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Crystals, Volume 7, Issue 1 (January 2017) – 30 articles

Cover Story (view full-size image): KSbTeO6 exhibits a defect pyrochlore structure defined in the cubic Fd3m symmetry. The mainly covalent network formed by vertex-sharing (Sb,Te)O6 octahedra, enables weak interatomic interactions with K+ ions. A combined XRD and NPD study showed that K+ are distributed at large multiplicity 32e Wyckoff sites with ¼ occupancy, placed in the center of large cages. The quite big anisotropic atomic displacement parameters account for the ease of ion exchange of this material to yield a product of technological importance, such as (H3O)SbTeO6. View this paper.
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1287 KiB  
Article
Synthesis, Crystal Structure and DFT Studies of 1,3-Dimethyl-5-propionylpyrimidine-2,4,6(1H,3H,5H)-trione
by Anamika Sharma, Yahya E. Jad, Hazem A. Ghabbour, Beatriz G. De la Torre, Hendrik G. Kruger, Fernando Albericio and Ayman El-Faham
Crystals 2017, 7(1), 31; https://doi.org/10.3390/cryst7010031 - 21 Jan 2017
Cited by 6 | Viewed by 4981
Abstract
Novel 1,3-Dimethyl-5-propionylpyrimidine-2,4,6(1H,3H,5H)-trione was synthesized and recrystallized from ethanol. The compound was characterized by 1H NMR, 13C NMR in CDCl3, DMSO-d6 and acetone-d6, elemental analysis and X-ray diffraction. The [...] Read more.
Novel 1,3-Dimethyl-5-propionylpyrimidine-2,4,6(1H,3H,5H)-trione was synthesized and recrystallized from ethanol. The compound was characterized by 1H NMR, 13C NMR in CDCl3, DMSO-d6 and acetone-d6, elemental analysis and X-ray diffraction. The NMR data observed that the title compound exists in the enol tautomer rather than keto, and it stabilized by strong H-bond as observed form the NMR data at different temperatures. Theoretical calculations (DFT) were carried out using Gaussian09 program package and B3LYP correlation function. Full geometry optimization of the keto and enol forms were carried out using 6-311G++(d,p) basis set. The structure and energy of the transition state between these two tautomers were calculated. The frontier orbital energy and atomic net atomic charges of the tautomers were presented. The experimental results of the title compound have been compared with the theoretical results and it was found that the experimental data are in a good agreement with the calculated values. The transition state calculations also support the stability of enol form compared to keto form at room temperature. Full article
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6760 KiB  
Article
Synthesis, Crystal Structure, Luminescence and Magnetism of Three Novel Coordination Polymers Based on Flexible Multicarboxylate Zwitterionic Ligand
by Yulu Ma, Lin Du, Kaimin Wang and Qihua Zhao
Crystals 2017, 7(1), 32; https://doi.org/10.3390/cryst7010032 - 20 Jan 2017
Cited by 8 | Viewed by 4374
Abstract
Three novel zwitterionic coordination polymers, namely, {[Zn(HCbdcp)2]·H2O} (1), {[Mn(Cbdcp)]·3H2O} (2) and {[Cu2(Cbdcp)(HCbdcp)Cl·H2O]·2H2O} (3), Cbdcp = 3,5-dicarboxy-1-(4-carboxybenzyl)pyridin-1-ium, have been prepared by a hydrothermal method and characterized [...] Read more.
Three novel zwitterionic coordination polymers, namely, {[Zn(HCbdcp)2]·H2O} (1), {[Mn(Cbdcp)]·3H2O} (2) and {[Cu2(Cbdcp)(HCbdcp)Cl·H2O]·2H2O} (3), Cbdcp = 3,5-dicarboxy-1-(4-carboxybenzyl)pyridin-1-ium, have been prepared by a hydrothermal method and characterized by X-ray single crystal diffraction analysis, powder X-ray diffraction analysis, IR spectroscopy, and thermogravimetric analysis. With the changing of metal centers, these complexes show distinct structures: a mononuclear 2D 44-sql network for 1, a 3D 6,6-connected-type topology for 2 and a novel dinuclear 2D layer for 3. These diverse architectures prove that coordination geometry of metal ions, coordination modes of carboxylate groups and the rotationally flexible CH2 linker played significant roles in the construction of CPs; moreover, they also indicated that H3CbdcpCl is an ideal organic candidate for the building of novel structures. The solid-state luminescent properties of complexes 13 were investigated, respectively. In addition, the magnetic properties of 2 and 3 were studied and both of them exhibit antiferromagnetic behaviors. Full article
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4533 KiB  
Article
Colloidal Nanocrystalline Semiconductor Materials as Photocatalysts for Environmental Protection of Architectural Stone
by Francesca Petronella, Antonella Pagliarulo, Marinella Striccoli, Angela Calia, Mariateresa Lettieri, Donato Colangiuli, Maria Lucia Curri and Roberto Comparelli
Crystals 2017, 7(1), 30; https://doi.org/10.3390/cryst7010030 - 20 Jan 2017
Cited by 17 | Viewed by 5560
Abstract
Rod-shaped TiO2 nanocrystals (TiO2 NRs), capped by oleic acid molecules (OLEA), were synthesized with controlled size, shape and surface chemistry by using colloidal routes. They were investigated for application as coating materials for preserving architectural stone of monumental and archaeological interest, [...] Read more.
Rod-shaped TiO2 nanocrystals (TiO2 NRs), capped by oleic acid molecules (OLEA), were synthesized with controlled size, shape and surface chemistry by using colloidal routes. They were investigated for application as coating materials for preserving architectural stone of monumental and archaeological interest, in consideration of their self-cleaning and protection properties. For this purpose, two different deposition techniques, namely casting and dipping, were tested for the application of a nanocrystal dispersion on a defined stone type, as a relevant example of porous calcarenites, namely the Pietra Leccese, a building stone widely used in monuments and buildings of cultural and historic interest of the Apulia region (Italy). The physical properties of the stone surface were investigated before and after the treatment with the prepared nanostructured materials. In particular, colour, wettability, water transfer properties and stability of the coating were monitored as a function of time and of the application method. The self-cleaning properties of the TiO2 NRs coated surfaces were tested under simulated and real solar irradiation. The obtained results were discussed in the light of the specific surface chemistry and morphology of TiO2 NRs, demonstrating the effectiveness of TiO2 NRs as an active component in formulations for stone protection. Full article
(This article belongs to the Special Issue Colloidal Nanocrystals: Synthesis, Characterization and Application)
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2347 KiB  
Review
Dirac Landau Level Spectroscopy in Pb1−xSnxSe and Pb1−xSnxTe across the Topological Phase Transition: A Review
by Thanyanan Phuphachong, Badih A. Assaf, Valentine V. Volobuev, Günther Bauer, Gunther Springholz, Louis-Anne De Vaulchier and Yves Guldner
Crystals 2017, 7(1), 29; https://doi.org/10.3390/cryst7010029 - 20 Jan 2017
Cited by 14 | Viewed by 8060
Abstract
Topological crystalline insulators (TCIs) are topological materials that have Dirac surface states occurring at crystalline symmetric points in the Brillouin zone. This topological state has been experimentally shown to occur in the lead–tin salts Pb1−xSnxSe and Pb1−xSn [...] Read more.
Topological crystalline insulators (TCIs) are topological materials that have Dirac surface states occurring at crystalline symmetric points in the Brillouin zone. This topological state has been experimentally shown to occur in the lead–tin salts Pb1−xSnxSe and Pb1−xSnxTe. More recent works also took interest in studying the topological phase transition from trivial to non-trivial topology that occurs in such materials as a function of increasing Sn content. A peculiar property of these materials is the fact that their bulk bands disperse following a massive Dirac dispersion that is linear at low energies above the energy gap. This makes Pb1−xSnxSe and Pb1−xSnxTe ideal platforms to simultaneously study 3D and 2D Dirac physics. In this review, we will go over infrared magneto-optical studies of the Landau level dispersion of Pb1−xSnxSe and Pb1−xSnxTe for both the bulk and surface bands and summarize work that has been done on this matter. We will review recent work on probing the topological phase transition in TCI. We will finally present our views on prospects and open questions that have yet to be addressed in magneto-optical spectroscopy studies on Pb1-xSnxSe and Pb1−xSnxTe. Full article
(This article belongs to the Special Issue Topological Crystalline Insulators: Current Progress and Prospects)
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6475 KiB  
Article
Ionic Liquid Crystals Modifier for Selective Determination of Terazosin Antihypertensive Drug in Presence of Common Interference Compounds
by Nada F. Atta, Mohammad H. BinSabt, Samar H. Hassan and Ahmed Galal
Crystals 2017, 7(1), 27; https://doi.org/10.3390/cryst7010027 - 20 Jan 2017
Cited by 19 | Viewed by 5224
Abstract
Electrochemical sensor was fabricated based on carbon paste electrode modified with an ionic liquid crystal ILC (2-chloro-1,3-dimethyl-imidazolidinium hexafluorophosphate) in presence of sodium dodecyl sulfate for the selective electrochemical determination of Terazosin (TZ) in presence of common interference compounds. The electrode performance was compared [...] Read more.
Electrochemical sensor was fabricated based on carbon paste electrode modified with an ionic liquid crystal ILC (2-chloro-1,3-dimethyl-imidazolidinium hexafluorophosphate) in presence of sodium dodecyl sulfate for the selective electrochemical determination of Terazosin (TZ) in presence of common interference compounds. The electrode performance was compared in presence of other ionic liquids ILs (1-Butyl-4-methyl pyridinium tetrafluoroborate) and (1-n-Hexyl-3-methyl imidazolium tetrafluoroborate). Ultrasensitive determination of Terazosin HCl at the ILC modified electrode in the linear dynamic ranges of 0.002 to 0.09 μmol·L−1 and 0.2 to 30 μmol·L−1 with correlation coefficients 0.996 and 0.995 and LODs 1.69 × 10−11 mol·L−1 and 6.43 × 10−9 mol·L−1, respectively, were obtained. Selective determination of TZ in presence of uric acid and ascorbic acid and simultaneous determination of binary mixtures of TZ/dopamine, TZ/paracetamol and TZ/Morphine were also determined successfully using the modified sensor. Full article
(This article belongs to the Section Liquid Crystals)
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2249 KiB  
Article
The New Method of XRD Measurement of the Degree of Disorder for Anode Coke Material
by Zhuo Zhang and Qi Wang
Crystals 2017, 7(1), 5; https://doi.org/10.3390/cryst7010005 - 18 Jan 2017
Cited by 18 | Viewed by 8615
Abstract
Quantitative analysis by X-ray powder diffraction of two cokes (pitch coke and petroleum coke) shows that their crystal structure changed with increasing temperature. The crystal data processing of the crystallization degree of disorder is used with further improvement of the proposed microcrystalline-stacking fault [...] Read more.
Quantitative analysis by X-ray powder diffraction of two cokes (pitch coke and petroleum coke) shows that their crystal structure changed with increasing temperature. The crystal data processing of the crystallization degree of disorder is used with further improvement of the proposed microcrystalline-stacking fault calculation method. With this improvement it is now possible to obtain the degree of stacking disorder of two cokes applied as anode materials at different graphitization temperatures. Raman spectroscopy verified the accuracy of this method, which is more reliable than the crystal structure refinement using the d002 method. This paper provides the theoretical analysis and interpretation of the relationship between the microstructure model of the material and quantitative data, discharge capacity, and the first charge-discharge efficiency. Full article
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3169 KiB  
Article
Influence of Alkyl Trimethyl Ammonium Bromides on Hydrothermal Formation of α-CaSO4·0.5H2O Whiskers with High Aspect Ratios
by Ruosong Chen, Sichao Hou, Jing Wang and Lan Xiang
Crystals 2017, 7(1), 28; https://doi.org/10.3390/cryst7010028 - 18 Jan 2017
Cited by 9 | Viewed by 6808
Abstract
In this paper, the influence of alkyl trimethyl ammonium bromides (CnH2n+1(CH3)3NBr, n = 10, 12, 14, 16, 18, abbreviated as ATAB) on the formation of alpha calcium sulfate hemihydrate (α-CaSO4·0.5H2O) whiskers [...] Read more.
In this paper, the influence of alkyl trimethyl ammonium bromides (CnH2n+1(CH3)3NBr, n = 10, 12, 14, 16, 18, abbreviated as ATAB) on the formation of alpha calcium sulfate hemihydrate (α-CaSO4·0.5H2O) whiskers under a hydrothermal condition (135 °C, 3.0 h) was analyzed. Specifically, it focuses on cetyl trimethyl ammonium bromide (C16H33(CH3)3NBr, abbreviated as CTAB). The rising CTAB concentration from 0 to 9.2 × 10−4 mol·L−1 led to the increase of the average aspect ratio of α-CaSO4·0.5H2O whiskers from 80 to 430, since the selective adsorption of CTAB on the negatively-charged side facets of the whiskers inhibited the growth of the whiskers along the direction normal to the lateral facets. The further increase of CTAB concentration above the critical micelle concentration (abbreviated as CMC) showed little effect on the morphology of α-CaSO4·0.5H2O whiskers, considering that CTAB tended to form micelles instead of being adsorbed on the whisker surfaces. Similar phenomena were observed in other ATABs (n = 10, 12, 14, 18). Full article
(This article belongs to the Special Issue Solution-Processed Inorganic Functional Crystals)
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2042 KiB  
Article
Numerical Modelling of the Czochralski Growth of β-Ga2O3
by Wolfram Miller, Klaus Böttcher, Zbigniew Galazka and Jürgen Schreuer
Crystals 2017, 7(1), 26; https://doi.org/10.3390/cryst7010026 - 17 Jan 2017
Cited by 43 | Viewed by 10865
Abstract
Our numerical modelling of the Czochralski growth of single crystalline β-Ga 2 O 3 crystals (monoclinic symmetry) starts at the 2D heat transport analysis within the crystal growth furnace, proceeds with the 3D heat transport and fluid flow analysis in the crystal-melt-crucible [...] Read more.
Our numerical modelling of the Czochralski growth of single crystalline β-Ga 2 O 3 crystals (monoclinic symmetry) starts at the 2D heat transport analysis within the crystal growth furnace, proceeds with the 3D heat transport and fluid flow analysis in the crystal-melt-crucible arrangement and targets the 3D thermal stress analysis within the β-Ga 2 O 3 crystal. In order to perform the stress analysis, we measured the thermal expansion coefficients and the elastic stiffness coefficients in two samples of a β-Ga 2 O 3 crystal grown at IKZ. Additionally, we analyse published data of β-Ga 2 O 3 material properties and use data from literature for comparative calculations. The computations were performed by the software packages CrysMAS, CGsim, Ansys-cfx and comsol Multiphysics. By the hand of two different thermal expansion data sets and two different crystal orientations, we analyse the elastic stresses in terms of the von-Mises stress. Full article
(This article belongs to the Special Issue Global Modeling in Crystal Growth)
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18162 KiB  
Article
Four Thermochromic o-Hydroxy Schiff Bases of α-Aminodiphenylmethane: Solution and Solid State Study
by Marija Zbačnik, Katarina Pičuljan, Jelena Parlov-Vuković, Predrag Novak and Andreas Roodt
Crystals 2017, 7(1), 25; https://doi.org/10.3390/cryst7010025 - 14 Jan 2017
Cited by 11 | Viewed by 6390
Abstract
More than a hundred years after the first studies of the photo- and thermochromism of o-hydroxy Schiff bases (imines), it is still an intriguing topic that fascinates several research groups around the world. The reasons for such behavior are still under investigation, [...] Read more.
More than a hundred years after the first studies of the photo- and thermochromism of o-hydroxy Schiff bases (imines), it is still an intriguing topic that fascinates several research groups around the world. The reasons for such behavior are still under investigation, and this work is a part of it. We report the solution-based and mechanochemical synthesis of four o-hydroxy imines derived from α-aminodiphenylmethane. The thermochromic properties were studied for the single crystal and polycrystalline samples of the imines. The supramolecular impact on the keto-enol tautomerism in the solid state was studied using SCXRD and NMR, while NMR spectroscopy was used for the solution state. All four imines are thermochromic, although the color changes of the single crystals are not as strong as of the polycrystalline samples. One of the imines shows negative thermochromism, and that one is in keto-amine tautomeric form, both in the solid state as in solution. Full article
(This article belongs to the Special Issue Thermo- and Photochromic Molecular Crystals)
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1293 KiB  
Article
Potassium Disorder in the Defect Pyrochlore KSbTeO6: A Neutron Diffraction Study
by José Antonio Alonso, Sergio Mayer, Horacio Falcón, Xabier Turrillas and María Teresa Fernández-Díaz
Crystals 2017, 7(1), 24; https://doi.org/10.3390/cryst7010024 - 13 Jan 2017
Cited by 7 | Viewed by 4801
Abstract
KSbTeO6 defect pyrochlore has been prepared from K2C2O4, Sb2O3, and 15% excess TeO2 by solid-state reaction at 850 °C. Direct methods implemented in the software EXPO2013 allowed establishing the basic structural [...] Read more.
KSbTeO6 defect pyrochlore has been prepared from K2C2O4, Sb2O3, and 15% excess TeO2 by solid-state reaction at 850 °C. Direct methods implemented in the software EXPO2013 allowed establishing the basic structural framework. This was followed by a combined Rietveld refinement from X-ray powder diffraction (XRD) and neutron powder diffraction (NPD) data, which unveiled additional structural features. KSbTeO6 is cubic, a = 10.1226(7) Å, space group F d 3 ¯ m , Z = 8 and it is made of a mainly covalent framework of corner-sharing (Sb,Te)O6 octahedra, with weakly bonded K+ ions located within large cages. The large K-O distances, 3.05(3)–3.07(3) Å, and quite large anisotropic atomic displacement parameters account for the easiness of K+ exchange for other cations of technological importance. Full article
(This article belongs to the Special Issue Structural Analysis of Crystalline Materials from Powders)
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6537 KiB  
Article
Synthesizing Iron Oxide Nanostructures: The Polyethylenenemine (PEI) Role
by Sergio Lentijo Mozo, Efisio Zuddas, Alberto Casu and Andrea Falqui
Crystals 2017, 7(1), 22; https://doi.org/10.3390/cryst7010022 - 12 Jan 2017
Cited by 15 | Viewed by 6478
Abstract
Controlled synthesis of anisotropic iron oxide nanoparticles is a challenge in the field of nanomaterial research that requires an extreme attention to detail. In particular, following up a previous work showcasing the synthesis of magnetite nanorods (NRs) using a two-step approach that made [...] Read more.
Controlled synthesis of anisotropic iron oxide nanoparticles is a challenge in the field of nanomaterial research that requires an extreme attention to detail. In particular, following up a previous work showcasing the synthesis of magnetite nanorods (NRs) using a two-step approach that made use of polyethylenenemine (PEI) as a capping ligand to synthesize intermediate β-FeOOH NRs, we studied the effect and influence of the capping ligand on the formation of β-FeOOH NRs. By comparing the results reported in the literature with those we obtained from syntheses performed (1) in the absence of PEI or (2) by using PEIs with different molecular weight, we showed how the choice of different PEIs determines the aspect ratio and the structural stability of the β-FeOOH NRs and how this affects the final products. For this purpose, a combination of XRD, HRTEM, and direct current superconducting quantum interference device (DC SQUID) magnetometry was used to identify the phases formed in the final products and study their morphostructural features and related magnetic behavior. Full article
(This article belongs to the Special Issue Colloidal Nanocrystals: Synthesis, Characterization and Application)
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2662 KiB  
Editorial
Crystal Indentation Hardness
by Ronald W. Armstrong, Stephen M. Walley and Wayne L. Elban
Crystals 2017, 7(1), 21; https://doi.org/10.3390/cryst7010021 - 12 Jan 2017
Cited by 6 | Viewed by 6089
Abstract
There is expanded interest in the long-standing subject of the hardness properties of materials. A major part of such interest is due to the advent of nanoindentation hardness testing systems which have made available orders of magnitude increases in load and displacement measuring [...] Read more.
There is expanded interest in the long-standing subject of the hardness properties of materials. A major part of such interest is due to the advent of nanoindentation hardness testing systems which have made available orders of magnitude increases in load and displacement measuring capabilities achieved in a continuously recorded test procedure. The new results have been smoothly merged with other advances in conventional hardness testing and with parallel developments in improved model descriptions of both elastic contact mechanics and dislocation mechanisms operative in the understanding of crystal plasticity and fracturing behaviors. No crystal is either too soft or too hard to prevent the determination of its elastic, plastic and cracking properties under a suitable probing indenter. A sampling of the wealth of measurements and reported analyses associated with the topic on a wide variety of materials are presented in the current Special Issue. Full article
(This article belongs to the Special Issue Crystal Indentation Hardness)
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1651 KiB  
Article
Synthesis, Crystal Structure, DFT Study of m-Methoxy-N′-(3-Methoxybenzoyl)-N-Phenylbenzohydrazide
by Ifzan Arshad, Javeria Yameen, Aamer Saeed, Jonathan M. White and Fernando Albericio
Crystals 2017, 7(1), 19; https://doi.org/10.3390/cryst7010019 - 12 Jan 2017
Cited by 5 | Viewed by 4245
Abstract
The crystal structure of m-methoxy-N′-(m-anisoyl)-N-phenylbenzohydrazide has been determined by means of single-crystal X-ray diffraction. The title compound crystallizes in the monoclinic space group P 21/c with unit cell parameters: a = 8.7338(1), b = 24.5602(3), c [...] Read more.
The crystal structure of m-methoxy-N′-(m-anisoyl)-N-phenylbenzohydrazide has been determined by means of single-crystal X-ray diffraction. The title compound crystallizes in the monoclinic space group P 21/c with unit cell parameters: a = 8.7338(1), b = 24.5602(3), c = 9.6929(1) Å, β = 113.186(2)°, V = 1911.23(4) Å3, Z = 4. The dihedral angles between the mean plane of the central benzene ring and two terminal aromatic rings are 72.44(4)° and 89.90(4)°, respectively. The two methoxyphenyl rings are orthogonal with a dihedral angle of 89.74(4)°. The crystal packing is stabilized by a combination of N–HO intermolecular hydrogen bonding and weak intermolecular C–HO interactions. The X-ray structure was compared with the optimized counterpart calculated by the B3LYP/6-311G basis set and the results showed that the optimized geometry can reproduce the crystal structure parameters well. Full article
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170 KiB  
Editorial
Acknowledgement to Reviewers of Crystals in 2016
by Crystals Editorial Office
Crystals 2017, 7(1), 20; https://doi.org/10.3390/cryst7010020 - 11 Jan 2017
Cited by 16 | Viewed by 3526
Abstract
The editors of Crystals would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2016.[...] Full article
3179 KiB  
Article
Role of Internal Radiation in Oxide Crystal Growth by Heat Exchanger Method
by Wencheng Ma and Lijun Liu
Crystals 2017, 7(1), 18; https://doi.org/10.3390/cryst7010018 - 09 Jan 2017
Cited by 2 | Viewed by 5527
Abstract
Internal radiation was investigated using the finite volume method for the heat exchanger method (HEM) growth of oxide crystals. Special attention was devoted to the temperature and thermal stress distributions in the bottom region of the grown crystal at the end of the [...] Read more.
Internal radiation was investigated using the finite volume method for the heat exchanger method (HEM) growth of oxide crystals. Special attention was devoted to the temperature and thermal stress distributions in the bottom region of the grown crystal at the end of the solidification process. The numerical results show that internal radiation strongly strengthens heat transport through the crystal. However, it causes isotherms to intensively concentrate in the crystal bottom region, leading to a significant increase in the temperature gradient and thermal stress in this region. Then, the effect of absorption coefficient on this phenomenon was numerically investigated. It was found that the radiation heat transfer rate at the bottom surface of the crystal monotonically decreases as the absorption coefficient is increased, while the conduction heat transfer rate first increases and then decreases as the absorption coefficient is increased, under the interaction between internal radiation and heat conduction. The variations of the maximum temperature gradient and thermal stress in the crystal bottom show the same tendency as the conduction heat transfer rate. This study indicates that the role of internal radiation on the heat transfer and thermal stress in oxide crystal by HEM process shows some differences from that by Czochralski and Kyropoulos processes. Full article
(This article belongs to the Special Issue Global Modeling in Crystal Growth)
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3103 KiB  
Article
Infrared Investigations of the Neutral-Ionic Phase Transition in TTF-CA and Its Dynamics
by Martin Dressel and Tobias Peterseim
Crystals 2017, 7(1), 17; https://doi.org/10.3390/cryst7010017 - 07 Jan 2017
Cited by 16 | Viewed by 6063
Abstract
The neutral-ionic phase transition in TTF-CA was investigated by steady-state and time-resolved infrared spectroscopy. We describe the growth of high-quality single crystals and their characterization. Extended theoretical calculations were performed in order to obtain the band structure, the molecular vibrational modes and the [...] Read more.
The neutral-ionic phase transition in TTF-CA was investigated by steady-state and time-resolved infrared spectroscopy. We describe the growth of high-quality single crystals and their characterization. Extended theoretical calculations were performed in order to obtain the band structure, the molecular vibrational modes and the optical spectra along all crystallographic axes. The theoretical results are compared to polarization-dependent infrared reflection experiments. The temperature-dependent optical conductivity is discussed in detail. We study the photo-induced phase transition in the vicinity of thermally-induced neutral-ionic transition. The observed temporal dynamics of the photo-induced states is attributed to the random-walk of neutral-ionic domain walls. We simulate the random-walk annihilation process of domain walls on a one-dimensional chain. Full article
(This article belongs to the Special Issue The Neutral–Ionic Phase Transition)
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489 KiB  
Article
Structural and Gas Retention Changes Induced by Ozonization of Cobalt(II) and Manganese(II) Hexacyanocobaltates(III)
by María Laura Ríos, Joelis Rodríguez-Hernández, Luis Felipe Del Castillo and Jorge Balmaseda
Crystals 2017, 7(1), 16; https://doi.org/10.3390/cryst7010016 - 07 Jan 2017
Cited by 1 | Viewed by 4079
Abstract
Transition metal hexacyanocobaltates are porous materials with open metal sites and a wide variety of pores. In this work, manganese(II) and cobalt(II) hexacyanocobaltates(III) have been selected to explore the interactions between the open metal sites located in their pores and the guest molecules: [...] Read more.
Transition metal hexacyanocobaltates are porous materials with open metal sites and a wide variety of pores. In this work, manganese(II) and cobalt(II) hexacyanocobaltates(III) have been selected to explore the interactions between the open metal sites located in their pores and the guest molecules: hydrogen, carbon dioxide, water and methanol. An experimental setup was designed and implemented to conduct post-synthesis modification of the solids with ozone. Samples were dehydrated, ozonized and saturated with methanol in situ. Ozone molecules acted on the open metal sites changing their oxidation state, causing a contraction of the unit cell and inducing a stronger interaction of the molecules of water and methanol with the lattice. This strengthening prevented the lattice from being evacuated without compromising its framework stability. The decomposition temperature decreased in all ozonized samples as a consequence of the elongation and weakening of the cobalt-carbon bond. Active infrared and Raman bands were used to monitor the interaction between the open metal sites at the framework surface and the guest molecules. The cell contraction and the presence of residual methanol molecules in the porosity reduced the hydrogen and carbon dioxide retention capacity of the samples. Full article
(This article belongs to the Section Crystal Engineering)
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3548 KiB  
Article
New Acetylenic Amine Derivatives of 5,8-Quinolinediones: Synthesis, Crystal Structure and Antiproliferative Activity
by Monika Kadela-Tomanek, Maria Jastrzębska, Ewa Bębenek, Elwira Chrobak, Małgorzata Latocha, Joachim Kusz, Dorota Tarnawska and Stanisław Boryczka
Crystals 2017, 7(1), 15; https://doi.org/10.3390/cryst7010015 - 07 Jan 2017
Cited by 17 | Viewed by 4774
Abstract
Acetylenic amine derivatives of the 5,8-quinolinedione were synthesized and characterized by the 1H and 13C NMR, IR spectroscopy and MS spectra. Additionally, the 6- and 7-substituted allylamine-5,8-quinolinediones were synthesized for comparison purposes. The crystal structure was determined for the 6-chloro-7-propargylamine-5,8-quinolinedione and [...] Read more.
Acetylenic amine derivatives of the 5,8-quinolinedione were synthesized and characterized by the 1H and 13C NMR, IR spectroscopy and MS spectra. Additionally, the 6- and 7-substituted allylamine-5,8-quinolinediones were synthesized for comparison purposes. The crystal structure was determined for the 6-chloro-7-propargylamine-5,8-quinolinedione and 7-chloro-6-propargylamine-5,8-quinolinedione. Additionally, the IR spectral analysis supplemented by the density functional theory (DFT) calculations were carried out. It was found that different positions of the propargylamine side chain had a distinct influence on crystal structure, formation of H-bonds and the carbonyl stretching IR bands. Correlation between the frequency separation Δν of the carbonyl IR bands and the position of the 6- and 7-substituents was found. The 7-substituted derivatives exhibited a higher frequency separation Δν. The observed correlation could provide an opportunity to use the IR spectroscopy to study substitution reactions. Cytotoxic activities against three human cancer cell lines for the 5,8-quinolinedione derivatives with different amine substituents, i.e., propargylamine, N-methylpropargylamine, 1,1-dimethylpropargylamine, allylamine and propylamine were also analysed with respect to their molecular structure. Full article
(This article belongs to the Section Crystal Engineering)
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60834 KiB  
Review
The Physics of the Hume-Rothery Electron Concentration Rule
by Uichiro Mizutani and Hirokazu Sato
Crystals 2017, 7(1), 9; https://doi.org/10.3390/cryst7010009 - 06 Jan 2017
Cited by 56 | Viewed by 11427
Abstract
For a long time we have shared the belief that the physics of the Hume-Rothery electron concentration rule can be deepened only through thorough investigation of the interference phenomenon of itinerant electrons with a particular set of lattice planes, regardless of whether d-states [...] Read more.
For a long time we have shared the belief that the physics of the Hume-Rothery electron concentration rule can be deepened only through thorough investigation of the interference phenomenon of itinerant electrons with a particular set of lattice planes, regardless of whether d-states are involved near the Fermi level or not. For this purpose, we have developed the FLAPW-Fourier theory (Full potential Linearized Augmented Plane Wave), which is capable of determining the square of the Fermi diameter, ( 2 k F ) 2 , and the number of itinerant electrons per atom, e/a, as well as the set of lattice planes participating in the interference phenomenon. By determining these key parameters, we could test the interference condition and clarify how it contributes to the formation of a pseudogap at the Fermi level. Further significant progress has been made to allow us to equally handle transition metal (TM) elements and their compounds. A method of taking the center of gravity energy for energy distribution of electrons with a given electronic state has enabled us to eliminate the d-band anomaly and to determine effective ( 2 k F ) 2 , and e/a, even for systems involving the d-band or an energy gap across the Fermi level. The e/a values for 54 elements covering from Group 1 up to Group 16 in the Periodic Table, including 3d-, 4d- and 5d-elements, were determined in a self-consistent manner. The FLAPW-Fourier theory faces its limit only for elements in Group 17 like insulating solids Cl and their compounds, although the value of e/a can be determined without difficulty when Br becomes metallic under high pressures. The origin of a pseudogap at the Fermi level for a large number of compounds has been successfully interpreted in terms of the interference condition, regardless of the bond-types involved in the van Arkel-Ketelaar triangle map. Full article
(This article belongs to the Special Issue Structure and Properties of Quasicrystals 2016)
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3821 KiB  
Article
Photo-Thermal Effects in 1D Gratings of Gold Nanoparticles
by Giovanna Palermo, Tiziana Ritacco, Dante Maria Aceti, Luigia Pezzi, Michele Giocondo and Antonio De Luca
Crystals 2017, 7(1), 14; https://doi.org/10.3390/cryst7010014 - 06 Jan 2017
Cited by 22 | Viewed by 4982
Abstract
This work investigates the heat delivered by a mono-layer 1D grating of gold nanoparticles (GNPs) created by photo-reduction through two-photon direct laser writing (2P-DLW) in a poly-vinyl alcohol (PVA) matrix doped with HAuCl4, under resonant laser radiation. We drop cast a [...] Read more.
This work investigates the heat delivered by a mono-layer 1D grating of gold nanoparticles (GNPs) created by photo-reduction through two-photon direct laser writing (2P-DLW) in a poly-vinyl alcohol (PVA) matrix doped with HAuCl4, under resonant laser radiation. We drop cast a film of a PVA + HAuCl4 mixture onto a glass substrate, in which we create gratings of 1 mm2 made by stripes of GNPs characterized by high polydispersivity. We demonstrate that, by controlling the pitch of the GNP stripes, we obtain different values of the photo-induced temperature variations. In the framework of thermo-plasmonics, the experimental investigation of the heat generation from a monolayer of gold nanoparticles represents a key element as a starting point to design thermo-smart platforms for sensing, solar energy harvesting and thermo-catalysis. Full article
(This article belongs to the Special Issue Thermo- and Photochromic Molecular Crystals)
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1701 KiB  
Article
Ivabradine Hydrochloride (S)-Mandelic Acid Co-Crystal: In Situ Preparation during Formulation
by Veronika Sládková, Ondřej Dammer, Gregor Sedmak, Eliška Skořepová and Bohumil Kratochvíl
Crystals 2017, 7(1), 13; https://doi.org/10.3390/cryst7010013 - 06 Jan 2017
Cited by 21 | Viewed by 7861
Abstract
The pharmaceutical salt ivabradine hydrochloride is indicated for the symptomatic treatment of chronic stable angina pectoris and chronic heart failure. It exhibits extensive polymorphism and co-crystallization, which could be a way to provide an alternative solid form. We conducted a co-crystal screen, from [...] Read more.
The pharmaceutical salt ivabradine hydrochloride is indicated for the symptomatic treatment of chronic stable angina pectoris and chronic heart failure. It exhibits extensive polymorphism and co-crystallization, which could be a way to provide an alternative solid form. We conducted a co-crystal screen, from which two hits were identified: with (S)-mandelic and (R)-mandelic acid. Both structures were determined from single-crystal X-ray diffraction data as co-crystals. The co-crystals were further characterized by common solid-state techniques, such as X-ray powder diffraction (XRPD), differential scanning calorimetry (DSC), solid-state NMR, IR and Raman spectroscopy, and dynamic vapor sorption (DVS). The co-crystal with (S)-mandelic acid was selected for further development; its physical and chemical stability was compared with two different polymorphs of the hydrochloride salt. The co-crystal exhibited a similar stability with the polymorph used in the original drug product and was, therefore, selected for formulation into the drug product. During the pre-formulation experiments, the in situ formation of the co-crystal was achieved during the wet granulation process. The following formulation experiments showed no influence of in situ prepared co-crystal on the overall stability of the bulk, when compared with pre-prepared co-crystal formulation. Full article
(This article belongs to the Special Issue Novel Pharmaceutical Cocrystals and Their Applications)
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2978 KiB  
Review
Advances in Single-Crystal Fibers and Thin Rods Grown by Laser Heated Pedestal Growth
by Gisele Maxwell, Bennett Ponting, Eminet Gebremichael and Ruben Magana
Crystals 2017, 7(1), 12; https://doi.org/10.3390/cryst7010012 - 04 Jan 2017
Cited by 20 | Viewed by 6787
Abstract
Single-crystal fibers are an intermediate between laser crystals and doped glass fibers. They have the advantages of both guiding laser light and matching the efficiencies found in bulk crystals, which is making them ideal candidates for high-power laser and fiber laser applications. This [...] Read more.
Single-crystal fibers are an intermediate between laser crystals and doped glass fibers. They have the advantages of both guiding laser light and matching the efficiencies found in bulk crystals, which is making them ideal candidates for high-power laser and fiber laser applications. This work focuses on the growth of a flexible fiber with a core of dopant (Er, Nd, Yb, etc.) and a polycrystalline clad of yttrium aluminum garnet (YAG) that will exhibit good wave guiding properties. Direct growth or a combination of growth and cladding experiments are described. Scattering loss measurements at visible wavelengths, along with dopant profile characterization with damage threshold results, are also presented. For single-pass amplification, a single-pass linear gain of 7.4 was obtained for 29 nJ pulses of 5 ns duration at 1 MHz repetition rate. We also obtained a laser efficiency of over 58% in a diode-pumped configuration. These results confirm the potential for single-crystal fibers to overcome the limitations of the glass fibers commonly used in fiber lasers, making them prime candidates for high-power compact fiber lasers and amplifiers. Full article
(This article belongs to the Special Issue Crystal Growth for Optoelectronic and Piezoelectric Applications)
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4596 KiB  
Article
From Rate Measurements to Mechanistic Data for Condensed Matter Reactions: A Case Study Using the Crystallization of [Zn(OH2)6][ZnCl4]
by Berkley G. Hillis, Bradley P. Losey, James Weng, Nezar Ghaleb, Feier Hou and James D. Martin
Crystals 2017, 7(1), 11; https://doi.org/10.3390/cryst7010011 - 31 Dec 2016
Cited by 9 | Viewed by 5434
Abstract
The kinetics of crystallization of the R = 3 hydrate of zinc chloride, [Zn(OH2)6][ZnCl4], is measured by time-resolved synchrotron x-ray diffraction, time-resolved neutron diffraction, and by differential scanning calorimetry. It is shown that analysis of the rate [...] Read more.
The kinetics of crystallization of the R = 3 hydrate of zinc chloride, [Zn(OH2)6][ZnCl4], is measured by time-resolved synchrotron x-ray diffraction, time-resolved neutron diffraction, and by differential scanning calorimetry. It is shown that analysis of the rate data using the classic Kolmogorov, Johnson, Mehl, Avrami (KJMA) kinetic model affords radically different rate constants for equivalent reaction conditions. Reintroducing the amount of sample measured by each method into the kinetic model, using our recently developed modified-KJMA model (M-KJMA), it is shown that each of these diverse rate measurement techniques can give the intrinsic, material specific rate constant, the velocity of the phase boundary, vpb. These data are then compared to the velocity of the crystallization front directly measured optically. The time-resolved diffraction methods uniquely monitor the loss of the liquid reactant and formation of the crystalline product demonstrating that the crystallization of this hydrate phase proceeds through no intermediate phases. The temperature dependent vpb data are then well fit to transition zone theory to extract activation parameters. These demonstrate that the rate-limiting component to this crystallization reaction is the ordering of the waters (or protons) of hydration into restricted positions of the crystalline lattice resulting in large negative entropy of activation. Full article
(This article belongs to the Special Issue Development of Time-Resolved X-Ray Crystallography)
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3010 KiB  
Article
Synthesis, Crystal Structure, and Nonlinear Optical Properties of a New Alkali and Alkaline Earth Metal Carbonate RbNa5Ca5(CO3)8
by Qiaoling Chen and Min Luo
Crystals 2017, 7(1), 10; https://doi.org/10.3390/cryst7010010 - 31 Dec 2016
Cited by 10 | Viewed by 5702
Abstract
A new nonlinear optical (NLO) material, RbNa5Ca5(CO3)8, has been synthesized by the hydrothermal method. The crystal structure is established by single-crystal X-ray diffraction. RbNa5Ca5(CO3)8 crystallizes in the hexagonal [...] Read more.
A new nonlinear optical (NLO) material, RbNa5Ca5(CO3)8, has been synthesized by the hydrothermal method. The crystal structure is established by single-crystal X-ray diffraction. RbNa5Ca5(CO3)8 crystallizes in the hexagonal crystal system with space group P63mc (No. 186). The structure of RbNa5Ca5(CO3)8 can be described as the adjacent infinite [CaCO3] layers lying in the a-b plane bridged through standing-on-edge [CO3] groups by sharing O atoms (two-fold coordinated) to build a framework with four types of tunnels running through the b-axis. The Rb, Na, and [Na0.67Ca0.33] atoms reside in these tunnels, respectively. The measurement of second harmonic generation (SHG) indicated that RbNa5Ca5(CO3)8 is a phase-matchable material, which had SHG responses of approximately 1×KH2PO4 (KDP). Meanwhile, the results from the UV-VIS diffuse reflectance spectroscopy study of the powder samples indicated that the UV cut-off edges of RbNa5Ca5(CO3)8 is about 203 nm. Full article
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6430 KiB  
Article
Designs of Plasmonic Metamasks for Photopatterning Molecular Orientations in Liquid Crystals
by Yubing Guo, Miao Jiang, Chenhui Peng, Kai Sun, Oleg Yaroshchuk, Oleg D. Lavrentovich and Qi-Huo Wei
Crystals 2017, 7(1), 8; https://doi.org/10.3390/cryst7010008 - 30 Dec 2016
Cited by 27 | Viewed by 7532
Abstract
Aligning liquid crystal (LC) molecules into spatially non-uniform orientation patterns is central to the functionalities of many emerging LC devices. Recently, we developed a new projection photopatterning technique by using plasmonic metamasks (PMMs), and demonstrated high-resolution and high-throughput patterning of molecular orientations into [...] Read more.
Aligning liquid crystal (LC) molecules into spatially non-uniform orientation patterns is central to the functionalities of many emerging LC devices. Recently, we developed a new projection photopatterning technique by using plasmonic metamasks (PMMs), and demonstrated high-resolution and high-throughput patterning of molecular orientations into arbitrary patterns. Here we present comparisons between two different types of metamask designs: one based on curvilinear nanoslits in metal films; the other based on rectangular nanoapertures in metal films. By using numerical simulations and experimental studies, we show that the PMMs based on curvilinear nanoslits exhibit advantages in their broadband and high optical transmission, while face challenges in mask designing for arbitrary molecular orientations. In contrast, the PMMs based on nanoapertures, though limited in optical transmission, present the great advantage of allowing for patterning arbitrary molecular orientation fields. Full article
(This article belongs to the Special Issue Micro and Nano Patterned Substrates for Liquid Crystal Alignment)
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2150 KiB  
Article
Synthesis, Crystal Structure of a Novel Mn Complex with Nicotinoyl-Glycine
by Xin Wang, Biqing Chen and Min He
Crystals 2017, 7(1), 3; https://doi.org/10.3390/cryst7010003 - 30 Dec 2016
Cited by 8 | Viewed by 5621
Abstract
A novel manganese complex, C16H26MnN4O12, was synthesized by the reaction of nicotinoyl-glycine and NaOH in an ethanol/water solution and structurally characterized by elemental analysis, UV-vis spectrum, IR spectrum and single-crystal X-ray diffraction analysis. The crystal [...] Read more.
A novel manganese complex, C16H26MnN4O12, was synthesized by the reaction of nicotinoyl-glycine and NaOH in an ethanol/water solution and structurally characterized by elemental analysis, UV-vis spectrum, IR spectrum and single-crystal X-ray diffraction analysis. The crystal of the complex belongs to the triclinic space group P1 with a = 7.8192(16) Å, b = 8.8800(18) Å, c = 9.0142(18) Å, α = 83.14(3)°, β = 65.27(3)°, γ = 81.67(3)°, V = 516.3(2) Å3, Z = 1, Dx = 1.542 mg·m−3, μ = 0.66 mm−1, F(000) = 271, and final R1 = 0.0381, ωR2 = 0.0964. The nicotinoyl-glycine ligand acts as a bridging ligand to connect the manganese ions by the hydrogen interactions; thus, the complex expands into a 3D supramolecular net structure. Full article
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3932 KiB  
Article
Reversible Single-Crystal-to-Single-Crystal Phase Transition of Chiral Salicylidenephenylethylamine
by Akifumi Takanabe, Takuro Katsufuji, Kohei Johmoto, Hidehiro Uekusa, Motoo Shiro, Hideko Koshima and Toru Asahi
Crystals 2017, 7(1), 7; https://doi.org/10.3390/cryst7010007 - 29 Dec 2016
Cited by 9 | Viewed by 6737
Abstract
The chiral crystal of enantiomeric (S)-N-3,5-di-tert-butylsalicylidene-1-phenylethylamine in the enol form [enol-(S)-1] undergoes a reversible single-crystal-to-single-crystal (SCSC) phase transition at Tc ≈ 3 °C from the room temperature α-form in orthorhombic space [...] Read more.
The chiral crystal of enantiomeric (S)-N-3,5-di-tert-butylsalicylidene-1-phenylethylamine in the enol form [enol-(S)-1] undergoes a reversible single-crystal-to-single-crystal (SCSC) phase transition at Tc ≈ 3 °C from the room temperature α-form in orthorhombic space group P212121 (Z′ = 1) to the low temperature β-form in the monoclinic space group P21 (Z′ = 2) with a thermal hysteresis of approximately 1.7 °C. A detailed comparison of the crystal structures of the α- and β-forms revealed that the 5-tert-butyl group of one molecule in the asymmetric unit of the β-form rotated by ca. 60°, and the dihedral angle between the phenyl and salicyl planes increased slightly in the β-form crystal. However, the changes in the molecular conformation and packing arrangement are small, which leads to the reversible SCSC phase transition with no destruction of the crystal lattice. The dielectric constant along the b-axis was small, probably due to the weak intermolecular interactions in the crystals. Full article
(This article belongs to the Section Crystal Engineering)
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2657 KiB  
Communication
Identification and Crystallization of Penicillin-Binding Protein/β-Lactamase Homolog (Rp46) from Ruegeria Pomeroyi
by Bum Han Ryu, Tri Duc Ngo, Wanki Yoo, Kyeong Kyu Kim and T. Doohun Kim
Crystals 2017, 7(1), 6; https://doi.org/10.3390/cryst7010006 - 29 Dec 2016
Cited by 5 | Viewed by 5204
Abstract
In spite of the enormous biological and clinical significance of penicillin-binding protein (PBP)/β-lactamase (βL), few of their many homologs (PBP)/βLs homologs) have been studied crystallographically, and have known functions. Herein, X-ray crystallographic study of a PBP/βL homolog (Rp46) from Ruegeria pomeroyi is described. [...] Read more.
In spite of the enormous biological and clinical significance of penicillin-binding protein (PBP)/β-lactamase (βL), few of their many homologs (PBP)/βLs homologs) have been studied crystallographically, and have known functions. Herein, X-ray crystallographic study of a PBP/βL homolog (Rp46) from Ruegeria pomeroyi is described. Multiple sequence alignments indicate that Rp46 has a conserved serine residue within the S70-X-X-K73 motif (Motif I), acting as the catalytic nucleophile. Moreover, an invariant tyrosine residue (Tyr185) and a Trp365-X-Gly motif (Motif III) were also identified. The recombinant Rp46 protein was expressed in Escherichia coli and purified to homogeneity judging from the SDS-PAGE analysis. Rp46 was crystallized using a solution consisting of 20% (w/v) PEG 3000, 0.1 M Tris-HCl, pH 7.0, 0.2 M calcium acetate, and the X-ray diffraction data were collected to a resolution of 1.90 Å with an Rmerge of 7.4%. The crystals of Rp46 belong to the space group I422, with unit cell parameters a = b = 141.26 Å, and c = 119.75. The structure determination and biochemical characterization are in progress. (Synopsis: A penicillin-binding protein/β-lactamase homolog (Rp46) from Ruegeria pomeroyi was identified and crystallized in the space group I4, and the diffraction data were collected to a resolution of 1.90 Å.) Full article
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2835 KiB  
Review
A Review on Polymer Crystallization Theories
by Michael C. Zhang, Bao-Hua Guo and Jun Xu
Crystals 2017, 7(1), 4; https://doi.org/10.3390/cryst7010004 - 29 Dec 2016
Cited by 110 | Viewed by 15642
Abstract
It is the aim of this article to review the major theories of polymer crystallization since up to now we still have not completely comprehended the underlying mechanism in a unified framework. A lack of paradigm is an indicator of immaturity of the [...] Read more.
It is the aim of this article to review the major theories of polymer crystallization since up to now we still have not completely comprehended the underlying mechanism in a unified framework. A lack of paradigm is an indicator of immaturity of the field itself; thus, the fundamental issue of polymer crystallization remains unsolved. This paper provides an understanding of the basic hypothesis, as well as relevant physical implications and consequences of each theory without too much bias. We try to present the essential aspects of the major theories, and intuitive physical arguments over rigorously mathematical calculations are highlighted. In addition, a detailed comparison of various theories will be made in a logical and self-contained fashion. Our personal view of the existing theories is presented as well, aiming to inspire further open discussions. We expect that new theories based on the framework of kinetics with direct consideration of long-range multi-body correlation will help solve the remaining problems in the field of polymer crystallization. Full article
(This article belongs to the Special Issue Global Modeling in Crystal Growth)
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1843 KiB  
Article
Applicability of Effective Medium Approximations to Modelling of Mesocrystal Optical Properties
by Oleksandr Zhuromskyy
Crystals 2017, 7(1), 1; https://doi.org/10.3390/cryst7010001 - 22 Dec 2016
Cited by 17 | Viewed by 5835
Abstract
Rigorous superposition T-matrix method is used to compute light interaction with mesocrystalline structures. The results are used to validate the applicability of effective medium theories for computing the effective optical constants of mesocrystal structures composed of optically isotropic materials. It is demonstrated that [...] Read more.
Rigorous superposition T-matrix method is used to compute light interaction with mesocrystalline structures. The results are used to validate the applicability of effective medium theories for computing the effective optical constants of mesocrystal structures composed of optically isotropic materials. It is demonstrated that the Maxwell-Garnett theory can fit the rigorous simulation results with an average accuracy of 2%. The thus obtained refractive indexes can be used with any electromagnetic simulation software to represent the response of mesocrystals composed of optically small primary particles arranged into a cubic type lattice structures. Full article
(This article belongs to the Special Issue Mesocrystals and Hierarchical Structures)
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