Flux Mapping and Magnetic Behavior of Grain Boundaries in Nd-Fe-B Magnets
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3000F microscope under the free-lens control mode. The internal magnetic field (0.02-3T) of the TEM was carefully calibrated by SQUID [9] and Hall probe [10] measurements. RESULTS AND DISCUSSION A. Maenetic flux mayDin2 It is essential that any method used for image analysis of local domain structure of magnetic material is simple, reliable and quantitative. The novel approach based on magnetic interferograms, created by PCF-imaging, complies with most of these demands. Recently, PCF microscopy was applied for induction mapping of closure domains in soft Fe- and Co-films [1, 2]. In the present work, we modified this method to analyze the hard magnets. Fig. 1 illustrates the principles of magnetic-flux observation and PCF-interferograms. We assumed that all the interactions of electron waves with a sample could be explained by their interactions with electromagnetic fields. Then, from the Schr6dinger equation the phase shift (AO) between the two electron beams T = R exp(iO), where 0 = tp / h, can be defined as [1]
A0:=Aqph=(2--,r/h)f-Vds - (elh)fAds= (2-ýI§, h)f.fVIds - (e/h)JBds,
(1)
Here, m and e are the electron mass and charge, and h = h / 27t is Planck's constant. V and A are the scalar and vector potentials (div A = 0), representing the electrostatic and magnetic field contributions. The contour integral of A is taken for a closed path along two electron trajectories, and the integral of B is performed for the normal component of flux density (Bn) over the surface enclosed by the two electron paths.
a
~Colveren electron
br
beam
Rr
flew Wavern
Fig. 1 (a) Principle of magnetic-flux observation, and (b) phase-coherent Foucault imaging. In a FEGTEM, the fringe pattern (interferogram) formed by the phase shift between intersecting coherent electron waves can be well described by the Eq.(l), which can be reduced to the following one, assuming a uniform film thickness (t) and absence of electrostatic stray field:
p h-= ( -mneV /2h).(oV).t +(4h)fJB .ds
C.Io t + (4h).i , -M
(2)
where V 0 is the inner potential. It is assumed here that V0 z 20V, Vo
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