Explanation Lattice parameter of α − Mn is 0.8931nm. Volume of the unit cell is calculated as follows: V = a 3 = ( 0.8931 × 10 − 8 ) 3 = 7.12 × 10 − 22 cm 3 The atom number of each cell is calculated as follows: ρ = (atom numbers per cell) × (atom mass) (unit cell volume) × (Avogadro number) 7.4 7g/cm 3 = ( x )(54 .938 g/mol) (7 .12 × 10 -22 cm 3 )(6 .02 × 10 23 atoms/mol) x = (7 .47g/cm 3 )(7 .12×10 -22 cm 3 )(6 .02×10 23 atoms/mol) (54 .938g/mol) x = 5 8 atoms/cell The β − M n volume is, volume = a 3 The lattice parameter a = 0.6326nm or 6.326 × 10 − 8 c m ∴ ( 6.326 × 10 − 8 ) 3 ⇒ 2.53 × 10 − 22 cm 3 The atom number of each cell is calculated using the density equation, ρ = (atom numbers per cell) × (atom mass) (unit cell volume) × (Avogadro number)

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The Space Lattice and Unit Cells

Every matter consists of atoms, molecules, and ions. If these atoms, molecules, and ions (micro-particles) are represented in a three-dimensional space-occupying certain specific points in space, then these arrangements are termed as space lattices and t…

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Chapter 3, Problem 3.40P

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Volume change percent when β−Mn is formed from the α−Mn .

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