Homework assignment (released on March 19th,due on March 26th,2019) 1.Show that a relationship between real and reciprocal lattice is r.d*=uh+vk+wlm (m is an integer). 2.For a known crystal structure of Mg,illustrate and calculate the direction and length of a,b and c in real space and a*,b*and c*in reciprocal space. Phase Structure Pearson a,b,c a,B,Atoms Point x y Occ type symbol (nm)Y() set space group Mg Mg hP2P0.320890 Mg 2c 0.3330.6670.2501. 63/mm0.320890 0.5210120 3.Find the total number of equivalent planes in the cubic structure (multiplicity factor)belonging to the following families: (a){100}(b){110}(c){111}(d){210}e{321} 4.Suppose you are going to carry out an X-ray experiment using a Cu target and Ni filter.If you want to make the intensity ratio of Ika/IkB=600,what thickness should you use for the Ni filter?The mass absorption coefficient of Ni to Cu-KB peak is 350cm2/g.For the Cu target,its Ika/IkB=5 without a filter. 5.You are asked by your professor to study a piece of a-Fe sample by X-ray diffraction.Please suggest the appropriate radiation (wavelength)for this study and estimate the minimum lattice spacing and the corresponding Miller index(hkl) that can be studied by X-ray diffraction(lattice constant of a-Fe:0.2866 nm)
Homework assignment (released on March 19 th , due on March 26 th , 2019) 1. Show that a relationship between real and reciprocal lattice is r·d*=uh+vk+wl=m (m is an integer). 2. For a known crystal structure of Mg, illustrate and calculate the direction and length of a, b and c in real space and a*, b* and c* in reciprocal space. Phase Structure type Pearson symbol space group a, b, c (nm) , , (o ) Atoms Point set x y z Occ Mg Mg hP2 P 63/m m c 0.3208 0.3208 0.5210 90 90 120 Mg 2c 0.333 0.667 0.250 1. 3. Find the total number of equivalent planes in the cubic structure (multiplicity factor) belonging to the following families: (a) {100} (b) {110} (c) {111} (d) {210} e {321} 4. Suppose you are going to carry out an X-ray experiment using a Cu target and Ni filter. If you want to make the intensity ratio of IK/IK=600, what thickness should you use for the Ni filter? The mass absorption coefficient of Ni to Cu-K peak is 350cm2 /g. For the Cu target, its IK/IK=5 without a filter. 5. You are asked by your professor to study a piece of -Fe sample by X-ray diffraction. Please suggest the appropriate radiation (wavelength) for this study and estimate the minimum lattice spacing and the corresponding Miller index (hkl) that can be studied by X-ray diffraction (lattice constant of -Fe: 0.2866 nm)