geometrical and crystallographic constraints determine the ... · unionid shells are characterized...

doi: 10.1098/rspb.2000.1415, 771-778268 2001 Proc. R. Soc. Lond. B

Antonio G. Checa and Alejandro Rodríguez-Navarro Unionidae (Bivalvia: Mollusca)the self-organization of shell microstructures in Geometrical and crystallographic constraints determine

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Geometrical and crystallographic constraintsdetermine the self-organization of shellmicrostructures in Unionidae (Bivalvia: Mollusca)Antonio G. Checa1* and Alejandro Rodr|̈guez-Navarro2

1Departamento de Paleontolog|̈a y Estratigraf|̈a, Universidad de Granada, Granada 18002, Spain2Savannah River Ecology Laboratory, University of Georgia, Drawer E, Aiken, SC 29802, USA

Unionid shells are characterized by an outer aragonitic prismatic layer and an inner nacreous layer. Theprisms of the outer shell layer are composed of single-crystal ¢bres radiating from spheruliths. Duringprism development, ¢bres progressively recline to the growth front. There is competition between prisms,leading to the selection of bigger, evenly sized prisms. A new model explains this competition processbetween prisms, using ¢bres as elementary units of competition. Scanning electron microscopy andX-ray texture analysis show that, during prism growth, ¢bres become progressively orientated with theirthree crystallographic axes aligned, which results from geometric constraints and space limitations.Interestingly, transition to the nacreous layer does not occur until a high degree of orientation of ¢bres isattained. There is no selection of crystal orientation in the nacreous layer and, as a result, the preferentialorientation of crystals deteriorates. Deterioration of crystal orientation is most probably due toaccumulation of errors as the epitaxial growth is suppressed by thick or continuous organic coats on somenacre crystals. In conclusion, the microstructural arrangement of the unionid shell is, to a large extent,self-organized with the main constraints being crystallographic and geometrical laws.

Keywords: biomineralization; bivalve shell; microstructure; nacre; composite prisms; self-organization

1. INTRODUCTION

Molluscs fabricate shells that are composites of calcite oraragonite crystals embedded within an organic matrix.The crystals display varied morphologies and structuralarrangements and are described as having di¡erentmicrostructures. In most cases, the shells are constructedof two or more superimposed layers with di¡erent micro-structures, which may even be composed of di¡erentcalcium carbonate polymorphs (i.e. calcite or aragonite)(Taylor et al. 1969).

Shell formation starts with the secretion of an outerorganic membrane or periostracum (¢gure 1). Thisorganic membrane acts as the substrate where shell-forming crystals (calcium carbonate in either the form ofcalcite or aragonite) nucleate. The shell-secreting epi-thelium or mantle supplies the Ca2 + and HCO¡3 ionsnecessary for the growth of calcium carbonate crystals.The mantle is separated from the inner shell surface by aspace. The organism can maintain a supersaturatedsolution (extrapallial £uid) within this space, therebyallowing shell-forming crystals to precipitate (Simkiss &Wilbur 1989). There is evidence from in vitro experimentsthat speci¢c proteins composing the shell organic matrixplay an important role in controlling the polymorphicphase, morphology and orientation of individual crystals(Addadi et al. 1987; Falini et al. 1995; Belcher et al. 1996).However, little is known about the role these proteinsplay in how crystals assemble into a given microstructure.Since di¡erent species have speci¢c shell microstructuresit is generally believed to be genetically directed (Addadi& Weiner 1992). Even more striking is the transitionbetween superimposed layers with di¡erent micro-

structures. For instance, in Unionidae the mantle secretestwo shell layers with di¡erent microstructures. Themantle has an oblique disposition with respect to theperiostracum, depositing the two di¡erent layers simulta-neously (¢gure 1). The more marginal areas of the mantlesecrete the outer shell layers. This is usually explained byassuming a zonation of the metabolic properties of theshell-secreting mantle surface (Beedham 1958). In thisway, di¡erent parts of the mantle could induce the devel-opment of di¡erent microstructures.

While understanding biomineralization processes hasbeen the main focus of studying shell growth, the know-ledge may also be applied to the fabrication of superiormaterials composed of highly orientated crystals of thesame size and morphologies (Aksay et al. 1996). Forinstance, the structure of mollusc shell, in particularnacre (which is formed by layers of aragonite tablets sand-wiched by an organic membrane), has excellent mechan-ical strength and fracture toughness, exceeding that of thearagonite single crystals composing it by several orders ofmagnitude (Currey 1977).

Most studies on mollusc shell growth have focused onthe physiological factors controlling shell growth(Saleuddin & Kunigelis, 1984; Simkiss & Wilbur 1989;Addadi & Weiner 1992) and the role of speci¢c proteinsin the control of crystal growth (Lowenstam & Weiner1989). However, much less attention has been paid tofundamental issues such as the geometrical and crystallo-graphic factors constraining the growth of crystals andthe development of aggregate micro-architectures. Forinstance, simple geometrical laws govern the growth ofcrystals. Crystal habit depends entirely upon the relativegrowth rates of crystal faces, which are in turn controlledby both crystal structure and growth conditions (i.e.supersaturation, temperature and impurities (proteins))

Proc. R. Soc. Lond. B (2001) 268, 771^778 771 © 2001 The Royal SocietyReceived 10 November 2000 Accepted 5 December 2000

doi 10.1098/rspb.2000.1415

*Author for correspondence ([email protected]).


http://rspb.royalsocietypublishing.org/

(Sunagawa 1987). The growth of a polycrystalline aggre-gate (i.e. shell) is much more complex as crystals growingtogether impinge on each other and compete for theavailable space, but its growth is still governed by crystal-lographic and geometrical laws (Grigor’ev 1965;Rodr|̈guez-Navarro & Garc|̈a-Ruiz 2000). In this paper,we focus on the evolution of the morphology and crystal-lographic orientation of crystals during shell growth inunionids in order to evaluate the importance of geome-trical and crystallographic factors versus biological factorson the development of shell micro-architectures.

2. MATERIAL AND METHODS

(a) MaterialShells of the Unionidae were studied including Unio elongatulus

Pfei¡er, 1825, (Canal Imperial de Aragön, Navarra, Spain), Uniocrassus Philippson, 1788 (River Meuse, Hastie© res, Belgium),Ambleminae Potomida littoralis (Lamarck, 1801) (Canal Imperialde Aragön, Zaragoza, Spain), Lamprotula sp. (locality unknown,China) and Caelatura bakeri (Adams, 1866) (Nyanza, Kenya).

(b) Optical and electron microscopyThin sections (30^40mm thick) of U. elongatulus and Lamprotula

sp. shells cut along a dorsoventral radius were prepared fortransmitted light microscopy. The mantle shell system wasstudied in living specimens of U. elongatulus and P. littoralis.Samples were initially ¢xed in 10% formalin and preserved in70% ethanol. Square pieces of the shell margin (usually theventral area) were cut very carefully in order to avoid damagingthe adjacent mantle margin.The mantle was later cut with preci-sion scissors.The samples were later completely decalci¢ed, ¢xedin bu¡ered cacodylate (0.1 M and pH 7.4) 2.5% glutaraldehydeand critical point^CO2 dried. They were later embedded inepoxy resin, sectioned to 1 mm (Ultracut S, Leica, Solms,

Germany) and stained with 1% toluidine blue. Samples weresuper¢cially decalci¢ed with 6% ethylenediaminetetraaceticacid for 20 min at room temperature for scanning electronmicroscope (SEM) examination. Outer and inner valve surfaces(sometimes with the periostracum partly removed with 5%NaOH) as well as transverse radial fractures of shells (intact oretched in 1% HCl for less than 1min) from all species (exceptP. littoralis) were observed in an SEM (DSM 950, Zeiss, Jena,Germany) after being sputtered with gold for 4 min.

(c) X-ray texture analysisThe orientation of the crystals of U. elongatulus and Lamprotula

shells was determined using an X-ray texture di¡ractometer(X’pert, Phillips, Amelo, The Netherlands) (Cullity 1977). Poledensities for 002 and 112 re£ections of aragonite were registeredin order to do this. These pole ¢gures show the three-dimen-sional distribution of orientation of the [001] and [112] crystaldirections. The stereographic projections of the pole ¢gures aredisplayed as counter plots. The scattering or degree of preferen-tial orientation of crystals can also be quanti¢ed from theseplots as full width at half maximum (FWHM) values of thepeaks in the pole ¢gures. The lower the FWHM value, thegreater the alignment of crystals. In order to study the evolutionof the orientation of crystals during shell growth, samples weremanually ground to di¡erent levels parallel to the outer shellsurface and the pole ¢gures registered.

3. RESULTS

(a) The internal structure of prismsUnionid shells consist of an outer aragonitic prismatic

layer and an inner nacreous layer with the prismatic layercomprising only ca. 10% of the total shell thickness. Shellgrowth occurs via spheruliths (spherical aggregates ofradiating crystal ¢bres) that nucleate within the gelatinous

772 A. G. Checa and A. Rodr|̈guez-Navarro Self-organization of shell microstructures

Proc. R. Soc. Lond. B (2001)

shell growthdirection

shell margin

outerperiostracum

innerperiostracum

growth lines

mantle

shell margin

(a)

(b)

prismatic layer

nacreous layer

Figure 1. (a) Drawing of a unionid shell with the main reference directions indicated and showing where shell pieces were cut forthe texture analysis. (b) Schematic of a cross-section of a shell showing the disposition of the di¡erent layers constructing it.Modi¢ed from Checa (2000).



inner periostracal surface (¢gure 2a,g). Initially, spheru-liths grow independently from each other but, as growthcontinues beyond the boundary of the inner perio-stracum, they start to impinge on one another anddevelop into polygonal prisms. Prisms grow vertically(inward) and later they usually become graduallyreclined towards the shell margin (¢gure 2b). In thisway, the prism main axis remains perpendicular to thegrowth front (see below). Its orientation changes gradu-ally from being inclined dorsal-wards to nearly parallelto the periostracum at the very margin. Prisms arecomposed of elongate crystals (¢bres) fanning out inthree dimensions from the main axis of the prismtowards the depositional surface. Longitudinallyfractured prisms, as observed through the SEM, showparticularly conspicuous ¢bres towards the edges ofprisms (¢gure 2c, f ). During prism growth, ¢bres fanout (giving the prisms a feather-like appearance in cross-section) (¢gure 2b,e) and become thicker, reaching up to2 mm in thickness at their most distal ends (¢gure 2c).Each ¢bre is a single, curved crystal with the c-axisparallel to the long axis as revealed by the undulatingextinction pattern with polarized light microscopy(¢gure 2b). As prisms grow longer, the mean divergenceof ¢bres with the main or long axis of the prismsdecreases. Values of 20^258 at the lower boundary of theprismatic layer are typical. At the same time, ¢bresachieve greater lengths and become straighter(¢gure 2b,c). The distribution of ¢bres within a prism isasymmetric. Fibres running forwards (pointing to theshell margin) grow more than those diverging backwards(¢gure 2c). In this way, while ¢bres remain strictlyperpendicular to the growth front, the prism long axisbecomes progressively advanced with respect to the axisof ¢bre divergence and the shell margin. Prisms showprominent concentric growth lines (¢gure 2a,e) that aremore or less centred in the spheruliths. They are perpen-dicular to the ¢bres and remain as organic sheets afterdecalci¢cation. These growth surfaces most probablyre£ect successive positions of the mantle. Interestingly,the deposition of these organic sheets does not seem tointerrupt or alter ¢bre growth and orientation.

(b) The size and shape of prismsDuring growth of the prismatic layer, bigger prisms

expand laterally at the expense of smaller ones, therebyblocking their space for growing. Prismatic units areprogressively lost so that only a few, big, evenly sizedprisms reach the transition to the nacreous layer (¢gure2a,e, f ). The thickness of the prismatic layer as well as thesize of the prisms (both in height and width) increases ina radial section from older to newer parts of the shell (i.e.the shell margin). The spacing among neighbouringprisms also increases in the same direction.

The variation in the aspect ratio (height to width) ofprisms is shown in ¢gure 3 as a function of their height.It can be observed that prisms show a trend of increasingelongation (higher aspect ratios) with increasing height.However, there is a tendency for the value of the aspectratio to saturate as the prisms’ size (height) increasesfurther. Furthermore, as the aspect ratio of the prismsincreases, the limit angle or maximum angle of diver-gence of ¢bres decreases.

(c) Transition to the nacreous layerLarge distal ¢bres of the surviving prisms become

transversely divided by organic sheets at the transitionzone from the prismatic to the nacreous layer and gradu-ally transform into stacked nacreous tablets (¢gure 2c).Fibres are highly aligned (within a range of 208) at thetransition zone. The ¢rst nacreous tablets grow epitaxiallyonto the distal ends of ¢bres, from which they inherittheir crystallographic orientation, having their c-axisperpendicular to the tablet surface. The transition tonacre is initiated in the rear part of a radial section of ashell within individual prisms and proceeds to the frontpart of the prism that is pointing towards the shellmargin (¢gure 2c). The ¢rst nacre sheets usually have aslightly wavy disposition that results from the divergingarrangement of ¢bres. Waviness soon fades out and thenacre sheets become £at as the nacreous layer growsthicker. Similar gradual transformations were observedby Dauphin et al. (1989) in Haliotis and Mutvei (1972) inNautilus.

(d) The inner surface of the shellThe inner surface of the inner nacreous layer shows a

terraced disposition of the aragonite sheets, which growtowards the shell margin (¢gure 2d). Sequential stages ofthe nacreous tablet nucleation and growth can beobserved when moving towards the shell edge. The shapeof aragonite tablets is rhombic, with the longest diagonalcoincident with the b-axis and the shortest coincidentwith the a-axis. The elongate crystal shape re£ects a fastergrowth rate along the b-axis than the a-axis. Note thatcrystals forming a nacre lamella or sheet are orientatedwith their longest diagonal (b-axis) towards the directionof shell growth and the shorter diagonal (a-axis) trans-versal to it and parallel to the shell margin. However,exceptions are sometimes noted in isolated tablets or evenclusters of tablets with orientation di¡ering signi¢cantlyfrom the common orientation (b-axis perpendicular to theshell edge), sometimes even being transverse (¢gure 2d ).

(e) Evolution of the orientation of crystals duringshell growth

The evolution of the orientation of crystals during shellgrowth was studied by registering pole ¢gures at di¡erentthickness within a shell of U. elongatulus. The pole ¢guresfrom the outer surface of the shell (thickness 0%), whichcorrespond to the initial stages of shell formation, show auniform distribution of intensity indicating that crystalsnucleate with a random orientation. At increasing thick-ness, corresponding to later stages of growth, the pole¢gures gradually show better-de¢ned peaks, indicatingthat crystals are progressively more aligned (¢gure 4).The degree of alignment of crystals is assessed by theFWHM value for these peaks (¢gure 4). The FWHMw-value in ¢gure 4c (left-hand graph), which wasmeasured from the 002 pole ¢gures, decreases rapidlyacross the prismatic layer, reaching a minimum just afterthe transition to the nacreous layer. It increases againacross the nacreous layer indicating that the scattering ofthe orientation of the c-axis of crystals follows the sametrend. Curiously, the scattering of the c-axis is greater inthe direction parallel to than the direction perpendicularto the shell margin. The spread of the orientation of the

Self-organization of shell microstructures A. G. Checa and A. Rodr|̈guez-Navarro 773




774 A. G. Checa and A. Rodr|̈guez-Navarro Self-organization of shell microstructures


(a) (b)

(c) (d )

(e) ( f )

(g) (h)

Figure 2. (Caption opposite.)



a- and b-axes, which was measured as the FWHM ¿-value from peaks of 112 pole ¢gures, follows the sametrend as that of the c-axis (¢gure 4c, right-hand graph),though the alignment of crystals along these axes isalways poorer than along the c-axis. These observationsimply that crystals that initiate shell growth are randomlyorientated. Crystals become rapidly aligned during thegrowth of the prismatic layer. However, their orientationdeteriorates slightly during the growth of the nacreouslayer.

Intraprismatic growth lines, which are formed byorganic material, cross cut the di¡erent prisms indicatingpulsating growth of the whole layer (¢gure 2a,e). Interest-ingly, the deposition of organic material does not seem tointerrupt the epitaxial growth of crystals from one layerto the next. In fact, SEM and X-ray texture analysisshows that, during shell growth, there is always conti-nuity in the preferential orientation of crystals and thatonly the degree of alignment changes.

4. DISCUSSION

(a) Competition between prismsCompetition between prisms was described and inter-

preted by Ubukata (1994) in several bivalves, includingunionids. He developed geometrical constructions basedon Grigor’ev’s (1965) model of the growth of aggregateminerals in order to show the e¡ect of several factors onprism selection. The main problem when these models areapplied to the composite prisms of unionids is that theyimply a free-growing surface (as in the formation of, forexample, quartz crystals growing on the wall of a rockcavity or geode). However, in unionids the mantle surfacelimits prism growth, as evidenced by growth lines. There-fore, unlike Grigor’ev’s (1965) model, the growth front ofprisms is permanently constrained by the position of themantle, thereby precluding the possibility of di¡erencesin the longitudinal growth rate among prisms. Taking thisinto consideration, we have developed a model in whichprism selection is not due to competition between prisms,but between the ¢bres of di¡erent prisms meeting at theinterprismatic surfaces (¢gure 5). When a prism out-

competes another it is apparent that its ¢bres run lessinclined to the growth front (¢gure 2 f ). A lesser inclina-tion angle implies a faster growth in parallel to thegrowth surface, which explains why less-inclined ¢bresoutcompete more-inclined ones. Therefore, competitionbetween prisms can be reduced to competition betweentheir constituent ¢bres. A growth rate normal to thegrowth surface is a negligible factor since ¢bre growth inthis direction is constrained by the rate of mantle displa-cement, which is uniform for ¢bres of all prisms growingat the same time.

(b) Genesis and evolution of crystal orientationIt has been suggested that crystal orientation is

imposed by epitaxial nucleation on the organic matrixsurface (Weiner & Traub 1980, 1984). However, thedegree of orientation of the organic constituents and therange over which they are orientated (a few microns) are

Self- organization of shell microstructures A. G. Checa and A. Rodr|̈guez-Navarro 775


Figure 2. (a) Oblique view of a partly dissolved inner periostracum and fractured outer prismatic layer of Lamprotula sp . Growthsurfaces cross cut adjacent prisms. Growth direction, top left to bottom right. Magni¢cation£ 420. (b) Polarized light micrographof the outer prismatic layer of U. elongatulus. Prisms are composed of ¢bres diverging from the prism main axis. Extinction bandsusually displace rearwards (right) during prism growth (to the bottom) indicating that ¢bres directed forwards to the shellmargin become progressively more developed at the expense of those directed backwards. Prisms curve to remain perpendicularto the growth front. Magni¢cation£ 190. (c) Transition between the prismatic and nacreous layers in Lamprotula sp.Prism-composing ¢bres gradually align parallel to the long axis of the prism. Transition to the nacreous layer occurs when thedegree of convergence reaches a certain threshold. Fibre distribution is asymmetric with those running forwards to the shellmargin (right) being more developed. This causes transition to the nacreous layer to proceed from the rear of the prism forwards.Magni¢cation£ 1800. (d ) View of the step-like arrangement of nacreous sheets at the internal growth surface of the shell ofP. littoralis. Rhombic nacreous tablets are orientated, with minor exceptions, with their longest diagonal (b-axis) parallel to theshell growth direction (upper left). Magni¢cation£ 1800. (e) Thin section through the outer prismatic layer of P. littoralis.Intraprismatic growth surfaces are perpendicular to ¢bres and, hence, concave towards the initial spherulith. They continueacross the di¡erent prisms, which indicates synchronized growth. Magni¢cation£ 190. ( f ) Prismatic shell of Lamprotula sp. Twoprisms outcompete a third trapped in-between. When ¢bres meet, those of the bigger prisms always form a higher angle with thelong axes of prisms. Magni¢cation£ 1800. (g) Outer shell surface of Lamprotula sp. with the periostracum removed. Initialspheruliths are statisticallyplaced towards the rear of prisms (lower right), which indicates an asymmetric development ofprisms. Magni¢cation£ 850. (h) Section through the prismatic and nacreous layers of U. elongatulus. Growth halts are markedby discontinuities. Growth resumes with prismatic layers that intrude into the nacreous layer and gradually wedge outinternally. Prism size decreases in the same direction, so that the relationship of width to height is kept. Magni¢cation£ 95.Scale bars: (a) 50 mm, (c,d, f ) 5 mm and (g) 10 mm.

0 20 40 60

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.080 100 120

height (m m)

aspe

ct r

atio

(H

/W)

140 160

H/W = 2.523°

H/W = 2.7521°

H/W = 3

limit angle of 19°

180 200 220 240

Lamprotula sp.Unio elongatulus

Figure 3. Aspect ratio (height to width (H/W)) of prisms as afunction of their size (height) measured for Unionidae shells.Values were obtained from SEM views of sections eitherparallel (U. elongatulus) or transversal (Lamprotula sp.) to themargin. Prisms become more elongate with size.



much less than those of aragonite crystals (in the order ofmillimetres) (Weiner & Traub 1984). In addition, such amechanism does not explain the evolution of the orienta-tion of crystals during shell growth and, contrary toobservation, it implies that the orientation of crystals isalready selected in early crystal growth stages. Conversely,we observed that preferential orientation of crystals in theshells of unionids develops during growth of the prismaticlayer, starting from randomly orientated crystals.

This progressive alignment of crystals during prismgrowth is due to geometric selection of crystals. Theprogressive alignment of ¢bres and the c-axis of crystalswith the main axis of the prisms is merely a geometricfeature. Initially, ¢bres of the spheruliths (from whichprisms initiate) radiate in all directions. As growthprogresses these ¢bres impinge on ¢bres of neighbouringspheruliths, thereby constraining further growth of ¢bresto the sides. Fibres only have free space for developingvertically. As the prismatic layer becomes thicker theorientation of ¢bres is further selected and only ¢bresorientated vertically (growing inward) continue to grow(¢gure 6). Sylin-Robert (1986) described a similar modelin explaining the development of a preferential orienta-tion of crystals in eggshells along their c-axis. However,in order to explain the orientation of crystals with theira^b-axis also aligned another mechanism must beinvoked. The horizontal displacement of the mantle at theshell margin frees some space for the expansion of ¢bres

in the a^b-plane towards the shell margin. This allowsgeometrical selection of ¢bres orientated with their hori-zontal, fastest, growth direction (b-axis) perpendicular tothe shell margin (¢gure 6). This process results in thecrystal ¢bres having their three axes aligned. However,the degree of alignment of crystals along the a^b-axes isless than that along the c-axis. The selection mechanism ismore e¤cient along the c-axis since the orientation ofcrystals is due to di¡erences in growth rates alongdi¡erent crystal directions and the c-axis is the overallfaster crystal growth direction.

(c) Transition to the nacreous layerInterestingly, the transition to nacre does not occur

until the angular divergence of ¢bres (and that of c-axes)within prisms falls below a certain threshold (withinca. 208). It seems as if a uniformly orientated substrate (orat least one with a reduced range of dispersion) is neces-sary for nacre to grow by epitaxy. This is not surprisingsince a main characteristic of nacre is that the tabletshave their c-axis aligned and orientated perpendicular tothe shell surface (e.g. Hedegaard & Wenk 1998). It isprobably not accidental that molluscan nacre is, in mostcases, preceded by some kind of ¢brous or prismatic(either aragonitic or calcitic) layer (Taylor et al. 1969).

Since ¢bres curve outwards, bigger prisms will attainthe c-axis dispersal threshold relatively late and couldgrow longer (higher aspect ratios) (¢gures 2 h and 3).

776 A. G. Checa and A. Rodr|̈guez-Navarro Self- organization of shell microstructures


0 20

60

50

40

30

20

10

40outersurface

innersurface

shell thickness (%)

a-axis

b-axis

c-axis

112 face

002

c c cD

f fD

112a

b(a)

(c)

(b)

001 face

FW

HM

c (d

eg)

60

50

40

30

20

10F

WH

Mc

(deg

)

nacreous layer nacreous layer

alignment of c-axisshell margin

alignment of a- and b-axis

shell growth directionpri

smat

icla

yer

pris

mat

ic la

yer

60 80 100 0 20 40outersurface

innersurface

60 80 100

Figure 4. (a) Single crystal of aragonite. (b) Distribution of crystal orientations measured at the boundary between theprismatic and nacreous layers. The subcentral position of unique maxima in the 002 pole ¢gure indicates that the crystals areorientated with their c-axis perpendicular to the shell surface. The positions of the four maxima displayed in the 112 pole ¢gureindicate that the crystals orientate with their b-axes parallel to the shell growth direction (horizontal line) and a-axes parallel tothe margin. (c) Evolution of the alignment of crystals across the shell thickness (left-hand graph) along the c-axis and (right-handgraph) along the a- and b-axes. Interestingly, the crystals become aligned within the prismatic layer (FWHM values decrease),whereas their alignment deteriorates as the nacreous layer becomes thicker (FWHM values increase).



More remarkable is the fact that the transition to nacreoccurs in the rear part of the prism ¢rst rather than inthe front part of the prism (¢gure 2c). The asymmetricaldistribution of ¢bres within prisms causes the c-axisdispersal threshold to be reached ¢rst at the back, withthe subsequent secretion of the ¢rst nacreous tablets, andto propagate forward later. The asymmetric developmentof prisms can be traced back to the initial spherulithstage. Spheruliths are usually more developed anteriorlysince growing spheruliths have more free space to expandforwards than backwards where older spheruliths arealready expanding (¢gure 2g).

Nacreous tablets inherit the crystallographic orienta-tion of the most distal ¢bres of prisms, which act asepitaxial mineral substrates. As the nacreous layer growsthicker the orientation of crystals deteriorates, as revealedby X-ray texture analysis and through the SEM (seeabove) (¢gure 4). In our opinion, this is probably due totwo factors. First, the orientation of crystals is not furtherselected by competition since crystals nucleate separatelyand only establish contact when fully grown (¢gure 2d ).Second, there may be an accumulation of errors in whichthe epitaxial growth of crystals from one nacre sheet tothe next is suppressed. There are porous organic coatsbetween nacre sheets that allow physical contact and,hence, epitaxy between crystals of di¡erent layers(Scha¡er et al. 1997). However, a thick or continuousorganic coat could prevent epitaxial growth and cause thenew crysal to have a random orientation (¢gure 7).

Finally, in our opinion, genetic factors must determinethe shape of the mantle and periostracum, which de¢nethe geometry of the cavity where shell mineralizationoccurs. In addition, cellular processes might be responsible

for the secretion of speci¢c organic components (i.e.proteins), which must certainly modulate the crystalgrowth. However, it should be noted that, once crystalgrowth is initiated, the subsequent arrangement of crys-tals is mostly determined by crystallographic constraintsand space limitations, with the resulting aggregate micro-structure being self-organized.

5. CONCLUSIONS

The microstructural development of the shell in Union-idae can be understood when the monocrystalline ¢bres(instead of prisms, into which they aggregate) of the outershell layer are considered as elementary units. In parti-cular, we have explained (i) competition and selectionbetween prisms, (ii) the development of the orientation of

Self-organization of shell microstructures A. G. Checa and A. Rodr|̈guez-Navarro 777


(a) (b)

r0/r’0 = 2

ttr’n

r’n+1r’n+2

rnrn+1rn+2

r’0r0

r’0r0

r0/r’0 = 1.5

Figure 5. Model for competition between composite prisms inUnionidae. When two ¢bres (rn and r0n) meet, the subsequentpair of impinging (rn + 1 and rn + 1’) can be obtained at ¢xeddistances (t) measured from their ends, perpendicular to theradii. When two prisms of di¡erent size collide, the ¢bres ofthe bigger prism always meet those of the smaller prism at alesser angle to the horizontal (growth front). Displacement isfaster as the di¡erence in width between prisms (r0/r00) isgreater. Two examples are provided for comparison.(a) r0/r00 ˆ 1.5 and (b) r0/r

00 ˆ 2.

(a)

(b)

(c)(d)

advance of the shell growth frontt = 6

t = 1

front

b-axis

front

rear

Figure 6. Competitive growth model for the alignment ofa- and b-axes of ¢bres during prism growth. (a) Sketch of alongitudinal section of prisms parallel to the shell growthdirection of the shell margin (right). See also ¢gure 1g.Prisms initiate as asymmetric spheruliths, with a moredeveloped frontal part, towards the shell margin. This causesthe rear prism to displace the one in front of it progressively,while, in turn, it is displaced by the prism behind (not shown).As a consequence, the ¢bres running in a frontal directionbecome progressively more developed. (b) View of prismsparallel to the shell surface. (c,d ) As ¢bres grow longer andthicker, competition in the a^b plane (cross-section of ¢bres)causes selection of those ¢bres having their fastest horizontalgrowth direction (b-axis) orientated parallel to the shellgrowth direction (arrow).



crystal ¢bres within the prismatic layer starting fromspheruliths, (iii) the transition from the prismatic to thenacreous layer, and (iv) increasing scattering of crystalorientation with addition of new nacreous sheets, as meregeometrical and crystallographic processes. These pro-cesses are regarded as epiphenomena arising from theanisotropic growth rates of biogenic aragonite crystals. Insummary, the inner periostracum serves as the substratefor nucleation of spheruliths, whereas the mantle suppliescalcium carbonate and organic components to the shellgrowth front via the extrapallial space. Finally, our obser-vations suggest that the physical factors determining theself-organization of shell microstructures deserve as muchattention as genetic ones in explaining the formation ofthe bivalve shell.

This study was ¢nanced by research project PB97-0790 of theDirecciön General de Ensen¬ anza Superior e InvestigaciönCient|̈¢ca (Ministerio de Educacion y Ciencia, MEC), researchgroup RNM-0178 (PAI, Junta de Andaluc|̈a) and an award(DE-FC09-96-SR18546) from the US Department of Energy tothe University of Georgia Savannah River Ecology Laboratory.We also thank the postdoctoral program of the MEC (Spain).We are very grateful to Professor Chris Romanek (SavannahRiver Ecology Laboratory), Robert C. Thomas (SavannahRiver Ecology Laboratory) and Professor Russell Messier (PennState University) for their useful comments and support.

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As this paper exceeds the maximum length normally permitted,the authors have agreed to contribute to production costs.

778 A. G. Checa and A. Rodr|̈guez-Navarro Self- organization of shell microstructures


orientated crystalinner shell surface

randomly orientated crystalorganic sheet

Figure 7. Model of accumulation of defects within thenacreous layer. Tablets of a new nacre sheet will growepitaxially on the previous sheet, provided that pores of theorganic sheet allow them to establish direct contact. Other-wise, new tablets will nucleate with random orientation.These defects accumulate since new nacre tablets can nucleateepitaxially on randomly orientated crystals.

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