Crystalline solids imperfections

Clearly, the most prominent imperfection in a crystalline solid is its surface, since it represents a cutoff of the lattice periodicity. The surface can be defined as constituting one atomic-molecular layer. This definition is sometimes not particularly useful, however. lu certaiu cases the system or property of iuterest requires that additioual layers be cousidered as the surface. ... 

Tills concept of a liquid as an imperfect crystal requires that the molecules in a liquid arc packed sufficiently loosely for comparatively free movement, i.c the energy required to move a molecule from a lailice site to a vacant space is not large compared with thermal energies. Under these conditions, shear flow of the liquid resembles closely the high temperature creep ol crystalline solids. A number of theories of the liquid slate have this concept as their starting point. 

Kroger, F.A. and Vink, H., Relations between the concentrations of imperfections in crystalline solids, Solid State Phys. 3, 1956, 307. 

The absolute zero of temperature cannot be reached experimentally (although Cp for a few solids have - exceptionally - been measured as low as 0.05 K). Crystalline solids are sometimes not entirely devoid of lattice imperfections. 

F.A. Kroger, The Chemistry of Imperfect Crystals. Imperfection Chemistry of Crystalline Solids, vol. 2, 2nd edn. (North-Holland, Amsterdam, 1973)... 

The early literature contains many references to the presence in production clinkers of glass, often in substantial proportions. This view was based partly on observations by light microscopy however, this method cannot distinguish glass from crystalline solids of the cubic system unless crystals with distinct faces have been formed, nor from crystalline materials of any kind if the crystals are below a certain size. It was also found that if clinkers believed to contain glass were annealed, their heats of solution in an acid medium increased, and this method was used to obtain approximate estimates of the glass content (LI 3). This evidence, too, is inconclusive, because the same effect would arise from the presence of small or structurally imperfect crystals. 

There are four main classifications of crystalline imperfections that exist in crystalline solids ... 

Kroger, F.A. and Vink, H.J., Relationships between the concentration of imperfections in crystalline solids, in Solid State Physics Advances in Research and Applications, Vol. 3, Seitz, R, Turnbull, T., Eds. Academic Press, New York, 1957, p. 307. 

Since our surroundings are three-dimensional, we tend to assume that crystals are formed by periodic arrangements of atoms or molecules in three dimensions. However, many crystals are periodic only in two, or even in one dimension, and some do not have periodic structure at all, e.g. solids with incommensurately modulated structures, certain polymers, and quasicrystals. Materials may assume states that are intermediate between those of a crystalline solid and a liquid, and they are called liquid crystals. Hence, in real crystals, periodicity and/or order extends over a shorter or longer range, which is a function of the nature of the material and conditions under which it was crystallized. Structures of real crystals, e.g. imperfections, distortions, defects and impurities, are subjects of separate disciplines, and symmetry concepts considered below assume an ideal crystal with perfect periodicity. ... 

The short-term potential for solid solution formation is low for minerals with small solubility products, such as aluminum oxides and aluminosilicates, because spontaneous dissolution and recrystallization is very slow in these minerals. Without recrystallization, trace metals cannot be incorporated into the mineral structures. Movement of metal ions into these mineral crystals by solid diffusion is not possible on the time scale of adsorption experiments ionic diffusion into most crystalline solids is negligibly slow at all but extremely high temperatures. Nevertheless, metals could diffuse into imperfect solids along interstices, pores, or other structural defects. 

All the foregoing discussion of crystalline solids has dealt with their perfect or ideal structures. Such perfect structures are seldom if ever found in real substances and, while low levels of imperfections have only small effects2 on their chemistry, the physical (i.e., electrical, magnetic, optical and mechanical) properties of many substances are often crucially affected by their imperfections. It is, therefore, appropriate to devote a few paragraphs to describing the main types of imperfection, or defect, in real crystalline solids. We shall not, however, discuss the purely mechanical imperfections such as mosaic structure, stacking faults, and dislocations, all of which are some sort of mismatch between lattice layers. 

As obtained from brain-tissue lecithin is a colorless or faintly yellowish, imperfectly crystalline solid, or sometimes of a waxy consistency. It is very hygroscopic. It does not dissolve in HaO, in which, however, it swells up and forms a mass like starch-paste. It dissolves in alcohol or ether, very sparingly in the cold, hut readily under the influence of heat. It dissolves in chloroform and in benzene. Lecithin is very prone to decomposition, particularly at slightly elevated temperatures. Its chlorid combines with PtCh to form an insoluble yellowish chloroplatinate. 

Diamido-triphenylmethane — CH,(C Hs)(CgH4,N H])3— is produced by the action of anilin chlorid and benzoic aldehyde upon each other in the presence of ZnClj. The salts of this base are blue, and are decomposed by alkalies with liberation of the base, which is a yellow, imperfectly crystalline solid, insoluble in water, soluble in benzene and in alcohol. 

Kroger, F. A., "Chemistry of Imperfect Crystals -Volume 1, Preparation, Purification, Crystal Growth, and Phase Theory Volume 2, Imperfection Chemistry of Crystalline Solids Volume 3, Applications of Imperfection Chemistry Solid State Reactions and Electrochemistry," North Holland-American Elsevier, New York (1974). 

Kroger, RA. and Vink, H.J. (1956) Relations between the concentrations of imperfections in crystalline solids, Solid State Phys. 3, 307. The original proposal of the notation that is now universally used to describe charged point defects. This is an invaluable paper when you have time to study it. The official notation is given in the lUPAC Red Book on the Nomenclature of Inorganic Chemistry, Chapter 1-6. Smyth, D.M. The Defect Chemistry of Metal Oxides, Oxford University Efi-ess, Oxford 2000. Clear and at the right level. 

Kroger, F. A., The Chemistry of Imperfect Crystals 2nd revised edition) Vol. 2. Imperfaction Chemistry of Crystalline Solids, North-Holland Publ., Amsterdam, 1974. 

A solid surface is intrinsically an imperfection of a crystalline solid by destroying the three-dimensional (3D) periodicity of the structure. That is, the unit cell of a crystal is usually chosen such that two vectors are parallel to the surface and the third vector is normal or oblique to the surface. Since there is no periodicity in the direction normal or oblique on the surface, a surface has a 2D periodicity that is parallel to the surface. By considering the symmetry properties of 2D lattices, one obtains the possible five 2D Bravais lattices shown in Figure 2. The combination of these five Bravais lattices with the 10 possible point groups leads to the possible 17 2D space groups. The symmetry of the surface is described by one of these 17 2D symmetry groups. 

The driving forces provide a motivation for sintering but the actual occurrence of sintering requires transport of matter, which in crystalline solids occurs by a process of diffusion involving atoms, ions, or molecules. Crystalline solids are not ideal in structure. At any temperature they contain various imperfections... 

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