Crystal density, estimated

New applications of the MOLPAK/WMIN computational method for estimating crystal densities of energetic materials have been investigated in collaboration with Prof. Herman L. Ammon and his co-workers at the University of Maryland. Finally, thermodynamic properties of HCTD and PCU have been determined by Prof. G. J. Kabo and his colleagues at Belarussian State University, Minsk, Belarus. 

One approach which has resulted in experimental implementation is that of Randolph and co-workers f88-92 >. Using a simulation (21) Randolph and Beckman demonstrated that in a complex RTD crystallizer, the estimation of nuclei density could be used to eliminate cycling or reduce transients in the CSD. Randolph and Low (gg) experimentally attempted feedback control by manipulation of the fines dissolver flow rate and temperature in response to the estimated nuclei density. They found that manipulation of fines flow rate upset the fines measurement indicating that changes in the manipulated variable disturbed the measured variable. Partial fines dissolution resulting from manipulation of the fines dissolver temperature appeared to reduce CSD transients which were imposed upsets in the nucleation rate. In a continuation of this work Randolph et. al. < 921 used proportional control of inferred nuclei density to control an 18 liter KCl crystallizer. 

To a chemist concerned Tyith the synthesis of new high-explosive compounds the ability to compute detonation properties (detonation pressure, energy, and velocity as well as product composition) from a given molecular structure and the known or estimated crystal density is a problem of the utmost importance. The calculated properties could be meaningful in the decision as to whether it is worth the effort to attempt a new and complex synthesis. One reason behind the recent development of detonation-properties programs for use on high-speed computers has been to supply this desired information. One such program, the ruby code,1 has recently been made available to a number of laboratories, the authors included. 

The rate of cooling from above the melting temperature has significant effects on lamellar thickness and perfection as well as on physical properties. " There is a progressive increase in lamellar thickness and measured density with slower rates of cooling from 380°C. Quenched specimens, in our work, have a specific gravity of 2.136 g/cm compared to 2.180 0.003 for specimens cooled at die very slow rate of 0.02 deg/min. Annealing a quenched sample for 5 hours at 312°C causes die density to increase to 2.158 g/cm. For perspective, the density of totally noncrystalline PTFE is estimated to be 2.00 and the perfect-crystal density is 2.301 g/cm by X-ray diffraction. 

An improvement on the basic volume additivity approach has been implemented by Blaive and co-workers with the use of molecular mechanics and atomic radii to estimate molecular volumes and both liquid and crystal densities. [10]... 

D. T. Cromer, H. L. Ammon and J. R. Holden, A Procedure of Estimating the Crystal Densities of Organic Explosives, Report LA-11142-MS, Los Alamos Scientific Laboratory, Los Alamos, NM (1981). 

The density of the crystal was estimated by flotation in benzene/ chloroform mixtures. It is recognized that the value is not very accurate and is almost certainly lower than the true value because of the difficulty of freezing the crystal completely from the viscous mother liquor. However, the method is sufficient to confirm the number of molecules per unit cell [8]. 

Crystal Density y Aperture y Estimated Saturation Sorptions, Cm at... 

The weight of all the atoms or ions in the unit cell can be calculated if the unit cell dimensions and the density of the crystal are known. This means that crystal density measurements are important in the early stages of a crystal structure analysis. A vertical column with a density gradient, calibrated with crystals of known density, is used to measure protein densities. These are determined by where along the column the crystal setdes and so that, by interpolation, its density can be estimated (39). This method must be done with care to ensure that the measurement is good. The density of a crystal is given by... 

A Procedure for Estimating the Crystal Densities of Organic Explosives. ... 

For example, a crystal of sodium nitrate (2260 kg m ) could be floated in about 50 mL of bromoform in a suitable flask, taking care that no air bubbles are attached, and then caused to achieve the just suspended state by slowly adding chloroform from a burette. At this point the crystal density may be assumed to be equal to that of the liquid mixture, which can readily be estimated. 

A continuous cooling crystallizer is required to produce potassium sulphate crystals (density pc = 2660kgm, volume shape factor a = 0.7) of 750pm median size Lm at the rate Pc = 1000 kg h. On the basis of pilot-plant trials, it is expected that the crystallizer will operate with steady-state nucleation/ growth kinetics expressed (equation 9.39 with j = 1 and i = 2) as B = 4 X IO MtG m s. Assuming MSMPR conditions and a magma density Mt = 250 kg m, estimate the crystallizer volume and other relevant operating conditions. 

The quantity, T, which for a steady state system refers to both liquid and solid phases, must not be confused with the crystal growth time, i.e. the age of a product crystal, t. In fact, it can be shown (Saeman, 1956) that for a classifying crystallizer t = AT. However, the quantities that present considerable difficulty in measurement or estimation are S, u, and V or W. The last two are related through the crystal density pc and the bed voidage e ... 

D. W. M. Hofmann, Fast estimation of crystal densities, Acta Cryst., B58,489-493 (2002). 

The detection sensitivity in this study can be estimated. Assuming PE being fully crystallized at 85.0"C, the of 0.21 (assuming crystal density of 1.0 g/cm ) is equivalent to the intensity of ca. 10 cm at 0.006 A . For the coil solution at 120.0°C, 4>cry = 0, the measured intensity is ca. 1 cm with 4% statistical errors. So the detection sensitivity of SANS for the volume fraction crystallinity, 4>det, is estimated to be ca. 10 (4% x 1 -y 10 x 0.21 = 8 X 10 ), comparable to that of light scattering while more than one decade better than that of SAXS. This is however a conservative estimate since the crystallinity at 85.0°C would be less than ideal, and all crystals are not in perfect lamellar stacks, but the order of magnitude should not be affected. 

In this paper, the properties of these new molecular structures will be discussed. Theoretical methods to estimate heats of formation, crystal densities and detonation properties will be presented. This will be followed by experimental results, as well. 

In this chapter, the control parameters and charge carrier mobilities of a few molecular crystals are estimated using the density functional theory and semiempirical methods. By performing extensive computation, the variation in electron and hole mobilities for different polymorphs of benzene, naphthalene, and octathio[8]circu-lene molecular crystals are studied systematically. 

During heat treatment Zerodur base glass phase separates first, Fig. 2.24, and later small nuclei of about 5 nm in size precipitate. Fig. 2.25. If the temperature is not increased too rapidly, a large number of nuclei are formed before any crystal nucleation and growth of h-quartz s.s. is initiated. If this condition is observed during ceramization, then a high density of small h-quartz s.s. crystals can be obtained. Crystal densities for the h-quartz s.s. crystals are estimated to be about 10 cm, whereas the density of the nuclei is not known but may be even higher. 

Here Pc is the crystal density, is the specific enthalpy of fusion and a is the specific surface free energy. Alternatively, the Thompson-Gibbs equation can be rearranged to provide estimates of crystal thicknesses from measurements of the melting temperature. 

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