DWBA - Revision history

KevinYager: /* Foundational */

2024-10-01T14:50:42Z

‎Foundational

KevinYager: /* Mathematical form */

2023-12-01T14:29:16Z

‎Mathematical form

KevinYager: /* Mathematical form */

2023-12-01T14:25:35Z

‎Mathematical form

KevinYager: /* Mathematical form */

2023-12-01T14:25:18Z

‎Mathematical form

KevinYager: /* Multiple Channels */

2019-04-16T12:50:03Z

‎Multiple Channels

KevinYager: /* Refraction Correction */

2019-04-16T12:49:49Z

‎Refraction Correction

KevinYager: /* References */

2018-03-06T17:05:51Z

‎References

KevinYager at 13:00, 25 July 2015

2015-07-25T13:00:04Z

KevinYager: /* Refraction Correction */

2015-04-23T14:56:19Z

‎Refraction Correction

KevinYager: /* Refraction Correction */

2015-04-23T14:51:06Z

‎Refraction Correction

@@ Line 61: / Line 61: @@
 * George H. Vineyard [http://journals.aps.org/prb/abstract/10.1103/PhysRevB.26.4146 Grazing-incidence diffraction and the distorted-wave approximation for the study of surfaces] ''Phys. Rev. B'' '''1982''', 26, 4146. [http://dx.doi.org/10.1103/PhysRevB.26.4146 doi: 10.1103/PhysRevB.26.4146]
 * S. K. Sinha, E. B. Sirota, S. Garoff, and H. B. Stanley [http://journals.aps.org/prb/abstract/10.1103/PhysRevB.38.2297 X-ray and neutron scattering from rough surfaces] ''Phys. Rev. B'' '''1988''', 38, 2297. [http://dx.doi.org/10.1103/PhysRevB.38.2297 doi: 10.1103/PhysRevB.38.2297]
 * M. Rauscher, T. Salditt, and H. Spohn [http://journals.aps.org/prb/abstract/10.1103/PhysRevB.52.16855 Small-angle x-ray scattering under grazing incidence: The cross section in the distorted-wave Born approximation] ''Phys. Rev. B'' '''1995''', 52, 16855. [http://dx.doi.org/10.1103/PhysRevB.52.16855 doi: 10.1103/PhysRevB.52.16855]
 * Michael F. Toney and Sean Brennan [http://journals.aps.org/prb/abstract/10.1103/PhysRevB.39.7963 Observation of the effect of refraction on x rays diffracted in a grazing-incidence asymmetric Bragg geometry] ''Phys. Rev. B'' '''1989''', 39, 7963. [http://dx.doi.org/10.1103/PhysRevB.39.7963 doi: 10.1103/PhysRevB.39.7963]

@@ Line 51: / Line 51: @@
 </math>
 While the coherent cross-section accounts for the [[specular rod]].
 ==References==

@@ Line 16: / Line 16: @@
 However, to account for [[reflection]] and [[refraction]] effects, the DWBA introduces additional terms. The figure below shows four different scattering events which are considered:
-'''TBD'''
 [[Image:Four terms.png|600px]]
 The first term is the BA, while the next 3 terms describe various specific multiple-scattering events. In principle, an infinite series of different combinations of reflection and scattering need to be included. However, as will be seen, higher-order terms are progressively more and more unlikely (and thus weak, in terms of their contribution to the total scattering). The DWBA, by considering these 4 terms, can adequately reproduce much GISAXS data. The various terms described above interfere coherently; thus the final scattering that is measured on the [[detector]] comes from their combination:

← Older revision		Revision as of 14:25, 1 December 2023
Line 17:		Line 17:

	'''TBD'''		'''TBD'''
		+	[[Image:Four terms.png\|600px]]

	The first term is the BA, while the next 3 terms describe various specific multiple-scattering events. In principle, an infinite series of different combinations of reflection and scattering need to be included. However, as will be seen, higher-order terms are progressively more and more unlikely (and thus weak, in terms of their contribution to the total scattering). The DWBA, by considering these 4 terms, can adequately reproduce much GISAXS data. The various terms described above interfere coherently; thus the final scattering that is measured on the [[detector]] comes from their combination:		The first term is the BA, while the next 3 terms describe various specific multiple-scattering events. In principle, an infinite series of different combinations of reflection and scattering need to be included. However, as will be seen, higher-order terms are progressively more and more unlikely (and thus weak, in terms of their contribution to the total scattering). The DWBA, by considering these 4 terms, can adequately reproduce much GISAXS data. The various terms described above interfere coherently; thus the final scattering that is measured on the [[detector]] comes from their combination:

@@ Line 79: / Line 79: @@
 ===Multiple Channels===
 * Byeongdu Lee, Insun Park, Jinhwan Yoon, Soojin Park, Jehan Kim, Kwang-Woo Kim, Taihyun Chang, and Moonhor Ree [https://pubs.acs.org/doi/abs/10.1021/ma047562d Structural Analysis of Block Copolymer Thin Films with Grazing Incidence Small-Angle X-ray Scattering] ''Macromolecules'' '''2005''', 38 (10), 4311–4323. [http://dx.doi.org/10.1021/ma047562d doi: 10.1021/ma047562d]
 ===Application of DWBA===

@@ Line 75: / Line 75: @@
 * D. W. Breiby, O. Bunk, J. W. Andreasen, H. T. Lemke and M. M. Nielsen [http://scripts.iucr.org/cgi-bin/paper?S0021889808001064 Simulating X-ray diffraction of textured films] ''J. Appl. Cryst.'' 2008, 41, 262-271. [http://dx.doi.org/10.1107/S0021889808001064 doi: 10.1107/S0021889808001064]
 * Lu, X.; [[Yager, K.G.]]; Johnston, D.; Black, C.T.; Ocko, B.M. '''[http://scripts.iucr.org/cgi-bin/paper?S0021889812047887 Grazing-incidence transmission X-ray scattering: surface scattering in the Born approximation]''' ''Journal of Applied Crystallography'' '''2013''', 46, 165–172. [http://dx.doi.org/10.1107/S0021889812047887 doi: 10.1107/S0021889812047887]
 ===Multiple Channels===

← Older revision		Revision as of 13:00, 25 July 2015
Line 1:		Line 1:
−	The '''Distorted Wave Born Approximation''' ('''DWBA''') is a theoretical approach in [[scattering]] theory (or, more generally, in [[quantum mechanics]]). In the Born approximation (BA), when calculating the interaction between matter and incident radiation ('scattering'), the total field inside the material is assumed to simply be the incident field. In other words, the modification of the field due to scattering events is assumed to be negligible; this is valid in the limit of weak scattering. Every particle simply sees the incident field, and scatters independently (though these scattered fields interfere with one another, giving rise to the usual appearance of [[scattering features]] in the far-field).	+	The '''Distorted Wave Born Approximation''' ('''DWBA''') is a theoretical approach in [[scattering]] theory (or, more generally, in [[quantum mechanics]]). In the [[Born approximation]] (BA), when calculating the interaction between matter and incident radiation ('scattering'), the total field inside the material is assumed to simply be the incident field. In other words, the modification of the field due to scattering events is assumed to be negligible; this is valid in the limit of weak scattering. Every particle simply sees the incident field, and scatters independently (though these scattered fields interfere with one another, giving rise to the usual appearance of [[scattering features]] in the far-field).

	The Born approximation is not valid in all cases; in particular, when scattering becomes very strong, the approximation is no longer valid. As one example, at some point one must consider [[multiple scattering]]: the scattered rays can, themselves, become sources of scattering. [[GISAXS]] and other grazing-incidence techniques typically probe regimes where the Born approximation is not valid. For instance, in GISAXS, the x-ray beam will be reflected by the film-substrate and film-ambient interfaces; and may in fact undergo multiple reflections ([[X-ray waveguiding\|waveguiding]]). This, and other [[dynamical scattering]] effects need to be accounted for in order to understand GISAXS data.		The Born approximation is not valid in all cases; in particular, when scattering becomes very strong, the approximation is no longer valid. As one example, at some point one must consider [[multiple scattering]]: the scattered rays can, themselves, become sources of scattering. [[GISAXS]] and other grazing-incidence techniques typically probe regimes where the Born approximation is not valid. For instance, in GISAXS, the x-ray beam will be reflected by the film-substrate and film-ambient interfaces; and may in fact undergo multiple reflections ([[X-ray waveguiding\|waveguiding]]). This, and other [[dynamical scattering]] effects need to be accounted for in order to understand GISAXS data.

@@ Line 73: / Line 73: @@
 * P. Busch, M. Rauscher, D.-M. Smilgies, D. Posselt and C. M. Papadakis [http://scripts.iucr.org/cgi-bin/paper?S0021889806012337 Grazing-incidence small-angle X-ray scattering from thin polymer films with lamellar structures - the scattering cross section in the distorted-wave Born approximation] ''J. Appl. Cryst.'' '''2006''', 39, 433-442. [http://dx.doi.org/10.1107/S0021889806012337 doi: 10.1107/S0021889806012337]
 * Rémi Lazzari, Frédéric Leroy, and Gilles Renaud [http://journals.aps.org/prb/abstract/10.1103/PhysRevB.76.125411 Grazing-incidence small-angle x-ray scattering from dense packing of islands on surfaces: Development of distorted wave Born approximation and correlation between particle sizes and spacing] ''Phys. Rev. B'' '''2007''', 76, 125411. [http://dx.doi.org/10.1103/PhysRevB.76.125411 doi: 10.1103/PhysRevB.76.125411]
+* D. W. Breiby, O. Bunk, J. W. Andreasen, H. T. Lemke and M. M. Nielsen [http://scripts.iucr.org/cgi-bin/paper?S0021889808001064 Simulating X-ray diffraction of textured films] ''J. Appl. Cryst.'' 2008, 41, 262-271. [http://dx.doi.org/10.1107/S0021889808001064 doi: 10.1107/S0021889808001064]
 ===Application of DWBA===