Phase transformations continuous

Spinodal decomposition and certain order-disorder transformations are the two categories of continuous phase transformations. Both arise from an order parameter instability in the case of spinodal decomposition, it is a conserved order parameter for continuous ordering, it is a nonconserved order parameter. 

The conditions for continuous phase transformations (described in Chapter 17) derive from considerations of the molar free energy of a homogeneous, spatially uniform system with no interfaces. For phase transformations involving nonconserved... 

We next examine further the case of a continuous phase transformation. Consider first the situation where H = 0. As long as T > Tc and T = Tc, the global minimum of the order parameter occurs at rjo = 0 cf. Eq. (7.5.5). But for T equilibrium values of the order parameter are specified by... 

Landau also recognized that continuous phase transformations in a group subgroup relationship could be described by an order parameter, which carries the information about the broken symmetry. This order... 

In situ HT investigation of the Lao,64Cao,o4Ti03 and Lao.eCao.iTiOs structures revealed the continuous phase transformations from orthorhombic to tetragonal structure (space group P4/mmm) above the temperatures 704... 

The thermodynamic differences between spinodal decomposition (a continuous phase transformation) and nucleation and growth (a discontinuous phase transformation) are illustrated in Figure 6.6. At a given temperature, the volume free... 

Spinodal decomposition is an example of a continuous phase transformation. In a spinodal transformation, a single phase separates into two phases via gradual changes in local composition. The spinodal decomposition process gradually occurs everywhere (small in degree, large in extent). 

Chapter 1 (Phase Equilibria in Binary and Ternary Hydro-thermal Systems, V. M. Valyashko, Russia) contains a description of the general trends of sub- and supercritical phase behavioin in binary and ternary systems taking into accoimt both stable and metastable equilibria. A presentation of the various types of phase diagrams aims to show the possible versions of phase transitions under hydrothermal conditions and to help the reader with the determination of where the phase equilibrium occurs in p-T-X space, and what happens to this equilibrium if the parameters of state are changed. Special attention is paid to continuous phase transformations taking place with variations of temperature. 

Here, Pc is the mixture density of the dense phase. U up i is defined by J Uf-U/), where Uf and U are mean velocities of the dilute and dense phases, respectively. This definition of mesoscale slip velocity differs a little bit from that in the cluster-based EMMS model, because the continuous phase transforms from the dilute phase to the dense phase. And their quantitative difference is l-f)PgUgc/Pc, which is normally negligible for gas-solid systems. Similarly, the closure of Fdi switches to the determination of bubble diameter. And it is well documented in literature ever since the classic work of Davidson and Harrison (1963). Compared to cluster diameter, bubble diameter arouses less disputes and hence is easier to characterize. The visual bubbles are normally irregular and in constantly dynamic transformation, which may deviate much from spherical assumption. Thus, the diameter of bubble here can also be viewed as drag-equivalent definition. 

Aging. When a gel is maintained in its pore Hquid, the stmcture and properties continue to change long after the gel point. This process is called aging. Four aging mechanisms can occur, singly or simultaneously polycondensation, syneresis, coarsening, and phase transformation (9,21). 

The structures and phase transformations observed in steels have been dealt with in some detail not only because of the great practical importance of steels, but also because reactions similar to those occurring in steels are also observed in many other alloy systems. In particular, diifusionless transformations (austenite -> martensite), continuous precipitation (austenite -> pearlite) and discontinuous precipitation (austenite -> bainite and tempering of martensite) are fairly common in other alloy systems. 

Symmetry considerations forbid any nonzero off-diagonal matrix elements in Eq. (68) when /(x) is even in x, but they can be nonzero if f(x) is odd, for example, /(x) = x. (Note that x itself transforms as Bi [284].) Figure 3 shows the outcome for the phase by the continuous phase tracing method for cycling... 

The family of phase transformations U(a) = expia, where a single parameter a may run continuously over real numbers, forms a unitary Abelian (commutative) group known as the [/( ) group. Compare 2.8.2.5... 

The solution is transformed to an oil-in-oil emulsion in which a polystyrene solution forms the disperse phase and the elastomer polyester component solution the continuous phase. The point of phase separation is observed experimentally by the onset of turbidity, due to the Tyndall effect. The conversion required for phase separation to occur depends basically on the solubility of the polystyrene chains in the elastomer solution, which in turn is governed by the elastomer concentration and compatibility of the two polymers. 

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