# Structure.homework__3-answer - MTLE-2100 Structure of...

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MTLE-2100 Structure of Engineering Materials, Homework #3 --Answer 1. Li 2 O forms in the anti-fluorite structure (anions in fcc positions; Li + ions occupy all the tetrahedral sites). a) Compute the value of the lattice constant. r Li+ = 0.59 Å , r O2- = 1.40 Å b) Calculate the density of Li 2 O c) What is the maximum radius of cation which can be accommodated in the vacant interstice of the anion array? a) ( 3/4)a = r O2- + r Li+ = 0.59 Å + 1.40 Å = 1.99 Å a = 1.99 Å x (4/ 3) = 4.5957 Å b) d = [4x16+8x6.94]/(4.5957x10 -8 ) 3 6.02x10 23 = 119.76/97.06329x10 -24 x6.02x10 23 =119.76/584.32x10 -1 = 2.050 g/cm 3 c) 3a - (2r O2- +4r Li+ ) = 3x4.5957 Å - (2x1.40 Å +4x0.59 Å ) = 2.80 Å . radius 1.40 Å a-2r O2- = 4.5957 Å - 2x1.40 Å =1.7957 Å radius = 0.898 Å 2. Calculate the distance between octahedral sites in the fcc and hcp close packed structures in the units of r O , the radius of the close-packed atom. Then explain why there are no common hcp-based ionic structures with all of the

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