Tricritical Points and Liquid-Solid Critical Lines

Abstract

Tricritical points separate continuous and discontinuous symmetry breaking transitions. They occur in a variety of physical systems and their mathematical models. A tricritical point is used to determine a liquid-solid phase transition line in the pressure-temperature plane [Aitta, J. Stat. Mech., 2006]. Excellent experimental agreement has been obtained for iron, the material having the most high pressure data. This allows extrapolation to much higher pressures and temperatures than available experimentally. One can predict the temperature at the liquid-solid boundary in the Earth's core where the pressure is 329 GPa. Light matter, present as impurities in the core fluid, is found to generate about a 600 K reduction of this temperature.Keywords: Tricritical point, phase transitions, critical phenomena, iron melting curve, temperature in the Earth's core Melting or solidification is a first order phase transition since the order changes discontinuously from liquid to solid. Landau (1937) gave a theoretical description for first order phase transitions and the point where they change to second order phase transitions (with a continuous change of order) [1]. Such a point was later named a tricritical point by Griffiths (1970) [2]. Tricritical points occur in a variety of physical systems. Examples of tricritical points are presented in Table 1 with the corresponding adjustable variables. Experimentally they were first found in fluid mixtures, compressed single crystals and magnetic and ferroelectric systems (see old reviews in [3] and [4]). Paper [11] is an example of two-dimensional melting.The rest of this paper provides bifurcation theoretical analysis for the solidification/melting problem for iron [12], following the earlier work in Paper [13] which presents the symmetry breaking analysis in the first experimentally studied nonequilibrium tricritical point.

Monoclinic–orthorhombic first-order phase transition in K2ZnSi5O12 leucite analogue; transition mechanism and spontaneous strain analysis

“…A value of B = 0 marks the occurrence of a tricritical point and for negative B values ( B < 0) the phase transition is said to be first order (e.g. Aitta, 2009); such a first-order transition will be characterised by the presence of discontinuities in symmetry-breaking and non-symmetry breaking strains, and perhaps by the occurrence of a two-phase region (e.g. also see Salje, 1990; Hayward et al , 2000; Tolédano, 2012).…”

Interior structure of Mars and other rock-and-iron planetary bodies

“…The process is then iteratively repeated until the mass is as correct as possible with a stabilized pressure profile. For the most massive objects, densities beyond the tricritical pressure are needed, but they are just estimated to be constant from equation ( 17) as in the theoretical model by Aitta (2006Aitta ( , 2010a), since we do not have accurate experimental data to know any better.…”

“…(P tc , T tc ) for iron was found using the most reliable experimental melting data selected by Aitta (2006). This Landau theory also predicts (Aitta 2010a) that the lowest possible temperature for iron-rich melt, as a function of pressure, is…”

“…A special point is where both these coefficients are simultaneously zero; this is called a tricritical point. A sixth order potential has at most three minima and thus this theory reveals that there are three critical conditions for the coexisting solid and liquid states of a pure material (Aitta 2010a). The most commonly known condition is the melting temperature which is the same as the solidification temperature.…”