Hydroxyapatite (HA), a calcium phosphate ceramic of the formula Ca10(PO4)6(OH)2, composes the inorganic phase of bone. Synthetic HA retains bioactive characteristics and for this reason is an attractive material for use in biomedical applications. Due to brittle mechanical properties HA cannot be used as a bulk material in load bearing applications, but it is a popular bioceramic coating and bone filler material.
Structure of HA
Hydroxyapatite is a hexagonal material, from space group P63/m, with 44 atoms per unit cell. Because of this large unit cell size, it is only recently that HA has been studied using quantum mechanical methods. Stoichiometric HA has a calcium-to-phosphate ratio of 1.67, and unit cell dimensions of a=b=9.432Å and c=6.881Å. The structure of an HA unit cell is shown below.
Figure 1. The HA structure viewed along the c-axis. The yellow polyhedrons represent the phosphate groups.1
The brittleness of HA can be understood by examining the nature of the chemical bonding in HA. Charge density mapping using DFT calculations and the local density approximation have shown the strong ionic character of bonding between the phosphate groups and the hydroxyl groups and calcium ions.7 The ionic interaction between the groups in HA is responsible for the material's brittle behavior.
Cation Substitutions in HA__
Substitutions can occur in HA for the calcium ions, the phosphate groups, or the hydroxyl groups. It is assumed that cations substitute into the lattice at calcium sites. Although there is a large quantity of experimental data regarding cation substitution in HA there is a limited understanding of the mechanisms of substitution or the exact locations of the substituted ions in the HA structure. The cation exchange properties of HA are important not only in biomaterials, but also for waste management and catalysis applications. Some cations that can be substituted into HA include zinc, magnesium, strontium, lanthanum, cadmium, lead, copper, and iron. Materials properties of HA including morphology, lattice parameters, stability, mechanical properties, and magnetic properties are affected by the incorporation of impurity cations.
Ca(1) and Ca(2) sites
One of the main complications in determining the location of cationic substitutions based only on experimental data is that the calcium ions in HA occur in two distinct sites, Ca(1) and Ca(2). There are four Ca(1) sites per unit cell, located at approximate unit cell heights of 0 and ½. There are six Ca(2) sites, located at approximate unit cell heights of ¼ and ¾. 2 The Ca(1) ions lie along a line parallel to the c-axis with hydroxyl groups in a ratio of 2:1. Ca(1) ions are connected to each other above and below by three shared oxygen ions, resulting in a “Ca(1) channel”. 3
Figure 2. The structure of the Ca(1) channel. 3
The Ca(2) ions each form triangles with two hydroxyl groups, and these triangles are perpendicular to the c-axis. This scheme forms an “OH channel”.
Figure 3. The structure of the OH channel. 3
The phosphate bonding to calcium ions is dependent on the oxygen coordination numbers, but it phosphate groups are linked by either two or three calcium ions. The Ca(1) and Ca(2) sites are compared in Figure 4 below.
Figure 4. a) HA structure viewed along the c-axis. b,c) Ca(2) d,e) Ca(1) 4
Case Study 1: Zinc
Zinc incorporation into HA may be interesting and useful because of the role zinc plays in the human body. Zinc occurs naturally in the human body and has functions in enzyme regulation, cell division, and bone formation. Zinc releasing calcium phosphate materials have been shown to stimulate bone growth, making zinc substituted HA attractive for tissue engineering and biomedical implant applications. Studying zinc substitution into HA is complicated by the fact that not only can zinc potentially substitute into two different calcium sites, but zinc can occur in multiple coordination environments.
Tang et al examined the local coordination structure of zinc substituted into HA using DFT5. They also performed an experimental study of zinc substituted HA. Zinc was incorporated into HA during a wet synthesis procedure. X-ray diffraction (XRD) and X-ray absorption near edge structure spectroscopy (XANES) were used to gather experimental information on zinc substituted HA. The XRD patterns for each sample showed peaks consistent with pure HA indicating that zinc substituted directly into the lattice and no secondary phases were formed. XANES spectra for each sample showed identical features, indicating a single dominant coordination environment. In fact, the XANES spectra were consistent with zinc occurring in a tetrahedral coordination environment. Previous experimental studies had shown that (Ca+Zn)/P=1.67, which indicated zinc must substituted into the calcium sites of the HA lattice.
DFT calculations were then used to predict the most stable structure of zinc substituted HA. CASTEP DFT code was used with the generalized gradient approximation (GGA) and the PBE exchange-correlation potential. The pure HA unit cell was determined first, and the resulting lattice parameters of a=b=9.488Å and c=6.849Å were within 1% of experimentally determined lattice parameter values. DFT calculations were then done for zinc substitution into each of the 10 Ca sites in the unit cell, although it is assumed that all Ca(1) sites would be identical as would all Ca(2) sites.
Formation energies for each substitution were calculated using the equation:
EZnHA and EHA values came directly from DFT calculations. All calculations were done at 0K. Results showed that the lowest formation energy occurred for zinc in a Ca(2) site, with its value being 4.636 eV. The highest formation energy, 4.940 eV, occurred at a Ca(1) site. All Ca(2) site energies were smaller than all Ca(1) site energies and all were within a small enough energy range (0.013 eV) to be considered equivalent. Thus, zinc substitution into Ca(2) sites is energetically favored.
The figure below shows the ideal structure for zinc substituted HA. Zinc occurs in tetrahedral coordination, and bonds to one hydroxyl group and three adjacent phosphate groups. The lattice parameter along the a-direction shrinks to 9.319Å.
Figure 5. a) Zinc incorporation into a Ca(2) site in the HA unit cell. B) Local coordination of Zn in HA. 5
Although it was determined that Ca(2) substitution is energetically favorable over Ca(1) substitution, both substitutions are energetically unfavorable (endothermic). In addition, it is unclear how cations choose between Ca(1) and Ca(2) sites. Clearly, although the structure of zinc substituted HA can be well described, the mechanism of this substitution needs to be further researched.
Case Study 2: Lead
Lead substitution in HA is interesting from the point of view of understanding lead uptake and retention in bone during lead poisoning. In addition, the ability of HA to trap lead may lend itself to waste management based applications.
Ellis et al combined experimental and theoretical studies to examine lead substitution in HA.4 DFT calculations were done using the planewave-pseudopotential approach in VASP code. The generalized gradient approximation (GGA) was used throughout. An embedded c luster approach was used for clusters containing 48-105 atoms. Bulk unsubstituted unit cell parameters were calculated and had good agreement with experimental values. It was calculated that a=b=9.560Å and c=6.863Å. Bulk parameters were also computed for the case where all Ca atoms are replaced by lead (PbHA), and they were found to be a=b=10.063Å and c=7.455Å. These also matched well with experimentally determined values (a=b=9.86Å and c=7.42Å).
Ellis et al considered the effect that local ordering of OH groups within the lattice would have on Ca sites before considering lead cation substitution into Ca sites. On large scale examination Oh groups can be considered disordered, but based on first-principal computations done by deLeeuw it was seen that on an atomic length scale local ordering of OH groups matters. Alignment of OH groups into chains along the c-axis results in reduced symmetry which effects the Ca(1) groups. Therefore, in Ellis’s calculations, lead cations could substitute into Ca(1a), Ca(1b), or Ca(2) sites.
Initially calculations were conducted on a single unit cell of HA with a single Pb2+ cation substitution. These calculations showed an energetic preference for substitution at the Ca(2) site. It is interesting to note, however, that the energy difference between the Ca(1a) and Ca(1b) sites was very large. The energetic preference for Ca(2) substitution compared to Ca(1a) was 0.035 eV and compared to Ca(1b) it was shown to be 0.102 eV. To verify this result using a more dilute substitution, the calculations were re-done using a 1x1x2 supercell. In this set of calculations, the Ca(2) substitution site’s energetic favorability was confirmed.
Because Ca(2) substitution is favorable, it is interesting to further examine the effect of substitutions at this location. Excess energy of PbxCa1-x HA structure as compared to pure HA and PbHA were calculated using the equation:
Values of x ranging from 0-1 were used, with the assumption that up to a value of 6 the Ca(2) site only would be occupied by lead. Various orientations of lead on Ca(2) sites were considered, as shown below.
Figure 6. Orientation of lead in Ca(2) sites on one Ca(2) triangle relative to the other.4
The resulting excess energy calculations are summarized below in Table 1 and in Figure 7.
Figure 7. Excess energy as a function of composition and neighbor conformation phase diagram.4
The configurations considered were only generated within a single unit cell, so more stable configurations may exist in larger supercells, but results suggest that from 0-60 atomic % substitution excess energies are all positive. These compositions are then assumed to be unstable with respect to dissociation into HA and PbHA. Furthur calculations, which took into account mixed configurations of Ca(1) and Ca(2) site substitutions resulted in the conclusion that lead exclusively occupies the Ca(2) sublattice up to 40 atomic %, and mixed configurations occur at 50 and 60%.
Lead-substituted HA (30% substitution) was synthesized using a wet synthesis approach and characterized using several techniques. Experimental results were compared to theoretical findings. Rietvald analysis of XRD patterns suggested that lead mainly occupied the Ca(2) sites (about 85% prevalence) and the lattice parameters were measured to be a=b= 9.5591Å and c=6.9722Å. Inductively coupled plasma optical emission spectroscop (ICP-OES), X-ray absorption (XANES and EXAFS), and Fourier Transform Infrared Reflectance Spectroscopy (FTIR) were also used to characterize the sample. It was concluded that the experimental data was not sufficient to determine the distribution of lead over the Ca(2) sites, but it was confirmed that Ca(2) site substitution was preferable over Ca(1) site.
Case Study 3: Beyond Bulk Substitutions
Many theoretical papers discuss ion substitutions on HA surface, or near-surface regions. Ma and Ellis address the issue of zinc substitution in the HA surface region for a hydrated HA surface using DFT. 6 Both experiments and calculations have shown that the (0 0 0 1) surface of HA is the dominant surface with respect to both vacuum and an aqueous environment. Ma and Ellis use DFT to study the hydration of this surface and the substitution of zinc for calcium at this surface. The case of the hydrated surface would be applicable for both biomedical conditions and for cases of ion substitution via exchange between solid HA and a surrounding cation solution.
DFT calculations using the generalized gradient approximation were first used to determine HA bulk lattice parameters. The parameters were found to be a=b=9.42Å and c=6.87Å, which were in good agreement with experimental values. 2x2x1 HA slabs were then constructed with different terminations and relaxed to determine which slab was the most stable. Assumptions used when determining the most stably-terminated slab were that each surface only has one type of termination and that phosphate groups remain intact. It was found that the slab in which the termination was a single Ca(1) atom per unit cell was the most energetically favorable, by a minimum of 1.68 eV and a maximum of 13.03 eV when compared to other slabs. This slab was selected for use in all following DFT calculations.
To determine the structure of the hydrated surface water molecules were added to the slab one at a time. Although geometrical measurements indicate that about 15 water molecules could fit on the surface of a slab, a maximum of 6 water molecules was used in this study. The figure below shows the resulting configurations after hydration for the HA (0 0 0 1) single Ca(1)-terminated surface. Because this consideration of Ma and Ellis’s work is mainly focused on the results of zinc substitution, the hydration results will be briefly summarized below Figure 8 without going into detail.
Figure 8. Hydration of surface with 1 (a) – 6 (f) water molecules adsorbed6.
DFT surface relaxation during surface hydration results:
-No water dissociation is detected
- Some O ions in surface phosphate groups are protonated by association with water
- Surface OH groups in hydroxyl channels remain immune to water molecules
The geometry upon substitution of zinc for surface calcium was calculated for the surface Ca(1) site as well as for one of the three surface Ca(2) sites on an unhydrated surface. The results are shown below. It was seen that the Zn(1)-M bonds shrink as compared to Ca(1)-M bonds. (M denoting the ions neighbors), but the zinc ion does not move from the original Ca(1) site. For zinc on the Ca(2) site it is seen that zinc moves about 0.5Å toward the central hydroxyl group with minimal shrinkage in bond lengths. Electronic structure was calculated using DFT cluster method and it was found that in both substitution cases zinc was less ionic than calcium.
Figure 9. Zinc substitution on unhydrated HA (0 0 0 1) surface. a) Ca(1), side view b) Ca(1), top view c) Ca(1), top view 6
Energies per unit cell for substitutions with the unhydrated surface were also calculated using the following equations:
Etotal = Esystem – Eisolated ions
Esub= Etotal ZnHA – Etotal HA
Ead = Etotal ZnHA – Etotal vacancy HA
Negative Etotal indicates a stable cluster and negative Esub and Ead values indicate thermodynamic favorability. As shown in Table 2 below, ion substitution in both cases of Ca substitution is endothermic, but zinc substitution for both vacancy sites is exothermic.
The calculations were repeated using the hydrated surface. These results are summarized in Table 3. It is shown that zinc substitution for calcium at the Ca(2) site is preferred.
Some guidelines have been proposed for determining which calcium site will be occupied during cation substitutions in bulk. It has been suggested that divalent cations larger than Ca2+ can be assumed to preferentially occupy Ca(2) sites and smaller cations will occupy Ca(1) sites. It is also suggested that electronegativity will also play a role in which calcium site will be preferentially occupied. However, Me and Ellis summarized some results for which these rules of ionic radius and electronegativity fail to correctly predict the correct calcium site for occupation by the substituting cation. In the table below, it is shown that only lead follows these ionic radius and electronegativity “rules”.
Table 4. 6
Although mechanisms for cation substitution and methods for predicting which calcium site will be occupied are unclear, it has been shown by several different DFT studies that by combining DFT computations with experimental results the structure of cation substituted hydroxyapatites can be determined.
Further investigation clearly needs to be done to determine the mechanism(s) of cation substitutions in HA. However, the ability to predict the structure of substituted HA is significant. Now that substituted structures are known they can be used in further computational studies. Unit cells with the equilibrium substituted structures can be built and used in DFT calculations to determine the effect of cation substitutions on HA materials properties. In this way substituted HA materials can be screened for use in various applications based on mechanical strength, magnetic properties, and other key material properties. Because it can be difficult and time consuming to determine which conditions will result in the desired substitution experimentally, and the preparation of HA powders can be time consuming, using DFT to screen materials before synthesizing them can save a lot of experimental time and effort which might otherwise be wasted synthesizing a substituted HA that may not even have appropriate properties for the desired application. An example of how DFT could be used to screen materials is described for iron substituted HA.
DFT Study on the Magnetic Properties of Iron-Substituted HA
Iron substituted HA has been shown to have paramagnetic properties. However, incorporating iron into the HA lattice effects the crystal structure and mechanical properties at high levels of iron substitution. It would be useful to determine the lowest amount of iron incorporation that will yield the desired magnetic properties computationally before starting experimental work.
First, the structure of iron substituted HA would need to be determined for iron of the appropriate valence. After determining quantitative values for the desired magnetic properties, DFT calculations could be done with incrementally increasing amounts of iron substituting for calcium in the HA lattice. In this way it would be possible to systematically search for the lowest amount of iron substitution which would result in the necessary magnetic properties.
1] Snyders R, et al. (2007) Experimental and ab initio study of the mechanical properties of hydroxyapatite. Applied Physics Letters 90, 193902.
2] Tamm T, Peld M. (2006) Computational study of cation substitutions in apatites. Journal of Solid State Chemistry 179, 1581-1587.
3] Terra J, et al. (2002) Characterization of electronic structure and bonding in hydroxyapatite: Zn substitution for Ca. Philosophical Magazine A 82:11, 2357-2377.
4] Ellis DE, et al. (2006) A theoretical and experimental study of lead substitution in calcium hydroxyapatite. Phys Chem Chem Phys 8, 967-976.
5] Tang Y, et al. (2009) Zinc incorporation into hydroxylapatite. Biomaterials 30, 2864-2872.
6] Ma X, Ellis DE. (2008) Initial stages of hydration and An substitution/occupation on hydroxyapatite (0 0 0 1) surfaces. Biomaterials 29, 257-265.
7]Louis-Achille V, et al. (1998) Local density calculation of structural and electronic properties for Ca10(PO4)6F2. Computational Materials Science 10, 346-350.