Ch2:Wave Diffraction the Reciprocal Lattice Objectives At the end of this Chapter,you should: 1. Understand the concept of the reciprocal lattice. 2.Know how to use the Bragg's law. 3.Know the relationship between Bragg's law and the Laue equation. 4. Know the drawing method and the concept of Brilluoin Zone. 5. Be able to calculate the structure factor of the typical crystal structures
At the end of this Chapter, you should: 1. Understand the concept of the reciprocal lattice. 2. Know how to use the Bragg’s law. 3. Know the relationship between Bragg’s law and the Laue equation. 4. Know the drawing method and the concept of Brilluoin Zone. 5. Be able to calculate the structure factor of the typical crystal structures Ch2：Wave Diffraction & the Reciprocal Lattice Objectives
2.1 The reciprocal lattice (direct)lattice reciprocal lattice primitive vectors a1,a2,a3 primitive vectors b1,b2,b3 Def. 1 6 -2 a b2=2n(a) b1∝a2×a3 because of orthogonality, then useb1·a1=2π 63-2 1 to determine the constant. Def. 2 b1·a1=2n,b1·a2=b1·a3=0, b2·a2=2n,b2·a3=b2·a1=0, b3·a3=2n,b3·a1=b3·a2=0
2.1
Reciprocal Lattice for Aluminium
Reciprocal Lattice for Aluminium
Simple cubic lattice Z a 2π/a y X a1=a元， 万=2π a2×a3 2元， a a,=ay, a1(a2×a) a3=a2 万=2π a3×a 2, a·(a2×a) a1(a2×a)=a3 万3=2π a1×a 2r. a1(a2×a3) 万(6×五)= Note:When the original lattice (the direct lattice)rotates, its reciprocal lattice rotates the same amount as well
FCC lattice BCC lattice Z An/a a X 6+》 6=2π ā×ā，-4机(+-2) a(a2×a)a2 a×a= 4π1 a+到 ，=2 a1(a2×a) 。2++) 日9 6=2π- axa a(a2×a3)=a3/4 低-)》