J. Phys. Chem. B 2000, 104, 4189-4194
`
`4189
`
`Inhibitory Effect of Magnesium and Zinc on Crystallization Kinetics of Hydroxyapatite
`(0001) Face
`
`Noriko Kanzaki,† Kazuo Onuma,*,‡ Gabin Treboux,‡ Sadao Tsutsumi,† and Atsuo Ito‡
`School of Science and Engineering, Waseda UniVersity, 1-6-1 Nishiwaseda, Shinjuku-ku,
`Tokyo, 169-8050 Japan, and National Institute for AdVanced Interdisciplinary Research, MITI,
`1-1-4 Higashi, Tsukuba-shi, Ibaraki, 305-8562 Japan
`ReceiVed: NoVember 9, 1999; In Final Form: February 1, 2000
`
`The effect of magnesium and zinc on the growth kinetics of a hydroxyapatite (0001) face in pseudophysiological
`solutions was investigated. The growth rates of the (0001) face were measured under various concentrations
`of magnesium or zinc using Moire phase shift interferometry coupled with surface observation by atomic
`force microscopy. The (0001) face grew not in a spiral growth mode but in a multiple two-dimensional
`nucleation growth mode. It was shown that the lateral growth of two-dimensional islands on the (0001) face
`was inhibited by the addition of magnesium or zinc, following an inhibition of the normal growth rate of the
`face. Although both cations inhibited growth, zinc was found to reduce the growth rate about 1000 times
`more effectively than magnesium.
`
`Introduction
`
`It is important to clarify the effect of trace elements on the
`growth mechanism of hydroxyapatite (Ca10(PO4)6(OH)2; HAP),
`an inorganic component of human bone and tooth, for correct
`understanding of the biomineralization process. In vivo, HAP
`grows in a solution which contains many essential trace elements
`besides calcium and phosphorus. Among these essential trace
`elements, magnesium and zinc have a great influence on the
`growth kinetics of HAP. For instance, it is well-known that
`magnesium inhibits phase transformation from amorphous
`calcium phosphate to HAP.1,2 From the viewpoint of bone-cell
`biology, zinc is known to promote bone formation by stimulating
`osteoblasts which are cells that produce bone HAP.3,4 Zinc-
`containing calcium phosphate implants have been found to have
`a stimulant effect on bone formation.5 However, an elevated
`amount of zinc might inhibit the growth of bone HAP.
`Indeed, inhibitory effects of magnesium and zinc on HAP
`crystal growth have been investigated, for example, such as a
`dual constant composition (DCC) method.6-8 It was confirmed
`that magnesium and zinc reduced the growth rate of HAP.
`However, the previous method did not discriminate between
`the growth rates of (101h0), a- and (0001), c-faces despite the
`high precision associated with the method. Moreover, surface
`observation of grown crystals was not performed in the previous
`studies although much information can be obtained through
`surface observation. It is thus necessary to measure the growth
`rate of each face separately with surface observation, using
`single-crystal HAP as a seed, to obtain more detailed information
`about the inhibitory effects. HAP crystal is bounded by a- and
`c-faces and has large anisotropy. Biologically, the inhibitory
`effects on the c-face are more important than that on the a-face
`since biological HAP grows mainly in the c-direction.9
`
`* To whom correspondence should be addressed: National Institute for
`Advanced Interdisciplinary Research, Cell Tissue Module Group, 1-1-4
`Higashi, Tsukuba-shi, Ibaraki, 305-8562 Japan. Tel.: +81-298-61-2557.
`Fax: +81-298-61-2565. E-mail: onuma@nair.go.jp.
`† School of Science and Engineering, Waseda University.
`‡ National Institute for Advanced Interdisciplinary Research.
`
`10.1021/jp9939726 CCC: $19.00 © 2000 American Chemical Society
`Published on Web 04/27/2000
`
`In the present study, we performed direct growth rate
`measurements of the c-face in the presence of magnesium and
`zinc in pseudophysiological solutions. Moire phase shift inter-
`ferometry was employed for the precise measurement of growth
`rates coupled with surface observation by atomic force micros-
`copy (AFM). The growth rates obtained were analyzed using
`theoretical equations of adsorption isotherms.
`
`Experimental Section
`1. HAP Seed Crystals. The seed crystals used in the present
`study were hydrothermally synthetic HAP single crystals
`bounded by a- and c-faces.10 The size of the seed crystals was
`1-4 mm and 20-50 (cid:237)m along the c- and a-directions,
`respectively. Single crystals were used after masking a-faces
`with epoxy resin for all experiments so that only one c-face
`grows.
`2. Pseudophysiological Solutions. The pseudophysiological
`solutions contain 140 mM NaCl, 1.0 mM K2HPO4(cid:226)3H2O, 2.5
`mM CaCl2, and either 0-1.5 mM MgCl2(cid:226)6H2O or 0-7.5 (cid:237)M
`ZnCl2. The pseudophysiological solutions were prepared using
`extrapure-grade reagents (Nacalai Tesque, Inc., Tokyo, Japan)
`and ultrapure CO2-free water, and were buffered at pH 7.4 by
`tris-(hydroxymethyl)aminomethane and 1 N HCl at 25 (cid:176)C.
`Supersaturation of the solutions was 22.0 with respect to HAP,
`as calculated from
`
`(cid:243) ) (Ip/ Ksp)1/18 - 1
`
`(1)
`
`where Ip and Ksp are the ionic product and solubility product,
`respectively. Ip was calculated using the dissociation constants
`described elsewhere.11 The activity coefficients were calculated
`using the Debye-Huckel limiting law.12 A Ksp value of 10-119
`was used in the present study.
`3. Moire Phase Shift Interferometry. Moire phase shift
`interferometry was used to measure growth rates of the c-face.
`Common-path two-beam interferometry with a Nomarsky prism
`was used to eliminate mechanical disturbance (Figure 1).13,14
`The interferometry used has a theoretical accuracy with 0.5 nm
`Exhibit 1102
`ARGENTUM
`IPR2017-01053
`
`000001
`
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`

`4190 J. Phys. Chem. B, Vol. 104, No. 17, 2000
`
`Kanzaki et al.
`
`Figure 1. Schematic drawing of common-path two-beam interferometry and a signal processing route using Moire phase shift technique. A two-
`dimensional phase distribution profile is constructed from an interferogram of c-face in real time.
`
`in height resolution. The process for reconstructing a three-
`dimensional height profile of the c-face from the interferogram
`is as follows. Three reference interferograms with phase shifts
`of (cid:240)/2 to each other are digitally composed in a signal processor
`as carrier fringes. Three Moire interferograms of intensity Ij (j
`) 1, 2, or 3) are created between the interferogram of the c-face
`and the three reference interferograms. These three Moire
`interferograms also have phase shifts of (cid:240)/2 to each other. A
`two-dimensional phase distribution profile, (cid:30)(x,y), on the c-face
`is calculated using
`(cid:30)(x,y) ) tan-1[(I3
`
`(2)
`
`- I2 )/(I1
`
`- I2 ) ]+ (cid:240)/4
`
`and is related to the three-dimensional height profile h(x,y) as
`h(x,y) ) (cid:30)(x,y)(cid:236)/4(cid:240)n
`
`(3)
`
`where (cid:236) and n are the wavelength of the laser and the refractive
`index of the solution, respectively. Therefore, the growth rate
`at a certain point on the c-face can be calculated from the change
`in the three-dimensional height profile, with time. All processes
`described above are finished in 1/30 s real time. Growth rates
`were measured at 25 ( 1 (cid:176)C.
`4. Surface Observation. The seed crystals were immersed
`in the pseudophysiological solutions for 4 h at 25(cid:176) C after being
`etched in a 1 N HCl solution. After the immersion, the crystals
`were immediately washed with ultrapure water, and the surface
`morphology of the c-face was observed using a NanoScope III-a
`AFM (Digital Instruments, Inc.). A tapping mode was employed
`for all the observations using silicon cantilevers with a spring
`constant of 20-50 N/m and a J-type (100 (cid:237)m scanning range)
`piezo scanner.
`
`Results
`1. Growing Phase. Growing phase at magnesium concentra-
`tions of 0.045 and 1.5 mM was identified using a micro-Raman
`spectroscopy, since it has been reported that whitlockite, having
`resemblance to (cid:226)-TCP, Ca3(PO4)2, could grow under a room
`temperature in magnesium containing solutions.15 The intense
`3- tetrahedron ((cid:238)1
`peaks for HAP corresponding to the PO4
`symmetric stretching vibration) around 962 cm-1 and the O-H
`stretching vibration around 3576 cm-1 were reported.16 The
`wavenumbers of center positions for (cid:238)1 peaks were observed
`at 960.8, 961.1, and 961.7 cm-1 for seed, growing phase at
`magnesium concentration of 0.045 and 1.5 mM, respectively.
`However, peaks for whitlockite which should appear around
`966 and 408 cm-1 were not detected on growing phase.17 The
`result showed that HAP grew as a major phase even in the
`presence of magnesium.
`
`Figure 2. Relative height as a function of time on the c-face at
`concentrations of (b) 0.03 mM magnesium, (4) 0.3 (cid:237)M zinc, (O) 0.75
`(cid:237)M zinc, (2) 0.75 mM magnesium, and (]) 4.5 (cid:237)» zinc.
`
`2. Growth Rate Measurement. Diminishing growth rates
`with time were observed in all growth rate measurements
`regardless of the concentration of either magnesium or zinc
`(Figure 2). The growth rates diminished more quickly with an
`increase of concentrations of magnesium and zinc. This phenom-
`enon was also observed in the solution without impurities and
`never due to decreasing supersaturation of the solutions during
`the growth. The reason of diminishing growth rates with time
`may be a strain accumulation caused by a structural mismatch
`between the seed surface and the grown layer, as suggested in
`our previous paper.13 The structural mismatch occurs because
`the crystallinity of the grown layer is lower than that of seed
`crystal. The strain accumulation proceeds during the growth and
`increases chemical potential of a bulk crystal following the
`decrease of driving force for the growth, although the super-
`saturation of the solution remains constant. It is expected that
`the high concentration of magnesium or zinc introduces defects
`in a structure of the grown layer and increases strain accumula-
`tion. The growth rate approached nearly zero after 4 h ofgrowth
`although the supersaturation remained unchanged with respect
`to HAP. Since the growth rate strongly depended on time, the
`initial growth rates at t ) 0 were used to represent the overall
`growth rates in the following analysis. The initial growth rate
`was calculated from the slope of the tangent line at t ) 0 of a
`fifth-order polynomial function fitted to the measured data.
`Zinc inhibited the growth of the c-face about 1000 times more
`effectively than magnesium (Figure 3). Zinc addition at a
`concentration of 1.5 (cid:237)M decreased the growth rate by 70%
`whereas a magnesium concentration of 1.5 mM is required to
`decrease the growth rate to the same level. Zinc inhibited the
`growth of the c-face more completely than magnesium (Figure
`3). Zinc reduced the growth rate by 90% at
`the highest
`concentration in the measured range, although magnesium
`reduced the growth rate by 70%. The total thickness of the
`
`000002
`
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`

`Crystallization Kinetics of Hydroxyapatite (0001) Face
`
`J. Phys. Chem. B, Vol. 104, No. 17, 2000 4191
`
`Figure 3. Growth rate of c-face as a function of impurity concentration (a) in the presence of magnesium and (b) in the presence of zinc.
`
`Figure 4. Total thickness of grown layer as a function of impurity concentration (a) in the presence of magnesium and (b) in the presence of zinc.
`
`Figure 5. AFM images of c-faces after 4 h ofgrowth at concentrations of (a) 0.03 mM magnesium, (b) 0.3 mM magnesium, (c) 1.5 mM magnesium,
`(d) 0.3 (cid:237)M zinc (e) 1.5 (cid:237)M zinc, and (f) 7.5 (cid:237)M zinc.
`
`grown layer ultimately decreased by about 95 and 80% with
`the presence of zinc and magnesium, respectively (Figure 4).
`3. Surface Observation. The growth of the c-face proceeded
`in a multiple two-dimensional nucleation mode (Figure 5). No
`spiral growth was observed. Even in the presence of magnesium
`or zinc, this growth feature was unchanged, except for a decrease
`in the diameter of two-dimensional islands. It was found that
`zinc reduced the diameter more effectively and completely than
`magnesium (Figure 6), as in the result of growth rate measure-
`ment (Figure 3). Therefore, zinc more strongly inhibits the lateral
`growth of two-dimensional islands than magnesium.
`The density of nuclei on the c-face was 1500-2000/(cid:237)m2
`regardless of the magnesium or zinc concentration. Therefore,
`
`the nucleation rate J can be assumed to be constant regardless
`of the magnesium or zinc concentration in the measured range
`at the present supersaturation with respect to HAP.
`4. Models for Impurity Adsorption. The relationship
`between the growth rate and the concentration of magnesium
`or zinc was analyzed using Langmuir and Temkin adsorption
`isotherms. When an impurity, either magnesium or zinc, poisons
`active growth sites on the c-face, the coverage by impurities,
`ı, for each adsorption model is described by
`ı ) KCi/(1 + KCi), Langmuir isotherm
`+ Z ln Ci, Temkin isotherm
`ı ) Z ln C0
`
`(5)
`
`(4)
`
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`

`4192 J. Phys. Chem. B, Vol. 104, No. 17, 2000
`
`Kanzaki et al.
`
`Figure 6. The diameter of two-dimensional islands nucleated on the c-face as a function of impurity concentration (a) in the presence of magnesium
`and (b) in the presence of zinc.
`
`Figure 7. (a) Langmuir plots and (b) Temkin plots; (b) kink model, (2) terrace model.
`
`the face growth rate R is related to the nucleation rate J and the
`step velocity V as
`
`where K and Ci are the adsorption constant for the Langmuir
`isotherm and an impurity concentration, respectively; C0 and Z
`are the adsorption constant for the Temkin isotherm and a
`constant, respectively. The ı affects the step velocity differently
`depending on whether the adsorption site is a kink of a step
`front or a surface terrace. When the adsorption site is the kink
`site, the step velocity is related to the impurity concentration
`as18-19
`
`- V
`
`V0/(V
`
`0
`- V
`(V
`
`0
`
`-1{1 + 1/KCi
`}, Langmuir isotherm (6)
`i) ) R
`l
`}, Temkin isotherm (7)
`{ln C0
`) ZR
`i)/V
`+ ln Ci
`
`0
`
`l
`
`where V0 and Vi are the step velocities in the absence and
`presence of impurities, respectively; Rl is an effectiveness factor
`for impurity adsorption at
`the kink site as a function of
`supersaturation. When the adsorption site is the surface terrace,
`the step velocity is related to the impurity concentration as18-19
`
`{V
`0/(V
`
`0
`
`- V
`
`i)}2 ) R
`
`s
`
`{(V
`
`0
`
`- V
`
`i)/V
`
`0
`
`}2 ) ZR
`
`2{ln C0
`
`s
`
`+ ln Ci
`
`-2{1+ 1/KCi
`}, Langmuir isotherm
`(8)
`}, Temkin isotherm
`(9)
`
`where Rs is an effectiveness factor for impurity adsorption on
`the surface terrace as a function of supersaturation. Because
`
`R (cid:181)
`J1/3 V2/3
`(10)
`eqs 6-9 may be described, using R, as follows when J is
`constant regardless of the impurity concentration:
`-1{1 + 1/KCi
`},
`3/2 - Ri
`Langmuir kink model (11)
`-2{1 + 1/KCi
`},
`Langmuir terrace model (12)
`{ln C0
`
`R0
`
`3/2/(R0
`
`3/2) ) R
`
`l
`
`{R0
`
`3/2/(R0
`
`3/2 - Ri
`
`3/2)}2 ) R
`
`s
`
`(R0
`
`3/2 - Ri
`
`3/2)/R0
`
`3/2 ) ZR
`
`l
`
`{(R0
`
`3/2 - Ri
`
`3/2)/R0
`
`3/2}2 ) ZR
`
`s
`
`},
`+ ln Ci
`Temkin kink model (13)
`2{ln C0
`},
`+ ln Ci
`Temkin terrace model (14)
`
`where R0 and Ri are face growth rates in the absence and
`presence of impurities, respectively.
`The adsorption of magnesium and zinc was well described
`3/2 - Ri
`3/2)
`3/2/(R0
`by the Langmuir kink model. The plots of R0
`(eq 11) showed linear dependence on 1/Ci in the whole range
`of magnesium and zinc concentrations although the plots of
`3/2)}2 (eq 13) showed nonlinear dependence
`{R0
`3/2 - Ri
`3/2/(R0
`
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`

`Crystallization Kinetics of Hydroxyapatite (0001) Face
`
`J. Phys. Chem. B, Vol. 104, No. 17, 2000 4193
`
`TABLE 1: Adsorption Constants of Magnesium and Zinc
`for the HAP c-face at pH 7.4 and at 25 (cid:176)C
`adsorption mechanism impurity
`concentration K or C0 (L/mol)
`1.97 (cid:2) 104
`<1.5 mM
`Langmuir kink model
`Mg
`2.13 (cid:2) 106
`<7.5 (cid:237)M
`kink model
`Zn
`1.12 (cid:2) 105
`<0.15 mM
`Temkin kink model
`Mg
`1.10 (cid:2) 1012
`>0.15 mM
`kink model
`Mg
`1.67 (cid:2) 107
`<3.0 (cid:237)M
`kink modyel
`Zn
`1.82 (cid:2) 1013
`>3.0 (cid:237)M
`kink model
`Zn
`4.38 (cid:2) 104
`<0.15 mM
`Temkin terrace model
`Mg
`2.26 (cid:2) 108
`>0.15 mM
`terrace model
`Mg
`7.13 (cid:2) 106
`<3.0 (cid:237)M
`terrace model
`Zn
`1.95 (cid:2) 109
`>3.0 (cid:237)M
`terrace model
`Zn
`on 1/Ci (Figures 7a and 7b). The adsorption constants for the
`Langmuir kink model were calculated as Kmg ) 1.97 ( 0.3 (cid:2)
`-1 ) 1.14) and Kzn ) 2.13 ( 0.3 (cid:2) 106 L/mol
`104 L/mol (Rl
`-1 ) 1.00).
`(Rl
`3/2
`On the other hand, in the Temkin isotherm, the plots of (R0
`3/2 and {(R0
`3/2}2 against ln Ci showed
`- Ri
`3/2 - Ri
`3/2)/R0
`3/2)/R0
`the presence of flexion points at a magnesium concentration of
`0.15 mM and a zinc concentration of 3.0 (cid:237)M (Figures 7c,d).
`Each linear part has a different Temkin adsorption constant.
`All adsorption constants for Langmuir and Temkin isotherms
`are listed in Table 1.
`
`Discussion
`The Langmuir kink model showed linear correlation for both
`magnesium and zinc (Figures 7c,d), although the Langmuir
`terrace model showed nonlinear correlation. The Temkin kink
`and terrace models showed linear correlation with flexion points
`(Figures 7c,d). Therefore, it is concluded that the mechanism
`of the inhibitory effect of magnesium and zinc best follows the
`Langmuir kink model. However, if the chemical composition
`and/or structure of impurity species changes with their concen-
`tration, activation energies for adsorption and physical or
`chemical bonding between the species and the c-face surface
`could also change with concentration. In this case, flexion points
`may appear in the relationship described by eqs 13 and 14, as
`shown in Figures 7c,d.
`The AFM observation was consistent with the Langmuir kink
`model. In the Langmuir kink model, the impurities adsorb at
`the kink sites of the step front and inhibit the growth. AFM
`images demonstrated a decrease in diameter of the two-
`dimensional islands with an increase in magnesium or zinc
`concentration. This decrease indicated a reduction in the velocity
`of lateral advancement of step fronts of the two-dimensional
`islands due to the adsorption of the impurities.
`In the Langmuir kink model, the coverage ı was calculated
`(eq 4) as ımg ) 0.94 (Cmg ) 1.5 mM) and ızn ) 0.90 (Czn )
`7.5 (cid:237)M). In the case of zinc, 90% of kinks were poisoned at
`the zinc concentration of 7.5 (cid:237)M, and the growth of the c-face
`was almost completely inhibited (Figure 3b). In the case of
`magnesium, despite 94% of kinks being poisoned at a magne-
`sium concentration of 1.5 mM, growth still proceeded with a
`growth rate of about 2 (cid:2) 10-2 nm/s (Figure 3a). This suggests
`that magnesium was detached from the HAP surface into the
`solution after adsorption, or that magnesium was partially
`incorporated into calcium sites in the HAP structure.
`The roughness of the step front of two-dimensional islands
`is estimated as follows. The value Rl in eq 6 can be calculated
`from the results in Figures 7a and 7b, and is given as18
`R
`) (cid:231)a/ln(1 + (cid:243))kTł0
`l
`
`(15)
`
`where (cid:231) is the edge free energy of the step, a is the size of the
`
`growth unit, k is the Boltzmann constant, T is the absolute
`temperature, and ł0 is the average distance between kinks,
`respectively. The edge free energy for the HAP c-face was found
`to be (cid:231) ) 3.3 kT in our previous study.14 ł0 is estimated as ł0
`(cid:25) a for the HAP c-face, which suggests that the edge of two-
`dimensional islands on the c-face is rough. This indicates that
`a relatively high concentration of impurities is required to poison
`the kink sites, inducing the reduction of the lateral growth of
`two-dimensional islands. Considering that zinc inhibited the
`growth of the c-face more effectively and completely than
`magnesium (Figure 3), the considerable difference in inhibitory
`effect between magnesium and zinc may indicate the difference
`in the size of chemical species of impurities when they adsorb
`on the c-face. It is thus assumed that magnesium and zinc
`adsorbed in the form of free magnesium ions and the zinc
`phosphate compound such as Zn3(PO4)2(cid:226)4H2O (hopeite), re-
`spectively, as presented in the previous report.6 Since the
`molecular size of hopeite is much larger than the size of a free
`cation, it can poisoned several kinks at the same time. This
`assumption is supported by the calculation of supersaturation
`with respect to magnesium phosphate and zinc phosphate. The
`solubility products for Mg3(PO4)2 and Zn3(PO4)2(cid:226)4H2O are
`10-23.98 and 10-35.29, respectively.20,21 The supersaturation of
`solutions used were from -0.99 to -0.76 with respect to Mg3-
`(PO4)2 and from -0.85 to 0.63 with respect to Zn3(PO4)2(cid:226)4H2O,
`respectively.21,22 Since magnesium phosphate is more soluble
`than the zinc phosphate compound, magnesium is more likely
`to take the form of free cations as compared with zinc, in the
`present study.
`On the other hand, zinc may show an inhibitory effect
`regardless of the size of chemical species of impurities. In our
`recent study, it was revealed by ab initio calculation that Zn3-
`(PO4)2 exists stably with two Zn-O bond lengths of 2.04 and
`1.77 Å, whereas each Ca3(PO4)2 or Mg3(PO4)2 has only one
`bond length, 2.30 Å (Ca-O) or 2.03 Å (Mg-O).23 The Zn-O
`bond length of 1.77 Å is obviously shorter than that of Ca-O.
`Indeed, it was found experimentally that two Zn-O bond
`lengths coexist in the hopeite structure. The mean bond lengths
`(Zn-O) are 2.099 and 1.963 Å reported in ref 24 and 2.106
`and 1.949 Å reported in ref 25. Each longer or shorter length is
`found in the ZnO6 octahedron or ZnO4 tetrahedron, respectively.
`On the other hand, calcium in the HAP structure are octahedrally
`coordinated to oxygen atoms from phosphate with a mean bond
`length of 2.36 Å (Ca-O).26 Zinc takes a tetrahedral coordination
`more easily than calcium, due to the smaller ionic radius of
`zinc than that of calcium.27 Therefore, the structural mismatch
`occurs between zinc phosphate and HAP when zinc ion
`combines with phosphate on the HAP surface. This structural
`mismatch causes the large inhibitory effect of zinc and
`completely inhibits the growth of the c-face. In contrast,
`magnesium in Mg3(PO4)2(cid:226)8H2O are octahedrally coordinated to
`oxygen atoms from phosphate with mean bond lengths of 2.08
`Å (Mg-O).28 This means that a serious structural mismatch
`may not occur, even though a magnesium ion combines with
`phosphate on the HAP surface. Although whitlockite was not a
`major growing phase as mentioned in a result section, it may
`be possible that whitlockite is formed as an inhibitor in
`magnesium containing solutions. In this case, however, the
`situation is the same as explained above. Since calcium in
`whitlockite is octahedrally coordinated to oxygen atoms from
`phosphate as well as calcium in HAP, a serious structural
`mismatch between whitlockite and growing HAP should not
`occur. Therefore, considerable difference in the inhibitory effect
`between magnesium and zinc can be explained.
`
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`

`4194 J. Phys. Chem. B, Vol. 104, No. 17, 2000
`The adsorption constant for zinc, Kzn ) 2.13 ( 0.3 (cid:2) 106
`L/mol (25 (cid:176)C and (cid:243) ) 22.0) in the present study which has
`lower coincidence with previous value, Kzn ) 1.5 (cid:2) 105 L/mol
`(37 (cid:176) C and (cid:243) ) 3.6) in ref 6, although the value for magnesium,
`Kmg ) 1.97 ( 0.3 (cid:2) 104 L/mol (25 (cid:176)C and (cid:243) ) 22.0), is
`comparable with the Kmg ) 1.54 (cid:2) 104 L/mol (37 (cid:176)C and (cid:243) )
`8.65) in ref 7. Two possibilities can be considered for the
`discrepancy of Kzn and coincidence of Kmg. In the first
`possibility, the difference in Kzn may be caused by the difference
`in supersaturation with respect to the zinc phosphate compound.
`Supersaturation with respect to the zinc phosphate compound
`in the present study is about 3.5 times higher at maximum as
`compared to that in ref 6 even at the same zinc concentration
`because of higher phosphate concentrations. In the second
`possibility, zinc could adsorb relatively stronger on the a-face
`than c-face in comparison with magnesium. This face-preferred
`adsorption could not detected by the DCC method where the
`growth rate obtained was the average between a- and c-faces.
`
`Acknowledgment. This study was supported by AIST
`(Agency of Industrial Science and Technology) and JRPS
`Research Fellow (Research Fellow of the Japan Society for the
`Promotion of Science).
`
`References and Notes
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