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Topic: Bragg reflection

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	Bragg's Law and Diffraction
		Although Bragg's law was used to explain the interference pattern of X-rays scattered by crystals, diffraction has been developed to study the structure of all states of matter with any beam, e.g., ions, electrons, neutrons, and protons, with a wavelength similar to the distance between the atomic or molecular structures of interest.
		Bragg's Law can easily be derived by considering the conditions necessary to make the phases of the beams coincide when the incident angle equals and reflecting angle.
		The Braggs used crystals in the reflection geometry to analyze the intensity and wavelengths of X-rays (spectra) generated by different materials.
	www.eserc.stonybrook.edu /ProjectJava/Bragg (847 words)

	Publications by Petr Mikulík
		The obtained expression for the reflectivity is effective for the so-called crystal truncation rod scattering as well as the usual Bragg reflection, including the special cases such as total reflection at grazing incidence, Bragg reflection at the Bragg angle Pi/2, and for both coplanar and noncoplanar reflections.
		The scattering phenomena studied are the specular reflection from planar multilayers with various stacking sequences (single layer, periodic, quasiperiodic), the diffuse scattering from rough multilayers, and the scattering from surface gratings and from multilayer gratings.
		The theories employed for the calculation are: the kinematical theory, the distorted-wave Born approximation, the dynamical theory and various approximations of the dynamical theory (the single-reflection approximation, the two-beam approximation and the multiple-beam approximation), developed in one unified formalism.
	www.sci.muni.cz /~mikulik/Publications.html (5241 words)

	Dynamical x-ray diffraction from multilayers on the Web
		After solving the dynamical diffraction problem for each of the layers, the reflection from the whole system is calculated with the help of the (2x2) recursive matrix algorithm, RMA [6], which is a development of our earlier (4x4) transfer matrix approach, TMA [1-5].
		Then, "Reflection" stands for the Miller indices of the Bragg reflection; "Sigma" is the rms height of substrate roughness expressed in Angstrom; "W0" and "Wh" are the Debye-Waller like corrections to the values provided by the X0h database for x0 and xh respectively.
		Initially, the Bragg spacings for all the layers are set equal to that in the substrate and their variation is solely specified through the parameter "da/a".
	sergey.gmca.aps.anl.gov /GID_SL.html (2825 words)

	[No title]
		It was consisted of 22 mm diameter circular waveguide and two Bragg reflectors in the form of waveguide sections with the same diameter and weak corrugation of side walls.
		In correspondence with calculations, two effective reflections into backward waves were observed in "cold" microwave measurements of the Bragg reflectors: in E11 wave in the vicinity of the frequency 31.5 GHz and in E12 wave in the vicinity of 37.5 GHz.
		The maximum reflection was 95% for te cathode-side reflector and 85% for the collector-side reflector for the both reflection zones.
	sunse.jinr.ru /~snsed/mwsyst.htm (300 words)

	Encyclopedia of Laser Physics and Technology - Fabry-Perots, fiber amplifiers, fiber sensors, fluorescence, frequency ...
		A fiber Bragg grating is a periodic or aperiodic perturbation of the effective refractive index in the core of an optical fiber.
		This leads to the reflection of light (propagating along the fiber) in a narrow range of wavelengths, for which a Bragg condition is fulfilled (→ Bragg mirrors).
		The fabrication of fiber Bragg gratings typically involves the illumination of the core material with ultraviolet laser light, which induces some structural changes and thus a permanent modification of the refractive index.
	www.rp-photonics.com /encyclopedia_f.html (11141 words)

	World Intellectual Property Organization (Site not responding. Last check: 2007-10-13)
		In order to reflect x- rays of the same wavelength efficiently, a crystal optical element must have a near constant incident angle with respect to the reflection planes of the crystal on every point of the surface.
		However, the Bragg condition cannot be satisfied on every point of the crystal using this approach due to the geometrical aberration of the Johann geometry in the Roland circle plane, which will limit the collection solid angle of the optic.
		The spacing d varies in the at least one direction and is determined from a Bragg equation, where a Bragg angle is an incident angle of an x-ray from a source impinging on the optical surface on at least some points of the optical surface.
	www.wipo.int /ipdl/IPDL-CIMAGES/view/pct/getbykey5?KEY=01/39211.010531&ELEMENT_SET=DECL (2722 words)

	Michiel de Dood - Photonic Crystals
		This Bragg reflection is a result of the periodicity of the structure and therefore occurs in any crystal no matter how small the difference in refractive index is. This concept is already known from x-ray diffraction and in this case the regular structure is formed by the atoms that are arranged regularly.
		In fact, this is the origin of the famous Bragg law that gives a relation between the spacing between different planes of atoms, the angle of incendence and the wavelength of the x-rays.
		Although reflection and transmission measurements are mostly used to reveal the existence and spectral position of a presumed photonic bandgap the actual data taken on a finite thickness crystal is much richer.
	www.dedood.demon.nl /PhotonicCrystals.html (5568 words)

	World Intellectual Property Organization (Site not responding. Last check: 2007-10-13)
		Accordingly, the confinement of light in the core is not based on total internal reflection but on Bragg reflection due to the regularity in the radial profile of refractive index.
		As a result, the diverging cylindrical wave is reflected by the annular layers in the cladding, and is confined in the core.
		Such a condition to achieve high reflectivity in the cladding and tight confinement of light to the core is called a pseudo quarter wavelength condition.
	www.wipo.int /ipdl/IPDL-CIMAGES/view/pct/getbykey5?KEY=01/88578.011122&ELEMENT_SET=DECL (6099 words)

	Introduction to the Calculation of Structure Factors (Site not responding. Last check: 2007-10-13)
		The Braggs, father and son, considered the diffraction of X-rays by a crystal to be more conveniently thought of in terms of reflection from regularly spaced, parallel planes in the crystal.
		between the incident beam and the reflecting plane is equal to the angle between the reflected beam and the plane.
		This establishes the principle that the phase difference between rays reflected from parallel planes in a crystal depends on the distances of the points of reflection measured perpendicular to the planes and not on the separation of the points of reflection measured parallel to the planes.
	www.se.iucr.org /iucr-top/comm/cteach/pamphlets/3/3.html (3461 words)

	ElectronicsWeekly.com - Reflective! (Site not responding. Last check: 2007-10-13)
		The difference between the two techniques in the paper is that one uses scattering to reflect light and the other uses Bragg reflection (as the Kent displays do).
		Bragg reflection is a phenomenon that happens when light hits layers that are spaced at a multiple of its wavelength.
		The reason for the lack of improvement in reflectivity is given as the restricted thickness of the layers used in the model.
	www.electronicsweekly.co.uk /Article5462.htm (926 words)

	Bragg Reflection of X-Rays
		The orientation of the set up and the positions of the instrument, should not be changed during the course of the experiment.
		The cube and the receiver (movable arm) must be adjusted accordingly, to measure the intensity of microwaves.
		Using the technique of Bragg diffraction of x-rays, crystallographers can determine the interatomic space inside the crystal if the wavelength of the x-rays is known.
	www2.potsdam.edu /honors/honors/ProfOrg/PHYS/islamma/Phys306_XRAY.htm (698 words)

	NREL: Measurements and Characterization - X-Ray Diffraction (Site not responding. Last check: 2007-10-13)
		The X-rays are diffracted (according to Bragg's law) as they are reflected from successive planes formed by the crystal lattice of the material.
		Measures the strain in a sample by recording the angular shift of a given Bragg reflection as a function of angle of incidence.
		Automatically measures the variations in intensity of a single Bragg reflection as the sample is tilted and rotated.
	www.nrel.gov /measurements/xray.html (363 words)

	Interactive guide to diffraction ..
		The corresponding Bragg reflection is a vector in reciprocal space with indices (h,k).
		The indices (h,k) of the Bragg reflection are inversely proportional to the axis intersections in direct space.
		The Bragg reflection follows the rotation of the direct lattice, while the shift does not affect the position of the Bragg reflections.
	www.uni-wuerzburg.de /mineralogie/crystal/teaching/ispace_r.html (435 words)

	Structure Solution from Powder Patterns - Powder Fit (Site not responding. Last check: 2007-10-13)
		The positions of the reflections in the powder pattern are solely determined by the current lattice parameters and the space group of the crystal (which may result in systematic absences), and the Bragg intensities for each reflection are used as fitting parameters.
		Reflections outside the specified range which have been refined because their tail falls partially within the range (see above) are not taken into account for this normalization and are occasionally refined to very large values greater than 100.
		Reflections falling entirely within excluded regions and reflections which are systematically absent due to the underlying symmetry of the lattice are not shown.
	rmn.ulaval.ca /labo/insight/doc/life/cerius46/csspr/powderfit.html (7983 words)

	X-ray diffraction topography
		A possibility to change this dimension is to use asymmetric reflections (increase and reduction) or to use large source to sample distances (increase; synchrotron case).
		In the low absorption Laue case and the Bragg case we obtain a characteristic pattern of interference fringes, and in the high absorption Laue case one fringe in the centre of the image (fig.
		If part of a crystal is misoriented in such a way that either diffraction cannot occur at the same time as from the rest of the crystal, or that the diffracted beam from the two parts (assumed to be rather perfect) of the crystal make different directions in space, this is called orientation contrast.
	www.esrf.fr /exp_facilities/ID19/homepage/DiffTopo/X-raytopography.htm (4136 words)

	Summary (Site not responding. Last check: 2007-10-13)
		The Bragg reflection spectra from the (111) planes of the crystals were measured as a function of the temperature in the range between 15 and 100
		The thermal hysteresis loop of the reflection peak position due to the phase transition in VO filling the opal voids was observed.
		The observable peaks are due to the Bragg diffraction of electromagnetic waves by the periodic structure of the samples and characterize the stop band in the [111] direction.
	www.edu.ioffe.ru /register?doc=nano2002/golubev.tex (1343 words)

	Gureyev (Site not responding. Last check: 2007-10-13)
		Using this property it is possible to analyse the distribution of the refractive index in an object by passing an X-ray beam through it and then reflecting it from a perfect crystal while possibly changing the incident angle by rotating the crystal [5, 8].
		Therefore, the reflection of a spherical wave with the source close enough to the crystal surface can be described using the RM approximation (18).
		In the refractometric mode the intensity distribution in the reflected wave on the exit surface of the crystal is concentrated near the isolated points at which the incident wavefront normals are at the exact Bragg position.
	www.sif.it /cimento/tocd/019.020304/51/51.html (2566 words)

	Jet-X AT MSSL: SODART (Site not responding. Last check: 2007-10-13)
		The graphite crystal and lithium target are surrounded by four imaging proportional counters that detect the Bragg reflected and the Thomson scattered x-rays (see).
		The Bragg polarimeter is sensitive in two narrow bands, the first order and second order Bragg peaks at 2.6 and 5.2 keV.
		The IPCs are part of the scattering polarimeter subassembly of the SXRP and are used to detect x-rays which have passed through a polarization analyzer, either reflected from a graphite crystal or scattered in a metallic lithium target.
	www.mssl.ucl.ac.uk /www_jetx/sxrp.html (735 words)

	Kyutt (Site not responding. Last check: 2007-10-13)
		The in-plane or parallel spacing was measured in the Laue geometry, and the out-of-plane or perpendicular component in the Bragg one.
		A crystal-analyser was adjusted to reflect the maximum intensity from the standard high-quality GaAs bulk crystal, and the analyser position was marked.
		According to (3), this is not the case of the experimentally observed defect arrangement.
	www.sif.it /cimento/tocd/019.020304/18/18.html (2301 words)

	Research Projects
		In a typical crystallography experiment, a large number of diffraction peaks or Bragg reflections are recorded on an area detector while rotating or oscillating a crystal specimen.
		The intensity recorded for each Bragg reflection depends only on the magnitude of its structure factor, but not on its phase, which is also needed to determine the atomic positions in a crystal.
		The final result is a simple analytical expression of a phase-sensitive diffracted intensity that is valid for all measured Bragg reflections and for the entire excitation range of the reference reflection G in a reference-beam diffraction experiment.
	staff.chess.cornell.edu /~shen/Research.html (2308 words)

	Untitled Document
		Bragg grating based systems for the measurement of strain in smart structures have been demonstrated many times, e.g.
		At the instant a reflection is detected from an FBG, the time of the detected reflection determines the reflected wavelength, as indicated by the graph in Figure 2.
		Figure 3 shows that the Fibre Bragg grating strain sensors function by reflecting selective wavelengths that depend on the state of strain experienced by the gratings.
	dspace.dial.pipex.com /town/pipexdsl/q/aqup61/aims/frames/overview.htm (2623 words)

	Optical characterization of opals
		A clear attenuation band in the optical transmission can be observed in each case due to the Bragg reflection caused by the (111) planes.
		As the sphere size decreases, the Bragg reflection moves linearly towards shorter wavelengths.
		As the angle increases, band 1 shifts to shorter wavelengths according to the Bragg law while band 2 shifts to longer wavelength.
	www.icmm.csic.es /cefe/reflectance.html (574 words)

	Text of MIJ-NSR Volume 6, Article 4 (Site not responding. Last check: 2007-10-13)
		In the as-deposited film, the Au (111) and Ni (111) Bragg reflections appeared, indicating that the Au and Ni films were grown with the (111) preferred orientation.
		N (111) reflection and the scattering intensity was monitored as a function of x-ray energy in the vicinity of Ni K-edge absorption.
		The results indicate that Ga is related to the Bragg peaks for Au and Ni, while Ga is not associated with the Ni (111) Bragg peak.
	nsr.mij.mrs.org /6/4/text.html (1748 words)

	LS Note 245: A Comparison of an Elliptical Multipole Wiggler and Crystal Optics for the Production of Circularly ... (Site not responding. Last check: 2007-10-13)
		The advantage of this approach is that the polarization properties on the tails of the diffraction peak change relatively slowly as a function of the incoming angle compared to the maxima.
		reflectivity as the Bragg angle for the Si (111) monochromator nears 45 degrees, which is accentuated by the detuning.
		The largest difference occurs at 3.5 keV where, due to the depolarization effects from the downstream optics, the phase retarder is a factor of 5 larger than the fully focused EMW beam and 30 larger than the unfocused 2x1 mm beam.
	www.aps.anl.gov /techpub/lsnotes/ls245/ls245.html (4478 words)

	Bragg reflection waveguides with a matching layer (Site not responding. Last check: 2007-10-13)
		It is demonstrated that Bragg reflection waveguides, either planar or cylindrical, can be designed to support a symmetric mode with a specified core field distribution, by adjusting the first layer width.
		Analytic expressions are given for this matching layer, which matches between the electromagnetic field in the core, and a Bragg mirror optimally designed for the mode.
		Either a planar or coaxial Bragg waveguide is shown to support a mode that has a TEM field distribution in the hollow region.
	www.opticsexpress.org /abstract.cfm?URI=OPEX-12-14-3156 (465 words)

	On Focusing in 2-Dimensions (Site not responding. Last check: 2007-10-13)
		Total reflection at grazing angles was first used for two-dimensional focusing in the so-called Kirkpatrick-Baez geometry, where one reflector focuses in one dimension.
		Also shown is the reflectivity of a total reflection coating (in this case Nickel) shown in blue.
		In addition, the multilayer has the advantage over total reflection that the angle of incidence are larger and that thus even more radiation can be intercepted even for optic at the same distance from the source (See to right).
	www.osmic.com /New_Developments/Why_CMF.htm (2001 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		The modification of the structure factor of a two-beam case reflection in the neighbourhood of a three-beam case causes a modification in the intensity distribution inside the Borrmann fan, which can be seen in section topographs.
		Theoretical and experimental methods for the characterization of the reflection properties of flat and bent crystals are presented.
		Comparisons of Bragg reflections from thermal oxide thin films on Si wafers were made for five sets of samples with various kinds of substrates.
	www.wiley-vch.de /contents/jc_2223/199804.html (1338 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		Fiduc ial information on the photon energy, the photon-energy rocking-curve width (0.7 eV), and control of the sample alignment was obtained from the reflectivity curves which were measured simultaneously to the electron-emission spectra with an I}{ \f0\fs20\dn4 0}{\f0\fs20 grid upstream of the sample.
		Note that for this centrosymmetric reflection, the (111) atomic planes bisect the Ge(111) double layer; consequently, F is not equal to 1, but, rather, it is equal to cos(\'b9/4) = \'c3 2/2 = 0.71.
		This reduction in amplitude reflects the spread of positions between the two identical atoms of the diamond-unit cell, which are displaced by a quarter of a (111) lattice constant along the [111] direction.
	www-ssrl.slac.stanford.edu /pubs/ar99/2586v387.rtf (1623 words)

	tutorial: from the magazine: oemagazine.com: Powered by oe magazine. The Monthly Publication of SPIE—The ... (Site not responding. Last check: 2007-10-13)
		If the spacing between those regions is such that all the partial reflections add up in phase—when the round trip of the light between two reflections is an integral number of wavelengths—the total reflection can grow to nearly 100%, even if the individual reflections are very small.
		To create a Bragg grating in an optical fiber, one needs to generate the required periodic pattern of UV light on the side of the fiber.
		The flat-top reflection and sharp edges of apodized FBGs are ideal for high reflection and high isolation from adjacent channels.
	oemagazine.com /fromTheMagazine/tutorial/tutorial101.html (2107 words)

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