Solid-state disorder

P York, DJW Grant. Entropy of processing A new quantity for comparing solid state disorder of pharmaceutical materials. Int J Pharm 30(2-3) 161-180, 1986. 

Fig. 19 A resorcin[4]arene homodimer in the solid state. Disordered pyrazine guest shown in dark gray.

York P, Grant DJW. A disruption index for quantifying the solid state disorder induced by additives or impurities. I. Definition and evaluation from heat of fusion. Int J Pharm 1985 25 57-72. 

An obvious implication of the rotational freedom of the Fes triangle about its pseudo threefold axis (at room temperature) is that the observed solid-state disorder has a dynamic rather than static nature and this has been recently demonstrated by Farrugia. ... 

The molecular structure, fluxional behavior, and solid-state disorder of binary carbonyl clusters and their ligand substitution derivatives still offer material for (animated) debate.f In this section we briefly describe our theoretical analysis of the molecular structures and isomers of several systems, sharing the possibility of exhibiting terminal or bridging carbonyl groups, and use that knowledge to interpret their crystal structures and solid-state behavior. 

Unlike the solid state, the liquid state cannot be characterized by a static description. In a liquid, bonds break and refomi continuously as a fiinction of time. The quantum states in the liquid are similar to those in amorphous solids in the sense that the system is also disordered. The liquid state can be quantified only by considering some ensemble averaging and using statistical measures. For example, consider an elemental liquid. Just as for amorphous solids, one can ask what is the distribution of atoms at a given distance from a reference atom on average, i.e. the radial distribution function or the pair correlation function can also be defined for a liquid. In scattering experiments on liquids, a structure factor is measured. The radial distribution fiinction, g r), is related to the stnicture factor, S q), by... 

Solid state NMR is a relatively recent spectroscopic technique that can be used to uniquely identify and quantitate crystalline phases in bulk materials and at surfaces and interfaces. While NMR resembles X-ray diffraction in this capacity, it has the additional advantage of being element-selective and inherently quantitative. Since the signal observed is a direct reflection of the local environment of the element under smdy, NMR can also provide structural insights on a molecularlevel. Thus, information about coordination numbers, local symmetry, and internuclear bond distances is readily available. This feature is particularly usefrd in the structural analysis of highly disordered, amorphous, and compositionally complex systems, where diffraction techniques and other spectroscopies (IR, Raman, EXAFS) often fail. 

In general, the specific information that can be obtained from a simple solid state NMR experiment depends on the personality of the nuclear isotope under study. In many cases, solid state NMR spectra are not as straightforwardly interpretable as in the preceding example. Furthermore, disordered materials, such as thin films. 

In order to address the possible influence of positional disorder, we have chosen to analyze the way basic operations such as translations and rotations affect the properties calculated for highly symmetric configurations. This approach could provide guidelines to prevent the loss of significant optical coupling between the ground state and the lowest excited state, and hence the quenching of luminescence in the solid state. 

There are three different substituted benzene compounds with the formula C6H4F2. Assume that the benzene rings pack similarly into their crystal lattices. If the positions of the H and F atoms are statistically disordered in the solid state, which isomer will have the least residual molar entropy ... 

The defects of the matrix play an important role on luminescent performances in these materials. Taking into consideration the preparation process of these compounds with the solid-state reaction of mixtures of BaC03, H3BO3, and NH4H2PO4 at different molar ratio, non-equal evaporation during the sintering process of these powders is inevitable and thus results in the formation of intrinsic defects, such as cation and oxygen vacancies. Positional disorder of B and Vacant B (Vb)" have been reported in SrBPOs crystals on the basis of... 

An important phenomenon when considering the differences between ice I and liquid water is that water achieves its maximum density not in the solid state, but at 4 °C, i.e. in the liquid state. The reasons for this were first discussed by Bernal Fowler (1933). They noted that the separation of molecules in ice I is about 0-28 nm, corresponding to an effective molecular radius of 014 nm. Close packing of molecules of such radius would yield a substance of density 1-84 g cm" . To account for the observed density of 10 g cm" , it was necessary to postulate that the arrangement of molecules was very open compared with the disordered, close-packed structures of simple liquids such as argon and neon. 

Cul) is not due to point defects but to partial occupation of crystallographic sites. The defective structure is sometimes called structural disorder to distinguish it from point defects. There are a large number of vacant sites for the cations to move into. Thus, ionic conductivity is enabled without use of aliovalent dopants. A common feature of both compounds is that they are composed of extremely polarizable ions. This means that the electron cloud surrounding the ions is easily distorted. This makes the passage of a cation past an anion easier. Due to their high ionic conductivity, silver and copper ion conductors can be used as solid electrolytes in solid-state batteries. 

Even when complete miscibility is possible in the solid state, ordered structures will be favored at suitable compositions if the atoms have different sizes. For example copper atoms are smaller than gold atoms (radii 127.8 and 144.2 pm) copper and gold form mixed crystals of any composition, but ordered alloys are formed with the compositions AuCu and AuCu3 (Fig. 15.1). The degree of order is temperature dependent with increasing temperatures the order decreases continuously. Therefore, there is no phase transition with a well-defined transition temperature. This can be seen in the temperature dependence of the specific heat (Fig. 15.2). Because of the form of the curve, this kind of order-disorder transformation is also called a A type transformation it is observed in many solid-state transformations. 

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