2. School of Materials Science and Engineering
Harbin Institute ofTechnology
Ramesh Paudel
Ph.D. Candidate
Electronic and Magnetic properties of Fe, Cr, FeCr
and FeCr3 : First Principles Study
3. Out line
• Introduction
• Theoretical Background
• Methods of Electronic Structure
Calculations
• Result and Discussion
• Conclusion
5. • The electronic and magnetic study of elements and alloys
are of great interest
• Different types of codes related to electronic structure is
also one of the great challenges in condensed matter physics
and quantum chemistry of solids in atomic scale
• TB-LMTO-ASA is mostly used technique for the calculation of
minimum energy, density of states, band structure, charge
density, optical properties etc.
• The electronic properties of Fe, Cr, FeCr and FeCr3 for
ordered system is interesting from practical points of view
6. Iron Chromium
Atomic number 26 Atomic number 24
Fe [Ar]3d64s2 Cr [Ar]3d54s1
Atomic mass 55.845amu Atomic mass 51.996amu
Density 7.86 g Density 7.15 g
Melting point C Melting point C
10. Born-Oppenheimer Approximation
Total Hamiltonian of the system
• In Born-Oppenheimer Approximation, we neglect the K.
E. of the nuclei.
• With this Hamiltonian we can developed Hartree-self
consistent field approximation.
11. Hartree-Fock equation
Where the exchange potential can be expressed as
• Exchange potential is difficult to derive in practice because it is
non-local and related to the interaction between all electrons in
the system.
• Hartree - fock approach has a highly computational cost and
therefore restricted to small system.
12. Density Functional Theory
• Hohenberg and Kohn proposed the Density Functional Theory
in 1964
• DFT is the method successfully describes the behavior of
atomic and molecular system.
• Low computational effort, simulate a large amount of
particles and easy to implement.
Khon – Sham (K-S) equation
Effective potential
• Local Density Approximation (LDA)
• Generalized Gradient Approximation (GGA)
13. Methods of electronic structure calculation
The linearised muffin-tin orbital(LMTO) method
Potential is assumed to be spherically symmetric close to nuclei (ion-
core) = MT-Sphere
Potential is assumed to be flat between = Interstitial
Muffin tin potential for single Electron
muffin tin sphere
14. Working process ofTB-LMTO-ASA
We make CTRL file
(Using space group, lattice parameter etc.)
Run File
Band structure, Density of states, Optical properties
Gnuplot, Xcrysden
19. Maximum occupancy occurs along the Fermi energy level
Contributes to magnetic and electronic properties
Band structure of t2g and eg orbital of Fe
20. Minimum value of lattice parameter of FeCr and FeCr3
Lattice parameter FeCr =5.36 a.u. Lattice parameter FeCr3 =5.35 a.u.
21. Band Structure of FeCr and FeCr3
-40
-20
0
20
40
60
G N P G H N
Energy(eV)
Band structure of all fecr
-40
-20
0
20
40
60
G N P G H N
Energy(eV)
band fecr3
22. Band structure of s and p orbital of FeCr
-50
-40
-30
-20
-10
0
10
20
30
40
G N P G H N
Energy(eV)
bnd of sfecr
-50
-40
-30
-20
-10
0
10
20
30
40
G N P G H N
Energy(eV)
bnd pFeCr
23. Band structure of t2g and eg Orbital of FeCr
-40
-20
0
20
40
60
G N P G H N
Energy(eV) bndt2gfecr
-40
-20
0
20
40
60
G N P G H N
Energy(eV)
egfecr
24. Density of States (DOS)
Total number of electronic states available per unit energy range
Total Density of States of Fe
DN DOS
UP DOS
Magnetic moment = 2.19µB
30. Elemental solid Fe and Cr shows nine bands along the
symmetry axis.
Magnetic moment of Fe is higher than Cr.
Ordered binary alloy FeCr and FeCr3 shows 18 and 36
bands, conduction bands and valance bands are
overlapping.
Contribution to magnetic moments due to electrons
present in s and p orbital is very less in both the elements
and p orbital is little bit high in FeCr.
31. Major contribution to magnetic moments is due to the
electrons present in d-orbital in metals.
Occupancy of the electrons in s and p orbital occurs
above and below the Fermi level.
Occupancy of the electrons in d-orbital occurs near Fermi
level.
TB-LMTO-ASA is useful to study the other ordered solid
for their magnetic and electronic properties
32. Conference /Work shop
• Poster presentation on the ‘Sixth national conference’
conducted by Nepal Academy of Science and Technology
(NAST) September 2012
• Participated in a program ‘ Kathmandu Summer School on ab
inito Simulation of Solids-2013 conducted by Central Dept. of
Physics .April 2013
• Participated at 8th USPEX work shop in India 20-24 January
2015
• Paper under review at University Grand Commission (UGC)
Nepal.
33. Prof. A. Mookerjee SNBCSS Kolkata, India
All the faculty members academic and non academic staffs of
Department of Physics, Tribhuvan University
Prof. Narayan Prasad Adhikari Tribhuvan University
Prof. Shanker Prasad Shrestha Tribhuvan University
My Friends and Family
Acknowledgements
