HW7-MEMS1054_AY2111

# 6 consider the inversion tetrad which can be

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6) Consider the inversion tetrad, which can be envisaged as a combination of the two point symmetry elements of an inversion center and a tetrad (a fourfold rotation axis), i.e., 4 1 => 4 . Does the presence of an inversion tetrad imply that the crystal also contains a proper tetrad and an inversion center? Hint – carefully inspect the symmetry of the diamond cubic structure parallel to the edges of the conventional cubic F unit cell. 7) For a planar crystal (or the basal plane of a regular three dimensional crystal) the follwing information is provided, draw the structure: a) The plane group is cm (centered lattice with defining symmetry of a reflection/mirror line), with lattice parameters a = 1.0 nm and b = 0.5 nm; b) A-type atoms at 0,y with y=1/2 c) B-type atoms at x,y and at -x,y with x=1/8 and y=1/4 8) Shown below are three tetragonal prisms that represent unit cells of crystals with tetragonal structure. Thus the lattice parameters are constrained to a=b and c a is allowed, while α = β = γ =90˚. (i) Detemine the point group symbols for these crystals following the international conventions. (ii) Draw a stereogram that represents the point groups you have identified for the three cases.

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9) Identify and mark all the major reflection and rotation symmetry elements present for the planar crystal structure shown below. Is this a square crystal? 10) Calculate the speed of an electron that moves in the column of a transmission electron microscope that operates with accelerating voltages U=200000 Volts. What is the maximum kinetic energy such electrons could impart to a crystal upon impact? 11) I have heard that selected are diffraction patterns obtained from a single crystal with a TEM instrument operating at 200kV can be considered to good approximation as planar sections through the reciprocal space lattice of the respective crystal with the normal to the section plane given by the incident electron beam direction relative to the crystal. IS THIS STATEMENT TRUE or FALSE? Explain…
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