PhD defence deck

Question 1

How much have the life expectancy, poverty rate and literacy rate changed the last 100 years?

Answer 1

34 to 71 years; 74 to 10%; 26 to 86%

Question 2

What is the relation between parallel TEM beam, image intensity and isolation of diffraction spots?

Answer 2

A parallel beam makes it easier to isolate the diffraction spots (they become smaller), but at the cost of lower image intensity.

Question 3

What does the Born-Oppenheimer approximation assume?

Answer 3

Fixed positions of the nuclei.

Question 4

What does the Hohenberg-Kohn theorems state?

Answer 4

That the system’s potential energy can be entirely explained by its electron density.

Question 5

What is the Kohn-Sham approach?

Answer 5

Building a non-interacting reference system from one-electron functions to enable simple calculation for major parts of the kinetic energy.

Question 6

What is the expression for the radial basis function kernel

Answer 6

k = exp[-(x - x’)/2*theta]

Question 7

What is the formula for the standard deviation of a sample?

Answer 7

sqrt([1/N]*sum(x_i - mu))

Question 8

What is the width of the rolling average used to calculate DFT potentials?

Answer 8

2*d, where d is the distance between atomic planes perpendicular to the GB plane.

Question 9

What is standard state in thermodynamics?

Answer 9

1 bar and 298 K

Question 10

How is the cluster energy defined?

Answer 10

E_Acc-v + E_gb-bulk - ( E_v + E_Acc ), where E_gb-bulk is the host structure without any defects.

Question 11

How is Poisson’s equation derived, and what are the assumptions?

Answer 11

Derived from: Gauss law, and Coloumbs law.

Assumptions: Linear, isotropic and homogeneous (epsilon constant) environment.

Question 12

How is the Debye length defined?

Answer 12

The distance where the electric potential will decrease with 1/e.

Question 13

How do you derive the Debye length?

Answer 13

http: //www.owlnet.rice.edu/~phys534/notes/week10_lectures.pdf
1. Start with Poisson’s equation
2. Assume that the concentration of charged species in the solution follows Boltzmann statistics.
3. Write out the Taylor series of the exponential.
4. The first term vanishes from charge neutrality, the second term, you define as the Debye length, such that the solution of the potential decays according to the Debye length.

Question 14

How much does increased GB width, trapping, and reduced area improve the impedance fit in the space charge impedance model?

Answer 14

Increased width: 1.6-3.0
Trapping: 1.0-1.6
Area: Maybe 2

Question 15

Which quantity do you have to take the logarithm of to show that a simple RC circuit gives a slope of 2

Answer 15

log 1/Z’. Then plot log 1/Z’ vs log w. (remember to split the expression in w-dependent parts before taking the log).

Question 16

What are some possible reasons for obtaining CPE with n < 1?

Answer 16

Surface roughness, distribution of reaction rates, varying thickness, non-uniform current… in general, various phenomena that we can categorize into this semi magical term called inhomogeneity.

Question 17

What is a linear medium (one of the assumption in Poisson’s equation)?

Answer 17

A medium where the relation between the electric field and the polarization is linear. Hence, ferroelectric materials are not linear in that sense.

Question 18

What is a prerequisite for magnetism?

Answer 18

Unpaired electrons, such that an electron has a spin which is not compensated by its “partner”.

Question 19

What are the sources of variance for an EELS (and EDX) concentration plot?

Answer 19

Actual concentration variance, instrumental error, conversion error.

Question 20

Which defects dominate under which conditions in BZY?

Answer 20

Protons dominate at high pH2O, vacancies at low pH2O and low pO2, holes at very high pO2.

Question 21

What is a ceramic?

Answer 21

An inorganic non-metallic solid made up of either metal or non-metal compounds that have been shaped and then hardened by heating to high temperatures.

Question 22

Explain stress vs strain

Answer 22

Stress is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material which is not a physical quantity.

Question 23

What is the projected augmented wave method (PAW)?

Answer 23

Roughly speaking, you get very oscialliting wave functions close to the cores, and this is computationally expensive. PAW replaces these wave functions with more smooth functions, increasing the computational efficiency of DFT calculations.

Question 24

What are hybrid functionals?

Answer 24

They are a mix of Kohn-Sham and Hartree-Fock functionals. They are very expensive, because calculating HF is based on the Slater determinant, where you included all particles in the wave functions - which also makes it much harder to parallelize than KS, where you have one wave function for each electron.

Question 25

What is the number you get in the DFT energy?

Answer 25

The energy gain from taking isolated atoms, separated infinitely far apart, and cluster them together.

Question 26

What is the difference between Monkhorst Pack and Gamma-centered?

Answer 26

MP is a way to distribute k-points; gamma centered is a special case of MP where you calculate the gamma k point, which is very important for hexagonal cells, but probably not for anything else. G (2x2x2) >= MP (2x2x2) in terms of computational cost.