Solid compressive pressure structural characterization

The development of the physical chemistry of rubber was greatly aided by the clear definition of an "ideal" state for this material. An ideal rubber is an amorphous, isotropic solid. The liquidlike structure of rubber was discovered very soon after the technique of X-ray scattering was developed. An isotropic material is characterized by physical properties that do not depend on the orientation of the sample. The deformation of an isotropic solid can be characterized by only two unique moduli the modulus of compression, K, and the shear modulus, G. A solid is characterized by equilibrium dimensions that are functions of temperature, pressure, and the externally imposed constraints. It is convenient to define a shape vector, L, whose components are the length, width, and height of a rectangular parallelepiped. For a system with no external constraints, the shape vector can be expressed as ... 

Initially, the compression does not result in surface pressure variations. Molecnles at the air/water interface are rather far from each other and do not interact. This state is referred to as a two-dimensional gas. Farther compression results in an increase in snrface pressure. Molecules begin to interact. This state of the monolayer is referred as two-dimensional liquid. For some compounds it is also possible to distingnish liqnid-expanded and liquid-condensed phases. Continnation of the compression resnlts in the appearance of a two-dimensional solid-state phase, characterized by a sharp increase in snrface pressure, even with small decreases in area per molecule. Dense packing of molecnles in the mono-layer is reached. Further compression results in the collapse of the monolayer. Two-dimensional structure does not exist anymore, and the mnltilayers form themselves in a non-con trollable way. 

At 21 GPa iodine transforms into the metallic structure of a bco type (iodine-II, a1 = 4h-8) [48], which on further compression continuously approaches bet, reaching this phase at 43 GPa (iodine-111), with the further equalization of interatomic distances. The axial ratio c/a of a ( ct-phase continuously approaches 1 and at 55 GPa there occurs a first-order phase transition into a fee structure (iodine-IV) which is stable up to 276 GPa [49, 50]. Bromine at 80 GPa transforms into a bee lattice. However, the onset of the metallic behavior takes place in the direction perpendicular to the layers via a progressive gap closure and at a pressure lower than the dissociation pressure (13 GPa for I2 and 25 GPa for Br2). In the layered direction the onset of a metallic behavior was also observed, but at a higher pressure [51]. Takemura et al. [52] discovered that between I and II phases there exists a new intermediate phase (iodine-V), using He as the pressurizing medium to obtain the pure hydrostatic compression and specify the pressure of the first transition (23.2-24.6 GPa). They characterized the new phase (a/cf type, iodine-V), and the phase II (at P = 25.6 —30.4 GPa). Reduction of volume at transitions I V is equal to 2.0 % and at V II only 0.2 %. Recently a new phase of solid bromine was revealed [53] at P > 80 GPa by Raman scattering experiments. This phase was found to be the same as the iodine-V with an incommensurate structure, discovered by Takemura et al. In... 

Liquid polymorphism in one-component fluids is an example of so-called anomalous phase behavior. This term is used to emphasized the difference with respect to the normal behavior characterizing prototypical (i.e., argon like) simple liquids. Anomalous behavior includes, in addition to polymorphism in the liquid and solid phases, reentrant melting, that is, melting by compression at constant temperature, and a number of other thermodynamic, dynamic, and structural anomalies, as, for example, the density anomaly (a decrease in density upon cooling), the diffusion anomaly (an increase of diffusivity upon pressurizing), and the structural anomaly (a decrease of structural order for increasing pressure). 

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