Valence transition pressures

FIGURE 4 Total energy differences between divalent and trivalent elemental lanthanide metals (open circles) and their sulphides (solid circles). The dashed line shows the experimental values for the lanthanide metals. The calculated energy differences have been uniformly shifted upwards by 43 mRy to reproduce the valence transition pressure of 6 kbar in SmS. 

The calculated valence transition pressures for EuO and EuS in the B1 structure are compared with experiment in Table 5. Experimentally, the transition of EuO (at room temperature) is continuous, as in SmSe and SmTe. For EuS, the experiments show no anomalous compression curve (Jayaraman et al., 1974), but the band gap closes at 16 GPa, just before the structural transition to the B2 structure occurs (at 20 GPa) (Syassen, 1986). Due to the ASA in the LMTO-ASA band structure method. 

Independent of the conditions inducing the valence transition (pressure, temperature or chemical alloying) the valence numbers observed just after the first-order transition, converge to u = 2.6 0.05. The theoretical answer to why just the ratio 3/2 of the two valence state populations stabilizes SmS at low volumes might be obtained in the framework of the thermodynamics of valence fluctuations (see e.g. Wohlleben (1984a,b)). 

Most electronic valence transitions shift to longer wavelengths at higher pressures drat is, the gap between the highest occupied orbital and lowest unoccupied orbital tends to decrease upon compression. The rates of shift usually are larger (1) for pure materials than for solutes in a solvent and (2) for stronger (more allowed) transitions. However, these correlations are not quantitative, and many transitions shift in the opposite... 

Optical absorption spectroscopy No intervalence transitions in visible region One mixed-valence transition in visible region absorption bands intensify at elevated pressures and low temperatures One or more mixed-valence transitions in visible region temperature lowers intensity of absorption bands, pressure intensifies Opaque metallic reflectivity in visible region... 

We can describe the process of pressure induced valence transitions (as in Fig. 1 of Ref. ( )) as a three step phenomenon. The first, in the pressure range P P] only qualitative changes in the wave functions (as described by Equation 1 ) are induced, for a given ground state configuration, 1.0, because... 

Besides the isomer shift, the experimental linewidth and the electric field gradient, information about the crystal-field anisotropy can also be obtained from Yb Mossbauer spectroscopy, as shown by Bonville et al. (1990) and Bonville and Hodges (1985) for YbCuAl. Furthermore, YbCuAl was investigated by Yb Mossbauer spectroscopy at pressures up to ISOkbar. The data give strong evidence for a valence transition towards the 4f (Yb ) configuration. At 4.2 K the transition is completed at about SOkbar (Schdppner et al. 1986). This behavior is paralleled by the pressure-dependent susceptibility measurements (Klaasse et al. 1977). 

In conclusion, the valence classification of Yb compounds, based on the SIC-LSD total energies, maps very well onto the physical properties observed experimentally. In particular, this allows to identify the third group of compounds as the heavy-fermion and mixed-valent systems on the trivalent side, and, on the divalent side, those systems that are likely to imdergo pressure-induced valence transitions. 

In both CeSe and CeTe, the only pressure transition observed is that from B1 to B2 with localized f-electrons in both phases. These are also first to occur according to the calculations, whereas valence transitions are predicted in the range of 40 GPa. Thus, the situation here is quite similar to that in CeSb and CeBi, apart from the tetragonal distortion in these compormds that was not formd for CeSe and... 

In Table 5, the calculated and available experimental data are collected for the isostructural pressure transitions in Yb chalcogenides. The general trends are reproduced by the calculations. Only for the case of YbO, the calculated transition pressure seems to be significantly too high. In the intermetallic YbAls compound, pressure induces a continuous increase of valence (Kumar et al., 2008), which is in good agreement with the calculated rate of depletion of the 14th f-band in the SIC-LSD calculations. 

More recent high pressure studies (>5 GPa) have revealed the existence of a -Ce, which is superconducting (Wittig, 1968) and has an atomic volume 3.2% smaller than a-Ce at the a a transition pressure (Ellinger and Zachariasen, 1974). From metallic radii considerations Ellinger and Zachariasen consider o -Ce to be tetravalent (see table 4.3), and thus to have no localized 4f electrons, which is consistent with its superconducting behavior. The existence of tetravalent a -Ce is in accord with the valency scheme proposed by Gschneidner and Smoluchowski (1963), and this valence rules out most of the other proposed valence schemes. 

Fig. 9.12. Pressure-volume relationship for Eu monochalcogenides (left fig.) and a plot of the log of bulk modulus against log of specific volume for R.E. monochalcogenides showing the straight line relationship. In the P-V relationship of Eu monochalcogenides the discontinuities are due to NaCI to CsCl transition. In EuO the first discontinuity is due to a valence transition in Eu (from Jayaraman et al., 1974).

According to the diagram presented in Fig. 4.24, energy of CTT is the lowest for Eu ". Therefore, in the materials in which the energy of the Eu " is located deeply in the band gap, the ITE related to the CTT in Eu " can influence the internal radiative transitions in Eu ". Because pressure causes an increase of the energy of the Eu " state with respect to the valence, band pressure could recover the Eu " emission when it is quenched at ambient conditions by nonradiative processes through the ITE related to the CTT. 

Svane A, Strange P, Temmerman WM et al (2001) Pressure-induced valence transitions in... 

Lattice constant variation of 4f levels pressure-induced valence transitions... 

High pressure has proven to be an extremely powerful variable for the study of electronic phenomena in the solid state. Modern solid state models can be tested by their ability to account for the phenomena seen as function of pressure. Since the pioneering high-pressure studies in the optical region, the term pressure tuning (Drickamer 1982) describes the experimentally controlled volume dependence of electronic levels. Pressure in the lanthanides induces mixed valence or valence transitions, induces heavy fermion supraconductivity in other words high pressure... 

---