Crystalline solids face-centered cubic unit cell

EXAMPLE 11.7 Relating Density to Ciystal Structure Aluminum crystallizes with a face-centered cubic unit cell. The radius of an aluminum atom is 143 pm. Calculate the density of solid crystalline aluminum in g/cm. ... 

Section 11.7 In a crystalline soUd, particles are arranged in a regularly repeating pattern. An amorphous solid is one whose particles show no such order. The essential structural features of a crystalline solid can be represented by its unit cell, toe smallest part of toe crystal that can, by simple displacement, reproduce the three-dimensional structure. The three-dimensional structures of a crystal can also be represented by its crystal lattice. The points in a crystal lattice represent positions in toe structure where there are identical environments. The simplest unit cells are cubic. There are three kinds of cubic unit cells primitive cubic, body-centered cubic, and face-centered cubic. 

Solids can be crystalline or amorphous. A crystalline solid has an ordered arrangement of structural units placed at crystal lattice points. We may think of a crystal as constructed from unit celb. Cubic unit cells are of three kinds simple cubic, body-centered cubic, and face-centered cubic. One of the most important ways of determining the structure of a crystalline solid is by x-ray diffraction. 

A crystalline solid contains three types of ions, Na, 0 , and Cl . The solid is made up of cubic unit cells that have ions at each corner, Na ions at the center of each face, and d ions at the center of the cells. What is the chemical formula of the compound What are the coordination numbers for the and Cl ions If the length of one edge of the unit cell is a, what is the shortest distance from the center of a Na ion to the center of an 0 ion Similarly, what is the shortest distance from the center of a Cr ion to the center of an ion ... 

Because every unit cell in a crystalline solid is adjacent to other unit cells, most of a cell s atoms are shared by neighboring cells. For example, in all types of cubic cells, each comer atom belongs to eight nnit cells [Figure 11.19(a)] a face-centered... 

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