Density of a Solid

Perhaps, however, the greatest virtue of structural foams is the ability to increase the ratio of part rigidity/weight. A foam of half the density of a solid material only requires a 25% increase in wall thickness to maintain the rigidity. 

The principal experimental method used to measure the density of a solid is determination of the mass of liquid displaced by a known mass of solid. It is essential that the solid have no appreciable solubility in the liquid, that all occluded air be removed from the solid and that the density of the displacement fluid be less than that of the solid lest the solid float. Densities of crystalline solids also can be determined from the dimensions of the unit cell. Davis and Koch discuss other methods for measuring the density of liquids and solids such as hydrostatic weighing of a buoy and flotation methods. 

The true density of a solid is the average mass per unit volume, exclusive of all voids that are not a fundamental part of the molecular packing arrangement [55]. This density parameter is normally measured by helium pycnometiy, where the volume occupied by a known mass of powder is determined by measuring the volume of gas displaced by the powder. The true density of a solid is an intrinsic property characteristic of the analyte, and it is determined by the composition of the unit cell. 

X-ray diffraction allows the dimensions of the unit cell to be accurately measured. If the structure type of the material is known, the ideal cell contents are also known. Thus, the unit cell of a crystal of composition M2O3 that adopts the corundum structure contains 12 M atoms and 18 O atoms (Supplementary Material, SI). This readily allows the theoretical density of a solid to be calculated. The weights of all of the atoms in the cell are added, and this is divided by the cell volume. 

It was realized at an early stage that a comparison of the theoretical and measured density of a solid can be used to determine the notional species of point defect present. The general procedure is ... 

Because of Vegard s law, it is clear that the density of a solid solution will also be expected to be a linear function of the densities of the parent phases that make up the limits of a solid solution. 

Carbonnel F, Rambaud JC, Mundler O, Jian R. Effect of energy density of a solid—liquid meal on gastric emptying and satiety. Am J Clin Nutr 1994 60 307—311. 

Compressibility. The bulk density of a solid is an essential value used in the analysis of its flow properties, such as when calculating mass flow hopper angles, opening sizes, bin loads, etc. Loose and/or packed density values are not sufficient. Bulk solids exhibit a range of densities that vary as a function of consolidating pressure. This range of densities, called the compressibility of the solid, can often be expressed on a log—log plot as a line or relationship. 

The thermal conductance of materials depends on temperature and decreases as the latter increases. It also depends on the density of a solid, increasing with density. The presence of foreign atoms in solid solutions contributes to growth of thermal resistance, i.e., to reduction of thermal conductance (Pampuch, 1971). 

The brackets represent concentration in moles per liter. Because the constant, the K, is dependent on concentration, we remove solids such as silver chloride (AgCl) from the expression. The concentration of a solid is constant. The density of a solid is a way to express the solid s concentration. Therefore, the Ksp of a solid dissolving is simply the product of the concentration of the ions produced. For... 

This expansion in principle also includes terms proportional to (n/ V)2 and all higher powers of (n/V). However, when the density n/V is much smaller than the density of a solid or liquid, so that most of the container is empty space, this expansion converges rapidly and the higher terms can be ignored. B(T) is called the second virial coefficient, and is a function of temperature. 

The density of a gas can be measured in the same way as the density of a solid or liquid—by dividing its mass by its volume. Because the particles in a gas are very spread out, gas densities are very small numbers and are usually described in units of grams per liter as opposed to grams/mL or grams/cm3 (as would be the case for solids or liquids). The AP test occasionally has gas density questions on it, so you should be familiar with the method for solving them. The equation for calculating gas density can be derived from the ideal gas equation. 

The density of a gas is similar to the density of a solid or a liquid. Density is found by dividing mass by volume. The density of a gas is usually reported in units of g/L. 

PROBLEM What is the density of a solid cube that has a length of 2.0 cm on each side and weighs 6.0 grams ... 

The limitations on the motion of the particles of solids account for the fact that they are said to have definite shape and definite volume. By definite shape, we mean that they do not take the shape of a container, the way that gases and liquids will. By definite volume, we mean that they do not expand or contract to occupy the entire container. This does not mean, however, that the volume of a solid is a constant. Solids do expand and contract in response to temperature changes. That is why, when you look up the density of a solid, it will always indicate the temperature at which the value for density is listed. 

Before considering how the first plane spacing was determined, we must digress to consider the subject of x-ray density. Normally the density of a solid is found by measuring the volume, usually of the order of a few cubic centimeters, and the weight of a particular specimen. But x-ray diffraction allows us to determine the lattice parameters of a crystal s unit cell, and therefore its volume, together with the number of atoms in the cell. We can therefore base a density... 

Density can be defined as ratio of the mass of an object to its volume therefore, the density of a solid is a reflection of the arrangement of molecules in a solid. In pharmaceutical development terms, knowledge of the true density of powders has been used for the determination of... 

The theoretical density of a solid with a known crystal structure can be determined by dividing the mass of all the atoms in the unit cell by the unit cell volume, (Chapter 1, Section 1.12). This information, together with the measured density of the sample, can be used to determine the notional species of point defect present in a solid that has a variable composition. However, as both techniques are averaging techniques they say nothing about the real organisation of the point defects. The general procedure is ... 

Different vertical loads can be applied to a bulk solid sample of known mass, and compression of the sample is recorded electronically (Thomson, 1997). With these data, powder contact volume versus compressive force or stress can also be represented. Bulk density of a solid is a function of consolidation stress and changes during flow as the stress changes. Because the mass consolidating load and volume are known, the relationship can be plotted as shown in Figure 6. 

If the density of a solid is to be determined, its volume is found out by immersing it in a known volume of a liquid in which it does not dissolve, and noting the sum of the volumes of the liquid and the solid. This can be done by placing a known weight of the solid in a known volume of the liquid contained in a graduated cylinder. The increase in volume after the solid has been added is the volume of the latter. Water is used most conveniently in the case of metals and other substances which are insoluble in water. In the case of salts that dissolve in water, benzene, kerosene, or carbon tetrachloride can be used. 

In this case, the "fine" particles and the "coarse" particles were separated so that the difference in size between individual particles was minimized. That is, most of the individual particles in each fraction were almost the same size. Both the fine and coarse particles have a sintering slope of 1/2 but it is the coarse particles which sinter to form a solid having a density closest to theoretical density. This is an excellent example of the effect of pore volume, or void formation, and its effect upon the final density of a solid formed by powder compaction and sintering techniques. Quite obviously, the fine particles give rise to many more voids than the coarser particles so that the attained density of the final sintered solid is much less than for the solid prepared using coarser particles. It is also clear that if one wishes to obtain a sintered product with a density close to the theoretical density, one needs to start with a particle size distribution having particles of varied diameters so that void volume is minimized. 

Higher efficiency for a given size, because of the high density of a solid relative to that of a gas... 

In effective medium theory, the overall electron density of a solid, p(r), is constructed as a superposition of the perturbed electron densities ... 

The actual density of a solid substance, even of a relatively small individual crystal, may be measured by determining the density of an inert liquid mixture in which the crystal remains just suspended. Examples of a convenient group of miscible organic liquids for many inorganic salts include chloroform (1492kgm at 20 °C), carbon tetrachloride (1594), ethyl iodide (1930), ethylene dibromide (2180), bromoform (2890) and methylene iodide (3325). 

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