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LAST NAME: FIRST NAME: STUDENT #:________ Page 1 of 12 UNIVERSITY OF TORONTO DEPARTMENT OF MATERIALS SCIENCE & ENGINEERING MSE 219F: STRUCTURE AND CHARACTERIZATION OF MATERIALS Midterm Examination October 28, 2010 Examiner: D.D. Perovic Instructions: a) Closed book examination; all equations are given in the Appendix b) Do all five questions; part marks are as indicated. c) Time allowed: 90 minutes Do not write in this box Question Marks 1 /9 2 /10 3 /12 4 /12 5 /12 Total /55
Transcript of UNIVERSITY OF TORONTO DEPARTMENT OF …exams.skule.ca/exams/MSE219H1_20159_621450155210MSE...a) On...
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UNIVERSITY OF TORONTO
DEPARTMENT OF MATERIALS SCIENCE & ENGINEERING
MSE 219F: STRUCTURE AND CHARACTERIZATION OF MATERIALS
Midterm Examination
October 28, 2010
Examiner: D.D. Perovic
Instructions: a) Closed book examination; all equations are given in the Appendix
b) Do all five questions; part marks are as indicated. c) Time allowed: 90 minutes
Do not write in this box
Question Marks 1 /9 2 /10 3 /12 4 /12 5 /12
Total /55
LAST NAME: FIRST NAME: STUDENT #:________
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1. Enter the correct answer for the following questions in the boxes to the right:
(1.5 marks) A solid in which all similar atoms are in similar positions relative to their
neighbours is said to: a) have long range order b) be non-crystalline c) be amorphous d) all of the above
(1.5 marks) Centrosymmetrical crystalline materials are: a) piezoelectric b) pyroelectric c) dielectric d) all of the above
(1.5 marks) A symmetric second rank tensor describing a triclinic crystal property has a maximum of:
a) 3 independent coefficients b) 4 independent coefficients c) 6 independent coefficients d) 9 independent coefficients
(1.5 marks) The pyroelectric tensor contains coefficients that relate: a) stress and temperature b) strain and temperature c) polarization and temperature d) polarization and stress
(1.5 marks) The 14 Bravais lattices are defined by the following: a) axial lengths and angles of the lattices b) axial lengths and angles and type of lattice c) axial lengths and point symmetry conditions d) axial angles and point symmetry conditions
(1.5 marks) A material in which the ordered regions contain only a few atoms is termed: a) crystalline b) polycrystalline c) anisotropic d) non-crystalline
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(10 marks) 2) The following diagram gives the structure of the AuCu compound
crystal structure.
a) On the basis of the crystallographic data given in the drawing,
determine the crystal system (N.B. All angles are 90˚).
Answer: crystal system =
b) Determine the motif for this structure and give the Pearson symbol.
Answer: motif =
Answer: Pearson symbol =
c) Determine the interplanar distance for the (311) planes in this
structure.
Answer:
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(12 Marks) 3(a) Determine the plane groups of the following patterns. Answer: Answer: Answer:
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3(b) Given below is a page from the International Tables for Crystallography for one of the plane groups.
a) What is the meaning of the following notations:
i) p31m Answer: ii) 3 m Answer: iii) 15 Answer:
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(12 marks) 4(a) STEREOGRAPHIC PROJECTIONS Given below is the (001) standard projection for cubic crystals showing all poles of the {100}, {110} and {111} families. In the figure only the (001), (010) and (100) are labeled. In the empty boxes label all other poles with their correct Miller indices.
(b) Show that the abbreviated international point group 6/mmm and the full international
point group 6/m 2/m 2/m both describe the stereographic projection shown below for a crystal of hexagonal symmetry.
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(12 marks) 5. TENSOR TRANSFORMATIONS
The electrical conductivity tensor for a hypothetical crystal in system has the following components (in units of 107Ω-1m-1).
We want to express the tensor in a new system ( ) which is related to the system as per diagram below:
a) Determine the direction cosines (lij) required for this transformation and present
the results in matrix form.
b) Write down the nine terms of the transformed tensor components.
c) Using the values of the tensor given above and the direction cosines determined in a), calculate all components of the tensor and give the answer in units of 107Ω-1m-1.
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5. TENSOR CALCULATIONS
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APPENDIX
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