Question

3. This problem is about X-ray Diffraction. Tungsten is a Body Centered Cubic (BCC) metal with an atomic radius of 1.371 A. [TOTAL: 50 points) (a) Draw a unit cell of tungsten. Calculate lattice constant a. [10] 10,0,0 Lattice constant a = (b) Write the expression for structure factor Fall. There will be {hkl} combinations that can produce diffraction while other combinations do not allow diffraction. Among the allowed ones, identify the five {hkl) combinations that gives the five lowest numbers for (r+k+F). The tungsten was ground into powders for powder diffraction experiment. If Cu Ka (1.541 [A] is used as a monochromatic X-ray source, calculate the "peak location" (20 values) for the five peaks. Then fill the table below. [20] Allowed (?+ +F) value (from the lowest) 2 theta (28) [" (degrees)] <<USE BELOW SPACE TO LEAVE YOUR CALCULATION >

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Answer 1

Solution al unit call & Tungsten in It forms a bec Structure means all o corner Orcubied hy and atom and one atom placed Centre of the Cube. edge of (cube) Total No. g alom Perunit cell far Tungsten = 8x + 1 & 1+1 = 2 = 0 t K Carnen akom . Carneradom central atom Pelation between odomis radias and Edge lewymgruen es Diagonal of the Cabe- u3a (a )= -0 9+9+2r rl → Zn Diagonal, the radiuse of alumin = = 444-0 - from above two ean Digoned of the Cake 13a - 491 Q : q-xon => a = X 1371 A° 5.989 fa=1.73 A° / ar [a= 173 pm) 13 This is the required lattice Constant