Amorphous solids defined

Describe the difference between ciystalline and amorphous solids. Define and describe the relationships between unit cells, crystal lattice, lattice vectors, and lattice points. (Section 12.2)... 

Defining order in an amorphous solid is problematic at best. There are several qualitative concepts that can be used to describe disorder [7]. In figure Al.3.28 a perfect crystal is illustrated. A simple fonn of disorder involves crystals containing more than one type of atom. Suppose one considers an alloy consisting of two different atoms (A and B). In an ordered crystal one might consider each A surrounded by B and vice versa. 

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... 

A crystalline solid is a solid in which the atoms, ions, or molecules lie in an orderly array (Fig. 5.16). A crystalline solid has long-range order. An amorphous solid is one in which the atoms, ions, or molecules lie in a random jumble, as in butter, rubber, and glass (Fig. 5.17). An amorphous solid has a structure like that of a frozen instant in the life of a liquid, with only short-range order. Crystalline solids typically have flat, well-defined planar surfaces called crystal faces, which lie at definite angles to one another. These faces are formed by orderly layers of atoms (Box 5.1). Amorphous solids do not have well-defined faces unless they have been molded or cut. 

This idea that the heat was transfered by a random walk was used early on by Einstein [21] to calculate the thermal conductance of crystals, but, of course, he obtained numbers much lower than those measured in the experiment. As we now know, crystals at low enough T support well-defined quasiparticles—the phonons—which happen to carry heat at these temperatures. Ironically, Einstein never tried his model on the amorphous solids, where it would be applicable in the / fp/X I regime. 

In the molten state polymers are viscoelastic that is they exhibit properties that are a combination of viscous and elastic components. The viscoelastic properties of molten polymers are non-Newtonian, i.e., their measured properties change as a function of the rate at which they are probed. (We discussed the non-Newtonian behavior of molten polymers in Chapter 6.) Thus, if we wait long enough, a lump of molten polyethylene will spread out under its own weight, i.e., it behaves as a viscous liquid under conditions of slow flow. However, if we take the same lump of molten polymer and throw it against a solid surface it will bounce, i.e., it behaves as an elastic solid under conditions of high speed deformation. As a molten polymer cools, the thermal agitation of its molecules decreases, which reduces its free volume. The net result is an increase in its viscosity, while the elastic component of its behavior becomes more prominent. At some temperature it ceases to behave primarily as a viscous liquid and takes on the properties of a rubbery amorphous solid. There is no well defined demarcation between a polymer in its molten and rubbery amorphous states. 

At the macroscopic level a solid is defined as a substance that has both a definite volume and a definite shape. At the microscopic level, solids may be one of two types—amorphous or crystalline. Amorphous solids lack extensive ordering of the particles. There is a lack of regularity of the structure. There may be small regions of order separated by large areas of disordered particles. They resemble liquids more than solids in this characteristic. Amorphous solids have no distinct, melting point. They simply get softer and softer as the temperature rises, leading to a decrease in viscosity. Glass, rubber, and charcoal are examples of amorphous solids. 

Most recently, kinetic data from the melt have been applied to the amorphous solid phase. This is based on the well-accepted assumptions that the chemistry in the melt is the same as in the latter phase and that all of the end group reactions take place in the latter phase [11, 21, 35], The activation energy AE, and the frequency factor A, defined in the following equation ... 

In amorphous solids there is a considerable disorder and it is impossible to give a description of their structure comparable to that applicable to crystals. In a crystal indeed the identification of all the atoms in the unit cell, at least in principle, is possible with a precise determination of their coordinates. For a glass, only a statistical description may be obtained to this end different experimental techniques are useful and often complementary to each other. Especially important are the methods based on diffraction experiments only these will be briefly mentioned here. The diffraction pattern of an amorphous alloy does not show sharp diffraction peaks as for crystalline materials but only a few broadened peaks. Much more limited information can thus be extracted and only a statistical description of the structure may be obtained. The so-called radial distribution function is defined as ... 

The six sections following the overview chapter deal with aspects of selective oxidation that range from theories and concepts to state-of-the-art engineering applications. Several chapters describe the synthesis, characterization, and performance of potentially attractive new catalytic materials. These catalysts range from single crystals with well-defined crystal faces to highly dispersed or amorphous solids. Most of the actual catalytic reactions studied involve the oxidation of hydrocarbons in the range from to C. ... 

Bulk crystalline or amorphous solid-state materials whose conductivity is intermediate between metals and insulators and whose resistance decreases with increasing temperature. The valance band of an undoped semiconductor is completely filled, whereas its conduction band is empty. The energy difference between the valence and conduction bands (the band-gap) defines a semiconductor (see Fig. 95). 

Further, neither the initial solid state nor the final solution state are well-defined. The initial state is a heterogeneous amorphous solid. The distribution of the fractions A and B depends upon the previous history of the sample, such as manner of extraction, precipitation, solvent... 

Fig. 2. Time—temperature—transformation (TTT) diagram where A represents the cooling curve necessary to bypass crystallization. The C-shaped curve separates the amorphous solid region from the crystalline solid region. Terms are defined in text.

Seldom in the study of heterogeneous catalysis does it prove possible to (I) specify precisely the concentration and nature of the active sites, (2) test whether these sites are of comparable strength and are distributed in a spatially and chemically well-defined manner, and (3) explore the structural and mechanistic features of the system using a wide range of complementary techniques, many of them in situ. Even rarer are situations in which both the access to the active sites and the shape of the reactants may be systematically and subtly varied, so that one is able to compare the performance of the active site in a crystalline environment with an essentially identical one embedded in an amorphous solid. 

An amorphous solid has some amount of short-range order but no long-range order. It has an approximately definite volume but no defined shape, as well as low diffusional mobility within the structure. 

The change in the physical mechanism of deformation from elasticity, viscoelasticity to plasticity depends on the time scales in which the amorphous solid is measured and relaxed. The dependene of stress-strain relationship on relaxation time is conceptualized in Fig. 18, where the yield stress is defined. The yield occurs when the product of the relaxation time and the applied strain rate reaches a constant value [28, 38, 39]. Using Eq. (50) and replacing yield stress components ... 

C-Phycocyanin is abundant in blue-green algae. Nearly 99% deuterated samples of this phycobiliprotein were isolated from the cyanobacteria that were grown in perdeuterated cultures [46] (99% pure D2O) at Argonne National Laboratory. This process yielded deuterated C-phycocyanin proteins (d-CPC) that had virtually all of the H—C bonds replaced by H—C bonds. One can obtain a lyophilized sample that is similar to amorphous solids as determined by neutron diffraction [43]. As it has been defined in previous papers [47-49], the level of hydration h = 0.5 corresponds to 100% hydration of C-phycocyanin, which leads to a coverage of about 1.5 monolayers of water molecules on the surface of the protein [50]. 

Solubility and speciation. Minimum requirements for reliable thermodynamic solubility studies include (i) solution equilibrium conditions (ii) effective and complete phase separation (iii) well-defined solid phases and (iv) knowledge of the speciation/oxidation state of the soluble species at equilibrium. Ideally, radionuclide solubilities should be measured in both oversaturation experiments, in which radionuclides are added to a solution untU a solid precipitates, and undersaturation experiments, in which a radionuchde solid is dissolved in aqueous media. Due to the difference in solubilities of crystalline versus amorphous solids and different kinetics of dissolution, precipitation, and recrystalhzation, the results of these two types of experiments rarely agree. In some experiments, the maximum concentrahon of the radionuchde source term in specific water is of interest, so the sohd that is used may be SF or nuclear waste glass rather than a pure radionuclide solid phase. 

Although real crystals display beautiful symmetries to the eye, they are not perfect. As a practical matter, it is impossible to rid a crystal of all impurities or to ensure that it contains perfect periodic ordering. So, we describe real crystals as perfect crystals with defects, and define means to characterize these defects. If so many defects are present that crystalline order is destroyed, we describe the material as an amorphous solid. 

Some noncrystalline solids, called amorphous solids, have no well-defined, ordered structure. Examples include rubber, some kinds of plastics, and amorphous sulfur. 

A crystal may be defined as a solid composed of atoms arranged in a pattern periodic in three dimensions. As such, crystals differ in a fundamental way from gases and liquids because the atomic arrangements in the latter do not possess the essential requirement of periodicity. Not all solids are crystalline, however some are amorphous, like glass, and do not have any regular interior arrangement of atoms. There is, in fact, no essential difference between an amorphous solid and a liquid, and the former is often referred to as an undercooled liquid. ... 

Some properties are more clearly defined than others. For example, solubility is defined as the amount of solid in equilibrium with the solvent. Solubility can affect the capacity of the crystallization process, as well as its ability to reject undesired compounds and minimize loss in the mother liquor. In addition, solubility varies widely from compound to compound or solvent to solvent. On the other hand, there are properties that are much less well characterized or understood. For example, the mechanism and condition for the formation of oil or amorphous solid remain unclear. The composition of oil and amorphous solid can be variable, and certainly can contain a much higher level of impurities than that in the crystalline solid, which leads to a real purification challenge. In addition, oil or amorphous solid generally is less stable and can create critical issues in drug formulation and storage stability. 

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