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Neutron Scattering Studies of Materials for Information Technology II. SANS. G.J. Mankey S. Al-Ghamdi, H. Alouach, F. Liu, P. Mani, Z. Zhao, I. Zoto V.V. Krishnamurthy Bhandar, M.Piao, A. Lane, D. Nikles, J. Weist, H. Fujiwara, J.W. Harrell MINT Center, The University of Alabama

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neutron scattering studies of materials for information technology ii sans

Neutron Scattering Studies of Materials for Information Technology II. SANS

  • G.J. Mankey
  • S. Al-Ghamdi, H. Alouach, F. Liu, P. Mani, Z. Zhao, I. Zoto
  • V.V. Krishnamurthy
  • Bhandar, M.Piao, A. Lane, D. Nikles, J. Weist,
  • H. Fujiwara, J.W. Harrell
  • MINT Center, The University of Alabama
  • J.L. Robertson (ORNL), L. Porcar (NIST), C. Glinka (NIST),
  • W.-T. Lee (ANL), F. Klose (ANL),
  • J. Mitchell (ANL), N. Cavadini (PSI)

These projects are funded by grants from NSF and DOE/EPSCoR

measurement techniques
Measurement Techniques
  • You won’t know the result until you open the box that contains the cat.
  • Only the correct measurement will answer your question.
  • Persistence and dedication are necessary.
small angle neutron scattering
Small Angle Neutron Scattering
  • Neutrons probe length scales comparable to TEM and soft x-rays.
  • Neutrons are a gentle probe since their energies are of the order of a few milli electron volts as opposed to hundreds to thousands of electron volts for x-rays and electrons.

ref: Charles Glinka, NIST

sans instrumentation
SANS Instrumentation
  • Nanoscale lengths are probed.

ref: Charles Glinka, NIST

small angle neutron scattering5
Small Angle Neutron Scattering
  • Probe must match momentum transfer to particle size via the relation: k = 2p/particle size
beamline ng7 at nist center for neutron research
Beamline NG7 at NIST Center for Neutron Research
  • Measurement Conditions
  • Radial Scan
  • sample-detector distance= 15.5 m
  • neutron wavelength
  •  = 6 Å
  • Couette shear cell
  • magnetic field:
  • 0-180 Oe
  • room temperature
  • shear rate: 0-4000 s-1
tem images of self assembled fe 49 pt 51 88 ag 12 nanoparticle films 25 tdot in 2
TEM Images of Self-Assembled [Fe49Pt51]88Ag12 Nanoparticle Films (25 Tdot/in2)

Before Annealing

Annealed at 400oC for 30 min

schematic of sans from domains of hexagonal nets
Schematic of SANS from Domains of Hexagonal Nets

f

  • The small angle neutron scattering pattern is basically the Fourier transform of the arrangement of particles in-plane.
  • At low q, a ring with radius 2p/a, where a is the average spacing, is observed for a domains of randomly oriented hexagonal array.
  • We integrate the intensity over f to represent the scattering pattern.

FFT

SANS

Pattern

Real Space

Reciprocal Space

schematic of sans of sintering
Schematic of SANS of Sintering
  • The ring characteristic of long range order loses intensity in the partially sintered system.
  • Intensity is shifted to low q from the ring.
  • The sintered system has a single circular blob of intensity at low q and no ring.

Ordered

Partial

Sintered

feptau drop dried samples sans intensity
FePtAu Drop Dried Samples: SANS Intensity
  • The sample with no heating (NH), exhibits a ring of intensity at 2p/particle spacing.
  • Annealing at 250 C produces larger particles as the intensity at low q is dramatically enhanced and the ring pattern disappears.
spin coated feptau films scattering intensity vs scattering vector
Spin Coated FePtAu Films:Scattering Intensity vs. Scattering vector
  • For the spin coated particle array, the 250 C anneal does not destroy the order.
  • There is a shift of the peak to higher q which shows the in-plane spacing is reduced by annealing.
  • Annealing at higher temperatures results in agglomeration.
data analysis
Data Analysis
  • For Fe, magnetic scattering is expected to be about 1/3 of the nuclear scattering.
  • The magnetic scattering contribution is expected to add to the nuclear scattering as the magnetization of the particles is along their long axis.
  • The neutron scattering intensity is fitted with: I() = A + B sin2( +  )
  • B/A is anisotropy.
  •  is the azimuthal angle.
  •  is the tilt angle.
scattering anisotropy
Scattering Anisotropy
  • Scattering is isotropic in zero field and zero shear conditions.
  • Particles are randomly oriented in zero field and zero shear
  • Anisotropic scattering is observed either in applied field or under the influence of shear particles align along the field or shear
shear rate dependence of tilt angle
Shear Rate Dependence of Tilt Angle
  • Tilt angle follows a power law behavior of

shear rate:

 = c-z

z is a dynamic exponent.

z depends on

(a) dimensionality

(b) type of aggregation

process

  • Experimental data shows

the field dependence of z.

V. V. Krishnamurthy et al., Phys. Rev. E 67, 51406 (2003).

theoretical study of nanoparticle dynamics
Theoretical Study of Nanoparticle Dynamics
  • The behavior of Fe nanoparticles in the magnetic dispersion under the influence of steady shear flow and static magnetic field is theoretically studied using the constitutive model.
  • The constitutive model: A. S. Bhandar and J. M. Wiest, J. Colloid and Interface Sci. (2002).
  • single-particle mean-field approach
  • the particles as rigid dumbbells dispersed in a solvent.
  • incorporates
    • Brownian motion
    • anisotropic hydrodynamic drag
    • a steric potential
    • magnetic forces (dipolar)
comparison of the sans results with the constitutive model calculations order parameter s
Comparison of the SANS Results with the Constitutive Model Calculations: Order Parameter S
  • f(u,t) is the orientational distribution function
  • f(u,t) du is the probability that a particle is within the solid angle du of orientation u at time t.
  • The scalar invariant S= tr(S.S.S)1/3 is the order parameter

S=0 Random orientation, S=1 perfect order

S<0 oblate ordering, S>0 prolate ordering

constitutive model calculations director flow angle
Constitutive Model Calculations: Director Flow Angle
  • Shear rate dependence of tilt angle is qualitatively similar to SANS observations.
  • The transition from field oriented state to shear oriented state is abrupt in the model.
  • Polydispersity plays a role in determining the sharpness of the transition.

V. V. Krishnamurthy et al., Phys. Rev. E 67, 51406 (2003).

magnetic devices

60 Oe

18 Oe

0 Oe

Ha

-18 Oe

-47 Oe

-10 Oe

MFM of CoNiFe Bars: 2.6 mm x 10.9 mm x 100 nm

Magnetic Devices
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