Transformation tricritical

Hard mode infrared spectroscopy indicates that Pi character is absent even at the microscale when Ca contents fall below Ange (Atkinson et al. 1999). Moreover, the character of the transition changes in response to anjncreasing albitic component. Endmember Ca-anorthite transforms tricritically from Pi to / I symmetry, but with an increase in Na+Si, the transition becomes second-order (Redfem 1990). Interestingly, Redfern et al. (1988) and Redfern (1992) present evidence that an increasing albitic component acts to increase critical temperatures of anorthitic solid solutions when samples are equally disordered with respect to Al and Si. Th effects of Al-Si order/disorder are addressed by Redfern in a chapter in this volume. 

Urusova MA, Valyashko VM. Tricritical phenomena in the NaCl-Na2B407-H20 system and the transformation laws of complete phase diagrams. Russ J Inorg Chem 1998 43 948-955. 

By varying the temperature or tuning the interaction the system can be transformed from one state to another. The point at which the zipped-unzipped transition takes place is a tricritical point and in its proximity a crossover is observed. In the asymptotic limit the mean number of monomers M in contact with each other at the tricritical point is assumed to behave as... 

When the coefficients a, and Oj vary, the characteristic curves transform, and, given Equation 57 is satisfied, the system has a CPC with a tricritical point (Figure 3.103). 

Now, the boundary of the tricritical region specified by inequality 120 is transformed, with the aid of Equations 116 and 123, to the condition... 

In the McMillan model, the smectic A-nematic transition can be continuous or discontinuous. If a is less than 0.7, then o decreases to zero continuously and S is continuous at the smectic A- nematic transition. If a is between 0.7 and 0.98, then a jumps to zero discontinuously and S has a small discontinuity at the smectic A-nematic transition. When a is greater than 0.98, the smectic phase transforms directly into the isotropic phase with discontinuities in both order parameters. So just as in the extended Landau-de Geimes theory for the smectic A phase, a tricritical point is predicted at a=0.7, which corresponds to a ratio in the smectic A—nematic transition temperature to the nematic-isotropic transition temperature of 0.87. A great deal of experimental work has been done on the smectic A-nematic transition, and the results seem to indicate that the tricritical point occurs when the ratio of the two transition temperatures is significantly larger than 0.87. 

The immiscibility regions of type b and d spreading from the binary subsystems are terminated by one nonvariant point in ternary systems (the double critical endpoint HN (Li = L2-G) and the tricritical point RN (Li = L2 = G), respectively). Disappearance of the immiscibility region of type c takes place only after transformation (through the tricritical or double critical points) into immiscibility region of type b or d. 

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