Pure Crystalline Solids

Crystalline solids are characterized by the regular and periodic spatial arrangement of entities at the nodes of a lattice. The nature of the entities thus arranged defines the nature of the solid. There are four distinct classes  

Solids are incompressible, which means that their derivative (dV IdP) is practically zero, so they do not have an equation of state 

Thermodynamic Modeling of Solid Phases, First Edition. Michel Soustelle. ISTE Ltd 2015. Published by ISTE Ltd and John Wiley Sons, Inc. 

However, solids do experience changes in volume, under the influence of temperature, which is characterized by its cubic expansion coefficient or its linear expansion coefficient. 

Similarly, when heat is applied to it, solids heat up. The extent of that rise in temperature is characterized by the solid s specific heat capacity. 

---

The reason for the constancy and sharpness of the melting j)oint of a pure crystalline solid can be appreciated upon reference to Fig. 7,10, 1, in which (a) is the vapour pressure curve of the solid and (6) that of the liquid form of the substance. Let us imagine a vessel, maintained at constant temperature, completely filled with a mixture of the above liquid and solid. The molecules of the solid can only pass into the liquid and the molecules of the liquid only into the solid. We may visualise two competitive processes taking place (i) the solid attempting to evaporate but it can only pass into the liquid, and (ii) the liquid attempting to distil but it can only pass into the solid. If process (i) is faster, the solid will melt, whereas if process (ii) proceeds with greater speed the... 

These effects are shown in Figure 17.4, where the entropy of ammonia, NH3> is plotted versus temperature. Note that the entropy of solid ammonia at 0 K is zero. This reflects the fact that molecules are completely ordered in the solid state at this temperature there is no randomness whatsoever. More generally, the third law of thermodynamics tells us that a completely ordered pure crystalline solid has an entropy of zero at 0 K. 

Third law of thermodynamics A natural law that states that the entropy of a perfectly ordered, pure crystalline solid is 0 at 0 K Thomson, J. J., 25 Three Mile Island, 525-526 Threonine, 622t Tin... 

A pure crystalline solid comes closest to the depiction in Figure 14-1 la. Nevertheless, each atom or molecule in a pure crystalline solid vibrates back and forth in its compartment, and this vibration can be thought of as similar to the depiction in 14-1 Ic. The vibrations move the atoms or molecules randomly about over the space available to them, making IV > 1 and S > 0. 

This is an expression of Nernst s postulate which may be stated as the entropy change in a reaction at absolute zero is zero. The above relationships were established on the basis of measurements on reactions involving completely ordered crystalline substances only. Extending Nernst s result, Planck stated that the entropy, S0, of any perfectly ordered crystalline substance at absolute zero should be zero. This is the statement of the third law of thermodynamics. The third law, therefore, provides a means of calculating the absolute value of the entropy of a substance at any temperature. The statement of the third law is confined to pure crystalline solids simply because it has been observed that entropies of solutions and supercooled liquids do not approach a value of zero on being cooled. 

As yet 20-electron diareneiron compounds have not been isolated as pure crystalline solids from iron vapor-arene reactions. However, infrared studies show that dibenzene-, ditoluene-, and dimesityleneiron are formed at low temperatures and decompose below -40°C (76). The... 

We describe here a series of organolithium compounds that can be prepared easily as pure crystalline solids. The synthesis involves a heteroatom assisted lithiation reaction6 of the parent hydrocarbon using butyllithium and can, moreover, be scaled up without difficulty. 

The pentafluoride has been mentioned (Section 17-C-2). The oxofluoride can be prepared in several ways (e.g., by action of C1F3 or BrF3 on Cr03) but the pure crystalline solid is obtained by the reaction ... 

Extraction-crystallization Extraction often is used in association with a crystallization operation. In the pharmaceutical and specialty chemical industries, extraction is used to recover a product compound (or remove impurities) from a crude reaction mixture, with subsequent crystallization of the product from the extract (or from the preextracted reaction mixture). In many of these applications, the product needs to be delivered as a pure crystalline solid, so crystallization is a necessary... 

At zero Kelvin (0 K), there is no energy available for a chemical to sample states. The absolute entropy, S, of a pure crystalline solid at 0 K is zero. Absolute entropy may be measured and calculated for different substances at different temperatures. 

To produce pure crystalline solids in an efficient manner, the designer of crystallization equipment takes steps to ensure the control of ... 

The thiocyanates 224 and 226 were obtained as analytically pure crystalline solids and the former was converted into l,2-benzisothiazolo[2,3-a]pyridinium perchlorate 225 (79TL3339 25% 90JCS(P1)2881 51%) and l,2-benzisothiazolo[4,3,2-/zzy] quinolinium perchlorate 227 (79TL3339 58% 90JCS(P 1)2881 85%) by reaction with bromine followed by perchloric acid (Scheme 79). 

Formation of Methylolureas. Under mildly alkaline conditions, both monomethylolurea and dimethylolurea are obtained in high yield and can be isolated as pure, crystalline solids [10]... 

Unexploded ordnance (UXO a.k.a. ordnance explosive wastes or OEW) represents a problem similar to that of packing facility discharges in that the explosive compounds released are relatively pure, crystalline solids. The environmental release of explosives from UXO would require either that the casing be broken, perhaps upon impact, or that not all of the explosive was burned upon detonation. In either case the source material would be dispersed in a spotty pattern. UXO is discussed in Part III. 

These classical characterization methods have been used even for 1,2-dioxetanes, which cannot be obtained as pure, crystalline solids, for example (lw).J6b... 

The homoleptic complex Co( -C3H5)3 (12) obeys the 18-electron rule (see Eighteen Electron Compound and could be expected to be stable by analogy to the abundant allyl chemistry of Ni. The compound has been prepared from Co(acac)3 and CsHsMgCl (equation 40) or, alternatively, from C0CI2 and CsHsMgCl/CsHsCl (equation 41) in about 50% yield. The latter method has also furnished a number of substituted allyl derivatives. Despite its favored electron count, complex (12) decomposes in solution around —60°C, and the pure crystalline solid decomposes spontaneously in an inert atmosphere at —20°C. The solid ignites spontaneously in air (cf. Co (allyl) 2 (ethylene) Li, Section 5.1.2). 

Since the last two terms in Eq. (11.74) can be calculated from heat capacities and heats of reaction, the only unknown quantity is ASS, the change in entropy of the reaction at 0 K. In 1906, Nernst suggested that for all chemical reactions involving pure crystalline solids, ASS is zero at the absolute zero the Nernst heat theorem. In 1913, Planck suggested that the reason that ASS is zero is that the entropy of each individual substance taking part in such a reaction is zero. It is clear that Planck s statement includes the Nernst theorem. 

As already stated, the entropy of a perfect, pure crystalline solid is zero at the absolute zero of temperature. Hence the value of G at T = 0 (termed GJ is equal to the value of // at T= 0, termed F/g (Fig. 8). Each polymorph yields an energy diagram similar to that of Fig. 6, although the values of G, H, and the slopes of the curves at a given temperature are expected to differ between different polymorphs. 

Ni(s) pure crystalline solid at 100°C under its own vapor pressure... 

Consider a pure crystalline solid. At absolute zero, the individual atoms or molecules in the lattice would be perfectly ordered and as well defined in position as they could be. Because none of them would have thermal motion, there is only one possible microstate. As a result, Equation 19.5 becomes S = k In W = k In 1 = 0. As the temperature is increased from absolute zero, the atoms or molecules in the crystal gain energy in the form of vibrational motion about their lattice positions. This means that the degrees of freedom and the entropy both increase. What happens to the entropy, however, as we continue to heat the crystal We consider this important question in the next section. 

---