Crystal densities calculation

In collaboration with Prof. Herman Ammon (University of Maryland), MOLPAK/WMIN computational methods [6-12] have been employed successfully to predict the crystal densities of (i) several isomerically pure monomethylated PCU alkene dimers [13] and (ii) several polycyclic epoxides [14]. The crystal densities calculated from X-ray crystal structure data are compared with the corresponding calculated values. Attempts have been made to address discrep>-ancies that may exist between computed densities and those derived from A-ray data by using advanced theoretical methods. 

One of the things that can be done with a knowledge of the unit cell dimensions is to calculate the crystal density. This is examined in the following example. 

Table 20. Calculated Crystal Densities and Releasable Energy Density for HEDCs and In-Service Explosives...

Calculate the population density, growth, and nucleation rates for a crystal sample of urea for which there is the following information. These data are from Bennett and Van Biiren [Chem. Eng. Frvg. Symp. Ser., 65(95), 44 (1969)]. Slurry density = 450 g/L Crystal density = 1.335 g/cm ... 

Taking the crystal density as 1770 kg/m and the volume shape factor,/v, as 0.47 calculate... 

To check this prediction, a number of MaxEnt charge density calculations have been performed with the computer program BUSTER [42] on a set of synthetic structure factors, obtained from a reference model density for a crystal of L-alanine at 23 K. The set of 1500 synthetic structure factors, complete up to a resolution of 0.555 A [45], was calculated from a multipolar expansion of the density, with the computer program VALRAY[ 46],... 

Lecomte, C. (1995) Experimental electron densities of molecular crystals and calculation of electrostatic properties from high resolution X-ray diffraction, Adv. in Molec. Struct. Res., 1, 261-302. 

Although the unit cell dimensions shown in Table 11.3 appear to be reasonably close to each other, the calculated cell volumes and crystal densities are divided... 

The importance of high density as a feature of potential fuel systems that seek to maximize net volumetric heat of combustion is well documented. The prediction of the crystal density of an unknown compound typically has been approached through the use of volume additivity procedures [29-32]. Here, the crystal-molecular volume ycm) is calculated by summing appropriate crystal-atomic or group volumes Vca Vcm = ca) and the corresponding crystal density is ob-... 

Volume additivity methods generally do not take into account crystal packing efficiency or molecular conformation effects and thus will afford identical calculated densities for positional and conformational isomers and for compounds that possess different multiples of the same functional group composition. As an example, a volume additivity calculation predicts that l,3,5-trinitro-l,3,5-triazacyclohex-ane (RDX), l,3,5,7-tetranitro-l,3,-5,7-tetraazacyclooctane (a-HMX), and /3-HMX all will possess the same crystal density, 1.783 g/cm [32]. In fact, the experimentally observed densities of these three compounds differ markedly (i.e., 1.806 [33], 1.839 [34], and 1.902 [35], respectively). 

As part of the study, the authors have collaborated with Prof. Ammon in an effort to perform useful crystal density modeling calculations for four... 

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 density of explosive fillings contained in munitions should be as close as possible to the theoretical maximum density (TMD) of formulations, which is calculated from the crystal densities of ingredients of an explosive formulation, taking into account their relative proportions. The density of a formulation directly affects its performance as is shown by an empirical relationship (Equation 3.1) ... 

Physical Properties.7—Tantalum is a white metal with a greyish tinge and is very similar to platinum in colour and general appearance. When it is heated to 1600° C. in vacuo it assumes a crystalline form.8 Examination of the powdered metal by X-ray analysis has shown that the arrangement of the atoms is on the plan of a body-centred cube of side 3 272 A, obtained by dividing the space of a crystal into equal closely packed cubes and placing an atom at each cube comer and each cube centre the distance between the nearest atoms is 2 883 A. The specific gravity of the fused metal is 16 6, - a sample drawn into wire 0 05 mm. diameter had a density of 16 5 10 the density calculated from X-ray data is 17 09.u... 

Allotrope Stability range, °C Crystal structure Lattice parameters, pm Reference temperature, °C Atoms per cell, Z Density, calculated, g/ cm3 Average M—M distance, pm... 

---