Variety of Aggregation and Growth Processes of Lanthanum Fluoride as a Function of La/F Activity Ratio. 2. Excess of F over La Region. Transformation of Amorphous to Crystalline Phase, POM, SAXS, WAXS, and XRD Study
CRYSTAL GROWTH & DESIGN 2005 VOL. 5, NO. 1 123-128
Nada Stubicˇar,*,† Mirko Stubicˇar,‡ Peter Zipper,§ and Boril Chernev§ Laboratory of Physical Chemistry, Chemistry Department, and Physics Department, Faculty of Science, University of Zagreb, Zagreb, Croatia, and Institute of Chemistry, University of Graz, Graz, Austria Received February 11, 2004;
Revised Manuscript Received September 7, 2004
ABSTRACT: Preparation of lanthanum hydroxy-fluorides using steady-state pF-stat experiments, which ensures constant, very low concentrations of the precipitation components and constant pH during the whole growth process, results in a structural evolution of objects with defined physical parameters and a variety of nonconventional morphologies. This structural evolution was characterized by a combination of techniques, namely, static and dynamic light scattering (SLS and DLS), small-angle and wide-angle X-ray scattering (SAXS and WAXS), X-ray diffraction (XRD), and polarized optical microscopy (POM). It is shown that after the immediate formation of an amorphous glassylike precursor, crystalline nanoparticles of high structural definition and monodispersity transit into hollow spheres with diameters of several hundred nanometers. These large vesicles contained smaller ones, which have shown the Maltese cross. After vesicle deformation and elongation into fibers with extreme length, the nanocrystals are transferred into ribbonlike mesostructures. Assuming rod-shaped nanoparticles with ellipsoidal cross-section, we calculate the semiaxes a ) 3.2 ( 0.2 nm and b ) 9.25 ( 0.3 nm from the cross-section radius of gyration Rc ) 4.9 ( 0.1 nm and thickness radius of gyration Rt ) 1.6 ( 0.1 nm as determined by SAXS measurements. These data yield an axial ratio F ) b/a ) 3. As was presented in part 1, rods of submicrometer size, determined by DLS, grown inside the ribbons, also have a semiaxis ellipsoidal ratio F ) 3.0 ( 0.1 and are monodisperse (the polydispersity index is defined as dw/dn ) 1.01). The same axial ratio F ) 3.0 ( 0.5 was determined by POM on the micron-size scale range. These are three independent methods, which confirm the consistency of morphology. The XRD data (providing an average structure, not a local one) suggest that mainly nonstoichiometric materials of tetragonal structure transform to the stoichiometric equilibrium hexagonal LaF3 structure. The shift of the two strongest peaks to longer distances occurs. This confirms the change in favor of the formation of longer La-F distances instead of shorter La-O distances, which were first formed during the transformation of amorphous gel to crystalline phase, shown on the WAXS and XRD diffractograms. These independent methods convincingly confirm the self-similarity of the particle shape and axial ratio and of the structure evolution in different scale lengths, as in a vast number of cases in the scientific literature. This conclusion is crucial in possible preparation of materials for special applications. Introduction Structural, optical, and electrical properties can be greatly augmented by the preparation of materials with anisotropic microstructures or with anisotropic particles dispersed in an isotropic matrix. The new applications need particles obtained with specific chemical control, with narrowly distributed physical characteristics, e.g., size distribution, shape, and aspect ratio (see also part 1). Particle shape control is complex and requires a fundamental understanding of the solution chemistry, interfacial reactions and kinetics, and their interactions with solid-state chemistry. Anisotropic particles of many compositions and shapes have been reported: γ-Fe2O3 and AgI,1 gold spheroids and nanorods,2 gibbsite Al(OH)3 platelike particles prepared from clay gels,3 and * To whom correspondence should be addressed. Marulic´ev trg 19/ II, P.O. Box 163, Hr-10001 Zagreb, Croatia. E-mail: stubicar@ chem.pmf.hr. Tel:++ 385-1-48 95 529. Fax: ++385-1-48 95 510. † Chemistry Department, University of Zagreb. ‡ Physics Department, University of Zagreb. § Institute of Chemistry, University of Graz.
calcium phosphate-polyaspartate “snowball”-like colloidal aggregates of the platelike nanocrystals;4 furthermore, soft matter such as layered liquid-crystalline assemblies of 1-decyl-3-methylimidazolium bromide (ionogel) capable of anisotropic ion conduction5 and “onionlike” multilayered poly(methyl-methacrylate)/polystyrene composite,6 to mention only a few very interesting studies (plus the references therein). Detailed understanding of the earliest stages of crystal growth or even the nucleation from aqueous solutions of potassium fluoride-lanthanum nitrate is a great challenge because a wide variety of different structures and interfaces, i.e., differently ordered heterogeneous mesophases and solid phases, have been formed. This could lead to the rational design of new materials and their wide application. The solid-state chemistry and physics of LaF3 and of LaOF, stoichiometric and nonstoichiometric phases,7 have been more extensively investigated than processes in solutions. Studying these processes deals with very short time scales (submillisecond range) as well as with very low
10.1021/cg049937s CCC: $30.25 © 2005 American Chemical Society Published on Web 11/18/2004
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concentrations (activities) in solution, which should be kept constant during the growth process investigated to avoid the interplay with secondary nucleation. A contribution to the knowledge about this subject is presented here, with special emphasis on formation of nanoscale particles and their morphological and structural characterization based mainly on the analysis of small-angle X-ray scattering (SAXS) measurements and a correlation with microscopic observations and with the analysis of dynamic light scattering (DLS) measurements. Experimental Section A. Materials. Chemicals and the preparation procedure have been described in part 18 of this series. Spontaneous precipitation, i.e., titration of La(NO3)3 with KF and vice versa up to pH above 6, was performed, as well as the constant composition method (CCM), pF-stat study, at very low supersaturation with respect to LaF3 (s) and at constant pH above 6. In this paper, the constant pH in each run was between 6 and 7.3, which is below the concentration in region II presented in Figure 1 in part 1, i.e., 10-3 > c(La(NO3)3 g 10-5 and 4 × 10-3 < c(KF) < 1 × 10-1. Hence most of the systems examined contained an excess of KF with the activity ratio a(La3+)/a(F-) ) 1/6 and 1/8. For example, when the concentration of lanthanum nitrate was 1 × 10-5 and potassium fluoride was 3 × 10-5 mol/L (concentration ratio 1/3), pHexp ) 6.2, because of reactions in solutions the activity ratio of La- to F-ions was calculated to be 1/8, and pHcalc ) 6.4; the solution was supersaturated only to the less soluble La(OH)3 (s) and undersaturated to the LaF3 (s) phase (log AP ) -19.03, s ) 3.49 and s ) 0.54 with respect to La(OH)3 and LaF3, respectively). Hence, a polymeric, glassylike, more or less turbid phase was obtained, which was the subject of this investigation. B. Methods. Six samples (suspensions) were withdrawn from the vessel at definite times during the pF-stat seeded growth (CCM); i.e., in these particular cases it was at m/m0 from 0.5 to 3.0, step 0.5. This means that in this particular case it was at 50-300% of growth, and the samples were denoted as 2-7, the same as in part 1 for 100-600% of growth. Here m/m0 ) 1.5-4, not 2-7; m0 is the initial mass of seeds added to the working solution. The same seeds described in part 18 were used in these experiments. These samples were subjected to DLS, SAXS and wide-angle X-ray scattering (WAXS), or X-ray diffraction (XRD) study: samples 4 (150%), 5 (200%), and 7 (300% of growth) were taken from the top and from the bottom of the volumetric flask, that is, the supernatant and the dense glassylike settled phase. XRD experiments were done on the suspension and further on the suspension after short centrifugation and dry powder after heating at 100 °C for 1 h. Polarized optical microscopy (POM) examination was done with sample 6 (250% of growth), immediately after putting the suspension between microscopic glasses (in droplet) and later on after water was partly evaporated due to light illumination. DLS experiments were performed at (25 ( 0.1) °C as was described in part 1.8 SAXS measurements were performed (in Graz) at room temperature, 22-23 °C, as well as WAXS measurements. A Kratky compact small-angle X-ray camera (A. Paar) with an entrance slit of 40 µm was used, together with the positionsensitive metal wire detector Braun PSD 50M. The X-ray source was the sealed tube, Philips PW 2253/11 with the copper target (Cu KR, λ ) 0.1542 nm), powered by generator Philips 1830, at 50 kV and 45 mA. The sample was in a horizontally placed, sealed Mark capillary of 1 mm diameter. The difference scattering curve (obtained by the subtraction of the appropriately scaled scattering curve of the solvent from that of the sample) was desmeared by means of the program ITP9,10 (indirect transformation program) in the m-scale range 0.4456-14.924 mm, i.e., in the range of the scattering vector
Stubicˇar et al. h ) 0.083-2.77 nm-1, which is equivalent to approximately 76-2.3 nm in real space. The constant background was subtracted during desmearing. The scattering vector h is defined, as usual, by
h ) 4π sin θ/λ
(1)
(θ is half of the scattering angle). WAXS measurements were performed with a Siemens D500 diffractometer (2θ/θ scan; 2θ steps, 0.1°). The X-ray source was the sealed tube Siemens FK 60-04 with a copper target and the generator Siemens Kristalloflex 710 H, at 40 kV and 30 mA. The detector was a scintillation counter. The sample in a Mark capillary of 1 mm diameter was placed vertically. Measurements were carried out between 6.5° and 60° (or 35°) in 2θ and were repeated 2-6 times for each sample, as were the SAXS measurements. XRD measurements were carried out (in Zagreb using the other diffractometer described earlier)11 on a suspension (see the caption of Figure 8), diffractogram a; immediately after its centrifugation, diffractogram b; ∼1/2 hour after that, diffractogram c; and ∼1 h after centrifugation, diffractogram d. The interplanar spacings, d, were calculated from the XRD data using Bragg’s equation:
d ) λ/(2 sin θ)
(2)
Also, the average characteristic particle dimension (diameter), D, was estimated using the formula by Scherrer:
D ) (0.9λ)/((∆θ) cos θ)
(3)
where λ is the wavelength of the X-rays, θ is Bragg’s angle (as was said above), and ∆θ is the width of the diffraction line at its half intensity maximum.
Results and Discussion A. POM Examination. Systems obtained by the pFstat method (details about preparation were described in the section Materials and in detail in part 1) all show heterogeneous features with optical anisotropy. In the early stage of growth, that is, at 50-200% of growth (samples denoted as 2-5), and also analyzing the supernatant solution of systems at 250% and 300% of growth (samples 6 and 7), there was observed the following. First, empty spherical beads were formed from the “isotropic” solutions, shown in Figure 1a. Afterward they became entrapped with solid particles, shown in Figure 1b. Both photos were taken with unpolarized light. Furthermore, we observed primary spherical well-defined monodisperse particles, which show the Maltese cross, being outside and inside the smaller and larger spherical vesicles, which are multilayers and show four yellow and four turquoise alternating sequences. Vesicles contain the monodisperse (according to the polydispersity index dw/dn from the DLS data also) primary particles (anisotropic spherulites), shown in Figure 1c-e, which were taken using polarized light and a λ plate. In the same system, we have observed aggregates: anisotropic dendrites (Figure 1f-h presented in part 1) and anisotropic fibers and helical, twisted ribbons, shown in Figure 1i. The dense phase from the bottom of the cell of the systems with the higher percentage of growth (samples 6 and 7) displays three-dimensional anisotropic ribbons, extremely long. They are shown in Figure 1j,l,m, with rod particles grown inside the ribbons, Figure 1j. In Figure 1k, images of rods were taken with unpolarized light. The ratios of the major and minor semiaxes of the rods
Transformation of Amorphous to Crystalline LaF3
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Figure 1. Optical microscopic pictures of the heterogeneous systems prepared from La(NO3)3-KF aqueous solutions, with the concentration ratio of 1/3.1 and the activity ratio of 1/8, at attained pH ) 6.4, above the isoelectric point (i.e., sample 6, that is at 250% of growth), prepared by the pF-stat method. (a) Empty spherical beads (hollows) formed first. (b) Large deformed beads, vesicles, entrapped with some solid particles. (c-e) The same as panels a and b taken with polarized light and a λ plate, show the Maltese cross; the multilayers show four yellow and four turquoise sequences alternating. (e) Inside the vesicle are about 30 monodisperse, anisotropic spheres, from the volume calculation; the magnification is 370×. (i-k) Anisotropic ribbonlike features; growing inside them are rod-shaped crystalline particles, magnification 230×, and (k) rods, unpolarized light, 370×. (l-n) Crystals and ribbons together taken using dark field microscopy: (l) four crystals connected at one edge, 230×; (m) anisotropic ribbon, 370×; (n) rhomboidal crystal consisting of sheets of different thicknesses, shown as the spectral colors (see arrow), 370×.
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with ellipsoidal cross-section in 2-D microscopic images, Figure 1j,k, are about 3: F ) 3.0 ( 0.5. Prisms of large crystals are shown together (probably belonging to the rhomboidal or tetragonal crystal structure, as was determined by XRD). Four of them are connected at one edge, as shown in Figure 1l. Large rhomboidal prisms which were grown sheet-by-sheet (or layer-by-layer) show spectral colors caused by the different thicknesses; notice the arrow in Figure 1n. Both hexagonal and tetragonal lanthanum oxy-fluorides possess the structure with distinct alternating layers of complex cation (LaO)n+n and of fluoride anions,7 resulting in the macroscopic texture of crystals. Three distinct motifs, granular (spherulites), fibrillar, and two-dimensional sheetlike, are shown in this particular pure inorganic system, for the first time to the knowledge of the author. A very nice helical twisted strip of a ribbon is displayed. We may suppose that inorganic polymerization reaction, i.e., hydrogen bonds with OH- groups at the surface (at the solid/liquid interface) play a great role here, together with dispersion forces. The F- anion as a highly electronegative anion is able to form strong HF (aq) ion pairs and to substitute water molecules of the aqueous cation (La3+)(H2O)9 leading to the formation of a precursor La(OH)3 and further LaF3. The resemblance to a number of other amphiphilic organic systems and mixed organicinorganic ones13,14 becomes obvious. B. DLS Study. Glassylike precipitates are not suitable for DLS measurements because of the very large size (we may say infinitely long) in one dimension of the particles and also because of a weak contrast between particles and solvent. Very slow relaxation modes of particle motion were measured at small angles, e.g., at θ ) 15°, but rather fast relaxation modes at θ ) 30°, shown in Figure 2a, also at the complementary large angles 120° and 130°. The correlation curve for θ ) 15° was well fitted to a linear function (the firstorder decay function corresponds to a monodisperse system). The other one at 30° is second-order decay function. The histogram of the hydrodynamic particle diameters calculated from the measured autocorrelation function is presented in Figure 2b, for the system obtained by titration of La(NO3)3 with KF up to c(La(NO3)3/c(KF) ) 1/3.2 and the attained pH ) 6.2 (from an acidic to neutral-mildly alkaline solution). The median weight average hydrodynamic diameter dH(15°) ) 9306 ( 386 nm (dw/dn ) 1.01), i.e., in the micron size range, which is beyond the upper confidence limit of DLS determination. However, this is to be expected for the long dimension of ribbons, shown on the microscopic images, although obtained with the different methods, in the different scale regions. This large dimension may be attributed to the distances between small crystalline particles inside the isotropic ribbon matrix, as well. However, the dH of the particles converted from the correlation curve measured at 30° gave median dH(weight average) ) (23.9 ( 3) nm, median dH(number average) ) (22.7 ( 3) nm, dw/dn ) 1.05. This q-dependence is quite the opposite of that shown for systems prepared with an excess of La(NO3)3, described in part 1 (Figures 7 and 8); i.e., at 30° here is a minimum instead of a maximum in size, but the values are the same, 24 nm (Figure 8).
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Figure 2. Panel a (upper): Correlation functions measured at θ ) 15° and 30°. Panel b (lower): Corresponding histogram of the hydrodynamic diameters (DLS) for particles of the glassy precipitate obtained by titration of La(NO3)3 with KF solution up to c(La(NO3)3)/c(KF) ) 1:3 and to the attained pH ) 6.2.
Figure 3. Logarithmic plot of the slit-smeared small-angle X-ray scattering intensity I(h) of sample 7, pF-stat growth up to 300% (after subtraction of the scattering of solvent), versus the modulus of the scattering vector, h.
C. SAXS Study. A typical SAXS difference curve obtained from the sample 7 dense phase (from the bottom of the cell) is presented in Figure 3. No peaks at small angles, below a scattering angle of 2θ ) 20°, were identified. The curve was desmeared by means of the ITP program9,10 (as was indicated above) and analyzed assuming rod-shaped particles (program specification “CYLI”). The number of splines was held
Transformation of Amorphous to Crystalline LaF3
Figure 4. Pair-distance distribution function of cross-section pc(r) of sample 7 as obtained by means of the ITP program, as well as the desmeared scattering intensity I(h).
Figure 5. Guinier plot of the cross-section factor, h I(h), of sample 7. The slope of the straight line fitted to the innermost part of the curve corresponds to the radius of gyration of the cross-section Rc ) 4.9 nm.
Figure 6. Guinier plot of the thickness factor, h2 I(h), of sample 7. The straight line fitted to the curve corresponds to the radius of gyration of the thickness Rt ) 1.6 nm.
constant (equal to 20), and the selected maximum diameter of the cross-section, Dmax, was varied. The most reliable result for the pc(r) function of the cross-section was obtained when Dmax was set to be 18 nm, shown in Figure 4. The Guinier plots of the cross-section factor, h I(h), and of the thickness factor, h2 I(h), of the desmeared scattering curve of sample 7 (cf. Figure 3) are presented in Figures 5 and 6, respectively. The analysis of the innermost part of the curves yielded the crosssection radius of gyration Rc ) 4.9 ( 0.1 nm and the thickness radius of gyration Rt ) 1.6 ( 0.1 nm. Assuming an ellipsoidal cross-section of the rodlike particles, we may estimate the semiaxes of the ellipsoid to be a ) 3.2 ( 0.2 nm and b ) 9.25 ( 0.3 nm; hence F ∼ 3 (exactly
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Figure 7. Wide-angle X-ray diffractograms of the glassylike phase prepared by the pF-stat method at 298.2 K from a solution of 1 × 10-5 mol/L La(NO3)3 and 3 × 10-5 mol/L KF at pH 6.1: grown up to 150% with regard to the initial mass of seeds (sample 4), 200% (sample 5), and 300% (sample 7, taken from the settled part) and that of distilled water.
2.9). A similar axial ratio would also result if the crosssection of the rods was assumed to be of a rectangular shape. In this case, the following edge lengths of the cross-section would result: A ) 5.5 ( 0.4 nm and B ) 16.0 ( 0.3 nm. It can be seen that all three approaches of analysis of the SAXS data are consistent and lead to very similar results for the maximum lateral dimension of rods: Dmax ) 18 nm, determined from the pc(r) function; 2b ) 18.5 nm or (A2 + B2)1/2 ) 17 nm, calculated from the radii of gyration Rc and Rt. Also the ratio F ) b/a ) 3.0 ( 0.1 is in full agreement with that determined by DLS for the rod particles and from the microscopic pictures (i.e., this is in fairly good agreement with the values 24 ( 3 nm and 8 ( 2 nm for the major and minor ellipsoidal semiaxes of rodlike particles determined by DLS (part 1). All three methods (SAXS, DLS, and POM) gave the same ratio of semiaxes although for particles in different length scales. D. WAXS (or XRD) Study. Wide-angle X-ray scattering and X-ray diffraction patterns for the glassylike phase are presented in Figures 7 and 8. No peaks were identified in the scattering angle range below 20°; i.e., no long-range order was detected in these systems. A broad amorphous “halo” is detected for the diluted samples 4 and 5, like that for water. Although there was a relatively small amount of initially added crystalline seeds, they could not be detected (3 mL of seeds in 200 mL of undersaturated working solution with regard to LaF3 at pH 6.2; they could be dissolved or transformed to the amorphous phase, or simply not present in the taken samples). The dense part of sample 7, the settled phase, diffractogram c in Figure 7, shows all six of the strongest peaks of the trigonal tysonite LaF3 structure,12 belonging to the following (hkl) reflections: (110), (111), (300), (113), (302), and (221). The two strongest peaks in the scattering angle range 2θ between 5° and 35°, belonging to the reflections (111) (I/I1 ) 100) at d2 ) 0.3231 nm and doublet (110) (I/I1 ) 40) at d1b ) 0.3596 nm and (002) (I/I1) ) 50 at d1a ) 0.3678 nm, started to develop after centrifugation of the diluted samples, as is presented in Figure 8. By decreasing the water content near the particles in the suspensions (due to the centrifugation and by increasing the time elapsed
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Figure 8. Transformation of the amorphous, nonstoichiometric glassylike phase to the equilibrium, stoichiometric, crystalline, hexagonal LaF3 phase. The glassylike phase was obtained either by titration of La(NO3)3 with KF up to the ratio c(La(NO3)3/c(KF) ) 1/3.2 and changing pH from the acidic region to pH ) 6.2 or by titration of KF with La(NO3)3 up to c(La(NO3)3/c(KF) ) 1/6 and pH ) 6.6, diffractogram a; immediately after its centrifugation, diffractogram b; ∼1/2 and ∼1 h after centrifugation, diffractograms c and d, respectively.
after centrifugation), the positions of the two mentioned peaks, d2 and d1, were shifted to longer distances. This seems to be contradictory, if the closer arrangement is supposed by ordering the crystal lattice. However, the La-F distances are longer than the corresponding La-O distances,7 and this undoubtedly confirms that the structure has changed in favor of fluoride. The position d2 in diffractogram d in Figure 7 and the positions of the other five strong peaks in the diffractogram of the dry glassy precipitate of the system with the excess of fluorine (c(La)/c(F) ) 1/8), as well as those of dry seeds, are identical to those for hexagonal LaF3 given in the JCPDF, Table 32-483. The only difference is the position of the first double peak which is in the table at d1a ) 0.3678 nm and d1b ) 0.3596 nm. Instead, our diffractograms have a broad (unresolved) peak at 0.3619 nm. The line breadths for the reflections (111) and (110) plus (002) give the average particle dimensions 18 and 27 nm, respectively (using Scherrer’s equation). The agreement between the calculated SAXS, DLS, and XRD data is very good. Conclusions The steady-state potentiometric pF-stat method was employed for the preparation of the hierarchical struc-
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tures starting from the amorphous precursor colloidal La(OH)3. The La(NO3)3 concentration in the working solution was very small (smaller than 10-4 mol/L), the KF concentration was in excess, and the attained pH was above 6. (1) The polarizing light microscopic pictures have shown well-defined spherical particles (monodisperse), which show Maltese crosses. They have been transferred into large anisotropic multilayer vesicles, further into anisotropic ribbons with rod-shaped crystalline particles grown inside, and finally into rhomboidal crystals consisting of sheets shown as different spectral colors. The axial ratio of rods from the POM pictures was calculated to be 3.0 ( 0.5. (2) The DLS analysis of the light scattering at small angles (10°) gave the size of the large ribbons (about 9 µm) and the size of small crystalline particles from the scattering at about 30° being 24 nm. This is exactly the same value as for LaF3 particles obtained from the stoichiometric solutions and/or from the solutions with the excess of La-nitrate over KF (part 1). (3) Nanoparticles were characterized by the SAXS method giving the radius of gyration Rc ) 4.9 ( 0.1 nm and the thickness radius of gyration Rt ) 1.6 ( 0.1 nm; from that the axial ratio of the assumed rod-shaped particles was calculated to be 3.0 ( 0.1. (4) The WAXS or XRD analysis gave the evidence about evolution of the structure from the truly amorphous to the equilibrium hexagonal LaF3 via the detection of the shorter La-O distances. Also the average particle dimension of 18 nm is in full agreement with the SAXS data obtained from the pc(r) function. Acknowledgment. Financial support from the Ministry of Science and Technology of the Republic of Croatia is acknowledged, Project No. 0119 622. The authors are grateful to Prof. Dr. Gary W. Poehlein for editing the manuscript. References (1) Adair, J. H.; Suvaci, E. Curr. Opin. Colloid Interface Sci. 2000, 5 (1-2), 160-167. (2) Jana, N. R.; Gearheart, L.; Obare, S. O.; Murphy, C. J. Langmuir 2002, 18, 922-927. (3) Van der Kooij, F. M.; Lekkerkerker, H. N. W. J. Phys. Chem. B 1998, 102, 7829-7832. (4) Peytcheva, A.; Colfen, H.; Schnablegger, H.; Antonietti, M. Colloid Polym. Sci. 2002, 280, 218-227. (5) Firestone, M. A.; Dzielawa, J. A.; Zapol, P.; Curtiss, L. A.; Seifert, S.; Dietz, M. L. Langmuir 2002, 18, 7258-7260. (6) Okubo, M.; Takekoh, R.; Izumi, J. Colloid Polym. Sci. 2001, 279, 513-518. (7) Ho¨lsa¨, J.; Sa¨ilynoja, E.; Rahiala, H.; Valkonen, J. Polyhedron 1997, 16, 3421-3427. (8) Stubicˇar, N. Cryst. Growth Des. 2005, 5, 113-122. (9) Glatter, O. J. Appl. Crystallogr. 1977, 10, 415-421. (10) Glatter, O.; Kratky, O. Small-Angle X-ray Scattering; Academic Press: New York, 1982. (11) Stubicˇar, M.; Bermanec, V.; Stubicˇar, N.; Kudrnovski, D.; Krumes, D. J. Alloys Compd. 2001, 316, 316-320. (12) http://database.iem.ac.ru/mincryst/s; card no. 4416, created 11/03/93, last edition 06/12/2000. (13) Mann, S. Biomineralization, Principles and Concepts in Bioinorganic Materials Chemistry; Oxford University Press: Oxford, 2001. (14) Hamley, I. W. Introduction to Soft Matter; Wiley: Chichester, 2000.
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