Rhombohedral-cubic phase transition

Fig. 3.6 Band stmcture and band-decomposed charge density plots for ihombohedral (a, b) and intermediate (e, f) phase AgBiSe2, respectively. Partial chaige density plots for c the VBM (valance band maximum) and d the CBM (conduction band minimum) of Ag-Bi-Se chain in the rhombohedral phase AgBiSe2. g The partial chaige density plots of Ag-Bi-Se chain for AgBiSe2 after the Ag/Bi atoms exchange during the rhombohedral-cubic phase transition...

Fig. 3.7 Projected density of states (PDOS) for rhombohedral left column) and intermediate right column) phase of AgBiSc2 during the rhombohedral-cubic phase transition...

Relational structures at different temperatures in the rhombohedral-cubic phase transition. As temperature increases, AgBiSea crystallized in the hexagonal phase is observed to undergo continuous phase transition to rhombohedral phase around 410 K and then to cubic phase around 580 K. Also the phase transitions take place reversibly as temperature decreases, that is, the cubic phase undergoes the continuous phase transition to rhombohedral phase around 560 K and then to the hexagonal phase around 390 K during cooling process. Our optimized lattice... 

C.J. Howard, B.J. Kennedy, and B.C. Chakoumakos, Neutron powder diffraction study of rhom-bohedral rare-earth aluminates and the rhombohedral to cubic phase transition. J. Phys.-Conden. Matter. 12(4), 349-365 (2000). 

The temperature dependence of conductivity of several compositions of ScSZ is shown in Figure 1 (a). The conductivity of 10 to 15mol% ScSZ were significantly changed around 560K. It was caused by the crystal phase transition between cubic and rhombohedral. The phase transition accompanied volume change, and may lead to the cell broken. To prevent the phase transition, we tried small... 

Figure 16.35 (Plate 1). All strontium myristate. Top left lOOx crossed polars - room-temperature lamellar. Top right lOOx crossed polars 90°C - lamellar. Middle left lOOx crossed polars, gypsum plate in, heated to 218°C - rhombohedral. Middle right 200 x crossed polars, gypsum plate in, cooled from rhombohedral-cubic phase boundary, oscillated near 210-215°C - rhombohedral (bright) and cubic (dark). Bottom left lOOx parallel polars, cooled to 210 from 218°C - cubic to rhombohedral transition. Bottom right 200 x crossed polars, gypsum plate in, cooled from 290°C and oscillated near 260° C - hexagonal...

Beister, H.J., Strossner, K., and Syassen, K. (1990). Rhombohedral to simple-cubic phase transition in arsenic under pressure, Phys. Rev. B 41, 5535-5543. 

Two modifications are known for polonium. At room temperature a-polonium is stable it has a cubic-primitive structure, every atom having an exact octahedral coordination (Fig. 2.4, p. 7). This is a rather unusual structure, but it also occurs for phosphorus and antimony at high pressures. At 54 °C a-Po is converted to /3-Po. The phase transition involves a compression in the direction of one of the body diagonals of the cubic-primitive unit cell, and the result is a rhombohedral lattice. The bond angles are 98.2°. 

Also known for some time is a phase transition at low temperature (111K), observed in studies with various methods (NQR, elasticity measurement by ultrasound, Raman spectrometry) 112 temperature-dependent neutron diffraction showed the phase transition to be caused by an antiphase rotation of adjacent anions around the threefold axis ([111] in the cubic cell) and to lower the symmetry from cubic to rhombohedral (Ric). As shown by inelastic neutron scattering, this phase transition is driven by a low-frequency rotatory soft mode (0.288 THz 9.61 cm / 298 K) 113 a more recent NQR study revealed a small hysteresis and hence first-order character of this transition.114 This rhombohedral structure is adopted by Rb2Hg(CN)4 already at room temperature (rav(Hg—C) 218.6, rav(C—N) 114.0 pm for two independent cyano groups), and the analogous phase transition to the cubic structure occurs at 398 K.115... 

Fig. 10 Medium-range PDF of PMN. Temperatm-e dependence (upper panel) is well explained by the transition from rhombohedral phase to the cubic phase (lower panel). The two PDF peaks at 8.5 and 9.09 A indicate 300 K as a characteristic temperature for crossover [18]...

Measurements of NMR for Ti, Ti [33], and Sr [34,35] were carried out for STO 16 and STO 18-96. Ti and Sr nuclear magnetic resonance spectra provide direct evidence for Ti disorder even in the cubic phase and show that the ferroelectric transition at Tc = 25 K occurs in two steps. Below 70 K, rhomb ohedral polar clusters are formed in the tetragonal matrix. These clusters subsequently grow in concentration, freeze out, and percolate, leading to an inhomogeneous ferroelectric state below Tc. This shows that the elusive ferroelectric transition in STO 18 is indeed connected with local symmetry lowering and impHes the existence of an order-disorder component in addition to the displacive soft mode [33-35]. Rhombohedral clusters, Ti disorder, and a two-component state are found in the so-called quantum paraelectric... 

The phase transition in barium titanate is of first order, and as a result, there is a discontinuity in the polarization, lattice constant, and many other properties, as becomes clear in Figure 1.7. It is also clear in the figure that there are three phase transitions in barium titanate having the following sequence upon cooling rhombohedral, orthorhombic, tetragonal and cubic. 

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