scudiero et al. 1999; Kanzaki et al. 2002). Our results confirm previous identifications, but use a more reliable methodology.

In what follows, we will briefly discuss brushite growth and dissolution in solutions without additives to provide a baseline. Kinetic data will suggest that , rather than Ca²⁺, incorporation is the rate-limiting step during growth. This may suggest a means to slow growth rate without additives. We will also describe the effect of three additives that have been used to alter DCPD cements: magnesium ions, citrate and the bisphosphonate, etidronate. We also compare citrate, which has three carboxyl groups, with oxalate, which has two. In general, images are used to indicate which surface steps interact with the additive, and step kinetics are used to provide additional information on the mechanism. Results show that magnesium slows the growth rate of all brushite steps. By contrast, citrate has little effect on the step kinetics, but lowers the density of steps on the surface. Oxalate has similar effects on kinetics, but stabilizes a facet not observed in the presence of citrate. On the other hand, etidronate binds specifically to polar steps and substantially increases the kinetics of non-polar steps.

2. Experimental methods

(a). Substrate preparation using gel crystal growth

Brushite crystal substrates were grown in 1 wt% agarose gels (low melt, Pierce) by the single diffusion method using CaCl₂·2H₂O (EM Science, 99.5%) and KH₂PO₄, KDP (ProChem, 99.999+%) as the calcium and phosphate sources, respectively. The stock solutions of each reagent were filtered, using a 0.2 μm polytetrafluoroethylene (PTFE) filter, prior to use. About 0.1 M KDP was added to the gel phase and the top solution contained 0.1 M CaCl₂·2H₂O. The final pH of both the gel phase and the top solution was adjusted to 5. The gel was allowed to set for 24 h before adding the top solution, and the vials were incubated at room temperature. The crystals were harvested from the gels, rinsed in water and dried and stored on ashless filter paper. The phase and chemistry of the substrates were validated by both powder X-ray diffraction (XRD) and Raman spectroscopy.

(b). Electron backscattered diffraction to identify step directions

EBSD was used to determine the surface orientation and the crystallographic directions that corresponded to etch pit edges as viewed by SPM. To determine crystallite orientation, a Tex SEM Laboratories, Inc. EBSD system integrated with an FEI Instruments Quanta 200 environmental scanning electron microscopy (SEM) instrument was used. The crystals were examined without any conductive coating, and the microscope was run at 20 kV in low vacuum mode with a water vapour pressure of 0.5 torr to help minimize charging. Individual diffraction patterns were collected by rastering the beam over small areas (approx. 5×5 μm) on the crystal surface instead of the typical collimating of the electron beam onto a spot, as this was discovered to locally charge up the crystal and lead to poor diffraction and cracking. The collected diffraction patterns were then indexed to determine the crystallite orientations.

(c). In situ scanning probe microscopy to measure step kinetics

In situ SPM was used to observe the crystal growth from dislocation hillocks on the {010} surface of platelet-like, gel grown brushite crystals. Crystals were anchored with a UV-curable adhesive (UV15, Masterbond) and freshly cleaved prior to imaging in solution using an atomic force microscope (Nanoscope III, Digital Instruments, Santa Barbara, CA, USA) equipped with a commercially available flow-through fluid cell. Solution flow rates (1.0–1.5 ml min⁻¹) were chosen such that step growth kinetics were not limited by bulk diffusion. The solution temperature entering the fluid cell was maintained at 37^°C by keeping the solution reservoir in an incubator at 40^°C and resistively heating the tubing leading from the incubator to the fluid cell to reduce cooling losses in the tubing. The fluid cell temperature was measured using a 0.005′′ diameter copper–constantan thermocouple (Omega) fitted to the outlet of the fluid cell.

All images were 2×2 μm and were acquired in contact mode using Si₃N₄ tips. The force between the tip and the sample was reduced to the minimum possible value that allowed the tip to remain in contact with the surface and did not have a measurable effect on the growth kinetics. Note that step-angle distortion exists in the images because the step front advances during the scan time. Images reported here are not corrected for this effect. Instead, the change in step angle in images acquired in scanned up and scanned down images was used to provide a measure of both the true step angle and the step velocity as given by the equations

2.1

where m_i is the apparent slope of the step in up (m_u) and down (m_d) scanned images, is the true slope of the step, v is the true velocity of the step, x_pix is the number of pixels per line and v_tip is the velocity of the tip in pixels per second given by v_tip=2(scan rate)(scan size). All images were processed and analysed with Image SXM (v. 1.81). In cases where solutions with different concentration conditions were exchanged, measurements were made using images acquired at least 3 min after the exchanges occurred to ensure that the new solution had equilibrated in the fluid cell. With a fluid cell volume of approximately 50 μl, this equilibration time is sufficient to refill the fluid cell more than 50 times with the flow rates used.

(d). Solution speciation

Solutions for SPM experiments were prepared making ‘A’ and ‘B’ solutions by the introduction of filtered (0.2 μm PTFE filter) stock solutions. The ‘A’ solution contained NaCl and CaCl₂·2H₂O and the ‘B’ solution contained KDP and KOH. The ‘B’ solution was then slowly added to the ‘A’ solution while stirring, the temperature was adjusted to 37^°C and the pH was adjusted by slow addition of 0.1 M KOH.

The base solutions used consisted of two formulations, the components of which are shown in table 1. These values all fall within range of concentrations found in human urine (Orme & Giocondi 2007). The supersaturation ratio, S, with respect to brushite is defined as

2.2

where a{X} is the ionic activity and K_sp is the solubility product for brushite at 37^°C (; Gregory et al. 1970). The activities of all solution species were calculated using the Davies extended form of the Debye–Hückel equation using mass balance expressions for total calcium and total phosphate with appropriate equilibrium constants by successive approximation for the ionic strength (table 2).

Table 1.

Base growth solutions used for in situ SPM measurements.

solution	[CaCl] (mM)	[KDP] (mM)	pH	IS (M)	S
1	0.85	60	6	0.15	1.53
2	1.35	5.1	6.5	0.04	1.32
3	8.5	8.5	5.6	0.15	1.56

Table 2.

Equilibria used to perform speciation calculation.

equilibria		reference
	12.18	Bjerrum & Unmack (1929)
	7.18	Bates & Acree (1943, 1945)
	2.21	Bates (1951)
	1.11	Smith & Alberty (1956)
	1	Smith & Alberty (1956)
	6.15	Zhang et al. (1991)
	2.77	Zhang et al. (1991)
	1.45	Zhang et al. (1991)

Several strategies were used to prepare growth solutions with various supersaturations or with additives. To measure kinetic coefficients, a titration technique was used to vary the supersaturation by increasing the calcium concentration using either base growth solution 1 or 2 (table 1). A similar technique was also used to investigate etidronate additives. Etidronate is known to complex with calcium; however, the micromolar quantities (compared with millimolar of calcium) were too small to substantially affect the supersaturation. It is also known that citrate and oxalate complex with Ca²⁺ and can act to lower the supersaturation for brushite when the concentrations are comparable to that of calcium. For these titration experiments, both CaCl₂ and potassium oxalate or sodium citrate were titrated simultaneously to keep the supersaturation constant. Finally, magnesium is known to lower the supersaturation of brushite by forming complexes with and for these experiments, individual solutions with different magnesium concentrations were prepared, keeping the supersaturation constant. Additive titrations of magnesium and oxalate used solution 1 as a base; experiments with etidronate used solution 3; and experiments with citrate used both solutions 1 and 3.

3. Results and discussion

(a). Step and surface structure

Brushite crystallizes in a non-centrosymmetric monoclinic structure. Curry & Jones (1971) identified the structure as space group Ia with lattice parameters a=5.812 Å, b=15.18 Å, c=6.239 Åand β=116.25^°. The Ia space group can also be described in an Aa or Cc setting and all three can be related by the use of transformation matrices found in the International Tables of Crystallography. While most experimental work is presented in class Ia, the Ia classification is not recognized in the standard tables and thus more recent papers instead use Aa and Cc. We use Cc to describe our EBSD results.

Brushite has a plate-like morphology dominated by {010} faces (Legeros & Legeros 1971). The structure (figure 2b,c) within the {010} plane is composed of two corrugated rows of Ca²⁺ (light blue spheres) and (grey tetrahedrons) that are offset in the 〈010〉 direction. Between these calcium- and phosphate-containing sheets are layers of water molecules bound to the calcium ions above and below the {010} plane. The weaker bonding of the water molecules to one another creates a cleavage plane between the two water layers perpendicular to the {010} face. For this reason, the {010} faces are fully hydrated even within the bulk structure.

Figure 2.

Brushite etch experiment and structure. (a) SPM micrograph of etch pits on the brushite surface. The inset shows the EBSD diffraction pattern. (b) Crystallographic model of a brushite (010) growth surface with step assignments for space group Cc. Note that the growth geometry is the mirror image of the etch geometry. (c) HPO₄ and Ca–O–H₂O clusters shown in the same orientation as (b). P, grey; O, red; H (HPO₄), black; Ca, light blue; O (H₂O), dark blue; H (H₂O), pink. All SPM images are oriented as indicated in (b).

Triangular etch pits and growth hillocks form on the {010} faces. Owing to the chiral nature of this crystal, the (010) and faces have unique steps and therefore the triangular etch pits (or growth hillocks) are mirror images of one another on each face. The etch pits shown in figure 2a were formed by etching in deionized water inside the SPM fluid cell. The images were acquired in fluid but without fluid flow once the etch pits had stabilized (no measurable step motion). The step-edge orientations were measured from SPM images by determining the angle the step makes with the image horizontal. Micrographs of the crystal’s orientation in the SPM and the SEM were obtained. These micrographs were used to compare the alignment in both systems, and the angle between the edge of the crystal in the two micrographs differed by only 0.25^°.

The Euler angles obtained from the EBSD were used to calculate the actual orientation of the crystal normal and step edges of the etch pits. We were able to unambiguously determine the surface orientation as (010), rather than , and assign the step directions on the as , [101]_Cc and . These values are also related to the Ia setting in table 3 and shown in relation to the brushite structure in figure 2b. All SPM images are oriented as shown in figure 2b.

Table 3.

Correlation between the step directions (from EBSD) and primary facets in three crystallographic classes used in the literature. Opposite signs are needed for both facets and steps to describe the face.

^aThe step direction is defined as the cross-product between the (010) face and the riser facet and thus is a vector lying within the (010) plane parallel to the step (rather than perpendicular to it). The direction of the step (advancing versus retreating) is made unique by choosing the (hkl) of the riser to point in the direction of the step motion.

^bThe facets are given in the direction of step motion for hillocks growing on a (010) facet and are assumed to create an angle that is obtuse with respect to the underlying plane as is suggested by macroscopic crystal habit.

The crystallographic orientations obtained in this work by EBSD agree with those previously reported using atomic resolution SPM (Scudiero et al. 1999; Kanzaki et al. 2002) and SEM (Ohta et al. 1979) for identification. While these techniques provided the correct assignments, they are more open to interpretation than EBSD. For example, atomic resolution SPM is subject to surface cleanliness, tip sharpness and scanning conditions. And, the previous SEM work was based upon comparisons between macroscopic morphology and etch pit shape. Given the considerable variation in brushite crystal habit, this requires assumptions regarding bounding facets. Performing EBSD in an SEM instrument has several advantages. No special sample preparation is required, and SEM micrographs can be directly compared with the morphological features from other imaging techniques. Most importantly, the diffraction method provides an unambiguous assignment of the crystallographic features of interest.

There are several features of the atomic structure that can play a role in crystallization dynamics. Within the crystal, each calcium ion is bonded to eight oxygen atoms (figure 2), six from neighbouring phosphates (in red) and two from water molecules (in dark blue). Thus, at a step edge, where oxygen atoms are not available from neighbouring phosphates, it is likely that the calcium ion will complete its coordination by binding water or OH⁻ groups from the solution. As a reminder that unfulfilled oxygen bonds exist on these edges, the step edges displayed in figure 2b are cut such that the CaO₈ coordination (figure 2c) remains intact. However, it should be noted that the exact form of the hydrated step edge is unknown. As the crystal grows, the oxygen atoms from the solution will need to be removed (or rearranged) to accommodate the adsorbing ion and thus dehydration is expected to be an important part of the activation barrier for growth and dissolution (Vandervoort & Hartman 1991). But, because two water molecules remain as part of the crystal structure, this effect may be expected to be smaller than for unhydrated crystals such as hydroxyapatite (HAP) and calcite.

It is also interesting that the {010} faces are fully hydrated as part of the bulk crystal structure and thus the removal of tightly bound water at an {010} surface is not a part of the activation barrier on this facet. In other words, the large surface area of this facet is due to low surface energy rather than to kinetic barriers associated with dehydration. And, in fact, brushite has a relatively low interfacial energy of 4.5 mJ m⁻² (Tang et al. 2005) compared with other biominerals such as 8 mJ m⁻² for apatite (Nancollas et al. 2006) or 13.1 mJ m⁻² for calcium oxalate monohydrate (COM; Wu & Nancollas 1999). Surface X-ray diffraction studies show that this water layer is crystalline, but not ice-like and does not impart order of water molecules into the solution as might be expected from ice (Arsic et al. 2004). The fully hydrated surface also suggests that proteins are less likely to bind strongly to these surfaces, as has been observed experimentally (Hanein et al. 1993; Flade et al. 2001). This is likely to play a role in the resorption properties of brushite cements.

(b). Impact of structure on processing

Beyond biocompatibility, two physicochemical properties that lead to brushite’s utility are its low surface energy compared with other calcium phosphate phases and its metastability at physiological pH values. When two minerals compete for common ions, both the kinetics of formation as well as the relative thermodynamic stability of the two solids play a role in the temporal evolution of a solid–solution mixture. In the case of brushite and apatite, the former has faster formation kinetics and the latter has greater stability.

At physiological pH, apatite is the more thermodynamically stable phase. The solubility product normalized per growth unit is 3.04×10⁻⁷ (McDowell et al. 1977) for HAP versus 4.8×10⁻⁴ (Gregory et al. 1970) for brushite. Accordingly, at sufficiently high pH, when is present, apatite will outcompete brushite for calcium and . However, from classical nucleation theory, the activation barrier associated with homogeneous nucleation from solution (Δg_nuc) has a magnitude that depends sensitively on the interfacial energy (γ_sl)

3.1

Accordingly, at the same driving force (Δμ), the solid with the lower interfacial energy, γ_sl, will have the lower nucleation barrier. From the kinetic perspective, brushite crystals will precipitate faster from solution owing to their lower interfacial energy.

(c). Step kinetics

Step kinetics reflect the first-order rate constants associated with the crystallization reaction A_(soln)→A_(crystal); for this reason, they are fundamental to understanding kinetic controls on crystallization dynamics. Crystallization occurs as Ca²⁺ and ‘growth units’ (Boistelle & Lopezvalero 1990) move from the solution phase, overcome an activation barrier and incorporate into a step at a crystal surface. With this picture in mind, the step velocity (v_s) for a two-component crystal, such as brushite, can be written as (Zhang & Nancollas 1998; Qiu & Orme 2008)

3.2

where β is the kinetic coefficient with units of velocity, K_sp is the solubility product converted from molar units to number density (3.87×10¹⁷ cm⁻³), Ω/2 is the average volume per growth unit (6.16×10⁻²³ cm³) and S represents the solubility product defined by equation (2.2). The kinetic coefficient is related to the first-order rate constant (k⁺) and contains the activation barrier associated with adsorption:

3.3

where b_⊥ is the lattice spacing perpendicular to the step, n_k is the number of growth units between kinks, v⁺ is the attempt frequency associated with adsorption and Δμ is the chemical potential difference between the solution and an activated state associated with the barrier. This equation implicitly assumes that the activation barriers associated with Ca²⁺ and ions are equivalent. A similar formalism is used to describe dissolution except that the relative undersaturation is given by 1−S^1/2.

(d). The relationship between hillock geometry and crystal parameters

At modest supersaturations, brushite grows in the form of triangular hillocks initiating at dislocations. The step directions depend on the underlying crystallography as described earlier, but the density of steps depends on the kinetics and the interfacial energy. Hillock geometry is not available from bulk experiments and is additional information that can be used to provide more detailed information on surface interactions. Hillock geometry depends upon the critical length, the step velocities in the different crystallographic directions and the driving force. Details are provided in Qiu & Orme (2008); here, we summarize pieces that are needed to explain the data presented in §3.

Steps emerging from a dislocation do not propagate until they reach a critical length. The critical length is proportional to the step free energy (γ) and the chemical potential

3.4

where the chemical potential is . For each of the three steps, there is a delay before the step reaches the critical length and begins to propagate. Thus, the time it takes to go around the spiral once, one period (T_s) is the sum of these three delay times. From the form of the critical length, it can be seen that the period is proportional to the interfacial energy and inversely proportional to the driving force. (Note that the critical lengths and velocities differ for each direction. More detailed expressions for L_c and T_s take this into account; however, the scaling is as shown.)

The density is related to the distance between steps, which is simply the velocity of the step in a given direction (i), multiplied by the spiral period, T_s, or terrace width, w_i=v_iT_s. Accordingly, changes in the critical length lead to changes in the step density. This relation also shows that so that the ratio of terrace widths in the three crystallographic directions is the same as the ratio of velocities, .

(e). Dissolution behaviour of brushite

The dissolution of brushite has previously been studied by SPM both in solutions without additives (Scudiero et al. 1999; Kanzaki et al. 2002) and in the presence of calcium chelators, such as poly(sodium)aspartate (Peytcheva & Antonietti 2001). Scudiero et al. (1999) discussed dissolution by both chemical and mechanical means. In undersaturated solutions, they measured the step velocities of the etch pits and found that the dissolution rate goes as , while the [100]_Cc step had no observable velocity. Note that step directions have opposite signs from those shown in figure 2 to describe etch pits rather than growth hillocks on the (010) face. Kanzaki et al. (2002) measured the step kinetics over a range of undersaturations and extracted a kinetic coefficient of  cm s⁻¹. (Their reported value was recalculated to reflect equation (3.2).) This value is approximately 40 times smaller than that found for growth. At this point, it is not yet known whether the difference between kinetic coefficients for growth and dissolution is a material’s property or whether it reflects differences in the solution environment.

(f). Growth behaviour of brushite without additives

To obtain the kinetic coefficient for growth, step velocity was measured as a function of the relative supersaturation (figure 3). Experiments were performed using calcium titration to increase the supersaturation, starting from two different base solutions: one with an order of magnitude higher phosphate concentration (filled circles) than the other (open circles). First, the velocity is linear with respect to the relative supersaturation as predicted by equation (3.2) and fits well even when constrained to go through the origin. However, it is also clear that step kinetics in solutions with more phosphate are faster than those with lower phosphate, even when the relative supersaturation ratio is the same. This implies that the activation barrier for Ca²⁺ and ions differs. As a result, the crystallization kinetics depends explicitly on the {}/{Ca²⁺} ratio, not just the product, as is assumed by equation (3.2). These data are complicated by the fact that the pH and ionic strength are also different for the two sets of data. However, a more controlled set of experiments performed at constant conditions of supersaturation, pH and ionic strength, and spanning two orders of magnitude in {}/{Ca²⁺} ratio (J. L. Giocondi, G. H. Nancollas & C. A. Orme 2009, unpublished data) have shown that incorporation is rate-limiting and that the growth rate can be doubled in solutions with high {} to {Ca²⁺} ratios.

Figure 3.

Plots of the velocity of the step as a function relative supersaturation (S^1/2−1). Solid points stem from a base solution with an order of magnitude greater phosphate concentration (0.85 mM CaCl₂, 60 mM KDP, pH = 6 and IS = 0.15 M) than the points plotted with open circles (1.3 mM CaCl₂, 5.1 mM KDP, pH = 6.5 and IS = 0.04 M). The supersaturation was increased by adding 0.1 and 0.05 mM aliquots of CaCl₂, respectively.

If we ignore the variation due to anion-to-cation ratio and use of equation (3.2), we obtain a kinetic coefficient of 0.26–0.3 cm s⁻¹. A comparison with calcium carbonate (Teng et al. 1999) and calcium oxalate (Weaver et al. 2007) shows that the kinetic coefficients are within a factor of 3 of one another (Qiu & Orme 2008). By contrast, the kinetic coefficient for HAP (Onuma et al. 1996) is two orders of magnitude smaller, a value more typical of protein crystallization. These differences are used to argue that calcium carbonate, calcium oxalate and brushite grow via anion and cation attachment, whereas HAP grows via incorporation of larger clusters of molecules (Onuma 2006).

For both CDHA and DCPD cement formation, the desired goal is to slow the growth rate of brushite crystallization (figure 1) to increase the setting time. Step kinetic data have demonstrated that incorporation is the rate-limiting step in brushite crystallization. If these solution results translate to slurries then brushite kinetics are expected to be slower and setting times longer, using mixtures with excess free calcium rather than excess free . Additionally, although purely as a speculation at this point, if it were possible to tune the growth units from single molecules to larger clusters by using solvents or surfactants, it may be possible to alter kinetic coefficients and hence growth rate.

(g). Step anisotropy

The anisotropic nature of the steps makes it interesting to correlate stable step structure and relative kinetic coefficients with the underlying crystal structure. Both growth and dissolution data report that the step has the slowest kinetics (Scudiero et al. 1999; Kanzaki et al. 2002; Tang et al. 2005). There are several features that make this step unique compared with the other two. First, along this step direction, the chains of calcium and hydrogen phosphate are bonded in the same plane rather than in a corrugated manner as they are in the other two directions. This means that this direction has tight ionic bonding within the step, giving it low step-specific energy. Scudiero et al. point out that the calcium ions within this step have five nearest-neighbour bonds compared with four nearest-neighbour bonds for the other steps. Another feature that may play a role in the dynamics (Abbona et al. 1994; Scudiero et al. 1999) of this step is that the acidic hydrogen atom points into solution at the step edge (figure 2, in black). It has been suggested that the OH⁻ groups hydrogen bond with water in solution, which must then be removed before the next crystallizing molecule can be adsorbed, leading to higher activation barriers for this step. The complementary [100]_Cc step, which is chemically similar within the plane of the step but does not have an OH⁻ group extending into solution, is not observed under normal conditions, supporting this idea. Interestingly, oxalate, at sufficiently high concentrations, causes the appearance of this step.

(h). Influence of additives on brushite growth

There are several generic ways that adsorbates can affect growth. They can incorporate into the crystal, change kinetic coefficients, pin steps and act as surfactants. Each of these alters the step kinetics in characteristic ways that allow the differing mechanisms to be distinguished. The interested reader is referred to recent reviews on this subject for more details (De Yoreo & Vekilov 2003; Qiu & Orme 2008).

(i). The impact of magnesium on brushite growth

Magnesium is the second most abundant divalent cation found in biological fluids such as serum, urine and saliva. It is found in the carbonated-hydroxyapatite of bones and teeth, and it is known that magnesium impurities inhibit both the nucleation and growth of calcium phosphates. Of interest to biological cements, magnesium can stabilize amorphous calcium phosphate against phase transformation (Termine et al. 1970), promote the formation of whitlockite (Mg-substituted tricalcium phosphate; Rowles 1968) and inhibit the transformation of brushite to octacalcium phosphate and HAP (Bigi et al. 1988). Previous studies of the effects of magnesium on the growth of brushite have found that magnesium acts as a growth inhibitor but it also stabilizes brushite against dissolution up to neutral pH (Abbona et al. 1986; Abbona & Franchini-Angela 1990).

SPM was used to look at the growth of brushite in growth solutions with up to [Mg²⁺]/[Ca²⁺] = 3. These results (figure 4) show that magnesium slows the growth rate of all steps at the highest magnesium concentrations. Specifically, the velocity of the step initially increases with the addition of magnesium, but then decreases linearly as a function of magnesium-to-calcium ratio (figure 4c). The rate of the step is similarly affected while the rate of the polar [101]_Cc is slowed the most. These growth rates are depicted pictorially in figure 4d, where the dotted line shows the initial step rates and the solid line shows the rates with magnesium. The changes in relative velocity as the magnesium concentration increased resulted in hillock morphologies that changed from the normal triangular shape to one with a greater proportion of [101]_Cc compared with . For this to occur, the [101]_Cc step has to become more serrated, giving it an overall curved appearance.

Figure 4.

SPM experiment to determine the effect of Mg²⁺ additives on brushite growth. SPM micrographs of brushite growth in (a) a pure growth solution and (b) with Mg²⁺. Both images are 2×2 μm. (c) Plot of the velocity of the step as a function of [Mg²⁺]/[Ca²⁺]. (d) Schematic drawing comparing the relative step growth kinetics in a pure solution (dashed line) with those with magnesium additives (solid line). The dislocation source is denoted by the dot.

The step density also increased owing to magnesium. The increased step density likely stems from reduced step free energy owing to the adsorption of magnesium onto surface steps. This would lead to a smaller critical length and a tighter winding of the spiral (equation (3.4)). This is supported by nucleation studies, where it was found that magnesium reduced the weighted average step-edge free energy for brushite from 29 pJ m⁻¹ in pure solutions to 17 pJ m⁻¹ in the presence of magnesium (Lundager Madsen 2008).

Additionally, the size of the magnesium ion suggests that it may be able to substitute for calcium in the brushite lattice. In the current experiments, magnesium was not detected by energy dispersive spectroscopy but a higher sensitivity technique is likely needed for overgrowth experiments. Previous experiments have demonstrated that magnesium incorporates into the brushite structure, resulting in increased lattice parameters (Lilley et al. 2005), and changes to the metal-phosphate bonds (Kumta et al. 2005). At lower concentrations, magnesium incorporates fully with concentrations up to 2.8 atomic % (Kumta et al. 2005). At higher concentrations (approx. 17 atomic %), Fourier transform infrared (FTIR) spectroscopy and XRD show that the magnesium is not fully incorporated into the structure but is also partially associated with amorphous CaP while the morphology transforms from plates to nano-sized spheres. FTIR spectroscopy also shows that the magnesium that is incorporated into the structure causes lattice strain. This strain may explain fluctuations on the and polar [101]_Cc steps as seen in SPM (figure 4b). The regular oscillations appear to be periodic, facetted steps. The morphology on the step can be contrasted with etidronate (figure 7b), which is more characteristic of random disorder.

Figure 7.

SPM experiment to determine the effect of etidronate additives on brushite growth. SPM micrographs of brushite growth in a (a) pure growth solution and (b) with etidronate showing the emergence of a new step direction. Both images are 2×2 μm. (c) Plot of the velocity of the step as a function of [etidronate]/[Ca²⁺]. (d) Schematic drawing comparing the relative step growth kinetics in a pure solution (dashed line) with those with etidronate additives (solid line). The dislocation source is denoted by the dot.

The implications for the use of magnesium in cement formulations are twofold. First, the inhibitory effect that magnesium has on brushite nucleation and growth can extend the setting time. Second, magnesium inhibits the hydrolysis of brushite to HAP, extending the range of solutions where brushite is stable, and also increasing the setting time. It should also be noted that the effect of magnesium on the supersaturation of brushite was corrected for in the SPM experiments. If this correction was not deliberately made, then magnesium can also be used to lower the supersaturation of brushite by complexing with . This complexation would lower the growth rate both by reduced supersaturation and removing the rate-limiting unit ().

(ii). The impact of citrate on brushite growth

It is well established that citrate, a small molecule with three carboxyl groups, has an inhibitory effect on CaP crystallization. This property is used beneficially to reduce kidney stone formation (Breslau et al. 1995) and, similarly, to extend the setting time (Bohner et al. 1996; Barralet et al. 2004) and shelf life (Gbureck et al. 2005) of CaP cements. To better understand the mechanisms that underlie this inhibitory action, parallel constant composition and SPM experiments were conducted.

Constant composition experiments showed that citrate, , inhibited the bulk growth rate of brushite seeds (Tang et al. 2005). Concentrations of 2.1 and 10 μM citrate reduced the growth rate by 50 and 95 per cent, respectively. Surprisingly, corresponding SPM experiments showed no reduction in step speed and, in fact, step kinetics increased by a small amount (figure 5a,b,g,e, lower line). On the other hand, step density did decrease in the presence of citrate. And, because the bulk growth rate relies on both of these factors, this could be used to partially reconcile the two experiments. This density effect proved reversible, as solutions were oscillated between pure and citrate-bearing, suggesting that citrate was not incorporating into the crystal structure, causing strain that would be sustained during subsequent growth cycles. Instead, it suggested a surface effect similar to a surfactant.

Figure 5.

SPM experiments to determine the effect of citrate additives on brushite growth. SPM micrographs of brushite growth in the absence (a,c) and presence (b,d) of citrate. All images are 2×2 μm. (e) Plots of the velocity of the step as a function of [citrate]/[Ca²⁺]. The bottom dataset corresponds to the SPM experiment in (a,b) at low citrate concentrations in base solution 3 while the top dataset corresponds to the SPM experiment in (c,d) at higher citrate concentrations in base solution 1. (f,g) Schematic drawing comparing the relative step growth kinetics in a pure solution (dashed line) with those with citrate additives (solid line at higher and low concentrations, respectively). The dislocation source is denoted by the dot.

As described earlier, the step density depends on how much time passes before steps emerging from a dislocation begin to propagate. This time is related to the critical length for step motion and correspondingly the step-edge free energy. When the step-edge free energy is small, critical lengths are small, and dislocation hillocks are tightly wound, with narrow terraces, whereas when step-edge free energies increase, a longer time is needed before a step reaches its critical length and terraces are correspondingly wider. Given this insight, the reduction in step density can be interpreted as an increase in step-edge free energy associated with citrate binding at the surface. Tang et al. (2005) verified this result by using a thin-layer, wicking method to measure the surface energies of brushite powders in the absence and presence of citrate, finding that the interfacial energy increased from 4.5 mJ m⁻² in pure solutions to 8.9 mJ m⁻² at 10 μM citrate. A higher interfacial energy is also expected to increase the barrier to nucleation (equation (3.1)), leading to a longer induction time, which was also verified experimentally.

Citrate’s effect was also examined over a significantly broader range of concentrations (figure 5c,d,f,e, upper line), more relevant for cements, than the study described earlier. The base solutions had a higher supersaturation and, for this reason, the baseline step speed (for the step) was approximately 16 nm s⁻¹. Despite substantially higher concentrations of citrate, spanning almost three orders of magnitude, and up to a 1 : 1 citrate-to-calcium ratio, the velocity of the step did not vary (figure 5e). It is interesting that under these conditions, the step density was not observed to decrease as it had at lower citrate-to-calcium ratios. The primary concentration-dependent effect was the steady slowing of the polar [101]_Cc step, as the citrate concentration increased. At the highest concentration tested (1 mM), the velocity of the polar step had decreased by a factor of approximately 3. The fact that only one step direction is observed to change suggests that citrate binds specifically to the [101]_Cc step; it seems likely that the negative carboxyl groups interact with the calcium-terminated polar step.

Overall, the implications for macroscopic crystallization are that brushite crystals are less likely to nucleate in the presence of citrate due to the higher nucleation barrier. This effectively expands the metastable regime and delays the precipitation of crystals. Also, brushite crystallites that do form have significantly slower growth rates either due to lower step density, at low concentrations, or, specific interactions at the polar step, at higher citrate-to-calcium ratios. Both of these effects would have the beneficial effect of increasing the setting time for cements. Somewhat trivially, chelating (if it were not explicitly corrected for, as in the experiments mentioned earlier) would also lower the growth rate by changing the supersaturation. And, at sufficiently high concentrations, citrate will even cause brushite to dissolve (Orme & Giocondi 2007).

(iii). The impact of oxalate on brushite growth

It is interesting to compare citrate, which has three carboxyl groups, with oxalate, which has two. The kinetics are similar in that neither affects the growth rate of the step (figure 6c). But, under the same conditions, citrate interacts with the polar step, whereas oxalate does not. Given that citrate and oxalate both have carboxyl moieties, this would suggest that the geometry (stereochemistry) is not well matched between oxalate and the polar step. Instead, oxalate causes a new facet to appear (figure 6b,d). The new facet is the mirror to brushite’s most stable step except that this is the direction that does not present a hydroxyl group at the step edge (in other words, a [100]_Cc step as discussed earlier).

Figure 6.

SPM experiment to determine the effect of oxalate additives on brushite growth. SPM micrographs of brushite growth in the absence (a) and presence (b) of oxalate showing the emergence of a new step direction. Both images are 2×2 μm. (c) Plot of the velocity of the step as a function of [oxalate]/[Ca²⁺]. (d) Schematic drawing comparing the relative step growth kinetics in a pure solution (dashed line) with those with oxalate additives (solid line). The dislocation source is denoted by the dot.

The effect of oxalate does not present any advantages to tuning cement processing. But, it does present clues and more stringent tests that may aid modellers in determining how additives interact with brushite surfaces. In addition, because calcium oxalate forms a solid product (as opposed to calcium citrate complexes, which are aqueous) it may have commonalities with brushite to apatite transitions. In the case of calcium oxalate, SPM has shown that the conversion from brushite to COM is a dissolution reprecipitation reaction, where brushite serves as a reservoir of calcium rather than an epitaxial template (Tang et al. 2006). This is similar to what might be anticipated if amorphous calcium phosphate were the precursor stage. Although no in situ experiments have yet captured the evolution of brushite to apatite, the brushite to COM transition may serve as a reasonable model to describe this process.

(iv). The impact of bisphosphonate on brushite growth

The bisphosphonate, etidronate (ethylene-1-hydroxy-1,1-diphosphonate), has been found to inhibit osteoclast activity and is considered therapeutic in diseases that require the regulation of bone remodelling (such as Pagets’s disease, osteoporosis and osteolytic tumours; Rodan & Martin 2000). Bisphosphates are structurally similar to pyrophosphate () except that the oxygen molecule that joins the two phosphate groups in pyrophosphates is substituted with a more robust carbon atom. This makes them less susceptible to biodegradation, an asset for their therapeutic use. The carbon substitution also has the advantage of adding two more binding sites, allowing a variety of side groups to be added to the molecule (Papapoulos 2006). Etidronate is a bisphosphonate with a hydroxyl bound to the central carbon. This configuration is thought to allow a tridentate binding to calcium ions (Papapoulos 2008).

The incorporation of bisphosphonates into cements is under consideration as a drug delivery mechanism (Grover et al. 2006). However, because of their structural similarity to pyrophosphates, some of the physicochemical effects observed for pyrophosphate may also pertain to etidronate. In cements, pyrophosphate has been shown to improve mechanical properties (Grover et al. 2006; Alkhralsat et al. 2008), reduce setting time (Bohner et al. 1996; Rodan & Martin 2000) and reduce the likelihood of conversion to apatite (Grover et al. 2006).

Although several studies have examined the effect of pyrophosphate on DCPD growth and dissolution, few studies discuss the interaction of etidronate with brushite. The only study that we are aware of (Grases et al. 2000) showed that etidronate inhibited both growth and nucleation more effectively than pyrophosphate.

To investigate this interaction further, SPM was employed to monitor DCPD step kinetics and morphology in the presence of up to 7 μM etidronate (figure 7). There are two significant findings. The first is that the images clearly show that etidronate interacted with, and inhibited growth on, the polar [101]_Cc steps of brushite. In fact, the second, mirror step can also be observed, changing the normal triangular step pattern into a four-sided trapezium. It should be noted that the second polar step () likely always has the same kinetics as the observed polar step because the two steps have the same surface chemistry. But the second polar step is not normally expressed owing to the geometry of the two bounding steps and . If the bounding steps were closer to parallel, then both polar steps would be observed, but because the bounding steps cross, the polar step is observed on the open end and not observed on the closed end. Etidronate stabilizes both polar steps to the degree that both steps can be observed. The second finding is that while the polar steps become slower, the fast step becomes significantly faster (figure 7c). The step velocity increased from 9 nm s⁻¹ without etidronate to 15 nm s⁻¹ at a concentration of 7 μM, an increase of 67 per cent. Recalling that the ratio of the terrace widths reflects the ratio of velocities (as described earlier), the velocities change from 9.2, 7.7 and 1.5 nm s⁻¹ to 15.1, 3.1, (3.1) and 1.5 nm s⁻¹ in the directions, respectively. The new polar step is shown in parentheses. The relative velocities are depicted schematically in figure 7d, where the dotted triangle represents the case without additive and the solid line reflects the case after etidronate addition. All velocities are referenced with respect to the dislocation origin (black dot).

These data suggest that the negative phosphate and possibly hydroxyl groups preferentially bind to the calcium-terminated polar steps. This is the primary source of etidronate’s inhibitory action on DCPD. Etidronate does not appear to bind strongly to the steps with mixed charge; the evidence for this is a fact that the velocity of the slow step does not change when etidronate is added. The step becomes less straight and well-defined, but does not slow. The change in morphology may be evidence of step pinning, but below the threshold necessary to alter the kinetics significantly. The other mixed charge step, , speeds up. Although, etidronate is clearly affecting this step, it is unlikely to be strongly bound, as this would block growth sites, slowing kinetics, as is observed for the polar steps.

The increase in step kinetics owing to additives has been observed for a number of other systems (Fu et al. 2005; Elhadj et al. 2006; Kim et al. 2006). In fact, magnesium, citrate and oxalate all show some evidence of this at low concentrations, with velocities slightly (but systematically) above the baseline value. There are a number of proposed mechanisms, including increasing kink density, increasing surface cation or anion concentrations, and altering activation barriers. It also seems unlikely that etidronate acts as a surface phosphate source—first, because the central carbon bond makes it unlikely that etidronate will break apart and second, because effects are seen with concentrations as low as 1 μM (compared with solution concentrations of in the millimolar range). A similar argument holds for calcium that may bind to etidronate and concentrate at the surface. Instead, it seems more reasonable that etidronate alters the water layer near the surface or acts as a bridge between the solution and the crystal, effectively lowering the barrier for Ca²⁺ or incorporation.

The change in hillock shape also suggests a change in macroscopic morphology. Macroscopic habit is dominated by the geometry of the growth steps. In the case of brushite, the macroscopic shape reflects the triangular hillocks on the (010) and faces, which are mirrors of one another. This is demonstrated schematically in figure 8a, showing long platelets dominated by the facets (which correspond to the slow steps). When etidronate is added, the macroscopic shape should reflect the new trapezium (figure 8b), which is dominated by the polar facets. By contrast, citrate or magnesium additives are not expected to alter the shape dramatically because the hillock remains approximately triangular even though the proportions change somewhat. Unfortunately, we do not have SEM images to verify this prediction. However, a similar stabilization of the two polar facets has been reported for brushite grown in the presence of sulphate ions (Pinto et al. 2009). This led to crystals elongated along the polar step directions. These results suggest that etidronate and sulphate bind more strongly to the polar steps than do either citrate or oxalate.

Figure 8.

Macroscopic habits predicted from hillock geometry (a) in the absence of additives, (b) in the presence of etidronate and (c) in the presence of citrate or magnesium. The facets associated with hillock step directions are indicated (table 3).

4. Conclusion and outlook

In summary, SPM data have shown the following. (i) Magnesium inhibits growth on all steps but relatively high Mg/Ca ratios are needed. Extracting the mechanism of interaction requires more modelling of the kinetic data, but step morphology is consistent with incorporation. (ii) Citrate has several effects depending on the citrate/calcium ratio. At the lowest concentrations, citrate increases the step free energy without altering the step kinetics; at higher concentrations, the polar step is slowed. (iii) Oxalate also slows the polar step but additionally stabilizes a new facet, with a [100]_Cc step. (iv) Etidronate has the greatest kinetic impact of the molecules studied. At 7 μM concentrations, the polar step slows by 60 per cent and a new polar step appears. However, at the same time, the increases by 67 per cent. It should be noted that all of these molecules complex calcium and can effect kinetics by altering the solution supersaturation or the Ca-to- ratio. For the SPM data shown, this effect was corrected for to distinguish the effect of the molecule at the crystal surface from the effect of the molecule on the solution speciation.

The goal of this paper is to draw connections between fundamental studies of atomic step motion and potential strategies for materials processing. It is not our intent to promote the utility of SPM for investigating processes in cement dynamics. The conditions are spectacularly different in many ways. The data shown in this paper are fairly close to equilibrium (S=1.6), whereas the nucleation of cements is initiated at supersaturation ratios in the thousands to millions. Of course, after the initial nucleation phase, the growth will occur at more modest supersaturations and as the cement evolves towards equilibrium, certainly some of the growth will occur in regimes such as shown here. In addition to the difference in supersaturation, cements tend to have lower additive-to-calcium ratios. As an example, the additive-to-calcium ratio is approximately 10⁻³ to 10⁻⁴ for a pyrophosphate-based cement (Grover et al. 2006).

Despite differences in growth conditions, the in situ SPM approach provides unique insights by providing details of where and how molecules inhibit or accelerate kinetics. This has the potential to aid in designing molecules to target specific steps and to guide synergistic combinations of additives. For example, it is unlikely that bulk techniques could deduce the simultaneous acceleration and inhibition effects of etidronate; or that citrate reduces growth rate by altering step density rather than step speed. In addition, SPM data translate to tractable questions for modellers. The questions change from ‘How does etidronate inhibit brushite growth?’ to ‘Why does etidronate bind strongly to the [101]_Cc step while it does not to the step?’ This is still a challenging question but it is far better defined.

Given that step chemistries are generally different, it seems reasonable to expect that the greatest inhibition will be achieved not with one, but with several synergistically chosen additives. For example, the most effective growth inhibitors for brushite would target the two fast steps, namely the non-polar and the polar [101]_Cc steps. Several molecules have been shown to slow the polar step, with etidronate as the most dramatic example. By contrast, only magnesium was observed to slow the step. Thus, a combination of high concentrations of magnesium to target the step with low concentrations of etidronate to target the polar steps should be a more effective combination than either alone. However, magnesium is not a particularly good inhibitor in the sense that high concentrations are needed, and it is not specific. More ideally, an inhibitor would be designed to interact specifically with the step, which would allow the two steps to be independently modified. Again, this provides an opportunity for tighter coupling with theoretical modelling. The question changes from ‘What types of molecules will inhibit brushite growth?’ to ‘What type of molecule will interact with the step?’ Similarly, to increase resorption rate, it would be most efficacious to target the slow-moving step, perhaps by targeting the hydroxyl group that seems to stabilize this step compared with its otherwise similar mirror, [100]_Cc.

In short, there are a number of opportunities where molecular scale imaging can provide new information that has the prospect to aid in optimizing calcium phosphate cements.