Valence discontinuous transitions

The present author (Mott 1949,1956,1961) first proposed that a crystalline array of one-electron atoms at the absolute zero of temperature should show a sharp transition from metallic to non-metallic behaviour as the distance between the atoms was varied. The method used, described in the Introduction, is now only of historical interest. Nearer to present ideas was the prediction (Knox 1963) that when a conduction and valence band in a semiconductor are caused to overlap by a change in composition or specific volume, a discontinuous change in the number of current carriers is to be expected a very small number of free electrons and holes is not possible, because they would form exdtons. 

Throughout we make use of the pseudogap model outlined in Chapter 1, Section 16- A valence and conduction band overlap, forming a pseudogap (Fig. 10.1). States in the gap can be Anderson-localized. A transition of pure Anderson type to a metallic state (i.e. without interaction terms) can occur when electron states become delocalized at EF. If the bands are of Hubbard type, the transition can be discontinuous (a Mott transition). 

Investigations of the solid-state chemistry of the americium oxides have shown that americium has properties typical of the preceding elements uranium, neptunium, and plutonium as well as properties to be expected of a typical actinide element (preferred stability of the valence state 3-j-). As the production of ternary oxides of trivalent plutonium entails considerable difficulties, it may be justified to speak of a discontinuity in the solid-state chemical behavior in the transition from plutonium to americium. A similar discontinuous change in the solid-state chemical behavior is certainly expected in the transition Am Cm. Americium must be attributed an intermediate position among the neighboring elements which is much more pronounced in the reactions of the oxides than in those of the halides or the behavior in aqueous solution. 

IV. Dual-yalaicy Semi-conductors (i) Different valence states of same ion in stoicheiometric proportion distributed over cation sites. Ordered at low temperatures some or all distributed statistically at high temperatures. Fea04 >115 jr (Fef+1D+) (p Fe + Di -)Or or (Fe + D+) (Fe +.Fe +lD )Or <115 (Fe +lD )CFe + otyor High electronic conduction (discontinuity at transition temp.). Intense optical absorption. 

At room temperature the pressure-induced phase transition in SmS differs from those in SmSe and SmTe in that it is discontinuous (55). It is not known whether it remains discontinuous at T=0. It was pointed out by Davis (56) that the two modes of behavior could be explained by assuming different mechanisms for the transition, i.e. an f6 - f5d delocalization in SmS and a simple Se(4p)—Sm(55) band-gap closing in the selenide and telluride. This suggestion was supported by APW calculations of the band structure of the Sm monochalcogenides. In the case of SmS the 4/states were found to lie in the band gap, but in SmSe and SmTe they were located below the p-valence bands,... 

The ramifications for a Gedanken experiment at T = 0 K are sketched in Fig. 4a, revealing the d.c. electrical conductivity for a macroscopic system such as Si P in which d, the average distance between one-electron centers, can be continuously tuned by changes in the composition of the system. For values of d below a critical distance, dc, i.e. d < <4) the system is metallic and the electronic wave-function is completely delocalized over the entire sample. For very large d d > dfj, we have an insulator with a valence electron wavefunction that is completely localized at the individual atomic sites. At a critical distance, d we then have, according to Mott, a first-order (discontinuous) metal-insulator transition. Thus, at r = 0 K one either has a non-metal or an insulator, for which the limiting (low temperature) d.c. electrical conductivity is zero, or a metal, with a finite conductivity at this base temperature. Whether the metal-insulator transition in Si P (Fig. 4a) is continuous or discontinuous is still a source of controversy. 

Magnetite, Fe30>4, is a unique material. It is a mixed-valency compound (Fe " and Fe " on crystallographic sites of the same symmetry) with a low electrical conductivity below 120K, and a nearly metallic conductivity above this temperature. Between 120 and 770 K, magnetite is an inverse spinel, (Fe )[Fe Fe ]04, and all the transition phenomena occur in the octahedral sites. For T > 770 K, the redistribution of Fe on tetrahedral sites becomes non-negligible (Wu Mason, 1981). The reversible, sharp discontinuity in conductivity was first observed by Okamura (1931). Ferroelectric features have also been observed at low temperatures (Rado Ferrari, 1975 Kato et al, 1983). 

For TmSe and TmTe, one observes continuous isostructural (B1 Bl) valence transitions over a wide volume range, for TmSe already starting at ambient conditions. The calculated discontinuous volume changes are in good agreement with the experimental volumes. 

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).

Fig. 20.4. Pressure-volume relationship for rare earth monochalcogenides. The anomalous relationships are due to valence changes of the rare earth ion towards the trivalent state. The discontinuity in SmTe and EuO near 400 k bar are due to NaCl-CsCl transition (from Jayaraman et al., 1974).

Figure 135 shows the relative change in the lattice constant a/uo as a function of pressure at room temperature, where a and Oq are the lattice constants at high and ambient pressure, respectively. Since there are no new Bragg peaks up to 13 GPa, the AuBes structure is stable at room temperature at least to 13 GPa. A discontinuous change in the value of fl/flo, to be caused by the y-oc transition in Ce metal (Franceschi and Olcese, 1969), is not observed in the present pressure range within experimental error. This result indicates that a discontinuous valence transition as observed at Tv is not induced by pressure up to 13 GPa at room... 

Fig. 93. The temperature dependence of the electrical resistivity of the YbCu4ln and LuCu4ln compounds (Muller et al. 1988). The discontinuity at 40 K indicates the temperature-induced valence transition.

The pressure-induced semiconductor-metal transition of a sample with y = 0.1 occurs at 4.8 kbar. No phase transition at pressures up to 10 kbar Is observed on a sample with y = 0.3. Figures in the paper show, for room temperature, an abrupt increase of the lattice constants from -5.66 to -5.86 A around y = 0.1 and then linearly to -5.94 A at y = 0.3. The valency changes abruptly from -2.5 to 2.05 around y = 0.1 and then remains nearly unchanged up to y = 0.4. The relative electrical resistivity q/qq of a sample with y = 0.3 decreases continuously with increasing pressure. A discontinuous drop of q/qq is observed on a sample with y = 0.1. 

It is now possible to form heterostructures in which the transition from one system to the other takes place over one atomic layer. When two such semiconductors are brought into intimate contact, the electron affinities (energy required to remove an electron from the bottom of the conduction band to vacuum state) must line up, and at thermal equilibrium, the Fermi levels must also line up. The result is band bending with discontinuities in both the valence (AEy) and conduction band (AEc) at the interface as shovm in Figure 22.13. (Recall that in homojunctions between n- and p-type material, the vacuum levels already lined up because both sides of the junction were the same material so no such discontinuities appeared.)... 

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