CME 261: Materials for Manufacturing
September 12, 2021
Assignment 2: CME 261
Total marks: 31 marks total + 6 extra credit marks
Due Date: Monday September 19, 2022, at 11:59pm (Submit via Blackboard Grade Scope)
Please note, this assignment should be uploaded electronically to the assignment submission box
(accessible via “HW Assignment” tab on the left panel) on Blackboard and only to Blackboard.
Submissions via email will not be accepted. The assignment should be uploaded as a single pdf file
(except if noted otherwise) before the deadline to avoid late penalties. The pdf can include photographs
of any derivations or mathematical formulae, as long as it is legible. Keep in mind file sizes when
uploading your assignment. Please note, you are allowed to overwrite your submission as many times as
you’d like. The TA will mark the latest submission only. This includes a situation where the last
submission is received after the deadline – this is the submission which will be marked for credit and it
will be penalized as late. Late submissions after 48 hours are not graded or accepted. For details on the
grading policy, please see the syllabus. Students are expected to complete all assignments individually.
TAs will attempt to return assignments as soon as possible after the late grading period has expired.
You should present all calculations in a clear and logical manner for full marks.
Q1. (15 marks total) Unit cells. Determine the number of atoms per unit cell and the densities (in
g/cm3) for the following crystalline structures:
(a) BCC molybdenum, lattice parameter = 0.315 nm (3 marks)
(b) HCP magnesium (full, not 1/3rd cell), lattice parmeter = 0.32 nm (c/a ratio of 1.624) (6 marks)
(c) Cadmium sulfide (zinc blende structure, see below), lattice parameter = 0.583 nm. The Cd atom
is on the origin and the S atom is on the (1/4,1/4,1/4) of the unit cell. (6 marks)
Cd
S
Please show all work for unit cell and density calculations.
Q2. (6 marks total + 3 extra credit marks) Crystal structure. Provide both the Bravais lattice and the
motif for the following unit cells. Additionally, specify the number of atoms per unit cell. Different atom
types are marked by different colors. Please use proper point coordinate notation for all motifs, as
CME 261: Materials for Manufacturing
September 12, 2021
discussed in lectures. Show your work/sketches for full marks. Please indicate your coordinate axes (3
marks each).
(a)
Top
Blue
view
Brown
Yellow
Front
view
(b)
Top
Blue
view
Front
view
Brown
CME 261: Materials for Manufacturing
September 12, 2021
(c) Extra credit – Optional
height c is the same as the base sides a
Top
Blue
view
Brown
c
Front
a
a
view
Q3. (8 marks total) Packing factor. Iron crystalizes in a BCC unit cell at room temperature while
gold crystalizes in an FCC unit cell. Calculate the void volume for each of the above unit cells. Is there
a connection between the void volume and the atomic packing factor? If so, show that relationship.
Hint: Void volume refers to the empty space within a unit cell that is not occupied by atoms. Show all
work/sketches for full marks. Atomic radii for Fe and Au are 0.126 nm and 0.166 nm, respectively.
Q4. (5 marks total) Crystal directions and planes. Calculate the planar packing factor (fractional area
occupied by atoms) or the linear packing density (atoms per unit length) for the followings (3 marks
each).
(a) Planar packing factor for the {110} plane in FCC. (3 marks)
(b) Linear packing density for the [111] direction in BCC. (2 marks)