Discontinuous phase transformations

The thermodynamics of phase equilibria is reviewed in Chapter 17 and the fundamental thermodynamic differences between conserved and nonconserved order parameters are reinforced with a geometrical construction. These order parameters are used in the kinetic analyses of continuous and discontinuous phase transformations. 

When silicon is deposited from the vapor phase at ambient temperature, it solidifies as amorphous silicon. Vapor deposited bilayers and multilayers of silicon with metals thus consist of polycrystallinc metal and amorphous silicon. The earliest observations of amorphous silicide formation by SSAR were made on such diffusion couples [2.51, 54], Similar results were also obtained earlier by Hauser when Au was diffused into amorphous Tc [2.56], Figure 2.15 shows an example of an amorphous silicide formed by reaction of amorphous silicon with polycrystallinc Ni-metal at a temperature of 350"C for reaction times of 2 and 10 s [2.55,57], The reaction experiments were carried out by a flash-healing method (see [2.55] for details). In this example, the amorphous phase grows concurrently with a crystalline silicide. The amorphous phase is in contact with amorphous Si and the crystalline silicide in contact with the Ni layer. As in the case of typical mctal/metal systems, the amorphous interlayer is planar and uniform. It is also interesting that the interface between amorphous silicon and the amorphous silicide appears to be atomically sharp despite the fact that both phases are amorphous. This suggests that amorphous silicon (a covalently bonded non metallic amorphous phase with fourfold coordinated silicon atoms) is distinctly different from an amorphous silicide (a metallically bonded system with higher atomic coordination number). These two phases are apparently connected by a discontinuous phase transformation. 

Our focus in this text will be on diffusional transformations. Diffusional transformations can be further subdivided into two main types continuous and discontinuous. Gibbs (of the Gibbs phase rule and the Gibbs free energy) articulated the difference between continuous and discontinuous phase transformations as follows ... 

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... 

The nucleation-and-growth process is an example of a discontinuous phase transformation. The new phase nucleates in highly localized regions with properties that are abruptly and distinctly different from the parent phase (large in... 

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. 

Composition Profile Measurement. Results of Zieba et al. (1997) will be given as an example of the measurement of solute distribution in an alloy undergoing a phase transformation. They studied discontinuous precipitation in cobalt-tungsten alloys, in which a Co-32 wt% W alloy was aged in the temperature range 875 K to 1025 K, and high spatial resolution X-ray microanalysis of thin foils by STEM was used to measure the solute distribution near the reaction front. 

When the free energies F of the two crystal structures are identical, the system is at a critical point. The identity of F does not imply identical fimctions (otherwise the two phases would be indistinguishable). Therefore, at the critical point first derivatives of F might differ and therefore enthalpy, volume, and entropy of the two phases would be different. These transformations are first-order phase transitions, according to Ehrenfest [105]. A discontinuous enthalpy imphes heat exchange at the transition temperature, which can easily be measured with DSC experiments. A discontinuous volume is evident under the microscope or, more precisely, with diffraction experiments on single crystals or powders. Some phase transitions are however characterized by continuous first derivatives of the free energy, whereas the second derivatives (specific heat, compressibility, or thermal expansivity, etc.) are discontinuous. These transformations are second-order transitions and are clearly softer. 

The linear log-log plots of reaction rate (in terms of oxygen consumption) versus time show for many alloys a discontinuity, or increase of reactivity. It appears that this transition is associated with the phase transformation in the protective film of Zr dioxide. The initial film formed on Zr is the cubic polymorph of Zr dioxide. After a period of oxidation this transforms to the tetragonal, and finally to the monoclinic (stable) form of Zr dioxide. When certain alloying constituents... 

CLASSIFICATION OF PHASE TRANSFORMATIONS CONTINUOUS VERSUS DISCONTINUOUS TRANSFORMATIONS... 

In this connection, we admit that we know little of the real nature and the process of the discontinuous phase transition of gels. Although the phenomenological theory predicts that the whole sample transforms from one phase to the other at a specified temperature (the transition temperature), there has been some experimental evidence that the transition in real gels never occurs in such a manner. For example, a serious deformation erf the sample [7] as well as the coexistence of phases [8] have been observed over a rather wide temperature range around the first-order transition point A curious, and at the same time important point is that these states seem not to be transient but stable states of the gels [8]. 

In our description of l.c. side chain polymers we will refer to the Ehrenfest scheme of classifying the phase transformations. In general an n-th order phase transformation is determined by a discontinuity at the point of the transition in the n-th derivative of the free enthalpy with respect to temperature T or pressure P. 

From the measurements of the birefringence in Fig. 12a further important aspect has to be mentioned. With increasing temperature An does not continuously tend to zero at the phase transformation temperature Tc but vanishes discontinuously. At the phase transformation the nematic phase, having a finite birefringence, coexists... 

From the dynamic mechanical investigations we have derived a discontinuous jump of G and G" at the phase transformation isotropic to l.c. Additional information about the mechanical properties of the elastomers can be obtained by measurements of the retractive force of a strained sample. In Fig. 40 the retractive force divided by the cross-sectional area of the unstrained sample at the corresponding temperature, a° is measured at constant length of the sample as function of temperature. In the upper temperature range, T > T0 (Tc is indicated by the dashed line), the typical behavior of rubbers is observed, where the (nominal) stress depends linearly on temperature. Because of the small elongation of the sample, however, a decrease of ct° with increasing temperature is observed for X < 1.1. This indicates that the thermal expansion of the material predominates the retractive force due to entropy elasticity. Fork = 1.1 the nominal stress o° is independent on T, which is the so-called thermoelastic inversion point. In contrast to this normal behavior of the l.c. elastomer... 

The discontinuity in the logfoT)-l/T relation which results from the phase transformation between HI to I, also appears in the Na2S0,-Si02 systems. The temperature at a break is nearly the same as the DTA result. Sodium sulfate mixed with SiC does not seem to be an appropriate solid electrolyte because of its low electrical conductivity and the presence of a transformation. 

Contrary to bubbling fluidization, gas flow in the form of bubbles is transformed to a continuous dilute phase, while solids in the emulsion are transformed into a discontinuous phase as clusters. 

Solomatov V. S. and Stevenson D. J. (1994) Can sharp seismic discontinuity be caused by non-equilibrium phase transformation Earth Planet. Sci. Lett. 125, 267-279. 

Wood E. J. and Rubie D. C. (1996) The effect of alumina on phase transformations at the 660-kilometer discontinuity from Fe-Mg partitioning experiments. Science 273, 1522-1524. 

The methods for determination of the electrical conductivity of solids are discussed in Section 2.1.7. For most materials, a change in electrical conductivity can be expected due to interaction of two solid phases. In a single phase transformation, the disorder in the solid must increase, causing an increase in conductivity which will be reversed when the new phase is formed. The change may be indicated by a change in temperature coefficient or by a sharp discontinuity. 

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