- Email: [email protected]
Biological control of crystallographic architecture: Hierarchy and co-alignment parameters
Acta Biomaterialia xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
Acta Biomaterialia journal homepage: www.elsevier.com/locate/actabiomat
Biological control of crystallographic architecture: Hierarchy and co-alignment parameters q B.J. Maier a,⇑, E. Griesshaber a, P. Alexa a, A. Ziegler b, H.S. Ubhi c, W.W. Schmahl a a
Ludwig Maximilian University Munich, GeoBioCenter and Department of Earth- and Environmental Sciences, Theresienstrasse 41, D-80333 Munich, Germany Central Facility for Electron Microscopy, University of Ulm, Albert Einstein Allee 11, D-89069 Ulm, Germany c Oxford Instruments, Halifax Road, High Wycombe HP12 3SE, UK b
a r t i c l e
i n f o
Article history: Available online xxxx Keywords: Biomineralization Hierarchical architecture Bivalve Nacre Electron backscatter diffraction
a b s t r a c t Mytilus edulis prismatic calcite and nacre layers exhibit a crystallographic structural hierarchy which differs substantially from the morphological hierarchy. This makes these biomaterials fundamentally different from classical crystalline materials. Morphological building units are defined by their surrounding organic matrix membranes, e.g. calcite fibers or nacre tablets. The crystallographic building units are defined by crystallographic co-orientation. Electron backscatter diffraction quantitatively shows how crystallographic co-orientation propagates across matrix membranes to form highly co-oriented low-mosaic composite-crystal grains, i.e. calcite fiber bundles with an internal mosaic spread of 0.5° full width at half maximum (FWHM) or nacre towergrains with an internal mosaic spread of 2° FWHM. These low-mosaic composite crystals form much larger composite-crystal supergrains, which exhibit a high mosaicity due to misorientations of their constituting calcite fiber bundles or nacre towergrains. For the aragonite layer these supergrains nucleate in one of three aragonite {1 1 0} twin orientations; as a consequence the nacre layer exhibits a twin-domain structure, i.e. the boundaries of adjacent supergrains exhibit a high probability for misorientations around the aragonite c-axis with an angle near 63.8°. Within the supergrains, the constituting towergrains exhibit a high probability for misorientations around the aragonite a-axis with a geometric mean misorientation angle of 10.6°. The calcite layer is composed of a single composite-crystal supergrain on at least the submillimeter length scale. Mutual misorientations of adjacent fiber bundles within the calcite supergrain are mainly around the calcite c-axis with a geometric mean misorientation angle of 9.4°. The c-axis is not parallel to the long axis of the fibers but rather to the (1 0 7) plane normal. The frequency distribution for the occurrence of misorientation angles within supergrains reflects the ability of the organism to maintain homoepitaxial crystallization over a certain length scale. This probability density is distributed log-normally which can be described by a geometric mean and a multiplicative standard deviation. Hence, those parameters are suggested to be a numerical measure for the biological control over crystallographic texture. Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
1. Introduction Mollusc shells are composite biomaterials which consist of biominerals embedded in an organic matrix. These hybrid composite materials exhibit extraordinary toughness as compared to the pure inorganic materials incorporated in the shells [1–4]. The mineral part usually exhibits a crystallographic texture [5] which is the
q Part of the Biomineralization Special Issue, organized by Professor Hermann Ehrlich. ⇑ Corresponding author. Tel.: +49 89 2180 4340. E-mail address: [email protected] (B.J. Maier).
key to understanding the interplay between mineral and organic matrix and therefore the materials design properties. Many bivalve shells consist of an outer calcite and an inner aragonite layer. The calcite layer is composed of calcite fibers 1–2 lm in diameter, reaching lengths of more than 100 lm [6], which are embedded in an organic matrix. They are single-crystal-like aligned and the whole layer is considered as a composite crystal [5] in the sense of strongly co-aligned crystallites forming an ordered architecture of components which in turn forms the composite crystal. Here, each component, i.e. a single calcite fiber, is a mesocrystal [5,7] as it is composed of strongly co-aligned nanocrystals commonly found in prismatic calcite (see Ref. [8] and references therein).
http://dx.doi.org/10.1016/j.actbio.2014.02.039 1742-7061/Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: Maier BJ et al. Biological control of crystallographic architecture: Hierarchy and co-alignment parameters. Acta Biomater (2014), http://dx.doi.org/10.1016/j.actbio.2014.02.039
2
B.J. Maier et al. / Acta Biomaterialia xxx (2014) xxx–xxx
The aragonite layer (nacre) is composed of aragonite tablets separated by organic membranes. It has been shown that nacre rapidly grows in towers and later expands sideways [9], and that the crystallographic lattice of adjacent tablets in such towers is co-oriented with [0 0 1] perpendicular to the platelet plane [10–14]. These findings strongly support the existence of mineral bridges across the interlamellar membranes which are responsible for the continuation of crystal orientation [15,16]. Recently we showed that nacre tablets in Mytilus edulis consist of spherical aragonite nanocrystals 50 nm in size, which are embedded in a 3-D organic framework [17]. This is analogous to the membrane-coated granules found in pearls [18]. These granules, initially composed of amorphous calcium carbonate [18,19], were observed to crystallize rapidly [18,20], i.e. prior to platelet formation, in contrast to other observations which demonstrate compartment formation by membranes prior to crystallization [21–23]. The aragonite nanocrystals exhibit a misorientation spread of 2° full width at half maximum (FWHM) which spans over several (up to 20) mesocrystalline [7] tablets to form composite crystals [17]. These data support the hypothesis that aragonite nacre grows by nanoparticle attachment followed by semicoherent homoepitaxial crystallization. The aim of this paper is to present a detailed orientation/misorientation analysis of the hierarchical crystalline building units present in the calcite and aragonite layers of the bivalve shell in order to establish qualitative numerical parameters for the degree of biological control over the crystallographic alignment of the mineral part, i.e. the crystallographic texture. For this purpose we have chosen to study the shell of M. edulis, which exhibits both calcite and nacre layers. 2. Materials and methods Specimens of M. edulis from Naples harbor (Italy, Mediterranean Sea) were cut into 300 lm thick wafers. For the nacre measurement the cut was applied along the longest axis of the shell from the hinge to the commissure. Thus, the measurement plane is perpendicular to the shell surface, which results in a side view of the nacre tablets. For the calcite measurement, the cut was applied perpendicular to the longest axis of the shell, which results in a cross-sectional view of the calcite fibers. The wafer surfaces were treated with several mechanical polishing steps and finished using etch-polishing with colloidal silica in a vibratory polisher. The samples were coated with 4 nm of carbon. Electron backscatter diffraction (EBSD) maps were obtained using a field emission gun scanning electron microscope equipped with an Oxford Instruments NordlysNano EBSD detector and AZtecHKL software. EBSD patterns were collected at about one-third of the longest axis from the hinge towards the commissure. An acceleration voltage of 8 kV was applied with 125 and 200 nm step resolution for nacre and calcite, respectively. The patterns were indexed using aragonite lattice parameters of a = 4.97 Å, b = 7.97 Å and c = 5.75 Å for nacre and calcite lattice parameters of a = 4.99 Å and c = 17.06 Å for the calcite fibers. The EBSD maps were evaluated using the MTEX package [24]. In order to visualize the organic matrix in the nacre layer, samples were polished using an Ultracut ultramicrotome (Leica). Glass and diamond knives (Diatome, Switzerland) were used to polish planes across the shell, similar to the method described previously in Ref. [25]. The polished planes were subsequently etched for 30, 60 and 90 s with an aqueous solution composed of 2.5% glutaraldehyde (in order to stabilize the organic components) and 0.01 mol l1 MOPS buffer adjusted to a pH of 6.5. Etching was stopped by washing the samples three times with 100% isopropanol. After critical point drying (Bal-Tec CPD 030), the samples were rotary shadowed with 3–4 nm platinum at an angle of 45° using a BAF 300 (Balzers). The exposed organic matrix was analysed by
field-emission scanning electron microscopy (FE-SEM) using a Hitachi S-5200 microscope.
3. Results 3.1. M. edulis nacre layer From an EBSD map the constituting crystal grains can be identified as sets of adjacent measurement pixels which give similar lattice orientation, i.e. which are misoriented by less than a certain threshold angle. Fig. 1b shows that grains determined with a threshold misorientation angle of 3.5° reproduce the nacre tablets quite well. Here grains with less than three measurement pixels were removed from the initially determined grain map and the grains were subsequently recalculated. This procedure removes, for example, grains which have been falsely determined due to misindexed measurement pixels. The EBSD band contrast, i.e. the experimental signal strength of each individual EBSD pattern, is superimposed as an additional gray value on the grain map in Fig. 1b. This reveals the organic membranes between the tablets as white stripes. The distribution of the aragonite c-axis (see the {0 0 1} pole figure in Fig. 1a) shows a single density maximum roughly perpendicular to the surface of the shell. The a-axis distribution shows a band of distinct density maxima perpendicular to the mean c-axis direction. The grains in Fig. 1b are color-coded according to the h angle of the {1 0 0} pole figure in Fig. 1a and therefore different color indicates different orientations rotated around the mean c-axis direction. Most of these grains are composed of stacks of several aragonite tablets, and these so-called towergrains can therefore be considered as composite crystals [5,17]. However, one should keep in mind that the threshold angle is arbitrary. A threshold angle smaller than 3.5° divides single aragonite tablets, while increasing the threshold angle increases the size of the towergrains until the whole nacre layer is a single grain at threshold angles above 60°. As a consequence, the following analysis carefully determines the properties of mutual misorientations for measurement pixels at grain boundaries of adjacent grains in order to establish meaningful threshold angles. Fig. 2a shows the distribution of misorientation angles between neighboring pixels which are misoriented by >0.3°, the instrumental resolution for the orientation measurement. This distribution shows a dominant maximum for very small-angle misorientations. This maximum has a FWHM of 2°, and it tails out up to 30° [17]. In the high-angle regime there is a doublet peak near 60° which indicates cyclic aragonite {1 1 0} triplet twinning for which the theoretical misorientation angle is 63.8° around [0 0 1] for the first and 52.4° around [0 0 1] for the second twin. For the grain boundary misorientations between tablet grains defined by a 3.5° misorientation threshold only a single maximum near 64° remains (see Fig. 2b). Hence, there is no cyclic {1 1 0} triplet twinning between tablet grains but possibly within them. To analyze the microstructure further, we also determine the rotation axes corresponding to the misorientations. Fig. 2c,d plot the rotation axis distribution, i.e. the frequency (probability) by which a certain crystallographic direction acts as a rotation axis at the grain boundary in the statistical ensemble provided by our map. The rotation axes are displayed in a symmetrical unique sector of the stereographic projection for the orthorhombic symmetry of the aragonite lattice. Fig. 2c shows results for boundaries with misorientation angles <30°, and Fig. 2d applies to boundaries with misorientation angles >0°. For the small-angle misorientations a high frequency of rotation axes close to the aragonite a-axis is revealed, with the a-axis itself showing the maximum probability. For large-angle misorientations a very high probability density is found for rotation axes close to the aragonite c-axis, which itself
Please cite this article in press as: Maier BJ et al. Biological control of crystallographic architecture: Hierarchy and co-alignment parameters. Acta Biomater (2014), http://dx.doi.org/10.1016/j.actbio.2014.02.039
B.J. Maier et al. / Acta Biomaterialia xxx (2014) xxx–xxx
3
Fig. 1. (a) Orientations of all measured EBSD pixels for Mytilus edulis nacre plotted as {1 0 0} and {0 0 1} pole figures. The points are colored after the polar h-angle of the {1 0 0} pole figure superimposed by a gray level representing the band contrast of the according measurement point. The contour lines give the orientation density. (b) Grains larger than three pixels determined from the measured EBSD pixels (125 nm resolution) using a misorientation threshold angle of 3.5°; coloring after (a). The thin gray lines represent grain boundaries with misorientation angles smaller than 30° while the thick black lines represent grain boundaries with a misorientation angles larger than 30°. As a subset to the latter, the thick red lines indicate {1 1 0} twin boundaries (60°–70° misorientation angle). (c) Grains larger than three pixels determined from the measured EBSD pixels using a misorientation threshold angle of 30°; coloring after (a). These supergrains represent co-aligned clusters of towergrains.
coincides with the maximum probability density. The choice of the 30° misorientation angle to separate the two regimes may appear
arbitrary, but this choice very clearly makes the maximum for the a-axis in the low-angle regime most pronounced. Hence, near 30°
Please cite this article in press as: Maier BJ et al. Biological control of crystallographic architecture: Hierarchy and co-alignment parameters. Acta Biomater (2014), http://dx.doi.org/10.1016/j.actbio.2014.02.039
4
B.J. Maier et al. / Acta Biomaterialia xxx (2014) xxx–xxx
within 35° of the aragonite a-axis and c-axis, respectively. As listed in Table 1, this region around the a-axis comprises 47.3% of all misorientations with angles <30°; the 35° region around the c-axis comprises 98.8% of all misorientations with angles >30°. For the a-axis misorientations the probability density F of a misorientation x can be well described with a log-normal distribution (Fig. 3a):
ðln xlÞ2 h e 2r 2 FðxÞ ¼ pffiffiffiffiffiffiffi 2prx
Fig. 2. Misorientation angle distribution of Mytilus edulis nacre grains determined with a threshold angle equal to the instrumental resolution of 0.3° (a) and 3.5° (b). The bottom plots show the rotation axis distribution of misorientations of grains determined with a threshold of 3.5° for misorientation angles <30° (c) and for misorientation angles >30° (d), respectively.
ð1Þ
where l and r are the mean value and the standard deviation of the underlying normal distribution, respectively, and h is a scaling parameter. We chose the log-normal distribution as it is asymmetric and always positive, fits well to the observed misorientation angle distribution, and because the log-normal distribution occurs frequently in natural phenomena [26]. Limpert et al. [26] proposed the geometric mean (median), l ¼ el , and multiplicative standard deviation, r ¼ er , as statistical parameters for describing a log-normal distribution similar to a normal distribution, so that 68.27 % of the data are within l =r and 95.45 % are within l =ðr Þ2 , where the operator = (times/divide) is analogous to the operator ± (plus/ minus) for normal distributions. The fit yields a geometric mean l of 10.6° and a multiplicative standard deviation r of 1.87°. The mode of the distribution, i.e. the most-frequently occurring misorientation angle at grain boundaries of adjacent towergrains, is 8.1°. 3.2. M. edulis calcite layer
misorientation angle a distinct change in the nature of the grain boundary occurs. In order to visualize this change in a map (Fig. 1b), grain boundaries with misorientation angles >30° are highlighted as thick black lines, while a subset of these, namely angles between 60° and 70° corresponding to {1 1 0} twin boundaries, are highlighted as thick red lines. It is evident that the highlighted boundaries enclose clusters of tablets and towergrains with similar color. These clusters can be treated as supergrains with a threshold misorientation angle of 30°. For clarity of this feature in the hierarchical structure, Fig. 1c shows a map of these supergrains. Within each supergrain, the constituting towergrains are co-oriented within 30° and with their small mutual misorientation corresponding to rotations mainly around the aragonite a-axis. In contrast, the boundaries between the supergrains are misoriented at the supergrain boundary by angles >30° and mainly by rotations around the aragonite c-axis, with a dominant probability for misorientations following the aragonite {1 1 0} twinning law. In order to provide a numerical descriptor of the biological control over crystallographic texture we derive some quantitative statistical parameters. Fig. 3a,b shows probability distributions of misorientation angles of rotation axes at the grain boundaries
Fig. 4a shows the {1 0 0} and {0 0 1} pole figures for all orientations measured in the fibrous calcite layer. A single-crystal-like texture is observed, and hence the whole calcite layer has previously been termed a composite crystal [5], as it is composed of co-aligned calcite fibers which are separated by organic matrix membranes. However, when it comes to grain determination, there is a difference between morphological and crystallographic hierarchy, similar to the nacre layer. Defining the threshold angle is again arbitrary within certain limits. Here, threshold angles <0.75° divide mostly single fibers. However, even with that smallest threshold angle, we observe bundles of several fibers which are co-aligned better than 0.75°. The larger the chosen threshold angle, the larger the bundles become, until the whole measured map becomes a single grain. This is the case for misorientation angles >27°. A careful examination of the misorientation angle distribution of ‘‘grains’’ determined with an angular resolution of 0.3° (see Fig. 5a) reveals a bimodal distribution (see inset of Fig. 5a). Extrapolating the trend of the second mode towards lower angles suggests a threshold angle of 2°. Fig. 4b shows the corresponding grain map which is color-coded by the symmetry-constrained azimuthal angle q of the {1 0 0} pole figure (see Fig. 4a). In addition, the band contrast
Fig. 3. (a) Misorientation angle distribution for rotation axes within 35° of the aragonite a-axis (a) and c-axis (b) for towergrains which were determined with a threshold angle of 3.5°. The insets show the according rotation axes. The red line in (a) represents a log-normal distribution fitted to the data.
Please cite this article in press as: Maier BJ et al. Biological control of crystallographic architecture: Hierarchy and co-alignment parameters. Acta Biomater (2014), http://dx.doi.org/10.1016/j.actbio.2014.02.039
B.J. Maier et al. / Acta Biomaterialia xxx (2014) xxx–xxx Table 1 Percentage of rotation axes within 35° from the aragonite a-, b-, and c-axis for different misorientation-angle regimes of misorientations at the grain boundary of towergrains (threshold of 3.5°). The total number of axes is 16384. Rotation axes r
°ðr; aÞ 35 °ðr; bÞ 35 °ðr; cÞ 35
Percentage for Misorientation angles <30°
Misorientation angles >30°
47.3 13.2 11.8
0.1 0.0 98.8
map of individual measurements is superimposed as an additional gray value which clearly reveals the grains as fiber bundles. Each fiber bundle consists of highly co-oriented calcite fibers. The mosaic spread within a fiber bundle is 0.5° FWHM. The fiber bundles themselves are mutually misoriented at their boundaries with angles typically >2°. These misorientations exhibit a dominant probability of having their rotation axes close to the calcite c-axis, as can be seen in Fig. 5b. The observed fiber bundles are similar to crystalline domains found in the prismatic calcite layer of Pinctada margaritifera [27]. The probability distribution for the misorientation angles at the grain boundaries of the fiber bundles is plotted in Fig. 5c. Similar to supergrain-internal misorientations in the nacre layer we fitted a log-normal distribution which yields a geometric mean l of 9.4° and a multiplicative standard deviation r of 1.66°; the most-frequently occurring misorientation angle is 7.2°. 4. Discussion Our analysis of structural hierarchy related to co-orientation or misorientation clearly shows how biological crystalline materials differ fundamentally from classical crystalline materials such as rocks, metals or ceramics. In classical crystalline materials the fundamental microstructural units are traditionally called grains, and the usual understanding of this term implies an identity of the morphological and the crystallographic distinction of one grain from neighboring grains. Our results show that for the investigated example of a biological hard material, the hierarchy of units defined by crystallographic co-orientation differs from the morphological hierarchy. Morphologically the nacre layer is divided into the well-known ‘‘aragonite platelets’’, which are filled with aragonite nanogranules
5
[18,22] embedded in an organic 3-D framework (see Fig. 6) [17]. The analysis of crystallographic co-orientation defines a hierarchy of co-oriented units: nanogranules, towergrains (co-oriented nanogranules across morphological platelets), and supergrains. We do not exclude further levels of hierarchy, which are beyond the resolution or range of the current experiment. The supergrains can be identified by grain boundaries which exhibit exclusively misorientations with angles >30° and rotation axes within 35° of the aragonite c-axis. For these the probability density of the misorientation angle shows a dominant maximum near 64°, which indicates {1 1 0} twinning. Each supergrain is composed of several towergrains which are separated by grain boundaries having misorientation angles <30° and almost every second rotation axis is within 35° of the aragonite a-axis. These observations indicate that the aragonite layer in the M. edulis shell can be regarded as a high-mosaic twinned composite crystal. Note that the twin domains in this composite crystal are supergrains and not potential twin domains within individual tablets. Each supergrain is a composite crystal with a high internal mosaicity. This internal mosaicity leads to deviations of misorientation angle and axis at the boundary of two adjacent twin domains from the ideal value of 63.8° around [0 0 1] for aragonite {1 1 0} twins. Such a picture is in accordance with the double-twinned configuration reported by Chateigner et al. [28], on the basis of X-ray diffraction. Suzuki et al. [29] reported a ‘‘low twin density’’ in nacre, which they concluded from the lack of XRD powder-diffraction line broadening. Line broadening is expected if the {1 1 0} twin domain walls have a separation in the order of 1 lm or lower, as is the case in cross-lamellar microstructures of gastropods [29]. In the nacre investigated in our study, the twin domains are supergrains, hence the separation between the twin domain walls is far too large to give any significant effect on powder XRD line broadening. Moreover, as already stated by Griesshaber et al. [17], while {1 1 0} describes the mirror-twin law only, the actual twin interfaces follow mainly the {0 0 1}-oriented boundaries between the platelets, or, more precisely, between the towergrains. In such a case the relevant line broadening has to be expected in the {0 0 1} reciprocal space direction. The twinned superstructure strongly suggests that each supergrain has a separate nucleation center, and the nucleation occurs in one of the three equivalent {1 1 0} twin orientations. Using the example of the pearl oyster Pinctada fucata, Saruwatari et al. [20], showed very convincing micrographs of individual ‘‘domes’’ of
Fig. 4. (a) Orientations of all measured EBSD pixels for Mytilus edulis calcite plotted as {1 0 0} and {0 0 1} pole figures. The points are colored after the symmetry-constrained azimuthal q-angle of the {1 0 0} pole figure superimposed by a gray level representing the band contrast of the according measurement point. The contour lines give the orientation density. (b) Grains larger than three pixels determined from the measured EBSD pixels (200 nm resolution) using a misorientation threshold angle of 2°, coloring after (a).
Please cite this article in press as: Maier BJ et al. Biological control of crystallographic architecture: Hierarchy and co-alignment parameters. Acta Biomater (2014), http://dx.doi.org/10.1016/j.actbio.2014.02.039
6
B.J. Maier et al. / Acta Biomaterialia xxx (2014) xxx–xxx
Fig. 5. (a) Misorientation angle distribution of Mytilus edulis calcite grains determined with a threshold angle equal to the instrumental resolution of 0.3°. The dotted line is a guide for the eye to indicate the trend of the distribution function associated with the peak near 7° misorientation. (b) Rotation axis distribution and (c) misorientation angle distribution of misorientations of grains determined with a threshold of 2°. The red line in (c) represents a log-normal distribution fitted to the data.
aragonite at the nacre growth front. These domes spread from nucleation centers on the nacre nucleation surface at the nacre/ prismatic interface, until they abut on each other. The final size of these individual domes compares very well with the 20 lm lateral width of our supergrains. The crystal orientation propagates within a supergrain in a homoepitaxial manner. However, the coorientation occasionally is highly disturbed between morphological tablet membranes of adjacent towergrains. This leads to misorientations with a geometric mean angle of 10.6° (individual angles up to 30°) where rotations around the aragonite a-axis are preferred. To explain the crystallographic preferred orientation Saruwatari et al. [20] invoked a competitive growth (‘‘geometrical selection’’) model, suggesting that the nacre aragonite nucleates with random orientation, and the crystallographic anisotropy of growth speed makes {0 0 1} orientations prevail. This model, however, leads to an axial texture, and it does not explain the additional preferred orientation in the a-b-plane, which we observe for M. edulis. In particular, the selection of {1 1 0} triplet–twin orientations leads us to the conclusion that the full 3-D crystallographic alignment already occurs at the stage of nucleation on some anisotropic substrate. The fact that the rotation axes for the misorientations between adjacent towergrains are most frequently close to the a-axis might be related to the recent observation of lineations within nacre tablets along the a-axis [16], which were later revealed as nanolaths of aragonite particles along the a-axis [30]. These features were explained in Ref. [31] as due to the expulsion of organic molecules from more mineralized zones along the a-axis by crystallization
Fig. 6. FE-SEM micrographs of a nacre tablet within the Mytilus edulis nacre layer showing the tablet-internal organic matrix framework (a) and the aragonite nanogranules filling the tablet compartment (b). The nanogranules are a specific feature of biologic aragonite as those are not observed in non-biological aragonite (see Fig. S2).
pressure. Our EBSD analysis does not indicate that these nanolaths are mutually misoriented as whole units; thus they appear to be a purely morphological hierarchical feature. This is underlined by the fact that internal misorientations of single towergrains do not exhibit a significant preference for a specific crystallographic direction as the rotation axis (see Supplementary Fig. S1). The a-axis corresponds to the shortest lattice parameter of aragonite, and is parallel to an O. . .O-edge of the CO3-group. We may assume that the aragonite nucleation on the substrate is directed by functional groups on the surface of the organic matrix, e.g. carboxyl groups, acting as a template similar to the carbonate group for the crystal. The c-axis alignment of the aragonite would require the plane of the carboxyl groups to be oriented parallel to the surface of the shell. Further, the crystal would tend to orient its a-axis parallel to the O. . .O edge of the carboxyl group. Alternatively, the directions of the remaining two O. . .O edges of the carbonate group in the aragonite would be selected with the same probability, which results in nucleation of the three {1 1 0} twin orientations with similar probability. While this mechanism selects the a-axis (and its two correspondents), and nothing selects the b-axis, the a-axis orientation would tend to be aligned, while the b-axis orientation is more sloppy, corresponding to a rotation around a. This may provide the simplest explanation for the observed alignment of aragonite. A difference in morphological and crystallographic hierarchy can also be attributed to the fibrous calcite layer. Instead of single
Please cite this article in press as: Maier BJ et al. Biological control of crystallographic architecture: Hierarchy and co-alignment parameters. Acta Biomater (2014), http://dx.doi.org/10.1016/j.actbio.2014.02.039
B.J. Maier et al. / Acta Biomaterialia xxx (2014) xxx–xxx
Fig. 7. A sketch illustrating mutual misorientations for different misorientation angle distributions with the according geometric mean, deviation, r . (a) small l , small r ; (b) small l , large r ; (c) large l , small r⁄; (d) large l , large r⁄.
fibers, bundles of fibers constitute low-mosaic composite crystals with a mosaic spread of only 0.5° FWHM. These co-oriented fiber bundles form the whole calcite layer, which in turn is regarded as a composite crystal [5]. However, the calcite layer exhibits a much larger mosaicity than single fiber bundles. The layer mosaicity is more comparable to the supergrains observed in the nacre layer, while the fiber bundles can be compared in terms of mosaicity to the towergrains in the nacre layer. Another difference of morphology and crystallographic orientation is revealed by the alignment of the fibers. SEM images revealed that the calcite fibers are inclined by an angle of 45° with respect to the plane tangent of the shell surface [32]. Combining selected-area electron diffraction patterns and XRD data, Feng et al. [32] deduced that the calcite c-axis is parallel to the long axis of the fibers. As a consequence, the (1 0 4) plane is parallel to the shell surface. However, Chateigner et al. [28] observed by XRD that the c-axis is inclined by 75° with respect to the shell-surface plane normal. The h1 1 0i directions lying in the shell-surface plane have an angle of 85° to the growth direction which is perpendicular to the growth lines. Our own unpublished XRD measurements confirm the orientation given by Chateigner et al. [28]. For that orientation the (1 0 7) plane normal, i.e. the (10 0 9) direction, is parallel to the fiber axis and the plane is parallel to the shell surface. This clearly demon(011) strates that the long axis of the fibers does not coincide with the calcite c-axis. Nevertheless, the misorientations at the fiber-bundle grain boundaries have a high probability to have their rotation axes close to the c-axis. The degree of biological control over crystallographic texture is reflected in the log-normal distribution fitted to the misorientation-angle frequency for misorientations at grain boundaries of the components of a composite crystal. The geometric mean l and the multiplicative standard deviation r of the log-normal distribution give a measure for the mosaicity of the composite crystal. For decreasing r the distribution becomes sharper and less skewed, while for decreasing l the distribution moves towards lower misorientation angles. A less skewed distribution means that most misorientations exhibit smaller angles with fewer exceptions towards higher angles. In other words, the smaller these parameters, the better are the components of the composite crystal co-aligned (see Fig. 7). A comparison of the values for the nacre supergrains and the calcite-layer supergrain shows that the latter exhibits a lower mosaicity, i.e. the most-frequent misorientation angle is smaller, as is the probability for the occurrence of large-angle misorientations. Such a comparison of the composite-crystal quality between different species should reflect species-dependent biological control of the crystallographic texture.
7
l , and multiplicative standard
5. Conclusions Aragonite tablets in the nacre layer and calcite fibers in the socalled prismatic layer have always been considered as building units of these materials. Our investigation shows that, in contrast to common non-biological materials, these clearly existing morphological units do not correspond to grains, i.e. to crystallographic building units. The analysis of misorientation indicates at least three hierarchical levels of crystalline structure which are schematically shown in Fig. 8: (1) Co-aligned submicrometer building units (nanogranules) that compose (2) crystal grains, which extend across the organic membranes which separate the morphological tablets or fiber units, respectively [5,17,18,22]. The mosaic spread of the order of 0.5–2° associated with the co-alignment of the nanogranules and/or rods is responsible for the very low angle peak in the frequency distribution of occurring misorientation angles (Figs. 2a and 5a). From our analysis we can support the conclusion of Jacob et al. [18] that ‘‘the granules can be recognized as durable basic building blocks of all higher order structures in nacre’’. These crystal grains of hierarchical level (2) are the towergrains of the nacre and the fiber bundles of the so-called prismatic calcite layer. It is important to stress again the fact that the tablets and fibers are not independent crystallographic units. What is co-oriented are the nanogranules inside the towergrains or fiber bundles. (3) A number of adjacent grains of level (2) (towergrains in nacre, fiber bundles for calcite) together constitute a larger composite crystal supergrain. The mutual misorientations between the grains of level (2) constituting the supergrains of level (3) have a geometric mean of 10.6°, and thus are considerably larger than their internal misorientations. In the frequency distribution of occurring misorientation angles (Figs. 2a and 5a) the second peak in the region 9–11° corresponds to the internal misorientation mosaic spread within the supergrains. In the case of calcite, this supergrain or larger composite crystal constitutes the entire layer on the micrometer scale. On a larger length scale the calcite c-axis rotates with the curvature of the shell valve, hence the whole layer is composed of radial-symmetric high-mosaic composite crystals which in turn consist of low-mosaic fiber-bundle composite crystals. In the case of nacre the collective of supergrains exhibits a twin-domain structure: each twin domain is a high-mosaic compositecrystal supergrain. Note that this twin-domain structure is on the length scale of 30 lm and not related to potential twinning inside of nacre tablets. The high-mosaic composite-crystal supergrains exhibit a strong directional ordering of the misorientation between its constituent grains of level (2). The calcite fiber bundles are
Please cite this article in press as: Maier BJ et al. Biological control of crystallographic architecture: Hierarchy and co-alignment parameters. Acta Biomater (2014), http://dx.doi.org/10.1016/j.actbio.2014.02.039
8
B.J. Maier et al. / Acta Biomaterialia xxx (2014) xxx–xxx
The crystallographically preferred 3-D orientation in the M. edulis shell is induced during the nucleation stage. Acknowledgements Financial support by the German Science Foundation DFG (GR 1235/9-1) is gratefully acknowledged. We thank A. Immenhauser, S. Hahn, E. Kessler and J. Dettmer, Ruhr-Universität Bochum, for providing well-prepared sections of Mytilus edulis. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.actbio. 2014.02.039. Appendix B. Figures with essential color discrimination Certain figures in this article, particularly Figs. 1–5, are difficult to interpret in black and white. The full color images can be found in the on-line version, at http://dx.doi.org/10.1016/j.actbio. 2014.02.039. References
Fig. 8. A sketch illustrating the crystallographic hierarchy levels present in the nacre layer. The numbers in dotted circles represent the according hierarchy level: aragonite nanogranules (1), towergrains (2), and supergrains (3). We emphasize again, that the tablet compartment is only a morphologic feature and does not represent a single crystallographic unit. Note that the mineral bridge is drawn in accordance to [16].
mutually misoriented mainly around the calcite c-axis. The towergrains within a nacre supergrain are mutually misoriented mainly around the aragonite a-axis. The biological control over the crystallographic texture, i.e. the ability of the organism—or system—to maintain a single-crystallike crystallographic alignment during crystallization, is reflected in the frequency distribution of misorientation angles on level (2) of the crystallographic hierarchy, i.e. the misorientation between the towergrains or fiber bundles. The probability density for these misorientation angles follows a log-normal distribution. A fit yields a geometric mean (median) l and a multiplicative standard deviation r (see Fig. 7), both defining easy parameters for the biological control over crystallographic texture for cross-species comparison.
[1] Smith BL, Schaffer TE, Viani M, Thompson JB, Frederick NA, Kindt J, et al. Molecular mechanistic origin of the toughness of natural adhesives, fibers and composites. Nature 1999;399(6738):761–3. [2] Currey JD, Zioupos P, Peter D, Casinos A. Mechanical properties of nacre and highly mineralized bone. Proc R Soc B Biol Sci 2001;268(1462):107–11. [3] Barthelat F, Rabiei R. Toughness amplification in natural composites. J Mech Phys Solids 2011;59(4):829–40. [4] Wang R, Gupta HS. Deformation and fracture mechanisms of bone and nacre. Annu Rev Mater Res 2011;41(1):41–73. [5] Schmahl WW, Griesshaber E, Kelm K, Ball A, Goetz A, Xu DY, et al. Towards systematics of calcite biocrystals: insight from the inside. Z Krist 2012;227(8):604–11. [6] Hahn S, Rodolfo-Metalpa R, Griesshaber E, Schmahl WW, Buhl D, Hall-Spencer JM, et al. Marine bivalve shell geochemistry and ultrastructure from modern low pH environments: environmental effect versus experimental bias. Biogeosciences 2012;9:1897–914. [7] Coelfen H, Antonietti M. Mesocrystals: inorganic superstructures made by highly parallel crystallization and controlled alignment. Angew Chem Int Ed 2005;44(35):5576–91. [8] Olson IC, Metzler RA, Tamura N, Kunz M, Killian CE, Gilbert PU. Crystal lattice tilting in prismatic calcite. J Struct Biol 2013;183(2):180–90. [9] Checa AG, Cartwright JHE, Willinger M-G. The key role of the surface membrane in why gastropod nacre grows in towers. Proc Natl Acad Sci USA 2009;106(1):38–43. [10] Gilbert PUPA, Metzler RA, Zhou D, Scholl A, Doran A, Young A, et al. Gradual ordering in red abalone nacre. J Am Chem Soc 2008;130(51):17519–27. [11] Coppersmith SN, Gilbert PUPA, Metzler RA. Theoretical characterization of a model of aragonite crystal orientation in red abalone nacre. J Phys A Math Theor 2009;42(12):125101. [12] Gries K, Kröger R, Kübel C, Schowalter M, Fritz M, Rosenauer A. Correlation of the orientation of stacked aragonite platelets in nacre and their connection via mineral bridges. Ultramicroscopy 2009;109(3):230–6. [13] Mukai H, Saruwatari K, Nagasawa H, Kogure T. Aragonite twinning in gastropod nacre. J Cryst Growth 2010;312(20):3014–9. [14] Olson IC, Kozdon R, Valley JW, Gilbert PUPA. Mollusk shell nacre ultrastructure correlates with environmental temperature and pressure. J Am Chem Soc 2012;134(17):7351–8. [15] Schäffer TE, Ionescu-Zanetti C, Proksch R, Fritz M, Walters DA, Almqvist N, et al. Does abalone nacre form by heteroepitaxial nucleation or by growth through mineral bridges? Chem Mater 1997;9(8):1731–40. [16] Checa AG, Cartwright JH, Willinger M-G. Mineral bridges in nacre. J Struct Biol 2011;176(3):330–9. [17] Griesshaber E, Ubhi HS, Huber J, Nindiyasari F, Maier BJ, Schmahl WW. Homoepitaxial meso- and microscale crystal co-orientation and organic matrix network structure in Mytilus edulis nacre. Acta Biomater 2013;9(12):9492–502. [18] Jacob D, Soldati A, Wirth R, Huth J, Wehrmeister U, Hofmeister W. Nanostructure, composition and mechanisms of bivalve shell growth. Geochim Cosmochim Acta 2008;72(22):5401–15. [19] Weiss IM, Tuross N, Addadi L, Weiner S. Mollusc larval shell formation: amorphous calcium carbonate is a precursor phase for aragonite. J Exp Zool 2002;293(5):478–91.
Please cite this article in press as: Maier BJ et al. Biological control of crystallographic architecture: Hierarchy and co-alignment parameters. Acta Biomater (2014), http://dx.doi.org/10.1016/j.actbio.2014.02.039
B.J. Maier et al. / Acta Biomaterialia xxx (2014) xxx–xxx [20] Saruwatari K, Matsui T, Mukai H, Nagasawa H, Kogure T. Nucleation and growth of aragonite crystals at the growth front of nacres in pearl oyster, Pinctada fucata. Biomaterials 2009;30(16):3028–34. [21] Bevelander G, Nakahara H. An electron microscope study of the formation of the nacreous layer in the shell of certain bivalve molluscs. Calcif Tissue Res 1969;3(1):84–92. [22] Rousseau M, Lopez E, Couté A, Mascarel G, Smith DC, Naslain R, et al. Sheet nacre growth mechanism: a voronoi model. J Struct Biol 2005;149(2):149–57. [23] Rousseau M, Meibom A, Géze M, Bourrat X, Angellier M, Lopez E. Dynamics of sheet nacre formation in bivalves. J Struct Biol 2009;165(3):190–5. [24] Bachmann F, Hielscher R, Schaeben H. Texture analysis with mtex – free and open source software toolbox. Solid State Phenom 2010;160:63–8. [25] Fabritius H, Walther P, Ziegler A. Architecture of the organic matrix in the sternal CaCO3 deposits of Porcellio scaber (Crustacea, Isopoda). J Struct Biol 2005;150:190–9. [26] Limpert E, Staehl WA, Abbt M. Log-normal distributions across the sciences: keys and clues. Bioscience 2001;51:341–52.
9
[27] Checa AG, Bonarski JT, Willinger MG, Faryna M, Berent K, Kania B, et al. Crystallographic orientation inhomogeneity and crystal splitting in biogenic calcite. J R Soc Interface 2013;10(86):20130425. [28] Chateigner D, Ouhenia S, Krauss C, Hedegaard C, Gil O, Morales M, et al. Voyaging around nacre with the X-ray shuttle: from bio-mineralisation to prosthetics via mollusc phylogeny. Mater Sci Eng A 2010;528:37–51. [29] Suzuki M, Kim H, Mukai H, Nagasawa H, Kogure T. Quantitative XRD analysis of 1 1 0 twin density in biotic aragonites. J Struct Biol 2012;180(3):458–68. [30] Wang S-N, Yan X-H, Wang R, Yu D-H, Wang X-X. A microstructural study of individual nacre tablet of Pinctada maxima. J Struct Biol 2013;183:404–11. [31] Checa AG, Mutvei H, Osuna-Mascaró, Bonarski JT, Faryna M, Berent K, et al. Crystallographic control on the substructure of nacre tablets. J Struct Biol 2013;183:368–76. [32] Feng QL, Li HB, Pu G, Zhang DM, Cui FZ, Li HD, et al. Crystallographic alignment of calcite prisms in the oblique prismatic layer of Mytilus edulis shell. J Mater Sci 2000;35:3337–40.
Please cite this article in press as: Maier BJ et al. Biological control of crystallographic architecture: Hierarchy and co-alignment parameters. Acta Biomater (2014), http://dx.doi.org/10.1016/j.actbio.2014.02.039
Contents lists available at ScienceDirect
Acta Biomaterialia journal homepage: www.elsevier.com/locate/actabiomat
Biological control of crystallographic architecture: Hierarchy and co-alignment parameters q B.J. Maier a,⇑, E. Griesshaber a, P. Alexa a, A. Ziegler b, H.S. Ubhi c, W.W. Schmahl a a
Ludwig Maximilian University Munich, GeoBioCenter and Department of Earth- and Environmental Sciences, Theresienstrasse 41, D-80333 Munich, Germany Central Facility for Electron Microscopy, University of Ulm, Albert Einstein Allee 11, D-89069 Ulm, Germany c Oxford Instruments, Halifax Road, High Wycombe HP12 3SE, UK b
a r t i c l e
i n f o
Article history: Available online xxxx Keywords: Biomineralization Hierarchical architecture Bivalve Nacre Electron backscatter diffraction
a b s t r a c t Mytilus edulis prismatic calcite and nacre layers exhibit a crystallographic structural hierarchy which differs substantially from the morphological hierarchy. This makes these biomaterials fundamentally different from classical crystalline materials. Morphological building units are defined by their surrounding organic matrix membranes, e.g. calcite fibers or nacre tablets. The crystallographic building units are defined by crystallographic co-orientation. Electron backscatter diffraction quantitatively shows how crystallographic co-orientation propagates across matrix membranes to form highly co-oriented low-mosaic composite-crystal grains, i.e. calcite fiber bundles with an internal mosaic spread of 0.5° full width at half maximum (FWHM) or nacre towergrains with an internal mosaic spread of 2° FWHM. These low-mosaic composite crystals form much larger composite-crystal supergrains, which exhibit a high mosaicity due to misorientations of their constituting calcite fiber bundles or nacre towergrains. For the aragonite layer these supergrains nucleate in one of three aragonite {1 1 0} twin orientations; as a consequence the nacre layer exhibits a twin-domain structure, i.e. the boundaries of adjacent supergrains exhibit a high probability for misorientations around the aragonite c-axis with an angle near 63.8°. Within the supergrains, the constituting towergrains exhibit a high probability for misorientations around the aragonite a-axis with a geometric mean misorientation angle of 10.6°. The calcite layer is composed of a single composite-crystal supergrain on at least the submillimeter length scale. Mutual misorientations of adjacent fiber bundles within the calcite supergrain are mainly around the calcite c-axis with a geometric mean misorientation angle of 9.4°. The c-axis is not parallel to the long axis of the fibers but rather to the (1 0 7) plane normal. The frequency distribution for the occurrence of misorientation angles within supergrains reflects the ability of the organism to maintain homoepitaxial crystallization over a certain length scale. This probability density is distributed log-normally which can be described by a geometric mean and a multiplicative standard deviation. Hence, those parameters are suggested to be a numerical measure for the biological control over crystallographic texture. Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
1. Introduction Mollusc shells are composite biomaterials which consist of biominerals embedded in an organic matrix. These hybrid composite materials exhibit extraordinary toughness as compared to the pure inorganic materials incorporated in the shells [1–4]. The mineral part usually exhibits a crystallographic texture [5] which is the
q Part of the Biomineralization Special Issue, organized by Professor Hermann Ehrlich. ⇑ Corresponding author. Tel.: +49 89 2180 4340. E-mail address: [email protected] (B.J. Maier).
key to understanding the interplay between mineral and organic matrix and therefore the materials design properties. Many bivalve shells consist of an outer calcite and an inner aragonite layer. The calcite layer is composed of calcite fibers 1–2 lm in diameter, reaching lengths of more than 100 lm [6], which are embedded in an organic matrix. They are single-crystal-like aligned and the whole layer is considered as a composite crystal [5] in the sense of strongly co-aligned crystallites forming an ordered architecture of components which in turn forms the composite crystal. Here, each component, i.e. a single calcite fiber, is a mesocrystal [5,7] as it is composed of strongly co-aligned nanocrystals commonly found in prismatic calcite (see Ref. [8] and references therein).
http://dx.doi.org/10.1016/j.actbio.2014.02.039 1742-7061/Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: Maier BJ et al. Biological control of crystallographic architecture: Hierarchy and co-alignment parameters. Acta Biomater (2014), http://dx.doi.org/10.1016/j.actbio.2014.02.039
2
B.J. Maier et al. / Acta Biomaterialia xxx (2014) xxx–xxx
The aragonite layer (nacre) is composed of aragonite tablets separated by organic membranes. It has been shown that nacre rapidly grows in towers and later expands sideways [9], and that the crystallographic lattice of adjacent tablets in such towers is co-oriented with [0 0 1] perpendicular to the platelet plane [10–14]. These findings strongly support the existence of mineral bridges across the interlamellar membranes which are responsible for the continuation of crystal orientation [15,16]. Recently we showed that nacre tablets in Mytilus edulis consist of spherical aragonite nanocrystals 50 nm in size, which are embedded in a 3-D organic framework [17]. This is analogous to the membrane-coated granules found in pearls [18]. These granules, initially composed of amorphous calcium carbonate [18,19], were observed to crystallize rapidly [18,20], i.e. prior to platelet formation, in contrast to other observations which demonstrate compartment formation by membranes prior to crystallization [21–23]. The aragonite nanocrystals exhibit a misorientation spread of 2° full width at half maximum (FWHM) which spans over several (up to 20) mesocrystalline [7] tablets to form composite crystals [17]. These data support the hypothesis that aragonite nacre grows by nanoparticle attachment followed by semicoherent homoepitaxial crystallization. The aim of this paper is to present a detailed orientation/misorientation analysis of the hierarchical crystalline building units present in the calcite and aragonite layers of the bivalve shell in order to establish qualitative numerical parameters for the degree of biological control over the crystallographic alignment of the mineral part, i.e. the crystallographic texture. For this purpose we have chosen to study the shell of M. edulis, which exhibits both calcite and nacre layers. 2. Materials and methods Specimens of M. edulis from Naples harbor (Italy, Mediterranean Sea) were cut into 300 lm thick wafers. For the nacre measurement the cut was applied along the longest axis of the shell from the hinge to the commissure. Thus, the measurement plane is perpendicular to the shell surface, which results in a side view of the nacre tablets. For the calcite measurement, the cut was applied perpendicular to the longest axis of the shell, which results in a cross-sectional view of the calcite fibers. The wafer surfaces were treated with several mechanical polishing steps and finished using etch-polishing with colloidal silica in a vibratory polisher. The samples were coated with 4 nm of carbon. Electron backscatter diffraction (EBSD) maps were obtained using a field emission gun scanning electron microscope equipped with an Oxford Instruments NordlysNano EBSD detector and AZtecHKL software. EBSD patterns were collected at about one-third of the longest axis from the hinge towards the commissure. An acceleration voltage of 8 kV was applied with 125 and 200 nm step resolution for nacre and calcite, respectively. The patterns were indexed using aragonite lattice parameters of a = 4.97 Å, b = 7.97 Å and c = 5.75 Å for nacre and calcite lattice parameters of a = 4.99 Å and c = 17.06 Å for the calcite fibers. The EBSD maps were evaluated using the MTEX package [24]. In order to visualize the organic matrix in the nacre layer, samples were polished using an Ultracut ultramicrotome (Leica). Glass and diamond knives (Diatome, Switzerland) were used to polish planes across the shell, similar to the method described previously in Ref. [25]. The polished planes were subsequently etched for 30, 60 and 90 s with an aqueous solution composed of 2.5% glutaraldehyde (in order to stabilize the organic components) and 0.01 mol l1 MOPS buffer adjusted to a pH of 6.5. Etching was stopped by washing the samples three times with 100% isopropanol. After critical point drying (Bal-Tec CPD 030), the samples were rotary shadowed with 3–4 nm platinum at an angle of 45° using a BAF 300 (Balzers). The exposed organic matrix was analysed by
field-emission scanning electron microscopy (FE-SEM) using a Hitachi S-5200 microscope.
3. Results 3.1. M. edulis nacre layer From an EBSD map the constituting crystal grains can be identified as sets of adjacent measurement pixels which give similar lattice orientation, i.e. which are misoriented by less than a certain threshold angle. Fig. 1b shows that grains determined with a threshold misorientation angle of 3.5° reproduce the nacre tablets quite well. Here grains with less than three measurement pixels were removed from the initially determined grain map and the grains were subsequently recalculated. This procedure removes, for example, grains which have been falsely determined due to misindexed measurement pixels. The EBSD band contrast, i.e. the experimental signal strength of each individual EBSD pattern, is superimposed as an additional gray value on the grain map in Fig. 1b. This reveals the organic membranes between the tablets as white stripes. The distribution of the aragonite c-axis (see the {0 0 1} pole figure in Fig. 1a) shows a single density maximum roughly perpendicular to the surface of the shell. The a-axis distribution shows a band of distinct density maxima perpendicular to the mean c-axis direction. The grains in Fig. 1b are color-coded according to the h angle of the {1 0 0} pole figure in Fig. 1a and therefore different color indicates different orientations rotated around the mean c-axis direction. Most of these grains are composed of stacks of several aragonite tablets, and these so-called towergrains can therefore be considered as composite crystals [5,17]. However, one should keep in mind that the threshold angle is arbitrary. A threshold angle smaller than 3.5° divides single aragonite tablets, while increasing the threshold angle increases the size of the towergrains until the whole nacre layer is a single grain at threshold angles above 60°. As a consequence, the following analysis carefully determines the properties of mutual misorientations for measurement pixels at grain boundaries of adjacent grains in order to establish meaningful threshold angles. Fig. 2a shows the distribution of misorientation angles between neighboring pixels which are misoriented by >0.3°, the instrumental resolution for the orientation measurement. This distribution shows a dominant maximum for very small-angle misorientations. This maximum has a FWHM of 2°, and it tails out up to 30° [17]. In the high-angle regime there is a doublet peak near 60° which indicates cyclic aragonite {1 1 0} triplet twinning for which the theoretical misorientation angle is 63.8° around [0 0 1] for the first and 52.4° around [0 0 1] for the second twin. For the grain boundary misorientations between tablet grains defined by a 3.5° misorientation threshold only a single maximum near 64° remains (see Fig. 2b). Hence, there is no cyclic {1 1 0} triplet twinning between tablet grains but possibly within them. To analyze the microstructure further, we also determine the rotation axes corresponding to the misorientations. Fig. 2c,d plot the rotation axis distribution, i.e. the frequency (probability) by which a certain crystallographic direction acts as a rotation axis at the grain boundary in the statistical ensemble provided by our map. The rotation axes are displayed in a symmetrical unique sector of the stereographic projection for the orthorhombic symmetry of the aragonite lattice. Fig. 2c shows results for boundaries with misorientation angles <30°, and Fig. 2d applies to boundaries with misorientation angles >0°. For the small-angle misorientations a high frequency of rotation axes close to the aragonite a-axis is revealed, with the a-axis itself showing the maximum probability. For large-angle misorientations a very high probability density is found for rotation axes close to the aragonite c-axis, which itself
Please cite this article in press as: Maier BJ et al. Biological control of crystallographic architecture: Hierarchy and co-alignment parameters. Acta Biomater (2014), http://dx.doi.org/10.1016/j.actbio.2014.02.039
B.J. Maier et al. / Acta Biomaterialia xxx (2014) xxx–xxx
3
Fig. 1. (a) Orientations of all measured EBSD pixels for Mytilus edulis nacre plotted as {1 0 0} and {0 0 1} pole figures. The points are colored after the polar h-angle of the {1 0 0} pole figure superimposed by a gray level representing the band contrast of the according measurement point. The contour lines give the orientation density. (b) Grains larger than three pixels determined from the measured EBSD pixels (125 nm resolution) using a misorientation threshold angle of 3.5°; coloring after (a). The thin gray lines represent grain boundaries with misorientation angles smaller than 30° while the thick black lines represent grain boundaries with a misorientation angles larger than 30°. As a subset to the latter, the thick red lines indicate {1 1 0} twin boundaries (60°–70° misorientation angle). (c) Grains larger than three pixels determined from the measured EBSD pixels using a misorientation threshold angle of 30°; coloring after (a). These supergrains represent co-aligned clusters of towergrains.
coincides with the maximum probability density. The choice of the 30° misorientation angle to separate the two regimes may appear
arbitrary, but this choice very clearly makes the maximum for the a-axis in the low-angle regime most pronounced. Hence, near 30°
Please cite this article in press as: Maier BJ et al. Biological control of crystallographic architecture: Hierarchy and co-alignment parameters. Acta Biomater (2014), http://dx.doi.org/10.1016/j.actbio.2014.02.039
4
B.J. Maier et al. / Acta Biomaterialia xxx (2014) xxx–xxx
within 35° of the aragonite a-axis and c-axis, respectively. As listed in Table 1, this region around the a-axis comprises 47.3% of all misorientations with angles <30°; the 35° region around the c-axis comprises 98.8% of all misorientations with angles >30°. For the a-axis misorientations the probability density F of a misorientation x can be well described with a log-normal distribution (Fig. 3a):
ðln xlÞ2 h e 2r 2 FðxÞ ¼ pffiffiffiffiffiffiffi 2prx
Fig. 2. Misorientation angle distribution of Mytilus edulis nacre grains determined with a threshold angle equal to the instrumental resolution of 0.3° (a) and 3.5° (b). The bottom plots show the rotation axis distribution of misorientations of grains determined with a threshold of 3.5° for misorientation angles <30° (c) and for misorientation angles >30° (d), respectively.
ð1Þ
where l and r are the mean value and the standard deviation of the underlying normal distribution, respectively, and h is a scaling parameter. We chose the log-normal distribution as it is asymmetric and always positive, fits well to the observed misorientation angle distribution, and because the log-normal distribution occurs frequently in natural phenomena [26]. Limpert et al. [26] proposed the geometric mean (median), l ¼ el , and multiplicative standard deviation, r ¼ er , as statistical parameters for describing a log-normal distribution similar to a normal distribution, so that 68.27 % of the data are within l =r and 95.45 % are within l =ðr Þ2 , where the operator = (times/divide) is analogous to the operator ± (plus/ minus) for normal distributions. The fit yields a geometric mean l of 10.6° and a multiplicative standard deviation r of 1.87°. The mode of the distribution, i.e. the most-frequently occurring misorientation angle at grain boundaries of adjacent towergrains, is 8.1°. 3.2. M. edulis calcite layer
misorientation angle a distinct change in the nature of the grain boundary occurs. In order to visualize this change in a map (Fig. 1b), grain boundaries with misorientation angles >30° are highlighted as thick black lines, while a subset of these, namely angles between 60° and 70° corresponding to {1 1 0} twin boundaries, are highlighted as thick red lines. It is evident that the highlighted boundaries enclose clusters of tablets and towergrains with similar color. These clusters can be treated as supergrains with a threshold misorientation angle of 30°. For clarity of this feature in the hierarchical structure, Fig. 1c shows a map of these supergrains. Within each supergrain, the constituting towergrains are co-oriented within 30° and with their small mutual misorientation corresponding to rotations mainly around the aragonite a-axis. In contrast, the boundaries between the supergrains are misoriented at the supergrain boundary by angles >30° and mainly by rotations around the aragonite c-axis, with a dominant probability for misorientations following the aragonite {1 1 0} twinning law. In order to provide a numerical descriptor of the biological control over crystallographic texture we derive some quantitative statistical parameters. Fig. 3a,b shows probability distributions of misorientation angles of rotation axes at the grain boundaries
Fig. 4a shows the {1 0 0} and {0 0 1} pole figures for all orientations measured in the fibrous calcite layer. A single-crystal-like texture is observed, and hence the whole calcite layer has previously been termed a composite crystal [5], as it is composed of co-aligned calcite fibers which are separated by organic matrix membranes. However, when it comes to grain determination, there is a difference between morphological and crystallographic hierarchy, similar to the nacre layer. Defining the threshold angle is again arbitrary within certain limits. Here, threshold angles <0.75° divide mostly single fibers. However, even with that smallest threshold angle, we observe bundles of several fibers which are co-aligned better than 0.75°. The larger the chosen threshold angle, the larger the bundles become, until the whole measured map becomes a single grain. This is the case for misorientation angles >27°. A careful examination of the misorientation angle distribution of ‘‘grains’’ determined with an angular resolution of 0.3° (see Fig. 5a) reveals a bimodal distribution (see inset of Fig. 5a). Extrapolating the trend of the second mode towards lower angles suggests a threshold angle of 2°. Fig. 4b shows the corresponding grain map which is color-coded by the symmetry-constrained azimuthal angle q of the {1 0 0} pole figure (see Fig. 4a). In addition, the band contrast
Fig. 3. (a) Misorientation angle distribution for rotation axes within 35° of the aragonite a-axis (a) and c-axis (b) for towergrains which were determined with a threshold angle of 3.5°. The insets show the according rotation axes. The red line in (a) represents a log-normal distribution fitted to the data.
Please cite this article in press as: Maier BJ et al. Biological control of crystallographic architecture: Hierarchy and co-alignment parameters. Acta Biomater (2014), http://dx.doi.org/10.1016/j.actbio.2014.02.039
B.J. Maier et al. / Acta Biomaterialia xxx (2014) xxx–xxx Table 1 Percentage of rotation axes within 35° from the aragonite a-, b-, and c-axis for different misorientation-angle regimes of misorientations at the grain boundary of towergrains (threshold of 3.5°). The total number of axes is 16384. Rotation axes r
°ðr; aÞ 35 °ðr; bÞ 35 °ðr; cÞ 35
Percentage for Misorientation angles <30°
Misorientation angles >30°
47.3 13.2 11.8
0.1 0.0 98.8
map of individual measurements is superimposed as an additional gray value which clearly reveals the grains as fiber bundles. Each fiber bundle consists of highly co-oriented calcite fibers. The mosaic spread within a fiber bundle is 0.5° FWHM. The fiber bundles themselves are mutually misoriented at their boundaries with angles typically >2°. These misorientations exhibit a dominant probability of having their rotation axes close to the calcite c-axis, as can be seen in Fig. 5b. The observed fiber bundles are similar to crystalline domains found in the prismatic calcite layer of Pinctada margaritifera [27]. The probability distribution for the misorientation angles at the grain boundaries of the fiber bundles is plotted in Fig. 5c. Similar to supergrain-internal misorientations in the nacre layer we fitted a log-normal distribution which yields a geometric mean l of 9.4° and a multiplicative standard deviation r of 1.66°; the most-frequently occurring misorientation angle is 7.2°. 4. Discussion Our analysis of structural hierarchy related to co-orientation or misorientation clearly shows how biological crystalline materials differ fundamentally from classical crystalline materials such as rocks, metals or ceramics. In classical crystalline materials the fundamental microstructural units are traditionally called grains, and the usual understanding of this term implies an identity of the morphological and the crystallographic distinction of one grain from neighboring grains. Our results show that for the investigated example of a biological hard material, the hierarchy of units defined by crystallographic co-orientation differs from the morphological hierarchy. Morphologically the nacre layer is divided into the well-known ‘‘aragonite platelets’’, which are filled with aragonite nanogranules
5
[18,22] embedded in an organic 3-D framework (see Fig. 6) [17]. The analysis of crystallographic co-orientation defines a hierarchy of co-oriented units: nanogranules, towergrains (co-oriented nanogranules across morphological platelets), and supergrains. We do not exclude further levels of hierarchy, which are beyond the resolution or range of the current experiment. The supergrains can be identified by grain boundaries which exhibit exclusively misorientations with angles >30° and rotation axes within 35° of the aragonite c-axis. For these the probability density of the misorientation angle shows a dominant maximum near 64°, which indicates {1 1 0} twinning. Each supergrain is composed of several towergrains which are separated by grain boundaries having misorientation angles <30° and almost every second rotation axis is within 35° of the aragonite a-axis. These observations indicate that the aragonite layer in the M. edulis shell can be regarded as a high-mosaic twinned composite crystal. Note that the twin domains in this composite crystal are supergrains and not potential twin domains within individual tablets. Each supergrain is a composite crystal with a high internal mosaicity. This internal mosaicity leads to deviations of misorientation angle and axis at the boundary of two adjacent twin domains from the ideal value of 63.8° around [0 0 1] for aragonite {1 1 0} twins. Such a picture is in accordance with the double-twinned configuration reported by Chateigner et al. [28], on the basis of X-ray diffraction. Suzuki et al. [29] reported a ‘‘low twin density’’ in nacre, which they concluded from the lack of XRD powder-diffraction line broadening. Line broadening is expected if the {1 1 0} twin domain walls have a separation in the order of 1 lm or lower, as is the case in cross-lamellar microstructures of gastropods [29]. In the nacre investigated in our study, the twin domains are supergrains, hence the separation between the twin domain walls is far too large to give any significant effect on powder XRD line broadening. Moreover, as already stated by Griesshaber et al. [17], while {1 1 0} describes the mirror-twin law only, the actual twin interfaces follow mainly the {0 0 1}-oriented boundaries between the platelets, or, more precisely, between the towergrains. In such a case the relevant line broadening has to be expected in the {0 0 1} reciprocal space direction. The twinned superstructure strongly suggests that each supergrain has a separate nucleation center, and the nucleation occurs in one of the three equivalent {1 1 0} twin orientations. Using the example of the pearl oyster Pinctada fucata, Saruwatari et al. [20], showed very convincing micrographs of individual ‘‘domes’’ of
Fig. 4. (a) Orientations of all measured EBSD pixels for Mytilus edulis calcite plotted as {1 0 0} and {0 0 1} pole figures. The points are colored after the symmetry-constrained azimuthal q-angle of the {1 0 0} pole figure superimposed by a gray level representing the band contrast of the according measurement point. The contour lines give the orientation density. (b) Grains larger than three pixels determined from the measured EBSD pixels (200 nm resolution) using a misorientation threshold angle of 2°, coloring after (a).
Please cite this article in press as: Maier BJ et al. Biological control of crystallographic architecture: Hierarchy and co-alignment parameters. Acta Biomater (2014), http://dx.doi.org/10.1016/j.actbio.2014.02.039
6
B.J. Maier et al. / Acta Biomaterialia xxx (2014) xxx–xxx
Fig. 5. (a) Misorientation angle distribution of Mytilus edulis calcite grains determined with a threshold angle equal to the instrumental resolution of 0.3°. The dotted line is a guide for the eye to indicate the trend of the distribution function associated with the peak near 7° misorientation. (b) Rotation axis distribution and (c) misorientation angle distribution of misorientations of grains determined with a threshold of 2°. The red line in (c) represents a log-normal distribution fitted to the data.
aragonite at the nacre growth front. These domes spread from nucleation centers on the nacre nucleation surface at the nacre/ prismatic interface, until they abut on each other. The final size of these individual domes compares very well with the 20 lm lateral width of our supergrains. The crystal orientation propagates within a supergrain in a homoepitaxial manner. However, the coorientation occasionally is highly disturbed between morphological tablet membranes of adjacent towergrains. This leads to misorientations with a geometric mean angle of 10.6° (individual angles up to 30°) where rotations around the aragonite a-axis are preferred. To explain the crystallographic preferred orientation Saruwatari et al. [20] invoked a competitive growth (‘‘geometrical selection’’) model, suggesting that the nacre aragonite nucleates with random orientation, and the crystallographic anisotropy of growth speed makes {0 0 1} orientations prevail. This model, however, leads to an axial texture, and it does not explain the additional preferred orientation in the a-b-plane, which we observe for M. edulis. In particular, the selection of {1 1 0} triplet–twin orientations leads us to the conclusion that the full 3-D crystallographic alignment already occurs at the stage of nucleation on some anisotropic substrate. The fact that the rotation axes for the misorientations between adjacent towergrains are most frequently close to the a-axis might be related to the recent observation of lineations within nacre tablets along the a-axis [16], which were later revealed as nanolaths of aragonite particles along the a-axis [30]. These features were explained in Ref. [31] as due to the expulsion of organic molecules from more mineralized zones along the a-axis by crystallization
Fig. 6. FE-SEM micrographs of a nacre tablet within the Mytilus edulis nacre layer showing the tablet-internal organic matrix framework (a) and the aragonite nanogranules filling the tablet compartment (b). The nanogranules are a specific feature of biologic aragonite as those are not observed in non-biological aragonite (see Fig. S2).
pressure. Our EBSD analysis does not indicate that these nanolaths are mutually misoriented as whole units; thus they appear to be a purely morphological hierarchical feature. This is underlined by the fact that internal misorientations of single towergrains do not exhibit a significant preference for a specific crystallographic direction as the rotation axis (see Supplementary Fig. S1). The a-axis corresponds to the shortest lattice parameter of aragonite, and is parallel to an O. . .O-edge of the CO3-group. We may assume that the aragonite nucleation on the substrate is directed by functional groups on the surface of the organic matrix, e.g. carboxyl groups, acting as a template similar to the carbonate group for the crystal. The c-axis alignment of the aragonite would require the plane of the carboxyl groups to be oriented parallel to the surface of the shell. Further, the crystal would tend to orient its a-axis parallel to the O. . .O edge of the carboxyl group. Alternatively, the directions of the remaining two O. . .O edges of the carbonate group in the aragonite would be selected with the same probability, which results in nucleation of the three {1 1 0} twin orientations with similar probability. While this mechanism selects the a-axis (and its two correspondents), and nothing selects the b-axis, the a-axis orientation would tend to be aligned, while the b-axis orientation is more sloppy, corresponding to a rotation around a. This may provide the simplest explanation for the observed alignment of aragonite. A difference in morphological and crystallographic hierarchy can also be attributed to the fibrous calcite layer. Instead of single
Please cite this article in press as: Maier BJ et al. Biological control of crystallographic architecture: Hierarchy and co-alignment parameters. Acta Biomater (2014), http://dx.doi.org/10.1016/j.actbio.2014.02.039
B.J. Maier et al. / Acta Biomaterialia xxx (2014) xxx–xxx
Fig. 7. A sketch illustrating mutual misorientations for different misorientation angle distributions with the according geometric mean, deviation, r . (a) small l , small r ; (b) small l , large r ; (c) large l , small r⁄; (d) large l , large r⁄.
fibers, bundles of fibers constitute low-mosaic composite crystals with a mosaic spread of only 0.5° FWHM. These co-oriented fiber bundles form the whole calcite layer, which in turn is regarded as a composite crystal [5]. However, the calcite layer exhibits a much larger mosaicity than single fiber bundles. The layer mosaicity is more comparable to the supergrains observed in the nacre layer, while the fiber bundles can be compared in terms of mosaicity to the towergrains in the nacre layer. Another difference of morphology and crystallographic orientation is revealed by the alignment of the fibers. SEM images revealed that the calcite fibers are inclined by an angle of 45° with respect to the plane tangent of the shell surface [32]. Combining selected-area electron diffraction patterns and XRD data, Feng et al. [32] deduced that the calcite c-axis is parallel to the long axis of the fibers. As a consequence, the (1 0 4) plane is parallel to the shell surface. However, Chateigner et al. [28] observed by XRD that the c-axis is inclined by 75° with respect to the shell-surface plane normal. The h1 1 0i directions lying in the shell-surface plane have an angle of 85° to the growth direction which is perpendicular to the growth lines. Our own unpublished XRD measurements confirm the orientation given by Chateigner et al. [28]. For that orientation the (1 0 7) plane normal, i.e. the (10 0 9) direction, is parallel to the fiber axis and the plane is parallel to the shell surface. This clearly demon(011) strates that the long axis of the fibers does not coincide with the calcite c-axis. Nevertheless, the misorientations at the fiber-bundle grain boundaries have a high probability to have their rotation axes close to the c-axis. The degree of biological control over crystallographic texture is reflected in the log-normal distribution fitted to the misorientation-angle frequency for misorientations at grain boundaries of the components of a composite crystal. The geometric mean l and the multiplicative standard deviation r of the log-normal distribution give a measure for the mosaicity of the composite crystal. For decreasing r the distribution becomes sharper and less skewed, while for decreasing l the distribution moves towards lower misorientation angles. A less skewed distribution means that most misorientations exhibit smaller angles with fewer exceptions towards higher angles. In other words, the smaller these parameters, the better are the components of the composite crystal co-aligned (see Fig. 7). A comparison of the values for the nacre supergrains and the calcite-layer supergrain shows that the latter exhibits a lower mosaicity, i.e. the most-frequent misorientation angle is smaller, as is the probability for the occurrence of large-angle misorientations. Such a comparison of the composite-crystal quality between different species should reflect species-dependent biological control of the crystallographic texture.
7
l , and multiplicative standard
5. Conclusions Aragonite tablets in the nacre layer and calcite fibers in the socalled prismatic layer have always been considered as building units of these materials. Our investigation shows that, in contrast to common non-biological materials, these clearly existing morphological units do not correspond to grains, i.e. to crystallographic building units. The analysis of misorientation indicates at least three hierarchical levels of crystalline structure which are schematically shown in Fig. 8: (1) Co-aligned submicrometer building units (nanogranules) that compose (2) crystal grains, which extend across the organic membranes which separate the morphological tablets or fiber units, respectively [5,17,18,22]. The mosaic spread of the order of 0.5–2° associated with the co-alignment of the nanogranules and/or rods is responsible for the very low angle peak in the frequency distribution of occurring misorientation angles (Figs. 2a and 5a). From our analysis we can support the conclusion of Jacob et al. [18] that ‘‘the granules can be recognized as durable basic building blocks of all higher order structures in nacre’’. These crystal grains of hierarchical level (2) are the towergrains of the nacre and the fiber bundles of the so-called prismatic calcite layer. It is important to stress again the fact that the tablets and fibers are not independent crystallographic units. What is co-oriented are the nanogranules inside the towergrains or fiber bundles. (3) A number of adjacent grains of level (2) (towergrains in nacre, fiber bundles for calcite) together constitute a larger composite crystal supergrain. The mutual misorientations between the grains of level (2) constituting the supergrains of level (3) have a geometric mean of 10.6°, and thus are considerably larger than their internal misorientations. In the frequency distribution of occurring misorientation angles (Figs. 2a and 5a) the second peak in the region 9–11° corresponds to the internal misorientation mosaic spread within the supergrains. In the case of calcite, this supergrain or larger composite crystal constitutes the entire layer on the micrometer scale. On a larger length scale the calcite c-axis rotates with the curvature of the shell valve, hence the whole layer is composed of radial-symmetric high-mosaic composite crystals which in turn consist of low-mosaic fiber-bundle composite crystals. In the case of nacre the collective of supergrains exhibits a twin-domain structure: each twin domain is a high-mosaic compositecrystal supergrain. Note that this twin-domain structure is on the length scale of 30 lm and not related to potential twinning inside of nacre tablets. The high-mosaic composite-crystal supergrains exhibit a strong directional ordering of the misorientation between its constituent grains of level (2). The calcite fiber bundles are
Please cite this article in press as: Maier BJ et al. Biological control of crystallographic architecture: Hierarchy and co-alignment parameters. Acta Biomater (2014), http://dx.doi.org/10.1016/j.actbio.2014.02.039
8
B.J. Maier et al. / Acta Biomaterialia xxx (2014) xxx–xxx
The crystallographically preferred 3-D orientation in the M. edulis shell is induced during the nucleation stage. Acknowledgements Financial support by the German Science Foundation DFG (GR 1235/9-1) is gratefully acknowledged. We thank A. Immenhauser, S. Hahn, E. Kessler and J. Dettmer, Ruhr-Universität Bochum, for providing well-prepared sections of Mytilus edulis. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.actbio. 2014.02.039. Appendix B. Figures with essential color discrimination Certain figures in this article, particularly Figs. 1–5, are difficult to interpret in black and white. The full color images can be found in the on-line version, at http://dx.doi.org/10.1016/j.actbio. 2014.02.039. References
Fig. 8. A sketch illustrating the crystallographic hierarchy levels present in the nacre layer. The numbers in dotted circles represent the according hierarchy level: aragonite nanogranules (1), towergrains (2), and supergrains (3). We emphasize again, that the tablet compartment is only a morphologic feature and does not represent a single crystallographic unit. Note that the mineral bridge is drawn in accordance to [16].
mutually misoriented mainly around the calcite c-axis. The towergrains within a nacre supergrain are mutually misoriented mainly around the aragonite a-axis. The biological control over the crystallographic texture, i.e. the ability of the organism—or system—to maintain a single-crystallike crystallographic alignment during crystallization, is reflected in the frequency distribution of misorientation angles on level (2) of the crystallographic hierarchy, i.e. the misorientation between the towergrains or fiber bundles. The probability density for these misorientation angles follows a log-normal distribution. A fit yields a geometric mean (median) l and a multiplicative standard deviation r (see Fig. 7), both defining easy parameters for the biological control over crystallographic texture for cross-species comparison.
[1] Smith BL, Schaffer TE, Viani M, Thompson JB, Frederick NA, Kindt J, et al. Molecular mechanistic origin of the toughness of natural adhesives, fibers and composites. Nature 1999;399(6738):761–3. [2] Currey JD, Zioupos P, Peter D, Casinos A. Mechanical properties of nacre and highly mineralized bone. Proc R Soc B Biol Sci 2001;268(1462):107–11. [3] Barthelat F, Rabiei R. Toughness amplification in natural composites. J Mech Phys Solids 2011;59(4):829–40. [4] Wang R, Gupta HS. Deformation and fracture mechanisms of bone and nacre. Annu Rev Mater Res 2011;41(1):41–73. [5] Schmahl WW, Griesshaber E, Kelm K, Ball A, Goetz A, Xu DY, et al. Towards systematics of calcite biocrystals: insight from the inside. Z Krist 2012;227(8):604–11. [6] Hahn S, Rodolfo-Metalpa R, Griesshaber E, Schmahl WW, Buhl D, Hall-Spencer JM, et al. Marine bivalve shell geochemistry and ultrastructure from modern low pH environments: environmental effect versus experimental bias. Biogeosciences 2012;9:1897–914. [7] Coelfen H, Antonietti M. Mesocrystals: inorganic superstructures made by highly parallel crystallization and controlled alignment. Angew Chem Int Ed 2005;44(35):5576–91. [8] Olson IC, Metzler RA, Tamura N, Kunz M, Killian CE, Gilbert PU. Crystal lattice tilting in prismatic calcite. J Struct Biol 2013;183(2):180–90. [9] Checa AG, Cartwright JHE, Willinger M-G. The key role of the surface membrane in why gastropod nacre grows in towers. Proc Natl Acad Sci USA 2009;106(1):38–43. [10] Gilbert PUPA, Metzler RA, Zhou D, Scholl A, Doran A, Young A, et al. Gradual ordering in red abalone nacre. J Am Chem Soc 2008;130(51):17519–27. [11] Coppersmith SN, Gilbert PUPA, Metzler RA. Theoretical characterization of a model of aragonite crystal orientation in red abalone nacre. J Phys A Math Theor 2009;42(12):125101. [12] Gries K, Kröger R, Kübel C, Schowalter M, Fritz M, Rosenauer A. Correlation of the orientation of stacked aragonite platelets in nacre and their connection via mineral bridges. Ultramicroscopy 2009;109(3):230–6. [13] Mukai H, Saruwatari K, Nagasawa H, Kogure T. Aragonite twinning in gastropod nacre. J Cryst Growth 2010;312(20):3014–9. [14] Olson IC, Kozdon R, Valley JW, Gilbert PUPA. Mollusk shell nacre ultrastructure correlates with environmental temperature and pressure. J Am Chem Soc 2012;134(17):7351–8. [15] Schäffer TE, Ionescu-Zanetti C, Proksch R, Fritz M, Walters DA, Almqvist N, et al. Does abalone nacre form by heteroepitaxial nucleation or by growth through mineral bridges? Chem Mater 1997;9(8):1731–40. [16] Checa AG, Cartwright JH, Willinger M-G. Mineral bridges in nacre. J Struct Biol 2011;176(3):330–9. [17] Griesshaber E, Ubhi HS, Huber J, Nindiyasari F, Maier BJ, Schmahl WW. Homoepitaxial meso- and microscale crystal co-orientation and organic matrix network structure in Mytilus edulis nacre. Acta Biomater 2013;9(12):9492–502. [18] Jacob D, Soldati A, Wirth R, Huth J, Wehrmeister U, Hofmeister W. Nanostructure, composition and mechanisms of bivalve shell growth. Geochim Cosmochim Acta 2008;72(22):5401–15. [19] Weiss IM, Tuross N, Addadi L, Weiner S. Mollusc larval shell formation: amorphous calcium carbonate is a precursor phase for aragonite. J Exp Zool 2002;293(5):478–91.
Please cite this article in press as: Maier BJ et al. Biological control of crystallographic architecture: Hierarchy and co-alignment parameters. Acta Biomater (2014), http://dx.doi.org/10.1016/j.actbio.2014.02.039
B.J. Maier et al. / Acta Biomaterialia xxx (2014) xxx–xxx [20] Saruwatari K, Matsui T, Mukai H, Nagasawa H, Kogure T. Nucleation and growth of aragonite crystals at the growth front of nacres in pearl oyster, Pinctada fucata. Biomaterials 2009;30(16):3028–34. [21] Bevelander G, Nakahara H. An electron microscope study of the formation of the nacreous layer in the shell of certain bivalve molluscs. Calcif Tissue Res 1969;3(1):84–92. [22] Rousseau M, Lopez E, Couté A, Mascarel G, Smith DC, Naslain R, et al. Sheet nacre growth mechanism: a voronoi model. J Struct Biol 2005;149(2):149–57. [23] Rousseau M, Meibom A, Géze M, Bourrat X, Angellier M, Lopez E. Dynamics of sheet nacre formation in bivalves. J Struct Biol 2009;165(3):190–5. [24] Bachmann F, Hielscher R, Schaeben H. Texture analysis with mtex – free and open source software toolbox. Solid State Phenom 2010;160:63–8. [25] Fabritius H, Walther P, Ziegler A. Architecture of the organic matrix in the sternal CaCO3 deposits of Porcellio scaber (Crustacea, Isopoda). J Struct Biol 2005;150:190–9. [26] Limpert E, Staehl WA, Abbt M. Log-normal distributions across the sciences: keys and clues. Bioscience 2001;51:341–52.
9
[27] Checa AG, Bonarski JT, Willinger MG, Faryna M, Berent K, Kania B, et al. Crystallographic orientation inhomogeneity and crystal splitting in biogenic calcite. J R Soc Interface 2013;10(86):20130425. [28] Chateigner D, Ouhenia S, Krauss C, Hedegaard C, Gil O, Morales M, et al. Voyaging around nacre with the X-ray shuttle: from bio-mineralisation to prosthetics via mollusc phylogeny. Mater Sci Eng A 2010;528:37–51. [29] Suzuki M, Kim H, Mukai H, Nagasawa H, Kogure T. Quantitative XRD analysis of 1 1 0 twin density in biotic aragonites. J Struct Biol 2012;180(3):458–68. [30] Wang S-N, Yan X-H, Wang R, Yu D-H, Wang X-X. A microstructural study of individual nacre tablet of Pinctada maxima. J Struct Biol 2013;183:404–11. [31] Checa AG, Mutvei H, Osuna-Mascaró, Bonarski JT, Faryna M, Berent K, et al. Crystallographic control on the substructure of nacre tablets. J Struct Biol 2013;183:368–76. [32] Feng QL, Li HB, Pu G, Zhang DM, Cui FZ, Li HD, et al. Crystallographic alignment of calcite prisms in the oblique prismatic layer of Mytilus edulis shell. J Mater Sci 2000;35:3337–40.
Please cite this article in press as: Maier BJ et al. Biological control of crystallographic architecture: Hierarchy and co-alignment parameters. Acta Biomater (2014), http://dx.doi.org/10.1016/j.actbio.2014.02.039