Phase diagrams polymorphism

Figure Al.3.23. Phase diagram of silicon in various polymorphs from an ab initio pseudopotential calculation [34], The volume is nonnalized to the experimental volume. The binding energy is the total electronic energy of the valence electrons. The slope of the dashed curve gives the pressure to transfomi silicon in the diamond structure to the p-Sn structure. Otlier polymorphs listed include face-centred cubic (fee), body-centred cubic (bee), simple hexagonal (sh), simple cubic (sc) and hexagonal close-packed (licp) structures.

Attachment of a hot or cold stage to the ordinary microscope stage allows the specimen to be observed while the temperature is changed slowly, rapidly, or held constant somewhere other than ambient. This technique is used to determine melting and freezing points, but is especially useful for the study of polymorphs, the determination of eutectics, and the preparation of phase diagrams. 

The polymorphism of certain metals, iron the most important, was after centuries of study perceived to be the key to the hardening of steel. In the process of studying iron polymorphism, several decades were devoted to a red herring, as it proved this was the P-iron controversy. P-iron was for a long time regarded as a phase distinct from at-iron (Smith 1965) but eventually found to be merely the ferromagnetic form of ot-iron thus the supposed transition from P to a-iron was simply the Curie temperature, p-iron has disappeared from the iron-carbon phase diagram and all transformations are between a and y. 

The recent book by Young [91Y02], Phase Diagrams of the Elements, presents an authoritative and comprehensive account of the influence of pressure on polymorphic and solid-liquid transitions. Both theoretical and experimental work are succinctly summarized. 

The Li-Zn phase diagram shows the presence of eight intermediate phases. Later x-ray diffraction results confirm the existence of five intermediate RT phases " . Polymorphism is shown by the three compounds shown in the Li-Cd phase system, and this has confused the interpretation of x-ray diffraction patterns ". 

The Ca-Cu system has been reexamined using thermal analysis and x-ray diffraction methods an independent study of the CaCuj-Cu section has also been completed. The resultant phase diagram, although similar to that in ref. 3 at the Cu-rich end, differs markedly for Ca-rich alloys. Supporting evidence for the modifications has been obtained from the Ca-Mg-Cu ternaiy system. Three intermediate compounds are formed in the system CaCuj (950 C) melts congruently, whereas CajCu (488 C) and CaCu (567°C) are formed in peritectic reactions. Single-crystal x-ray diffraction studies verify the stoichiometry of CajCu and examine the polymorphism of CaCu. ... 

Fig, 18a,b, The polymorphic behaviour of the phasmidic-like mesogens a molecular model with six terminal chains b phase diagram for the binary mixture of double swallow-tailed compound (I) with conventional rod-like mesogen (II) (adapted from Letko et al. [123])... 

The surface phase diagram of vanadium oxides on Rh(l 11) has been investigated in a series of papers of our group [4, 18, 19, 90, 101-103]. It is characterized by pronounced polymorphism and many different oxide structures have been detected as a function of coverage and growth temperature. The vanadium oxide structures for coverages up to the completion of the first monolayer formed on Rh(l 11) under the different preparation conditions may be subdivided into highly oxidized phases... 

The importance of temperature-controlled scanning calorimetry for measurements of heat capacity and of scanning transitiometry for simultaneous caloric and pVT analysis has been demonstrated for polymorphic systems [9]. This approach was used to study an enantiotropic system characterized by multiphase (and hindered) transitions, the role of heat capacity as a means to understand homogeneous nucleation, and the creation of (p, T) phase diagrams. The methodology was shown to possess distinct advantages over the more commonly used combination of characterization techniques. 

Figure 5.12 (a) The p-T phase diagram of Si. The melting lines for the low-pressure polymorph of Si and the liquid-liquid phase transition are calculated by using the two-state model and the parameters given in Table 5.2. (b) Iso-concentration lines for species B in the p-T plane, (c)) The fraction of species B as a function of temperature at constant pressure p = 2 GPa. 

Figure 8. Binary melting-point phase diagram of NBMe3. White and black circles represent the temperatures of the beginning and the end of fusion of the stable polymorph, respectively, while white and black squares are those of the metastable one.

If one of components or compounds in a binary system undergoes polymorphic transformations, there will be horizontal lines in the phase diagram separating the stable region of each polymorph. The figures given below represent two possible forms which a system can take when such transformations take place. Prove that conditions lying on these horizontal lines are univariant. 

Let us leave to the specialists in phase equilibria to argue whether these are individual phases or compositional polymorphs of the same phase. The results presented appear to be sufficient for the reader to appreciate how complicated phase relations may be and how careful it is necessary to be when interpreting any experimental data on both phase diagrams and compound-layer formation in diffusion couples, especially in those cases where the two-phase fields are narrow compared to the homogeneity ranges of chemical compounds. 

C. Wibowo, K. D. Samant, K. M. Ng, High-Dimensional Solid-Liquid Phase Diagrams Involving Compounds and Polymorphs, AIChEJ.,... 

The phase diagram of the system Rh—Bi is rather complex on the Bi—rich side. RhBi2 undergoes a polymorphic transformation (127, 128) at 430° C. The arsenopyrite-type low-temperature modification trans-... 

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