Crystal proportion

A crystal material is excited by the force imposed on it by an internal I v mounted mass. A voltage is produced by the crystal proportional to accel eration. This voltage is then amplified by a charge amplifier type signal conditioner from whence the signal can be transmitted long distance. (1.000 feet is not uncommon) to the monitor/readout unit. It is calibrated in terms of gravitational units (g), which are proportional to force. Force is ttnc of the most reliable indicators of equipment distress. 

The piezo-electric effect of deformations of quartz under alternating current (at a frequency in the order of 10 MHz) is used by coating the crystal with a selectively binding substance, e. g. an antibody. When exposed to the antigen, an antibody-antigen complex will be formed on the surface and shift the resonance frequency of the crystal proportionally to the mass increment which is, in turn, proportional to the antigen concentration. A similar approach is used with surface acoustic wave detectors [142] or with the surface plasmon resonance technology (BIAcore, Pharmacia). 

FAs in a crystal can induce a local deformation of the lattice. When they are substitutional, this is caused by the difference between their atomic radii and those of the atoms they replace and also by their chemical affinity with the surrounding atoms. According to Vegard s law,1 substitutional atoms having a smaller (larger) atomic radius than the atom they replace should produce a uniform lattice contraction (expansion) of the crystal proportional to their concentration. With reference to the unperturbed lattice parameter ao of cubic crystal, the change Aa of the lattice parameter produced by a concentration Nf of FAs can be expressed as ... 

We have seen that the intensities of diffraction are proportional to the Fourier transfomi of the Patterson fimction, a self-convolution of the scattering matter and that, for a crystal, the Patterson fimction is periodic in tln-ee dimensions. Because the intensity is a positive, real number, the Patterson fimction is not dependent on phase and it can be computed directly from the data. The squared stmcture amplitude is... 

Here is the original, many-body potential energy fiinction, while Vq is a sum of single-particle spring potentials proportional to As X —> 0 the system becomes a perfect Einstein crystal, whose free energy... 

The oxime is freely soluble in water and in most organic liquids. Recrystallise the crude dry product from a minimum of 60-80 petrol or (less suitably) cyclohexane for this purpose first determine approximately, by means of a small-scale test-tube experiment, the minimum proportion of the hot solvent required to dissolve the oxime from about 0-5 g. of the crude material. Then place the bulk of the crude product in a small (100 ml.) round-bottomed or conical flask fitted with a reflux water-condenser, add the required amount of the solvent and boil the mixture on a water-bath. Then turn out the gas, and quickly filter the hot mixture through a fluted filter-paper into a conical flask the sodium chloride remains on the filter, whilst the filtrate on cooling in ice-water deposits the acetoxime as colourless crystals. These, when filtered anddried (either by pressing between drying-paper or by placing in an atmospheric desiccator) have m.p. 60 . Acetoxime sublimes rather readily when exposed to the air, and rapidly when warmed or when placed in a vacuum. Hence the necessity for an atmospheric desiccator for drying purposes. 

The theory underlying the removal of impurities by crystaUisation may be understood from the following considerations. It is assumed that the impurities are present in comparatively small proportion—usually less than 5 per cent, of the whole. Let the pure substance be denoted by A and the impurities by B, and let the proportion of the latter be assumed to be 5 per cent. In most instances the solubilities of A (SJ and of B (/Sb) are different in a particular solvent the influence of each compound upon the solubility of the other will be neglected. Two cases will arise for an3 particular solvent (i) the impurity is more soluble than the compound which is being purified (/Sg > SA and (ii) the impurity is less soluble than the compound Sg < S ). It is evident that in case (i) several recrystallisations will give a pure sample of A, and B will remain in the mother liquors. Case (ii) can be more clearly illustrated by a specific example. Let us assume that the solubility of A and 5 in a given solvent at the temperature of the laboratory (15°) are 10 g. and 3 g. per 100 ml. of solvent respectively. If 50 g. of the crude material (containing 47 5 g. of A and 2-5 g. of B) are dissolved in 100 ml. of the hot solvent and the solution allowed to cool to 15°, the mother liquor will contain 10 g. of A and 2-5 g. (i.e., the whole) of B 37-5 g. of pure crystals of A will be obtained. 

By cooling the solution in a freezing mixture (ice and salt, ice and calcium chloride, or solid carbon dioxide and ether). It must be borne in mind that the rate of crystal formation is inversely proportional to the temperature cooling to very low temperatures may render the mass... 

In Section 1.3 it was noted that the energy of adsorption even for a perfect crystal differs from one face to another. An actual specimen of solid will tend to be microcrystalline, and the proportion of the various faces exposed will depend not only on the lattice itself but also on the crystal habit this may well vary amongst the crystallites, since it is highly sensitive to the conditions prevailing during the preparation of the specimen. Thus the overall behaviour of the solid as an adsorbent will be determined not only by its chemical nature but also by the way in which it was prepared. 

The state of the surface is now best considered in terms of distribution of site energies, each of the minima of the kind indicated in Fig. 1.7 being regarded as an adsorption site. The distribution function is defined as the number of sites for which the interaction potential lies between and (rpo + d o)> various forms of this function have been proposed from time to time. One might expect the form ofto fio derivable from measurements of the change in the heat of adsorption with the amount adsorbed. In practice the situation is complicated by the interaction of the adsorbed molecules with each other to an extent depending on their mean distance of separation, and also by the fact that the exact proportion of the different crystal faces exposed is usually unknown. It is rarely possible, therefore, to formulate the distribution function for a given solid except very approximately. 

The number and kind of defects in a given specimen, as well as the crystal habit and with it the proportion of different crystal faces exposed, will in general depend in considerable degree on the details of preparation. The production of a standard sample of a given chemical substance, having reproducible adsorptive behaviour, remains therefore as much an art as a science. 

The measurement of mass using a quartz crystal microbalance is based on the piezoelectric effect.When a piezoelectric material, such as a quartz crystal, experiences a mechanical stress, it generates an electrical potential whose magnitude is proportional to the applied stress. Gonversely, when an alternating electrical field is... 

Ruby Laser. Ruby (essentially alumina) owes its well-known color to the presence of very small proportions of chromium ions (Cr +) distributed through it. Ruby lasers do not use natural rubies because of the imperfections they contain. Instead, synthetic single crystals of chromium... 

Figure 8.28 shows how the X-rays fall on the solid or liquid sample which then emits X-ray fluorescence in the region 0.2-20 A. The fluorescence is dispersed by a flat crystal, often of lithium fluoride, which acts as a diffraction grating (rather like the quartz crystal in the X-ray monochromator in Figure 8.3). The fluorescence may be detected by a scintillation counter, a semiconductor detector or a gas flow proportional detector in which the X-rays ionize a gas such as argon and the resulting ions are counted.

Solubility Properties. Fats and oils are characterized by virtually complete lack of miscibility with water. However, they are miscible in all proportions with many nonpolar organic solvents. Tme solubiHty depends on the thermal properties of the solute and solvent and the relative attractive forces between like and unlike molecules. Ideal solubiHties can be calculated from thermal properties. Most real solutions of fats and oils in organic solvents show positive deviation from ideaHty, particularly at higher concentrations. Determination of solubiHties of components of fat and oil mixtures is critical when designing separations of mixtures by fractional crystallization. 

The glass-ceramic phase assemblage, ie, the types of crystals and the proportion of crystals to glass, is responsible for many of the physical and chemical properties, such as thermal and electrical characteristics, chemical durabiUty, elastic modulus, and hardness. In many cases these properties are additive for example, a phase assemblage comprising high and low expansion crystals has a bulk thermal expansion proportional to the amounts of each of these crystals. 

Lead zirconate [12060-01 -4] PbZrO, mol wt 346.41, has two colorless crystal stmctures a cubic perovskite form above 230°C (Curie point) and a pseudotetragonal or orthorhombic form below 230°C. It is insoluble in water and aqueous alkaUes, but soluble in strong mineral acids. Lead zirconate is usually prepared by heating together the oxides of lead and zirconium in the proper proportion. It readily forms soHd solutions with other compounds with the ABO stmcture, such as barium zirconate or lead titanate. Mixed lead titanate-zirconates have particularly high piezoelectric properties. They are used in high power acoustic-radiating transducers, hydrophones, and specialty instmments (146). 

Positional Distribution Function and Order Parameter. In addition to orientational order, some Hquid crystals possess positional order in that a snapshot at any time reveals that there are parallel planes which possess a higher density of molecular centers than the spaces between these planes. If the normal to these planes is defined as the -axis, then a positional distribution function, can be defined, where is proportional to the... 

Chiral nematic Hquid crystals are sometimes referred to as spontaneously twisted nematics, and hence a special case of the nematic phase. The essential requirement for the chiral nematic stmcture is a chiral center that acts to bias the director of the Hquid crystal with a spontaneous cumulative twist. An ordinary nematic Hquid crystal can be converted into a chiral nematic by adding an optically active compound (4). In many cases the inverse of the pitch is directiy proportional to the molar concentration of the optically active compound. Racemic mixtures (1 1 mixtures of both isomers) of optically active mesogens form nematic rather than chiral nematic phases. Because of their twist encumbrance, chiral nematic Hquid crystals generally are more viscous than nematics (6). 

---