Dynamics of crystal size distributions with size-dependent rates

The growth and dissolution dynamics of nonequilibrium crystal size distributions (CSDs) can be determined by solving the governing population balance equations (PBEs) representing reversible addition or dissociation. New PBEs are considered that intrinsically incorporate growth dispersion and yield complete CSDs. We present two approaches to solving the PBEs, a moment method and a numerical scheme. The results of the numerical scheme agree with the moment technique, which can be solved exactly when powers on mass-dependent growth and dissolution rate coefficients are either zero or one. The numerical scheme is more general and can be applied when the powers of the rate coefficients are non-integers or greater than unity. The influence of the size dependent rates on the time variation of the CSDs indicates that as equilibrium is approached, the CSDs become narrow when the exponent on the growth rate is less than the exponent on the dissolution rate. If the exponent on the growth rate is greater than the exponent on the dissolution rate, then the polydispersity continues to broaden. The computation method applies for crystals large enough that interfacial stability issues, such as ripening, can be neglected. (C) 2002 Elsevier Science B.V. All rights reserved.

Size and temperature dependent stability and phase transformation in single-crystal zirconium nanowire

A novel size dependent FCC (face-centered-cubic) -> HCP (hexagonally-closed-pack) phase transformation and stability of an initial FCC zirconium nanowire are studied. FCC zirconium nanowires with cross-sectional dimensions < 20 are found unstable in nature, and they undergo a FCC -> HCP phase transformation, which is driven by tensile surface stress induced high internal compressive stresses. FCC nanowire with cross-sectional dimensions > 20 , in which surface stresses are not enough to drive the phase transformation, show meta-stability. In such a case, an external kinetic energy in the form of thermal heating is required to overcome the energy barrier and achieve FCC -> HCP phase transformation. The FCC-HCP transition pathway is also studied using Nudged Elastic Band (NEB) method, to further confirm the size dependent stability/metastability of Zr nanowires. We also show size dependent critical temperature, which is required for complete phase transformation of a metastable-FCC nanowire.

Shape and size mimicry in the design of ternary molecular solids: towards a robust strategy for crystal engineering

2- and 5-methylresorcinol form co-crystals with 4,4'-bipyridine in which some of the bipyridine molecules are loosely bound. These molecules can be replaced with other molecules of a similar shape and size to give a general method for the engineering of a ternary co-crystal.

A Monte Carlo study of crystal structure transformations

The Metropolis algorithm has been generalized to allow for the variation of shape and size of the MC cell. A calculation using different potentials illustrates how the generalized method can be used for the study of crystal structure transformations. A restricted MC integration in the nine dimensional space of the cell components also leads to the stable structure for the Lennard-Jones potential.

Crystal structure of the amino acid-vitamin complex lysine pantothenatestar, open

L-Lysine d-pantothenate, a 1:1 amino acid-vitamin complex, crystallizes in the monoclinic space group P21 with Image Full-size image (1K) .The structure has been solved by direct methods and refined to an R value of 0.053 for 1868 observed reflections. The zwitterionic positively charged lysine molecules in the structure assume the sterically most favourable conformation with an all-trans side chain trans to the α-carboxylate group. The pantothenate anion has a somewhat folded conformation stabilised by an intramolecular bifurcated hydrogen bond. The unlike molecules aggregate into separate alternating layers. The molecules in the lysine layers form a head-to-tail sequence parallel to the a-axis. The interactions which hold the adjacent layers together include those between the side chain amino group of lysine and the carboxylate group in the pantothenate anion. The geometry of these interactions is such that each carboxylate group is sandwiched between two amino groups in a periodic arrangement of alternating carboxylate and amino groups.

Preparation and x-ray characterization of four new crystal forms of Jacalin, a lectin from Artocarpus integrifolia

Four new crystal forms of the anti-T lectin from jackfruit (Artocarpus integrifolia) have been prepared and characterized. Three of them, two monoclinic (P21, A = 59·4 Å, B = 83·3 Å, C = 63·5 Å, β = 107·7°; C2, A = 106·1,Å, B = 53·9 Å, C = 128·0 Å, β = 95·0 Å) and one orthorhombic (C2221, A = 98·1 Å, B = 67·3 Å, C = 95·1 Å) were grown with 2-methylpentan-2,4-diol (MPD) as the precipitant while the fourth, an hexagonal from (P6122, A = b = 129·6 Å, C = 157·9 Å), was obtained in the presence of methyl-ga-Image -galactopyranoside with polyethylene glycol 4000 as the precipitant. The reported relative molecular mass (Mr) of the lectin was found to be inconsistent with the solvent content of the crystals estimated using measured densities. The Mr was redetermined using size-exclusion chromatography in the presence of methyl-α-Image -galactopyranoside and Ferguson-plot analysis of mobilities in polyacrylamide gel electrophoresis. The redetermined Mr (66,000) is consistent with the measured crystal densities. The orthorhombic and the hexagonal forms, which have one half molecule and one molecule, respectively, in the asymmetric unit, are suitable for high-resolution X-ray analysis.

Crystal structure of dimeric FabZ of Plasmodium falciparum reveals conformational switching to active hexamers by peptide flips

The crystal structure of beta-hydroxyacyl acyl carrier protein dehydratase of Plasmodium falciparum (PfFabZ) has been determined at a resolution of 2.4 angstrom. PfFabZ has been found to exist as a homodimer (d-PfFabZ) in the crystals of the present study in contrast to the reported hexameric form (h-PfFabZ) which is a trimer of dimers crystallized in a different condition. The catalytic sites of this enzyme are located in deep narrow tunnel-shaped pockets formed at the dimer interface. A histidine residue from one subunit of the dimer and a glutamate residue from the other subunit lining the tunnel form the catalytic dyad in the reported crystal structures. While the position of glutamate remains unaltered in the crystal structure of d-PffabZ compared to that in b-PfFabZ, the histidine residue takes up an entirely different conformation and moves away from the tunnel leading to a His-Phe cis-trans peptide flip at the histidine residue. In addition, a loop in the vicinity has been observed to undergo a similar flip at a Tyr-Pro peptide bond. These alterations not only prevent the formation of a hexamer but also distort the active site geometry resulting in a dimeric form of FabZ that is incapable of substrate binding. The dimeric state and an altered catalytic site architecture make d-PfFabZ distinctly different from the FabZ structures described so far. Dynamic light scattering and size exclusion chromatographic studies clearly indicate a pH-related switching of the dimers to active hexamers. (c) 2006 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserv.

Mechanism of crystal structure transformations. Part 3. - Factors affecting the anatase-rutile transformation

The particle size and crystallite size of anatase increase markedly in the region of the crystal structure transformation. The unit cell of anatase seems to expand prior to the transformation to rutile. This expansion has been attributed to a displacive transformation of the type defined by Buerger. Smaller particle size and larger surface area seem to favour the transformation. The kinetics of the transformation of anatase prepared by the hydrolysis of titanium sulphate have been studied at different temperatures and are found to be considerably different from the kinetics of the transformation of pure anatase. The transformation becomes immeasurably slow below ∼695 ± 10°C compared to ∼610°C for pure anatase. An induction period is observed in the transformation of anatase obtained from sulphate hydrolysis and the duration decreases with increase in temperature. The activation energy is ∼120 kcal/mole, a value higher than that for the pure anatase-rutile transformation. The results have been interpreted in terms of the relative rates of nucleation and propagation processes. The activation energy for the nucleation process seems to be much larger than for the propagation process. The kinetics of the transformation of anatase samples doped with different amounts of sulphate ion impurity have also been studied and the transformation is found to be progressively decelerated with increase in the impurity concentration. The energy of activation for the transformation appears to increase progressively with increase in impurity concentration.

Analysis of Nonlinear Optical Properties of Photonic Crystal Beam-splitters

The paper analyses electromagnetic wave propagation through nonlinear photonic crystal beam-splitters. Different lattice configurations of Y-junction beam-splitters are simulated and propagation properties are investigated with introducing nonlinearity with varying the rod size in crystal lattice. It is seen that nonlinear photonic crystal shows a considerable band-gap even at low refractive contrast. The division of power in both arms of beam-splitters can be controlled by varying the nonlinearity.

Grain size effect on the phase transformation temperature of nanostructured CuFe2O4

We report a large decrease in tetragonal to cubic phase transformation temperature when grain size of bulk CuFe2O4 is reduced by mechanical ball milling. The change in phase transformation temperature was inferred from in situ high temperature conductivity and x-ray diffraction measurements. The decrease in conductivity with grain size suggests that ball milling has not induced any oxygen vacancy while the role of cation distribution in the observed decrease in phase transformation temperature is ruled out from in-field Fe-57 Mossbauer and extended x-ray absorption fine structure measurements. The reduction in the phase transformation temperature is attributed to the stability of structures with higher crystal symmetry at lower grain sizes due to negative pressure effect. (C) 2011 American Institute of Physics. doi: 10.1063/1.3493244]

The Reaction of a Nitro-Capped Cobalt(III) Cage Complex With Base: the Crystal Structure of a Contracted Cage Complex, and the Mechanism of Its Formation

The synthesis, properties and crystal structure of the cage complex (1-hydroxy-8-methyl-3,6,10,13,15,18-hexaazabicyclo[6.6.5]nonadecane)cobalt(III) chloride hydrate ([Co(Me,OH-absar)] C13.H2O) are reported. The mechanism of the formation of this contracted cavity cage from a nitro-capped hexaazabicycloicosane type cage has been investigated. Treatment of (1-methyl-8-nitro-3,6,10,13,16,19-hexaazabicyclo[6.6.6]icosane)cobalt(III) chloride ([Co(Me,NO2-sar)] 3+) with excess base in aqueous solution leads initially to rapid (t1/2 < 1 ms) and reversible deprotonation of one coordinated secondary amine. This species undergoes a retro-Mannich type reaction and imine hydrolysis (t1/2 almost-equal-to 90 s). Quenching the reaction with acid gives rise to a pair of isomeric intermediate species which have been isolated and characterized. They have a pendant arm macrocyclic structure, resulting from the loss of a methylene unit from one of the arms of the cap. Heating either isomer in aqueous solution gives the new cage compound with the contracted cap. It is postulated that this occurs through a Nef reaction, resulting in the formation of a ketone which then condenses with the coordinated primary amine. A comparison with the corresponding bicycloicosane analogue indicates a reduced chromophoric cavity size for the contracted cage. The reduction potential of the cobalt(III)/cobalt(II) couple is 170 mV more negative for the smaller cage, and, in the electronic spectrum of the cobalt(III) complex, the d-d transitions are both shifted to higher energy, corresponding to a stronger ligand field.

Crystal Structure Engineering by Fine-Tuning the Surface Energy: The Case of CdE (E = S/Se) Nanocrystals

We prove that CdS nanocrystals can be thermodynamically stabilized in both wurtzite and zinc-blende crystallographic phases at will, just by the proper choice of the capping ligand. As a striking demonstration of this, the largest CdS nanocrystals (similar to 15 nm diameter) ever formed with the zinc-blende structure have been synthesized at a high reaction temperature of 310 degrees C, in contrast to previous reports suggesting the formation of zinc-blende CdS only in the small size limit (< 4.5 nm) or at a lower reaction temperature (<= 240 degrees C). Theoretical analysis establishes that the binding energy of trioctylphosphine molecules on the (001) surface of zinc-blende CdS is significantly larger than that for any of the wurtzite planes. Consequently, trioctylphosphine as a capping agent stabilizes the zinc-blende phase via influencing the surface energy that plays an important role in the overall energetics of a nanocrystal. Besides achieving giant zinc-blende CdS nanocrystals, this new understanding allows us to prepare CdSe and CdSe/CdS core/shell nanocrystals in the zinc-blende structure.

Polycrystal versus single-crystal strain rate sensitivity of cadmium

Taking polycrystalline cadmium as an example and by utilizing the predicted temperature or strain rate-dependence of the (Hall-Petch) stress-grain size parameters, a reasonably quantitative explanation is given for the grain size dependence of apparent activation volume measurements. The explanation involves the theoretical relation of these measurements to single-crystal measurements.

A comparative study of dragonfly inspired flapping wings actuated by single crystal piezoceramic

A dragonfly inspired flapping wing is investigated in this paper. The flapping wing is actuated from the root by a PZT-5H and PZN-7%PT single crystal unimorph in the piezofan configuration. The nonlinear governing equations of motion of the smart flapping wing are obtained using the Hamilton's principle. These equations are then discretized using the Galerkin method and solved using the method of multiple scales. Dynamic characteristics of smart flapping wings having the same size as the actual wings of three different dragonfly species Aeshna Multicolor, Anax Parthenope Julius and Sympetrum Frequens are analyzed using numerical simulations. An unsteady aerodynamic model is used to obtain the aerodynamic forces. Finally, a comparative study of performances of three piezoelectrically actuated flapping wings is performed. The numerical results in this paper show that use of PZN-7%PT single crystal piezoceramic can lead to considerable amount of wing weight reduction and increase of lift and thrust force compared to PZT-5H material. It is also shown that dragonfly inspired smart flapping wings actuated by single crystal piezoceramic are a viable contender for insect scale flapping wing micro air vehicles.

Approaching theoretical strengths by synergistic internal and external size refinement

Refinement of the internal grain size leads to strengthening by retarding dislocation motion. There have also been recent reports that a reduction in external diameter enhances the strength of single crystal pillars. Here we show, in a hitherto unexplored domain, a synergistic increase in strength by a combined reduction in internal (0.5 mu m) and external (20-50 mu m) dimensions, with strengths at failure approaching the theoretical value. (c) 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.