American Mineralogist, Volume 95, pages 1224–1236, 2010
Time-resolved in situ studies of apatite formation in aqueous solutions
Olaf BOrkiewicz,1,* JOhn rakOvan,1 and christOpher l. cahill2
1
Department of Geology, Miami University, 114 Shideler Hall, Oxford, Ohio 45056, U.S.A.
Department of Chemistry, The George Washington University, 725 21st Street NW, Washington, D.C. 20052, U.S.A.
2
aBstract
Formation of hydroxylapatite through the precipitation and evolution of calcium phosphate
precursor phases under varying conditions of temperature (25–90 °C), pH (6.5–9.0), and calcium to
phosphorus ratio (1.0, 1.33, 1.5, and 1.67) comparable to those found in many sediments and soils
were studied. The products of low-temperature precipitation were analyzed by ex situ X-ray diffraction and SEM, as well as time-resolved in situ synchrotron X-ray diffraction. Rietveld refinement was
used for quantitative evaluation of relative abundances during phase evolution. The results of ex situ
investigations conducted at ambient temperature and near-neutral pH indicate formation of amorphous
calcium phosphate, which over the course of experiments transforms to brushite and ultimately hydroxylapatite. The results of in situ X-ray diffraction experiments suggest a more complex pathway
of phase development under the same conditions. Some of the initially formed amorphous calcium
phosphate and/or crystalline brushite transformed to octacalcium phosphate. In the later stage of the
reactions, octacalcium phosphate transforms quite rapidly to hydroxylapatite. This is accompanied or
followed by the transformation of the remaining brushite to monetite. Hydroxylapatite and monetite
coexist in the sample throughout the remainder of the experiments. In contrast to the near-neutral pH
experiments, the results from ex situ and in situ diffraction investigations performed at higher pH yield
similar results. The precipitate formed in the initial stages in both types of experiments was identified
as amorphous calcium phosphate, which over the course of the reaction quite rapidly transformed to
hydroxylapatite without any apparent intermediate phases. This is the first application of time-resolved
in situ synchrotron X-ray diffraction to precipitation reactions in the Ca(OH)2-H3PO4-H2O system. The
results indicate that precursors are likely to occur during the natural or induced (e.g., with application
of Ca+PO4 amendments) formation of hydroxylapatite in many sedimentary environments.
Keywords: Calcium phosphates, precursor phases, hydroxylapatite, time-resolved in situ X-ray
diffraction, synchrotron
intrOductiOn
Calcium phosphates are of great significance in a range of
fields including geology, chemistry, biology, medicine, and
materials science. Among these compounds apatite, with the
ideal chemistry Ca10(PO4)6(OH,F,Cl)2, has gained considerable
attention owing to its many functional properties that allow for
a wide range of applications such as hard tissue analogues, catalysts, liquid-chromatographic columns, phosphors, and chemical
sensors. Recently there has been interest in apatite as a metal
sequestration agent in water treatment, in contaminated soil remediation, and in radioactive waste confinement (Bostick et al.
1999; Chen et al. 1997a, 1997b; Ewing 1999, 2001; Ewing and
Wang 2001, 2002). The unique crystal structure and chemistry of
apatite allow for numerous substitutions of both metal cations and
anionic complexes (Hughes and Rakovan 2002; Pan and Fleet
2002; Rakovan and Hughes 2000). High stability with respect
to pH and temperature, low solubility (Elliott 1994; Hughes and
Rakovan 2002; Rakovan 2002), high affinity for many substituent elements and high sorption capacity make it an excellent
candidate for heavy metal stabilization (Arey et al. 1999; Chen
* E-mail: [email protected]
0003-004X/10/0809–1224$05.00/DOI: 10.2138/am.2010.3168
et al. 1997a; Fuller et al. 2002; Jeanjean et al. 1995; Laperche et
al. 1997, 1996; Ma et al. 1995; Mandjiny et al. 1998; Manecki
et al. 2000a, 2000b; Miyake et al. 1986; Perrone et al. 2001;
Suzuki et al. 1981, 1982, 1983, 1984, 1985; Takeuchi and Arai
1990; Traina and Laperche 1999; Xu et al. 1994). New strategies
involving use of mineral formation in contaminated soils and
sediments, referred to here as metal stabilization by phosphate
amendment, proceed by precipitation and incorporation of metal
ions into mineral structures, most importantly apatite. The idea
of this application is formation of a co-precipitated mineral that
will not dissolve or leach over a long period of time. After incorporation into mineral structures, metals are far less dispersible,
are less bioavailable and thus pose a substantially reduced health
and environmental risk.
From biological studies of hydroxylapatite formation, it has
been found that at low pressure and temperature the formation
of hydroxylapatite is often preceded by the precipitation of other,
less stable, phosphate minerals that over time transform to apatite
(Heughebaert and Nancollas 1984a, 1984b; Hohl et al. 1982;
Rakovan 2002). Numerous studies designed to mimic conditions
found in biological systems report formation of different precursor
phases depending on the experimental conditions such as calcium
and phosphorous concentrations, temperature, ionic strength,
1224
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BORkIEWICz ET AL.: APATITE FORMATION PATHWAyS
solution pH, and degree of supersaturation (Derooij et al. 1984;
Lanzalaco et al. 1984; Nancollas and Barone 1976; Rakovan 2002;
Salimi et al. 1984; Wang and Nancollas 2008). The list of observed precursors includes amorphous calcium phosphate (ACP),
dicalcium phosphate dehydrate (DCPD) = brushite, octacalcium
phosphate (OCP), tricalcium phosphate (TCP), and dicalcium
phosphate anhydrate (DCPA) = monetite (Fig. 1).
The experimental conditions in many of the aforementioned
studies are close to those found in pore waters of many soil and
sediment environments. Most soil pHs vary from 5 to 9, although
the range of known pHs is from 2 to 11 (Birkeland 1999). Rainfall
pH values lie within the range from 3.0 to 9.8, but on average are
slightly acidic with pH of 5.7 (Hillel 2007). Soil pH below 5.7 is
caused mainly by the formation of carbonic acid within the soil
created by the combination of CO2 and water. Concentrations of
CO2 more than 10× greater than atmospheric values are feasible
due to respiration by plant roots and by microorganisms (Brook
et al. 1983). The temperature encountered in soil and sediment
environments ranges from below freezing to around 60 °C, and
depends on the geographic setting of the environment.
Considering the similarities between the biological conditions described above and the near Earth-surface conditions,
one should expect that the formation of calcium phosphate
precursor phases will also take place in the natural formation
of sedimentary apatites (e.g., phosphorites) as well as during in
situ metal stabilization by phosphate amendments. In the latter
case, precursors to apatite may significantly influence the fate
and transport of contaminant species in treated soils and sediments. Compatibility of the contaminants with precursor phases
and behavior of these species during structural transformation
of precursors to apatite may ultimately control the efficiency of
the sequestration and stabilization.
To date, efforts to characterize crystallization pathways (in
vivo studies) have mainly relied on ex situ investigations. While
studies of this kind offer insight into the nature and structure
of the phases formed during the course of crystallization, they
provide incomplete details of phase development sequences.
Even with a perfectly designed and executed sampling scheme,
one must be concerned with how ex situ analysis may affect
precipitates once removed from the solution. This study is an
effort to extend the application of in situ experimental techniques
to Ca(OH)2-H3PO4-H2O system. We report results on phase
formation and development during crystal growth of hydroxylapatite from solution employing both ex situ investigation and
in situ time-resolved powder X-ray diffraction using synchrotron
radiation. Basic phase identification of the precipitates was
complemented with Rietveld structural refinement of time-resolved data sets, which provided quantitative analysis (relative
abundances) of crystalline phases throughout the experiments.
This study is part of the multifaceted investigation focused on
the role of calcium phosphate precursor phases on the uptake of
heavy metals and radionuclides for the purpose of environmental
remediation. The results, however, also have potential implications for the formation of biological apatites, as well as natural
sedimentary apatites.
ex situ x-ray diffractiOn
Methods
figure 1. Calculated solubility isotherms of calcium phosphate
phases in the system Ca(OH)2-H3PO4-H2O at 37 °C. Phases present
on the diagram: hydroxylapatite, HAp [Ca10(PO4)6(OH)2]; tricalcium
phosphate, TCP [Ca3(PO4)2]; octacalcium phosphate, OCP [Ca4H(PO4)3];
dicalcium phosphate anhydrous, DCPA (monetite) [CaHPO 4]; and
dicalcium phosphate dihydrate, DCPD (brushite) [CaHPO4·2H2O];
redrawn from Elliot (1994).
To investigate the formation and evolution of calcium phosphates under
conditions similar to those found in soils and sediments, a series of 10 ex situ
solution growth experiments was performed (see experimental details in Table
1). All experiments (ES-1 to ES-10) were reproduced in triplicate with consistent
results. In general, experiments can be divided into those conducted at near-neutral
pH and those at high pH. Each of these groups consists of experiments carried
out at three different temperatures: 25, 45, and 90 °C. Two starting solutions of
(A) 0.1 mol/L calcium acetate Ca(CH3COO)2·H2O and (B) 0.06 mol/L ammonium
phosphate (NH4)2HPO4 were prepared from the respective analytical-reagent
grade solids (Fisher Scientific) dissolved in water purified using a NanoPure
filtering system. The experiments were carried out by instantaneous mixing of
150 mL each of solutions A and B. The pH was measured at ambient temperature
with a glass combination electrode (Metrohm) calibrated against NIST-traceable
buffer solutions (Fisher Scientific) and was found to be ~7.2 and 8.0 for the
abovementioned calcium- and phosphate-containing solutions, respectively. No
attempts to alter the pH were made for the experiments intended to be performed
Table 1. Experimental details of ex situ X-ray diffraction investigation
Sample ID
pH
Ca/P
Mixing
T (°C)
Duration (days)
ES-1
6.5
1.67
Instantaneous
25
7
ES-2
6.5
1.67
Instantaneous
45
7
ES-3
6.5
1.67
Instantaneous
90
7
ES-4
6.5
1.67
Drop-wise
25
terminated after mixing
ES-5
6.5
1.67
Drop-wise
45
terminated after mixing
ES-6
6.5
1.67
Drop-wise
90
terminated after mixing
ES-7
9.0
1.67
Instantaneous
25
7
ES-8
9.0
1.67
Instantaneous
45
7
ES-9
9.0
1.67
Instantaneous
90
7
ES-10
9.0
1.67
Drop-wise
90
terminated after mixing
Note: ACP = amorphous calcium phosphate, B = brushite, HAP = hydroxylapatite.
Initial precipitate
ACP+B*
B+HAP
HAP
–
–
–
ACP
ACP
ACP
–
Intermediate phases
ACP+B*
B+HAP
HAP
–
–
–
HAP
HAP
HAP
–
Final products
B
HAP+B
HAP
B+ACP
B+HAP
HAP
HAP
HAP
HAP
HAP
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BORkIEWICz ET AL.: APATITE FORMATION PATHWAyS
at near-neutral conditions. The pH of solutions directly after mixing A and B was
6.3 and dropped to the value of 5.7 over the duration of the experiment. In the
second set of experiments, the pH of both starting solutions was set to 9.0 using
1 M NH4OH prior to mixing and was kept at this value throughout the duration of
the experiment by autotitration with a Metrohm 842 Titrando/846 Dosino chemstat. For the elevated-temperature experiments starting solutions were brought to
the desired temperature (45 or 90 °C) prior to mixing and kept at that temperature
throughout the experiment. Mixing of the calcium and phosphate solutions resulted
in the immediate formation of a precipitate, which was sampled shortly after mixing, dried overnight at 60 °C and analyzed by X-ray diffraction. The remaining
slurry was stirred at 300 rpm for 7 days. Aliquots of the precipitate were collected
periodically, dried overnight at 80 °C, and analyzed by powder X-ray diffraction.
In addition to instantaneous mixing of starting solutions, a series of experiments was
conducted where solution A was added to solution B in a drop-wise fashion. These
experiments were carried out at near-neutral pH and at three different temperatures:
25, 45, and 90 °C. High-pH experiments with drop-wise addition were conducted
at 90 °C only. Each experiment was terminated shortly after the addition of 150
mL of A was finished. The resulting precipitate was collected, dried overnight at
room temperature, and analyzed by powder X-ray diffraction.
X-ray diffraction analyses of the dry samples were carried out on a Scintag
Pad-X1 powder autodiffractometer with Bragg-Brentano geometry using Ni-filtered
CuKα radiation (1500 W sealed tube with a Cu target at 45 kV and 35 mA). The
powder data were collected at ambient temperature in the range of 2θ = 4–60° in
the step mode with a step of 0.02° and a counting time of 1 s. Phase identification
was performed with the X-ray diffraction analytical software Jade 6.0 by Materials Data, Inc. (MDI) using the Powder Diffraction File (PDF). PDF card entry no.
09-0077 was used as a reference for brushite, no. 09-0080 for monetite, no. 09-0432
for hydroxylapatite, and no. 44-0778 for octacalcium phosphate.
SEM analyses
The aliquots of solids from ex situ experiments (as well as
the final products of the in situ experiments) were studied with
scanning electron microscopy to determine the size and shape of
the precipitates. In so doing, all samples were dried in air, crushed
using mortar and pestle and homogenized. A small aliquot of each
powder was attached to a double-sided sticky carbon tab, which
was glued to an aluminum sample stub. Secondary electron images of dry samples were obtained using a field emission zeiss
Supra 35VP microscope set at 20 kV acceleration voltage under
variable pressure conditions, allowing for analyses of uncoated
samples with significantly limited or completely eliminated
sample charging.
Results
Mixing of the Ca2+ and PO43– solutions at different temperatures resulted in the formation of various initial precipitates
(Table 1). The initial precipitate formed at 25 °C (ES-1) was a
mixture of predominantly amorphous solid (amorphous calcium
phosphate [ACP]) and small amounts of brushite. The diffraction
pattern exhibited very low intensity peaks superimposed on a
broad hump indicative of amorphous material (Fig. 2a). Over
the course of 7 days of stirring, much of the amorphous phase
transformed to brushite. The presence of three weak and broad
diffraction peaks between 2θ = 31–34° may also indicate the
presence of poorly crystalline apatite in the sample (Fig. 2a).
The 45 °C (ES-2, Table 2) experiment resulted in the formation of a mixture of mostly brushite, of relatively high crystallinity, judging by the intensity and width of the diffraction peaks (i.e.
FWHM of 0.13 for 020 reflection at 2θ = 11.7°) (Fig. 2b), and
possibly a small amount of poorly crystalline hydroxylapatite.
The hydroxylapatite identification is based on the presence of a
peak at 2θ = 26° and a broad diffraction feature in the 2θ = 31°
– 34° region. After 3 days of solution stirring hydroxylapatite
figure 2. Diffraction patterns obtained during low-pH ex situ
experiments ES-1 (a), ES-2 (b), and ES-3 (c). Bottom pattern represents
the initial precipitate, upper the final product of the reactions; B =
brushite, H = hydroxylapatite.
is clearly identifiable, as more characteristic peaks can be seen
in the diffractogram and the doublet of diffraction peaks at 2θ
= 31° becomes partially resolved. Brushite, however, remains
the dominant phase of this sample. After 7 days, however,
hydroxylapatite is the only phase detected by X-ray diffraction
(Fig. 2b). In a similar experiment conducted at 90 °C (ES-3,
BORkIEWICz ET AL.: APATITE FORMATION PATHWAyS
Table 2. Experimental details of in situ X-ray diffraction investigations
carried out at pH = 6.5
Sample pH Ca/P
T (°C) Duration
Initial
Intermediate Final
ID
(h)
precipitate
phases
products
IS-1
6.5 1.67 Ambient
8
B+ACP
B+ACP
B+ACP
IS-2
6.5 1.67
45
8
B+ACP
B+M
M+HAP
IS-3
6.5 1.67
60
8
B+ACP
B+M
M+HAP
IS-4
6.5 1.67
85
8
B+ACP
B+M
M+HAP
IS-5
6.5 1.50
85
8
B+ACP
B+M
M+HAP
IS-6
6.5 1.00
85
8
B+ACP
B+M
M+HAP
IS-7
6.5 1.33
85
8
B+ACP
B+M
HAP+M
Note: ACP = amorphous calcium phosphate, B = brushite, HAP = hydroxylapatite,
M = monetite.
Table 1), hydroxylapatite of low crystallinity is the first phase
to form (Fig. 2c). Hydroxylapatite is the only phase present in
the sample throughout the duration of the experiment, but the
crystallinity of the sample improves significantly over the course
of 5 days at 90 °C (Fig. 2c).
The results of the experiments carried out with the drop-wise
addition of calcium-bearing reagent at 25 and 45 °C are consistent
with those described for the instantaneous-mixing experiments
(Table 1). For the experiments at 90 °C (ES-6), however, the
decrease in the rate of reagent mixing appears to have drastically
influenced the crystallinity of the resulting precipitate; drop-wise
1227
addition resulted in the precipitation of relatively well crystalline
apatite in the very initial stages of the reaction.
ACP was the initial precipitate in the experiments conducted
at pH = 9, at ambient temperature, with instantaneous mixing
of the starting solutions (ES-7, Table 1). Over the course of the
experiment, ACP transformed to hydroxylapatite. Although the
diffraction data are not shown, no apparent intermediate phase(s)
were detected.
Poorly crystalline hydroxylapatite was the initial precipitate
after the mixing of the starting solutions (pH = 9) at 45 and 90
°C, ES-8 and ES-9 (Table 1), respectively. The crystallinity of the
precipitate improved over the course of the experiment, although
to a lesser extent than was observed for experiments conducted
at 90 °C and near-neutral conditions. An experiment carried out
at 90 °C, pH = 9, and calcium and phosphate concentrations used
previously, where the calcium-bearing reagent was added to the
phosphate solution in a drop-wise fashion yielded hydroxylapatite of high-crystallinity in the early stage of experiment, as was
observed for near-neutral pH experiment.
Scanning electron micrographs of precipitates formed during
ex situ experiments are presented in Figure 3. Micrographs show
three different phases: Figure 3a shows the X-ray amorphous
precipitate formed in the early stages of the ES-1 (25 °C); Figure
figure 3. Scanning electron micrographs of the products of ex situ experiments: (a) amorphous calcium phosphate, (b) brushite, and (c and
d) hydroxylapatite.
1228
BORkIEWICz ET AL.: APATITE FORMATION PATHWAyS
3b shows brushite formed in the early stages of ES-2 (45 °C);
and Figures 3c–3d display hydroxylapatite, final product of the
experiment ES-3 (Table 1). The morphology of the precipitate
formed in the low-temperature experiment (Fig. 3a) is difficult to
define, yet the individual crystallites appear to be of micrometer
dimensions. The micrograph of brushite reveals characteristic
tabular habit of the crystals. The size varies from submicrometer
to several micrometers. Somewhat unusual and rather interesting results were obtained during analysis of the hydroxylapatite
samples. In addition to prismatic, needle-like crystals, crystals
of platy habit and various sizes (submicrometer to tens of micrometers) are visible on the micrograph, indicating bimodal
morphology of the precipitates. Very often those crystals form
spherical aggregates of intergrown crystals (Fig. 3d).
in situ x-ray diffractiOn and rietveld
refinement
Methods
The steps for preparing the samples prior to in situ X-ray data collection were
identical to the sample preparation procedure for the ex situ quick-mixing experiments (Table 1). Two starting solutions of (A) calcium acetate Ca(CH3COO)2·H2O
and (B) ammonium phosphate [(NH4)2HPO4] were prepared from the respective
analytical-reagent grade solids (Fisher Scientific) and distilled water. Two sets of
experiments at two different pH conditions were conducted; the first at near-neutral
pH (5–6) and the second at high pH (9–10) (see Tables 2 and 3 for experimental
details). For high-pH experiments, the pH of the starting solutions was adjusted
to the desired value with 1 M NaOH solution. The ratio of calcium to phosphorus
(Ca/P) in the starting solutions was adjusted to different values for different
experiments. These covered a range of Ca/P ratios, corresponding to the molar
ratios of the respective ions found in phases proposed previously in literature as
precursors to hydroxylapatite: brushite (ratio of 1.0), OCP (1.33), TCP (1.5), and
in hydroxylapatite (1.67). This was achieved by fixing the concentration of the
Ca-bearing solution and varying the concentration of phosphate between 0.06
and 1.0 mol/L. In each experiment, 10 mL of starting solution (A) and 10 mL of
starting solution (B) were mixed at ambient temperature with vigorous stirring. To
maintain the desired pH in the growth solution, a few drops of NaOH was added
shortly after mixing in the case of high-pH experiments. The resulting precipitate
was partially vacuum-filtered through a Millipore 0.22 µm filter and the sample
slurry was loaded into the reaction cell (described below) and analyzed within ~10
min of the initial precipitation.
Apparatus
Two different synchrotron sources were used to study the
formation and evolution of solid phases during low-temperature
calcium phosphate formation. Time-resolved capabilities of
these beamlines, along with high flux, brightness, and collimation of the incident radiation, compared to conventional
sealed tube sources, proved to be of particular significance
in the study of formation and evolution of metastable, poorly
crystalline and/or nano-sized precursor phases. The first set
of experiments was conducted at beamline X7B of the National Synchrotron Light Source (NSLS), Brookhaven National
Laboratory. Monochromatic radiation of 0.922 Å was selected
Table 3. Experimental details of in situ X-ray diffraction investigations
carried out at pH = 9.0
Sample pH Ca/P
T (°C) Duration
Initial
Intermediate
Final
ID
(h)
precipitate
phases
products
IS-8
9.0 1.67
90
8
ACP
HAP
HAP
IS-9
9.0 1.33
90
8
ACP
HAP
HAP
IS-10
9.0 1.50
90
8
ACP
HAP
HAP
IS-11
9.0 1.00
90
8
ACP
HAP
HAP
Note: ACP = amorphous calcium phosphate, HAP = hydroxylapatite.
from incident white radiation via 2 Si (111) monochromators.
The wavelength was determined from a unit-cell refinement
of LaB6 (NIST SRM660a). The size of the incident beam was
set to be 0.5 × 0.5 mm via two upstream slits. The sample cell
was mounted to a horizontally oriented rotational stage and the
diffracted X-rays were collected as a series of 100 s exposures
by means of a MAR345 full imaging plate (IP) detector with a
built-in scanner for online reading. Data collection proceeded
continuously during the entire course of each experiment.
Temporal resolution of the analyses was ~3 min and included
time needed for erasing, exposing, and reading the IP. Integration of the diffraction rings was performed by FIT2D software
(Hammersley et al. 1996). Time resolution was made possible
as full diffraction patterns collected over the course of an experiment were analyzed and plotted as a function of time via
an in-house-produced Interactive Data Language (IDL) routine.
For the elevated-temperature experiments the sample was heated
from ambient to various temperatures (45, 65, 90, and 110 °C)
by means of a forced-air heater. The temperature was varied via
an Omega controller and monitored with a Chromel-Alumel
thermocouple located at the heater exhaust, ca. 3 mm beneath
the sample cell. The actual sample temperature was determined
by placing an additional thermocouple inside the reaction cell
during calibration runs.
The second set of experiments was conducted at beamline
11 ID-C of the X-ray Operation and Research/Basic Energy
Science Synchrotron Radiation Center (XOR/BESSRC) at the
Advance Photon Source (APS), Argonne National Laboratory.
The monochromatic high-energy photon beam of the wavelength
of 0.10749 Å was selected from the incident beam via a Si (311)
single-crystal monochromator. Diffracted X-rays were collected
by means of a MAR345 full imaging plate (IP) detector. The
temperature of the experiments was controlled and maintained
by means of an Oxford Instruments Cryosystem Cryostream
700 Plus capable of providing external heating of up to 220 °C.
As in the experiments performed at X7B of NSLS, the actual
sample temperature was determined by performing calibration
runs with a thermocouple inside the reaction cell.
All in situ diffraction experiments were performed in a
reaction cell that was custom designed by the authors and built
by the Miami University Instrumentation Laboratory. The cell
consists of a block of aluminum with a window located in the
center and a 3 mm diameter cylindrical post attached to the side
of the block. A sheet of kapton tape is attached to one side of the
cell and slurry containing the initial precipitate is loaded into the
window of the cell. Another sheet of the tape is attached to the
back of the cell to seal the sample holder. Two rubber gaskets,
two aluminum plates, and four bolts with nuts are used to further
improve sealing of the cell. The seal has proven to be effective by
containing water over extended periods of time under elevated
temperatures (up to 210 °C of external heat applied) during test
runs carried out at Miami University and the NSLS.
Processing of individual diffraction patterns and phase
identification was carried out by means of the X-ray diffraction analytical software Jade 6.0 by Materials Data, Inc (MDI)
using the Powder Diffraction File (PDF). The same set of PDF
entries used in the ex situ X-ray diffraction was used for phase
identification with the synchrotron data.
BORkIEWICz ET AL.: APATITE FORMATION PATHWAyS
1229
Rietveld refinements
Kinetic data analysis
Rietveld refinements of selected data sets from in situ
time-resolved experiments at near-neutral pH were performed
with the General Structure Analysis System (GSAS) program
of Larson and von Dreele (1994) using EXPGUI interface by
Toby (2001). The starting structural parameters for brushite
were taken from Schofield et al. (2004), for octacalcium phosphate from Mathew et al. (1988), for monetite from Catti et al.
(1977), and for hydroxylapatite from Hughes et al. (1989). The
diffraction pattern backgrounds were fitted using a first-order
Chebyshev polynomial with 20 to 24 background terms. For
patterns with more complex backgrounds, manual fitting using
a Chebyshev polyniomal with up to 26 terms was employed.
Peak profiles were modeled with a pseudo-Voigt profile function
as parameterized by Thompson et al. (1987) with asymmetry
corrections from Finger et al. (1994) and microstrain anisotropic
broadening terms from Stephens (1999). The main goal of the
refinements was not to determine precise atomic and thermal displacement parameters for phases under consideration, but rather
to conduct quantitative analyses of the samples’ mineralogical
composition (proportion of the different crystalline phases) at
various stages of the reaction. Furthermore, the Rietveld method
was used to examine potential changes in unit-cell dimensions
throughout the duration of the experiment and phase evolution.
The fraction of amorphous material in the precipitates was not
refined in the Rietveld analyses because of the ambiguity of the
contribution of water to the background of the diffraction patterns. The background, the peak profile, and unit-cell parameters
of all phases, as well as the relative crystalline phase fractions,
were allowed to vary. Structural parameters (i.e., atomic positions) were allowed to vary only in case of brushite and only in
instances where it was the dominant phase with well-defined
diffraction peaks and where there was significant discrepancy
in intensity between calculated and observed peaks. Attempts to
open atomic position and thermal displacement parameters for
other phases resulted in refinement failure. The March-Dollase
model for preferred orientation was used in all refinements, but
differed little from unity.
Over 100 Rietveld refinement analyses were performed in
an attempt to illustrate changes in the crystalline phase content
of the sample during various experiments. Although the value
of χ2 varied for different analyses and experiments, it remained
in the range of 1.001–7.590 with Rwp varying between 0.01 and
0.05 and R(F2) between 0.011 and 0.154. The final observed,
calculated, and difference patterns for representative samples
from three different experiments are presented in Figure 4.
The results of the Rietveld refinements of data sets for three
different time-dependent experiments—IS-2, IS-3, and IS-4
(Table 2)—are presented in Figure 5. This figure illustrates
phase evolution and the change in the relative abundance of
phases in the samples at various stages of those experiments.
Results of experiments at three different temperatures at nearneutral pH are shown. Each is representative of all the experiments conducted at similar conditions. Rietveld analysis of the
high-pH experiments were not conducted because of the simple
mineralogical evolutions of those experiments (ACP transforming directly to hydroxylapatite).
An attempt was made to extract quantitative information
about the kinetics of phase evolution in our system at nearneutral pH at three different temperatures (45, 60, and 90 °C)
by employing the nucleation-growth model described by the
Avrami-Erofe’ev Equation 1 (Avrami 1939, 1940, 1941),
α = 1 – exp{–[k(t – t0)]n}
(1)
relating the extent of reaction, α, and the reaction time, t, correlated by the rate constant, k and the Avrami exponent, n.
The value of n contains information related to the nucleation
mechanism, growth dimensionality, and reaction mechanism
(Hulbert 1969). The most straightforward and reliable way of
extracting kinetic parameters from a crystallization curve is to
use the Sharp and Hancock method (Hancock and Sharp 1972),
consisting of taking logarithms of the Avrami-Erofe’ev equation,
to give Equation 2:
ln[–ln(1 – α)] = nln(k) + nln(t)
(2)
and plotting ln[–ln(1 – α)] vs. ln(t). If the reaction kinetics conform to Avrami-Erofe’ev nucleation-growth model the plot yields
a straight line, whose slope permits determination of n and the
ln[–ln(1 – α)] intercept allows k to be calculated.
Typically the first step during such analyses consists of
choosing an isolated, non-overlapping, strong peak for each
phase involved in the reaction, selecting a region 1 °2θ above
and below the center of each reflection and calculating a background function and peak profile using an automated Gaussianfitting routine. The value of the extent of reaction (α) at time (t)
for a given reflection hkl is then calculated using α(t) = Ihkl(t)/
Ihkl(max), where Ihkl(t) represents the integrated intensity of the
hkl reflection at time t, and Ihkl(max) is the maximum intensity
of that reflection during the experiment. In the case of our data,
however, due to the severe peak overlap, an increased profile
width, and complex background of the diffraction pattern, this
approach was possible only in the case of brushite and monetite.
The Bragg reflections corresponding to octacalcium phosphate
and hydroxylapatite present in the diffraction patterns either
overlap with each other and coincide with peaks of brushite and/
or monetite or are of too low intensity to allow for a reliable fit.
The integrated peak area of the Bragg reflections for brushite
(020) and monetite (001) was determined using the program
XFIT (Cheary and Coelho 1992). The extent of the reaction for
the transformation has been calculated and the kinetic parameters,
n and k, have been derived using Sharp and Hancock method as
described above. The results, interpretation, and discussion of
the limitation of this kinetic study are offered in the Discussion
section of this manuscript.
results
Near-neutral pH experiments
In all experiments conducted at neutral pH, independent
of the Ca/P ratio, the initial precipitate formed during ex situ
mixing of the starting solution, was identified as mixture of
1230
BORkIEWICz ET AL.: APATITE FORMATION PATHWAyS
ACP and brushite. In the first experiment (IS-1 in Table 2), the
ex situ prepared slurry was loaded into the reaction cell and
analyzed for the duration of 8 h at ambient temperature. During
this time, brushite and ACP are the only phases observed (Fig.
6). The large background hump observed in the pattern is the
result of X-ray scatter off the growth solution and amorphous
phase(s) present in the sample.
To promote transformation of the initial precipitates to
hydroxylapatite, the above experiment was repeated at higher
temperatures (IS-2 in Table 2). After loading the reaction cell
and sealing, the sample was heated to 45 °C over 15 min and
held for 6 h. After ~10 min, the onset of OCP is observed in the
diffraction data. Weak diffraction peaks corresponding to OCP
PDF can be observed in the low-angle range of the diffractogram
(Fig. 7). Rietveld refinement of the corresponding data set also
indicates formation of OCP. Shortly after the appearance of
OCP (15 min into the run), the onset of poorly crystalline hydroxylapatite is observed and the quantity of this phase increases
rapidly thereafter. At the 20 min mark, the sample contains 7
wt% OCP, 30 wt% hydroxylapatite, and 63 wt% brushite. Over
the next 40 min, the sample composition and relative abundance
of phases remain roughly unchanged, although the quantity of
hydroxylapatite increases slightly. At the 1 h mark, the amount
of OCP starts to drop and the phase disappears completely 30
min later. This is accompanied by the increase in hydroxylapatite
a
b
c
figure 4. Final observed (crosses), calculated (solid line), and
difference (lower) patterns for Rietveld refinement of samples from
three different experiments; (a) 55 min mark of IS-02, sample containing
OCP, brushite, and hydroxylapatite; (b) 55 min mark of IS-03, sample
containing brushite and hydroxylapatite; (c) 55 min mark of IS-04,
sample containing monetite and hydroxylapatite.
figure 5. Phase evolution with time for IS-02 (a), IS-03 (b), and
IS-04 (c).
BORkIEWICz ET AL.: APATITE FORMATION PATHWAyS
1231
figure 6. Time-resolved plot of the experiment IS-1. Near-neutral
pH at 25 °C temperature. All peaks present in the diffractogram
correspond to brushite (PDF 09-0077).
figure 7. Time-resolved plot of the experiment IS-2 showing phase
evolution in the system at 45 °C; B = brushite, M = monetite. HAP peaks
obscured in the view.
quantity. Approximately 2 h into the run, the onset of monetite
can be observed. With the increasing quantity of monetite, the
contribution from brushite drops and the phase disappears 4.5 h
into the run. At this point, the sample contains similar quantities
of monetite (53 wt%) and hydroxylapatite (47 wt%). From this
point on, however, monetite becomes the dominant phase and
the final product of the experiments contains 66 wt% monetite
and 34 wt% hydroxylapatite.
In the next experiment, the temperature inside of the reaction cell was increased to 60 °C over 15 min and held for 6 h
(IS-3, Table 2). The pathway of phase transformation remained
unchanged at this temperature condition (i.e., same as the 45 °C
experiment), and the rate was only slightly affected. OCP appeared within first 5 min of the experiment and disappeared after
45 min (see Fig. 5b). The onset of hydroxylapatite and monetite,
as well as the disappearance of brushite occur at very similar
points in time as these in IS-2. It is to be noted, however, that the
quantity of hydroxylapatite formed is somewhat lower than in
the previous experiment. The contribution of hydroxylapatite in
the sample reaches its maximum of around 29 wt% at the 50 min
mark and remains at this level throughout the remainder of the
experiment. The onset of monetite occurs within 2 h of the experiment and is accompanied by the rapid disappearance of brushite.
Monetite quickly becomes the dominant phase in the sample and
makes up 71 wt% of the final product of the reaction.
Additional increase in the reaction temperature (from ambient to 90 °C over 15 min, run IS-4 in Table 1) considerably
increased the phase transformation rate. The onset of OCP can
be observed at 5 min into the run, followed shortly by the onset
of hydroxylapatite (10 min) (Fig. 5c). Within another 10 min,
the quantity of hydroxylapatite increases significantly (up to
40 wt%) and OCP disappears completely. This is followed by
quick formation of monetite. At the 30 min mark, monetite
makes up 54 wt% of the sample with hydroxylapatite constituting 46 wt%. Throughout the remaining part of the experiment,
as in the previous experiment, monetite and apatite are the only
two crystalline phases present in the sample. In the final stages
of the experiment, the quantity of hydroxylapatite decreases
slightly to a value of 38 wt%.
To investigate the influence of Ca/P ratio in the starting solution on the formation and development of calcium phosphates,
the ratio was varied in subsequent experiments without change
in the target temperature of the run or the rate of temperature
ramp-up (i.e., ambient to target temperature in 15 min). Change
in Ca/P to 1.0 (TCP stoichiometry) and 1.5 (brushite stoichiometry) did not influence the crystallization rate or pathways,
which are consistent with the description presented above. The
same is true for starting solutions with Ca/P ratio of 1.33 (OCP
stoichiometry). The final reaction mixture, however, contained
a slightly larger quantity of hydroxylapatite than was observed
in previous experiments (46% of the final sample composition).
Final products of in situ experiments at near-neutral pH were
analyzed by scanning electron microscopy. A typical product of
in situ experiments at near-neutral pH is presented in Figure 8a.
Crystals of mainly tabular habit and several micrometers in size
are visible in the micrograph.
High-pH experiments
A series of experiments at pH = 10 were also carried out, at
four different Ca/P ratios, corresponding to the stoichiometry of
TCP, brushite, OCP, and hydroxylapatite. Increase of pH in the
starting solutions and in the resulting initial mixture significantly
changed the identity of the initial precipitate. The initial phase
was ACP at all Ca/P ratios investigated (Fig. 9). Over the course
of the experiment, ACP transformed quickly (in <10 min at 90
°C) to poorly crystalline hydroxylapatite without any apparent
intermediate phases (Fig. 9). This pathway was consistent for all
experiments regardless of Ca/P ratio used. Subtle changes in the
structure of the amorphous hump prior to the onset of diffraction
peaks corresponding to apatite suggest the potential precipitation of a short-lived intermediate phase, but the identification of
this phase was not possible by means of X-ray diffraction. The
degree of crystallinity of the precipitated apatite did not seem to
improve throughout the duration of the experiments. A typical
final product from the high-pH in situ experiments is shown on
a SEM micrograph in Figure 8b.
1232
BORkIEWICz ET AL.: APATITE FORMATION PATHWAyS
figure 8. Electron microphotograph of typical final products of in situ experiments at near-neutral (a) and high pH (b).
discussiOn
Precursor development pathways
Most calcium phosphate solutions (pH > 4.5), in which apatite
growth experiments were carried out, are initially supersaturated
with multiple calcium phosphate phases, but to the greatest extent
with hydroxylapatite (Fig. 1) (Elliott 1994; Rakovan 2002). The
activation barrier to nucleation of a phase is related directly to
the surface-solution interfacial free energy (surface free energy).
This barrier, and hence the degree of supersaturation necessary
to overcome it and form a nucleus, increases with the increase in
the surface free energy. Thus, it is not uncommon for a thermodynamically less stable phase to nucleate and grow if its surface free
energy is significantly lower than that of a more stable phase. This
view of relative phase stability and the formation of precursor
phases can be cast in another way. When crystals are very small,
in the nano-particle range, the total surface free energy can be
larger than the total bulk free energy. Thus, there can be changes
in the relative stability of different phases in the nano-particle
size range compared to larger crystals. This has been shown
experimentally in several calorimetric studies of polymorphs as
a function of size (see review in Navrotsky 2004). Formation
of precursor phases in the Ca(OH)2-H3PO4-H2O system during
growth experiments of apatite from solution has been the focus of
many in vivo studies conducted over the past three decades, the
vast majority of which indicate development of various precursor
phases that ultimately transform to hydroxylapatite. As we have
indicated herein, formation of a particular phase and the pathway
of transformation to apatite depend greatly on the experimental
conditions such as calcium and phosphorous concentrations and
ratios, ionic strength, and solution pH.
The list of proposed and observed precursors include ACP
(Eanes 1970; Eanes et al. 1967, 1973; Eanes and Posner 1965;
Termine and Eanes 1972; Weber and Eanes 1967); brushite
(Francis and Webb 1971); OCP (Brown 1966; Brown et al.
1987); and TCP (Eanes et al. 1967). Christoffersen et al. (1989)
suggested formation of one form of ACP, denoted ACP1, followed by transformation to a second type of ACP (ACP2), which
in turn transformed to OCP and finally hydroxylapatite. More
recently, Liu et al. (2001) investigated mechanisms and kinetics
of hydroxylapatite precipitation from aqueous solution at the
conditions of high pH (10–11) and at relatively high calcium ion
concentrations, reaching 0.5 mol/L. The influence of temperature
on the reaction rate, particle size, and morphology were also examined. The authors suggested quick transformation of initially
formed OCP into ACP, which in turn undergoes transformation
to calcium-deficient hydroxylapatite and finally hydroxylapatite.
These authors noted that the temperature greatly influences the
rate of ACP to hydroxylapatite transformation, changing it from
24 h to 5 min for 25 and 60 °C, respectively. The particle size and
morphology of precipitated calcium orthophosphates were also
affected by the reaction temperature. Arifuzzaman and Rohani
(2004) investigated the influence of initial calcium and phosphorus concentration on the precipitated phases, nucleation pH (pH at
which nucleation occurred) and product size distribution at 25 °C
during the synthesis of calcium orthophosphates. They reported
formation of brushite at pH below 6.5 and gel-like ACP in their
experiment conducted at pH 7.1. The nucleation pH showed a
decreasing trend as the concentration of Ca and P increased in the
reactor. The size distribution and span of the products seemed to
be independent of the initial calcium and phosphorous concentration. Although the formation of several metastable calcium
phosphate phases during apatite crystallization is documented
in the literature (see above), the exact pathway and kinetics of
these reactions has been subject to debate.
In this study, formation and evolution of precursor phases
during apatite formation at conditions simulating those found in
Earth-surface environments were investigated by ex situ X-ray
diffraction as well as synchrotron-based in situ time-resolved
X-ray diffraction. The results of ex situ investigations conducted
at ambient temperature and near-neutral pH indicate formation
of amorphous calcium phosphate, which in the course of experiment transforms to brushite and ultimately to hydroxylapatite.
Initial formation of ACP in the absence of any detectible crystalline phase has been reported by multiple authors (Feenstra and
Debruyn 1979; Madsen and Christensson 1991; Termine and
Eanes 1972). Christoffersen et al. (1989) investigated formation
of calcium phosphates at neutral pH in the range of temperature
BORkIEWICz ET AL.: APATITE FORMATION PATHWAyS
figure 9. Diffraction patterns obtained during high-pH in situ
experiment IS-4. The y-axis represents intensity and relative non-linear
time scale. H = hydroxylapatite
between 15 and 42 °C and reported formation of brushite in addition to ACP shortly after the mixing of the reagents only in the
experiments conducted at 15 °C. In the experiments conducted
at higher temperature, formation of brushite was not detected.
It has to be noted, however, that this study involved a degree of
supersaturation much lower than that used in our experiments,
which could affect initial stages of precipitate formation. Madsen
and Christensson (1991) reported formation of brushite in the
initial stages of high-supersaturation experiments of pH = 5.0, but
not earlier than 2 h from the start of the experiment. At increasing
pH (up to 7.5), the delay of brushite crystallization increased to
one or several days. Feenstra and Debruyn (1979) also suggested
that the first step in the formation of hydroxylapatite at high supersaturations and neutral to slightly alkaline pH is nucleation of
ACP, followed by transformation to OCP and ultimately hydroxylapatite. They suggested that ACP serves as a template for the
heterogeneous nucleation of OCP, which in turn might serve as
a template for epitaxial growth of hydroxylapatite. The results of
our ex situ study and many earlier investigations clearly indicate
the amorphous character of the calcium phosphate phase formed
in the initial stages of the experiments at ambient temperature
and near-neutral pH. These results, however, are contradicted
1233
by in situ X-ray diffraction experiments reported herein. In
all experiments, regardless of Ca/P ratio, the initial precipitate
formed at the conditions of low temperature and near-neutral
pH was identified as a mixture of amorphous calcium phosphate
and crystalline brushite. The presence of brushite in the initial
mixture in previously described experiments, however, cannot
be ruled out completely. The detection of the crystalline phase in
synchrotron-based experiments may be attributed to the greater
X-ray flux of the synchrotron source compared to conventional
X-ray tubes, which results in a better signal to noise ratio. The
amorphous humps present in the diffraction patterns of in situ
runs have contributions from water and ACP. The presence of
ACP is assumed based on the results of ex situ experiments in
this study and in literature reports. The results of in situ X-ray
diffraction experiments suggest a more complex pathway of
phase development and evolution in the Ca(OH)2-H3PO4-H2O
system than do the ex situ diffraction experiments. Initially
formed ACP and brushite transform to OCP. The transformation of brushite to OCP, however, is only partial over the time
observed. This is indicated by a slight decrease in the intensity
of brushite peaks and coexistence of OCP and brushite peaks
in the sample for an extended period of time, particularly at
lower reaction temperatures (45 and 60 °C). In the later stage of
the reaction, OCP transforms quite rapidly to hydroxylapatite,
which is accompanied and/or followed by the transformation of
brushite to monetite. Monetite and hydroxylapatite coexist in the
sample throughout the remainder of the experiment. The rate of
this transformation is highly dependent on temperature of the
reaction, increasing with increasing temperature.
A similar pathway of phase evolution, involving transformation of initially formed brushite to hydroxylapatite, passing
through OCP, has been recently reported by Abraham et al.
(2005), who studied the maturation process of dental calculus by
synchrotron X-ray fluorescence. Indeed, formation of brushite
as a precursor phase to hydroxylapatite has been suggested by
several authors and many studies reported the transformation of
an initially formed ACP to hydroxylapatite or non-stoichiometric
hydroxylapatite via OCP (Christoffersen et al. 1989; Eanes and
Meyer 1977; Meyer and Eanes 1978; Tung and Brown 1983a,
1983b). In none of these studies, however, did monetite form
during the experiment.
The results from ex situ and in situ diffraction experiments
performed at higher pH are far more consistent than experiments
at near-neutral pH. The precipitate formed in the initial stages of
both sets of experiments was ACP. Also, the pathway of phase
evolution was found to be identical for the ex situ and in situ
experiments—initially formed ACP quite rapidly transforms
to hydroxylapatite, without any apparent intermediate phases.
No monetite formation was observed in the case of high-pH
experiments. These findings are in good agreement with various
reports in the literature (Arifuzzaman and Rohani 2004; Liu et
al. 2001).
Presence of monetite
The presence of monetite in the later stages of many in situ
experiments conducted at near-neutral pH and the limited transformation to hydroxylapatite is somewhat surprising. Although
monetite is less soluble than brushite under all conditions of
1234
BORkIEWICz ET AL.: APATITE FORMATION PATHWAyS
normal temperature and pressure (Fig. 1) and might be expected
to be found more frequently, it does not appear to occur in dental
calculus or other pathological calcifications, nor has it been found
in normal calcifications (Elliott 1994). Less frequent occurrence
of monetite in comparison to brushite was attributed by young
and Brown (1982) to its slow crystal growth relative to brushite.
They also suggested that brushite precipitates more readily from
solutions because of the lower surface energy of its hydrated
structure at the nucleation stage (more favored thermodynamically) and the ease of the hydrated ion incorporation into a hydrated crystal compared to an anhydrous one. young and Brown
(1982) also suggested that monetite is difficult to detect by X-ray
diffraction methods, so its occurrence may be more frequent than
presently thought. In our experiments, monetite was not found
in any of the ex situ experiments nor was it detected in the in
situ experiments conducted at high pH. It formed, however, in
considerable quantities (10–75 wt% of the crystalline reaction
products) in all in situ experiments carried out at near-neutral
pH and becomes the dominant calcium phosphate phase in the
Ca(OH)2-H3PO4-H2O system at conditions under consideration.
Ozawa et al. (1980) reported monetite formation on heating of
brushite at 60 to ~90 °C in water and concluded that the reaction
proceeded via three steps: (1) formation of acidic phosphorate
ion; (2) dissolution of calcium bis-(hydrogenphosphate); and (3)
precipitation of monetite. The study also indicated continuous
drop of the reaction pH from ~7.0 to a value of 3.5. Although
difficult to confirm, similar conditions may have existed in our
reaction cell during in situ investigations and the reactions may
have followed a similar pathway. In our experiments, however,
rapid formation of monetite was observed even at lower reaction temperature (45 °C). This could be explained by the slow
loss of water from the micro-reactor causing brushite dehydration at higher temperatures and transformation to monetite, but
this suggestion is inconsistent with our findings after the cell
inspection performed at the end of each experimental run. In all
experiments described herein, the reaction cell contained similar
amounts of liquid at the start and the end of the experimental
runs. The local heating of the sample by the synchrotron X-ray
beam was also considered as a possible cause for monetite formation. This scenario, however, is contradicted by the results
of the IS-1 experiment, in which brushite and ACP are the only
phases detectable over 8 h at ambient temperature.
Given the sealed nature of the cell used in this study, one
should also consider the influence of the vapor pressure present inside the cell on phase evolution during the experiment.
Although Skinner (1973) reported formation and stability of
monetite and apatite at elevated pressure, the conditions of
these experiments were far different from those explored in our
investigations. The pH in all experiments reported by Skinner
was below 3.7, whereas the temperature was 300 °C or higher
with pressures up to 2 kbar. Comparison of Skinner’s results
to ours is therefore not appropriate. No reports on the formation and stability of monetite at conditions comparable to ours
have been found. Although the influence of pressure cannot be
entirely eliminated, formation of monetite was not observed at
similar reaction conditions in the in situ experiments at higher
pH. Last, one should also take into consideration the limited
amount of growth solution available for the reaction in the cell
used during in situ diffraction experiments. Although care has
been taken to include as much solution as possible, the solid to
growth solution ratio in this kind of experiment was much higher
compared to ex situ investigation. Limited availability of calcium
and phosphate in the system may have influenced the pathway of
phase evolution; however, this effect is not supported by previous investigations. Also, no such effect was observed in the in
situ experiments conducted at identical calcium and phosphate
concentration but higher pH.
Kinetics
The character of the sample (crystallinity, crystallite size,
identity of the phases present, peak overlap), which affects the
quality of the diffraction data and the complex nature of the
phase evolution in the system under investigation, has limited the
feasible kinetic analysis to only one reaction—transformation of
brushite to monetite. The Avrami exponent n has been extracted
from data for the reactions at 45, 60, and 90 °C using Sharp
and Hancock method over the region 0.1 < α < 0.9 and yielded
values of 4.9, 4.7, and 0.6 for the respective reaction temperatures. The values of n > 4 may indicate a reaction following an
interface-controlled reaction with an increasing nucleation rate
(Christian 1965), whereas the value ~0.5 may point toward a twodimensional diffusion-controlled model for the conversion of
brushite to monetite, suggesting a change in reaction mechanism
with the change in the temperature. It has to be noted, however,
that although the Avrami-Erofe’ev expression provides a simple
means of exponent n and rate constant k determination, and
has been successfully used to model crystal growth in multiple
systems (Ahmed et al. 2008a, 2008b; Du and O’Hare 2008; Du
et al. 2008; Tobler et al. 2009; Walton et al. 2001; Walton and
O’Hare 2001), the interpretation of n and k value is often far from
straightforward (Walton et al. 2001). Because a given value of n
does not always unequivocally allow for different types of reaction mechanisms to be distinguished, independent experimental
information is usually required to establish the mechanism. One
should consider the possible contributions of errors arising from
many sources, including but not limited to: changing composition
of products with α, rates of nucleation and/or growth varying
with crystallographic surface, changes in the kinetic behavior
during the course of reaction, the influence of the distribution
of particle sizes, errors in measurement of the final yield that
may distort the shape of the α-time curve (Bamford and Tipper
1980). Also, the data for the 90° C reaction exhibits quite considerable scatter of the data points, significantly reducing the fit
coefficient for the linear regression. Given the risks associated
with kinetic analysis even in a perfectly behaving system, the
limited useable data for the system under consideration and
varying characteristics of the heat sources used in the collection
of various data sets presented in this study, the authors would
therefore like to limit the interpretation of the kinetic results.
We fully recognize the significance of kinetic analyses to our
understanding of the processes involved in growth and evolution
of crystalline phases, but it is our strong opinion that an attempt
to quantify kinetics using these particular data may lead to an
over-interpretation of our results. The aforementioned reaction of
brushite to monetite transformation may indeed provide insights
into the kinetics and mechanisms of the precursors’ development
BORkIEWICz ET AL.: APATITE FORMATION PATHWAyS
during crystal growth of hydroxylapatite, but unfortunately
it is merely a part of the multi-directional phase evolution in
the calcium orthophosphate system. It is also our intention to
implement a quantitative approach to kinetics and mechanisms
of our experiments in a forthcoming publication and relate those
findings to the results of the current publication. Experiments
described therein were performed under much more constrained
and thermally stable conditions and should provide data more
suited for such analyses.
acknOwledgments
Support for this research was provided by NSF Grant EAR-0409435.
Brookhaven National Laboratory and the National Synchrotron Light Source are
supported under contract DE-AC02-98CH10886 with the U.S. Department of
Energy by its Division of Chemical Sciences, Office of Basic Energy Research.
Use of the Advanced Photon Source was supported by the U.S. Department
of Energy, Office of Science, Office of Basic Energy Sciences, under contract
no. W-31-109-Eng-38. We thank Jonathan Hanson of the Brookhaven National
Laboratory and yang Ren of the Argonne National Laboratory for their assistance
with diffraction experiments. William Lack and Barry Landrum of the Miami
Instrumentation Laboratory are gratefully acknowledged for maintaining our
X-ray instrumentation and building our experimental reaction cells for in situ data
collection. We also gratefully acknowledge Jeffrey A. Post for his valuable advice
regarding Rietveld refinement.
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Manuscript received deceMber 9, 2008
Manuscript accepted april 4, 2010
Manuscript handled by steven higgins