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Topic: Octahedral

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	SPuDS
		A superscript is used to denote the phase of the octahedral tilting in neighboring layers.
		The size of the octahedron and the optimum magnitude of the octahedral tilting distortion is calculated utilizing the bond valence model, which is used to quantitatively describe inorganic bonding in ionic solids.
		The octahedral tilt angle is adjusted in order to minimize the GII with the A-site ions located at their highest symmetry positions (in the center of the cube defined by the eight surrounding octahedral cations).
	www.unf.edu /~michael.lufaso/spuds/index.html (2901 words)

	Tetrahedral and Octahedral Sites in Closest Packing
		Tetrahedral and octahedral sites in closest packing can be occupied by other atoms or ions in crystal structures of salts and alloys.
		The octahedral hole is located at the center of any four spheres that form a square.
		Since the ratio of 0.5 is between 0.414 and 0.732, the sodium ion prefers an octahedral coordination.
	www.science.uwaterloo.ca /~cchieh/cact/c123/tetrahed.html (878 words)

	octahedral group
		The tetrahedral group and the octahedral group are subgroups of the continuous group of 3-dimensional rotations SO(3).
		The vertices of a 24-cell and its dual correspond to the 24 elements of the octahedral group.
		In the stereographic projection of the 24-cell and its dual the rotational axis of a rotational symmetry is given by the line of the origin to a vertex.
	members.home.nl /fg.marcelis/octahedr.htm (637 words)

	Performance of Second 50 Completed ATP Projects — Status Report Number 3
		Machining operations take place within the octahedral frame, and the struts, or the pods of the hexapod, directly translate the force generated during the machining operation to the six vertices of the octahedral frame.
		Under the ATP award, Ingersoll planned to use a laboratory prototype octahedral hexapod machine (which they had constructed prior to the ATP project with their own funding) to develop detailed baseline data on the performance of the design.
		Using an octahedral hexapod purchased from Ingersoll, a project at NIST's Manufacturing Engineering Laboratory, supported in part by ATP intramural funds, is addressing these problems by setting common performance-evaluation procedures and developing measurement methods to achieve high positioning accuracy.
	www.atp.nist.gov /eao/sp950-3/immc.htm (2128 words)

	[No title]
		In this illustration, eight of the octahedral holes are outlined in green.
		For the sake of clarity, not all of the octahedral holes are outlined.
		In the fluorite structure, the fluorude ions reside within the tetrahedral holes formed by the face-centered cubic array of calcium ions, and the octahedral holes are vacant.
	www.uncp.edu /home/mcclurem/lattice/lattice.html (1929 words)

	Octahedral Research Satellite 4
		ORS 4 (Octahedral Research Satellite 4), also known as Environmental Research Satellite-18 (ERS-18), was launched on 28 April 1967.
		The elliptical orbit had an apogee of 111,553 km, a perigee of 8631 km, and an inclination of 32.9 degrees.
		This led to the belief that there was an additional cosmic or galactic gamma-ray component above the one accounted for by the intergalactic electrons scattering on the 3 degree Kelvin background radiation.
	heasarc.gsfc.nasa.gov /docs/heasarc/missions/ors4.html (413 words)

	CHRISTOPHER MARZEC -- EVOLUTION to T=7 LATTICE
		Interestingly, this is compatible with the octahedral lattice observed by Salunke et al.
		Their octahedral capsid could not have a pentameric capsomere at a four-fold symmetry axis, so these axes must be vacant.
		It is straightforward to show that the square configuration is of lower energy than the parallelogram configuration, so the quadralateral tends to mature into a square, which aids in situating the four MU's that are appended off the sides of each square.
	www.albany.edu /~cmarzec/accretion.oct.html (757 words)

	Octahedral Symmetry
		Octahedral coordination of a metal occurs when six bonded atoms of coordinating ligands occupy sites that would correspond to the six vertices (corners) of a regular octahedron surrounding the metal atom.
		A regular octahedron is shown on the left, octahedral coordination in the middle, and the two are superimposed in the figure on the right.
		The reason we call it octahedral coordination is that the bonded atoms of the ligand(s) are present at what would be the verticies of a regular octahedral solid surrounding the metal.
	www.iumsc.indiana.edu /morphology/symmetry/octahedral.html (525 words)

	Crystal Field Theory
		It is straightforward as long as the number of d electrons is less than or equal to 3 (or greater than or equal to 8).
		This should be similar to the octahedral case.
		The splitting in a tetrahedral field is much smaller than the splitting in an octahedral case.
	bouman.chem.georgetown.edu /S02/lect32/lect32.htm (626 words)

	The Octahedral Scheme
		The grid for an octahedral scheme is constructed from two superimposed rectilinear grids; if the points of the first grid are located at cube corners, then the points of the second will occur at the centers of the cubes defined by the first.
		It is interesting to note that there is no dispersion error along the six axial directions; this should be compared with the cubic rectilinear scheme, for which wave propagation is dispersionless along the diagonal directions (there are eight such directions).
		Figure A.9: The octahedral scheme (A.29)-- (a) numerical grid and connections, where grey/white coloring of points indicates a division into mutually exclusive subschemes at the stability bound; (b)
	ccrma-www.stanford.edu /~bilbao/master/node214.html (291 words)

	NCSSM Distance Learning T.I.G.E.R. - Chemistry page 8 (Site not responding. Last check: 2007-10-11)
		This diagram shows the trans geometric isomer of octahedral complex ion formed between Co ion, ethylene diamine, and Cl This file is from an online Chemistry course.
		This diagram shows the cis geometric isomer of octahedral complex ion formed between Co ion, ethylene diamine, and Cl This file is from an online Chemistry course.
		This diagram shows the cis and trans isomers of the octahedral complex ion formed between Co ion, ammonia, and Cl This file is from an online Chemistry course.
	www.dlt.ncssm.edu /TIGER/chem8.htm (545 words)

	Crystal Field Theory
		MnO is therefore a model for an octahedral complex in which a transition-metal ion is coordinated to six ligands.
		As a result, the splitting observed in a tetrahedral crystal field is the opposite of the splitting in an octahedral complex.
		As a result, we have to worry about high-spin versus low-spin octahedral complexes only when there are four, five, six, or seven electrons in the d orbitals.
	chemed.chem.purdue.edu /genchem/topicreview/bp/ch12/crystal.php (1278 words)

	Creative Chemistry Octahedral Molecules
		As a result, they all have an octahedral arrangment of electron pairs around the central atom.
		Therefore, the electron pairs still have an octahedral arrangment, but because one of the axial atoms is "missing", the atoms have a square pyramidal arrangement.
		Therefore, the electron pairs still have an octahedral arrangement, but because two of the axial atoms are "missing", the atoms have a square planar arrangement.
	www.creative-chemistry.org.uk /molecules/octahedral.htm (153 words)

	Stark's Conjecture in the Octahedral case (Site not responding. Last check: 2007-10-11)
		He verified this for five examples where the representations are `tetrahedral,' that is, the representations have projective image A_4, the group of even permutations on four elements, in PGL_2(C).
		If the image is S_4, the group of permutations of four elements, then the representation is said to be octahedral.
		I have been working on Chinburg's version of Stark's conjecture when the representations are octahedral over Q. It turns out that there are two types of octahedral representations which are of interest.
	www.ma.utexas.edu /~kfogel/research.html (782 words)

	[No title]
		In a matrix of these octahedral units each oxygen will be bonded to two aluminum ions, leaving it with a remaining -1 charge.
		As we have already seen, the octahedral layer consists of two planes of oxygen ions, each ion of which is bonded with two of the smaller aluminum ions which are located in the space created between the larger oxygen ions when they come together in this close packed structure.
		Thus, during the process of mineral formation the octahedral layer might be filled with divalent ions rather than the aluminum ions we have been using to this point.
	pubpages.unh.edu /~harter/crystal.htm (1711 words)

	Slides32 (Site not responding. Last check: 2007-10-11)
		If that spherical distribution were instead clumped at the corners of an octahedron, the energies could go up further, or down some, depending on whether or not they pointed directly at the concentrations of charge.
		2 orbital in an octahedral crystal field points directly at some of the field charges.
		Summary of the five d-orbital arrangements in an octahedral crystal field of charges.
	www.andrew.cmu.edu /course/09-105/S98Slides30a.html (419 words)

	7 - Lecture notes for Clay Mineralogy
		Asbestoform minerals are used in commercial applications because they have beneficial properites of high tensile strength, resistivity to chemical attack, electrical insulation, and high temperature stability.
		Note in the figure below that the top of octahedral sheet is composed of all hydroxyls.
		Orienation of hydroxyl group is influenced by octahedral sheet charge distribution.
	www.gly.uga.edu /schroeder/geol6550/CM07.html (730 words)

	Octahedral machine tool frame (US5259710)
		Forces generated by the operation of the machine tool are received by the frame at its nodes, being the nodes of opposed parallel triangular panels, upper and lower, in the specific examples illustrated.
		The octahedral frame displays superior rigidity due to its inherently closed kinematic loop, and to the virtual absence of bending stress in its constituent members accomplished by nodal loading.
		Movable machine elements are mounted upon six extensible and retractable servo-struts emanating in pairs from the nodes of a given triangular panel of the octahedral frame while opposing fixed elements located within the octahedral frame are supported tripodally from the frame nodes associated with a single triangular panel of the frame.
	www.delphion.com /details?pn=US05259710__ (400 words)

	Pyrophyllite and Talc
		As usual, the octahedral sheet may be dioctahedral or trioctahedral.
		In either case, each octahedral cation is coordinated by four apical oxygens that are shared with tetrahedral cations (two from each tetrahedral sheet) and by two hydroxyl ions that are not shared with the tetrahedral cations.
		There is an octahedral Fe analogue called minnesotaite, and there are "ferroan" talcs with significant Fe and Mg simultaneously.
	www.msu.edu /course/css/825/snapshot.afs/teppen/Pyro_and_Talc.htm (527 words)

	Chemical Innovation - Sorption, catalysis, separation design
		Octahedral molecular sieves and octahedral layered manganese oxide materials exhibit good conductivity, high porosity, and good thermal stability.
		The dimensions of the channels and interlayer spacings in these materials can be adjusted to fit various applications, and chemical reactions at the active sites can be varied by substituting different metals into the structure or by changing the valence of the manganese ions.
		Octahedral solid materials are built from six-coordinate metal atoms surrounded by an octahedral array of anions (oxygen, in this case).
	pubs.acs.org /hotartcl/ci/00/mar/suib.html (3861 words)

	Chemistry : Chapter 10 : Crystal Field Splitting (Site not responding. Last check: 2007-10-11)
		In an "octahedral field," six atoms interact on either side of all three axes.
		Consequently, each level of the octahedral arrangement is resplit (Figure 10.27).
		It is high spin and in an octahedral field.
	www.wwnorton.com /chemistry/concepts/chapter10/ch10_2.htm (580 words)

	IngentaConnect Jahn-Teller distortions, cation ordering and octahedral tilting i... (Site not responding. Last check: 2007-10-11)
		This phenomenon, referred to as orbital ordering, is usually observed indirectly from the cooperative Jahn–Teller distortions (CJTDs) that result as a consequence of the orbital ordering.
		This paper examines the interplay between orbital ordering, octahedral tilting and cation ordering in perovskites.
		perovskites, octahedral tilting tends to enhance the magnitude of the J–T distortions.
	www.ingentaconnect.com /content/bsc/ayb/2004/00000060/00000001/art00002 (283 words)

	Phyllosilicates
		The simplest phyllosilicates result from bonding one silicate layer to one octahedral layer.
		The next group of phyllosilicates have one octahedral layer sandwiched between two tetrahedral layers.
		The simplest 2:1 structure is that of talc; the dioctahedral analogue is pyrophyllite.
	www.geoclassroom.com /mineralogy/phyllosilicates.html (600 words)

	Chapter 18f - The Octahedral Cluster Puzzle (Site not responding. Last check: 2007-10-11)
		The numbers of R-D blocks arranged in octahedral clusters are given by the following series: 6, 19, 44, 85,...
		It is especially desirable that a dissection of the octahedral cluster be interlocking because it would fit so poorly into a box.
		There is a four-piece dissection of the 19-block octahedral cluster that is interlocking and assembles in one order only.
	www.johnrausch.com /puzzlingWorld/chap18f.htm (186 words)

	Octahedral Geodesic Domes
		Octahedral domes have their own unique symmetry patterns.
		The Octa Dome 4 SZ is a four frequency octahedral dome with the square at top,
		Four lower hexagon areas are vertical, making a good place to add a door and windows.
	www.gardendome.com /octa_dome_types.html (979 words)

	Octahedral tilting evolution and phase transition in orthorhombic NaMgF3 perovskite under pressure
		Rietveld refinement of monochromatic synchrotron x-ray powder diffraction data was used to study the evolution of octahedral tilting in the orthorhombic NaMgF
		octahedral framework were observed to increase with increasing pressure.
		The compression mechanism was observed to be dominated by the shortening of the octahedral Mg-F bond below 6 GPa, and then controlled by the increase of the octahedral tilting above 12 GPa.
	www.agu.org /pubs/crossref/2005/2004GL022068.shtml (320 words)

	Octahedral Research Satellite 3
		ORS 3 (Octahedral Research Satellite 3), also known as Environmental Research Satellite-17 (ERS-17), was launched on 20 July 1965.
		It was put into an elliptical orbit with apogee 112,694 km, perigee 153 km, at an inclination of 34.4 degrees.
		These, and other similar system malfunctions, made the data very hard to interpret.
	heasarc.gsfc.nasa.gov /docs/heasarc/missions/ors3.html (233 words)

	Mineral Specimen for sale of Diamond (3.81 carat octahedral crystal) from Mirny, Republic of Sakha (Yakutia), Siberia, ...
		Diamond (3.81 carat octahedral crystal) from Mirny, Republic of Sakha (Yakutia), Siberia, Russia.
		This mineral specimen of Diamond (3.81 carat octahedral crystal) from Mirny, Republic of Sakha (Yakutia), Siberia, Russia is available for sale from John Betts - Fine Minerals, mineral dealer located in New York City, New York.
		The crystal is octahedral form with many complex crystal patterns (trigons) on the surfaces.
	www.johnbetts-fineminerals.com /jhbnyc/gifs/28955.htm (237 words)

	CJM - Octahedral Galois Representations Arising From Q-Curves of Degree 2
		Octahedral Galois Representations Arising From Q-Curves of Degree 2
		Generically, one can attach to a Q-curve $C$ octahedral representations $\rho\colon\Gal(\bar{\mathbf{Q}}/\mathbf{Q})\rightarrow\GL_2(\bar\mathbf{F}_3)$ coming from the Galois action on the $3$-torsion of those abelian varieties of $\GL_2$-type whose building block is $C$.
		Going the other way, we can ask which $\mod 3$ octahedral representations $\rho$ of $\Gal(\bar\mathbf{Q}/\mathbf{Q})$ arise from Q-curves in the above sense.
	journals.cms.math.ca /cgi-bin/vault/view/fernandez1092 (153 words)

	Polymorf - Knowhwere- Octahedral summary (Site not responding. Last check: 2007-10-11)
		The number of octahedral interstices in a crystal structure is equal to the number of
		occupation rate of their octahedral voids can be deduced a priori.
		composition of minerals with interstitial atoms occupying both octahedral and
	www.polymorf.net /matter46.htm (128 words)

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