Amorphous, defined

Pressure-area isotherms for many polymer films lack the well-defined phase regions shown in Fig. IV-16 such films give the appearance of being rather amorphous and plastic in nature. At low pressures, non-ideal-gas behavior is approached as seen in Fig. XV-1 for polyfmethyl acrylate) (PMA). The limiting slope is given by a viiial equation... 

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... 

The dissipation factor (the ratio of the energy dissipated to the energy stored per cycle) is affected by the frequency, temperature, crystallinity, and void content of the fabricated stmcture. At certain temperatures and frequencies, the crystalline and amorphous regions become resonant. Because of the molecular vibrations, appHed electrical energy is lost by internal friction within the polymer which results in an increase in the dissipation factor. The dissipation factor peaks for these resins correspond to well-defined transitions, but the magnitude of the variation is minor as compared to other polymers. The low temperature transition at —97° C causes the only meaningful dissipation factor peak. The dissipation factor has a maximum of 10 —10 Hz at RT at high crystallinity (93%) the peak at 10 —10 Hz is absent. 

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

According to a widely accepted concept, lignin [8068-00-6] may be defined as an amorphous, polyphenoHc material arising from enzymatic dehydrogenative polymerization of three phenylpropanoid monomers, namely, coniferyl alcohol [485-35-5] (2), sinapyl alcohol [537-35-7] (3), and /)-coumaryl alcohol (1). 

A similar effect occurs in highly chiral nematic Hquid crystals. In a narrow temperature range (seldom wider than 1°C) between the chiral nematic phase and the isotropic Hquid phase, up to three phases are stable in which a cubic lattice of defects (where the director is not defined) exist in a compHcated, orientationaHy ordered twisted stmcture (11). Again, the introduction of these defects allows the bulk of the Hquid crystal to adopt a chiral stmcture which is energetically more favorable than both the chiral nematic and isotropic phases. The distance between defects is hundreds of nanometers, so these phases reflect light just as crystals reflect x-rays. They are called the blue phases because the first phases of this type observed reflected light in the blue part of the spectmm. The arrangement of defects possesses body-centered cubic symmetry for one blue phase, simple cubic symmetry for another blue phase, and seems to be amorphous for a third blue phase. 

The only clearly defined crystalline compositions are three forms of phosphoric acid and hemihydrate, pyrophosphoric acid, and crystalline P O q. The phosphoric acids obtained in highly concentrated solutions or by mixing phosphoric acid with phosphoms pentoxide are members of a continuous series of amorphous (excluding [Y OO]) condensed phosphoric acid mixtures. Mixtures having more than 86% P2O5 contain some cyclic metaphosphoric... 

Condensed phosphates are derived by dehydration of acid orthophosphates. The resulting polymeric stmctures are based on a backbone of P—O—P linkages where PO tetrahedra are joined by shared oxygen atoms. The range of materials within this classification is extremely broad, extending from the simple diphosphate, also known as pyrophosphate, to indefinitely long-chain polyphosphates and ultraphosphates (see Table 1). Both weU-defined crystalline and amorphous materials occur among the condensed phosphates. 

As is to be expected, inherent disorder has an effect on electronic and optical properties of amorphous semiconductors providing for distinct differences between them and the crystalline semiconductors. The inherent disorder provides for localized as well as nonlocalized states within the same band such that a critical energy, can be defined by distinguishing the two types of states (4). At E = E, the mean free path of the electron is on the order of the interatomic distance and the wave function fluctuates randomly such that the quantum number, k, is no longer vaHd. For E < E the wave functions are localized and for E > E they are nonlocalized. For E > E the motion of the electron is diffusive and the extended state mobiHty is approximately 10 cm /sV. For U <, conduction takes place by hopping from one localized site to the next. Hence, at U =, )J. goes through a... 

E — E is defined as the fl-gap which leads to the existence of semiconducting behavior in amorphous materials. 

Amorphous silica, ie, silicon dioxide [7631-86-9] Si02, does not have a crystalline stmcture as defined by x-ray diffraction measurements. Amorphous silica, which can be naturally occurring or synthetic, can be either surface-hydrated or anhydrous. Synthetic amorphous silica can be broadly divided into two categories of stable materials (1) vitreous silica or glass (qv), which is made by fusing quart2 at temperatures greater than approximately 1700°C (see Silica, vitreous silica), and microamorphous silica, which is discussed herein. 

Cane sugar is generally available ia one of two forms crystalline solid or aqueous solution, and occasionally ia an amorphous or microcrystalline glassy form. Microcrystalline is here defined as crystals too small to show stmcture on x-ray diffraction. The melting poiat of sucrose (anhydrous) is usually stated as 186°C, although, because this property depends on the purity of the sucrose crystal, values up to 192°C have been reported. Sucrose crystallines as an anhydrous, monoclinic crystal, belonging to space group P2 (2). 

As-polymerized PVDC does not have a well-defined glass-transition temperature because of its high crystallinity. However, a sample can be melted at 210°C and quenched rapidly to an amorphous state at <—20°C. The amorphous polymer has a glass-transition temperature of — 17°C as shown by dilatometry (70). Glass-transition temperature values of —19 to — 11°C, depending on both method of measurement and sample preparation, have been determined. 

Physical properties of a-crystaUine metallic arsenic are given in Table 1. The properties of P-arsenic are not completely defined. The density of P-arsenic is 4700 kg/m it transforms from the amorphous to the crystalline form at 280 °C and the electrical resistivity is reported to be 107 H-cm. 

Hydroxide. Freshly precipitated cerous hydroxide [15785-09-8] Ce(OH)2, is readily oxidized by air or oxygenated water, through poorly defined violet-tinged mixed valence intermediates, to the tetravalent buff colored ceric hydroxide [12014-56-17, Ce(OH)4. The precipitate, which can prove difficult to filter, is amorphous and on drying converts to hydrated ceric oxide, Ce02 2H20. This commercial material, cerium hydrate [23322-64-7] behaves essentially as a reactive cerium oxide. 

In the case of an amorphous polymer the glass transition temperature will define whether or not a material is glass-like or rubbery at a given temperature. If, however, the polymer will crystallise, rubbery behaviour may be limited since the orderly arrangement of molecules in the crystalline structure by necessity limits the chain mobility. In these circumstances the transition temperature is of less consequence in assessing the physical properties of the polymer. 

The classification of amorphous carbon films according to carbon bond type and hydrogen content can be represented in a triangular diagram, Fig. 6 [e.g., 70]. The comers at the base of the triangle correspond to graphite (100% sp carbon) and diamond (100% sp carbon). The apex represents 100% H, but the upper limit for formation of solid films is defined by the tie line between the compositions of polyethene, -(CH2) -, and polyethyne, -(CH) -. 

It may occasion surprise that an amorphous material has well-defined energy bands when it has no lattice planes, but as Street s book points out, the silicon atoms have the same tetrahedral local order as crystalline silicon, with a bond angle variation of (only) about 10% and a much smaller bond length disorder . Recent research indicates that if enough hydrogen is incorporated in a-silicon, it transforms from amorphous to microcrystalline, and that the best properties are achieved just as the material teeters on the edge of this transition. It quite often happens in MSE that materials are at their best when they are close to a state of instability. 

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