Two-dimensional shapes - Overton Grange Maths KS4
... Tessellations can also be made using more than one shape. Here is a tessellation made from squares and regular octagons. Tessellating is like tiling a flat surface so that there are no gaps between the tiles and so that the tiles do not overlap. ...
... Tessellations can also be made using more than one shape. Here is a tessellation made from squares and regular octagons. Tessellating is like tiling a flat surface so that there are no gaps between the tiles and so that the tiles do not overlap. ...
Nonlinear Raman-Nath second harmonic generation with structured
... Cherenkov radiation [7–13], nonlinear Raman-Nath and nonlinear Bragg diffraction [9,14– 16] have been intensively studied in NPCs. And various patterns of 2D nonlinear photonic structures have also been demonstrated, including square, hexagonal lattices, annular periodical, or even random structures ...
... Cherenkov radiation [7–13], nonlinear Raman-Nath and nonlinear Bragg diffraction [9,14– 16] have been intensively studied in NPCs. And various patterns of 2D nonlinear photonic structures have also been demonstrated, including square, hexagonal lattices, annular periodical, or even random structures ...
FABRICATION OF A DISORDERED AND NANO
... synthesis of a variety of equilibrium and non-equilibrium phases and phase mixtures. Mechanical alloying has also been successfully utilized in order to extend the solid solubilities in many commercially important alloy systems. Many intermetallic compounds which have high melting points and are dif ...
... synthesis of a variety of equilibrium and non-equilibrium phases and phase mixtures. Mechanical alloying has also been successfully utilized in order to extend the solid solubilities in many commercially important alloy systems. Many intermetallic compounds which have high melting points and are dif ...
Heesch`s Tiling Problem
... T is a topological disk whose boundary is a simple closed curve. But also implicit in the word “tile” is our intent to use congruent or reflected copies of T to cover the plane without gaps or overlapping; that is, we want to tessellate the plane with copies of T . In a minor abuse of language, one ...
... T is a topological disk whose boundary is a simple closed curve. But also implicit in the word “tile” is our intent to use congruent or reflected copies of T to cover the plane without gaps or overlapping; that is, we want to tessellate the plane with copies of T . In a minor abuse of language, one ...
4 Diffraction over isolated obstacles or a general terrestrial path
... the classical residue series formula. A computer program GRWAVE, available from the ITU, provides the complete method. A subset of the outputs from this program (for antennas close to the ground and at lower frequencies) is presented in Recommendation ITU-R P.368. The following subsections describe ...
... the classical residue series formula. A computer program GRWAVE, available from the ITU, provides the complete method. A subset of the outputs from this program (for antennas close to the ground and at lower frequencies) is presented in Recommendation ITU-R P.368. The following subsections describe ...
Crystalline Solids: Diffraction
... Many mixed oxides of transition metals crystallise into a cubic structure called the perovskite structure, with primitive cell ABO3 , in which A and B are cations with different size and valence. The small cation, generally A2+ , is surrounded by an octahedron of oxygen atoms, while the large cation ...
... Many mixed oxides of transition metals crystallise into a cubic structure called the perovskite structure, with primitive cell ABO3 , in which A and B are cations with different size and valence. The small cation, generally A2+ , is surrounded by an octahedron of oxygen atoms, while the large cation ...
The crystallization of biological macromolecules under
... distribution. Later, video monitoring revealed that crystals grow more frequently in the bulk of the solution than on solid surfaces, contrary to what happens under normal gravity. New crystal habits were obtained in a few instances and sometimes crystals have grown in space when they did not on ear ...
... distribution. Later, video monitoring revealed that crystals grow more frequently in the bulk of the solution than on solid surfaces, contrary to what happens under normal gravity. New crystal habits were obtained in a few instances and sometimes crystals have grown in space when they did not on ear ...
ht the Polysynthetic Structure of some Porphyritic Quartz Crystals in
... which may, I think, be explained in the same way. Sections of these compound crystals in thin slices under the microscope are lozenge-shaped, though the outer boundary of eash lozenge is broken by the projecting ends of minute felspar crystals. These felspar corporations appear to have originally gr ...
... which may, I think, be explained in the same way. Sections of these compound crystals in thin slices under the microscope are lozenge-shaped, though the outer boundary of eash lozenge is broken by the projecting ends of minute felspar crystals. These felspar corporations appear to have originally gr ...
Growth and Characterization of Pure and Ammonium nickel (II
... evaporation method. The PXRD patterns of the grown crystals confirm the inclusion of dopant into the pure crystal lattice. The presences of functional groups were confirmed using FT-IR spectrum by identifying the peaks in their characteristic regions. In UV-vis-NIR spectra, due to considerable absor ...
... evaporation method. The PXRD patterns of the grown crystals confirm the inclusion of dopant into the pure crystal lattice. The presences of functional groups were confirmed using FT-IR spectrum by identifying the peaks in their characteristic regions. In UV-vis-NIR spectra, due to considerable absor ...
5.1 Ni Redox Potential in Different Compounds
... levels. The oxygen p bands are filled and the transition metal d bands are empty or partially occupied. Crystal field theory [2-4] demonstrates that the interaction of the d orbitals with the electrostatic potential due to the negatively charged oxygen ions of the octahedron produces an increase in ...
... levels. The oxygen p bands are filled and the transition metal d bands are empty or partially occupied. Crystal field theory [2-4] demonstrates that the interaction of the d orbitals with the electrostatic potential due to the negatively charged oxygen ions of the octahedron produces an increase in ...
The real structure of Na3BiO4 by electron microscopy, HR
... 15.00 2q for 16 h. The samples were spun during measurement for better particle statistics. The powder pattern exhibits several peaks of small amounts of sodium hydroxide and bismuth oxide. Data reduction was performed using the GUFI program [30]. Indexing with ITO [31] led to a hexagonal cell with ...
... 15.00 2q for 16 h. The samples were spun during measurement for better particle statistics. The powder pattern exhibits several peaks of small amounts of sodium hydroxide and bismuth oxide. Data reduction was performed using the GUFI program [30]. Indexing with ITO [31] led to a hexagonal cell with ...
The discovery of X-rays diffraction: from crystals to DNA. A case
... assume that only a few definite wavelengths are present in the incident beam. W.L. Bragg assumed instead that the X-rays beam is composed of a continuous range of wavelengths and that the diffraction patterns are due to an effect of reflection of the beam upon the crystal planes After having observe ...
... assume that only a few definite wavelengths are present in the incident beam. W.L. Bragg assumed instead that the X-rays beam is composed of a continuous range of wavelengths and that the diffraction patterns are due to an effect of reflection of the beam upon the crystal planes After having observe ...
Guerra F., Leone M., Robotti N. The discovery of X
... assume that only a few definite wavelengths are present in the incident beam. W.L. Bragg assumed instead that the X-rays beam is composed of a continuous range of wavelengths and that the diffraction patterns are due to an effect of reflection of the beam upon the crystal planes After having observe ...
... assume that only a few definite wavelengths are present in the incident beam. W.L. Bragg assumed instead that the X-rays beam is composed of a continuous range of wavelengths and that the diffraction patterns are due to an effect of reflection of the beam upon the crystal planes After having observe ...
Quasicrystal
A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical crystallographic restriction theorem, can possess only two, three, four, and six-fold rotational symmetries, the Bragg diffraction pattern of quasicrystals shows sharp peaks with other symmetry orders, for instance five-fold.Aperiodic tilings were discovered by mathematicians in the early 1960s, and, some twenty years later, they were found to apply to the study of quasicrystals. The discovery of these aperiodic forms in nature has produced a paradigm shift in the fields of crystallography. Quasicrystals had been investigated and observed earlier, but, until the 1980s, they were disregarded in favor of the prevailing views about the atomic structure of matter. In 2009, after a dedicated search, a mineralogical finding, icosahedrite, offered evidence for the existence of natural quasicrystals.Roughly, an ordering is non-periodic if it lacks translational symmetry, which means that a shifted copy will never match exactly with its original. The more precise mathematical definition is that there is never translational symmetry in more than n – 1 linearly independent directions, where n is the dimension of the space filled, e.g., the three-dimensional tiling displayed in a quasicrystal may have translational symmetry in two dimensions. The ability to diffract comes from the existence of an indefinitely large number of elements with a regular spacing, a property loosely described as long-range order. Experimentally, the aperiodicity is revealed in the unusual symmetry of the diffraction pattern, that is, symmetry of orders other than two, three, four, or six. In 1982 materials scientist Dan Shechtman observed that certain aluminium-manganese alloys produced the unusual diffractograms which today are seen as revelatory of quasicrystal structures. Due to fear of the scientific community's reaction, it took him two years to publish the results for which he was awarded the Nobel Prize in Chemistry in 2011.