Phase Transitions and the Chemistry of Solids

Solid Sictie and Structural Chemistry Unit, Indian Institute of Science, Bangalore-560012, India Received January 27, 1983 (Revised Manuscript Received September 1, 1983) 

We all know that when a liquid transforms to a crystal, there is a change in order the crystal has greater order than the liquid. The symmetry also changes in such a transition the liquid has more symmetry than a crystal since the liquid remains invariant under all rotations and translations. Landau introduced the concept of an order parameter, , which is a measure of the order resulting from a phase transition. In a first-order transition (e.g., liquid-crystal), the change in is discontinuous, but in a second-order transition where the change of state is continuous, the change in is also continuous. Landau proposed that G in a second-order (or structured) phase transition is not only a function of P and T but also of and expanded G as 

Many physical properties diverge near Tc, i.e., show anomalously large values as Tc is approached from either side. The divergences in different phase transitions are, however, strikingly similar. These divergences can be quantified in terms of critical exponents, X  

Another important aspect of phase transitions in solids is the presence of soft modes. Operationally, a soft mode is a collective excitation whose frequency decreases anomalously as the transition point is reached. In second-order transitions, the soft mode frequency goes to zero at Tc, but in first-order transitions, the phase change occurs before the mode frequency goes to zero. Soft modes have been found to accompany a variety of solid-state transitions, including those of superconductors and organic solids.2,5 Occurrence of soft modes in phase transitions can be inferred from Landau s treatment wherein atomic displacements may themselves be considered to represent an order parameter. 

On the basis of our knowledge of crystal chemistry, we can predict the nature of structural changes in the 

---

Oyumi, Y. and Brill, T.B. (1985) Thermal Decomposition of Energetic Materials 6. Solid-Phase Transitions and the Decomposition of 1,2,3-Triaminoguanidinium Nitrate Journal of Physical Chemistry 89, 4325-4329. 

The study of how fluids interact with porous solids is itself an important area of research [6], The introduction of wall forces and the competition between fluid-fluid and fluid-wall forces, leads to interesting surface-driven phase changes, and the departure of the physical behavior of a fluid from the normal equation of state is often profound [6-9]. Studies of gas-liquid phase equilibria in restricted geometries provide information on finite-size effects and surface forces, as well as the thermodynamic behavior of constrained fluids (i.e., shifts in phase coexistence curves). Furthermore, improved understanding of changes in phase transitions and associated critical points in confined systems allow for material science studies of pore structure variables, such as pore size, surface area/chemistry and connectivity [6, 23-25],... 

Enzymes, such as the one we used in our demonstration, are governed by the principles of chemical kinetics—one of the many links between the basic principles of chemistry and the intricate chemistry of life. Our rapid and cursory survey of biochemistry here, combined with our previous discussions of biochemical systems, shows that in life all our chemical principles come into play acid-base reactions, redox reactions, chemical bonding, intermolecular forces, concentration, solids and solubility, kinetics, and even phase transitions and the gaseous phase. 

Crystallography is a very broad science, stretching from crystal-structure determination to crystal physics (especially the systematic study and mathematical analysis of anisotropy), crystal chemistry and the geometrical study of phase transitions in the solid state, and stretching to the prediction of crystal structures from first principles this last is very active nowadays and is entirely dependent on recent advances in the electron theory of solids. There is also a flourishing field of applied crystallography, encompassing such skills as the determination of preferred orientations, alias textures, in polycrystalline assemblies. It would be fair to say that... 

Ames Laboratory (Iowa State University, USA) investigating new solid state phases based on reduced rare earth halides. Since 1993, she has held a position at the University Jaume 1 of Castello (Spain) and became Associate Professor of Physical Chemistry in 1995. During the second semester of 2005, she held a visiting professor position at the Laboratory of Chemistry, Molecular Engineering and Materials of the CNRS-Universtity of Angers (France). Her research has been focussed on the chemistry of transition metal clusters with special interest in multifunctional molecular materials and the relationship between the molecular and electronic structures of these systems with their properties. She is currently coauthor of around 80 research papers on this and related topics. 

The existence of a solid itself, the solid surfaces, the phenomena of adsorption and absorption of gases are due to the interactions between different components of a system. The nature of the interaction between the particles of a gas-solid system is quite diverse. It depends on the nature of the solid s atoms and the gas-phase molecules. The theory of particle interactions is studied by quantum chemistry [4,5]. To date, one can consider that the prospective trends in the development of this theory for metals and semiconductors [6,7] and alloys [8] have been formulated. They enable one to describe the thermodynamic characteristics of solids, particularly of phase equilibria, the conditions of stability of systems, and the nature of phase transitions [9,10]. Lately, methods of calculating the interactions of adsorbed particles with a surface and between adsorbed particles have been developing intensively [11-13]. But the practical use of quantum-chemical methods for describing physico-chemical processes is hampered by mathematical difficulties. This makes one employ rougher models of particle interaction - model or empirical potentials. Their choice depends on the problems being considered. 

NMR studies of solutions of inter-metallic phases led to recognition of the potential use of polyatomic Zintl ions as reagents for the generation of new cluster compounds (Eichhorn et al., 1988). Examples of transition-metal derivatives have been discussed in Chapter 5 and the structures of the ions themselves were used as examples of ligand-free main-group clusters in Chapter 2 (Corbett, 1985 Fassler, 2001). The following examples illustrate recent developments in the chemistry of these clusters derived from solid-state syntheses. 

A variety of related structures can be identified with 6,8, and 12-fold coordination of the A cation and four or sixfold coordination of the anion. In fact, the chemistry of ABO4 temarys is extremely complicated with solid solutions and phase transitions being common. Lattice defects may be introduced easily by appropriate dopings. Scheelites and its relatives have been studied intensively for their properties as heterogeneous catalysts, as host materials for impurity activated luminescent materials, and for specialized optical uses see Oxide Catalysts in Solid-state Chemistry and Section 4.4). 

Incidentally, I had been an experimental physical chemist in the field of structural chemical thermodynamics and working, for a long time on phase transitions in the solid by main use of calorimetry. Although I am not the specialist in the field of Solution Chemistry discussed in the present conference, I am very much convinced that the selected subjects of "Structure, Fluctuation and Relaxation... 

---