What is a Crystal

In the preceding pages, we have defined the idea of a crystal by the three-dimensional periodicity of the atomic distribution the crystal is thus characterized by long-range order. This classical definition of the crystal is of fundamental importance and, because of this, is the central theme of the present work. However, it does not include all structures which are rigorously ordered, and represents only an idealization of real crystals whose order is never perfect. 

These are crystal structures which have perfect long-range order but which are only approximately periodic, incommensurate crystals on the one hand, and quasi-crystals on the other. 

The resulting structure is not strictly periodic in the b direction. The atomic positions of an incommensurate structure made up of several types of atom are 

The translations = i/a + yb + wc are those of the periodic structure whose atomic positions are following equation (1.22) q is the wave vector of the 

Quasi-crystals have macroscopic symmetries which are incompatible with a crystal lattice (Section 2.4.1). The first example was discovered in 1984 when the alloy AlMn is rapidly quenched, it forms quasi-crystals of icosahedral symmetry (Section 2.5.6). It is generally accepted that the structure of quasicrystals is derived from aperiodic space filling by several types of unit cell rather than one unique cell. In two-dimensional space, the best-known example is that of Penrose tiling. It is made up of two types of rhombus and has fivefold symmetry. We assume that the icosahedral structure of AlMn is derived from a three-dimensional stacking analogous to Penrose tiling. As is the case for incommensurate crystals, quasi-crystals can be described by perfectly periodic lattices in spaces of dimension higher than three in the case of AlMn, we require six-dimensional space. 

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The discovery of quasicrystals has led to a paradigm change in crystallography, expressed even in a new definition of what is a crystal by... 

Steurer W (2007) What is a crystal Introductory remarks to an ongoing discussion. Z Kristallogr 222 308-309... 

What is a crystal We need a mathematical description of a crystal in order to understand, even in a qualitative way, how crystals diffract X-rays and why we see the patterns we do ... 

Just what is a crystal A crystal is built up by a periodic repetition, in three dimensions, of an object or motif. A unit cell can be chosen to... 

What is a crystal The boundary between crystalline and amorphous (or liquid) matter is variable and poorly defined. However, translational symmetry, even if only imperfectly attained, is fundamental to the determination (Chapter 3), the description (Chapter 2) and the theoretical interpretation of solid state structures. It represents the principal characteristic of the majority of solids. For this reason, this is the general theme of the present work. 

From the above, it seems that crystals can be either periodic or aperiodic and that the conventional notion of a crystal pertains to the former variety. That is, the term crystal generally refers to a periodic crystal, unless otherwise stated (indeed, aperiodic crystals constitute a very small proportion of all crystals and their study is a far more specialized field). The interested reader is encouraged to peruse a series of short discussions on the topic what is a crystal in Zeitschrift fur Kristallografie. ... 

Fine glassware is mistakenly referred to as crystal because of it beauty and clarity—it is actually glass and not crystalline. This confusion came about because Baroque period artisans cut natural quartz crystals to make crystal chandeliers. Later, glassmakers were able to produce cut glass that rivaled the quartz crystals in beauty, but the term "crystal" remained. So what is a crystal ... 

A magnetic semiconductor thin him is made by doping ZnO with the 3d3 7 ion Co2+. The crystal hied splitting of the d orbitals in a tetrahedral site is opposite to that in an octahedral site, with the lower pair of levels labeled e and three upper orbitals labeled t2- (a) What is the spin state of the Co2+ ion in ZnO (b) What is the expected magnetic moment on the Co2+ ions (c) The spectrum has an absorption peak at 660 nm. What is the crystal held splitting of the Co2+ ion in the tetrahedral crystal held of ZnO ... 

Let us begin with the common statement (5.79) of the third law. If we inquire What is the meaning of a perfect crystal , the most direct answer appears to be It is a crystal with S0 = 0. This circular definition insures that (5.79) is impervious to falsification, but reduces the statement to a meaningless tautology. 

The High-Temperature and UV-Transmission Glasses. The last types of glass found in the laboratory are the quartz and UV-transmission glasses. From the many names that are used to describe this type of material, there may be confusion as to what to call it. It is often just called quartz, but this name can be deceiving because the term quartz could equally refer to the mineral quartz (which is a crystal) or amorphous silica (which is a glass). 

On the basis of Eq. (6.2.17) introduce E as the energy carried per particle moving under the influence of an appropriate force. Show that if reasonable estimates of E can be made, the Seebeck coefficient serves as a measure of chemical potential. What is the reference energy for this particular case What is a reasonable value of E for an electron in a crystal or for an ion in solution ... 

Examine sugar through a lens. What is its crystal form ... 

The NaCl lattice has the cubic unit cell shown in Fig. 10-7. KBr crystallizes in this lattice, (a) How many K ions and how many Br ions are in each unit cell (b) Assuming the additivity of ionic radii, what is a (f) Calculate the density of a perfect KBr crystal, (d) What minimum value of r+/r. is needed to prevent anion-anion contact in this structure ... 

For example, the polycyclic disulfide shown in Fig. 7 was calculated to have the structure (a), which is what is found crystal-lographically (Wahl et al., 1975) rather than the alternative structure (b). Since it is known that the torsional angle preferred about the... 

In the context of crystal engineering strategies a frequently asked question [30] is given the molecular structure of an organic substance, what is its crystal... 

Strength deserves a more subtle comment, because it brings about the definition of the hydrogen bond. What is a hydrogen bond The answer to this question is controversial and depends on the objective of the investigator. For the purpose of crystal engineering, however, Etter s elaboration of the Linus Pauling definition of ahon is probably the most appropriate ... 

When applied to crystalline solids, the paradigm shift leads directly from supramolecular chemistry to crystal engineering. What is a (molecular) crystal if not an organized entity of higher complexity held together by in-termolecular forces (J.M. Lehn) Who can deny that the collective properties of such a giant supermolecule are the result of the convolution of intermolecular non-covalent bonding between molecular/ionic components with the periodicity of the crystal. 

Erwin Schrodinger (1887-1961), one of the founders of quantum mechanics, in his famous essay [37] on What is Life based on lectures delivered in Dublin in 1943, at the height of the war (by the way, in our opinion — a must reading for anyone interested in biological physics), coined the special term aperiodic crystal. This is intentionally an oxymoron. Aperiodic cr3 tal is a crystal in the sense that every atom or... 

What are liquid crystals How do lyotropic crystalline arrays differ from thermotropic What are mesophases How do smectic liquid crystalline arrangements differ from nematic What is a mesogen ... 

But what is a physical sense of parameter Tj The answer is given by a theorem related to a more general question, whether true one- or two- dimensional crystals... 

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