Download - Thin films II
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Thin films II
Kinematic theory - works OK for mosaic crystals & other imperfect matls
Doesn't work for many, more complicated films
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Thin films II(see Batterman & Cole, Dynamical Diffraction of X-rays by Perfect
Crystals. Rev. Mod. Phys. 36, p 681 (1964))
The Borrmann effect
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Thin films II(see Batterman & Cole, Dynamical Diffraction of X-rays by Perfect
Crystals. Rev. Mod. Phys. 36, p 681 (1964))
The Borrmann effect
!!!
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Thin films II(see Batterman & Cole, Dynamical Diffraction of X-rays by Perfect
Crystals. Rev. Mod. Phys. 36, p 681 (1964))
The Borrmann effect
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Thin films II(see Batterman & Cole, Dynamical Diffraction of X-rays by Perfect
Crystals. Rev. Mod. Phys. 36, p 681 (1964))
Past discussions of diffraction – 2 beams, in & out("kinematic theory")
But these beams coherently coupled – energy swapped back & forth betwn them
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Thin films II
Past discussions of diffraction – 2 beams, in & out("kinematic theory")
But these beams coherently coupled – energy swapped back & forth betwn them
Must consider all of field as a unit("dynamical theory")
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Thin films II
For Borrmann effect, dynamical theorypredicts standing wave in diffractingmedium
Two solutions – one for no absorption,one for enhanced absorption
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Thin films II
Dynamical theory changes Ewald construction
In dynamical theory, more than one sphere
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Thin films II
Dynamical theory changes Ewald construction
In dynamical theory, more than one sphere
Determine loci of permitted Ewald spheres – the "dispersionsurface". Drawing vectors from points on this surface to reciprocal lattice points gives allowed waves
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Thin films II
Main problem – solve Maxwell's eqns. for medium with periodic, anisotropic, complex dielectric constant
assume solutions consistent with Braggs' law
obtain solns of waves w/ permitted wave vectors
tips of these vectors form dispersion surface
dispersion surface used to generate all diffraction effects
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Thin films II
Correct for index of refraction in medium
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Thin films II
Correct for index of refraction in medium
Nature of dispersion surfaces
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Thin films II (see James, Optical Principles of the Diffraction of X-rays,(1962))
Each lattice point occupied by a dipole set into oscillation by radiation field of electromagnetic wave passing thru crystal
Oscillation of dipoles produces radiation and create radiation field
Oscillation is itself a planewave advancing thru latticenormal to lattice planes
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Thin films II (see James, Optical Principles of the Diffraction of X-rays,(1962))
Each lattice point occupied by a dipole set into oscillation by radiation field of electromagnetic wave passing thru crystal
Oscillation of dipoles produces radiation and create radiation field
Oscillation is itself a planewave advancing thru latticenormal to lattice planes
Dipoles in lattice planeoscillate in phase
Two waves result, one going up, other down
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Thin films II (see James, Optical Principles of the Diffraction of X-rays,(1962))
Think now of two waves:
scattered wave shown in diagram, wave vector k, velocity = c
dipole wave, wave vector K, velocity = nearly c
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Thin films II (see James, Optical Principles of the Diffraction of X-rays,(1962))
Think now of two waves:
scattered wave shown in diagram, wave vector k, velocity = c
dipole wave, wave vector K, velocity = nearly c
Can be shown that:
K = k(1+), small
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Thin films II (see James, Optical Principles of the Diffraction of X-rays,(1962))
Actually, K is an infinite set of vectors
In reciprocal space
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Thin films II (see James, Optical Principles of the Diffraction of X-rays,(1962))
Actually, K is an infinite set of vectors
In reciprocal space
In real space
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Thin films II (see Bowen and Tanner)
K slightly smaller than k
Interaction of incident and diffracted beams takes place atand/or near
O
H
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Thin films II (see Bowen and Tanner)
Deviations in dynamical theory are extremely small
Highly magnified view req'd
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Thin films II (see Bowen and Tanner)
Deviations in dynamical theory are extremely small
Highly magnified view req'd
Interaction takes place on hyperbolic surfacesnear L
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Thin films II (see Bowen and Tanner)
Unfortunately, cannot use dynamical theory to extract structure directly from rocking curves
But, can use it to simulate rocking curves
These then compared to experimental curves and refined
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Thin films II
MnxHg1-xTe on CdTe on GaAs substrate
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Thin films II
Graded layers
Simulated rocking curves for InxGa1-xAs on InP &AlxGa1-xAs on GaAs