Correlation between Luminescence and EPR Spectroscopy as Evidence of Ytterbium Pair Formation in Li6Ln(BO3)3:Yb3+ (Ln=Gd,Y) Borate Single Crystals

Synthesized powders and grown single crystals of nominal compositions Li₆Ln(BO₃)₃:Yb³⁺ (Ln=Y, Gd) were investigated by means of powder and single‐crystal X‐ray diffraction (XRD), as well as optical near‐IR spectroscopy in conjunction with electron paramagnetic resonance (EPR) spectroscopy. The appearance of two distinct zero‐phonon lines suggests the existence of two kinds of Yb³⁺ ions in the single crystals. The XRD results exclude the possibility of a phase transition occurring between room and low temperatures. EPR spectra of single crystals show the presence of both isolated ions and pairs of ytterbium ions substituted for Y³⁺. A strong temperature dependence of the intensity of Yb–Yb pairs resonance lines coincides with temperature dependence of emission peak at 978 nm, confirming a common origin of the defect giving rise to these spectra. Calculated from EPR spectra, the distance between pairs of Yb³⁺ is in good agreement with crystallographic ones: R=3.856 Å, R_cryst=3.849 Å.     

X‐Ray and Electron Diffraction Study of Poly(p‐dioxanone)

Summary: Solution‐grown lamellar crystals of poly(p‐dioxanone) (PPDX) have been crystallized isothermally from butane‐1,4‐diol at 100 °C. The crystal structure of PPDX has been determined by interpretation of X‐ray fiber diagrams of PPDX fibers and electron diffraction diagrams of lozenge‐shaped chain‐folder lamellar crystals. The unit cell of PPDX is orthorhombic with space group P2₁2₁2₁ and parameters: a = 0.970 nm, b = 0.742 nm, and c (chain axis) = 0.682 nm. There are two chains per unit cell, which exist in an antiparallel arrangement.

Transmission electron micrograph of PPDX chain‐folded lamellar crystals obtained by isothermal crystallization and its electron diffraction diagram.     

Electron diffraction and computer modeling of poly(naphthalic anhydride) crystal structure

Single crystals of poly(naphthalic anhydride) (PNA) have been grown using our confined thin film melt polymerization technique. Lamellae, 70–100 Å thick, are found for the crystals polymerized at 180°C with thinner lamellae for a 200°C polymerization temperature. In addition, irregular lath-shaped crystals are found for both polymerization temperatures, apparently formed by a solid-state polymerization process within the original needle-like monomer crystals. The crystal structure of PNA has been studied by electron diffraction (ED) and computer modeling based on seven different zonal ED patterns. It is found that, in most cases, two or three different zonal patterns are superimposed with a common plane, suggesting variable chain tilting even in individual lamellae. Shearing of the material shortly after the initiation of polymerization, permitted obtaining an additional [010] zone ED pattern. A monoclinic unit cell with one chain, two repeat units is proposed based on measurements of 21 independent reflections; the space group is Pc11; a = 6.26 Å, b = 4.33 Å, c = 18.60 Å, and α = 122.5°. The computer-simulated (Cerius²) molecular conformation and chain packing are described with the corresponding simulated electron diffraction patterns being in good agreement with the observed ones. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1575–1588, 1997     

Single crystals of regio-selectively substituted cellulose hetero-esters

Lamellar single crystals of some regio-selectively substituted cellulose hetero-esters: cellulose propionate diacetate (CPDA, 2,3-di-O-acetyl-6-O-propionyl cellulose), cellulose acetate dipropionate (CADP, 6-O-acetyl-2,3-di-O-propionyl cellulose), cellulose butyrate diacetate (CBDA, 2,3-di-O-acetyl-6-O-butyryl cellulose) and cellulose acetate dibutyrate (CADB, 6-O-acetyl-2,3-di-O-butyryl cellulose), have been prepared at high temperature in a mixture of dibenzyl ether andn-tetradecane. The CPDA crystals were lozenge-shaped whereas those of CADP, CBDA and CADB had a ribbon morphology. CPDA crystals gave well-resolved electron diffractograms from which the reciprocal lattice parameters a^*=0.807 nm^–1,b ^*=0.400 nm^–1 and ^*=90° could be determined. Systematic absences occurred at every odd reflection along the two orthogonal axesa ^*andb ^*. Thus, the CPDA diffraction pattern is consistent with a p_gg symmetry. For CADP, the electron diffraction pattern is consistent with a p_mg two-dimensional space group withb the unique axis along the ribbon direction. The diagram yields the reciprocal lattice parameters a^* = 0.902 nm^–1,b ^*=0.651 nm^–1 and ^*=90°. The CBDA electron diffractogram yields the following cell parameters and two-dimensional space group:a ^*=0.482 nm^–1,b ^*=0.659 nm^–1 and ^*=90°, and a p_gg symmetry; and that of CADB:a ^*=0.834 nm^–1,b ^*=0.645 nm^–1 and ^*=90°, and a p_mg symmetry.     

The Crystal Structure of InGaO3(ZnO)4: A Single Crystal X‐ray and Electron Diffraction Study

The crystal structure of the mixed oxide InGaO₃(ZnO)₄ has been determined from electron diffraction and single‐crystal X‐ray diffraction data. The compound crystallises in a hexagonal space group (P6₃/mmc; No. 194), deduced from convergent beam electron diffraction (CBED). Single crystals of InGaO₃(ZnO)₄ were grown from a K₂MoO₄ flux in sealed platinum tubes. Single crystal structure refinement from XRD data [a = 3.2850(2) Å; c = 32.906(3) Å; Z = 2; 4232 data, R₁ = 0.0685] reveals a compound with oxygen anions forming a closest‐packed arrangement. Within this packing In³⁺ cations occupy octahedral interstices, forming layers of edge sharing octahedra. In between these layers are regions with composition [Zn₄GaO₅]⁺ forming a wurtzite type of structure. Inversions of the ZnO₄ tetrahedra occurs (i) at the InO₆ octahedral layer and (ii) halfway in the wurtzite type region, where the inversion boundary is built by Ga³⁺ in trigonal bipyramidal coordination with a long Ga–O_apical distance of 2.19(1) Å. The site occupation of Zn²⁺ and Ga³⁺, respectively, was confirmed by bond valence sum calculations. The compounds described here have the same structural charactistics as other known members with general formula ARO₃(ZnO)_m with m = integer.     

Synthesis,Crystal Structures,and Optical/Electronic Properties of Sphere–Rod Shape Amphiphiles Based on a [60]Fullerene?Oligofluorene Conjugate

A series of sphere–rod shape amphiphiles, in which a [60]fullerene (C₆₀) sphere was connected to the center of an oligofluorene (OF) rod through a rigid linkage (OF‐C₆₀), were designed and synthesized. Alkyl chains of various lengths were attached onto the OFs on both sides of the C₆₀ spheres. These compounds, denoted as alkyl‐OF‐C₆₀, were fully characterized by ¹H NMR, ¹³C NMR, and FTIR spectroscopy and by MALDI‐TOF mass spectrometry. The morphologies and structures of their crystals were elucidated by wide‐angle X‐ray diffraction (WAXD) and by electron diffraction in transmission electron microscopy (TEM). Butyl‐OF‐C₆₀ forms a monoclinic unit cell (a=1.86, b=3.96, c=2.24 nm; α=γ=90°, β=68°; space group P2), octyl‐OF‐C₆₀ also forms a monoclinic unit cell (a=2.21, b=4.06, c=1.81 nm; α=γ=90°, β=75.5°; space group C2m), and dodecanyl‐OF‐C₆₀ forms a triclinic structure (a=1.82, b=4.35, c=2.26 nm; α=93.1°, β=94.5°, γ=92.7°; space group P1). The inequivalent spheres and rods were found to pack into an alternating layered structure of C₆₀ and OF in the crystals, thus resembling a “double‐cable” structure. UV/Vis absorption spectroscopy revealed an electron perturbation between the two individual chromophores (C₆₀ and OF) in their ground states. Fluorescence spectroscopy exhibited complete fluorescence quenching of their solutions in toluene, thus suggesting an effective energy transfer from OF to C₆₀. Cyclic voltammetry indicated that the energy‐level profiles of C₆₀ and OF remained essentially unchanged. This work has broad implications in terms of understanding the self‐assembly and molecular packing of conjugated materials in crystals and has potential applications in organic field‐effect transistors and bulk heterojunction solar cells.     

Crystal morphology of the γ (triclinic) phase of isotactic polypropylene and its relation to the α phase

γ-phase crystals of isotactic polypropylene (iPP) obtained from low-molecular-weight extracts of pyrolyzed polymers are examined by electron microscopy and electron diffraction. γ-phase crystals differ from α-phase crystals in three important respects: (i) they are elongated along the b^* rather than the a^* axis, (ii) the chain axis is inclined at 50° to the lamellar surface (indexed as 101) rather than normal to it, and (iii) they show screw dislocations, while α crystals do not. γ crystals are nucleated on the lateral (010) faces of a α crystals; the b_α and b axes are parallel. Virtually no nucleation of the α phase takes place on the γ phase, which is therefore not involved in the repetitive lamellar branching leading to iPP quadrites. Crystallization of the γ phase appears to be favored by or linked to the absence of chain folds and may be involved in the macroscopic curvature of iPP branches.     

Structural data and thermal studies on nylon-12,10

The structure and morphology of Nylon-12, 10 lamellar crystals has been investigated using transmission electron microscopy, selected area electron diffraction, and x-ray diffraction. Additional data have been obtained from uniaxially oriented fibers. The unit cell parameters of two crystalline structures have been determined. They are similar to those usually found in other polyamides (α and β form). Calorimetric (DSC) studies on nylon 12, 10 were also carried out. Melting curves indicate that changes in the internal structure occur when scanning speeds less than 80°C min^?1 are used. ©1995 John Wiley & Sons, Inc.     

X-ray diffraction and scanning electron microscopy of galvannealed coatings on steel

The formation of Fe–Zn intermetallic compounds, as relevant in the commercial product galvannealed steel sheet, was investigated by scanning electron microscopy and different methods of X-ray diffraction. A scanning electron microscope with high resolution was applied to investigate the layers of the galvannealed coating and its topography. Grazing incidence X-ray diffraction (GID) was preferred over conventional Bragg–Brentano geometry for analysing thin crystalline layers because of its lower incidence angle α and its lower depth of information. Furthermore, in situ experiments at an environmental scanning electron microscope (ESEM) with an internal heating plate and at an X-ray diffractometer equipped with a high-temperature chamber were carried out. Thus, it was possible to investigate the phase evolution during heat treatment by X-ray diffraction and to display the growth of the ζ crystals in the ESEM.     

Molecular ordering in some liquid aromatic hydrocarbons

This study presents a comparison of the structures and molecular correlations for the linear aromatic hydrocarbons: benzene, naphthalene, and anthracene in the liquid phase, performed for the first time by the method of X-ray diffraction. Also for the first time the X-ray diffraction results obtained for anthracene at 513?K have been reported. Monochromatic radiation CuK_α was used to determine the scattered radiation intensity between S _min?=?4π?sin?Θ_min/λ?=?0.417?Å^?1 and S _max?=?4π?sin?Θ_max/λ?=?7.06?Å^?1. The mean angular distributions of X-ray scattered intensity were measured and the differential radial distribution functions of electron density (DRDFs) were calculated. The mean distances between the neighbouring molecules and the mean coordination numbers were found. The most probable models of local ordering of these molecules were suggested. Correlations have been found between the number of benzene rings in the molecules studied and their physical properties.     

ZnO衍射花样180°不唯一性的消除

晶体电子衍射花样涉及到界面、位错等缺陷的晶体学性质测定时,需要设法消除180°不唯一性这一问题.应用Tecnai G~2 F20场发射透射电镜精密的倾斜样品台使晶体做有系统的倾转,观察衍射花样的变化并加以分析,从而消除了ZnO粉末单晶花样的180°不唯一性.     

Molecular structure of phenylsilane: a study by gas-phase electron diffraction and ab initio molecular orbital calculations

The molecular structure of phenylsilane has been determined accurately by gas-phase electron diffraction and ab initio MO calculations at the MP2(f.c.)/6-31G* level. The calculations indicate that the perpendicular conformation of the molecule, with a Si–H bond in a plane orthogonal to the plane of the benzene ring, is the potential energy minimum. The coplanar conformation, with a Si–H bond in the plane of the ring, corresponds to a rotational transition state. However, the difference in energy is very small, 0.13 kJ mol⁻¹, implying free rotation of the substituent at the temperature of the electron diffraction experiment (301 K). Important bond lengths from electron diffraction are: <r_g(C–C)>=1.403±0.003 Å, r_g(Si–C)=1.870±0.004 Å, and r_g(Si–H)=1.497±0.007 Å. The calculations indicate that the C_ipso–C_ortho bonds are 0.010 Å longer than the other C–C bonds. The internal ring angle at the ipso position is 118.1±0.2° from electron diffraction and 118.0° from calculations. This confirms the more than 40-year old suggestion of a possible angular deformation of the ring in phenylsilane, in an early electron diffraction study by F.A. Keidel, S.H. Bauer, J. Chem. Phys. 25 (1956) 1218.     

Synthesis and structure analysis of tetragonal Li7La3Zr2O12 with the garnet-related type structure

We have successfully synthesized a high-purity polycrystalline sample of tetragonal Li₇La₃Zr₂O₁₂. Single crystals have been also grown by a flux method. The single-crystal X-ray diffraction analysis verifies that tetragonal Li₇La₃Zr₂O₁₂ has the garnet-related type structure with a space group of I4₁/acd (no. 142). The lattice constants are a=13.134(4) Å and c=12.663(8) Å. The garnet-type framework structure is composed of two types of dodecahedral LaO₈ and octahedral ZrO₆. Li atoms occupy three crystallographic sites in the interstices of this framework structure, where Li(1), Li(2), and Li(3) atoms are located at the tetrahedral 8a site and the distorted octahedral 16f and 32g sites, respectively. The structure is also investigated by the Rietveld method with X-ray and neutron powder diffraction data. These diffraction patterns are identified as the tetragonal Li₇La₃Zr₂O₁₂ structure determined from the single-crystal data. The present tetragonal Li₇La₃Zr₂O₁₂ sample exhibits a bulk Li-ion conductivity of σ_b=1.63×10⁻⁶ S cm⁻¹ and grain-boundary Li-ion conductivity of σ_gb=5.59×10⁻⁷ S cm⁻¹ at 300 K. The activation energy is estimated to be E_a=0.54 eV in the temperature range of 300–560 K.     

Polymorphism of N,N'-diacetylbiuret studied by solid-state 13C and 15N NMR spectroscopy, DFT calculations, and X-ray diffraction

The molecular configuration and crystal structure of solid polycrystalline N,N′′‐diacetylbiuret (DAB), a potential nitrogen‐rich fertilizer, have been analyzed by a combination of solid‐ and liquid‐state NMR spectroscopy, X‐ray diffraction, and DFT calculations. Initially a pure NMR study (“NMR crystallography”) was performed as available single crystals of DAB were not suitable for X‐ray diffraction. Solid‐state ¹³C NMR spectra revealed the unexpected existence of two polymorphic modifications (α‐ and β‐DAB) obtained from different chemical procedures. Several NMR techniques were applied for a thorough characterization of the molecular system, revealing chemical shift anisotropy (CSA) tensors of selected nuclei in the solid state, chemical shifts in the liquid state, and molecular dynamics in the solid state. Dynamic NMR spectroscopy of DAB in solution revealed exchange between two different configurations, which raised the question, is there a correlation between the two different configurations found in solution and the two polymorphic modifications found in the solid state? By using this knowledge, a new crystallization protocol was devised which led to the growth of single crystals suitable for X‐ray diffraction. The X‐ray data showed that the same symmetric configuration is present in both polymorphic modifications, but the packing patterns in the crystals are different. In both cases hydrogen bonds lead to the formation of planes of DAB molecules. Additional symmetry elements, a two‐fold screw in the case of α‐DAB and a c‐glide plane in the case of β‐DAB, lead to a more symmetric (α‐DAB) or asymmetric (β‐DAB) intermolecular hydrogen‐bonding pattern for each molecule.     

Some aspects of doping mechanism in Polyschwefelnitrid (SN)x

(SN)x crystals doped with iodine atoms showed ten or more additional diffuse streaks perpendicular to the b^*-axis, appearing between the layer lines of the electron diffraction pattern of pristine (SN)x. However, only four of these were observed in the X ray diffraction pattern. These four diffuse streaks suggest that the iodine atoms are structured with a one-dimensional order. The extra diffuse streaks can be explained by the double diffraction between the four streaks and the spotty diffractions of (SN)x. The double diffraction results from the microfibrillar nature of the (SN)x. From X-ray microanalysis of doped (SN)x, the iodine content in the specimen was found to change mainly in the direction along the chain axis and almost constant in the direction perpendicular to it. The distribution of iodine atoms indicates that the dopants diffuse preferentially along the molecular axis through disordered domains between fine fibrils comprised in (SN)x crystals. Then the dopants are settled in the narrow disordered domains and give the extra streaked diffraction.     

Structure and morphology of the aliphatic polyester poly(δ‐valerolactone) in solution‐grown,chain‐folded lamellar crystals

Poly(δ‐valerolactone) (PVL) crystals in the form of chain‐folded lamellae were prepared by isothermal crystallization from a 2‐methylbutane‐2‐ol solution. Wide‐angle and small‐angle X‐ray diffraction data, obtained from PVL lamellae sedimented to form oriented mats, were supplemented with morphological and structural data from electron microscopy, both imaging and diffraction. The diffraction signals index on an orthorhombic unit cell with the parameters a = 0.747 ± 0.002 nm, b = 0.502 ± 0.002 nm, and c (chain axis) = 0.742 ± 0.002 nm. Similar unit cell parameters were obtained from crystals grown from 1‐octanol and also from drawn melt‐pressed films. The evidence supports a model containing two antiparallel chain segments in the unit cell. The c value of 0.742 nm is appropriate for an all‐trans or onefold helical backbone conformation for the straight stems. Possible slight perturbations at the ester units from the all‐trans backbone conformation are discussed. Computerized modeling was used to optimize the adjacent‐reentry folded structure. The setting angles, with respect to the a axis, are ±58° for the corner and center chains. The lamellae are 7.26 ± 0.05 nm thick, and the chains run orthogonal to the lamellar surface. The chains fold in the diagonal (110) and (11¯0) planes in an alternating fashion. The X‐ray diffraction data suggest that a proportion of adjacent paired antiparallel entities, or hairpin units, are c‐axis‐sheared, and a relationship to the results obtained from drawn films is discussed. A brief comparison is also made with related polymer structures. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2622–2634, 2001     

Complex Interrupted Tetrahedral Frameworks in the Nitridosilicates M7Si6N15 (M=La,Ce, Pr)

A new structure type of nitridosilicates with an interrupted framework has been identified for M₇Si₆N₁₅ with M=La, Ce, and Pr. The materials have been synthesized in a radio‐frequency furnace at temperatures between 1550–1625 °C, starting from the respective metals, metal nitrides, and silicon diimide. The crystal structure of Ce₇Si₆N₁₅ has been determined by using single‐crystal X‐ray diffraction. Besides ordered crystals 1 with a complicated triclinic superstructure and multiple twinning (P , no. 2; a=13.009(3), b=25.483(5), c=25.508(10) Å; α=117.35(3), β=99.59(3), γ=99.63(3)°; V=7114(2) ų; Z=18; R1=0.0411), disordered crystals 2 with identical composition exhibiting a trigonal average structure (R , no. 148) have also been observed (a=43.420(6), c=6.506(2) Å; V=10 623(3) ų; Z=27; R1=0.0309). Pr₇Si₆N₁₅ ( 3 ) and La₇Si₆N₁₅ ( 4 ) are isostructural with 1 as evidenced by twinned single‐crystal data for 3 (P , no. 2; a=12.966(3), b=25.449(10), c=25.459(10) Å; α=117.28(3), β=99.70(4), γ=99.60(4)°; V=7068(4) ų; Z=18; R1=0.0526) and powder diffraction data for 4 (P , no. 2; a=13.109(9), b=25.606(18), c=25.609(18) Å; V=7223(12) ų; Z=18; R_P=0.0194; R_F=0.0936). The crystal structure of M₇Si₆N₁₅ (M=La, Ce, Pr) is built up exclusively of corner‐sharing tetrahedrons that appear as Q²‐, Q³‐, and Q⁴‐type tetrahedrons forming different ring sizes within a less condensed three‐dimensional network. Among the characteristic structural motifs are saw‐blade‐shaped 12‐rings and finite chains consisting of four corner‐sharing SiN₄ tetrahedrons. High‐resolution transmission electron micrographs indicate both ordered and disordered crystallites. In the diffraction patterns of disordered rhombohedral crystals, diffuse maxima appear in reciprocal space at those positions in which sharp superstructure reflections are found in the case of the respective ordered crystallites. Magnetic susceptibility measurements of Ce₇Si₆N₁₅ show paramagnetic behavior with an experimental magnetic moment of 2.29 μ_B per Ce, thereby corroborating the existence of Ce³⁺.     

Crystallization of single phase (K,Na)-clinoptilolite

A single phase (K, Na)-clinoptilolite was hydrothermally crystallized without seed crystals from a reactant mixture of (K, Na)-aluminosilicate gel slurry through homogeneous mixing at 150 °C for 144 h. Compositions of the reactant mixtures and reaction temperatures to obtain the clinoptilolite were restricted within narrow limits in the case of syntheses without seed crystals, while the compositions and temperatures were expanded into wide ranges in the case of syntheses with 1 wt.-% of seed crystals. Coexistence of Na⁺- and K⁺-ions with appropriate ratios in the reactant mixture, and homogeneous mixing of this mixture, were indispensable for the crystallization of clinoptilolite. The crystals obtained were characterized by X-ray diffraction, chemical analysis, thermal analysis (DTA/TG), electron microscopy, and electron diffraction. The crystals were assigned as clinoptilolite, not heulandite, based on their chemical compositions and thermal stability.     

Poly(triazine imide) with intercalation of lithium and chloride ions [(C3N3)2(NH(x)Li(1-x))3⋅LiCl]: a crystalline 2D carbon nitride network

Poly(triazine imide) with intercalation of lithium and chloride ions (PTI/Li⁺Cl^?) was synthesized by temperature‐induced condensation of dicyandiamide in a eutectic mixture of lithium chloride and potassium chloride as solvent. By using this ionothermal approach the well‐known problem of insufficient crystallinity of carbon nitride (CN) condensation products could be overcome. The structural characterization of PTI/Li⁺Cl^? resulted from a complementary approach using spectroscopic methods as well as different diffraction techniques. Due to the high crystallinity of PTI/Li⁺Cl^? a structure solution from both powder X‐ray and electron diffraction patterns using direct methods was possible; this yielded a triazine‐based structure model, in contrast to the proposed fully condensed heptazine‐based structure that has been reported recently. Further information from solid‐state NMR and FTIR spectroscopy as well as high‐resolution TEM investigations was used for Rietveld refinement with a goodness‐of‐fit (χ²) of 5.035 and wRp=0.05937. PTI/Li⁺Cl^? (P6₃cm (no. 185); a=846.82(10), c=675.02(9) pm) is a 2D network composed of essentially planar layers made up from imide‐bridged triazine units. Voids in these layers are stacked upon each other forming channels running parallel to [001], filled with Li⁺ and Cl^? ions. The presence of salt ions in the nanocrystallites as well as the existence of sp²‐hybridized carbon and nitrogen atoms typical of graphitic structures was confirmed by electron energy‐loss spectroscopy (EELS) measurements. Solid‐state NMR spectroscopy investigations using ¹⁵N‐labeled PTI/Li⁺Cl^? proved the absence of heptazine building blocks and NH₂ groups and corroborated the highly condensed, triazine‐based structure model.     

Microstructure and unit-cell orientation in α-polypropylene

The microstructure of melt-grown dendritic aggregates of the monoclinic α phase of isotactic polypropylene has been examined by optical microscopy, electron microscopy, and electron diffraction. Whereas the tightly crosshatched structure of such dendrites grown in the usual manner from the melt had not heretofore permitted unequivocal determination of unit-cell orientation, crystallization on mica at high temperatures eliminates this problem by suppressing branching and allowing lamellae to grow uninterruptedly to many micrometers in length. In this manner, it is shown that the preferred growth direction in single crystals of α-polypropylene is a^*. X-ray diffraction analysis of unidirectionally crystallized specimens shows that the a^* axis becomes radial in spherulites of this polymorph. Implications of this growth axis in terms of the branching model and of the crystallographic identification of the amorphous surfaces are discussed. Addition of large amounts of melt diluents is found to impart a distinct curvature to the dendritic crystals, causing their concave sides to face preferentially toward the centers of the resulting spherulitic aggregates.