Results second-order phase transitions

Curran [61C01] has pointed out that under certain unusual conditions the second-order phase transition might cause a cusp in the stress-volume relation resulting in a multiple wave structure, as is the case for a first-order transition. His shock-wave compression measurements on Invar (36-wt% Ni-Fe) showed large compressibilities in the low stress region but no distinct transition. 

MnAs exhibits this behavior. It has the NiAs structure at temperatures exceeding 125 °C. When cooled, a second-order phase transition takes place at 125 °C, resulting in the MnP type (cf. Fig. 18.4, p. 218). This is a normal behavior, as shown by many other substances. Unusual, however, is the reappearance of the higher symmetrical NiAs structure at lower temperatures after a second phase transition has taken place at 45 °C. This second transformation is of first order, with a discontinuous volume change AV and with enthalpy of transformation AH. In addition, a reorientation of the electronic spins occurs from a low-spin to a high-spin state. The high-spin structure (< 45°C) is ferromagnetic,... 

In spite of these uncertainties we can derive some more general results from the above gap equations. With increasing temperature both condensates, 5 and 5, are reduced and eventually vanish in second-order phase transitions at... 

Addition of reversibility of the reactions in the ZGB model generally does change the qualitative behavior [45-50]. The main results found by these authors is that addition of only A desorption removes the first-order phase transition, whereas B2 desorption removes the second-order phase transition. When all reactions are reversible, a first-order transition is still present for appropriately chosen rate parameters. 

One should note that in the MF approach no second order phase transition is present. Contrary to this, MC simulations with diffusion [45,46,54-56] do show this transition, even when the results are extrapolated to infinitely fast diffusion. This means that, at least in this case, MC simulations with fast diffusion do not show the same results as MF calculations. This is remarkable since it is generally assumed that in the fast diffusion limit, both approaches should be equivalent. The MC method is certainly correct, and we believe that the discrepancies show that the MF approach is not always valid. This is the reason why we have chosen the MC approach to study CO oxidation on Pt(lOO) surfaces, as will be discussed in the next section. 

At this point one is tempted to anticipate the results of the quantitative analysis and suppose that the liquid phase has / >p , the glass phase has pglass transition temperature. If so, the transition would be second order because the infinite cluster is formed sharply." Calculations based on the model show that it cannot be second order in most circumstances, but is first order, with a range of values of p around p excluded. Elimination of the simplifications we have introduced wipes out the second-order phase transition, but the first-order phase transition persists in the circumstances we believe to hold experimentally, as we shall discuss after presenting the calculations. 

At a phase transition the heat capacity will often show a characteristic dependence upon the temperature (a first-order phase transition is characterised by an infinite heat capacity at the transition but in a second-order phase transition the heat capacity changes discontinuously) Monitoring the heat capacity as a function of temperature may therefore enable phase transitions to be detected. Calculations of the heat capacity can also be compared with experimental results and so be used to check the energy model or the simulation protocol. 

Fig. 82. Specific heat of two UBe,3 samples (+, Ott et al. 1984b , Mayer et al. 1986a) in a plot of dt against f c = CIC (T ), t=TIT. Solid line is theoretical result for a strong-coupling superconductor with isotropic gap. Inset shows difference between experimental data and the theoretical result in a plot of hcit against t. Dashed curve represents idealized second-order phase transition at 0.6 K. Note that a similar peak is obtained if the theoretical result for a strong-coupling superconductor with axial gap is chosen (Steglich et al. 1987c). Dash-dotted line is a schematic extrapolation of the normal-state data necessary to meet entropy balance at T. ...

A number N is defined as N = h /h, h being the height of the transition peak when the mass m or the heating rate Tp are multiplied by two. The theoretical values of N will be determined in the case of an isothermal first order phase transition, a second order phase transition and a non-isothermal first order phase transition (case of an impure material). Only results will be givei here, the detailed theory being described elsewhere... 

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