Tammann relation

The theoretical explanation of the Fulcher-Tammann relation is based either on the free volume theory or on the concept of the temperature-dependent size of structural units taking part in viscous flow (cf. Doremus, 1973). The Fulcher-Tammann relation predicts a rapid increase of viscosity to an infinite value at To, while in fact in the transformation range approaches a constant and relation (6) is thus complied with. 

Tammann has, by a large amount of experimental evidence, apparently refuted the hypothesis of a critical point of fusion— against which of course there is no a priori objection. In some cases (e.g., with ice) new crystalline modifications appear when the temperature and pressure are modified, and in all cases the pair of relations L = 0, Ar = 0 (cf. 89) were never simultaneously satisfied. 

S. Lussana found that the temp. 6 of maximum density of 0 65 and 1 30 per cent, soln. of potassium nitrate is related with the press, p respectively by 0=2 89—00133(p—l), and 0=1 84—0 0124(p—l). The lowering of the vapour pressure of aq. soln. of lithium nitrate at different temp, has been measured by G. Tammann, and by A. T. Lincoln and D. Klein 42 at>25°, and the results show that the relative lowering of the vap. press, with increasing cone, increases in accord with the assumption that the salt forms hydrates in aq. soln. The vap. press, of aq. soln. of sodium nitrate have been measured by C. Dieterici, A. Smits, W. W. J. Nicol, G. Tammann, and by A. T. Lincoln and D. Klein. According to VOL. n, 3 G... 

As the exponential relation does not describe viscosity over a wider temperature range, various empirical equations have been suggested for practical purposes the Fulcher-Tammann relationship has found the widest application ... 

Their Tammann temperatures are low. As a consequence, these lattices are in a metastable state, near these temperatures. If two structures are closely related, as we shall see in the next section, the two solids will be able to form either coherent interfaces or solid solutions. In these cases, "hybrid crystals, in which microdomains of both phases coexist, can be formed according to UBBELOHDE s theory (43), which considers strain energy E and internal surface energy ri (44). The free enthalpy of a domain (1) in a matrix of structure (2) is given by ... 

CONSISTENCY OF THE VOGEL - FULCHER - TAMMANN (VFT) EQUATIONS FOR THE TEMPERATURE-, PRESSURE-, VOLUME-AND DENSITY- RELATED EVOLUTIONS OF DYNAMIC PROPERTIES IN SUPERCOOLED AND SUPERPRESSED GLASS FORMING LIQUIDS/SYSTEMS... 

According to the Phase Rule, each different variety of ice constitutes a separate phase and, consequently, it must be possible to obtain not only the ordinary triple point for solid— liquid— vapour which has already been described, but also other triple points at which the other forms of ice exist. Of such forms Bridgman has distinguished no fewer than four, besides ordinary ice, these different forms being designated ice I. (ordinary ice), ice II., ice III., ice V., ice VI. The existence and stability relations of another form, ice IV., discovered by Tammann, do not appear to be definitely settled. 

Thus this equation holds only on the assumption that the difference in specific heat between the solid substance and the supercooled liquid increases proportionally with the absolute temperature. In many actual cases this appears to be approximately true thus Tammann discovered the above relation purely empirically e.g. for naphthalene... 

In most of its relationships water is included with those substances which have an abnormal behaviour Tammann s relation should therefore be limited to the so-called normal t liquids, for which it appears to hold fairly approximately. 

In polymers, the glass transition phenomenon has been related to the dielectric a-relaxation processes through the Vogel-Fulcher-Tammann (VET) equation [9], and it can be characterized by means of their molecular dynamics analysis. 

It is well known that the viscosity of a liquid decreases upon heating. This would usually be expected to fit to an Arrhenius type of behavior. That is, the natural logarithm of the viscosity should vary in a linear manner with temperature. All of the I Ls for which the temperature dependence of the viscosity has been studied deviate from this behavior [7, 9, 11, 14, 20]. Rather, they fit a Vogel-Tammann-Fulcher interpretation where the viscosity of the IL at any given temperature is better related to a material-specific temperature such as the difference between the temperatare of the study and the glass transition temperature of the IL. 

The WLF expression has been shown [12] to be related to the Vogel-Fulcher-Tammann-Hesse equation [14—16],... 

The fluorite-related lanthanide oxides exhibit unusual diffusional properties. The conventional rule-of-thumb is that atomic mobility in a solid does not become significant until one-half of the melting point temperature (the Tammann temperature) is reached. In these oxides this value is about 1200°C. At the Tammann temperature the metal atoms in lanthanide oxides just begin to become mobile as confirmed by the temperatures required for solid-state reactions. The oxygen substructure, to the contrary, is mobile below 300°C. This leads to a situation where equilibration and reaction must be considered for each substructure separately (see Bevan and Summerville 1979). This places the lanthanide oxides with fluorite-related structures in the category of fast-ion conductors along with, e.g., calcia-stabilized zirconia as indicated in table 18. 

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