Amorphous
Metals
Introduction
Amorphous silicon steels are of interest for use in transformer cores
and other electrical power applications since their use in these devices
leads to more efficient power conversion. This can lead to very large
savings in the electrical power generation and transmission industry since
these devices are so pervasive. In order to use these materials the amorphous
metals must usually be cast in thin ribbon form and then wrapped into
the proper shape. This can lead to plastic deformation, often through
the formation of shear bands, and result in permanent magnetization that
interferes with device operation. We have used atomic force and magnetic
force microscopy to study these shear bands and their corresponding magnetizations.
Figure 1 shows three dimensional renderings of some of our results from
AFM and MFM imaging on the tensile side of a bent FeBSi ribbon. The tensile
side (or top side) is the side that has been stretched during the bend.
From the AFM image on the left we see the shear bands that form during
plastic deformation. These are typically less than 50 nanometers tall.
An interesting feature that has not been observed previously is the curvature
of the shear bands which may help understand the residual stress if further
modeling is carried out. The middle panel shows the corresponding MFM
image and the right panel is the difference image between the MFM and
topograph to show more clearly where the shear bands and magnetic domain
changes coincide. From the magnetic data, we see that each shear band
has a pattern of domains emanating from terrace edges with characteristic
interdigitated zig-zag patterns.
Observing many of these patterns lets us determine some general features.
Near the tops of shear steps, the general domain structure is banded along
the width of the ribbon with a small angle zigzag structure and strongest
MFM signal. As these propagate across the terrace, the zigzags diminish,
may condense into a fewer number of domains, and often deviate from the
step edge perpendicular. At the bottom of a shear step, the MFM signal
is weaker and domains begin to acquire components parallel to the shear
steps, in some cases forming loops. Zigzag structures are occasionally
observed here but they rarely extend far from the step. Between the shear
steps, the MFM signal weakens and the magnetic structure becomes a convolution
of the above descriptions. On a narrow terrace with two shear step tops,
the banding and zigzag structure can propagate all the way across. Alternatively,
for a terrace bounded by a top edge on one side and a bottom edge on the
other, the general domain structures meet in the middle and coalesce.
Based on previous results (described below), on the tensile side of bending
we seem to be observing structure consistent with tensile stress along
the surface normal and/or in-plane compressive stress. The features we
observe appear to be z-oriented domains with in-plane closure domains
acquiring a zigzag structure due to their head-to-head orientation.
Figure 2 shows AFM and MFM images from the compressive side of a bent
ribbon. The compressive side (or bottom side) is the one that has been
compressed during the bend. The shear band structures are similar to those
on the tensile side, but the magnetic structures are different, indicating
the different stress fields present.
The most regular magnetic feature on the compressive side is the straight
line parallel to (and coincident with) the step edges. The rest of the
magnetic structure can be classified as "banded" and oriented
roughly perpendicular to the step edges, but the domain walls are curved
and the width of the domains and curvature of the walls changes with distance
from the step. The features are sometimes continuous across the step edges
unlike those on the tensile side of bending. These features are reminiscent
of "lozenge" domains[1] which may provide a clue to the forces
behind their structure.
Magnetic structure
A material’s magnetic structure is determined by the configuration
of spins which minimizes the total magnetic energy. In deformed, amorphous
melt-spun ribbons, without external fields, this includes contributions
from shape and stress anisotropies, and magnetostatic and magnetic exchange
effects. The anisotropies determine the easy magnetization direction and
the final magnetic structure is a compromise between shape anisotropy
aligning the magnetization (M) with the longest axis, stress anisotropy
aligning M along the direction of largest stress, and demagnetizing effects
breaking large domains into smaller ones and setting up closure domains
to contain the flux. Domain structures will be discussed below. Shape
anisotropy effects can be large due to the high aspect ratio of melt spun
ribbons. Rapid quenching and process-induced stress anisotropy can have
the strongest effect, manifested through the magnetoelastic energy,
to lowest order, where lambda is the material dependent magnetostriction
constant and the gammas are the direction cosines of M with respect to
the principal stress axes. For positive lambda materials, such as FeBSi
alloys, M will align along the direction of most positive (or least negative)
stress. In plastic deformation, the final stress state is a superposition
of the stress due to the damage structures with residual stress, which
occurs on unloading.
Domain formation minimizes the net magnetization by breaking it up into
smaller domains having different orientations (demagnetization) and closure
domains keeping flux within the material. Demagnetization segregates spins
into oppositely aligned domains separated by 180¾ domain walls. These
fine domains have a net overall attraction for each other and lower the
total energy. They also satisfy the magnetoelastic energy since they point
along (parallel or antiparallel to) the easy axis. Any excessive stray
field flux is reduced by in-plane closure domains, separated from the
vertical domains by 90¾ walls.
The actual observed domain structure is often complicated by defects,
microstructure, and the material’s previous exposure to fields. In
general, increasing the number of domains lowers the total energy. However,
smaller domains mean more domain walls. Despite these complications, conclusions
can be drawn from MFM data since they reproduce general features of stress-induced
domain structures observed and understood from previous experiments by
Livingston et.al.[2], [3], [4], [5] using Bitter-pattern optical and Lorentz-force
scanning electron microscopies on various materials. For in-plane magnetization,
the general trend is for the domains to segregate into bands of alternating
orientation in the surface direction normal to the easy axis. For out
of plane magnetization, the magnetization breaks into bands, but meanders
in the surface plane unless some other aspect influences its direction.
In-plane closure domains also form and sometimes acquire a zigzag boundary
structure. Explanations of zigzags arising from head-to-head domains such
as these include rapidly alternating oblique orientation of the walls’
surface projection and energy gained by lengthening the wall and spreading
out the magnetic pole distribution a head-to-head region approximates.[6],
[7], [8]
Previous results on FeBSi materials
Lakshmanan et.al.[9], [10], [11] have used Bitter pattern optical microscopy
to examine shear-band-induced magnetic structure in Fe78B13Si9.
From two dimensional optical data on the tensile side of bending, they
observed fine, zigzag closure domains normal to shear step edges. These
domains decreased in intensity farther from the shear step, gained components
parallel to step edges farther from the step, and were ~3 times longer
on the elevated side of the shear steps as compared to the lower side.
These features persisted after the steps were electropolished away, indicating
that the magnetic structure arose from subsurface stress associated with
the shear band. On the compressive side of bending, the domain patterns
were described as straight 180¾ domain walls separating in-plane domains
oriented at 90¾ to the shear steps. These patterns did not persist upon
electropolishing. Instead, a thin collection of colloid at the shear step
was observed, indicating a stress-induced in-plane anisotropy on both
sides of the step, but that the step itself was necessary to nucleate
the domains and induce demagnetization energy.
From the magnetic data, Lakshmanan et. al. inferred compressive and tensile
side "dislocation array" structures. These qualitatively account
for the topography and magnetic structure that they observed in their
optical experiments but the concept of a dislocation in amorphous material
is not defined. However, knowing displacements, the concept of a dislocation
core can be useful in a continuum model to calculate stresses associated
with shear bands and compare to observed magnetic structure.
Summary
We have used AFM and MFM to add new insight into the nature of deformation
of magnetic amorphous materials. Other work referenced on our publications
page includes interesting results from indentation studies as well. In
particular, for both types of deformation studies, AFM has provided new
information about the physical shape and the height-width distributions
of shear bands formed during the process. Combining these with the stress
states inferred from the magnetic images will help us put together a coherent
picture of the mechanical effects underlying deformation of these materials.
References
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