γ
Fe57
Fe57
γ
Mössbauer Spectroscopy
of Cobalt Ferrites
Andrew Watson
Dr. Kelly Krieble
Outline
• The Mössbauer Effect:
• What is it and how does it work?
• Materials (Cobalt Ferrites)
• Applications & Production
• The Spinel Crystal Structure
• Current and Future Data
• Conclusions
The Mössbauer Effect:
What is it?
• Absorption / emission
• “[J]ust like a gun recoils when firing a bullet” [1],
an atom must recoil when emitting / absorbing a
γ-ray.
• Atoms, etc. have “excited states”, which require
an exact amount of energy to attain, too much or
too little will not do.
• If a γ-ray strikes an atom, it must have an energy
greater than the energy of this transition, due to
the recoil of the atom.
• Conversely, due to recoil, a γ-ray emitted from
said atom will have slightly less than this
transition energy.
E2
E1
ΔE
ΔE+ER
E0
[2]
The Mössbauer Effect:
What is it?
• Classical vs. Quantum Mechanical Models
• Classical Model - γ-rays need an exact energy to be
absorbed into / emitted from an atom. ZERO
overlap.
• Quantum Mechanical Model – wider acceptable
range of energies due to Heisenberg’s Uncertainty
Principle
• However, this “overlapping” region is very small
and very rare. Recoilless emission / absorption
almost never happens with a lone atom.
• Resonant absorption / emission
E-ER
E
E+ER
Classically
E-ER
E+ER
Q-Mechanically
γ
Fe57
γ
Fe57
γ
Fe57
γ
Fe57
γ
The Mössbauer Effect:
How does it work?
• Crystal Lattices…
• …relative to a single atom, have effectively an infinite mass.
• When a single γ-ray strikes a crystal, energy can still be lost
in recoil, but it must be lost in discrete quanta called
“phonons”, and the recoil is distributed to the entire solid.
• This recoil is sometimes so small that not even a single
phonon is released. This is known as a “recoilless emission /
absorption.”
γ
γ
E=Eγ
E=Eγ
The Mössbauer Effect:
Definition
The Mossbauer effect is the recoilless,
resonant emission and absorption of
gamma rays
The Mössbauer Effect:
Can any crystal exhibit it?
• To successfully exhibit the effect, a crystal lattice needs to
meet a few requirements:
• “As resonance only occurs when the transition energy of
the emitting and absorbing nucleus match exactly, the
effect is isotope specific”[1].
• Essentially, what is needed is a “favorable” ratio of recoil
energy to excitation energy
[1]
The Mössbauer Effect:
Why is it significant?
Mössbauer spectroscopy gives us
information about a few types of nuclear
interactions:
Isomer Shift
Hyperfine Splitting
The Mössbauer Effect:
Isomer Shift
“For a source made of compound s, and an absorber of
compound a, the peak of the absorption curve will move from
zero velocity of source relative to absorber, found if s and a
are the same compound, to a value given by…
γ
s
a
The Mössbauer Effect:
Isomer Shift
“δ(v) = (4/5)πe2R2(ΔR/R)[|Ψ(0)|s2-|Ψ(0)|a2]
Where R = (Re+Rg)/2 and ΔR = Re-Rg …
Hence δ(v) = K(|Ψ(0)|s2-|Ψ(0)|a2). K depends only on the nuclear
characteristics and is a constant for a given Mössbauer transition.
It can be seen that the magnitude of this shift, called the isomer
shift…is determined by the difference in the electron densities at the
nuclei of the atoms containing the Mössbauer nuclei in the source and
absorber.”[5]
The Mössbauer Effect:
Zeeman Splitting
Nuclear energy levels
Magnetic effect, dipoles align
Materials (Cobalt Ferrites)
Sample Creation
• Cardiff University, Wales:
• Powders of 99.9% pure Co3O4, 97%+ pure Mn3O4, and Fe-oxide
mixed to desired ratios for 30 minutes to thoroughly blend powders
• Samples are ground together, pressed into a ½” dia. ¾” slug, then
heated in a furnace at 1000°C for an hr., cooled for 24 hrs., repeat
• Samples ground again, pressed into a slug, then heated at 1350°C
for 24 hrs., cooled again for several hours
Materials (Cobalt Ferrites)
Spinel Structure
• Named after the mineral “spinel” - MgAl2O4
• Basic structure: AB2O4
• Includes A-site (tetrahedral) and B-site (octahedral) atoms
• Preferences for different sites affect magnetic properties
http://www.tf.uni-kiel.de/matwis/amat/def_en/kap_2/basics/b2_1_6.html
Materials (Cobalt Ferrites)
Superexchange
• Allows two atoms which are not touching to interact through an intermediate atom
• Two magnetic cations interact through a non-magnetic anion
• Electrons act as dipoles, dipoles align
Applications
• energy and transportation industries, actuators
• noncontact stress and torque sensors to help address energy efficiency,
environmental, and safety issues
• If used as torque sensors for electronic power steering assists a 5%
improvement in fuel efficiency would be realized over hydraulic power
steering…”[6]
Fitting Data
‘Lor’
‘z0’
‘dz’
‘shift0’
‘rel area’
= FWHM of intrinsic Lorentzian
= Center of Hyperfine Field
Gaussian Distribution
= FWHM of HFD Gaussian
= shift value when z0 = 0
= area above the curve
“The full width at half maximum (FWHM) is a
parameter commonly used to describe the width of
a ‘bump’ on a curve or function. It is given by the
distance between points on the curve at which the
function reaches half its maximum value.”
[4]
[3]
Data
Ge-series: 0.1, 0.2, 0.3, 0.4, 0.6
(Co[1+x]Ge[x]Fe[2-2x]O[4])
Co-series: 0.2, 0.6, 0.9, 1.1, 1.2, 1.8, 2.2
(Co[x]Fe[3-x]O[4])
Quenched samples: from 600°C, 800°C, 1000°C, 1200°C, 1400°C
Al-series: 0.08, 0.25, 0.54, 0.73, 0.92
approx. (CoAl[x]Fe[2-x]O[4])
More Data
More Data
Conclusions
Ge-series: “Bump” in data was normalized with new samples
Co-series: 3-site pattern suggests the samples are
a 2-phase mixtures of spinel structure and another phase
Quenched: Differences are subtle.
“By other measurements, we believe that we see the evidence of site
occupancy changes that you might expect. The ones quenched from the
lowest temperature appear to have the most Co in octahedral (B) sites, and
least in tetrahedral (A) sites, and the ones quenched from the higher
temperatures appear to approach a more random arrangement…”
– Dr. John Snyder
Sources!
1. Mössbauer Spectroscopy Group, Royal Society of Chemistry (RSC) website, Introduction to
Mössbauer Spectroscopy Part 1. Accessed July 1 2010.
http://www.rsc.org/membership/networking/interestgroups/mossbauerspect/intropart1.asp
2. International Board on the Applications of the Mössbauer Effect (IBAME) and Mössbauer Effect
Data Center (MEDC), Mössbauer Effect website . Accessed July 1 2010.
http://www.mossbauer.org/mossbauer.html
3. Weisstein, Eric W. "Lorentzian Function." From MathWorld--A Wolfram Web
Resource. http://mathworld.wolfram.com/LorentzianFunction.html
4. "Gaussian Distribution." Wikipedia . Wikimedia, 08 July 2010. Web. 9 July 2010.
http://en.wikipedia.org/wiki/Gaussian_function
5. Maddock, Alfred. Mössbauer Spectroscopy: Principles and Applications. 1st ed. Chichester:
Horwood Publishing, 1997. 9. Print.
6. Snyder, Ph.D., J.E., and D.C. Jiles. New Substituted Cobalt Ferrite-Based Magnetoelastic
Materials: Understanding a New Class of Oxide-Based Smart Materials. The Wolfson Centre for
Magnetics, 2007. 7. Print.