macroscopic elastic anisotropy in tough ceramics from the single crystal elastic behaviour
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The modern techniques for engineering analysis are based on a deep understanding of the proportional relationship between stress and strain and the description in terms of isotropic elastic constants, in many cases, is enough. In anisotropic materials the knowledge of the elastic constants is important for the manufacturing process and for micro mechanical modelling behaviour of the material to develop the new composite materials. Theoretical calculations of elastics constants and anisotropies are applied to tough ceramics ZrO2, HfO2 and in rutile TiO2 and SnO2. Their dependence of the residual hydrostatic stress in the crystal are given. The microscopic elastic anisotropy determined in this work, could be applied in the macro scale in the case the constituent grains have a preferred orientation in the crystal lattice or the grains shape is not spherical (faceted) and it is aligned to a common crystal axis. To cover the case where the grains are distributed at randomly, the Voigt-Reuss-Hill polycrystalline approach is applied to obtain the average values of Young, bulk, shear modules, Poisson coefficient and sound velocity in the transversal and longitudinal modes. These theoretical results, could be useful in the interpretation of experimental results obtained with the method known as diffraction elastic constant (DEC).Keywords:
Hydrostatic stress
Lattice constant
FeVO4 crystallites were prepared by sonochemical method using NH4VO3 and Fe(NO3)3 · 9H2O as source precursors.The phase,morphology and optical properties of as-prepared samples were characterized by XRD,SEM,UV-vis absorption spectra and DSC.The results show that the synthesized FeVO4 crystallites have triclinic structure.The particle size of the crystallites decrease gradually and change more uniformity with the increase of ultrasonic irradiation power from 300 W to 500 W.UV-vis absorption spectra show that FeVO4 crystallites exhibit strong absorption in visible band,the grain size decreases and the corresponding bandgaps decrease about from 2.17 eV to 2.08 eV with the increase of ultrasonic irradiation power.
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The lattice constants of tetragonal PbTiO3 grown by organometallic chemical vapor deposition, vary with average crystallite size in the thin film as determined from line broadening in x-ray diffraction patterns. The a- and c-lattice constants become equal when the average crystallite size decreases to below ∼5 nm. These data agree with the change in lattice constants as a function of average crystallite size found recently for submicron PbTiO3 powder.
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Tetragonal crystal system
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The influence of grain size on the lattice constant in some nanocrystallites was studied by computing the interactive cohesive energy of the nanocrystallites. The relationships of the lattice constant with the grain size in NaCl, CsCl structure ionic crystallites, FCC, BCC structure metal crystallites and FCC, BCC, SCC structure molecular crystallites was studied respectively. The results are in good agreement with the above experimental ones qualitatively.
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Powder Diffraction
Fluorite
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CdS crystallites with rod- and flower-like architectures were synthesized using a facile hydrothermal growth method. The hexagonal crystal structure of CdS dominated the growth mechanisms of the rod- and flower-like crystallites under specific growth conditions, as indicated by structural analyses. The flower-like CdS crystallites had a higher crystal defect density and lower optical band gap value compared with the rod-like CdS crystallites. The substantial differences in microstructures and optical properties between the rod- and flower-like CdS crystallites revealed that the flower-like CdS crystallites exhibited superior photoactivity, and this performance could be further enhanced through appropriate thermal annealing in ambient air. A postannealing procedure conducted in ambient air oxidized the surfaces of the flower-like CdS crystallites and formed a CdO phase. The formation of heterointerfaces between the CdS and CdO phases mainly contributed to the improved photoactivity of the synthesized flower-like CdS crystallites.
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In this work, we report on the structure and formation energy of uncovered MgCl2 crystallites of different shapes (hexagonal and square), sizes (up to crystallites composed of 157 MgCl2 units), and edges (crystallites presenting the (104) and (110) edges). Both uncovered crystallites and crystallites covered by dimethyl ether were considered. Our results indicate that the formation energy of uncovered crystallites, irrespective of shape, size, and edges, linearly depends on the density of vacancies (measured as the ratio between the number of Mg vacancies and the number of MgCl2 units in the crystallite) and that larger crystallites that present (104) edges are favored. In the case of crystallites completely covered by dimethyl ether, our results indicate that the formation energy of crystallites, again irrespective of shape, size, and edges, inversely depends on the dimethyl ether/Mg ratio. As opposed to uncovered crystallites, in the presence of dimethyl ether, smaller crystallites presenting (110) edges are favored. The knowledge acquired with both uncovered and dimethyl ether-covered crystallites was used to achieve insight into the behavior of carbon monoxide-covered crystallites by performing calculations on a limited number of small crystallites.
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