上海交通大学：《Structural and Chemical Characterization of Materi》教学资源_homework assignment3-19

Homework assignment (released on March 19th)

Homework assignment (released on March 19th)

1.Show that a relationship between real and reciprocal lattice is r.d*=uh+vk+wl=m (m is an integer). r.d*=(ua+vb+wc)(ha*+kb*+lc*) a*.b=a*.c=b*.a=b*.c=c*.a=c*.b=0 a*.a=b*.b=c*.c=1 r.d*=uh+vk+w/ a

1.Show that a relationship between real and reciprocal lattice is r·d*=uh+vk+wl=m (m is an integer). r·d*=(ua+vb+wc)·(ha*+kb*+lc*) r·d*=uh+vk+wl

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 Struct Pearson a,b,, Atoms Poin X Occ ure symbol (nm) B,Y t set type space (e) group Mg Mg hP2 P 0.3208 90 Mg 2c 0.333 0.667 0.250 1. 63/mm 0.3208 90 C 0.5210 120 a*=bxc/a(bxc) b*=cxa/b(cxa) c*=axb/c●(axb) Direction Unit

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 Struct ure type Pearson symbol space group a, b, c (nm) , ,  ( o ) Atoms Poin t 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. c a b a* b* c*  a*=bxc /a•(bxc) b*=cxa /b•(cxa) c*=axb /c•(axb) Direction Unit

3.Find the total number of equivalent planes in the cubic structure(multiplicity factor)belonging to the following families: (a)K100}(b){110}(c){111}(d){210}e{321} hkl 100 110 111 210 321 multiplicity 6 12 8 24 48 factor

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} hkl 100 110 111 210 321 multiplicity factor 6 12 8 24 48

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-Kg peak is 350cm2/g.For the Cu target,its Iko/lke=5 without a filter

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. m t e I I −  = 0

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). 175 150 125 →。日)/x 100 75 50 25 0.020.040060.080.190.12 1 nm 入 ZTargetZSample+1 or ZTarget>>ZSample

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)

Co,Fe,Mn,Cr,Mo,Ag 2dsin0=nλ d=nλ/2sin0 d≥λ/2 d=a/(h2+k2+l2)1/2

Co,Fe,Mn,Cr,Mo,Ag 2dsinθ=nλ d=𝑛λ/2sinθ d≥λ/2 d=a/(h2+k2+l2 ) 1/2