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Formula Sheets / Chemistry

Chapter 16

Solid State

Revise with flashcards Download this chapter (PDF) All Chemistry formulas (PDF)

Unit cells Packing and density Defects

Unit cells

Atoms per cell
SC $1,$ BCC $2,$ FCC $4;$ corner $\frac{1}{8},$ face $\frac{1}{2},$ edge $\frac{1}{4},$ body $1$
Edge and radius
SC $a = 2 r;$ BCC $3 a = 4 r;$ FCC $2 a = 4 r$
Coordination number
SC $6,$ BCC $8,$ FCC / HCP $12$

Packing and density

Density
$d = \frac{Z M}{N _{A} a ^{3}}$
Packing efficiency
SC $52.4%,$ BCC $68%,$ FCC / HCP $74%$
Voids
in close packing of $N$ spheres: $N$ octahedral $, 2 N$ tetrahedral
Radius ratio
$\frac{r ^{+}}{r ^{-}} : 0.225$ – $0.414$ tetrahedral (CN 4) $; 0.414$ – $0.732$ octahedral (CN 6) $; 0.732$ – $1$ cubic (CN 8)

Defects

Schottky: density falls $;$ Frenkel: density unchanged $;$ metal excess (F-centres) gives colour

Environmental Chemistry Solutions