Crystal constant

OH- (g). The heat of formation of OH (g) can be estimated by the method of lattice energies. Using the approximate formula for the lattice energy, with rough estimates of the crystal constants of NaOH, KOH, and RbOH from their densities and molecular weights, we have calculated from the data on these substances, for OH- (g), Qf= — 64, —58, and —56, respectively. Lederle1 calculated a value of —81. 

Estimating the film constant from the crystal constant involves a complicated problem of the composite system. In general the film constant e is expressed in an abbreviated form by... 

The nickel single crystal(MARZ grade 99.995%, supplied by MRC) was metallographically polished down to 1 pm diamond paste, then chemically polished as described by Graham and Cohen (15). Transmission x-ray diffraction measurements confirmed the (100) direction of. the face to 0,0.5°. The specimen, of area o>2 cm2, was spot-welded to a nickel rod fastened to the specimen manipulator. It could be heated by electron bombardment or radiativity and cooled to vloO K through the nickel rod and a LN -cooled copper braid. A control unit held the crystal temperature (via a chromel-alumel thermocouple spot-welded to the back of the crystal) constant to within 1 K. 

O Sullivan discussed the influence of particle size on quantitative Raman monitoring in slurries [40], A system of P-form D-mannitol in toluene in the presence of sucrose was studied. It was found that although keeping the number and size of mannitol crystals constant the measured Raman signal varied with different particle size of the sucrose. These results show that particle size must always be taken into consideration in quantitative measurements and a linear relationship can not be taken for granted. 

Metallic bonds are generally weaker than either covalent or ionic bonds, which explains why metallically bonded minerals (true metals), like silver, gold, and copper, can be worked— beaten into flat sheets, or drawn into thin wires. In metallic bonds, electrons move about the crystal constantly flowing between adjacent atoms, redistributing their charge. Because of this flow of electrons, true metals are also good electrical conductors. 

Another example in a different system would be the following Suppose we have a semicrystalline material and there are chains which connect two crystalline domains of that material with each other. There is no reason why the lengths of those chains which are in the amorphous area between the crystalline site should be the same. There will always be a distribution of chain lengths. Then if one keeps one crystal constant and moves the other as soon as the stress is greater than the bond strength of the shortest chain, a rupture of this chain will occur. As the distance between the crystals increases, more and more chains will break. Eventually, a crack will form which may then propagate by additional processes. 

The chemically inert character of sulfur hexafluoride is responsible for the almost complete lack of exchange of fluorine atoms between SFe and HF (249). It does react with hot alkali metals, however, and a study has been made of the rate of reaction of Na atoms with SF6 gas using the sodium diffusion flame technique. The rate constant at 247° is 2.23 X 10-1 cm mole-1 sec-1 and the energy of activation for the reaction SF6 + Na — SF6 + NaF, is about 37 keal. A film of sodium on a glass wall does not react with SF at room temperature. The reaction sets in at about 200° (57). The fluorides, SF , SF4, and S2F2, have no effect upon the viscosity of liquid sulfur in the range 180-195° (93). Sulfur hexafluoride forms a solid hydrate which has a crystal constant of 17.21 A. It decomposes just above 0° (285). 

It was often found that, contrary to the theoretical prediction, the value of n is non-integer [Avrami, 1939]. The Avrami model is based on several assumptions, such as constancy in shape of the growing crystal, constant rate of radial growth, lack of induction time, uniqueness of the nucleation mode, complete crystallinity of the sample, random distribution of nuclei, constant value of radial density, primary nucleation process (no secondary... 

Total number of seeds based on total operating volume of the crystallizer Constant in Eq. (53)... 

Crystallization constants for gutta percha Isothermal ciystallization temperature (K)... 

The absence of a simple, well substantiated potential expression makes it impossible to estimate lattice constants, angles, lattice energies and other crystal constants it has merely been possible, by comparing several lattices of the diamond or wurtzite type, to derive empirical rules for atomic distances in relation to bond strengths, which show that, under otherwise identical conditions, the stronger linkage corresponds to the smaller atomic distance. 

The currently-accepted method for averaging single crystal constants to compute bulk properties was proposed by Hill (1952). Based on energy arguments, he proved that Voigt s method provided the upper bound and Reuss s method the lower bound such that the arithmetic mean of their averages would yield more accurate results than either individual average. This is expressed as... 

Computed from experimental single crystal constants, see text Converted from the isothermal result using Gschneidner s (1964) values for a, shock compression results for vb in eq. (8.8). 

Fig. 8.52. Temperature dependence of Young s ( ), shear (G), and bulk (K) moduli computed from the single crystal constants of yttrium.

Computed from experimental single crystal constants From shock compression results for in eq. (8.8). 

Fig. 8.59. Poisson s ratio (v) and theta ) of praseodymium computed from the single crystal constants shown in fig. 8.57.

Fig. 8.69. Poisson s ratio (i ) and theta (0) of gadoiinium. Computed from single crystal constants shown in fig. 8.67. Breaks in the curves Indicate that data for Ctz, used in the computations, were taken in a magnetic field at temperatures below the break.

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