Isostructural phase transition

In CeS, the first transition occnrs to the B1 phase with delocalized f-electrons (Svane et al., 1999), that is, the theory predicts an isostructural phase transition in CeS similar to CeP. The calculated transition pressure is 10.1 GPa with a volume collapse of 6%. These findings are in excellent agreement with the experiment of Croft and Jayaraman (1980), but at variance with the results of Vedel et al. (1986), who observe a soft anomaly in the pV-curve but no discontinuity. These results may indicate the proximity of a critical point. At higher pressures, CeS transforms into the B2 phase. According to the present calculations, this occurs in two steps. First, at a pressure of 24.3 GPa, CeS goes into the bivalent B2 phase with a 4.6% volume change. In the second step, at a pressure of 29.5 GPa, the tetravalent B2 phase is reached with a 3.6% volume collapse (Svane et al., 1999). Unfortunately, no experiments have been performed beyond 25 GPa (Leger, 1993). 

FIGURE 14 Cohesive energy of CeP (in Ry/formula unit) as a function of specific volume (in formula unit). Two crystal structures, the B1 and B2, are considered, and each with two different treatments of the Ce f-electrons. The full drawn curves correspond to calculations with one localized f-electron per Ce atom, whereas the dashed curves correspond to itinerant f-electrons. The dotted line marks the common tangent at the isostructural phase transition in the B1 structure. 

Fig. 4.8 Pressure behavior of the reduced atomic volume for several silicon clathrates. The behavior for diamond-structured Si is also shown. Arrows indicate the pressure at which the isostructural phase transition occurs depending on the guest atom, except for Na for which the phase diagram of silicon in the diamond structure is followed...

Analysis of in situ synchrotron diffraction and spectroscopy data first revealed the presence of the unusual isostructural phase transition occurring within semiconductor clathrate materials, that was associated with a large change in the compressibility but with no apparent change in the crystal stmcture (Fig. 4.8) [69,74]. The pressure range associated with this unexpected transformation occurs between 13-16 GPa, but it also appears to depend upon the hydrostatic nature of the pressurization conditions. Various possible explanations for the transition have been advanced, including the presence of electronic [73,79] or phonon instabilities [71], or potential vacancy formation occurring on the framework silicon sublattice [80]. 

Fig. 4.9 Evolution of the order parameter predicted for an isostructural phase transition based on the Landau theory of transitions through expansion of the free energy in terms of an order parameter that is consistent with the symmetry constraints of the phase transformation...

A very different behavior of the ESR data has been obtained in the system Sci j Gd Hi.9 investigated by Venturini and Morosin (1977). They studied powdered samples at X-band frequencies in the temperature range 16Korringa slope as an isostructural phase transition. And indeed, measurements of the lattice constants revealed a low-temperature cell with a slightly smaller volume. 

Fig. 20.7. Lattice parameter vs temperature for SmS alloys substituted with different trivalent rare earth ions (left) and for Smi, GdjS alloys (middle and right). The abrupt changes in the lattice parameter are due to first-order but isostructural phase transition. To be noted is the anomalous thermal expansion (right figure) of Smi jGd,S alloys (from Jayaraman et al., 1975a).

Fig. 20.9. Lattice parameter change with temperature (upper figure) and composition (lower figure) in the Sm., Yi compounds. The abrupt changes are due to first order isostructural phase transition. In the bottom of lower figure the valence calculated from the lattice parameter is shown (from Tao and Holzberg, 1975).

There is an interesting difference for one metal of the lanthanide series with respect to the heavy actinide metals. While high density ( volume collapse ) and low structural symmetry simultaneously appear at the same pressure in Cm, Bk, and Cf (Benedict 1987), and only low structural symmetry, with no appreciable volume decrease, is observed in Am, the lanthanide metal Ce is the only one where volume collapse (by 16%, in an isostructural phase transition) and formation of a low-symmetry structure occur successively at two different pressures (Staun Olsen et al. 1985a). 

D.L. Farber, J. Badro, C.M. Aracne, D.M. Teter, M. Hanfland, B. Canny, B. Couzinet, Experimental evidence for a high-jnessure isostructural phase transition in osmium. Phys. Rev. Lett. 93(9), 095502-095506 (2004)... 

The ionic models discussed in section 1.12 involve some sort of empiricism in the evaluation of repulsive and dispersive potentials. They thus need accurate parameterization based on experimental values. They are useful in predicting interaction energies within a family of isostructural compounds, but cannot safely be adopted for predictive purposes outside the parameterized chemical system or in cases involving structural changes (i.e., phase transition studies). 

Synthesis was by heating above 450 °C in evacuated quartz vessels of the stoichiometric components. The isostructural I MCl series underwent a phase transition in the range 350-410 °C, and became monohydrated in air. The K2MC15 series was also isostructural. 

In ZSM-5, which is nominally isostructural with silicalite, the temperature,Tt, at which the transition occurs depends on the level of "impurities (i.e. species other than silica, such as the residual aluminium in the framework, cations, adsorbed water and organics). ZSM-5 with relatively high Al contents is orthorhombic at room temperature because the transition occurs at Tt<20°C. The sample of silicalite treated with 2M (but not with 0.5M) base solution was orthorhombic, and it is clear that treatment with a strong base introduces sufficient amount of "impurities" for the phase transition to take place below the room temperature. 

Among the thiocyanates another order-disorder phase transition is possible. This involves a transition from an ordered structure similar to potassium thiocyanate to a disordered structure isostructural with potassium cyanate. This has been observed in potassium thiocyanate at 145 °C but has not been observed up to 300 °C in the nearly isostructural sodium salt. Iqbd (41) has suggested an explanation for this behaviour in terms of the greater anisotropy of the inter-ionic interaction potential in potassium thiocyanate compared with the sodium salt. 

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