Crystal tetragonal symmetry

Dark green octahedral crystals (tetragonal symmetry). Oxidizes in air and dec on contact with water. Should be stored in sealed ampuls, df 4.725. mp 590", bp 791. Heat of formation (solid) 250.9 kca] / mo] at 0. Fteely sol in water (dec). Also so] in polar organic solvents. Insol in nonpolar solvents such as hydrocarbons and ethyl ether. 

For the alkali metal doped Cgo compounds, charge transfer of one electron per M atom to the Cgo molecule occurs, resulting in M+ ions at the tetrahedral and/or octahedral symmetry interstices of the cubic Cgo host structure. For the composition MaCgg, the resulting metallic crystal has basically the fee structure (see Fig. 2). Within this structure the alkali metal ions can sit on either tetragonal symmetry (1/4,1/4,1/4) sites, which are twice as numerous as the octahedral (l/2,0,0) sites (referenced to a simple cubic coordinate system). The electron-poor alkali metal ions tend to lie adjacent to a C=C double... 

In the crystal structure of these phases with tetragonal symmetry (P4/mbm, D h) the boron covalent sublattice is formed by chains of octahedra, developing along the c axis and by pairs of B atoms, bonding the octahedra in the xOy plane (see Fig. 1). The resulting three-dimensional skeleton contains tunnels parallel to the c axis that are filled by metal atoms . ... 

Since the surfaces of crystals have specific symmetries (usually triangular, square, or tetragonal) and indenters have cylindrical, triangular, square, or tetragonal symmetries, the symmetries rarely match, or are rotationally misaligned. Therefore, the indentations are often anisotropic. Also, the surface symmetries of crystals vary with their orientations relative to the crystallographic axes. A result is that crystals cannot be fully characterized by single hardness numbers. 

Hardness also depends on which face of a non-cubic crystal is being indented. The difference may be large. For a crystal with tetragonal symmetry the face that is normal to the c-axis can be expected to be different from those that are normal to the a-axes. Similarly the basal faces of hexagonal crystals are different from the prism faces. One extreme case is graphite where the resistance to indentation on the basal plane is very different than the resistance on the prism planes. 

Rotating single-crystal measurements also permitted the extraction of the orientation of the magnetic tensor in the molecular reference frame and the experimental easy axis was found to coincide with the idealized tetragonal axis of the coordination dodecahedron of Dy. Crystal field calculations assuming idealized tetragonal symmetry permitted the reproduction of magnetic susceptibility data for gz = 19.9 and gxy 0 [121]. More elaborated calculations such as ab initio post Hartree-Fock CASSCF confirmed this simple analysis [119]. 

Tetragonal structure, of ferroelectric crystals, 11 95, 96 Tetragonal symmetry, 8 114t Tetragonal zirconia polycrystals, 5 571 Tetrahedral... 

Under the action of a crystal field component of lower symmetry each state of Ok will split up further. Under tetragonal symmetry (D ), Tig and Eg decompose as follows ... 

The above equations have been obtained on the assumption that no orbital states have energies close to that of the ground state. This means that they should be applicable to d3, d5, and d8 for crystal fields which are close to octahedral in symmetry. They should be applicable to d4 and d9 also, when the distortion from octahedral symmetry is tetragonal, since in this case matrix elements of are zero between the ground state and the nearby excited state, d2, d6, and d1 in octahedral symmetry must be treated in a manner similar to that used for dl in Sec. III.D. For other crystal-field symmetries, the treatment used depends on whether the crystal field gives low-lying excited states that have nonzero matrix elements of with the ground state. 

Tetragonal unit cells. In crystals of tetragonal symmetry the unit cell is a rectangular box with two edges equal (a) and the third (c) different from the first two. The spacings of hkO planes—those parallel. to c—are in the same ratios as those of the hkO planes of cubic crystals, that is, in the ratios 1/Vl2 l/ /(l2+12) 1/V22 l/ /(22+l2), and so on. But the 001 spacing is not related in any simple way to a the ratio cfa may have any value and is different for every tetragonal crystal and... 

Term symbols, 26-27, A7-A12 Tetrachloroiodate anion. 209 Tetragonal crystal system, 75, 78 Tetragonal symmetry. 403-404 Tetrahedral complexes, 401-403, 418-420, 441. 448-455, 474-477... 

The magnetic field H mixes the A u and E u states. Therefore the decay of the Au emission shortens and its intensity increases upon application of the field. The A lu emission is more allowed (i.e. it does not need vibronic assistance) and the emission pattern has changed (Fig. 10). From the orientation of the crystal in the magnetic field it can again be deduced that the emitting RES has tetragonal symmetry. Nevertheless, also this system leaves still problems for further study [20, 31],... 

These systems can be described in terms of their symmetry elements. A triclinic crystal has only a center of symmetry. Monoclinic crystals have a single axis of twofold rotational symmetry. Orthorhombic crystals have three mutually perpendicular axes of twofold symmetry. With tetragonal symmetry, there is a single axis of fourfold symmetry. Cubic crystals are characterized by four threefold axes of symmetry, the <111> axes. There is a single axis of threefold symmetry in the rhombohedral system. The hexagonal system involves a single axis of sixfold symmetry. 

The presence of the higher order harmonics of the magnetic helix in the incommensurate phase is characteristic for the temperature interval where the Lifshits invariant is comparable with an anisotropy invariant [11], For magnetic systems with a one-parametric thermodynamic potential the propagation vector q is not equal to zero already at the temperature where the system orders, T1 =TP. As an anisotropy invariant is proportional to rj for a crystal with tetragonal symmetry, then it becomes comparable with Lifshits invariant proportional to q t] 2 much below Ti near the transition into a low-temperature commensurate phase. However, in copper metaborate q grows sharply from approximately zero at temperature 7) < Tp (Fig. 7) [5],... 

At temperatures below Tc BaTi03 belongs to the tetragonal crystal class (symmetry group 4mm) it is optically uniaxial, and the optic axis is the x3 axis (nQ = 2.416, ne = 2.364). When an electric field is applied in an arbitrary direction the representation quadric for the relative impermeability is perturbed to... 

Tl2Ba2Cu06 phase exists in two crystal symmetries, tetragonal and orthorhombic. All the other phases are found to exist mostly in tetragonal symmetries. 

Only few direct pressure syntheses have been reported. LiTiMF6 phases (M = Mn—Ni) were prepared from respective binary fluorides at T = 700-1200°C and 15-70 kbar [27]. The products crystallized in Na2SiF6 and PbSb206 type structures. On the other hand, pressure induced phase transitions are common, e.g. KMnF3 transforms from cubic to tetragonal symmetry. However, in contrast to oxide containing perovkites, the transition temperature rises with increasing pressure [28]. 

The AnH2 (An = Ac, Np-Bk) have the fluorite structure. Thft2 is unique in that it has tetragonal symmetry. In /3-UH3, the metal atoms have a coordination number of 12 and the H atoms occupy tetrahedral intersites. For the other AnH3 (An = Np Bk), the crystals have a trigonal structure. 

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