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Neutron Scattering Studies of Materials for Information Technology II. SANS

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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
- 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

- 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

- 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

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

- 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 [Fe49Pt51]88Ag12 Nanoparticle Films (25 Tdot/in2)

Before Annealing

Annealed at 400oC for 30 min

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

- 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

- 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

- 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.

Small Angle Neutron ScatteringExperimental GeometryShear Cell Environment

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 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

- 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

- 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

- 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

- 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).

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