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Lattice Parameters and Density

As noted in Chap. 1, every unit cell can be characterized by six lattice parameters — three edge lengths a, b, and c and three interaxial angles a, j3, and 7. On this basis, there are seven possible combinations of a, h, and c and a, ff and 7 that correspond to seven crystal systems (see Fig. 1.2). In order of decreasing symmetry, they are cubic, hexagonal, tetragonal, rhombohedral, orthorhombic, monoclinic, and triclinic. In the remainder of this section, for the sake of simplicity the discussion is restricted to the cubic system for which a — b c and a = / = 7 = 90°. Consequently, this system is characterized by only one parameter, usually denoted by a. [Pg.75]

The lattice parameter is the length of the unit cell, which is defined to be the smallest repeat unit that satisfies the symmetry of the crystal. For [Pg.75]

One of the major attributes of ceramics is that as a class of materials, they are less dense than metals and hence are attractive when specific (i.e., per unit mass) properties are important. The main factors that determine density are, first, the masses of the atoms that make up the solid. Clearly, the heavier the atomic mass, the denser the solid, which is why NiO, for example, is denser than NaCl. The second factor relates to the nature of the bonding and its directionality. Covalently bonded ceramics are more open structures and tend to be less dense, whereas the near-close-packed ionic structures, such as NaCl, tend to be denser. For example, MgO and SiC have very similar molecular weights ( 40 g) but the density of SiC is less than that of MgO (see Worked Example 3.4, and Table 4.3). [Pg.76]

Starting with the radii of the ions or atoms, calculate the theoretical densities of MgO and SiC. [Pg.76]

The density of any solid can be determined from a knowledge of the unit cell. The density can be calculated from [Pg.76]


The mean systematic deviation between the observed and the calculated values of the unit cell s mass—or, what amounts to the same thing, the density-increases as S/Ti decreases. Now, the sulfides belonging to the TiS2 and Ti2S3 phases are always well crystallized, and the errors in measuring lattice parameters and densities are of the same order. It is thus not unreasonable that the increase of this deviation should be due to the creation of sulfur vacancies, which proceeds simultaneously with the insertion of titanium. The observation has been previously made in connection with other analogous systems in which there is a transition from the compound MX2 to MX. [Pg.207]

Calcined EU2O3 is body-centered-cubic (C-form) with a density of 7.28 g/cm and an atom density of 2.49 x 10 atoms Eu/cm. Conversion from cubic to monoclinic (B-form) takes place at 1075°C. The monoclinic form lattice parameters and density are listed in Table 1. The reverse reaction (monoclinic-to-cubic) does not take place upon cooling to room temperature. [Pg.609]

The inverse calculation is also possible the content of the unit cell may be determined from the known chemical composition, lattice parameters and density of a material. Assume that the total mass of all atoms located in one unit cell is m. Also, assume that the unit cell volume is V. The latter is known from diffraction analysis as soon as lattice parameters have been established (see Eq. 5.41) Thus, provided the gravimetric density (p) of the crystalline material has been measured, the mass of one unit cell can be easily calculated ... [Pg.500]


See other pages where Lattice Parameters and Density is mentioned: [Pg.232]    [Pg.505]    [Pg.1241]   


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