Article pubs.acs.org/JPCB
Fast Crystal Growth in o‑Terphenyl Glasses: A Possible Role for Fracture and Surface Mobility C. Travis Powell, Hanmi Xi, Ye Sun, Erica Gunn, Yinshan Chen, M. D. Ediger, and Lian Yu*
Downloaded by SUNY UPSTATE MEDICAL UNIV on September 7, 2015 | http://pubs.acs.org Publication Date (Web): July 23, 2015 | doi: 10.1021/acs.jpcb.5b05389
School of Pharmacy and Department of Chemistry, University of WisconsinMadison, 777 Highland Avenue, Madison, Wisconsin 53706, United States ABSTRACT: Molecular liquids can develop a fast mode of crystal growth (“GC growth”) near the glass transition temperature. This phenomenon remains imperfectly understood with several explanations proposed. We report that GC growth in o-terphenyl conserves the overall volume, despite a 5% higher density of the crystal, and produces fine crystal grains with the same unit cell as normally grown crystals. These results indicate that GC growth continuously creates voids and free surfaces, possibly by fracture. This aspect of the phenomenon has not been considered by previous treatments and is a difficulty for those models that hypothesize a 5% strain without voids. Given the existence of even faster crystal growth on the free surface of molecular glasses, we consider the possibility that GC growth is facilitated by fracture and surface mobility. This notion has support from the fact that GC growth and surface growth are both highly correlated with surface diffusivity and with fast crystal growth along preformed cracks in the glass.
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explanations proposed.2,3,5,12,13 Understanding this phenomenon is relevant for developing amorphous materials that are stable against crystallization. A recent result pertinent to understanding GC growth is that the free surface of molecular glasses can grow crystals even more rapidly.14−16 For OTP, surface crystal growth is 10 times faster than bulk GC growth with similar temperature dependence (activation energy) (Figure 1). Similar to GC growth, the surface process is active in the glassy state but inactive above the glass transition temperature Tg. These similarities suggest an underlying connection between the two processes and the possibility to understand GC growth through the now better understood surface process. Recent work has shown that the velocity of surface crystal growth is proportional to the coefficient of surface diffusion,17 suggesting that surface diffusion enables surface crystal growth. In this study, we inquire whether GC growth is also a process facilitated by surface (interfacial) mobility. The treatment of GC growth as a surface-facilitated process has support from a seemingly unrelated study.18 Paeng et al. report that during GC growth molecular mobility is enhanced by the advancing growth front. The enhancement is up to a factor of 4, consistent with a local tension up to 8 MPa. This tension is much smaller than that expected for a strain of 5% which corresponds to the density difference between the crystal and the glass of OTP19 and matches the reported cavitation tension.20 This finding leads to the notion that GC growth must continuously produce voids, perhaps by fracture, which limits the buildup of stress.
INTRODUCTION
As molecular liquids are cooled to become glasses, a fast mode of crystal growth can abruptly emerge,1−6 causing the growthfront velocity to transition from being limited by bulk diffusion7−9 to vastly exceeding this limit. This so-called glass-to-crystal (GC) growth mode is illustrated in Figure 1 for o-terphenyl (OTP).2,10,11 This phenomenon was first noted by Greet and Turnbull1 in 1967 and was studied systematically by Oguni and co-workers since 1995.2 At present, the phenomenon remains poorly understood, with at least five
Figure 1. Crystal growth velocities in amorphous o-terphenyl (OTP) on a free surface us (blue circles, ref 15), in the bulk ub (black squares), and along cracks in the glass uf (discussed later). The bulk growth is diffusion-controlled at high temperatures (ref 10) and escapes this control at low temperatures (GC mode; refs 2 and 4). The second yaxis shows bulk diffusivity (open red squares, ref 11). © 2015 American Chemical Society
Received: June 5, 2015 Revised: July 10, 2015 Published: July 10, 2015 10124
DOI: 10.1021/acs.jpcb.5b05389 J. Phys. Chem. B 2015, 119, 10124−10130
Article
Downloaded by SUNY UPSTATE MEDICAL UNIV on September 7, 2015 | http://pubs.acs.org Publication Date (Web): July 23, 2015 | doi: 10.1021/acs.jpcb.5b05389
The Journal of Physical Chemistry B
Figure 2. Interface positions during crystal growth. Time is set to zero when the crystal front reaches the air interface and counted back. (a) 298 K; inset pictures at −99 and 0 s. (b) 245 K; inset pictures at −580, −200, and 0 min.
coverslips made of vinyl acetate plastic, both as-received and after being coating with 10 nm of gold. Scanning electron microscopy (SEM) was performed with a field-emission LEO 1530 operated at 6 kV and 12−14 mm working distance using an in lens secondary electron detector. The samples were coated with 10 nm of gold to prevent charging with a Denton Vacuum Desk II (50 mTorr pressure, 45 mA current, and 30 s deposition). Atomic force microscopy (AFM) was performed in tapping mode with a Veeco Multimode IV scanning probe microscope. For these experiments, GC crystals were grown for 12 h at 248, 243, and 228 K using a DSC cell as the temperature controller. Samples were analyzed either immediately or after a short storage at 263 K, with no change in microstructure noted as a result of storage. A Bruker D8 Advance X-ray diffractometer equipped with a Cu Kα source was used to perform powder diffraction measurements in the Bragg−Brentano geometry. OTP GC crystals used for this analysis were grown in the reservoir of a circulating cooler (Polyscience) at 245 ± 2 K in 5 days. Before analysis, the small amount of normal crystals grown from the seeds prior to cooling to 245 K was scraped off with a razor. For 2D X-ray diffraction, we used a Bruker-AXS SMART APEX2, a three-circle single crystal X-ray diffractometer with a sealed tube Cu Kα radiation source. The X-ray beam diameter was 0.5 mm. Crystals of OTP were grown in X-ray transmitting capillary tubes (Charles Supper; 0.2 or 1 mm diameter, 10 μm wall thickness) and analyzed in the transmission geometry. The liquid in a capillary tube was seeded from top to initiate crystal growth and transferred to a 243 ± 2 K circulator bath to grow GC crystals. The capillary was mounted on a fixed goniometer head at 54.7° relative to the lab floor and perpendicular to the X-ray beam; measurements were made with or without rotating the tube about its axis. The detector was centered on the transmitted beam and protected with a beam stop. The detector was 4 cm from the sample, covering 5°−35° in 2θ. Differential scanning calorimetry (DSC) was performed with a TA Instruments Q2000. Crimped aluminum pans were used to eliminate the free surface of the OTP liquid, preventing fast surface crystal growth. OTP crystals were grown either in the DSC cell or in a 245 K circulating cooler. In the latter case, the sample was transferred to the DSC cell waiting at 278 K in less
Previous studies have examined the role of volume contraction in the crystallization of glasses, and these studies have reached opposite conclusions.3,13,21 The higher density of the crystal is expected to create a tension on the surrounding amorphous material. This tension relaxes quickly in a lowviscosity liquid but not in a rigid glass. Some argue that the unrelaxed tension enhances mobility and accelerates crystal growth,3,13 while others propose that the tension decreases the thermodynamic driving force for crystallization, thereby slowing crystal growth.21 None of these models consider void formation as a mechanism of stress release, and this idea is evaluated here. We studied the effect of GC growth on the overall volume of the system and characterized the resulting crystals by microscopy, X-ray diffraction, and calorimetry. We find that GC growth in OTP conserves the overall volume and produces fine crystallites with the same unit cell as normally grown crystals. These results indicate that GC growth continuously produces voids and free surfaces, possibly through fracture. We report that in a fractured glass crystal growth can accelerate along the cracks to the same velocity as on free surfaces. We discuss the possibility that GC growth results from fast crystal growth along surfaces created by fracture.
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EXPERIMENTAL SECTION OTP was purchased from Aldrich and used as-received. To observe crystal growth through a light microscope (Olympus BH2-UMA), a liquid film 15 μm thick was prepared between silicate coverslips by melting OTP crystals. Crystallization was initiated by touching the liquid edge with OTP crystals. Crystallization at 298 K yielded “normal crystals”. To grow GC crystals, the liquid film was crystallized only partially and quickly transferred a cold stage (Linkam THMS 600) waiting at a chosen temperature. To observe the volume change associated with crystal growth, a liquid film was prepared between coverslips with its thickness set by spacers to be 20 μm (copper TEM grids) or 150 μm (silicate coverslips). Crystal growth was induced as described above and the advance of a growth front toward a liquid/air interface was followed over a distance of approximately 1 mm. Experiments were performed at 298 K in the normal mode of crystal growth and at 243−248 K in the GC mode. As a control, experiments were performed with 10125
DOI: 10.1021/acs.jpcb.5b05389 J. Phys. Chem. B 2015, 119, 10124−10130
Article
The Journal of Physical Chemistry B than 10 s and, once in the cell, was cooled to 213 K and analyzed at a heating rate of 10 K/min.
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RESULTS GC Growth Produces a Polycrystalline Material with 5% Voids. In this section we report that GC growth conserves the overall volume, and its product has the same unit cell as normally grown crystals; these results lead to the conclusion that voids are created during GC growth because Vglass = Vcrystal + Vvoids. To observe the effect of GC growth on the overall volume of the system, we followed the movement of a liquid/ air interface as a crystal growth front advanced toward it (Figure 2). Liquid flow during crystal growth will move the liquid/air interface toward the crystals by an amount xL given by x L = (ρC /ρL − 1)xC
Figure 3. X-ray diffraction patterns of GC and normal crystals of OTP grown in 10 μm thick films measured in reflection (Bragg−Brentano geometry). Peaks were observed at identical diffraction angles, indicating GC crystals have the same unit cell and density as normally grown crystals. All peaks are h0l, indicating preferred growth along b in parallel with the substrate. Simulated pattern is for an isotropic sample.
(1)
where xC is the advance distance of the growth front and ρC and ρL are respectively the densities of the crystal and the liquid (or glass). The experiment was set up to be approximately onedimensional; that is, the growth front and the liquid/air interface were approximately planar and parallel to each other. Figure 2a shows that at 298 K the expected retraction of the liquid/air interface indeed occurs. The line labeled “expected xL” indicates the expected interfacial position calculated from the average crystal growth velocity. At this temperature (Tg + 52 K), the pull of crystal growth is felt by the liquid at least 1 mm away from the growth front. In contrast, in the regime of GC growth, we observed no retraction of the liquid/air interface toward the approaching growth front (Figure 2b). This lack of retraction was confirmed at 243−248 K (Tg − 3 K to Tg + 2 K) and two different sample thicknesses (20 and 150 μm). These results indicate that the GC growth process does not alter the overall volume of the system. It is noteworthy that at 298 K OTP has relatively low viscosity (1 Pa s),22 but its viscosity is substantially higher near Tg, where GC growth is activated. Nevertheless, the liquid is sufficiently mobile to flow on the time scale of our measurements; for example, at 245 K, its volume relaxation time is 70 s in a disk geometry that approximates ours.1 This indicates that flow should occur during our experiment lasting for several hours, had there been sufficient stress to drive liquid flow. The lack of flow means that the stress produced by crystal growth is small. This finding agrees with the report of Paeng et al. that crystal growth alters liquid mobility only within 10 μm from the growth front.18 At the resolution of our measurements (1 μm) we observed no flow in the last 10 μm as the growth front approaches the liquid/air interface. It is expected that at temperatures below 245 K liquid dynamics slows down so much that flow is not expected on the time scale of crystal growth. However, on the ground of the consistent microstructure of GC growth (see later), we speculate that crystallization-induced stress remains small and GC growth inherently has a weak stress field on the adjacent amorphous material. Product of GC Growth Has the Same Unit Cell as Normally Grown Crystals. To measure the X-ray diffraction of GC crystals, we performed both 1D reflection experiment with films in the Bragg−Brentano geometry (Figure 3) and 2D transmission experiment with samples in capillary tubes (Figure 4). The BB measurement had higher angular resolution, allowing more precise comparison of peak positions; the 2D
Figure 4. (a) Illustration of the 2D XRD experiment. d (tube diameter) = 0.2 or 1 mm. Liquid OTP was first crystallized in the normal mode at 298 K and then in the GC mode at 243 K. (b) Diffraction pattern of normal crystals (region 1 in (a)). Dashed arrow is the projection of the tube axis. (c) Diffraction pattern of GC crystals (region 2 in (a)). Patterns (b) and (c) have peaks at identical diffraction angles; the anisotropic diffraction is consistent with the baxis preferentially pointing in the tube axis.
measurement is more informative on crystal orientation and total diffraction strength. Both measurements show that GC crystals and normally grown crystals diffract at the same angles; 10126
DOI: 10.1021/acs.jpcb.5b05389 J. Phys. Chem. B 2015, 119, 10124−10130
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The Journal of Physical Chemistry B the diffraction pattern is consistent with the only known crystal structure of OTP (P212121, a = 18.582 Å, b = 6.024 Å, and c = 11.729 Å).23 Given that GC growth conserves the overall volume, it follows that the product must contain 5% voids, with 5% being the density difference between the crystal and the glass.19 These voids are dispersed among crystalline domains of the known density. OTP crystals grow faster along b (the shortest unit-cell axis) as expected by the Bravais−Friedel−Donnay−Harker model and observed for solution-grown crystals.24 In the BB reflection geometry (Figure 3), all diffraction peaks are h0l reflections, from crystals oriented with their b-axes being parallel to the substrate. In the transmission geometry (Figure 4), the diffraction pattern consists of concentric rings of uneven intensities; the diffraction approximately perpendicular to the capillary tube is from (h0l) planes and that approximately parallel to the tube from planes with nonzero k. These selection rules indicate that OTP crystals are oriented with their b-axes preferentially pointing in the direction of open growth (tube axis). The angular distribution of the grains is Gaussian about the tube axis with σ = 23°. Our data show that GC crystals have diffraction peaks of similar widths as normal crystals, indicating that they are not so small as to cause observable broadening of diffraction peaks. Microstructure of GC Crystals. Through a light microscope (LM), the product of GC growth has fine, unresolved textures (Figure 5a), in contrast to the large domains of
Figure 6. (a) AFM images of OTP crystals grown in the GC mode at 243 K. (b) GC crystals after annealing at 313 K for 30 min. Color scale = 500 nm in height.
AFM images of GC crystals as-grown and after 30 min at 313 K (Tm − 16 K). Note that the consistency between the grain structures observed by AFM (Figure 6a) and SEM (Figure 5b) for the as-grown material. The annealed sample (Figure 6b) shows larger and elongated grains. The direction of elongation is approximately the direction of crystal growth and hence likely the b direction. Consistent with its fine-grained structure, we find that the product of GC growth, though highly crystalline, has significant excess enthalpy over normally grown crystals. Figure 7 shows the DSC traces of normally grown crystals, GC crystals asgrown, and GC crystals after annealing. All three samples show prominent and similar endotherms of melting, indicating similar degrees of crystallinity. Note, however, a small exothermic event of the as-grown GC sample just before melting. This event corresponds to the coarsening of small
Figure 5. (a) OTP crystals grown normally (298 K) and in the GC mode (248 K) viewed through a light microscope between crossed polarizers. Arrow shows growth direction. (b) SEM image of GC crystals grown at 243 K.
normally grown crystals. At higher resolution, SEM shows that GC crystals are composed of grains ca. 500 nm in size (Figure 5b). The grain structure is insensitive to the crystallization temperature from 228 to 248 K, indicating it is an inherent property of the GC growth process. Given its 5% porosity, the product of GC growth is likely an assembly of crystalline domains of the “true” crystal density separated by voids. The grain structure produced by GC growth is stable during observation under ambient conditions; however, annealing at higher temperatures coarsens the grains. Figure 6 compares
Figure 7. DSC traces of OTP crystals grown in the normal and GC modes and GC crystals after annealing at 313 K for 3 days. Heating rate is 10 K/min. GC crystals melt 0.9 K below normal crystals and exhibit an exothermic event before melting. Annealing increases the melting point to its normal value and eliminates the exothermic event. 10127
DOI: 10.1021/acs.jpcb.5b05389 J. Phys. Chem. B 2015, 119, 10124−10130
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The Journal of Physical Chemistry B
been considered by the previous models.2,3,5,12,13 Because free surfaces can accelerate crystal growth (Figure 1),14,15 our finding suggests a new way to understand GC growth as a surface-facilitated transformation. This possibility has support from the observation (Figure 8) that crystal growth is faster along cracks in a glass than through the bulk. To further evaluate this idea, Figure 9 shows the available data on OTP,2,15 indomethacin (IMC),15 and nifedipine
grains (Figure 6) and disappears after annealing. At 10 K/min, GC crystals melt 0.9 K below the normal melting point. This is not an equilibrium melting point but can be regarded as a metastable melting point, similar to that of a metastable polymorph.25 Integrating the DSC curves, we obtain ΔHex = 1.1 ± 0.3 J/g for the excess enthalpy of (unannealed) GC crystals over normally grown crystals. The corresponding excess entropy is estimated to be ΔSex = ΔHex/Tm = (1.1 J/g)/ (329 K) = 0.003 J/(g K), which agrees with the reported 0.002 ± 0.001 J/(g K) for GC crystals formed at 248 K.2 From ΔHex and ΔSex, we obtain ΔGex = 0.3 J/g for the excess free energy of GC crystals formed at 245 K. The latter value agrees reasonably well with the expected surface energy (0.5 J/g) for fine-grained GC crystals. (For this estimation, ΔGex = Aγ, where γ is surface tension and A is surface area. A ≈ 6/(aρ), where a is grain size and ρ is the crystal density. Taking γ = 0.050 N/m,26,27 a = 500 nm, and ρ = 1.2 g/cm3, we obtain ΔGex = 0.5 J/g.) Fast Crystal Growth along Cracks. The creation of voids by GC growth suggests a role of fracture and surface crystal growth in understanding this process. To explore this connection, we examined crystal growth in OTP glasses that contained cracks. Tunnel cracks were created by cooling an OTP glass film sandwiched between less thermally expansive substrates (silicate coverslips) to allow the development of lateral tension.28 Figure 8 shows a sample that contained cracks
Figure 9. Velocities of GC growth ub and surface crystal growth us plotted against surface diffusivity Ds for OTP,2,15 IMC,15 and NIF15,16 glasses.
(NIF),15,16 in the format us vs Ds and ub vs Ds, where us is the velocity of surface crystal growth, ub is the velocity of bulk crystal growth (GC mode), and Ds is the surface diffusion coefficient. We include only those systems for which all three properties are known. As noted alrealy,17 us is roughly proportional to Ds, consistent with the notion that surface crystal growth is supported by surface diffusion. It is also evident that, apart from a vertical shift, the bulk GC growth rate ub has a similar relation to Ds. The line drawn through the ub data describes the overall trend; this line describes the OTP and IMC data very well and the NIF data less well. As a broad pattern, GC growth in these three different molecular glasses has a similar kinetic barrier as surface diffusion, as does surface crystal growth. This result supports the notion that GC growth can be treated as a surface-facilitated transformation. In this model of GC growth, we imagine that the process steadily creates free surfaces, which in turn accelerate the local crystal growth. The velocity of GC growth can be regarded as the velocity of surface crystal growth reduced by a factor f, which is expected to depend on the ease of creating free surfaces (fracture toughness in the case of fracture) and the stability of the free surfaces on the time scale of crystal growth. For the three systems in Figure 9, f = 0.1 describes the average behavior, with NIF deviating the most from the overall trend. The similar f values for these systems may reflect their similar fracture toughness and density change on crystallization. We anticipate this model to be successful in explaining several features of GC growth: (1) Conservation of the overall volume. The steady creation of voids limits the buildup of tension on the surrounding amorphous material. (2) Similar activation energies of surface and bulk crystal growth (Figure 9). Assuming that surface diffusion is the rate-
Figure 8. Fast crystal growth along cracks in an OTP glass at 233 K. The sample is 50 μm thick between two silicate coverslips.
formed in this way. Observe that crystal growth is much faster along a crack than perpendicular to it (into the bulk). The velocity of growth along the cracks for this sample is the same as that observed on the free surface (uf in Figure 1). In general, the growth velocity along a crack is expected to depend on the dimensions of the tunnel; for the sample in Figure 8, the tunnel height h is 50 μm (film thickness), and its width is estimated to be on the order of 100 nm from the removal of stress within a distance h from the crack.28
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DISCUSSION AND CONCLUDING REMARKS This study has found that GC growth conserves the overall volume of the system and produces a polycrystalline material that has the same unit cell as normally grown crystals. The product of GC growth consists of submicron grains with a small excess enthalpy. Given that the crystal is 5% denser than the glass, our results indicate that GC growth continuously creates voids and free surfaces. This property of GC growth has not 10128
DOI: 10.1021/acs.jpcb.5b05389 J. Phys. Chem. B 2015, 119, 10124−10130
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The Journal of Physical Chemistry B
To be fair, all models of GC growth have difficulty explaining the fiber growth. On balance, we consider the present model to have the best potential to explain the known facts about GC growth. An attractive feature of this model is that it simultaneously treats two seemingly unrelated phenomena (surface and bulk crystal growth in molecular glasses) on the basis of a single rate-limiting step, namely, surface diffusion. Finally, we comment on the relevance of our results for evaluating other models of GC growth. The steady creation of voids near the growth front presents a difficulty for those models that hypothesize strains up to 5% without voids in order to explain the molecular mobility necessary to support GC growth.3,13 This feature of GC growth is irrelevant (at least superficially) for those models that do not use local stresses to explain fast crystal growth. To the extent the 500 nm grains observed here are the elemental units of growth, it is of interest to consider its connection with the various models that invoke a length scale. Oguni and co-workers view GC crystals as an aggregation of “homogeneous nuclei”, each a few nanometers in size.2 Stevenson and Wolynes envision GC growth as a network assembly of nanocrystals created by spontaneous nucleation.12 The units of growth in these models are far smaller than the observed 500 nm, although the models allow for aligned aggregation of molecular clusters, perhaps increasing the coherence length. Caroli and Lemaı̂tre hypothesize a size of 100 nm for their “rugged spherulites”, which is closer to the observed 500 nm.13
limiting step for GC growth, this result follows. This assumption seems valid for OTP and IMC but needs improvement for NIF. (3) Solid-state crystal growth terminated by fluidity. GC growth is known to be fully active only in the glassy state but disrupted above Tg (at the onset of fluidity).6 The present model anticipates this property since surface crystal growth has the same property.15 Hasebe et al. report that the onset of fluidity disrupts surface crystal growth on molecular glasses because the flowing liquid wets and embeds upward growing surface crystals. For bulk GC growth, a flowing liquid would heal existing cracks and prevent new cracks from forming, frustrating the growth process. Musumeci et al. report that the highest level of fluidity at which GC growth can exist depends on the velocity of crystal growth u, according to the empirical relation D/u = 7 pm, where D is bulk diffusivity. The present model would explain this result as follows. For GC growth to propagate, cracks must not heal on the time scale of crystal growth. The time scale for crystal growth can be written as τu = a/u, where a is the molecular diameter. Zhang et al. report that the time scale for cracks to heal in a glass film is roughly the structural relaxation time,29 but as Li et al. argue, bulk diffusion becomes the more efficient mechanism for shrinking small cavities (
Fast Crystal Growth in o‑Terphenyl Glasses: A Possible Role for Fracture and Surface Mobility C. Travis Powell, Hanmi Xi, Ye Sun, Erica Gunn, Yinshan Chen, M. D. Ediger, and Lian Yu*
Downloaded by SUNY UPSTATE MEDICAL UNIV on September 7, 2015 | http://pubs.acs.org Publication Date (Web): July 23, 2015 | doi: 10.1021/acs.jpcb.5b05389
School of Pharmacy and Department of Chemistry, University of WisconsinMadison, 777 Highland Avenue, Madison, Wisconsin 53706, United States ABSTRACT: Molecular liquids can develop a fast mode of crystal growth (“GC growth”) near the glass transition temperature. This phenomenon remains imperfectly understood with several explanations proposed. We report that GC growth in o-terphenyl conserves the overall volume, despite a 5% higher density of the crystal, and produces fine crystal grains with the same unit cell as normally grown crystals. These results indicate that GC growth continuously creates voids and free surfaces, possibly by fracture. This aspect of the phenomenon has not been considered by previous treatments and is a difficulty for those models that hypothesize a 5% strain without voids. Given the existence of even faster crystal growth on the free surface of molecular glasses, we consider the possibility that GC growth is facilitated by fracture and surface mobility. This notion has support from the fact that GC growth and surface growth are both highly correlated with surface diffusivity and with fast crystal growth along preformed cracks in the glass.
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explanations proposed.2,3,5,12,13 Understanding this phenomenon is relevant for developing amorphous materials that are stable against crystallization. A recent result pertinent to understanding GC growth is that the free surface of molecular glasses can grow crystals even more rapidly.14−16 For OTP, surface crystal growth is 10 times faster than bulk GC growth with similar temperature dependence (activation energy) (Figure 1). Similar to GC growth, the surface process is active in the glassy state but inactive above the glass transition temperature Tg. These similarities suggest an underlying connection between the two processes and the possibility to understand GC growth through the now better understood surface process. Recent work has shown that the velocity of surface crystal growth is proportional to the coefficient of surface diffusion,17 suggesting that surface diffusion enables surface crystal growth. In this study, we inquire whether GC growth is also a process facilitated by surface (interfacial) mobility. The treatment of GC growth as a surface-facilitated process has support from a seemingly unrelated study.18 Paeng et al. report that during GC growth molecular mobility is enhanced by the advancing growth front. The enhancement is up to a factor of 4, consistent with a local tension up to 8 MPa. This tension is much smaller than that expected for a strain of 5% which corresponds to the density difference between the crystal and the glass of OTP19 and matches the reported cavitation tension.20 This finding leads to the notion that GC growth must continuously produce voids, perhaps by fracture, which limits the buildup of stress.
INTRODUCTION
As molecular liquids are cooled to become glasses, a fast mode of crystal growth can abruptly emerge,1−6 causing the growthfront velocity to transition from being limited by bulk diffusion7−9 to vastly exceeding this limit. This so-called glass-to-crystal (GC) growth mode is illustrated in Figure 1 for o-terphenyl (OTP).2,10,11 This phenomenon was first noted by Greet and Turnbull1 in 1967 and was studied systematically by Oguni and co-workers since 1995.2 At present, the phenomenon remains poorly understood, with at least five
Figure 1. Crystal growth velocities in amorphous o-terphenyl (OTP) on a free surface us (blue circles, ref 15), in the bulk ub (black squares), and along cracks in the glass uf (discussed later). The bulk growth is diffusion-controlled at high temperatures (ref 10) and escapes this control at low temperatures (GC mode; refs 2 and 4). The second yaxis shows bulk diffusivity (open red squares, ref 11). © 2015 American Chemical Society
Received: June 5, 2015 Revised: July 10, 2015 Published: July 10, 2015 10124
DOI: 10.1021/acs.jpcb.5b05389 J. Phys. Chem. B 2015, 119, 10124−10130
Article
Downloaded by SUNY UPSTATE MEDICAL UNIV on September 7, 2015 | http://pubs.acs.org Publication Date (Web): July 23, 2015 | doi: 10.1021/acs.jpcb.5b05389
The Journal of Physical Chemistry B
Figure 2. Interface positions during crystal growth. Time is set to zero when the crystal front reaches the air interface and counted back. (a) 298 K; inset pictures at −99 and 0 s. (b) 245 K; inset pictures at −580, −200, and 0 min.
coverslips made of vinyl acetate plastic, both as-received and after being coating with 10 nm of gold. Scanning electron microscopy (SEM) was performed with a field-emission LEO 1530 operated at 6 kV and 12−14 mm working distance using an in lens secondary electron detector. The samples were coated with 10 nm of gold to prevent charging with a Denton Vacuum Desk II (50 mTorr pressure, 45 mA current, and 30 s deposition). Atomic force microscopy (AFM) was performed in tapping mode with a Veeco Multimode IV scanning probe microscope. For these experiments, GC crystals were grown for 12 h at 248, 243, and 228 K using a DSC cell as the temperature controller. Samples were analyzed either immediately or after a short storage at 263 K, with no change in microstructure noted as a result of storage. A Bruker D8 Advance X-ray diffractometer equipped with a Cu Kα source was used to perform powder diffraction measurements in the Bragg−Brentano geometry. OTP GC crystals used for this analysis were grown in the reservoir of a circulating cooler (Polyscience) at 245 ± 2 K in 5 days. Before analysis, the small amount of normal crystals grown from the seeds prior to cooling to 245 K was scraped off with a razor. For 2D X-ray diffraction, we used a Bruker-AXS SMART APEX2, a three-circle single crystal X-ray diffractometer with a sealed tube Cu Kα radiation source. The X-ray beam diameter was 0.5 mm. Crystals of OTP were grown in X-ray transmitting capillary tubes (Charles Supper; 0.2 or 1 mm diameter, 10 μm wall thickness) and analyzed in the transmission geometry. The liquid in a capillary tube was seeded from top to initiate crystal growth and transferred to a 243 ± 2 K circulator bath to grow GC crystals. The capillary was mounted on a fixed goniometer head at 54.7° relative to the lab floor and perpendicular to the X-ray beam; measurements were made with or without rotating the tube about its axis. The detector was centered on the transmitted beam and protected with a beam stop. The detector was 4 cm from the sample, covering 5°−35° in 2θ. Differential scanning calorimetry (DSC) was performed with a TA Instruments Q2000. Crimped aluminum pans were used to eliminate the free surface of the OTP liquid, preventing fast surface crystal growth. OTP crystals were grown either in the DSC cell or in a 245 K circulating cooler. In the latter case, the sample was transferred to the DSC cell waiting at 278 K in less
Previous studies have examined the role of volume contraction in the crystallization of glasses, and these studies have reached opposite conclusions.3,13,21 The higher density of the crystal is expected to create a tension on the surrounding amorphous material. This tension relaxes quickly in a lowviscosity liquid but not in a rigid glass. Some argue that the unrelaxed tension enhances mobility and accelerates crystal growth,3,13 while others propose that the tension decreases the thermodynamic driving force for crystallization, thereby slowing crystal growth.21 None of these models consider void formation as a mechanism of stress release, and this idea is evaluated here. We studied the effect of GC growth on the overall volume of the system and characterized the resulting crystals by microscopy, X-ray diffraction, and calorimetry. We find that GC growth in OTP conserves the overall volume and produces fine crystallites with the same unit cell as normally grown crystals. These results indicate that GC growth continuously produces voids and free surfaces, possibly through fracture. We report that in a fractured glass crystal growth can accelerate along the cracks to the same velocity as on free surfaces. We discuss the possibility that GC growth results from fast crystal growth along surfaces created by fracture.
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EXPERIMENTAL SECTION OTP was purchased from Aldrich and used as-received. To observe crystal growth through a light microscope (Olympus BH2-UMA), a liquid film 15 μm thick was prepared between silicate coverslips by melting OTP crystals. Crystallization was initiated by touching the liquid edge with OTP crystals. Crystallization at 298 K yielded “normal crystals”. To grow GC crystals, the liquid film was crystallized only partially and quickly transferred a cold stage (Linkam THMS 600) waiting at a chosen temperature. To observe the volume change associated with crystal growth, a liquid film was prepared between coverslips with its thickness set by spacers to be 20 μm (copper TEM grids) or 150 μm (silicate coverslips). Crystal growth was induced as described above and the advance of a growth front toward a liquid/air interface was followed over a distance of approximately 1 mm. Experiments were performed at 298 K in the normal mode of crystal growth and at 243−248 K in the GC mode. As a control, experiments were performed with 10125
DOI: 10.1021/acs.jpcb.5b05389 J. Phys. Chem. B 2015, 119, 10124−10130
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The Journal of Physical Chemistry B than 10 s and, once in the cell, was cooled to 213 K and analyzed at a heating rate of 10 K/min.
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RESULTS GC Growth Produces a Polycrystalline Material with 5% Voids. In this section we report that GC growth conserves the overall volume, and its product has the same unit cell as normally grown crystals; these results lead to the conclusion that voids are created during GC growth because Vglass = Vcrystal + Vvoids. To observe the effect of GC growth on the overall volume of the system, we followed the movement of a liquid/ air interface as a crystal growth front advanced toward it (Figure 2). Liquid flow during crystal growth will move the liquid/air interface toward the crystals by an amount xL given by x L = (ρC /ρL − 1)xC
Figure 3. X-ray diffraction patterns of GC and normal crystals of OTP grown in 10 μm thick films measured in reflection (Bragg−Brentano geometry). Peaks were observed at identical diffraction angles, indicating GC crystals have the same unit cell and density as normally grown crystals. All peaks are h0l, indicating preferred growth along b in parallel with the substrate. Simulated pattern is for an isotropic sample.
(1)
where xC is the advance distance of the growth front and ρC and ρL are respectively the densities of the crystal and the liquid (or glass). The experiment was set up to be approximately onedimensional; that is, the growth front and the liquid/air interface were approximately planar and parallel to each other. Figure 2a shows that at 298 K the expected retraction of the liquid/air interface indeed occurs. The line labeled “expected xL” indicates the expected interfacial position calculated from the average crystal growth velocity. At this temperature (Tg + 52 K), the pull of crystal growth is felt by the liquid at least 1 mm away from the growth front. In contrast, in the regime of GC growth, we observed no retraction of the liquid/air interface toward the approaching growth front (Figure 2b). This lack of retraction was confirmed at 243−248 K (Tg − 3 K to Tg + 2 K) and two different sample thicknesses (20 and 150 μm). These results indicate that the GC growth process does not alter the overall volume of the system. It is noteworthy that at 298 K OTP has relatively low viscosity (1 Pa s),22 but its viscosity is substantially higher near Tg, where GC growth is activated. Nevertheless, the liquid is sufficiently mobile to flow on the time scale of our measurements; for example, at 245 K, its volume relaxation time is 70 s in a disk geometry that approximates ours.1 This indicates that flow should occur during our experiment lasting for several hours, had there been sufficient stress to drive liquid flow. The lack of flow means that the stress produced by crystal growth is small. This finding agrees with the report of Paeng et al. that crystal growth alters liquid mobility only within 10 μm from the growth front.18 At the resolution of our measurements (1 μm) we observed no flow in the last 10 μm as the growth front approaches the liquid/air interface. It is expected that at temperatures below 245 K liquid dynamics slows down so much that flow is not expected on the time scale of crystal growth. However, on the ground of the consistent microstructure of GC growth (see later), we speculate that crystallization-induced stress remains small and GC growth inherently has a weak stress field on the adjacent amorphous material. Product of GC Growth Has the Same Unit Cell as Normally Grown Crystals. To measure the X-ray diffraction of GC crystals, we performed both 1D reflection experiment with films in the Bragg−Brentano geometry (Figure 3) and 2D transmission experiment with samples in capillary tubes (Figure 4). The BB measurement had higher angular resolution, allowing more precise comparison of peak positions; the 2D
Figure 4. (a) Illustration of the 2D XRD experiment. d (tube diameter) = 0.2 or 1 mm. Liquid OTP was first crystallized in the normal mode at 298 K and then in the GC mode at 243 K. (b) Diffraction pattern of normal crystals (region 1 in (a)). Dashed arrow is the projection of the tube axis. (c) Diffraction pattern of GC crystals (region 2 in (a)). Patterns (b) and (c) have peaks at identical diffraction angles; the anisotropic diffraction is consistent with the baxis preferentially pointing in the tube axis.
measurement is more informative on crystal orientation and total diffraction strength. Both measurements show that GC crystals and normally grown crystals diffract at the same angles; 10126
DOI: 10.1021/acs.jpcb.5b05389 J. Phys. Chem. B 2015, 119, 10124−10130
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The Journal of Physical Chemistry B the diffraction pattern is consistent with the only known crystal structure of OTP (P212121, a = 18.582 Å, b = 6.024 Å, and c = 11.729 Å).23 Given that GC growth conserves the overall volume, it follows that the product must contain 5% voids, with 5% being the density difference between the crystal and the glass.19 These voids are dispersed among crystalline domains of the known density. OTP crystals grow faster along b (the shortest unit-cell axis) as expected by the Bravais−Friedel−Donnay−Harker model and observed for solution-grown crystals.24 In the BB reflection geometry (Figure 3), all diffraction peaks are h0l reflections, from crystals oriented with their b-axes being parallel to the substrate. In the transmission geometry (Figure 4), the diffraction pattern consists of concentric rings of uneven intensities; the diffraction approximately perpendicular to the capillary tube is from (h0l) planes and that approximately parallel to the tube from planes with nonzero k. These selection rules indicate that OTP crystals are oriented with their b-axes preferentially pointing in the direction of open growth (tube axis). The angular distribution of the grains is Gaussian about the tube axis with σ = 23°. Our data show that GC crystals have diffraction peaks of similar widths as normal crystals, indicating that they are not so small as to cause observable broadening of diffraction peaks. Microstructure of GC Crystals. Through a light microscope (LM), the product of GC growth has fine, unresolved textures (Figure 5a), in contrast to the large domains of
Figure 6. (a) AFM images of OTP crystals grown in the GC mode at 243 K. (b) GC crystals after annealing at 313 K for 30 min. Color scale = 500 nm in height.
AFM images of GC crystals as-grown and after 30 min at 313 K (Tm − 16 K). Note that the consistency between the grain structures observed by AFM (Figure 6a) and SEM (Figure 5b) for the as-grown material. The annealed sample (Figure 6b) shows larger and elongated grains. The direction of elongation is approximately the direction of crystal growth and hence likely the b direction. Consistent with its fine-grained structure, we find that the product of GC growth, though highly crystalline, has significant excess enthalpy over normally grown crystals. Figure 7 shows the DSC traces of normally grown crystals, GC crystals asgrown, and GC crystals after annealing. All three samples show prominent and similar endotherms of melting, indicating similar degrees of crystallinity. Note, however, a small exothermic event of the as-grown GC sample just before melting. This event corresponds to the coarsening of small
Figure 5. (a) OTP crystals grown normally (298 K) and in the GC mode (248 K) viewed through a light microscope between crossed polarizers. Arrow shows growth direction. (b) SEM image of GC crystals grown at 243 K.
normally grown crystals. At higher resolution, SEM shows that GC crystals are composed of grains ca. 500 nm in size (Figure 5b). The grain structure is insensitive to the crystallization temperature from 228 to 248 K, indicating it is an inherent property of the GC growth process. Given its 5% porosity, the product of GC growth is likely an assembly of crystalline domains of the “true” crystal density separated by voids. The grain structure produced by GC growth is stable during observation under ambient conditions; however, annealing at higher temperatures coarsens the grains. Figure 6 compares
Figure 7. DSC traces of OTP crystals grown in the normal and GC modes and GC crystals after annealing at 313 K for 3 days. Heating rate is 10 K/min. GC crystals melt 0.9 K below normal crystals and exhibit an exothermic event before melting. Annealing increases the melting point to its normal value and eliminates the exothermic event. 10127
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The Journal of Physical Chemistry B
been considered by the previous models.2,3,5,12,13 Because free surfaces can accelerate crystal growth (Figure 1),14,15 our finding suggests a new way to understand GC growth as a surface-facilitated transformation. This possibility has support from the observation (Figure 8) that crystal growth is faster along cracks in a glass than through the bulk. To further evaluate this idea, Figure 9 shows the available data on OTP,2,15 indomethacin (IMC),15 and nifedipine
grains (Figure 6) and disappears after annealing. At 10 K/min, GC crystals melt 0.9 K below the normal melting point. This is not an equilibrium melting point but can be regarded as a metastable melting point, similar to that of a metastable polymorph.25 Integrating the DSC curves, we obtain ΔHex = 1.1 ± 0.3 J/g for the excess enthalpy of (unannealed) GC crystals over normally grown crystals. The corresponding excess entropy is estimated to be ΔSex = ΔHex/Tm = (1.1 J/g)/ (329 K) = 0.003 J/(g K), which agrees with the reported 0.002 ± 0.001 J/(g K) for GC crystals formed at 248 K.2 From ΔHex and ΔSex, we obtain ΔGex = 0.3 J/g for the excess free energy of GC crystals formed at 245 K. The latter value agrees reasonably well with the expected surface energy (0.5 J/g) for fine-grained GC crystals. (For this estimation, ΔGex = Aγ, where γ is surface tension and A is surface area. A ≈ 6/(aρ), where a is grain size and ρ is the crystal density. Taking γ = 0.050 N/m,26,27 a = 500 nm, and ρ = 1.2 g/cm3, we obtain ΔGex = 0.5 J/g.) Fast Crystal Growth along Cracks. The creation of voids by GC growth suggests a role of fracture and surface crystal growth in understanding this process. To explore this connection, we examined crystal growth in OTP glasses that contained cracks. Tunnel cracks were created by cooling an OTP glass film sandwiched between less thermally expansive substrates (silicate coverslips) to allow the development of lateral tension.28 Figure 8 shows a sample that contained cracks
Figure 9. Velocities of GC growth ub and surface crystal growth us plotted against surface diffusivity Ds for OTP,2,15 IMC,15 and NIF15,16 glasses.
(NIF),15,16 in the format us vs Ds and ub vs Ds, where us is the velocity of surface crystal growth, ub is the velocity of bulk crystal growth (GC mode), and Ds is the surface diffusion coefficient. We include only those systems for which all three properties are known. As noted alrealy,17 us is roughly proportional to Ds, consistent with the notion that surface crystal growth is supported by surface diffusion. It is also evident that, apart from a vertical shift, the bulk GC growth rate ub has a similar relation to Ds. The line drawn through the ub data describes the overall trend; this line describes the OTP and IMC data very well and the NIF data less well. As a broad pattern, GC growth in these three different molecular glasses has a similar kinetic barrier as surface diffusion, as does surface crystal growth. This result supports the notion that GC growth can be treated as a surface-facilitated transformation. In this model of GC growth, we imagine that the process steadily creates free surfaces, which in turn accelerate the local crystal growth. The velocity of GC growth can be regarded as the velocity of surface crystal growth reduced by a factor f, which is expected to depend on the ease of creating free surfaces (fracture toughness in the case of fracture) and the stability of the free surfaces on the time scale of crystal growth. For the three systems in Figure 9, f = 0.1 describes the average behavior, with NIF deviating the most from the overall trend. The similar f values for these systems may reflect their similar fracture toughness and density change on crystallization. We anticipate this model to be successful in explaining several features of GC growth: (1) Conservation of the overall volume. The steady creation of voids limits the buildup of tension on the surrounding amorphous material. (2) Similar activation energies of surface and bulk crystal growth (Figure 9). Assuming that surface diffusion is the rate-
Figure 8. Fast crystal growth along cracks in an OTP glass at 233 K. The sample is 50 μm thick between two silicate coverslips.
formed in this way. Observe that crystal growth is much faster along a crack than perpendicular to it (into the bulk). The velocity of growth along the cracks for this sample is the same as that observed on the free surface (uf in Figure 1). In general, the growth velocity along a crack is expected to depend on the dimensions of the tunnel; for the sample in Figure 8, the tunnel height h is 50 μm (film thickness), and its width is estimated to be on the order of 100 nm from the removal of stress within a distance h from the crack.28
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DISCUSSION AND CONCLUDING REMARKS This study has found that GC growth conserves the overall volume of the system and produces a polycrystalline material that has the same unit cell as normally grown crystals. The product of GC growth consists of submicron grains with a small excess enthalpy. Given that the crystal is 5% denser than the glass, our results indicate that GC growth continuously creates voids and free surfaces. This property of GC growth has not 10128
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The Journal of Physical Chemistry B
To be fair, all models of GC growth have difficulty explaining the fiber growth. On balance, we consider the present model to have the best potential to explain the known facts about GC growth. An attractive feature of this model is that it simultaneously treats two seemingly unrelated phenomena (surface and bulk crystal growth in molecular glasses) on the basis of a single rate-limiting step, namely, surface diffusion. Finally, we comment on the relevance of our results for evaluating other models of GC growth. The steady creation of voids near the growth front presents a difficulty for those models that hypothesize strains up to 5% without voids in order to explain the molecular mobility necessary to support GC growth.3,13 This feature of GC growth is irrelevant (at least superficially) for those models that do not use local stresses to explain fast crystal growth. To the extent the 500 nm grains observed here are the elemental units of growth, it is of interest to consider its connection with the various models that invoke a length scale. Oguni and co-workers view GC crystals as an aggregation of “homogeneous nuclei”, each a few nanometers in size.2 Stevenson and Wolynes envision GC growth as a network assembly of nanocrystals created by spontaneous nucleation.12 The units of growth in these models are far smaller than the observed 500 nm, although the models allow for aligned aggregation of molecular clusters, perhaps increasing the coherence length. Caroli and Lemaı̂tre hypothesize a size of 100 nm for their “rugged spherulites”, which is closer to the observed 500 nm.13
limiting step for GC growth, this result follows. This assumption seems valid for OTP and IMC but needs improvement for NIF. (3) Solid-state crystal growth terminated by fluidity. GC growth is known to be fully active only in the glassy state but disrupted above Tg (at the onset of fluidity).6 The present model anticipates this property since surface crystal growth has the same property.15 Hasebe et al. report that the onset of fluidity disrupts surface crystal growth on molecular glasses because the flowing liquid wets and embeds upward growing surface crystals. For bulk GC growth, a flowing liquid would heal existing cracks and prevent new cracks from forming, frustrating the growth process. Musumeci et al. report that the highest level of fluidity at which GC growth can exist depends on the velocity of crystal growth u, according to the empirical relation D/u = 7 pm, where D is bulk diffusivity. The present model would explain this result as follows. For GC growth to propagate, cracks must not heal on the time scale of crystal growth. The time scale for crystal growth can be written as τu = a/u, where a is the molecular diameter. Zhang et al. report that the time scale for cracks to heal in a glass film is roughly the structural relaxation time,29 but as Li et al. argue, bulk diffusion becomes the more efficient mechanism for shrinking small cavities (
