Phase equilibrium and crystal structure

Planck s formulation The entropy of pure phases in internal equilibrium approaches a constant value (independent of pressure, phase state and crystal structure) as the temperature approaches zero. 

If we look at the mechanistic and crystallographic aspects of the operation of polycomponent electrodes, we see that the incorporation of electroactive species such as lithium into a crystalline electrode can occur in two basic ways. In the examples discussed above, and in which complete equilibrium is assumed, the introduction of the guest species can either involve a simple change in the composition of an existing phase by solid solution, or it can result in the formation of new phases with different crystal structures from that of the initial host material. When the identity and/or amounts of phases present in the electrode change, the process is described as a reconstitution reaction. That is, the microstructure is reconstituted. 

FIGURE 23.7 Cr-Ni Phase Diagram Because chromium and nickel form solids with crystal structures that differ from each other, an alloy mixture of the two metals does not form a solid solution at all compositions. A two-phase region exists at compositions between the possible compositions of the two different structures. In the two-phase region, both crystal structures coexist in equilibrium. 

Several surface-specific structural phase transitions are observed in ice. We will focus here on complementary aspects of the basic phenomena of interfacial melting, surface roughening, and molecular kinetics and their application to the equilibrium and growth structures of ice crystals. A central issue is how the interfacial structure at ice/vapor, ice/gaseous-atmosphere and ice/water interfaces influences the adsorption potential, the growth shapes and surface transport properties. The environmental relevance concerns die fact that ice dominates the crystal growth phenomena we observe... 

Impure metals and alloys exhibit all the structural features and crystal defects of the pure meteils already discussed. In addition, however, impure metals and alloys exhibit many structures which are not observed in pure metals, and which, in many instances, have an extremely important effect on the properties, particularly the corrosion resistance. However, before dealing with the structure of impure metals and alloys, it is necessary to consider the concept of metallurgical components, phases, constituents and equilibrium phase diagrams. 

At high pressures, solid II can be converted (slowly) to solid III. Solid III has a body-centered cubic crystal structure. Line bd is the equilibrium line between solid II and solid III, while line be is the melting line for solid III.P A triple point is present between solid II, solid III, and liquid at point b. Two other triple points are present in this system, but they are at too low a pressure to show on the phase diagram. One involves solid II, liquid, and vapor while the other has solid I, solid II, and vapor in equilibrium. 

When two metals A and B are melted together and the liquid mixture is then slowly cooled, different equilibrium phases appear as a function of composition and temperature. These equilibrium phases are summarized in a condensed phase diagram. The solid region of a binary phase diagram usually contains one or more intermediate phases, in addition to terminal solid solutions. In solid solutions, the solute atoms may occupy random substitution positions in the host lattice, preserving the crystal structure of the host. Interstitial soHd solutions also exist wherein the significantly smaller atoms occupy interstitial sites... 

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