The Solid State Crystals

An ideal crystal is a periodic array of atoms with a certain pattern (unit) repeating itself infinitely in space. The simplest crystal contains one atom in the repeating unit however, there are no limitations on the total number of atoms or molecules that can be part of this unit. 

A crystal can be represented as a lattice with an atom or group of atoms attached to every lattice point. This group of atoms is called the basis. The position of any point in the lattice can be generated from the three translation vectors, a i, a 2, a 3 such that the crystal looks the same from every aspect when viewed from the position r or from the point  

The lattice is a regular periodic array of points in space and the choice of translation vectors is not unique. A set of vectors, known as cell vectors, is termed primitive when the cell that they define has the smallest possible volume. 

Because of the regularity in a well-ordered solid, we can describe its structure, properties, and behaviors using mathematical models. That connects the study of the solid phase to physical chemistry We can model our understanding of the solid state. That s what physical chemistry does provide models for understanding matter. Because much of matter is in (or can be in) the solid state, a model for understanding the solid phase is useful, just as having a model for the gas phase is useful. This chapter introduces some of the concepts used to understand the solid phase. 

How do we determine these regular arrangements As with spectroscopy, we can use electromagnetic radiation as a probe. But rather than absorbing or emitting radiation, crystalline solids can diffract radiation under certain conditions. These conditions are dictated by the structure of the crystal, and there is a simple rule for relating the diffraction effect to the crystal s structure. 

We will also find that the type of crystal a certain compound makes is not necessarily arbitrary, that there is a recognizable energy of interaction between the components of certain crystals, that crystals are not perfect, and that society actually takes advantage of such imperfections in a big way. 

Unless otheiwise noted, all art on this page is Cengage Learning 2014. 

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Scheme 3 shows the details of the synthetic strategy adopted for the preparation of heteroleptic cis- and trans-complexes. Reaction of dichloro(p-cymene)ruthenium(II) dimer in ethanol solution at reflux temperature with 4,4,-dicarboxy-2.2 -bipyridine (L) resulted the pure mononuclear complex [Ru(cymene)ClL]Cl. In this step, the coordination of substituted bipyridine ligand to the ruthenium center takes place with cleavage of the doubly chloride-bridged structure of the dimeric starting material. The presence of three pyridine proton environments in the NMR spectrum is consistent with the symmetry seen in the solid-state crystal structure (Figure 24). 

Many distibines and dibismuthines have lighter colors in solutions or melts than in the solid state. Crystals of these thermochromic distibines or dibismuthines consist of linear chains of the dimetal compounds with short intermolecular metal-metal contacts. Delocalization of electrons along the chains is possibly responsible for the bathochromic shift between fluid and solid phases. Usually, the /raor-conformation is adopted by the tetraorganodimetal compounds in the solid state. (CF3)4As2 shows the /ra r-conformation also in the gas phase. Photoelectrospectroscopic measurements on Me4Sb2 revealed the presence of gauche- (12%) and trans- (88%) conformed in the gas phase.52... 

In the solid state, crystal packing forces should be considered since they can appreciably affect the crystal structure. For example, as previously mentioned, the replacement of the tetraethylammonium cation by the bis(triphenylphos-phine)iminium cation for the [ W2(CO)io(m2-H)] species dramatically changes the solid-state structure of the monoanion. For further insight into the possible influence of packing forces on the nature of the Cr-H-Cr bond in the [Cr2-(CO)io(M2-H)]- monoanion, a neutron diffraction study of the corresponding bis(triphenylphosphine)iminium salt, that has been shown by x-ray diffraction... 

The experimental observations in the case of 1,3-diphenyl-2-indanones 157 and 158 demonstrate convincingly that the stereochemical integrity of the two radical centers is maintained to high levels when reactions are carried out in the solid state. Crystals... 

The reaction of McsAl with methylamine proved to be very interesting. Two products were suggested by NMR. After considerable effort the solid-state crystal structures of the reaction products confirmed cis- and trani-stereoisomers of [Me2Al-N(H)Me]3. Both isomers contained nonplanar AI3N3 rings a chair conformation was observed for the c -[Mc2Al-N(H)Me]3 isomer, while a boat confirmation was shown for the trans-isomer. 

As predicted computationally, the trans-ACPC oligomers revealed a different type of helical conformation in both solution and the solid state. Crystal structures of the trans-ACPC hexamer and octamer displayed the 12-helical conformation (Figure 29).238 241 The spectral data of the ACPC oligomers in solution are consistent with the crystallographic observations. 

Structural and Physical Aspects. - The stability of the various conformers of the phosphines oxides (269)- 211) has received theoretical consideration. A new triclinic polymorph of triphenylphosphine sulfide has been structurally characterised, together with a related triclinic polymorph of triphenylphos-phine. Two reports of the solid state crystal structure of the phenolic phosphine oxide (272) have appeared. A crystallographic study has confirmed that the product of electrochemical oxidation of o-diphenylphosphinoben-zenethiol is the disulfide-bridged bis(phosphine oxide) (273). Solid-state structural studies of the dioxides (274), the (i )-(-I-)-isomer of (275), 1-hexynyl(diphenyl)phosphine oxide,tribenzylphosphine oxide, and tris(t-butyl)phosphine selenide," have also been reported. 

This book should serve both as a state-of-art overview of what s going on in frontier areas (theoretical evaluation of noncovalent interactions, hydrogen-bonded crystals, coordination networks, solid-state reactivity and reactions taking place in the solid state, crystal polymorphism, etc.) and as an entry point to the fundamental methods and techniques required for a successful investigation of crystalline solids (crystallography, solid-state NMR spectroscopy, atomic force microscopy etc.). 

Solid-state C NMR analysis of two fiusemide crystal forms revealed differences in chemical shifts [39]. Marked differences between solution and solid state appear for the carboxyl group and for pyrane ring carbons however, most likely the conformation in solution is not the same as those present in the solid-state crystal forms. 

Figure 12. X-ray crystal structure of /i-oclabromo-rneso-octamethyl-calix[4]pyrrole compound 10. The molecule adopts a chair-like flattened 1,2-alternate conformation in the solid state. Crystal structure originally published in Gale, P. A. Sessler, J. L. Allen, W. E. Tvermoes, N. A. Lynch, V. Chem, Commun. 1997, 665, Diagram produced using data from the Cambridge Crystallographic Database.

This results says that from above two free wave fimetions that onee considered previously as sin plays the role of the lower ground state, while that with eos is the excited one in the erystal configuration moreover, under the potential perturbation they separate in what is usually known in solid state theory as being the valence and conduction bands. We success therefore to construct this more realistic picture of the solid state crystals with the useful tool as stationary perturbation algorithm is. 

Kim YM, Lee SH, Lee HY, Roh YR (2003) Measurement of all the material properties of PMN-PT single erystal grown by the solid-state-crystal-growth (SSCG) method, IEEE Ultrasonics Symposium 1987-1990... 

Bile salts are chiral rigid molecules. They serve as important building blocks in the synthesis of both cyclic and acyclic hosts." " Natural bile acids are employed for enantioseparation of racemates of various classes of organic compounds by enantioselective inclusion complex-ation in the solid state." " " Crystals of bile acids contain... 

Kuroda et al. have demonstrated that co-crystal formation with n-benzo quinone can be mediated by molecular diffusion. Mixing, in the solid state crystals of p-benzoquinone with either 2,2 -biphenol or 4,4 -biphenol crystals rapidly results in the formation of highly coloured co-crystals, in which the components are held together through charge-transfer interactions and hydrogen bonds (Figure 8.10). 

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