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## Crystal structure

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**Crystal structure**Unit Cells, density, and 3-dimensional geometry.**Cubic crystal structures**• Simple cubic (sc) • Body-centered cubic (bcc) • Face-centered cubic (fcc)**How many atoms/cell?**• A corner atom has 1/8 atom inside the cube. • A body-centered atom is entirely within the cube • A face-centered atom has ½ atom inside the cube**Cubic crystal structures**SC BCC FCC SC (8 x 1/8)=1 atom/cell BCC (8 x 1/8)+1=2 atoms/cell FCC (8 x 1/8)+ (6 x ½)=4 atoms/cell**a=edge of a cell, r=radius of atom**• SC a=2r**a=edge of a cell, r=radius of atom**• BCC (√3)a=4r**a=edge of a cell, r=radius of atom**• FCC (√2)a=4r**A word about volume**• r is usually expressed in picometers(10-12m) • V (cube)= a3 • Your best bet is to convert: mm3Lml**Conversion factors**• L=6.02 x 1023 atoms/mol • D=__g/ml • FM=___g/mol • V=___ml/cell • 1m3=1000L • 1L=1000ml**Tasks**• What is the crystal structure? • What is the radius of the atom? • What is the volume of the unit cell? • What is the density?**Tasks**• What is the crystal structure? Find atoms/cell • What is the radius of the atom? Find r • What is the volume of the unit cell? Find a3 • What is the density? Find g/ml**Ex:**• What is the crystal structure? Find atoms/cell Manganese has a density of 7.4 g/ml, the length of the unit cell is 291 pm.**Ex:**• What is the radius of the atom? Find r Chromium has a BCC structure and a density of 7.19 g/ml**Ex:**• What is the volume of the unit cell? Find a3 Copper has a FCC structure and a density of 8.96 g/ml**Ex:**• What is the density? Find g/ml Strontium has BCC structure and r=215 pm**Ex:**• What is the crystal structure? Find atoms/cell Nickel has a density of 8.9 g/ml. Its atomic radius is 125 pm