Phase diagram coupled

The identification of the superconducting phase YBagCug-O7 g provides an example in which knowledge of thermodynamics, i.e. the Gibbs phase rule and the theory of equilibrium phase diagrams coupled with X-ray diffraction techniques led to success. Further, the use of databases that can now be easily accessed and searched on-line provided leads to a preliminary structure determination. The procedures outlined here are among the basic approaches used in solid state chemistry research, but by no means are they the only ones. Clearly the results from other analytical techniques such as electron microscopy and diffraction, thermal... 

With these simplifications, and with various values of the as and bs, van Laar (1906-1910) calculated a wide variety of phase diagrams, detennining critical lines, some of which passed continuously from liquid-liquid critical points to liquid-gas critical points. Unfortunately, he could only solve the difficult coupled equations by hand and he restricted his calculations to the geometric mean assumption for a to equation (A2.5.10)). For a variety of reasons, partly due to the eclipse of the van der Waals equation, this extensive work was largely ignored for decades. 

With the availabihty of computers, the transfer matrix method [14] emerged as an alternative and powerful technique for the study of cooperative phenomena of adsorbates resulting from interactions [15-17]. Quantities are calculated exactly on a semi-infinite lattice. Coupled with finite-size scaling towards the infinite lattice, the technique has proved popular for the determination of phase diagrams and critical-point properties of adsorbates [18-23] and magnetic spin systems [24—26], and further references therein. Application to other aspects of adsorbates, e.g., the calculation of desorption rates and heats of adsorption, has been more recent [27-30]. Sufficient accuracy can usually be obtained for the latter without scaling and essentially exact results are possible. In the following, we summarize the elementary but important aspects of the method to emphasize the ease of application. Further details can be found in the above references. 

Transition probability, non-adiabatic coupling, Longuet-Higgins phase-based treatment, two-dimensional two-surface system, scattering calculation, 152-155 Triangular phase diagram, geometric phase... 

The information available on aqueous polymer blends is qualitative in nature because of the lack of a suitable theory to interpret the experimental observations. Mixed gels can be comprised of an interpenetrating network, a coupled network (as discussed above), or a phase-separated network [2]. The latter is the most common as the blends have a tendency to form two phases during gelation. In such cases the miscibility and thermodynamic stability have to be empirically investigated and proper conditions for miscible blends identified. This involves a phase diagram study as is described in [3]. 

Nuclear Overhauser effect Occurs as a result of cross-relaxation between dipolar-coupled spins resulting from spin spin interactions through space. Phase diagram Summarizes the pressure and temperature conditions at which each phase of a homogeneous material is most stable. 

A schematic illustration of the method, and of the correlation between binary phase diagram and the one-phase layers formed in a diffusion couple, is shown in Fig. 2.42 adapted from Rhines (1956). The one-phase layers are separated by parallel straight interfaces, with fixed composition gaps, in a sequence dictated by the phase diagram. The absence, in a binary diffusion couple, of two-phase layers follows directly from the phase rule. In a ternary system, on the other hand (preparing for instance a diffusion couple between a block of a binary alloy and a piece of a third... 

Figure 2.42. The Cu-Zn system phase diagram and microstructure scheme of the diffusion couple obtainable by maintaining Cu and Zn blocks in contact for several days at 400°C. Shading indicates subsequent layers, each one corresponding to a one-phase region. The two-phase regions are represented by the interfaces between the one-phase layers (adapted from Rhines 1956).

L. Kaufman, Coupled phase diagrams and thermochemical data for transition metal binary systems-VI, CALPHAD, 3 (1979) 45-76. 

Fig. 29. Phase diagram of the model Eq. (22) for coadsorption of two kinds of atoms in the temperature-coverage space. Circles indicate a second-order phase transition, while crosses indicate first-order transitions. Point A is believed to be a tricritical point and point B a bicritical point. The dashed curve shows the boundary from the Blume-Capel model on a square lattice with a nearest-neighbor coupling equal to 7 in the present model (for - 0 Eq. (22) reduces to this model), only the ordered phase I then occurs. From Lee and Landau. )...

This book is intended to be a comprehensive guide to what has become known as CALPHAD. This is an acronym for the CALcuIation of PHAse Diagrams but it is also well defined by the sub-title of the CALPHAD journal. The Computer Coupling of Phase Diagrams and Thermochemistry. It is this coupling which, more than any other factor, defines the heart of this subject area. 

The book begins with a chapter describing the history and growth of CALPHAD. This provides a useful point of departure for a more detailed account of the various strands which make up the CALPHAD approach. Chapters 3 and 4 then deal with the basic thermodynamics of phase diagrams and the principles of various experimental techniques. This is because one of basic pillars of the CALPHAD approach is the concept of coupling phase diagram information with all other available thermodynamic properties. It is a key factor in the assessment and characterisation of the lower-order systems on which the properties of the higher-... 

Broadly speaking, the first application of CALPHAD methods was intrinsically coupled to experimental thermodynamic or phase-diagram measurements. For... 

Phase diagrams " and magnetic properties have also been investigated. Magnetic coupling between the iron double layers is weak, but within the layers it is strong. 

Kaufman, L., Nell, J, Taylor, K., and Hayes, F. (1981). CALPHAD Comput. Coupling Phase Diagrams Thermochem. 5, 185. 

---