The crystal structure of lithium sulfide (Li_2S), is pictured here. The length o

Question

The crystal structure of lithium sulfide (Li_2S), is pictured here. The length of the unit cell is 5.88 x 10^2 pm. For this structure, determine the coordination numbers of Li^+ and S^2- the number of formula units in the unit cell the density of Li_2S Refer to Figure 12-44 and Figure 12-48. Suppose that the two planes of icons pictured in Figure 12-44 correspond to the top and middle planes of icons in the NaCl unit cell in Figure 12-48. If the X-rays used have a wavelength of 154.1 pm, at what angle theta would the diffracted beam have its greatest intensity?

Explanation / Answer

108 Looking at the figure we can deduce,

(a) the coordination number of Li = 4 and S^2- = 8

(b) the number of formula units in the unit cell 4

(c) Volume of unit cell = (5.88 x 10^-8 cm)^3 = 2.03 x 10^-22 cm^3

mass of one Li2S = 45.95/6.023 x 10^23 = 7.63 x 10^-23 g

mass of 4 Li2S in unit cell = 3.05 x 10^-22 g

density = 3.05 x 10^-22/2.03 x 10^-22 = 1.50 g/cm^3

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