From the figure below (i) Determine the Miller indices for the plane. (ii) Let the length of all the three base vectors of the direct lattice a = 5 nm. Calculate the distance of the lattice planes (346).
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- By determining the temperature at which the magnetic moment vanishes for a two- dimensional Ising system on a square lattice, show analytically that the phase transition temperature is determined by the equation T- 2Ju² ken(1+√2)solve properlyShow that the volume of the first Brillouin zone is 8³/Vc, where Vc is the volume of a crystal primitive cell. (Hint: remember that Wigner-Seitz cell has the same volume as parallelepiped formed by three basis vectors of a primitive cell)
- E4,a Q₁ Given = AX (a-x), A, a are = limit ofxña at tro ~ (x, 0) Constant 1- Find A for normalized (1x₁) 2- If (AV, 0) represents the wave function of aparticle find all bil in infinite square well outside the well N(x,0) find (x, t)Suppose you measure A with eigenvalues A1, A2, and A3 with corresponding eigenvectors |1), 2), and |3), respectively, on wave function ) = a|1) + B|2) + y|3). Assuming degeneracy where A3, what normalized wave function does ) collapse to when normalized measuring A brings a value of 1? O a[1) + y|3) a² +y? a²+y? O alı)+r|3) Va2+y2
- Solve the following.The primitive translation vectors of the bcc lattice are given: ä₂ = (²) (1 - 1 + k) az = (-) (² + 1 = k) a₁ (²7) (-²+j+ k) a) Find the volume of the primitive cell. b) Find the primitive translations of the reciprocal lattice c) Sketch the first Brillouin zone of the bcc lattice.Does a real lattice vector have a corresponding unique reciprocal vector?