COMPUTATIONAL PROJECTS (preliminary)
1. Spectroscopic properties of materials from the DFT calculations.
Calculate core-level shifts (CLS) in random Ag-Pd alloys as a function of concentration within the initial state model, and within the model of complete screening. Compare results with each other, and to the experiment.
Day 1 Ag, Pd, Lattice parameter, Bulk modulus, el. structure BGFM
Day 2 Ag-Pd, eq. Alloy properties, BGFM
Day 3 Ag, Pd, Ag50Pd50 SQS-16 supercell, VASP
Day 4 Ag-Pd CLS at Ag and Pd at 50-50 concentration BGFM
Day 5 Analysis SQS results, discuss
Literature: W. Olovsson, C. Göransson, T. Marten, and I.A. Abrikosov, Phys. Stat. Sol. (b) 243, 2447 (2006)
2. Superconductivity of B doped diamond.
All the superconducting elements are metals. Neither diamond nor boron are, thus, superconductors. A sensational discovery has been recently presented, that is B doped diamond has been shown to become a superconductor (E. A. Ekimov et al., Nature 428, 542 (2004).).
Calculate the electronic structure (energy dispersion curves and DOS) of diamond (at the equilibrium lattice parameter) using VASP. Compare the obtained band gap to the experiment. Compare the calculated lattice parameter to the experiment.
Assuming, that doping of diamond with B just adds holes to C valence band, calculate the electronic structure of B doped diamond. Compare your results to the recent photoemission experiment (T. Yokoya et al., Nature 438, 647 (2005).).
Day 1 C (diamond) bulk properties, band gap, BGFM
Day 2 Density of states for B doped diamond at different concentrations within the coherent potential approximation (CPA). BGFM
Day 3 Diamond and B in diamond within the virtual crystal approximation
(VCA): band structure, DOS etc. VASP
Day 4 B in diamond by the supercell VASP
Day 5 Analysis of the supercell results, discussion
Literature: E. A. Ekimov et al., Nature 428, 542 (2004); T. Yokoya et al., Nature 438, 647 (2005); Richard M. Martin, Electronic Structure. Basic Theory and Practical Methods (Cambridge University Press, Cambridge, 2004), §16.4 and/or A. V. Ruban and I. A. Abrikosov, Rep. Prog. Phys. 71, 046501 (2008), §3.4
3. Properties of Fe-Co alloys for electromagnetic applications.
Most of the modern technological materials are based on iron. The applications are different, and involve mechanical, as well as magnetic properties. In order to tune the properties of iron for the particular application, it is alloyed with other elements. Many commercial alloys include later transition metals, like chromium, cobalt, and nickel.
In particular, for steels used in electromagnetic applications it is important to maximize magnetic moment of the sample. This is done by alloying Fe with Co. Investigate magnetic properties of Fe-Co alloys. Compute magnetic moment of the body centered cubic (bcc) Fe-Co alloys in a complete concentration interval, and suggest an alloy composition, most suitable for this application. Compare you result to the experiment.
Day 1: Fe, Co, Lattice parameter, Bulk modulus, different crystal structures,
Day 2: Fe-Co alloy properties, DOS, magnetic moment BGFM
Day 3: Fe, Co, and ordered B2 Fe-Co compound, VASP
Day 4: Fe-Co alloys simulated with supercells of increasing size, local
environment effects. Linear scaling LSGF
Day 5: Analysis and discussion
Literature: Landolt-Börnstein, Numerical Data and Functional Relationship
in Science and Technology, Landolt-Börnstein, New Series, Vol.
III/19a, edited by D. Bonnenberg, K. A. Hempel, and H. P. Y. Wijn (Springer-Verlag, Berlin, 1986)
4. Properties of Fe-based alloys used as construction materials for nuclear energy
The binary bcc Fe-Cr alloy is the base of many important industrial steels, especially in the nuclear industry. A moderate amount of Cr has proven to be most beneficial when it comes to the stability of the alloy. Compute the mixing enthalpies of the bcc Fe-Cr alloy, and determine the composition at which the alloy is most stable. Compare calculated mixing enthalpies with available experimental information (R. Hultgren et al., Selected Values of the Thermodynamic Properties of Binary Alloys, Ohio 1973, pages 694-703). If there are any differences, explain them. (Hint: consider the experimental temperature at which the measurements were done. Compare it with the Curie temperature for Fe-Cr alloys. Calculate mixing enthalpies for paramagnetic bcc Fe-Cr alloys using the model of local moment disorder)
Day 1. Fe, Cr lattice parameter, bulk modulus, crystal structures, magnetism.
Day 2. Ferromagnetic Fe-Cr alloy: properties, mixing enthalpy, DOS, magnetic
Day 3. Fe, Cr bulk properties, B2 Fe-Cr compound, VASP
Day 4. Disordered Local Model for paramagnetic Fe-Cr alloys. Compare results
with FM calculations and with experiment BGFM
Day 5. Analysis and discussion
Literature: R. Hultgren et al., Selected Values of the Thermodynamic Properties of Binary Alloys, Ohio 1973, pages 694-703
5. Magnetic properties of dilute magnetic semiconductors (adv.).
A promising direction in modern electronics is spintronics, where one would like to use the electron spin, in addition to the electron charge, in device applications. One of the problems here is the spin injection. Recently, Ohno et al. ( Science 281, 951 (1998); Nature 407, 790 (1999); Nature 408, 944 (2000) ) suggested to doping semiconductor materials (like GaAs) with transition metal impurities (Mn), to obtain the dilute magnetic semiconductors (DMS ).
It is known from the experiment and first-principles calculations that Mn impurities predominantly substitute Ga atoms, and that the magnetic moment per impurity is about 2 mu_B. Calculate magnetic moments of Mn impurities in GaAs. Compare to the experimental value.
What happens with magnetic moment if one allows some Mn atoms to occupy also interstitial positions?
Day 1. GaAs, Lattice parameter, Bulk modulus, band gap, BGFM
Day 2. Substitutional Mn in GaAs: magnetic moment M as a function of
c_Mn. Ferromagnetic (FM) and disordered local moment DLM magnetic
structure, DOS. BGFM
Day 3. Mn in GaAs, supercell. Investigate the effect of local lattice relaxations
on the magnetic moment and DOS VASP
Day 4. Mn in GaAs, substitutional and interstitial: Magnetic moments
as a function of their concentrations, antiferromagnetic AF vs FM
Day 5. Analysis of results and discussion
Literature: Tomasz Dietl and Hideo Ohno, MRS BULLETIN/OCTOBER 2003, 714-719 (www.mrs.org/publications/bulletin)
6. Pressure induced alloying of immiscible elements.
The Earth’s core is mostly Fe, but it is also lighter than pure Fe should be at these conditions (T~6000 K, P~300 GPa). It is currently unknown what light element is present in the core, but Mg is thought to be excluded. Indeed, Fe and Mg are almost immiscible at ambient conditions, due to large size mismatch of the alloy components. Check if this statement is still true at megabar pressure?
Hint: calculate mixing enthalpy of Fe-Mg alloys as a function of pressure and composition.
Day 1. Fe, Mg bulk properties of the hcp structure. BGFM
Day 2. Fe-Mg hcp alloy, mixing enthalpy at ambient conditions. BGFM
Day 3. Fe, Mg bulk properties, Mg impurity in Fe supercell. VASP
Day 4. Fe-Mg alloy as function of pressure. BGFM
Mg impurity in Fe VASP
Day 5. Analysis of results and discussion.
- Massalski, T. B., Structure and stability of alloys, in Physical Metallurgy Vol. 1 (eds. R. W. Cahn and P. Haasen), 134-204 (North-Holland, Amsterdam, 1996).
- Haitani, T., Tamura, Y., Motegi, T., Kono, N., Tamehiro H. Solubility of iron in pure magnesium and cast structure of Mg-Fe Alloys, Materials Science Forum 419, 697-702 (2003).
- de Boer, F. R., Boom, R., Mattens, W. C. M., Miedema, A. R., & Niessen, A. K., Cohesion in metals. Transition metal alloys. North-Holland Physics Publishing, Amsterdam, 758 p. (1988).
7. Ordered and disorder phases in Cu-Au (adv.).
Calculate the energy differences between ordered and disordered Cu-Au alloys at 25, 50, and 75 at% using the BGFM method. Compare your results to Cu-Au phase diagram. Do they make sense? Calculate the electronic structure (DOS) for ordered and disordered alloys. Do you see the difference? Compare the evolution of the DOS as a function of the short-range order (SRO) parameter for Cu75Au25 alloy with the photoemission experiment taken at different temperatures.
Day 1. Cu, Au, bulk properties BGFM
Day 2. Properties of the fcc Cu-Au alloy and ordered L12 and L10 compounds.
Day 3. Properties of the fcc Cu-Au alloy simulated by supercell SQS-16 and
ordered L12 and L10 compounds. VASP
Day 4. Electronic structure of fcc Cu75Au25 alloy as a function of the SRO
Day 5. Analysis of SQS results and discussion
Literature: A. V. Ruban and I. A. Abrikosov, Rep. Prog. Phys. 71, 046501 (2008), Sec. 3;
R. G. Jordan et al., J. Phys. F 15, L135 (1985).
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Last updated: 09/20/11