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Influence of some foreign metal ions on crystal growth kinetics of brushite (CaHPO4·2H2O)
Journal of Crystal Growth 312 (2010) 2983–2988
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Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Influence of some foreign metal ions on crystal growth kinetics of brushite (CaHPO4 2H2O) Silvia Rosa a, Hans E. Lundager Madsen b,n a b
Dipartimento di Scienze Mineralogiche e Petrologiche, Universita degli Studi di Torino, Via Valperga Caluso 35, 10125 Torino, Italy Department of Basic Sciences and Environment, Faculty of Life Sciences, University of Copenhagen, Thorvaldsensvej 40, 1871 Frederiksberg C, Denmark
a r t i c l e in fo
abstract
Article history: Received 10 June 2010 Accepted 12 July 2010 Communicated by R. Kern Available online 22 July 2010
Brushite, CaHPO4 2H2O, has been precipitated at 25 1C in the presence of Mg2 + , Ba2 + or Cu2 + at concentrations up to 0.5 mM. When initial pH is sufficiently low to exclude nanocrystalline apatite as the initial solid phase, overall crystal growth rate may be determined from simple mass crystallization by recording pH as function of time. A combination of surface nucleation (birth-and-spread) and spiral (BCF) growth was found. Edge free energy was determined from the former contribution and was found to be a linear function of chemical potential of the additive, indicating constant adsorption over a wide range of additive concentrations. Average distances between adsorbed additive ions as calculated from slopes of plots are compatible with lattice parameters of brushite: 0.54 nm for Mg2 + , 0.43 nm for Ba2 + and 0.86 nm for Cu2 + . With the latter a sharp decrease in growth rate occurred early in the crystallization process, followed by an equally sharp increase to the previous level. When interpreted in terms of the Cabrera–Vermilyea theory of crystal growth inhibition, the results are consistent with an average distance between Cu ions of 0.88 nm, in perfect agreement with the above value. & 2010 Elsevier B.V. All rights reserved.
Keywords: A1. Impurities A1. Surface processes A2. Growth from solutions B1. Calcium compounds B1. Phosphates
1. Introduction One of the important aspects of kinetics of crystal growth from solution is the influence of low concentrations of dissolved substances other than the crystallizing solute and, in the case of reaction crystallization of an electrolyte, the counter ions of its ion constituents (typically chloride or nitrate and sodium or potassium ions). Such foreign substances are termed additives or impurities depending on, whether they are added in controlled amounts with a purpose or not. In the latter case the concentration, and even the chemical identity, of the foreign substance is often unknown. Hence only the former case enables a systematic study of the effect; therefore, the term additive will be used exclusively in the following. Brushite (CaHPO4 2H2O) is the least stable of the sparingly soluble calcium phosphates under most conditions of pH and temperature [1]. Nevertheless, it is usually the primary or secondary product of precipitation in neutral or moderately acid solution at temperatures up to and including 40 1C [2,3]. The so-called amorphous calcium phosphate occurring as primary precipitate and often recrystallizing into brushite has been shown to be nanocrystalline hydroxyapatite (Ca5OH(PO4)3, in the following abbreviated HAP) [4]. As the latter phase is the stable end
n
Corresponding author. Tel.: +45 3533 2407; fax: + 45 3533 2398. E-mail address: [email protected] (H.E. Lundager Madsen).
0022-0248/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2010.07.029
product in a wide range of precipitation conditions, this observation clearly demonstrates the importance of surface free energy and thus crystal size in determining the course of a crystallization process: nanocrystalline HAP particles are unstable due to their smallness. Even in the absence of foreign substances brushite shows great variability in morphology under varying conditions of crystallization [5]. In particular, the presence or absence of HAP nanocrystals as the primary product shows a strong influence, because the formation of this phase lowers the supersaturation with respect to brushite, and in addition the nanocrystals may serve as heteronuclei for brushite as well. As a result, more regular crystals are formed than in the case of direct crystallization of brushite. The change of size and morphology of brushite crystals under the influence of foreign di- or trivalent metal ions at a concentration of 1% of that of calcium ion ranges from hardly detectable to highly significant [6]. In general, the effect of the additive depends on the presence or absence of nanocrystalline HAP like in the pure system, though there is no systematic trend. A likely explanation of this is that some additives are included in the HAP crystals, while others are not; we shall return to this point later on. When only one phase is crystallizing, the course of the process may be followed by recording pH as a function of time. From such recordings with a duration of 1 h it was evident that nearly all the additives investigated, a total of 14, are inhibitors of brushite
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crystal growth, the only important exception being Pb2 + , which apparently promotes brushite crystallization. With half the additives inhibition was so strong that no kinetic analysis could be carried out. In the remaining cases, including two experiments with no additive, crystal growth could be shown to follow the birth-and-spread mechanism (surface nucleation), and the edge free energy of the steps at the surface could be determined. All the additives caused significant lowering of this parameter compared to the controls, ranging from 25% for Sr2 + and Ba2 + to 80% for Pb2 + [6]. This effect tends to increase the rate of crystal growth by surface nucleation, because the rate expression for this mechanism contains the factor ! 2 4l s exp 3ðkTÞ2 ln b where l is the edge free energy, s is the area of a growth unit in the surface layer, b is the saturation ratio, and a square nucleus has been assumed (factor 4). We may thus conclude that inhibition is connected with the value of a kinetic factor in front of the above exponential. In this paper we report a series of investigations on the effect of the additives Mg2 + , Ba2 + , Pb2 + and Cu2 + on crystal growth rate of brushite with the aim of determining the dependence of additive concentration. In addition, previous results on crystal size and morphology were subject to further study [6].
2. Experimental pH was measured with a Radiometer pH/ion meter model PHM 240, using a Metrohm Solitrode combination electrode. For calibration ISO standard buffers were used: potassium hydrogen phthalate, 0.05 m, pH¼4.008, and potassium dihydrogen phosphate +sodium hydrogen phosphate, both 0.025 m, pH¼6.865 m, both pH values applying to 25 1C. The pH meter was connected to a serial port of a PC, which stored the readings at suitable time intervals. Crystals were characterized by optical microscopy using a Zeiss Jenapol polarizing microscope and a few samples by FT-IR spectroscopy using a Nicolet Magna-IR 560 spectrometer. The spectra were recorded on KBr tablets. All solutions were prepared from analytical reagent chemicals dissolved in demineralized water further purified by passing through a filter with activated carbon and a Silhorko Silex-1 mixed-bed ion exchange column. Stock solutions were 0.1 M calcium nitrate, potassium dihydrogen phosphate and potassium hydrogen phosphate as well as nitrates of magnesium, barium, lead and copper. Kinetic experiments were carried out at 25 1C by adding 10 mL Ca(NO3)2 to a mixture of 9.2 mL KH2PO4 and 0.8 mL K2HPO4 in a large test tube immersed in a thermostat. Additive solution was added to the calcium nitrate solution prior to mixing with the phosphate in an amount not exceeding 0.1 mL. The pH electrode was inserted and moved up and down a few times to ensure mixing of reactants, and pH recording was started. Initially a value was stored once a minute. The time interval was doubled each time pH had changed by less than 0.01 during the preceding interval, taking the maximal length of 64 min. Samples of the precipitate were then withdrawn for characterization. A variant of the method was used to check the effect of continuous stirring with a propeller. The test tube was then replaced by a jacketed beaker connected to a circulation thermostat. However, stirring turned out to induce secondary nucleation to such a degree that results were irreproducible. We therefore relied on natural convection for mass transport.
3. Calculations The process of precipitation is Ca2 + + HPO24 + 2H2O-CaHPO4 2H2O
For each formula unit of brushite crystallizing a hydrogen phosphate ion is removed from the solution, thereby changing the proportion of phosphate species and hence pH. As we know the initial concentrations of all species, knowledge of pH is sufficient for calculation of solution composition and hence the amount of brushite precipitated, provided that only this solid phase is present. The calculations are based on literature values of the relevant equilibrium constants, i.e. acid dissociation constants [7] and stability constants of calcium phosphate complexes [8]. To calculate supersaturation, the solubility product of brushite is needed as well [8]. Finally, we have to know stability constants of complexes involving the additives in order to calculate their ion activities in solution [7]. Calculations were carried out using a previously described computer program [9]. Assuming that crystals grow homothetically, i.e. without habit change, and that the number of growing crystals is constant after the initial nucleation stage, we may calculate the relative crystal growth rate as a function of supersaturation from the amount of brushite precipitated at different times. It is assumed that the average linear dimension of a crystal is proportional to the third root of the amount precipitated, and hence that the average rate R of advancement of a crystal face is proportional to the rate of change of this quantity. Determination of absolute growth rate in m/s requires knowledge of crystal size distribution at the end of an experiment, whence we shall use arbitrary, but consistent units in the graphs. For the polynuclear mechanism of surface nucleation we have ! 2 4l s Rn ¼ KS1=3 ðcCa cCa,eq Þ2=3 ðln bÞ1=6 exp ð1Þ 3ðkTÞ2 ln b which is a simplified version of a kinetic equation derived by Christoffersen et al. [10] to account for calcium phosphate crystal growth and analogous to the expression of Simon et al. [11] for nonelectrolyte crystal growth. Here S is the average saturation ratio per ion constituent, and cCa and cCa,eq are the actual and equilibrium concentrations of calcium. It is thus assumed that the metal ion determines the rate of incorporation of growth units. The saturation ratio b of brushite is defined as
b¼
aðCa2 þ ÞaðHPO2 4 Þ Ksp
ð2Þ
A logarithmic plot of R divided by the expression between the rate constant K and the exponential, in the following denoted f(b), against 1/ln b should yield a straight line, and l may then be calculated from the slope. In the previous investigation [6] only surface nucleation kinetics was observed. This may be explained by the fact that pH recording was stopped after 1 h, when b was still about 5. In the present study recordings were continued almost to the point of saturation, whence we should take into account the possibility of spiral growth (BCF mechanism [12]) as well. The rate expression to be used is [13] Rs ¼ bðcCa cCa,eq Þln b
ð3Þ
The rate constant b may be obtained by regression analysis on data in the range of low supersaturations, where surface nucleation is negligible. In the higher range, where both mechanisms are likely to contribute to the overall growth rate,
S. Rosa, H.E. Lundager Madsen / Journal of Crystal Growth 312 (2010) 2983–2988
Rn may be determined using a relation proposed by Gilmer [14]: R3n 3 d3
t
þ
Rs t ¼1 d
ð4Þ
where t is the time it takes to fill a layer of thickness d, so the overall growth rate R equals d/t.
4. Results The concentration of calcium as well as the total concentration of phosphate was 50 mM in all experiments. In addition to a few experiments without additive to check consistency with previous results, the following ranges of additive concentrations were used: Mg 0.05–0.50 mM, Ba 0.09–0.50 mM, Pb 0.25–0.50 mM and Cu 0.06–0.50 mM. After a few experiments with lead it was clear that reproducibility was poor, and that results were out of line with previous ones [6]. For this reason, further work with this additive was discontinued. In the other cases calculated initial pH and saturation ratio were 5.441 70.002 and 30.970.2, respectively. With the solubility product of brushite, pKsp ¼6.591 [8], we find the values at saturation: cCa,eq ¼0.0454 70.001 M and pH¼3.976 70.002. Fig. 1 shows typical crystals obtained in a control experiment and with the three other additives at a concentration of 0.50 mM. The photographs were taken with circularly polarized light to avoid extinction with certain crystal orientations. It is evident from the photographs that the additives studied in the present investigation have little influence on crystal size and habit, and that the crystals are generally rather irregular. Furthermore, examination of a number of crystals with conoscopic illumination showed that the optic axis angle 2 V varied between 401 and 801, the value for a regular crystal being 88.21 [15]. As this reflects variability of at least one of the principal refractive indices, we cannot trust birefringence for measuring crystal thickness, and this in connection with the irregular habit of crystals means that accurate determination of crystal size
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distribution by polarization microscopy is not possible. Therefore we may only determine relative, not absolute growth rates. Fig. 2 shows the infrared spectrum of brushite crystallized without additive. The additives had no influence on the spectrum, as may be seen from those presented in the Supplementary material. The spectra agree with previously published spectra of brushite [16,17]. In the first few minutes of an experiment a notable increase in growth rate was often observed. This represents the nucleation stage, where the number of growing crystals is still increasing. Points from this part of the process have been left out in the following graphs, as they are of no use in the kinetic analyses. Fig. 3 shows results from the experiments with barium as additive, plotted as a test for spiral growth according to (3). The interplay of two different growth mechanisms is obvious from the
Fig. 2. Infrared spectrum of brushite from experiment without additive. The other spectra were identical (see Supplementary material).
Fig. 1. Typical crystals from experiments without additive (bl) and with the three additives.
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Fig. 3. Test for spiral growth for results with Ba. Regression lines for the range of low supersaturation are shown.
Fig. 5. Results from experiment with 0.50 mM Cu. Note that time goes from right to left. Arrow: see text.
Fig. 4. Test for surface nucleation for results with Ba. Regression lines are shown.
fact that growth rates recorded in the higher range of supersaturations are higher than those predicted from the BCF mechanism. Similar behaviour has been observed for both nonelectrolyte [18] and electrolyte systems [13]. Eliminating the contribution of spiral growth from the overall growth rate with the aid of Gilmer’s equation (4), we obtain the growth rate by surface nucleation as a function of supersaturation. Fig. 4 shows a semilogarithmic plot of the results for barium as additive. For magnesium the results were similar, whereas copper caused less regular behaviour, in particular in the higher range of concentrations. An example of a plot of growth rate vs. supersaturation is shown in Fig. 5. With this and a couple of other experiments at high copper concentrations kinetic analysis in the range of low supersaturations was not possible, so any contribution from spiral growth at high supersaturations was ignored. For lower copper concentrations spiral growth kinetics could still be detected and evaluated and its contribution to the overall growth rate eliminated as with the other additives. At the lowest copper concentration, 0.06 mM, there was no clear evidence of crystal growth by surface nucleation, as growth rates in the whole range of supersaturations were not significantly higher than those predicted by the spiral growth mechanism. Plots of the results for surface-nucleation kinetics are shown in Fig. 6. The slopes of the regression lines in Figs. 4 and 6 and the corresponding plots for magnesium as additive are given,
Fig. 6. Test for surface nucleation for results with Cu as additive.
Fig. 7. Plots of edge free energies vs. ion activities of the additives.
according to (1), by 2
a¼
4l s 3ðkTÞ2
ð5Þ
We take s ¼ a2 , where a is the third root of the volume of a growth unit in the crystal, known from the crystal structure determination by Curry and Jones [19], viz. a ¼0.498 nm. The resulting values of l are plotted vs. activity of the foreign metal ion in Fig. 7.
S. Rosa, H.E. Lundager Madsen / Journal of Crystal Growth 312 (2010) 2983–2988
Three preliminary experiments without additive and with different total volumes and slightly different initial supersaturations, carried out to check reproducibility, yielded edge free energies differing by 1.7 pJ/m between the highest and the lowest value. The standard deviation of each value, resulting from scatter of points about the regression line, ranged from 0.4 to 1.3 pJ/m. This uncertainty is representative for results with additives as well and corresponds to that found in the previous investigation [6].
5. Discussion
where L3 is the step excess of additive. This relation is a onedimensional analogue of the Gibbs adsorption isotherm [24]. Since at constant temperature we have dm3 ¼RT d ln a3, the linearity of graphs in Fig. 7 indicates that L3 is constant in the range of concentrations studied for a given additive. If we multiply the slope of a graph, with chemical potential as abscissa, by Avogadro’s constant, we get the number of foreign metal ions per unit length, and the reciprocal of this quantity is the average distance between neighbouring ions along the step. For the three additives studied, we found the following values: Mg : 0:54 70:05 nm
Like in the previous investigation [6] it is found that the foreign metal ions lower the edge free energy as determined from surface nucleation kinetics. This has a consequence for spiral growth kinetics as well, as Fig. 2 shows: growth rate increases with increasing additive concentration. This inference, of course, depends on the assumption that crystal size distribution does not vary too much with additive concentration; inspection of Fig. 1 shows this to be a reasonable assumption. Now the distance y0 between steps of a growth spiral is related to the radius rn of the critical surface nucleus by y0 ¼19rn for both a rounded [20] and polygonized spirals [21], and we have, according to the two-dimensional Gibbs–Kelvin equation r* ¼
ls kT ln b
ð6Þ
Hence the density of steps in the growth spiral increases with decreasing edge free energy. It should be noted, however, that this theory has recently been questioned, at least for crystals of sparingly soluble salts with steps of low kink density [22,23]. Considering the irregular growth of the lateral faces of brushite crystals as evident from Fig. 1, we believe that the theory may nevertheless be valid for the present case. Despite the irregular behaviour of systems containing copper (Fig. 5), kinetic analysis of the results was possible (Fig. 6). As Fig. 6 shows, the copper ion activities are lower than those of the other additives at the same concentrations, which reflects the higher stabilities of phosphato complexes of Cu [7]. The linearity of the semilogarithmic plots in Fig. 7 indicates that edge free energy of crystals growing from a solution with foreign metal ions is a linear function of the chemical potential of the additive. As shown in the previous work [6], this may be understood by regarding the system as a ternary one (1: solvent, 2: crystallizing solute, 3: additive) and considering the Gibbs–Duhem equation for a step of length l on the crystal surface: Sl dT þldl þ
3 X
nli dmi ¼ 0
ð7Þ
i¼1
here Sl is the entropy of the step, and nli is the excess (amount of substance, positive, negative or zero) of component no. i at the step. These amounts depend on the precise position defined for the step in the same way as an interface excess depends on the Gibbs dividing surface [24]. We may choose the step position such that n12 ¼ 0. The solution is dilute, so the chemical potential of solvent is very close to that of pure water, hence dm1 E0. Alternatively we may consider the system at a given supersaturation, i.e. constant chemical potential of solute meaning dm2 ¼0, and fix the step such that n11 ¼ 0. At constant temperature the first term in (7) is 0, so in either case we end up with, after division by l, @l ¼ L3 ð8Þ @m3 T, m1=2
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Ba : 0:426 70:009 nm
Cu : 0:86 70:08 nm
These values are of the same magnitude as the lattice parameters; for instance, the monoclinic unit cell of brushite has a ¼0.5812 nm, and the closest Ca–Ca distance is 0.3891 nm [19]. The smaller value for barium compared with magnesium despite the fact that Ba2 + is larger than Mg2 + may be explained on the basis of hydration of the ions in aqueous solution, making, e.g., magnesium sulfate much more soluble in water than barium sulfate. Therefore we may expect adsorbed magnesium ions to be hydrated to some degree and thus taking up more space. The still higher value for copper has other causes such as strong bonding to phosphate. Thus the stability constant of the 1:1 complex of the hydrogen phosphate ion with Cu2 + is at least an order of magnitude higher than that of the complexes with the other metal ions involved in the present study except Pb2 + [7]. Sometimes during a crystallization process a sharp decrease in growth rate occurs, followed by increase to the former level. This is most pronounced with copper as additive in the range of high concentrations; an example is shown in Fig. 5, where the arrow indicates such a growth rate minimum. Such behaviour may be interpreted in terms of the Cabrera–Vermilyea theory [25], according to which the foreign metal ions impede the advancement of a step when their distance apart is smaller than the diameter dn of the critical nucleus. We have dn ¼ 2rn with rn given by (6). The value of l to be used in the calculation is obtained by first calculating a(Cu2 + ) from the known composition of the solution at the time of the minimum and then inserting this value in the expression for the regression line in Fig. 7. Table 1 shows the results for the three experiments with the highest copper concentrations. For the remaining experiments the minima were less pronounced and occurred at much lower supersaturations, and the uncertainty of results was rather high. The average value of dn is the free space between adsorbed ions. To calculate the central distance d between ions we must add twice the radius of a copper ion, which is equal to 0.072 nm [26]. We thus get d ¼ 0:88 7 0:06 nm in perfect agreement with the value found from the dependence of l on a(Cu2 + ). The fact that crystals resume their previous growth rate level after the minimum seems to indicate that copper ions somehow disappear from the steps, possibly by
Table 1 Parameter values for copper as additive from Cabrera–Vermilyea theory. cCu (mM)
bmin
l (pJ m 1)
dn (nm)
0.50 0.50 0.25 Average
6.38 9.26 11.53
11.7 12.4 16.2
0.76 0.67 0.80 0.74 7 0.06
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incorporation in the crystal. This hypothesis is supported by the results of previous studies on the influence of copper on phase transformation of brushite [27]. The possible uptake of copper by brushite crystals may also be responsible for some of the irregularities otherwise observed with this additive. Calculations show that the solutions containing copper are supersaturated initially with respect to the two copper phosphates CuHPO4 H2O and Cu2OHPO4 (libethenite), so crystallization of one or both of these substances could lead to irregular behaviour as well. Previous studies indicate, however, that the latter will only nucleate at a much higher supersaturation than that existing in the systems of the present study, and that the rate of growth of the former is much lower than that of brushite at similar supersaturations [28]. The situation is quite different with lead, which forms a series of phosphates with much lower solubilities than those of the analogous calcium phosphates, but with significantly higher rates of nucleation and crystal growth [29]. Crystallization of one or more lead phosphates at the same time as crystallization of brushite is the most likely explanation of the failure of our studies with this additive. Finally we may notice that previous studies showed that copper has a much stronger effect on brushite crystallization under conditions where the initial product of precipitation is nanocrystalline HAP than when this phase is not formed [6]. This is the opposite of the behaviour with most other additives, and it may be related to the fact that copper ions, unlike many other divalent metal ions, are not likely to be coprecipitated with the calcium phosphates more basic than brushite, i.e. octacalcium phosphate and HAP [27]. Thus in this case the concentration of copper ions in solution when brushite crystals start to grow at a relatively low supersaturation will be relatively high.
6. Conclusion From simple precipitation experiments with pH recording it has been shown that ions of magnesium, barium or copper influence the rate of growth of brushite crystals in a way that can be interpreted as resulting from a lowering of the edge free energy caused by adsorption of the foreign ions. Based on a thermodynamic analysis leading to a one-dimensional analogue of Gibbs’ adsorption isotherm, it is inferred from the linear dependence of edge free energy on chemical potential of the additive that the degree of adsorption is independent of additive concentration in the range studied.
Acknowledgement This work has been presented as a poster at the 40th Anniversary Conference of the British Association for Crystal Growth, Bristol, September 2009.
Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jcrysgro.2010.07.029.x
References ¨ [1] N. Bjerrum, in: Nordiska (19. Skandinaviska) Naturforskarmotet, Helsingfors 1936, p. 344; Selected Papers, Munksgaard, Copenhagen, 1949, p. 245. [2] H.E. Lundager Madsen, G. Thorvardarson, J. Crystal Growth 66 (1984) 369. [3] H.E. Lundager Madsen, F. Christensson, J. Crystal Growth 114 (1991) 613. [4] E.I. Suvorova, P.A. Buffat, J. Microsc. 196 (1999) 46. [5] F. Abbona, F. Christensson, M. Franchini Angela, H.E. Lundager Madsen, J. Crystal Growth 131 (1993) 331. [6] H.E. Lundager Madsen, J. Crystal Growth 310 (2008) 2602. [7] R.M. Smith, A.E. Martell, Critical Stability Constants, vol. 4, Inorganic Complexes, Plenum, New York, 1976. [8] T.M. Gregory, E.C. Moreno, W.E. Brown, J. Res., Natl. Bur. Stand. 74A (1970) 461. [9] Y. Berland, M. Olmer, M. Grandvuillemin, H.E. Lundager Madsen, R. Boistelle, J. Crystal Growth 87 (1988) 494. [10] M.R. Christoffersen, J. Dohrup, J. Christoffersen, J. Crystal Growth 186 (1998) 283. [11] B. Simon, A. Grassi, R. Boistelle, J. Crystal Growth 26 (1974) 77. [12] W.K. Burton, N. Cabrera, F.C. Frank, Philos. Trans. Roy. Soc. 243 (1961) 299. [13] H.E. Lundager Madsen, B. Tranberg Christensen, J. Crystal Growth 237–239 (2002) 60. [14] G.H. Gilmer, J. Crystal Growth 36 (1976) 15. [15] H.E. Lundager Madsen, J. Crystal Growth 310 (2008) 617. [16] L. Tortet, J.R. Gavarri, G. Nihoul, J. Solid State Chem. 132 (1997) 6. ˇ [17] M. Trpovska, B. Soptrajanov, P. Malkov, J. Mol. Struct. 480-481 (1999) 661. [18] H.E. Lundager Madsen, R. Boistelle, J. Crystal Growth 46 (1979) 681. [19] N.A. Curry, D.W. Jones, J. Chem. Soc. A. (1971) 3725. [20] N. Cabrera, M.M. Levine, Philos. Mag. 1 (1956) 450. [21] E. Budevski, G. Staikov, V. Bostanov, J. Crystal Growth 29 (1975) 316. [22] A.A. Chernov, J.J. De Yoreo, L.N. Rashkovich, J. Optoelectron. Adv. Mater. 9 (2007) 1191. [23] J.J. De Yoreo, L.A. Zepeda-Ruiz, R.W. Friddle, S.R. Qiu, L.E. Wasylenki, A.A. Chernov, G.H. Gilmer, P.M. Dove, Cryst. Growth Des. 9 (2009) 5135. [24] J.G. Kirkwood, I. Oppenheim, Chemical Thermodynamics, McGraw-Hill, New York, 1961 Chapter 10, as well as many other textbooks on thermodynamics or surface science. [25] N. Cabrera, D.A. Vermilyea, in: R.H. Doremus, B.W. Roberts, D. Turnbull (Eds.), Growth and Perfection of Crystals, Wiley, New York1958, pp. 393–408. [26] J. Emsley, The Elements, Clarendon Press, Oxford, 1989, p. 54. [27] H.E. Lundager Madsen, Acta Chem. Scand. A 29 (1975) 277. [28] H.E. Lundager Madsen, J. Crystal Growth 275 (2005) e191. [29] M. Ayati, H.E. Lundager Madsen, J. Crystal Growth 208 (2000) 579.
Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Influence of some foreign metal ions on crystal growth kinetics of brushite (CaHPO4 2H2O) Silvia Rosa a, Hans E. Lundager Madsen b,n a b
Dipartimento di Scienze Mineralogiche e Petrologiche, Universita degli Studi di Torino, Via Valperga Caluso 35, 10125 Torino, Italy Department of Basic Sciences and Environment, Faculty of Life Sciences, University of Copenhagen, Thorvaldsensvej 40, 1871 Frederiksberg C, Denmark
a r t i c l e in fo
abstract
Article history: Received 10 June 2010 Accepted 12 July 2010 Communicated by R. Kern Available online 22 July 2010
Brushite, CaHPO4 2H2O, has been precipitated at 25 1C in the presence of Mg2 + , Ba2 + or Cu2 + at concentrations up to 0.5 mM. When initial pH is sufficiently low to exclude nanocrystalline apatite as the initial solid phase, overall crystal growth rate may be determined from simple mass crystallization by recording pH as function of time. A combination of surface nucleation (birth-and-spread) and spiral (BCF) growth was found. Edge free energy was determined from the former contribution and was found to be a linear function of chemical potential of the additive, indicating constant adsorption over a wide range of additive concentrations. Average distances between adsorbed additive ions as calculated from slopes of plots are compatible with lattice parameters of brushite: 0.54 nm for Mg2 + , 0.43 nm for Ba2 + and 0.86 nm for Cu2 + . With the latter a sharp decrease in growth rate occurred early in the crystallization process, followed by an equally sharp increase to the previous level. When interpreted in terms of the Cabrera–Vermilyea theory of crystal growth inhibition, the results are consistent with an average distance between Cu ions of 0.88 nm, in perfect agreement with the above value. & 2010 Elsevier B.V. All rights reserved.
Keywords: A1. Impurities A1. Surface processes A2. Growth from solutions B1. Calcium compounds B1. Phosphates
1. Introduction One of the important aspects of kinetics of crystal growth from solution is the influence of low concentrations of dissolved substances other than the crystallizing solute and, in the case of reaction crystallization of an electrolyte, the counter ions of its ion constituents (typically chloride or nitrate and sodium or potassium ions). Such foreign substances are termed additives or impurities depending on, whether they are added in controlled amounts with a purpose or not. In the latter case the concentration, and even the chemical identity, of the foreign substance is often unknown. Hence only the former case enables a systematic study of the effect; therefore, the term additive will be used exclusively in the following. Brushite (CaHPO4 2H2O) is the least stable of the sparingly soluble calcium phosphates under most conditions of pH and temperature [1]. Nevertheless, it is usually the primary or secondary product of precipitation in neutral or moderately acid solution at temperatures up to and including 40 1C [2,3]. The so-called amorphous calcium phosphate occurring as primary precipitate and often recrystallizing into brushite has been shown to be nanocrystalline hydroxyapatite (Ca5OH(PO4)3, in the following abbreviated HAP) [4]. As the latter phase is the stable end
n
Corresponding author. Tel.: +45 3533 2407; fax: + 45 3533 2398. E-mail address: [email protected] (H.E. Lundager Madsen).
0022-0248/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2010.07.029
product in a wide range of precipitation conditions, this observation clearly demonstrates the importance of surface free energy and thus crystal size in determining the course of a crystallization process: nanocrystalline HAP particles are unstable due to their smallness. Even in the absence of foreign substances brushite shows great variability in morphology under varying conditions of crystallization [5]. In particular, the presence or absence of HAP nanocrystals as the primary product shows a strong influence, because the formation of this phase lowers the supersaturation with respect to brushite, and in addition the nanocrystals may serve as heteronuclei for brushite as well. As a result, more regular crystals are formed than in the case of direct crystallization of brushite. The change of size and morphology of brushite crystals under the influence of foreign di- or trivalent metal ions at a concentration of 1% of that of calcium ion ranges from hardly detectable to highly significant [6]. In general, the effect of the additive depends on the presence or absence of nanocrystalline HAP like in the pure system, though there is no systematic trend. A likely explanation of this is that some additives are included in the HAP crystals, while others are not; we shall return to this point later on. When only one phase is crystallizing, the course of the process may be followed by recording pH as a function of time. From such recordings with a duration of 1 h it was evident that nearly all the additives investigated, a total of 14, are inhibitors of brushite
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crystal growth, the only important exception being Pb2 + , which apparently promotes brushite crystallization. With half the additives inhibition was so strong that no kinetic analysis could be carried out. In the remaining cases, including two experiments with no additive, crystal growth could be shown to follow the birth-and-spread mechanism (surface nucleation), and the edge free energy of the steps at the surface could be determined. All the additives caused significant lowering of this parameter compared to the controls, ranging from 25% for Sr2 + and Ba2 + to 80% for Pb2 + [6]. This effect tends to increase the rate of crystal growth by surface nucleation, because the rate expression for this mechanism contains the factor ! 2 4l s exp 3ðkTÞ2 ln b where l is the edge free energy, s is the area of a growth unit in the surface layer, b is the saturation ratio, and a square nucleus has been assumed (factor 4). We may thus conclude that inhibition is connected with the value of a kinetic factor in front of the above exponential. In this paper we report a series of investigations on the effect of the additives Mg2 + , Ba2 + , Pb2 + and Cu2 + on crystal growth rate of brushite with the aim of determining the dependence of additive concentration. In addition, previous results on crystal size and morphology were subject to further study [6].
2. Experimental pH was measured with a Radiometer pH/ion meter model PHM 240, using a Metrohm Solitrode combination electrode. For calibration ISO standard buffers were used: potassium hydrogen phthalate, 0.05 m, pH¼4.008, and potassium dihydrogen phosphate +sodium hydrogen phosphate, both 0.025 m, pH¼6.865 m, both pH values applying to 25 1C. The pH meter was connected to a serial port of a PC, which stored the readings at suitable time intervals. Crystals were characterized by optical microscopy using a Zeiss Jenapol polarizing microscope and a few samples by FT-IR spectroscopy using a Nicolet Magna-IR 560 spectrometer. The spectra were recorded on KBr tablets. All solutions were prepared from analytical reagent chemicals dissolved in demineralized water further purified by passing through a filter with activated carbon and a Silhorko Silex-1 mixed-bed ion exchange column. Stock solutions were 0.1 M calcium nitrate, potassium dihydrogen phosphate and potassium hydrogen phosphate as well as nitrates of magnesium, barium, lead and copper. Kinetic experiments were carried out at 25 1C by adding 10 mL Ca(NO3)2 to a mixture of 9.2 mL KH2PO4 and 0.8 mL K2HPO4 in a large test tube immersed in a thermostat. Additive solution was added to the calcium nitrate solution prior to mixing with the phosphate in an amount not exceeding 0.1 mL. The pH electrode was inserted and moved up and down a few times to ensure mixing of reactants, and pH recording was started. Initially a value was stored once a minute. The time interval was doubled each time pH had changed by less than 0.01 during the preceding interval, taking the maximal length of 64 min. Samples of the precipitate were then withdrawn for characterization. A variant of the method was used to check the effect of continuous stirring with a propeller. The test tube was then replaced by a jacketed beaker connected to a circulation thermostat. However, stirring turned out to induce secondary nucleation to such a degree that results were irreproducible. We therefore relied on natural convection for mass transport.
3. Calculations The process of precipitation is Ca2 + + HPO24 + 2H2O-CaHPO4 2H2O
For each formula unit of brushite crystallizing a hydrogen phosphate ion is removed from the solution, thereby changing the proportion of phosphate species and hence pH. As we know the initial concentrations of all species, knowledge of pH is sufficient for calculation of solution composition and hence the amount of brushite precipitated, provided that only this solid phase is present. The calculations are based on literature values of the relevant equilibrium constants, i.e. acid dissociation constants [7] and stability constants of calcium phosphate complexes [8]. To calculate supersaturation, the solubility product of brushite is needed as well [8]. Finally, we have to know stability constants of complexes involving the additives in order to calculate their ion activities in solution [7]. Calculations were carried out using a previously described computer program [9]. Assuming that crystals grow homothetically, i.e. without habit change, and that the number of growing crystals is constant after the initial nucleation stage, we may calculate the relative crystal growth rate as a function of supersaturation from the amount of brushite precipitated at different times. It is assumed that the average linear dimension of a crystal is proportional to the third root of the amount precipitated, and hence that the average rate R of advancement of a crystal face is proportional to the rate of change of this quantity. Determination of absolute growth rate in m/s requires knowledge of crystal size distribution at the end of an experiment, whence we shall use arbitrary, but consistent units in the graphs. For the polynuclear mechanism of surface nucleation we have ! 2 4l s Rn ¼ KS1=3 ðcCa cCa,eq Þ2=3 ðln bÞ1=6 exp ð1Þ 3ðkTÞ2 ln b which is a simplified version of a kinetic equation derived by Christoffersen et al. [10] to account for calcium phosphate crystal growth and analogous to the expression of Simon et al. [11] for nonelectrolyte crystal growth. Here S is the average saturation ratio per ion constituent, and cCa and cCa,eq are the actual and equilibrium concentrations of calcium. It is thus assumed that the metal ion determines the rate of incorporation of growth units. The saturation ratio b of brushite is defined as
b¼
aðCa2 þ ÞaðHPO2 4 Þ Ksp
ð2Þ
A logarithmic plot of R divided by the expression between the rate constant K and the exponential, in the following denoted f(b), against 1/ln b should yield a straight line, and l may then be calculated from the slope. In the previous investigation [6] only surface nucleation kinetics was observed. This may be explained by the fact that pH recording was stopped after 1 h, when b was still about 5. In the present study recordings were continued almost to the point of saturation, whence we should take into account the possibility of spiral growth (BCF mechanism [12]) as well. The rate expression to be used is [13] Rs ¼ bðcCa cCa,eq Þln b
ð3Þ
The rate constant b may be obtained by regression analysis on data in the range of low supersaturations, where surface nucleation is negligible. In the higher range, where both mechanisms are likely to contribute to the overall growth rate,
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Rn may be determined using a relation proposed by Gilmer [14]: R3n 3 d3
t
þ
Rs t ¼1 d
ð4Þ
where t is the time it takes to fill a layer of thickness d, so the overall growth rate R equals d/t.
4. Results The concentration of calcium as well as the total concentration of phosphate was 50 mM in all experiments. In addition to a few experiments without additive to check consistency with previous results, the following ranges of additive concentrations were used: Mg 0.05–0.50 mM, Ba 0.09–0.50 mM, Pb 0.25–0.50 mM and Cu 0.06–0.50 mM. After a few experiments with lead it was clear that reproducibility was poor, and that results were out of line with previous ones [6]. For this reason, further work with this additive was discontinued. In the other cases calculated initial pH and saturation ratio were 5.441 70.002 and 30.970.2, respectively. With the solubility product of brushite, pKsp ¼6.591 [8], we find the values at saturation: cCa,eq ¼0.0454 70.001 M and pH¼3.976 70.002. Fig. 1 shows typical crystals obtained in a control experiment and with the three other additives at a concentration of 0.50 mM. The photographs were taken with circularly polarized light to avoid extinction with certain crystal orientations. It is evident from the photographs that the additives studied in the present investigation have little influence on crystal size and habit, and that the crystals are generally rather irregular. Furthermore, examination of a number of crystals with conoscopic illumination showed that the optic axis angle 2 V varied between 401 and 801, the value for a regular crystal being 88.21 [15]. As this reflects variability of at least one of the principal refractive indices, we cannot trust birefringence for measuring crystal thickness, and this in connection with the irregular habit of crystals means that accurate determination of crystal size
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distribution by polarization microscopy is not possible. Therefore we may only determine relative, not absolute growth rates. Fig. 2 shows the infrared spectrum of brushite crystallized without additive. The additives had no influence on the spectrum, as may be seen from those presented in the Supplementary material. The spectra agree with previously published spectra of brushite [16,17]. In the first few minutes of an experiment a notable increase in growth rate was often observed. This represents the nucleation stage, where the number of growing crystals is still increasing. Points from this part of the process have been left out in the following graphs, as they are of no use in the kinetic analyses. Fig. 3 shows results from the experiments with barium as additive, plotted as a test for spiral growth according to (3). The interplay of two different growth mechanisms is obvious from the
Fig. 2. Infrared spectrum of brushite from experiment without additive. The other spectra were identical (see Supplementary material).
Fig. 1. Typical crystals from experiments without additive (bl) and with the three additives.
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Fig. 3. Test for spiral growth for results with Ba. Regression lines for the range of low supersaturation are shown.
Fig. 5. Results from experiment with 0.50 mM Cu. Note that time goes from right to left. Arrow: see text.
Fig. 4. Test for surface nucleation for results with Ba. Regression lines are shown.
fact that growth rates recorded in the higher range of supersaturations are higher than those predicted from the BCF mechanism. Similar behaviour has been observed for both nonelectrolyte [18] and electrolyte systems [13]. Eliminating the contribution of spiral growth from the overall growth rate with the aid of Gilmer’s equation (4), we obtain the growth rate by surface nucleation as a function of supersaturation. Fig. 4 shows a semilogarithmic plot of the results for barium as additive. For magnesium the results were similar, whereas copper caused less regular behaviour, in particular in the higher range of concentrations. An example of a plot of growth rate vs. supersaturation is shown in Fig. 5. With this and a couple of other experiments at high copper concentrations kinetic analysis in the range of low supersaturations was not possible, so any contribution from spiral growth at high supersaturations was ignored. For lower copper concentrations spiral growth kinetics could still be detected and evaluated and its contribution to the overall growth rate eliminated as with the other additives. At the lowest copper concentration, 0.06 mM, there was no clear evidence of crystal growth by surface nucleation, as growth rates in the whole range of supersaturations were not significantly higher than those predicted by the spiral growth mechanism. Plots of the results for surface-nucleation kinetics are shown in Fig. 6. The slopes of the regression lines in Figs. 4 and 6 and the corresponding plots for magnesium as additive are given,
Fig. 6. Test for surface nucleation for results with Cu as additive.
Fig. 7. Plots of edge free energies vs. ion activities of the additives.
according to (1), by 2
a¼
4l s 3ðkTÞ2
ð5Þ
We take s ¼ a2 , where a is the third root of the volume of a growth unit in the crystal, known from the crystal structure determination by Curry and Jones [19], viz. a ¼0.498 nm. The resulting values of l are plotted vs. activity of the foreign metal ion in Fig. 7.
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Three preliminary experiments without additive and with different total volumes and slightly different initial supersaturations, carried out to check reproducibility, yielded edge free energies differing by 1.7 pJ/m between the highest and the lowest value. The standard deviation of each value, resulting from scatter of points about the regression line, ranged from 0.4 to 1.3 pJ/m. This uncertainty is representative for results with additives as well and corresponds to that found in the previous investigation [6].
5. Discussion
where L3 is the step excess of additive. This relation is a onedimensional analogue of the Gibbs adsorption isotherm [24]. Since at constant temperature we have dm3 ¼RT d ln a3, the linearity of graphs in Fig. 7 indicates that L3 is constant in the range of concentrations studied for a given additive. If we multiply the slope of a graph, with chemical potential as abscissa, by Avogadro’s constant, we get the number of foreign metal ions per unit length, and the reciprocal of this quantity is the average distance between neighbouring ions along the step. For the three additives studied, we found the following values: Mg : 0:54 70:05 nm
Like in the previous investigation [6] it is found that the foreign metal ions lower the edge free energy as determined from surface nucleation kinetics. This has a consequence for spiral growth kinetics as well, as Fig. 2 shows: growth rate increases with increasing additive concentration. This inference, of course, depends on the assumption that crystal size distribution does not vary too much with additive concentration; inspection of Fig. 1 shows this to be a reasonable assumption. Now the distance y0 between steps of a growth spiral is related to the radius rn of the critical surface nucleus by y0 ¼19rn for both a rounded [20] and polygonized spirals [21], and we have, according to the two-dimensional Gibbs–Kelvin equation r* ¼
ls kT ln b
ð6Þ
Hence the density of steps in the growth spiral increases with decreasing edge free energy. It should be noted, however, that this theory has recently been questioned, at least for crystals of sparingly soluble salts with steps of low kink density [22,23]. Considering the irregular growth of the lateral faces of brushite crystals as evident from Fig. 1, we believe that the theory may nevertheless be valid for the present case. Despite the irregular behaviour of systems containing copper (Fig. 5), kinetic analysis of the results was possible (Fig. 6). As Fig. 6 shows, the copper ion activities are lower than those of the other additives at the same concentrations, which reflects the higher stabilities of phosphato complexes of Cu [7]. The linearity of the semilogarithmic plots in Fig. 7 indicates that edge free energy of crystals growing from a solution with foreign metal ions is a linear function of the chemical potential of the additive. As shown in the previous work [6], this may be understood by regarding the system as a ternary one (1: solvent, 2: crystallizing solute, 3: additive) and considering the Gibbs–Duhem equation for a step of length l on the crystal surface: Sl dT þldl þ
3 X
nli dmi ¼ 0
ð7Þ
i¼1
here Sl is the entropy of the step, and nli is the excess (amount of substance, positive, negative or zero) of component no. i at the step. These amounts depend on the precise position defined for the step in the same way as an interface excess depends on the Gibbs dividing surface [24]. We may choose the step position such that n12 ¼ 0. The solution is dilute, so the chemical potential of solvent is very close to that of pure water, hence dm1 E0. Alternatively we may consider the system at a given supersaturation, i.e. constant chemical potential of solute meaning dm2 ¼0, and fix the step such that n11 ¼ 0. At constant temperature the first term in (7) is 0, so in either case we end up with, after division by l, @l ¼ L3 ð8Þ @m3 T, m1=2
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Ba : 0:426 70:009 nm
Cu : 0:86 70:08 nm
These values are of the same magnitude as the lattice parameters; for instance, the monoclinic unit cell of brushite has a ¼0.5812 nm, and the closest Ca–Ca distance is 0.3891 nm [19]. The smaller value for barium compared with magnesium despite the fact that Ba2 + is larger than Mg2 + may be explained on the basis of hydration of the ions in aqueous solution, making, e.g., magnesium sulfate much more soluble in water than barium sulfate. Therefore we may expect adsorbed magnesium ions to be hydrated to some degree and thus taking up more space. The still higher value for copper has other causes such as strong bonding to phosphate. Thus the stability constant of the 1:1 complex of the hydrogen phosphate ion with Cu2 + is at least an order of magnitude higher than that of the complexes with the other metal ions involved in the present study except Pb2 + [7]. Sometimes during a crystallization process a sharp decrease in growth rate occurs, followed by increase to the former level. This is most pronounced with copper as additive in the range of high concentrations; an example is shown in Fig. 5, where the arrow indicates such a growth rate minimum. Such behaviour may be interpreted in terms of the Cabrera–Vermilyea theory [25], according to which the foreign metal ions impede the advancement of a step when their distance apart is smaller than the diameter dn of the critical nucleus. We have dn ¼ 2rn with rn given by (6). The value of l to be used in the calculation is obtained by first calculating a(Cu2 + ) from the known composition of the solution at the time of the minimum and then inserting this value in the expression for the regression line in Fig. 7. Table 1 shows the results for the three experiments with the highest copper concentrations. For the remaining experiments the minima were less pronounced and occurred at much lower supersaturations, and the uncertainty of results was rather high. The average value of dn is the free space between adsorbed ions. To calculate the central distance d between ions we must add twice the radius of a copper ion, which is equal to 0.072 nm [26]. We thus get d ¼ 0:88 7 0:06 nm in perfect agreement with the value found from the dependence of l on a(Cu2 + ). The fact that crystals resume their previous growth rate level after the minimum seems to indicate that copper ions somehow disappear from the steps, possibly by
Table 1 Parameter values for copper as additive from Cabrera–Vermilyea theory. cCu (mM)
bmin
l (pJ m 1)
dn (nm)
0.50 0.50 0.25 Average
6.38 9.26 11.53
11.7 12.4 16.2
0.76 0.67 0.80 0.74 7 0.06
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incorporation in the crystal. This hypothesis is supported by the results of previous studies on the influence of copper on phase transformation of brushite [27]. The possible uptake of copper by brushite crystals may also be responsible for some of the irregularities otherwise observed with this additive. Calculations show that the solutions containing copper are supersaturated initially with respect to the two copper phosphates CuHPO4 H2O and Cu2OHPO4 (libethenite), so crystallization of one or both of these substances could lead to irregular behaviour as well. Previous studies indicate, however, that the latter will only nucleate at a much higher supersaturation than that existing in the systems of the present study, and that the rate of growth of the former is much lower than that of brushite at similar supersaturations [28]. The situation is quite different with lead, which forms a series of phosphates with much lower solubilities than those of the analogous calcium phosphates, but with significantly higher rates of nucleation and crystal growth [29]. Crystallization of one or more lead phosphates at the same time as crystallization of brushite is the most likely explanation of the failure of our studies with this additive. Finally we may notice that previous studies showed that copper has a much stronger effect on brushite crystallization under conditions where the initial product of precipitation is nanocrystalline HAP than when this phase is not formed [6]. This is the opposite of the behaviour with most other additives, and it may be related to the fact that copper ions, unlike many other divalent metal ions, are not likely to be coprecipitated with the calcium phosphates more basic than brushite, i.e. octacalcium phosphate and HAP [27]. Thus in this case the concentration of copper ions in solution when brushite crystals start to grow at a relatively low supersaturation will be relatively high.
6. Conclusion From simple precipitation experiments with pH recording it has been shown that ions of magnesium, barium or copper influence the rate of growth of brushite crystals in a way that can be interpreted as resulting from a lowering of the edge free energy caused by adsorption of the foreign ions. Based on a thermodynamic analysis leading to a one-dimensional analogue of Gibbs’ adsorption isotherm, it is inferred from the linear dependence of edge free energy on chemical potential of the additive that the degree of adsorption is independent of additive concentration in the range studied.
Acknowledgement This work has been presented as a poster at the 40th Anniversary Conference of the British Association for Crystal Growth, Bristol, September 2009.
Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jcrysgro.2010.07.029.x
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