CHALMERS TEKNISKA HÖGSKOLA
Graduate School in Material Science
2002-10-24
time: 13.15-17.15
Room: FB
Examination in Materials Science, Structure and Properties
Instructor:
Help allowed:
Lars Börjesson
Pocket calculator
Note: Choose any eight problems out of twelve offered in this examinations. Work
with those eight problems only. Your exam grade is based on points earned on
those eight problems only. Maximum number of points is accordingly 8x3=24. The
course grade is based on a sum, , where 0.5(number of points earned on
questions for study)+ exam points. Grade 3 corresponds to 12<≤17, grade 4 to
17<≤20, and grade 5 to >20. Passing grade for graduate students corresponds to
grade 4, which means that for them  has to exceed 17 points.
Results of the exam will be available 2002-11-14 in room F3116 and F5102, Physics
research building, or by phone 772 33 07, or by e-mail duncan@fy.chalmer.se
Electronic structure
1.
The origin of metallic behavior of materials lies in the tendency of outer
(valence) electrons on an atom to lower their energy by spreading their
wave function, thus allowing motion throughout the material. This tendency
is very general and will occur unless electrons can lower their energy more
effectively in some alternative way. One alternative way for energy
lowering is for an outer electron on one atom to find a low energy quantum
state on another atom. In the latter case the outer electrons are tied up in a
covalent or ionic bond. Based on this introduction answer the following
questions:
a) why are most elements metals?
(2p)
b) do you expect the following materials to show metallic behavior: MgO,
RbI, SiC.
(1p)
2)
Diamond is an insulator with an energy gap of 5.5 eV. Silicon is a
semiconductor with an energy gap of 1.1 eV. Based on above facts explain
the following optical properties of these materials in the visible region (1.83.1 eV)
a) why is diamond transparent insulator in the visible region?
(1p)
b) why does silicon reflect visible light like any good metal?
(1p)
c) What optical properties would you expect for an insulator with an energy
gap of about 2.5 eV.
(1p)
Polymers
3.
Describe the two most important requirements to achieve high crystallinity
in a polymer. Polymer chains in highly crystalline polymers often arrange in
large aggregates called spherulites. Describe the arrangement of the
polymer chains in the spherulites.
(3p)
4.
Describe how the viscosity of a polymer melt depends on the molecular
weight and on the shear rate. Explain what is happening on a molecular
level.
(3p)
Composites & Nanocomposites
5.
Why are fibres, and not some other shape, the most frequent choice for
advanced composites? Give at least 3 (three) reasons.
(0.75p)
a) Sketch and briefly describe the structure of a carbon fibre; in doing so
remember to specify bonds present in this fibre.
(0.75p)
b) Proceed from fibre pull-out test and explain what is a critical fibre length.
Why is it important to know this length?
(0.75p)
c) Cationic exchange is an important mechanism towards nanocomposites.
Explain cationic exchange.
(0.75p)
Amorphous materials
6.
a) You have a piece of material in your hand and would like to know if it is
amorphous or not. How do you proceed to find this out?
(1.5p)
b) Which material classes can be produced in the amorphous state? What are
the limitations?
(1.5p)
Materials Properties/ Applications
Electrical and thermal properties:
7.
Make a sketch of the variation of Fermi function f(E) with temperature for a
typical metal (T = 0K, 300K, 1000K). How does that relate to the band
structure (describe briefly)? What is different in case of an insulator?
Explain!
(3 p)
Dielectric and magnetic properties
8.
The following data are obtained for a Cu-Ni-Fe-alloy during the generation
of a ferromagnetic hysteresis loop.
H [A/m]
6 104
1 104
0
-1 104
-2 104
-3 104
-4 104
-5 104
-6 104
B [T]
0.65
0.58
0.56
0.53
0.46
0.30
0
-0.44
-0.65
Plot the data and determine remanence and coercivity of this material!
Phase diagrams and phase transformation
9.
Time did not appear in any quantitative way in the discussion of phase
diagrams. Phase diagrams describe equilibrium states and those states
should be stable and unchanging with time. However, these equilibrium
structures take time to develop, and the approach to equilibrium can by
mapped on a time scale.
How do we call the schematic illustration of the microstructural
development upon time? Make a sketch of such a diagram for a simple
solidification reaction (liquid → solid).
(3 p)
(3 p)
Biomaterials
10) a) Describe the events at the implant surface which occur over time from
the initial manufacturing of the implant to the long term incorporation of
the implant into the surrounding tissue.
(1.5 p)
b) What are two major surface properties that can strongly influence the tissue
response to an implant surface?
(0.5p)
c) What are the relevant feature sizes on a material surface needed to be
considered for 1) protein adsorption and 2) cell adhesion? Explain why
these features sizes are important
(0.5p)
d) Do cells see the implant surface? Explain!
(0.5p)
Simulations of materials properties
11) a) Electronic-structure (EL), molecular-dynamics (MD), Metropolis Monte
Carlo (MC), and kinetic Monte Carlo (KMC) simulations are four
important techniques used in atomic-scale computational materials science.
Which technique is most suitable if you would like to
(2.5p)
i) determine the free energy difference for myoglobin in solution with and
without an attached CO molecule
ii) determine the bulk modulus for iron at 100 GPa
iii)simulate the growth of GaAs on GaAs(001)
iv) simulate the phase transition in brass (sv. mässing) from an ordered to a
disordered alloy
v) determine the change in energy if a Ga atom is replaced by an In atom in
a GaAs crystal
b) What is the typical size of the time-step used in a molecular-dynamics
simulation of a metal using a classical inter-atomic model potential:
1 fs, 1 ps or 1 ns?
Electrical properties of insulators
12)
Good Luck
Lars, Uta, Mats, Igor, Rodney, Julie, Göran, Stanislaw and Duncan
(0.5p)
(3p)