Article pubs.acs.org/crystal
Microstructural Variation of Biogenic Calcite with Intracrystalline Organic Macromolecules Taiga Okumura,*,† Michio Suzuki,† Hiromichi Nagasawa,‡ and Toshihiro Kogure† †
Department of Earth and Planetary Science, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan ‡ Department of Applied Biological Chemistry, Graduate School of Agricultural and Life Sciences, The University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-8657, Japan ABSTRACT: The influence of intracrystalline organic macromolecules on the microstructure and properties of host crystals has been investigated by micro- and macroscopic analyses for several biogenic calcites: prisms in the outer layers of pearl oysters (Pinctada fucata), oysters (Crassostrea nippona), and pen shells (Atrina pectinata); folia in the inner layers of C. nippona and scallops (Patinopecten yessoensis); and coccoliths of Pleurochrysis carterae. Thermogravimetric analysis showed that the three prisms contain more intracrystalline organic matter than the folia and coccolith. Transmission electron microscopy (TEM) revealed that Fresnel contrasts, which probably correspond to the intracrystalline organic macromolecules, are distributed inhomogeneously and partition the calcite crystals into subgrains with small misorientations in the prisms of P. f ucata and C. nippona. From peak broadening in powder X-ray diffraction (XRD), we found a large variance of lattice spacing (Δd/d) in the two prisms. On the other hand, intracrystalline macromolecules in the prisms of A. pectinata are distributed rather homogeneously and do not influence the crystal structure, as revealed by diffraction contrast in TEM. XRD of the prisms in A. pectinata indicates significantly smaller Δd/d than that for the other two prisms. In the folia and coccolith, intracrystalline macromolecules were scarcely observed in TEM, and the estimated Δd/d is small.
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INTRODUCTION Biominerals often possess well-regulated structures with superior properties.1,2 Such superiority may be ascribed to the fact that biominerals are not pure inorganic crystals because they contain a certain amount of organic matter. Mollusk shells, for example, contain organic components of up to 5% of the entire weight,3 which may influence the polymorph selection,4,5 morphology,6 and mechanical properties1 of biominerals. Calcium carbonate crystals are the most abundant biominerals. Calcite, one of the polymorphs of calcium carbonate, is the most thermodynamically stable polymorph under ambient conditions, but it is mechanically weak because of the perfect {104} cleavage planes. Biogenic calcite is, however, much more resistant to fractures than abiotic calcite because {104} cleavage planes generally do not develop at the fractures. This is attributed to the existence of organic matter within the crystals,7 but it has not been elucidated at the atomic scale how organic matter modifies the calcite crystals to prevent the cleavages. The relationships between intracrystalline organic matter and calcium carbonate crystals have been investigated using X-ray diffraction (XRD). High-resolution synchrotron XRD analysis indicated that anisotropic lattice distortion and crystallite size exist in the calcite prismatic layers of bivalves, and the anisotropy has been ascribed to intracrystalline organic matter.8 © 2011 American Chemical Society
However, although XRD techniques can quantitatively estimate such anisotropy in the whole specimens, they do not tell us the actual interaction between organic matter and crystals at the micro- or nanoscopic scale. On the other hand, electron beam techniques enable us to observe directly organic matter within biogenic crystals. Voidlike contrasts in calcium carbonate crystals of shells were observed using transmission electron microscopy (TEM) in the past, but they were interpreted as electron-beam damage or heat-induced artifacts caused by electron beams or ion beams during sample preparation.9,10 However, energy-dispersive Xray spectroscopy (EDS) and electron energy-loss spectroscopy (EELS) have recently revealed that these contrasts correspond to organic matter, presumably organic macromolecules, considering their size. These intracrystalline organic macromolecules can be visualized as dark contrasts in high-angle annular dark-field (HAADF) images, using scanning TEM (STEM), or as bright Fresnel contrasts in underfocused, brightfield TEM images.11,12 Spatial relationships between the organic molecules and diffraction contrasts of the crystals in TEM are also valuable.12 Received: July 22, 2011 Revised: November 16, 2011 Published: November 28, 2011 224
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This study used macroscopic to micro- or nanoscopic methods to investigate the relationships between biogenic calcite crystals and intracrystalline organic macromolecules. First, thermogravimetric analysis (TGA) was conducted in order to estimate the amount of organic matter inside calcite crystals. Next, variance of lattice spacing was determined from peak broadening in XRD patterns. Finally, TEM observations were performed to obtain the distribution of intracrystalline organic macromolecules and to understand how they influence the microstructure of the crystals.
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Figure 2. SEM images of the folia of C. nippona (A) and P. yessoensis (B), after the treatment of the foliated layers with a NaClO solution.
EXPERIMENTAL SECTION
sodium dodecyl sulfate and 0.25 mg of Proteinase K in 400 μL of the Na-borate buffer. This treatment was carried out for 24 h at 34 °C with constant stirring. Next, the suspension solution was centrifuged, the supernatant was discarded, and then the pellet was resuspended in a 5% NaClO oxidizing agent solution in 0.1 M NaOH. This treatment was carried out for 16 h at 37 °C with constant stirring. After the NaClO treatment, the suspension solution was centrifuged and washed four times in double distilled water and twice in ethanol. Owing to these treatments, the calcite crystals of the coccolith were free from inter- and extracrystalline organic matter and separated into individual crystal units (Figure 3).
Materials. In the present study, we investigated several biogenic calcites: the outer prismatic layers of pearl oysters (Pinctada f ucata), oysters (Crassostrea nippona), and pen shells (Atrina pectinata); the inner foliated layers of C. nippona and scallops (Patinopecten yessoensis); and the coccoliths of Pleurochrysis carterae. The prismatic layers are composed of calcite prisms surrounded by interprismatic organic walls. The foliated layers consist of bladelike calcite folia. The coccolith of P. carterae is made up of calcite crystals on the rim of an oval-shaped organic base plate. Unlike the prisms, the calcite of the folia and coccolith reflect the euhedral, rhombohedral morphology.13,14 Therefore, we chose these biogenic calcite samples for comparison with the prisms. Finally, Iceland spar, a transparent geological calcite crystal with perfect rhombohedral morphology, was used as a representative of abiotic calcite. Methods. Thermogravimetric Analysis (TGA). Using Thermo plus EVO TG 8120 (Rigaku), TGA was performed in order to estimate the amount of intracrystalline organic matter. From ambient temperature (∼20 °C) to 600 °C, a heating rate of 10 °C/min was adopted. All samples were dried at 60 °C for 24 h before analyses. Then 5−25 mg of the dried samples was placed into the instrument. The shell samples (prisms and folia) were pretreated with a sodium hypochlorite (NaClO) solution for more than 2 days to remove interand extracrystalline organic matter. Due to this treatment, the individual prisms in the prismatic layers separated because of the removal of interprismatic organic walls, as reported by Nudelman et al.15 (Figure 1). On the other hand, the folia did not separate like the
Figure 3. SEM images of the coccoliths of P. carterae before (A) and after (B) the dissolution treatment of organic matter. Calcite crystals are attached to the rim of oval-shaped organic base plates in part A, whereas the base plates are not observed and individual calcite crystals separate from one another in part B. Estimation of Variance of Lattice Spacing (Δd/d) from XRD Patterns. The variance of lattice spacing, which was called “microstrain fluctuations” in a previous paper,17 in calcite was estimated from peak broadening in XRD patterns. Powder XRD patterns were obtained using a RINT-Ultima+ diffractometer (Rigaku) with graphitemonochromated Cu Kα radiation emitted at 40 kV and 20 mA. In order to minimize peak broadening of reflection due to the instrument, we adopted a 0.15 mm receiving slit, a 0.5° divergence slit, and a 0.5° antiscatter slit. The scan rate was 0.1°/min. The samples were placed in the dimple of a glass sample holder. As the amount of the coccolith sample was small, a nonreflecting silicon sample holder was used for the coccolith to improve the signal-tonoise ratio. The shell samples (prisms and folia) were pretreated with NaClO in the same manner as that for TGA. The treatment to dissolve the organic matter was not conducted for the coccolith. We examined the same Iceland spar powder sample three times in order to estimate the error of measurement and the three shell samples each one time to examine individual variability. The variance of the lattice spacing (Δd/d) of the samples was estimated using Williamson−Hall plots18 as follows:
Figure 1. Scanning electron microscope (SEM) images of the prisms of P. fucata (A), C. nippona (B), and A. pectinata (C), after the treatment of the prismatic layers with a NaClO solution. Interprismatic organic walls were completely dissolved and individual prisms separated. prisms even though the interspacing organic matter between the folia vanished (Figure 2). These shell samples and Iceland spar were then ground into powder in an alumina mortar. We weighed the same Iceland spar powder sample three times in order to estimate the error of measurement and the three shell samples each one time to examine individual variability. Using the method employed by Westbroek et al.,16 inter- and extracrystalline organic matter, including the base plates, was completely removed from the coccolith. First, a 10.9 mg frozen pellet of the coccolith was suspended in 5 mL of chloroform−methanol (3:1) and centrifuged. Then, the supernatant was discarded. After this, the pellet was washed four times in 5 mL of chloroform−methanol, once in 5 mL of methanol, and once in a sodium borate buffer (0.1 M, pH 8). The resulting pellet was resuspended in a solution of 5 mg of
⎛ Δd ⎞ 2 sin θ Δ(2θ) cos θ 0.94 + =⎜ ⎟ ⎝ d ⎠ λ L λ
(1)
#tab;where θ is the Bragg angle of the analyzed peak, Δ(2θ) is the fullwidth at half-maximum (FWHM) of the peak, λ is the X-ray wavelength (1.54056 Å for Cu Kα1), and L is the crystallite size. Plotting the left-hand side of [Δ(2θ) cosθ]/λ against (2 sin θ)/λ for a 225
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number of reflections, Δd/d is obtained from the slope of the regression line. However, not only local lattice strain and crystallite size but also instruments contribute to line broadening. Here, we adopted Warren’s method19 to correct for the effects from the instrument, which is given by the following:
[Δ(2θ)]2 = [Δ(2θ)M ]2 − [Δ(2θ)I ]2
(2)
where Δ(2θ)M is the measured FWHM of the diffraction peak and Δ(2θ)I is the FWHM due to the instrument. Δ(2θ)I was estimated using the diffraction pattern of a powdered silicon wafer with adequate grain size, measured under the same geometrical conditions. The contribution of Cu Kα2 to the diffraction patterns was removed with a program installed in the apparatus, assuming that the intensity ratio of Cu Kα1 and Cu Kα2 is 2:1. Transmission Electron Microscope (TEM) Observations. The biogenic calcite crystals were observed using a JEM-2010UHR TEM (JEOL) operated at 200 kV. Cross-sectional specimens of the shell samples (prisms and folia) for TEM examination were prepared using ion-milling. Fractured shells were embedded in epoxy resin and cut using a diamond wheel to laths ∼ 1 mm thick in the appropriate direction, to observe calcite from a direction perpendicular to the caxes. The laths were thinned to ∼50 μm by mechanical grinding and finished by argon ion-milling. Finally, thin amorphous carbon was coated to prevent charge-up. A sample of the coccolith was suspended in ethanol, and a drop of the suspension was put on a microgrid. The homogeneity of the distribution of intracrystalline organic macromolecules in underfocused TEM images was evaluated by the fractal dimension (D), which is often used to describe the complexity of forms and space-filling properties of an object.20 Homogeneity and the value of D are positively related. We used the box-counting method defined by Russell et al.21 to estimate the value of D. First, the original TEM images (1024 × 1024 pixels) were binarized by dividing them into several dozen areas and selecting a suitable threshold in each area. Noise was then removed from the binary images, and regular grids of boxes of variable side-length (ε) were superimposed on the binary images. The side-length (ε) used in this study was 20, 21, 22, 23, ..., 210 pixels. Next, logN(ε) was plotted against log(1/ε) for each ε value, where N(ε) is the number of boxes covering the organic macromolecules. Finally, the value of D was calculated from the slope of the linear regression of logN(ε) against log(1/ε). Calculated D results in values between 1 and 2, and a higher D value indicates more homogeneous distribution of the organic macromolecules. We used the correlation coefficient of the linear regression to evaluate the goodness of fit. All processing was carried out using PopImaging 4.00 (Digital being kids).
Figure 4. (A) Weight loss curves of Iceland spar and the prism of A. pectinata. (B) Weight loss of the various calcite powders from 200 to 550 °C, measured by TGA. The same Iceland spar powder sample was weighed three times. For the prisms and folia, three shell samples were weighed, each one time. Error bars indicate the standard deviation of the measurements.
connected in spite of NaClO treatment (Figure 2), implying that the intercrystalline organic matter of the folia still remained (see the TEM results described later). Hence, the amounts of the intracrystalline organic matter in the folia may be less than those represented in Figure 4B. Variance of Lattice Spacing Determined from XRD Patterns. Figure 5 shows Williamson−Hall plots for each sample. The plots of the three prisms (Figure 5B−D) vary more widely than those of the other samples, possibly because the calcite prisms possess anisotropic lattice distortion and crystallite size.8 The prisms of P. f ucata and C. nippona have the regression line with steeper slopes (Figure 5B and C), indicating large variance of lattice spacing. Figure 6 shows the values of Δd/d. The value of ∼0.02% for Iceland spar may have been caused by grinding the single crystal to a powder form. The values of Δd/d in the prisms of P. f ucata and C. nippona are approximately twice as much as those in the folia and coccolith. In contrast, the value of Δd/d in the prisms of A. pectinata is nearly equal to that in the folia. TEM Observations. Parts A−C of Figure 7 show underfocused, bright-field TEM images of the calcite prisms. The specimens were tilted so as not to show intense diffraction contrast in the images. Spherule-like, bright Fresnel contrasts are distinct. These spherule-like contrasts were also well observed in the specimens prepared by crushing the prisms, indicating that they are not artifacts induced by the ion-milling process. We showed previously that these contrasts of several to ten-odd nanometers correspond to intracrystalline organic macromolecules in biominerals.12 However, such contrasts are very rare within the crystals of the folia and coccolith (Figure 8). In the underfocused images of the folia (Figure 8A−D), the
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RESULTS TGA. The results of the TGA analysis are presented in Figure 4. Since the dominant source of weight loss below 200 °C is regarded as the evaporation of water, and CaCO3 decomposition into CaO and CO2 starts above 600 °C, weight loss from 200 to 550 °C was presumed to be that owing to the combustion of organic matter.8,22 In Figure 4A, the weight loss curves of Iceland spar and the prisms of A. pectinata are shown as representatives of abiotic and biogenic calcite. From this, the evaporation of physically adsorbed water almost finishes by 100 °C. Iceland spar loses weight at a constant rate above 200 °C; therefore, the weight loss of ∼0.2% from 200 to 550 °C for Iceland spar is regarded as instrumental errors. Thus, weight loss exceeding 0.2% in the biogenic calcite represents the amount of organic matter. Considering this offset, the amounts of organic matter in the three prism samples are approximately twice as much as those in the folia and coccolith (Figure 4B). As described in the Experimental Section, the inter- and extracrystalline organic matter of the prisms and coccolith was completely removed (Figures 1 and 3B). On the other hand, the folia were still 226
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Figure 5. Williamson−Hall plots and their regression lines of Iceland spar (A); the prisms in P. fucata (B), C. nippona (C), and A. pectinata (D); the folia in C. nippona (E) and P. yessoensis (F); and the coccolith of P. carterae (G).
contrasts inside the crystal. These observations are consistent with the TGA results that the amount of the intracrystalline organic matter is higher in the prisms than in the folia and coccolith (Figure 4B). In the prism samples, the Fresnel contrasts of P. f ucata and C. nippona appear to be not homogeneously distributed but mostly linearly aligned (Figure 7A and B). In contrast, those of A. pectinata spread out rather homogeneously (Figure 7C). Binary images were obtained from these images with the image processing mentioned above (Figure 7D−F). White parts correspond to the locations of the Fresnel contrasts. These binary images clarify the differences of the distribution of the Fresnel contrasts between the prisms. The Fresnel contrasts, corresponding to the organic macromolecules, divide the crystals into subgrains of a few hundred nanometers in P. f ucata and C. nippona (Figure 7D and E). We determined the homogeneity of the distribution of intracrystalline organic macromolecules by the fractal dimension (D) using the binary images. A higher D value indicates more homogeneous distribution. The D values were 1.44, 1.47, and 1.55 in the prisms of P. f ucata, C. nippona, and A. pectinata, respectively, indicating higher homogeneity in A. pectinata than in P. f ucata and C. nippona. The accuracy of the fractal dimension analysis is verified by the high correlation coefficient values of 0.995,
Figure 6. Variance of lattice spacing (Δd/d) determined from Williamson−Hall plots. The same Iceland spar powder sample was examined three times. For the prisms and folia, three shell samples were examined, each one time. Error bars indicate the standard deviation of the measurements.
Fresnel contrasts concentrate at the boundaries of the folia as “intercrystalline” organic matter but are found scarcely inside the crystals. The intercrystalline organic matter also shows spherule-like contrasts arranged at the crystal boundaries (Figure 8B and D), unlike the intercrystalline organic sheets in nacre. Figure 8E shows an underfocused TEM image of one of the small calcite units of the coccolith, showing no Fresnel 227
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H). The locations of the diffraction contrast almost match the arrangement of the Fresnel contrasts of the intracrystalline organic macromolecules. It is supposed that such linear (or planar) arrangements of the organic macromolecules induce small misorientations between the crystals on both sides with dislocation and/or local lattice strain. Such dislocation or local lattice strain appears as diffraction contrast in Figure 7G and H and probably corresponds to a large variance of lattice spacing estimated by XRD (Figure 6). In the prisms of A. pectinata, on the contrary, smooth bend contours are clearly observed as dark bands in the crystal, indicating that they are nearly strainfree single crystals (Figure 7I). Such bend contours are also found in the folia samples (Figure 8A and C). The coccolith also shows smooth band contrasts similar to bend contours, but in this case they are thickness fringes (Figure 8E). These observations are also consistent with the results of XRD, namely small variance of lattice spacing in the samples other than the prisms of P. f ucata and C. nippona (Figure 6).
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DISCUSSION This study has clearly demonstrated the correspondence between local lattice strain estimated from peak broadening in XRD patterns and microstructures observed by TEM for several biogenic calcites. For the prisms of P. f ucata and C. nippona, in which a large variance of lattice spacing was detected, we propose that the arrangements of organic macromolecules form “subgrain” structures, which cause local lattice strain at the subgrain boundaries where the organic macromolecules are concentrated. Similar subgrain structures with small misorientations at the boundaries were recently reported in the outmost calcite layer of a limpet.23 In mollusk shells, several studies using atomic force microscopy (AFM) revealed submicrometer granules surrounded by “cortices” which are interpreted as organic matter and/or amorphous calcium carbonate.24,25 Such granules may be comparable with the subgrains observed with TEM in this study. However, these
Figure 7. Bright-field TEM images with an underfocused condition of the prisms of P. fucata (A), C. nippona (B), and A. pectinata (C). Parts D−F are binarized images of parts A−C, respectively. Bright-field TEM images of the prisms of P. fucata (G), C. nippona (H), and A. pectinata (I), with crystal orientation to form intense diffraction contrast.
0.994, and 0.995 for P. f ucata, C. nippona, and A. pectinata, respectively. In the bright-field TEM images with crystal orientation to form intense diffraction contrast, the prisms of P. f ucata and C. nippona exhibit distinctive diffraction contrast (Figure 7G and
Figure 8. Bright-field TEM images with an underfocused condition of the folia of C. nippona (A, B) and P. yessoensis (C, D) and the coccolith of P. carterae (E). Parts B and D are enlarged views of the squares in parts A and C, respectively. Arrows indicate the intercrystalline organic matter in the foliated layers. 228
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polysaccharides as intracrystalline organic matter.30 We cannot recognize in the present study what organic components were observed as spherule-like Fresnel contrasts in TEM, but this would be a challenging task in the future. It is interesting to study the structure and composition of intracrystalline organic macromolecules and disclose their functions, for instance, their effects on the mechanical properties of calcite crystals. Berman et al.31 reported that the intracrystalline organic matter extracted from sea urchin skeletons selectively adsorbs onto specific crystal planes of calcite and modifies the crystals to prevent {104} cleavages. It has not been explained, however, how the organic macromolecules actually interact with the crystals. Future work could focus on in vitro crystal growth experiments with organic macromolecules which have been extracted from the biominerals and identified using molecular biological techniques. In the experiments, the reproducibility of similar organic− inorganic nanostructures as described in the present study can also be examined.
AFM images have some inconsistencies with our observations. First, the sizes of the granules in the AFM images are smaller than the subgrains in TEM. Second, although the organic macromolecules surrounding the subgrains are spherule-like and discontinuous, the cortices are continuous. Finally, we never observed such subgrains in the folia, but AFM studies reported similar granular structures even in these samples. The origin of these discrepancies between TEM and AFM images must be examined in the near future. Compared to the prisms of P. f ucata and C. nippona, the folia and coccoliths contain lower amounts of organic macromolecules within the crystals and exhibit small variance of lattice spacing. The morphologies of the calcite crystals in the folia and coccolith reflect the euhedral, rhombohedral shape,13,14 which is probably the result of the low amount of the macromolecules and the small local lattice strain in the crystals. In contrast, the prisms apparently do not reflect the rhombohedral morphology. Although they have the same prismatic structures, the internal structure of the prism in A. pectinata is considerably different from those in P. f ucata and C. nippona; the former is like a monolithic single crystal, and the latter shows subgrain structures. Our results indicate that this difference is not owing to the amount of intracrystalline organic macromolecules but their distinct distribution within the crystals. It is, however, unclear why the organic macromolecules are incorporated into the crystals homogeneously or inhomogeneously, depending on the species. Li et al.26 obtained calcite crystals in vitro with polymers which are distributed homogeneously inside the crystals. Such polymer/crystal composites' syntheses will give hints to understand the distribution of intracrystalline organic macromolecules in biogenic crystals. The subgrain structures formed with the organic macromolecules in the prisms of P. f ucata and C. nippona are similar to the mesocrystals,27 which are superstructures consisting of crystalline nanoparticles of some hundred nanometers to micrometers, attached to each other with almost the same crystal orientation. Mesocrystals are initially a loose aggregation of nanoparticles interspaced by organic matter strongly interacting with the crystals. When the aggregation becomes more structured, the organic matter is incorporated and arranged inside the mesocrystals. For example, acidic proteins are believed to interact strongly with calcite crystals because of their ability to bind with calcium ions.3 One possible explanation for the nonexistence of the mesocrystal-like texture in the structure of the prism of A. pectinata is that the organic macromolecules within the prisms bind less to the calcite crystals than those of P. f ucata and C. nippona. Actually, the prismatic layer in A. pectinata is considerably thicker than those in P. f ucata and C. nippona, which may suggest the nonexistence of distinct crystal-growth inhibitors to bind strongly to the crystals. On the contrary, this speculation may be refuted by the finding that the prisms of Atrina rigida, which is closely related to A. pectinata, contain large amounts of acidic amino acids, such as aspartic acids, which bind strongly to calcium ions.15 However, only the abundance of acidic amino acids in macromolecules (e.g., proteins) does not support the binding ability of calcium carbonate crystals. Other factors, such as protein size and stereochemical matching, are also important.28,29 In addition, biogenic crystals are known to contain not only proteins but also other organic components, such as polysaccharides and lipids. For example, the prisms were reported to contain a certain amount of sulfated
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CONCLUSIONS We examined the microstructures of several biogenic calcites and the distribution of organic macromolecules in them using TEM as well as macroscopic characterizations using TGA and XRD, and the correspondence between the results from these different techniques was discussed. Inhomogeneous distribution of organic macromolecules in the prisms of P. f ucata and C. nippona forms subgrain structures with small misorientations between the grains, which cause local lattice strain and broaden the reflection peaks in the XRD patterns. In the prisms of A. pectinata, such subgrain structures were not observed and local lattice strain is small, though they contain a similar amount of intracrystalline organic macromolecules to those of P. f ucata and C. nippona. In this case, the organic macromolecules are distributed homogeneously in the crystals. Such difference may be originated from the different affinities of the macromolecules to the crystals.
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AUTHOR INFORMATION Corresponding Author *Telephone and Fax: +81-3-5841-4019. E-mail: okumura@eps. s.u-tokyo.ac.jp.
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ACKNOWLEDGMENTS We are grateful to Mr. S. Akera (Tasaki Shinju Co., Ltd.), Prof. K. Okano (Akita Prefectural University), and Prof. T. Sasaki (The University of Tokyo) for providing us the shells of pearl oysters, oysters, and scallops, respectively. We also wish to thank Mr. C. A. Thomson of the University of Tokyo’s GCOE program for the English proofreading and editing of this paper. This work was supported by a Grant-in-Aid for scientific research (Nos. 17GS0311, 22248037, and 22228006) from the Ministry of Education, Culture, Sports, Science and Technology of Japan, and T.O. was in part supported by a Research Fellowship of the Japan Society for the Promotion of Science (JSPS).
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