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MLE2101
NATIONAL UNIVERSITY OF SINGAPORE
Sample Questions similar to those to be expected in a
MID-TERM EXAMINATION
MLE2101 – Structures of Materials
(Semester 1; AY 2008/2009)
Time Allowed: will be 60 Minutes
INSTRUCTIONS TO CANDIDATES
1.
The examination paper will contain 4-5 questions. This sample contains a
collection of 11 questions taken from or similar to several previous midterm
exams. In a single exam the marks would add up to 100 marks giving you an
indication on the fraction of the total exam time that you are supposed
supposed to spend on a particular question.
2.
.
In the exam try to answer ALL questions. This compilation is not considered
to be a homework assignment but aims at providing you with further relevant
material to check yourself that you are well-prepared for the exam.
3.
The exam will be an OPEN BOOK examination. You are allowed to consult
any of the textbooks, lecture notes that you brought yourself, but you are not
allowed to exchange materials with other students or to access information
from external sources.
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MLE2101
NATIONAL UNIVERSITY OF SINGAPORE
Question 1:
(12 marks total )
(a) What is a “crystalline material”?
(b) Name at least two experimental techniques to find out whether a solid
material is crystalline. For each of the techniques briefly explain how the
expected results relate to the definition that you have given in part (a).
(c) What is the difference between a crystal structure and a crystal lattice?
Question 2:
(24 marks)
(pattern A)
(pattern B)
(a) Indicate the position of the symmetry elements and of the unit cell in the patterns
shown (above as well as) on page 5. Indicate your matric number on the
separate page and submit it along with your answer book.
(b) To which of the 17 plane symmetry groups do the wallpaper patterns belong (cf.
overview on page 4)?
Question 3:
(24 marks)
(a) From the stereographic projection of the symmetry
elements shown to the right determine the crystal
class and the crystal system.
(b) Redraw the stereographic projection in your
answer book and indicate the face poles of crystal
faces that are symmetry equivalent to the one
general face shown above (marked by an arrow).
In your sketch distinguish between faces in the
northern and southern hemisphere.
(c) For another crystal belonging to the same crystal class assume that all crystal
faces belong to a single form. The normal to one of the faces is parallel to one of
the three-dimensional axes.
How many faces does this crystal exhibit?
Which regular polyhedron has the same orientation of face normals?
Note: In this graph the broken lines are meant as a guide to the eye only.
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MLE2101
NATIONAL UNIVERSITY OF SINGAPORE
Question 4
(40 marks)
The graph displays a symmetry diagram for a primitive orthorhombic space
group (in the non-standard orientation: a horizontal, b vertical, c normal to
page). Note that the “half-arrows” indicate a twofold screw axis within the
plane of projection, while full arrows refer to twofold rotation axes.
(a) Specify the full Hermann-Mauguin symbol for this space group.
(b) Give the coordinates of all symmetry copies generated from an atom at
the general position x, y, z.
(c) Determine the multiplicity (i.e. the number of symmetry copies incl. the
original atom) for an atom at the special position 1/4 1/2 0.
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MLE2101
NATIONAL UNIVERSITY OF SINGAPORE
Question 5:
(25 marks total )
(a) Briefly explain how to derive the Miller index of a net plane.
(b) Sketch the axial intercepts of a lattice plane with Miller indices (2 0 3) for
an orthorhombic lattice.
(c) Briefly explain the difference between the symmetry operations that define
the point group and those that define the space group of a crystal.
(d) Which characteristic features in the symmetry of a macroscopic crystal
with {100}, {110}, {310}, {111} and {123} faces show you whether the
crystal is cubic?
(e) Name 3 families of crystal faces from the list in part (d) that belong to a
common zone.
Question 6:
(15 marks total )
(a) Explain the generation of (i) the characteristic X-ray line spectrum and (ii)
the continuous spectrum in a conventional X-ray tube.
(b) Why do X-ray protection devices often contain lead?
Question 7:
(20 marks)
(pattern A)
(pattern B)
(c) Indicate the position of the symmetry elements and of the unit cell in the two
patterns shown above as well as on a separate page. Indicate your matric
number on the separate page and submit it along with your answer book.
(d) To which of the 17 following plane symmetry groups do the wallpaper patterns
belong (cf. overview on following page)?
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MLE2101
NATIONAL UNIVERSITY OF SINGAPORE
Question 8
(25 marks)
The graph displays a symmetry diagram for a primitive orthorhombic space
group in standard orientation (a vertical, b horizontal, and c normal to page).
“Half-arrows” indicate a twofold screw axis within the plane of projection.
(a) Specify the full and the short Hermann-Mauguin symbol for this space
group.
(b) Explain the meaning of the symbols used in both types of space group
names and their sequence (for the given crystal system).
Question 9
(15 marks)
For each of the following two point-group symmetry diagrams, identify the crystal
class and crystal system
(A)
(B)
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MLE2101
NATIONAL UNIVERSITY OF SINGAPORE
Question 10:
(18 marks)
Answer the following questions in your own words using not more than two
sentences per question:
(a) What is a crystal?
(b) What is the difference between a lattice and a crystal structure?
(c) What is the difference between a crystal system and a crystal class?
(d) How many symmetry copies (including the original) does a 41 axis
generate and how many of them are located within a single unit cell.
(e) What is the rotation matrix of a 2-fold rotation axis along the y-axis?
(f) What characterizes (i) the unit cell metrics and (ii) the symmetry of a cubic
crystal?
Question 11
(22 marks)
(a) Describe the principle of a laboratory X-ray tube
(b) What determines the minimum wavelength of the braking radiation?
(c) Name two differences between a spallation source and a neutron reactor?
(d) Why should neutrons be moderated before using them for crystal diffraction
experiments?
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MLE2101
NATIONAL UNIVERSITY OF SINGAPORE
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MLE2101
NATIONAL UNIVERSITY OF SINGAPORE
Matric number: _____________
Answer question 2(a) on this page and submit it along with your answer book.
Pattern A
Pattern B
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MLE2101
NATIONAL UNIVERSITY OF SINGAPORE
Matric number: _____________
Answer question 7 (i) on this page and submit it along with your answer book.
Pattern A
Pattern B
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