MSE
Part-5+XRD(2)+theory(2018)+CP.ppt

# Hkl miller index for the plane of interest u j v j w

• Notes
• 67

This preview shows pages 27–37. Sign up to view the full content.

(hkl)  :   Miller index for the plane of interest u v j  w j  :     j -th  atom position Overall intensity  I ~ |F|  = F•F*        * complex conjugate

This preview has intentionally blurred sections. Sign up to view the full version.

Class Business: Nov 19 (M) • No class business • Today’s lecture  Chapter-5(3): Diffraction theory   Chapter 5(5) Intensity calculation-1
u, v, w = 0, 0, 0 Scattering by a Unit Cell:  Simple Cubic

This preview has intentionally blurred sections. Sign up to view the full version.

u, v, w = 0,   0,    0               1/2,1/2,1/2 Scattering by a Unit Cell:      Body Centered Cubic
u, v, w =   0,     0,  0                1/2, 1/2, 0 Another quiz problem for today= Derive the structure factor for base-centered cubic!                 Scattering by a Unit Cell:                             Base Centered Cubic

This preview has intentionally blurred sections. Sign up to view the full version.

x y z   2 2 2 exp 2 2 2 exp 2 2 2 exp 0 2 exp l k i f l h i f k h i f i f F = f (1 + e i (h+k) + e i (k+l) + e i (l+h) =    Scattering by a Unit Cell:            Face Centered Cubic
For (hkl):   h 2 +k 2 +l 2      for  cubic   1 100 2 110 3 111 4 200 5 210 6 211 7 ---- 8 220 9 221 300 10 11 12 13 14 15 16 17 18 etc 310 311 222 320 321 ---- 400 410    322 411    330 x y z F              |F| 2 0 0 h, k, l   mixed 4f 16f 2 h, k, l   unmixed 1 11 1 9 8 7 6 5 4 3  XRD (Au)    (111) (200) (220) (311) (400) (331) Diffraction angle  (222) 2

This preview has intentionally blurred sections. Sign up to view the full version.

Structure Factors   j=1 N Lattice F |F| 2 hkl SC f f 2 all BCC 0 0 h+k+l = odd number 2f 4f 2 h+k+l = even number FCC 0 0 h, k, l   mixed 4f 16f 2 h, k, l   unmixed NaCl 4(f Na  - f Cl )  16(f Na  - f Cl 2   h+k+l = odd number 4(f Na  + f Cl )  16(f Na  + f Cl 2   h+k+l = even number Diamond 0 0 h, k, l   mixed 4f(1- i ) 32f 2 h, k, l   unmixed   and  h+k+l = odd 0 0 h, k, l   unmixed   and (h+k+l)/2 = odd 8f 64f 2 h, k, l   unmixed   and (h+k+l)/2 = even Zinc-blende 0 0 h, k, l   mixed 4(f Zn - i f S 16{(f Zn ) 2 + (f S ) 2 } h, k, l   unmixed  and  h+k+l = odd 4(f Zn -f S 16{(f Zn ) - 2f Zn f + (f S ) 2 } h, k, l   unmixed   and (h+k+l)/2 = odd 4(f Z +f S 16{(f Zn ) +2f Zn f + (f S ) 2 } h, k, l   unmixed   and (h+k+l)/2 = even
Class Business: Nov 21 (W) • No class business • Today’s lecture  Chapter-5(4): Diffraction theory  Peak intensity calculations • Start working on HW4;  Critical to the final exam!    Chapter 5(5) Intensity calculation-1   Chapter 5(6) Intensity calculation-1

This preview has intentionally blurred sections. Sign up to view the full version.

Structure Factors   j=1 N Lattice F |F| 2 hkl SC f f 2 all BCC 0 0 h+k+l = odd number 2f 4f 2 h+k+l = even number FCC 0 0 h, k, l   mixed 4f 16f 2 h, k, l   unmixed NaCl 4(f Na  - f Cl )  16(f Na  - f Cl 2   h+k+l = odd number 4(f Na  + f Cl )  16(f Na  + f Cl 2   h+k+l = even number Diamond 0 0 h, k, l   mixed 4f(1- i ) 32f 2
This is the end of the preview. Sign up to access the rest of the document.
• Fall '12
• p
• Diffraction, Neutron diffraction, X-ray scattering techniques

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern