Face-centered cubic symmetry

The SMA effect can be traced to properties of two crystalline phases, called martensite and austenite, that undergo facile solid-solid phase transition at temperature Tm (dependent on P and x). The low-temperature martensite form is of body-centered cubic crystalline symmetry, soft and easily deformable, whereas the high-temperature austenite form is of face-centered cubic symmetry, hard and immalleable. Despite their dissimilar mechanical properties, the two crystalline forms are of nearly equal density, so that passage from austenite to a twinned form of martensite occurs without perceptible change of shape or size in the macroscopic object. 

P0O2 at low temperature, possesses a face-centered cubic symmetry similar to fluorite, but converts into a high-temperature tetragonal form at 80 °C. The two allofropic forms coexist, even at room temperature. This is due to the heat evolved by a particle collisions with the crystal lattice. 

Two crystal modifications yellow, low temperature fern, face-centered cubic symmetry red, high-temperature fotra, tetragonal symmetry. Darkens in color on healing, chocolate brown at sublimation temp of 885. Dec into the dements at 5(X> under vacuum slowly reduced to the metal in hydrogen at 200. Heat of formation 30 kcal/mole. Sol in aq solns of ammonium carbonate, phosphoric acid. 

The thermochromism of Ag2[HgI4] is due to an order-disorder transition which involves no less than three phases. According to Ketalaar (33), both the yellow low-temperature 0 modification and the red high-temperature oc form contain iodide ions which are cubic close-packed, while the silver and mercury ions occupy some of the tetrahedral holes. The 0 form has tetragonal symmetry, with the mercury ion situated at the corners of a cubic unit cell and the silver ions at the midpoints of the vertical faces. As the temperature is increased it becomes possible for the silver and mercury ions to occupy each others lattice sites and also the two extra lattices sites Hop and bottom face centers of the unit cubel which were unoccupied at lower temperatures. Above 52°C. the mercury and silver ions are completely disordered. The a modification has. therefore, averaged face-centered cubic symmetry. More recently, magnetic (39) and dielectric polarization (37, 39) measurements confirm the presence of a third phase, the 0 modification. With an increase... 

Elemental composition, ionic charge, and oxidation state are the dominant considerations in inorganic nomenclature. Coimectivity, ie, which atoms are linked by bonds to which other atoms, has not generally been considered to be important, and indeed, in some types of compounds, such as cluster compounds, it caimot be appHed unambiguously. However, when it is necessary to indicate coimectivity, itaUcized symbols for the connected atoms are used, as in trioxodinitrate(A/,A/), O2N—NO . The nomenclature that has been presented appHes to isolated molecules (or ions). Eor substances in the soHd state, which may have more than one crystal stmcture, with individual connectivities, two devices are used. The name of a mineral that exemplifies a particular crystal stmcture, eg, mtile or perovskite, may be appended. Alternatively, the crystal stmcture symmetry, eg, rhombic or triclinic, may be cited, or the stmcture may be stated in a phrase, eg, face-centered cubic. 

Fig. 2. Structures for the solid (a) fee Cco, (b) fee MCco, (c) fee M2C60 (d) fee MsCeo, (e) hypothetical bee Ceo, (0 bet M4C60, and two structures for MeCeo (g) bee MeCeo for (M= K, Rb, Cs), and (h) fee MeCeo which is appropriate for M = Na, using the notation of Ref [42]. The notation fee, bee, and bet refer, respectively, to face centered cubic, body centered cubic, and body centered tetragonal structures. The large spheres denote Ceo molecules and the small spheres denote alkali metal ions. For fee M3C60, which has four Ceo molecules per cubic unit cell, the M atoms can either be on octahedral or tetrahedral symmetry sites. Undoped solid Ceo also exhibits the fee crystal structure, but in this case all tetrahedral and octahedral sites are unoccupied. For (g) bcc MeCeo all the M atoms are on distorted tetrahedral sites. For (f) bet M4Ceo, the dopant is also found on distorted tetrahedral sites. For (c) pertaining to small alkali metal ions such as Na, only the tetrahedral sites are occupied. For (h) we see that four Na ions can occupy an octahedral site of this fee lattice.

The term crystal structure in essence covers all of the descriptive information, such as the crystal system, the space lattice, the symmetry class, the space group and the lattice parameters pertaining to the crystal under reference. Most metals are found to have relatively simple crystal structures body centered cubic (bcc), face centered cubic (fee) and hexagonal close packed (eph) structures. The majority of the metals exhibit one of these three crystal structures at room temperature. However, some metals do exhibit more complex crystal structures. 

Fig. 9 a b Coordination mode of the outer Cu2+ ions and the Nd3+ ions at the two vertices of the huge octahedral cluster Nd6Cu24 j for 9. Symmetry codes for A and B are y, z, x and 0.5 - z, 1 — x, —0.5 + y, respectively, c Each cluster nodes link to 12 other cluster units through 12 trans-Cu(pro)2 groups, d 3D open-framework of 9. e Face-centered cubic network... 

Any study of colloidal crystals requires the preparation of monodisperse colloidal particles that are uniform in size, shape, composition, and surface properties. Monodisperse spherical colloids of various sizes, composition, and surface properties have been prepared via numerous synthetic strategies [67]. However, the direct preparation of crystal phases from spherical particles usually leads to a rather limited set of close-packed structures (hexagonal close packed, face-centered cubic, or body-centered cubic structures). Relatively few studies exist on the preparation of monodisperse nonspherical colloids. In general, direct synthetic methods are restricted to particles with simple shapes such as rods, spheroids, or plates [68]. An alternative route for the preparation of uniform particles with a more complex structure might consist of the formation of discrete uniform aggregates of self-organized spherical particles. The use of colloidal clusters with a given number of particles, with controlled shape and dimension, could lead to colloidal crystals with unusual symmetries [69]. 

The number of independent elements of 4> may be restricted by symmetry. In the face-centered cubic structure, for example, the force constant matrix for two atoms 1/2 1/2 0 apart is given by (Willis and Pryor 1975)... 

In the face-centered cubic structure of silicon, atoms are located at 1/8 1/8 1/8 and at the center-of-symmetry related position of —1/8 —1/8 —1/8. The static structure factor can therefore be expressed simply as... 

The metal substrates used in the LEED experiments have either face centered cubic (fee), body centered cubic (bcc) or hexagonal closed packed (hep) crystal structures. For the cubic metals the (111), (100) and (110) planes are the low Miller index surfaces and they have threefold, fourfold and twofold rotational symmetry, respectively. 

One could follow a similar practice and construct a similar hexagonal sandwich with two layers (B, Q of filler, but a cubic cell of higher symmetry can be. constructed the second system is thus characterized as cubic closest packed. The relation between the cubic unit cell (which is identical to the face-centered cubic cell we <... 

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