Summary: Crystal Structures

Read the summary and the most important questions on Crystal structures

• Exam 1

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• What is the difference between a crystal and a quasi crystal?

  A quasi crystal only has rotational symmetry but no translational symmetry. Defining characteristic of a crystal is translational symmetry.

• What are the essential symmetry elements in a triclinic lattice? What are the restrictions on its lattice parameters and angles?

  No symmetry ( except translation) --> lattice parameters are unrestricted a/=b,/=c alpha/=beta/=gamma (90/=120) /= --> not equal to

• What is the difference between space groups and point groups?

  In space groups lattices are combined with different symmetry operations consistent with these lattices and including symmetry operations with translation (glide plane, screw axis) 
  Point groups leave to the translations. 

• Give all orientations corresponding to the {100} lattice planes for an orthonombic lattice.

  {...} indicates all equivalent directions. Orthorhombic lattice --> All directions are different so {100} = (100)

• What is the difference between primitive lattice and non-primitive Bravis lattices?

  Primitve lattice point: One lattice point per unit cel
  
  Non-pimitive: More than one lattice point per unit cell. You can always define a primitve cell but the lattice parameter  will show the symmetry less clearly. 

• X-rays can be diffracted from a crystal but normal optical light cannot, why?

  Diffraction occurs when the wavelength of the radiation is smaller than the spacing between the scattering objects. X-rays have a short wavelength and optical light has a wavelength much larger than atomic spacing.

• In drawing the direct and reciprocal lattices for a 2-dimensional crystal. How can the two spaces be constructed?

  For the direct x axis: a, y-axis: b. Reciprocal: use 180-theta to determine the angle between a and b, a* becomes longer than b*

• Calculate the length of the reciprocal lattice vector, which formula to use.

  Use: a* a= 2pi --> a*acos(theta-90)= 2pi
  
  a*=2pi/acos(theta-90)

• Cr has a bcc crystal structure with lattice constants 0.288 nm. Write down the structure factor for this crystal Fhkl= sum(Fj*e^2pi(i)(XjH+YjK+ZjL)

  BCC: Atoms at position (000) and (0.5,0.5,0.5) F=Fcr+Fcr^2pi(i)(0.5h+0.5k+0.5l) = Fcr +Fcre^2pi(i)(h+k+l) = Fcr(1+e^2pi(i)(h+k+l)

• What are systematic absences, how do they ontstaan and Derive the systematic absences in the diff action pattern

  Symmetric absences: Reflections that are 0 due to symmetry. Due to internal symmetry of the crystal the value of the structural value (for hkl) is 0
  For Cr h+k+l = even --> F= for (1+1) = 2Fcr
  For Cr h+k+l = odd --> F=for (1-1) =0 So systematic absences for h+k+l =odd