Cubic-rhombohedral transition

Results of Rietveld refinement of neutron powder data for Na-A zeolite at various temperatures above and below the cubic-rhombohedral transition. The space group used in each refinement is as shown. In the rhombohedral refinements, the positional parameters were constrained to satisfy Fm3c symmetry as discussed in text, f is the fractional occupancy and N the number of reflections included in this refinement. Also shown in columns I and II are the X-ray single crystal results of Pluth and Smith(t), but with their anisotropic temperature factors converted to the average isotropic values. Neutron... 

We therefore conclude that there is strong evidence for interpreting the cubic-rhombohedral transition in terms of ordering of Na(2) ions. The decrease in Ryp is small, but the ordered model contains only two additional parameters and the improvement in R p is comparable to those which follow from relaxation of the more restrictive constraints described above. 

LaCo03 is rhombohedral from room temperature to 1000°C. For LSCF perovskite, the phase structure depends on the dopant level and temperature. In the La0 8Sr0 2CO, l ev03 system, the room-temperature phases are rhombohedral and orthorhombic for 0 < y < 0.7 and 0.8 < y < 1, respectively [79], For y = 0.8, i.e., I. a, xSrxCo0 2Fe0 sO3 the orthorhombic/rhombohedral transition at room temperature occurs at x = 0.3. When Sr content is increased to x > 0.6, the second phase was observed, while the main phases were rhombohedral for 0.6 < x < 0.8 and cubic for x > 0.8 [80],... 

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). 

FIGURE 35 Tentative phase diagram of the NdAlOs-SmAlOj pseudobinary system. The letters U C, Rh, and O designate liquid, cubic, rhombohedral, and orthorhombic phase fields, respectively. Transition temperatures in the Ndi- Sm AlOj solid solution were taken from Yoshikawa et al. (1998). Besides, the transition and melting temperatures in NdAlOj and SmAlOj reported by Howard et al. (2000), Portnoj and Timofeeva (1986), Wu and Pelton (1992), Coutures and Coutures (1984) were used. Linear fits of observed critical temperatures To-Rh(jf) = 16(11) + 1043 (14) X Ti (x) = 2313(41) + 30(58) x x. 

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...

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... 

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. 

The ternary Ge halides, MGeX3 (M = Rb, Cs X = Cl, Br, I) are polymorphic with various distorted perovskite-like (p. 963) structures which reflect the influence of the nonbonding pair of electrons on the Ge" centre. Thus, at room temperature, rhombohedral CsGel3 has three Ge-I at 275 pm and three at 327 pm whereas in the high-temperature cubic form (above 277°C) there are six Ge-I distances at 320 pm as a result of position changes of the Ge atoms (reversible order-disorder transition). Again, RbGel3 has a lemon-yellow, orthorhombic form below —92° an intermediate, bordeaux-red orthorhombic perovskite form (—92° to —52°) a black rhombohedral form (—52° to —29°) and... 

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... 

Whereas the first microscopic theory of BaTiOs [1,2] was based on order-disorder behavior, later on BaTiOs was considered as a classical example of displacive soft-mode transitions [3,4] which can be described by anharmonic lattice dynamics [5] (Fig. 1). BaTiOs shows three transitions at around 408 K it undergoes a paraelectric to ferroelectric transition from the cubic Pm3m to the tetragonal P4mm structure at 278 K it becomes orthorhombic, C2mm and at 183 K a transition into the rhombohedral low-temperature Rm3 phase occurs. 

The individual satelhte transitions cannot be resolved above Tc due to exchange of Ti ions between off-center sites. Discrimination between tetragonal, orthorhombic, and rhombohedral breaking of the cubic symmetry can be obtained from the angular dependence of the second moments M2 of the satelhte background [9]. 

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... 

---