Homework assignment(released on April 2nd)
Homework assignment(released on April 2nd)
1.Calculate the Multiplicity,LP factor (using the equation in the lecture note,=1.54 A),and Structure Factor(Fpki)for the first 5 peaks in Mg(HCP structure).There are two atoms per unit cell at (0,0,0)and at (1/3,2/3,1/2)respectively 1.Peaks of HCP Mg For HCP Mg.the lattice constants a=b=0.32nm,c=0.52nm.According to Braggs'Law: 2dhk1sin0hkl=入 first peaks occur when lattice spacing is large.For hexagonal structures, 1= 4(h2+hk+k2)2 di 3a2 +C2 and structure extinction happens when I is odd and h+2k=3n. The largest lattice spacings and corresponding indices are (hkil) dhkl/nm 0hk/° Multiplicity LP (1010) 0.28 16.1 6 23.1 传+) 0.26 17.2 2 20.1 2f (0002) (1011) 0.25 18.4 12 17.5 0.19 24.0 12 9.6 (1012) (1120) 0.16 28.8 6 6.3 The calculated parameters are appended to the table above.Note that LP factor is calculated by 1+c0s220 LP= cos0 sin20 And structure factor by =∑fep2ai0+ky+z
1. Calculate the Multiplicity, LP factor (using the equation in the lecture note, =1.54 A), and Structure Factor (Fhkl) for the first 5 peaks in Mg (HCP structure). There are two atoms per unit cell at (0, 0, 0) and at (1 /3 , 2 /3 , 1 /2 ) respectively
2.A face centered cubic structured single crystal with a lattice constant of ao is studied by a monochromatic X-ray radiation whose wavelength is A=a/2: 1)Illustrate by drawing the reciprocal lattice of this crystal and indicate its lattice constant. 1/ao 2/a0 2
2.A face centered cubic structured single crystal with a lattice constant of a0 is studied by a monochromatic X-ray radiation whose wavelength is λ= a0 /2: 1)Illustrate by drawing the reciprocal lattice of this crystal and indicate its lattice constant. 1/a0 2/a0 ?
Reciprocal lattice ●Defined by its primitive vectors(原胞基矢)(a1,a2,a3); Generating three reciprocal primitive vectors(a*,b*,c*) a*=a2Xa3la1●(a2Xag) b*=a3xa/a2(a3xa) c*=a xa2/a3(a xa2) https://en.wikipedia.org/wiki/Reciprocal lattice
Reciprocal lattice ⚫ Defined by its primitive vectors（原胞基矢）(a1 ,a2 ,a3 ); ⚫ Generating three reciprocal primitive vectors(a*,b*,c*) https://en.wikipedia.org/wiki/Reciprocal_lattice a*=a2xa3 /a1 •(a2xa3 ) b*=a3xa1 /a2 •(a3xa1 ) c*=a1xa2 /a3 •(a1xa2 )
primitive cell(原胞)is a minimum volume cell corresponding to a single lattice point of a structure https://en.wikipedia.org/wiki/Primitive cell
• primitive cell（原胞） is a minimum volume cell corresponding to a single lattice point of a structure https://en.wikipedia.org/wiki/Primitive_cell