Atomic radius determining from unit cell

Calculations Determining the unit cell type from the measured density and atomic radius of metals in the cubic system the atomic radius of a metal atom is determined from the crystal type and the edge length of a unit cell, which are both obtained by x-ray diffraction (see Major Technique 3 in text). 

Physical Properties. The absorption of x-rays by iodine has been studied and the iodine crystal structure determined (12,13). Iodine crystallizes in the orthorhombic system and has a unit cell of eight atoms arranged as a symmetrical bipyramid. The cell constants at 18°C (14) are given in Table 1, along with other physical properties. From the interatomic distances of many iodine compounds, the calculated effective radius of the covalendy bound iodine atom is 184 pm (15). 

Answer Several steps are required to solve this problem. First we determine the volume of a unit cell from the known density. Next we calculate the edge length of the unit cell from its volume. Finally, from the edge length of the ceU, we find the radius of one Au atom. 

We are now able to determine the side length of a unit cell for different well known lattice structures from the atomic radius according to Table 2- 3. We also know the number of atoms in each unit cell and thus we can calculate the density of a metal from the way the atoms in the metal is packed and the atomic radius of the metal atoms. We are going to try this in the following example. 

The volume of the unit cell is determined from the atomic radius since we know the connection between the side length of the unit cell b and the atomic radius r according to Table 2- 3 on page 84. 

Jsx-Js-Ph P-phase with 4/3 ML Pb. Pb atoms are represented by large hatched circles and Ge atoms are shown by open circles. The unit cell contains one Pb atom in cite and three Pb atoms displaced from the bridge site towards the T site (labeled off-centered Ti Pb). In (b) the distances between atoms and the Pb (covalent) radius are shown to scale. The coordinates of atoms as determined by XRD [99V1] are listed in Table 68. 

Another layered structure has been determined [343] on Ag3TlTe2 which, from its formula, might be a normal valence compound with monovalent cations. Its orthorhombic cell can be built up from layer packs Ag—Te—(Ag + Tl)—Te—Ag. These AgaTlTe2 units are stacked in such a way that the atoms of the two contacting Ag layers form zig-zag chains in [100] direction with a rather short Ag—Ag distance of 3.05 A which seems to indicate bonding between the layer units. For Ag ions (ionic radius 1.26 A) such an Ag—Ag distance would not be critical. However, if the outer Ag atoms of each layer unit really were ionized we would rather expect that adjacent units would shift by b/2 in order to increase the Ag—Ag distance. Anyway, on vapor-depositing the AgaTlTe2 films onto NaCl crystals, plate-like textures always formed. 

The values for actual phases that take the structure can be calculated from the unit-cell (and atomic) parameters of the phases. Each phase can therefore be represented by a point on the diagram since its reduced strain parameter and radius ratio can be determined from d, D, and From the positions of the points representing a number of phases with the structure it is possible to determine whether chemical bond or geometric factors control the stability of the structure, as explained on pp. 139-146. 

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