Glasses crystallize rapidly at free surfacesby growing crystals upwardYe Suna, Lei Zhua, Kenneth L. Kearnsa,1, Mark D. Edigera, and Lian Yua,b,2

aUniversity of Wisconsin-Madison, Department of Chemistry, Madison, WI 53706; and bUniversity of Wisconsin-Madison, School of Pharmacy, Madison,WI 53705

Edited by Frank H. Stillinger, Princeton University, Princeton, NJ, and approved February 23, 2011 (received for review December 2, 2010)

The crystallization of glasses and amorphous solids is studied inmany fields to understand the stability of amorphous materials,the fabrication of glass ceramics, and the mechanism of biominer-alization. Recent studies have found that crystal growth in organicglasses can be orders of magnitude faster at the free surface thanin the interior, a phenomenon potentially important for under-standing glass crystallization in general. Current explanations dif-fer for surface-enhanced crystal growth, including released tensionand enhanced mobility at glass surfaces. We report here a featureof the phenomenon relevant for elucidating its mechanism: Despitetheir higher densities, surface crystals rise substantially above theglass surface as they grow laterally, without penetrating deep intothe bulk. For indomethacin (IMC), an organic glass able to growsurface crystals in two polymorphs (α and γ), the growth front canbe hundreds of nanometers above the glass surface. The process ofsurface crystal growth, meanwhile, is unperturbed by eliminatingbulk material deeper than some threshold depth (ca. 300 nm for αIMC and less than 180 nm for γ IMC). As a growth strategy, theupward-lateral growth of surface crystals increases the system’ssurface energy, but can effectively take advantage of surfacemobility and circumvent slow growth in the bulk.

Crystallization is a ubiquitous process, producing countlesssolids in the natural and man-made world. Glasses and amor-

phous solids are formed by avoiding crystallization while coolingliquids, condensing vapors, or drying solutions. The solidity of aglass might suggest resistance to crystallization; its very existenceimplies that crystallization is avoidable. And yet glasses can crys-tallize, sometimes surprisingly fast. The crystallization of glassesis of interest in many fields for understanding the stability ofamorphous materials (1), the fabrication of glass ceramics, andthe mechanism of biomineralization, for which crystallization ofamorphous solid precursors is considered a key step (2).

Recent studies have discovered that different modes of crystalgrowth can emerge as a liquid is cooled to form a glass (3–8),causing crystal growth fronts to advance at velocities much fasterthan predicted by standard theories. One such growth mode [theglass-to-crystal (GC) mode] exists in the bulk and can cause anincrease of crystal growth rate by a factor of 104 with a tempera-ture drop by a few kelvin (3, 4). Another new growth mode occursat the free surface and can lead to much faster crystal growth thanin the bulk (5–8). Although these phenomena have been observedprominently in organic glasses, they may be relevant for under-standing glass crystallization in general. These phenomena seemto have counterparts in nonorganic glasses, but differences arealso evident. Fast crystal growth is known for metallic glasses andamorphous silicon, but the abrupt activation of GC growth is re-ported only for organic glasses. Surface-enhanced crystal growthoccurs in amorphous selenium (9) and silicon (10, 11), but is con-sidered nonexistent for metallic (12) and silicate (13–15) glasses.

This study concerns the mechanism of surface-enhanced crys-tal growth of glasses. Current views differ on how crystal growthrate should change on going from the bulk to the surface of aglass. Some focus on the consequences of growing higher densitycrystals in lower density glasses (16–19) This process, according toone model (16), creates an elastic strain and lowers the thermo-

dynamic driving force and the rate of crystallization. The effect isbelieved to diminish on going from the bulk to the surface, result-ing in faster crystallization at the surface. In contrast, Tanakaargues that the stress around a crystal growing in a glass “shouldprovide the free volume to the particles surrounding the crystal,increase their mobility, and help further crystallization” (17).According to this model, crystal growth should be slower at thesurface. Another view of surface crystallization (5, 6, 10, 11)focuses on the greater molecular mobility at glass surfaces, whichhas been inferred from various experiments (20–22). Here thereasoning is that if crystal growth rate is limited by molecularmobility, the enhanced mobility at surfaces can accelerate crystalgrowth. In yet another view, the different packing of molecules atthe surface is believed to alter the rate of crystallization (19).

We report here a feature of surface-enhanced crystal growththat may be central for understanding the phenomenon. We haveobserved that surface crystals rise substantially above the glasssurface as they grow laterally, without penetrating deep into thebulk. For indomethacin (IMC) [1-(4-chlorobenzoyl)-5-methoxy-2-methyl-1H-indole-3-acetic acid], a model organic glass ableto grow surface crystals in two polymorphs, the growth front canbe hundreds of nanometers above the glass surface. The processof surface crystal growth, meanwhile, is not perturbed by elimi-nating the bulk material deeper than some threshold depth (ca.300 nm for the α polymorph and less than 180 nm for the γ poly-morph). The upward-lateral growth of surface crystals is not an-ticipated by current theories. As a growth strategy, it increases thesystem’s surface energy, but can effectively take advantage of sur-face molecular mobility and circumvent slow growth in the bulk.This finding may be relevant for understanding the crystallizationof glasses and amorphous solids in general.

Results and DiscussionMicrostructures of Surface Crystals: Upward-Lateral Growth. Twopolymorphs (α and γ) can crystallize at the surface of an IMCglass. The structures of these polymorphs are known (23, 24)and both are denser than the glass (25). Fig. 1 and Fig. 2 showtypical images collected with light microscopy (LM) and atomicforce microscopy (AFM) of α and γ IMC grown at the surfaceof a 15-μm thick film at 40 °C (2 °C below the glass transition tem-perature Tg). Both polymorphs formed circular polycrystallinepatches (“cylindrites”) observable in a few days. Polymorphs wereidentified using Raman spectra, melting points, and crystalmorphologies. Through a light microscope, the crystals of α IMCappeared more opaque than those of γ IMC; its growth front com-prised individual fibers protruding into the amorphous region.In contrast, crystals of γ IMC were more transparent and hadsmoother growth fronts.

Author contributions: M.D.E. and L.Y. designed research; Y.S., L.Z., and K.L.K. performedresearch; Y.S. analyzed data; and Y.S. and L.Y. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1Saginaw Valley State University, Department of Chemistry, University Center, MI 48710.2To whom correspondence should be addressed. E-mail: lyu@pharmacy.wisc.edu.

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AFM measurements consistently showed that the glass sur-faces were smooth with an rms roughness of a few nanometers.There was no difference between an uncrystallized glass surfacenear a growing crystal and one that was far away. AFM measure-ments showed that the fibers of α IMC at the growth front werehundreds of nanometers high above the amorphous surface(Fig. 1 C and D). On the surface of an α IMC cylindrite, AFMidentified fibers of similar dimensions with an rms roughness ofca. 100 nm. For α IMC, the growth of surface crystals apparentlyoccurs by the extension and branching of crystal fibers that areabove the amorphous surface.

In comparison to α IMC, the growth front of γ IMC wassmoother and not segregated into individual fibers (Fig. 2 Aand B). The morphological difference between α and γ IMC isanticipated from their structures (23, 24); for example, the stan-dard Bravais–Friedel–Donnay–Harker model predicts that singlecrystals of α IMC grow as rods elongated along b and those ofγ IMC grow as prisms approximately equally developed in alldimensions. Despite having a different morphology, the γ IMCgrowth front was also higher than the glass surface, by ca. 100 nm(Fig. 2 B and C). A crystallized region of γ IMC had smoothertexture than that of α IMC with an rms roughness of ca. 50 nm.

Side-ViewObservation of Surface Crystal Growth.The process of sur-face crystallization was observed from the side to assess the depthof penetration of surface crystals as they grow laterally. For thisexperiment, liquid IMC was spread between two coverslips bycapillarity and cooled to room temperature (Tg − 20 °C) to makea glass disc 40 μm thick. This glass disc had its top and bottomsurfaces in contact with coverslips but its side surface exposed toair, where surface crystallization could occur. Surface crystalliza-tion began spontaneously or upon scratching with a tungsten nee-

dle. Fig. 3A shows the progress of the surface crystal growth of γIMC at 40 °C. Viewed between crossed polarizers, these crystalsappeared bright against a dark background. As crystal growthprogressed along the side surface, little growth occurred intothe amorphous interior. This result indicates that crystal growthwas much faster at the surface than in the bulk. The aspect ratioof the surface crystal layer indicates that the bulk growth wasapproximately 1,000 times slower. The surface crystal growth rateof γ IMC from this experiment [log u ðin m∕sÞ ¼ −8.91� 0.06]agrees with that previously measured using glasses with largeexposed surfaces (5).

The thickness of the propagating surface crystal layer was toothin to be accurately measured by LM. This experiment yieldedonly an upper bound of a few micrometers for this thickness,which is the combined result of the light microscope’s resolutionand the thickness of the glass disc (ca. 40 μm). The actual thick-ness of the surface crystal layer could be smaller.

In this experiment, scratching always nucleated γ IMC, whilecrystals of α IMC could appear spontaneously. Polymorphs wereidentified by Raman microscopy and by heating the sample tofully crystallize amorphous IMC and analyzing the crystalsformed adjacent to the surface crystals. Under our conditions,γ IMC crystals were slightly more visible than α IMC crystals, per-haps a result of their higher birefringence. The low visibility ofα IMC crystals led to occasional observations that the growthof γ IMC crystals would apparently stop, because they had runinto difficult-to-see α crystals. The obstructing α crystals wererevealed on closer examination or by heating the sample so thatthey grew larger. The same upper bound of a few micrometerswas placed on the thickness of α IMC surface crystals.

20 µm B

C

200µmA

2µm

A B

10.00 20.0µm

500

-500

0

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D

Fig. 1. LM (A) and (B) and AFM (C) images of α IMC crystals grown at thesurface of a 15-μm thick glass at 40 °C. The AFM scan in C covered the squarein B. Arrow indicates advance direction of crystal growth front. (D) Heightprofile along line AB in C. The crystals can be hundreds of nanometers abovethe glass surface.

A

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5.02.50 10.07.5µm

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Fig. 2. LM (A) and AFM (B) images of γ IMC crystals grown at the surface of a15-μm thick glass at 40 °C. Arrow indicates crystal growth direction. (C) Heightprofile along line AB in B. The growth front can be 100 nm above the glasssurface.

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Surface Crystal Growth in Glass Films of Different Thicknesses. Wevaried the thickness of amorphous IMC films (50 nm–15 μm)to assess the dependence of surface crystal growth on the amountof bulk material underneath. Fig. 4A shows that crystals of α IMCgrown in films thicker than ca. 300 nm had similar morphologies(including the height and width of crystal fibers as determined byAFM) as those grown in the 15-μm thick film, whereas crystalsgrown in thinner films had different morphologies. In films thin-ner than 220 nm, the crystal fibers were less dense, allowing iden-tification of individual fibers, and were surrounded by white,highly reflective areas (Fig. 4B). These white areas were the bareSi substrate exposed by dewetting. This crystallization-induceddewetting was confirmed by AFM. Fig. 4C shows the AFM image

of a crystal fiber of α IMC grown in a 50-nm thick film. This crys-tal is surrounded by the bare Si substrate. The finger patternbetween the exposed Si and amorphous IMC is characteristicof dewetting.

Fig. 5A compares the processes of surface crystal growth in twofilms of different thicknesses. In the 410-nm thick film, crystalgrowth yielded a compact and nearly circular surface cylindriteand the growth front advanced at a constant rate u. In the 100-nmthick film, crystal growth yielded a loose network of resolvablefibers and the growth front advanced more slowly and atuneven speeds. For this film, it is difficult to report a single growth

IMCglass

air

γ IMC

50µm

t = 96 h

400µm

298 h

IMCglass

air

γ IMC

A

B

Fig. 3. Side views of IMC surface crystals (bright lines) growing at 40 °C.(A) Progress of γ IMC growth. (B) Enlarged view of γ IMC.

400 µm

480 nm 410 nmd = 15 µm 290 nm

220 nm 180 nm 140 nm 100 nm

A

50 µm d = 100 nm 4 µm

Si

d = 50 nm

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IMCglass

Fig. 4. (A) Crystals of α IMC grown at 40 °C in films of various thicknessesd. Films of different d had different interference colors. (B) Enlarged viewof crystal fibers grown in a 100-nm thick film, which were surrounded bydewetted Si (white, high reflectivity areas). (C) AFM image of a crystal fiberof α IMC grown in a 50-nm thick film. The crystal is 400 nm high above theexposed Si substrate surrounding it.

Fig. 5. Crystals of α IMC growing in films (A) 410-nm thick and (B) 100-nmthick. Growth in the 410-nm thick film yielded a compact cylindrite and had aconstant growth rate that matches those observed in thicker films. Growth inthe 100-nm thick film yielded a loose network of fibers and had a slower rate,which decreased further over time. (C) Growth rate of α IMC vs. film thickness.For thinner films, in which growth rates decreased over time, the earlygrowth rates are plotted. (D) Growth rate of γ IMC vs. film thickness. For thispolymorph, film thickness did not strongly affect the growth rate and mor-phology within the range of thickness studied.

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rate and an average linear growth rate was calculated from theincrease of the area covered by crystals. We found that the growthrate in the 100-nm thick film was significantly slower than that inthe 410-nm thick film and decreased over time. Fig. 5C sum-marizes the data on the effect of film thickness on crystal growthrate for α IMC. The crystal growth rate changes little with filmthickness until it decreases below ca. 300 nm. For the thinner films,Fig. 5C reports the early stage faster growth rates.

In this study, crystals grown in spin-coated films were mainly αIMC, but γ IMC could be observed occasionally. This polymorphtended to nucleate from a narrow band of material at the edge ofspin-coated films, where the material was thicker and rougher.We did not observe γ IMC in films thinner than 180 nm. When-ever observable, γ IMC crystals had similar morphologies andgrowth rates [log u ðm∕sÞ ¼ −8.8] as those grown in the bulkfilm (5) (Fig. 5D), and no crystallization-induced dewetting wasobserved.

This study has found that surface crystals on an IMC glass risehundreds of nanometers above the glass surface as they growlaterally. The upward-lateral growth is by no means obvious forthe surface crystallization of glasses given that the crystals aredenser than the glass and that such a growth process increasesthe system’s surface area and surface energy. A similar crystalgrowth process has been observed in vapor-deposited amorphoussilicon films (ca. 100-nm thick) annealed in ultrahigh vacuum(10). In the latter system, hemispherical grains tens of nan-ometers in radius grow at the surface of amorphous silicon uponannealing at 500–600 °C, well below the melting point of amor-phous silicon (1,100 °C, ref. 26). It is significant that similarupward-lateral growth characterizes the surface crystallization oftwo systems that differ in solid-state bonding, crystal microstruc-ture, and annealing temperature.

Depth of Penetration of Surface Crystals at the Growth Front.Although our AFM measurements have determined the heightof surface crystals above the IMC glass, data are still lacking onthe depth of these crystals, besides an upper bound of a fewmicrometers from optical microscopy. To understand the processof surface crystal growth, it is pertinent to ask how deep surfacecrystals penetrate into the bulk. For this inquiry, the questionshould be posed for crystals at the growth front, where newgrowth occurs, because crystals behind the front would be ex-pected to thicken over time as they grow into the bulk.

We recall the observation that the process of surface crystalgrowth is not perturbed by reducing the glass thickness to a fewhundred nanometers (300 nm for the growth of α IMC and<180 nm for γ IMC). This observation suggests that at the steadystate, an advancing growth front does not have a substantialportion beneath the surface. If that portion is, for example, 1 μmdeep, one would expect that the growth process be perturbedupon reducing the glass thickness to 1 μm. We also recall the factthat crystal growth in the bulk IMC glass is approximately 1,000times slower than at the surface. Thus, as the raised crystalsadvance across the surface, the concurrent growth into the bulkwould be substantially slower. Finally, we note that in the case ofamorphous silicon, surface crystals have been observed to riseabove the amorphous surface without penetrating deep into thebulk (10). It is our view that the same picture holds for oursystem. This conclusion clearly depends on the large differencebetween surface and bulk crystal growth rates: If the two ratesare comparable, a growth front at the surface can well penetratedeep into the bulk.

How do Crystals Grow Hundreds of Nanometers Above Glass Surface?One could imagine different mechanisms of material transportresulting in upward-lateral growth of crystals, according towhether molecules arrive at the crystals through the bulk, acrossthe surface, or from the vapor and whether they join the bottom

of a crystal, lifting it up (as in the growth of tin whiskers, ref. 27),or the side or top of a crystal. If vapor-phase transport sustainsthe growth of surface crystals on an IMC glass (Fig. 6, Arrow V),the growth rate u is not expected to exceed the rate of vapor de-position, which is the same as the rate of desorption udes for asample surrounded by a stagnant vapor. At 40 °C, u≈1 nm∕s,whereas udes≈0.001 nm∕s [measured by following vacuum deso-rption with a quartz crystal microbalance (28)]. Vapor-phasetransport therefore cannot sustain the steady-state growth ofIMC surface crystals.

If bulk-phase transport sustains the growth of surface crystalson an IMC glass (Fig. 6, Arrow B), the growth should not stopafter the surface is covered with crystals because there is stillamorphous material underneath. But the surface morphologyis apparently “frozen in” once a growth front passes the region.Moreover, the time required for the surface crystal to gain onelayer of molecules at 40 °C (ca. 1 s for u≈1 nm∕s) is substantiallyshorter than the time required for an average molecule to diffusethe distance of its diameter in the bulk liquid near Tg [typically100 s (28)]. We believe that surface transport (Fig. 6, Arrow S) isthe most likely for supplying molecules to sustain the growth ofsurface crystals. This mechanism is consistent with the observa-tions that fast crystal growth occurs only at free surfaces, thatcoating the surface with 10 nm of gold or 3–20 nm of polymereliminates the fast crystal growth (6), and that the expected rateof surface diffusion (a few orders of magnitude faster than bulkdiffusion) is plausibly rapid enough to support the observed rateof crystal growth.

Concerning where molecules join a growing crystal, because agrowing α IMC fiber lengthens over time, the growth-at-bottommechanism (hair-like growth) would involve elevation of newgrowth sections relative to stationary already grown sections,yielding a product with incoherent sections and grain boundariesand intermediate products with uneven heights. None of thesefeatures were observed. The most plausible scenario for theupward-lateral growth of IMC surface crystals appears to be thatcrystallizing molecules originate from the glass surface, are drawnto the crystal by its lower chemical potential, and deposit atgrowth sites either at or above the glass surface. This model ofsurface crystal growth can resolve the apparent paradox (13) thatthe mobile surface layer is only a few nanometers thick but thepropagating surface crystal layer is hundreds of nanometers thick.

Implications for Current Models of Surface-Enhanced Crystal Growth.It is of interest to evaluate the various models of surface-enhanced crystal growth against its known properties, includingthe findings of this study. To recap the experimental observations:crystal growth in glasses can be much faster at the surface thanin the bulk; surface crystal growth can be inhibited if the surface isin contact with another material (a silicate coverslip, a 10 nmlayer of gold, or a 3–20 nm layer of polymer) (6); surface crystalscan rise hundreds of nanometers above the glass surface as theygrow laterally; and the propagating surface crystal layer can behundreds of nanometers thick.

We now consider three models of surface-enhanced crystalgrowth, namely, those that attribute the phenomenon to a reduc-tion of crystallization-induced stress or strain at surfaces (16, 19),to surface molecular mobility (5, 6, 10, 11), or to the different

glass

crystal

vapor

uudes

B

S

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glasssurface

Fig. 6. Various pathways for molecules to join a crystal growing at a glasssurface: from the vapor (V), from the bulk (B), and from the surface (S). Thevelocity of lateral growth is u. This study found that the growing crystal risesabove the glass surface.

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molecular packing at surfaces (19). In choosing these models foranalysis, we have regarded it as unlikely that the surface crystal-lization of IMC glasses is caused by other effects proposed (12).For example, surface oxidation (or some other chemical modifi-cation) seems irrelevant because the growth mode exists in bothdry air and vacuum; surface contamination seems unimportantbecause IMC glasses prepared by liquid cooling, spin-coating,and vapor deposition show similar crystal growth rates at the sur-face; and IMC being a pure substance, component segregation isirrelevant.

In the tension-release model, the process of growing higherdensity crystals in lower density glasses is thought to cause stress(19) or strain (16) in the system and the effect is believed todiminish on going from the bulk to the surface, resulting in fastercrystal nucleation and growth. This type of model may have dif-ficulty explaining the fact that surface-enhanced crystal growth isinhibited comparably by coatings of different moduli (gold, poly-mer, or silicate glass) and thicknesses (3 nm to 1 mm) (5, 6).Schmelzer and coworkers (16) model a surface crystal as a sphe-rical cap with its flat face level with the glass surface and theremainder buried in the bulk. This picture would be invalid forIMC, whose surface crystals rise above the glass surface as theygrow laterally and do not penetrate deep into the bulk. For sucha system, crystallization-induced tension, if present, must be eval-uated differently.

The surface mobility model of surface crystallization attributessurface-enhanced crystal growth to the higher mobility of surfacemolecules (5, 6, 10, 11). This model can explain the inhibitionof surface-enhanced crystal growth by coatings of differentmaterials and thicknesses, which presumably quench surfacemolecular mobility to bulk levels. This model is consistent withthe upward-lateral growth of surface crystals. In fact, this growthprocess provides a natural solution for the apparent difficulty ofexplaining the formation of surface crystals on the micrometerscale by the transport of molecules in a mobile surface layer onlya few nanometers thick. In this model, crystallizing moleculeswould be drawn continuously to the crystal, climb up, and depositthemselves at growth sites.

Because the packing of molecules at the glass surface can bedifferent from that in the bulk (surface reconstruction), it mightbe speculated (19) that this difference could lead to faster crystalgrowth at the surface. This scenario would be plausible if the sur-face crystal layer was only a few nanomters thick but seemsunlikely for a system like IMC, whose surface crystal layer canbe hundreds of nanometers thick.

Generality of Surface-Enhanced Crystal Growth. Attributing surface-enhanced crystal growth to released tension or enhanced mobilityat surfaces implies the generality of the phenomenon. Becausethe phenomenon occurs in such diverse materials as amorphoussilicon and organic glasses, does it also occur in other materials?Why is it considered absent in metallic (12) and silicate (13–15)glasses?We first note that the surfaces of some solids are so easilyoxidized or otherwise chemically altered that surface-enhancedcrystallization might not be easily observed. In fact, it is onlyin ultrahigh vacuum that the surface crystal growth was observedin amorphous silicon (10, 11). Second, some studies of glass crys-tallization were in fact conducted in the liquid state to shortenobservation times. These studies might not observe surface-enhanced crystal growth if the phenomenon is more pronouncedin glasses. Finally, a fast bulk mode of crystal growth (GC mode)has been observed to emerge in some organic liquids near theglass transition temperature, causing an abrupt increase of crystalgrowth rate (3, 4). For such systems, surface-enhanced crystalgrowth could be less noticeable. It is conceivable that under sui-table conditions, more cases of fast crystal growth at free surfacescould be observed.

Concluding RemarksThis study has identified a feature of surface-enhanced crystalgrowth of glasses that may be important for understanding thephenomenon, namely, that surface crystals rise substantiallyabove the glass surface as they grow laterally, without penetratingdeep into the interior. For IMC, an organic glass able to growsurface crystals in two polymorphs (α and γ), the growth frontcan be hundreds of nanometers above the glass surface. The sur-face growth process, meanwhile, is unperturbed by eliminatingthe bulk material deeper than some critical depth (ca. 300 nmfor α IMC and less than 180 nm for γ IMC). In films thinner than300 nm, growth morphologies and growth rates of α IMC werealtered by crystallization-induced dewetting. The upward-lateralgrowth observed with the organic glass IMC has a counterpart ina substantially different system: amorphous silicon thin filmsannealed in ultrahigh vacuum.

The upward-lateral growth of surface crystals is by no meansobvious given that the crystals are denser and that the processincreases the system’s surface energy. This property of surfacecrystal growth suggests a general mechanism that takes advantageof surface molecular mobility and circumvents slow growth inthe bulk. In this model, crystallizing molecules would be drawncontinuously to the crystal, climb up, and deposit themselvesat growth sites. This model is significantly different from othermodels of surface crystallization in discussion; for example, thetension-release model and the surface-ordering model. Our find-ing is relevant for understanding the crystallization of glasses oramorphous solids in developing stable amorphous materials,fabricating glass ceramics, and controlling biomineralization.Further understanding of surface-enhanced crystal growth couldbenefit from high-resolution, real-time microscopy measure-ments that elucidate the mechanism of crystal growth, from thestudy of surface molecular mobility for organic glasses that exhi-bit the phenomenon, and from critical tests of the various models.

Materials and MethodsIMC (γ polymorph) was purchased from Sigma-Aldrich and used as received.Morphologies of surface crystals were examined with an LM (Olympus BH2-UMA) and an AFM (Veeco Multimode IV Scanning Probe Microscope). TheAFM was operated in both the contact and the tapping mode at 1 s per line;a typical scan covered a 10 × 10 μm2 area. Before AFM analysis, a 10–20 nmgold coating was applied to the sample by sputtering to halt surface crystalgrowth. A Raman microscope (Thermo Scientific DXR) was used to identifypolymorphs (29).

IMC glasses of thicknesses 50 nm–15 μm were prepared. The 15-μm thickfilm was prepared by melting crystalline IMC at 175 °C between two micro-scope coverslips, cooling the liquid film to room temperature, and removingthe top coverslip. Films thinner than 500 nm were prepared by spin-coating(Laurell spin coater WS-400-6NPP-LITE). IMC solutions in ethanol were coatedon Si wafers (525-μm thick with 2–3 nm native SiO2) by spinning at 2,000 rpm(occasionally 1,000 and 3,000 rpm) for 60 s. The resulting films had uniforminterference colors, which correlated with their thicknesses. The films were

d(n

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0 2 4 6 8 10 12 14wt % IMC

Fig. 7. Thickness d (measured by ellipsometry and QCM) vs. IMC solutionconcentration. Data are shown for films spin-coated at 2,000 rpm.

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dried overnight in vacuum at room temperature. A few films were preparedby physical vapor deposition onto substrates held at 42 °C (Tg) at a rate of1.5 Å∕s. No difference was observed in the rate or morphology of crystalgrowth in vapor-deposited and spin-coated films of the same thickness.

Fig. 7 shows the thicknesses of amorphous films obtained by spin-coatingIMC solutions of different concentrations (2–12.3 wt %). Film thicknesswas measured by ellipsometry (Rudolph AutoEL II nulling ellipsometeroperating at 405, 632, and 830 nm or J. A. Woollam spectroscopic ellips-ometer) and with a Quartz Crystal Microbalance (QCM) (Stanford ResearchSystem QCM200). For ellipsometry, polarized light was incident on a thin filmat a 70° incidence angle, and the reflectance of s- and p-polarized light wasrecorded. The data was fitted with a Cauchy film model to yield the film’s

index of refraction and thickness. From data on 10 films of different thick-nesses, the index of refraction of the IMC glass at 20 °C was found to be:nðλÞ ¼ Aþ B∕λ2 þ C∕λ4, where λ is the wavelength in nanometers (400–1,000 nm), A ¼ 1.601� 0.003, B ¼ 0.013� 0.002, and C ¼ 0.0007� 0.0003.For QCM, a film was coated directly on the QCM sensor and its thicknesswas calculated from the mass reported by the QCM, the sensor area, andthe density of IMC glass (1.31 g∕cm3) (25).

ACKNOWLEDGMENTS. We thank the National Science Foundation (NSF)(DMR-0804786 and DMR-0907031) and NSF funded University of WisconsinMaterials Research Science and Engineering Centers for supporting this work.

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