Transitions first-order

Coefficients a, B, and C in equation 5.175 have the usual meanings in the Landau expansion (see section 2.8.1) and for the (second-order) displacive transition of albite assume the values = 1.309 cal/(mole X K) and B, = 1.638 kcal/mole (Salje et al., 1985). is the critical temperature of transition = Bla = 1251 K). The corresponding coefficients of the ordering process are = 9.947 cal/(mole X K), B = -2.233 kcal/mole, = 10.42 kcal/(mole X K), and = 824.1 K. With all three coefficients being present in the Landau expansion relative to substitutional disorder it is obvious that Salje et al. (1985) consider this transition first-order. A is a T-dependent coupling coefficient between displacive and substitutional energy terms (Salje et al., 1985) ... 

Can We Call These Phase Transitions First-Order ... 

The Ehrenfest17 classification of phase transitions (first-order, second-order, and lambda point) assumes that at a first-order phase transition temperature there are finite changes AV 0, Aft 0, AS VO, and ACp VO, but hi,lower t = hi,higher t and changes in slope of the chemical potential /i, with respect to temperature (in other words (d ijdT)lowerT V ((9/i,7i9T)higherT). At a second-order phase transition AV = 0, Aft = 0, AS = 0, and ACp = 0, but there are discontinuous slopes in (dV/dT), (dH/<)T), (OS / <)T), a saddle point in and a discontinuity in Cp. A lambda point exhibits a delta-function discontinuity in Cp. 

Note that on the mean field level at %c a second-order transition is predicted for f=H2, while taking fluctuations into account renders the transition first order [192,210,211], as also found experimentally [231]. Although the nature of surface effects on this transition is quite different for the first-order case [6] than for the second-order case [12], we discuss mostly the second-order case here. The constant pc in Eq. (43) is the density of the chains (pc=l/N if a Flory-Huggins lattice with lattice spacing unity is invoked), and the constants e0 and u0 can be derived [197] from the random phase approximation as... 

Will the order of the transition (first order or continuous) remain the... 

Since the SmAj-N and SmA -N transitions are expected to be second order (low Ja n/Jn-i) values [97]) and the SmA,-SmAd transition first-order (symmetry arguments), the meeting point should be a bi-critical point. Moreover the topology of the p-T phase diagram obtained resembles that of a diagram exhibiting known bicritical points [106]. 

In the mean-field picture one expects the phase transition to be genetically second order. However, as one adjust materials parameters to reduce the temperature width of the nematic phase, parametrized in K-M theory by the dimensionless ratio the coupling drives the transition first order, with the point in material-parameter space where this happens being termed the Landau Tricritical Point (LTP). 

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