167:
sample perpendicular to the direction of the primary beam that initially hit the sample. The scattering pattern contains the information on the structure of the sample. The major problem that must be overcome in SAXS instrumentation is the separation of the weak scattered intensity from the strong main beam. The smaller the desired angle, the more difficult this becomes. The problem is comparable to one encountered when trying to observe a weakly radiant object close to the Sun, like the Sun's corona. Only if the Moon blocks out the main light source does the corona become visible. Likewise, in SAXS the non-scattered beam that merely travels through the sample must be blocked,
2923:
3316:
55:. Depending on the angular range in which a clear scattering signal can be recorded, SAXS is capable of delivering structural information of dimensions between 1 and 100 nm, and of repeat distances in partially ordered systems of up to 150 nm. USAXS (ultra-small angle X-ray scattering) can resolve even larger dimensions, as the smaller the recorded angle, the larger the object dimensions that are probed.
3328:
233:) of many adjacent pinhole patterns. The resulting smearing can be easily removed using model-free algorithms or deconvolution methods based on Fourier transformation, but only if the system is isotropic. Line collimation is of great benefit for any isotropic nanostructured materials, e.g. proteins, surfactants, particle dispersion and emulsions.
208:
and the wastefulness of the collimation process—only those photons are allowed to pass that happen to fly in the right direction—the scattered intensity is small and therefore the measurement time is in the order of hours or days in case of very weak scatterers. If focusing optics like bent mirrors or bent
228:
Line-collimation instruments restrict the beam only in one dimension (rather than two as for point collimation) so that the beam cross-section is a long but narrow line. The illuminated sample volume is much larger compared to point-collimation and the scattered intensity at the same flux density is
166:
of X-rays is brought to a sample from which some of the X-rays scatter, while most simply go through the sample without interacting with it. The scattered X-rays form a scattering pattern which is then detected at a detector which is typically a 2-dimensional flat X-ray detector situated behind the
207:
beam to a small circular or elliptical spot that illuminates the sample. Thus the scattering is centro-symmetrically distributed around the primary X-ray beam and the scattering pattern in the detection plane consists of circles around the primary beam. Owing to the small illuminated sample volume
86:
SAXS is used for the determination of the microscale or nanoscale structure of particle systems in terms of such parameters as averaged particle sizes, shapes, distribution, and surface-to-volume ratio. The materials can be solid or liquid and they can contain solid, liquid or gaseous domains
229:
proportionally larger. Thus measuring times with line-collimation SAXS instruments are much shorter compared to point-collimation and are in the range of minutes. A disadvantage is that the recorded pattern is essentially an integrated superposition (a self-
42:
scattering behaviour of X-rays when travelling through the material, recording their scattering at small angles (typically 0.1 – 10°, hence the "Small-angle" in its name). It belongs to the family of small-angle scattering (SAS) techniques along with
1213:
Filippov, Sergey K.; Verbraeken, Bart; Konarev, Petr V.; Svergun, Dmitri I.; Angelov, Borislav; Vishnevetskaya, Natalya S.; Papadakis, Christine M.; Rogers, Sarah; Radulescu, Aurel; Courtin, Tim; Martins, José C. (2017-08-17).
1060:
Filippov, Sergey K.; Chytil, Petr; Konarev, Petr V.; Dyakonova, Margarita; Papadakis, ChristineM.; Zhigunov, Alexander; Plestil, Josef; Stepanek, Petr; Etrych, Tomas; Ulbrich, Karel; Svergun, Dmitri I. (2012-08-13).
1108:
Filippov, Sergey K.; Franklin, John M.; Konarev, Petr V.; Chytil, Petr; Etrych, Tomas; Bogomolova, Anna; Dyakonova, Margarita; Papadakis, Christine M.; Radulescu, Aurel; Ulbrich, Karel; Stepanek, Petr (2013-11-11).
1836:
Janisova, Larisa; Gruzinov, Andrey; Zaborova, Olga V.; Velychkivska, Nadiia; Vaněk, Ondřej; Chytil, Petr; Etrych, Tomáš; Janoušková, Olga; Zhang, Xiaohan; Blanchet, Clement; Papadakis, Christine M. (2020-01-28).
1569:
Filippov, Sergey K.; Bogomolova, Anna; Kaberov, Leonid; Velychkivska, Nadiia; Starovoytova, Larisa; Cernochova, Zulfiya; Rogers, Sarah E.; Lau, Wing Man; Khutoryanskiy, Vitaliy V.; Cook, Michael T. (2016-05-31).
498:
Burger, Virginia M., Daniel J. Arenas, and Collin M. Stultz. "A structure-free method for quantifying conformational flexibility in proteins." Scientific reports 6 (2016): 29040. DOI: 10.1038/srep29040 (2016).|
1733:
Kaberov, Leonid I.; Kaberova, Zhansaya; Murmiliuk, Anastasiia; Trousil, JiĹ™Ă; Sedláček, OndĹ™ej; Konefal, Rafal; Zhigunov, Alexander; Pavlova, Ewa; VĂt, Martin; Jirák, Daniel; Hoogenboom, Richard (2021-06-28).
2179:
2932:
1428:"A Novel Approach to Increase the Stability of Liposomal Containers via In Prep Coating by Poly[ N -(2-Hydroxypropyl)Methacrylamide] with Covalently Attached Cholesterol Groups"
212:
crystals or collimating and monochromating optics like multilayers are used, measurement time can be greatly reduced. Point-collimation allows the orientation of non-isotropic systems (
1686:
Sergeeva, Olga; Vlasov, Petr S.; Domnina, Nina S.; Bogomolova, Anna; Konarev, Petr V.; Svergun, Dmitri I.; Walterova, Zuzana; Horsky, Jiri; Stepanek, Petr; Filippov, Sergey K. (2014).
762:
Zhang, Xiaohan; Niebuur, Bart-Jan; Chytil, Petr; Etrych, Tomas; Filippov, Sergey K.; Kikhney, Alexey; Wieland, D. C. Florian; Svergun, Dmitri I.; Papadakis, Christine M. (2018-02-12).
1924:
1572:"Internal Nanoparticle Structure of Temperature-Responsive Self-Assembled PNIPAM- b -PEG- b -PNIPAM Triblock Copolymers in Aqueous Solutions: NMR, SANS, and Light Scattering Studies"
2216:
1164:
Riabtseva, Anna; Kaberov, Leonid I.; Noirez, Laurence; Ryukhtin, Vasyl; Nardin, Corinne; Verbraeken, Bart; Hoogenboom, Richard; Stepanek, Petr; Filippov, Sergey K. (February 2018).
78:). However, owing to the random orientation of dissolved or partially ordered molecules, the spatial averaging leads to a loss of information in SAXS compared to crystallography.
3193:
3188:
1328:
Chaves, Matheus
Andrade; Oseliero Filho, Pedro Leonidas; Jange, Camila Garcia; Sinigaglia-Coimbra, Rita; Oliveira, Cristiano Luis Pinto; Pinho, Samantha Cristina (July 2018).
1736:"Fluorine-Containing Block and Gradient Copoly(2-oxazoline)s Based on 2-(3,3,3-Trifluoropropyl)-2-oxazoline: A Quest for the Optimal Self-Assembled Structure for 19F Imaging"
905:"Formation of core/corona nanoparticles with interpolyelectrolyte complex cores in aqueous solution: insight into chain dynamics in the complex from fluorescence quenching"
95:-like materials can be studied. The method is accurate, non-destructive and usually requires only a minimum of sample preparation. Applications are very broad and include
811:"Coassembly of Poly( N -isopropylacrylamide) with Dodecyl and Carboxyl Terminal Groups with Cationic Surfactant: Critical Comparison of Experimental and Simulation Data"
2728:
1063:"Macromolecular HPMA-Based Nanoparticles with Cholesterol for Solid-Tumor Targeting: Detailed Study of the Inner Structure of a Highly Efficient Drug Delivery System"
3244:
809:
Fanova, Anastasiia; Šindelka, Karel; Uchman, Mariusz; Limpouchová, Zuzana; Filippov, Sergey K.; Pispas, Stergios; Procházka, Karel; Štěpánek, Miroslav (2018-09-25).
2472:
960:"Temperature-induced structure switch in thermo-responsive micellar interpolyelectrolyte complexes: toward core–shell–corona and worm-like morphologies"
2233:
70:
is that a crystalline sample is not needed. Furthermore, the properties of SAXS allow investigation of conformational diversity in these molecules.
707:
Fanova, Anastasiia; Janata, Miroslav; Filippov, Sergey K.; Ĺ louf, Miroslav; NetopilĂk, Miloš; Mariani, Alessandro; Ĺ tÄ›pánek, Miroslav (2019-08-27).
668:
Hollamby, Martin J.; Aratsu, Keisuke; Pauw, Brian R.; Rogers, Sarah E.; Smith, Andrew J.; Yamauchi, Mitsuaki; Lin, Xu; Yagai, Shiki (2016-08-16).
1839:"Molecular Mechanisms of the Interactions of N-(2-Hydroxypropyl)methacrylamide Copolymers Designed for Cancer Therapy with Blood Plasma Proteins"
670:"Simultaneous SAXS and SANS Analysis for the Detection of Toroidal Supramolecular Polymers Composed of Noncovalent Supermacrocycles in Solution"
582:
Pedersen, JS (1994). "Determination of size distribution from small-angle scattering data for systems with effective hard-sphere interactions".
452:
Patil, N; Narayanan, T; Michels, L; Skjønsfjell, ETB; Guizar-Sicairos, M; Van den Brande, N; Claessens, R; Van Mele, B; Breiby, DW (May 2019).
1506:"Time-Resolved SAXS Studies of the Kinetics of Thermally Triggered Release of Encapsulated Silica Nanoparticles from Block Copolymer Vesicles"
1426:
Zaborova, Olga V.; Filippov, Sergey K.; Chytil, Petr; Kováčik, Lubomir; Ulbrich, Karel; Yaroslavov, Alexander A.; Etrych, Tomaš (April 2018).
903:
Murmiliuk, Anastasiia; MatÄ›jĂÄŤek, Pavel; Filippov, Sergey K.; Janata, Miroslav; Ĺ louf, Miroslav; Pispas, Stergios; Ĺ tÄ›pánek, Miroslav (2018).
512:
Pedersen, JS (July 1997). "Analysis of small-angle scattering data from colloids and polymer solutions: modeling and least-squares fitting".
87:(so-called particles) of the same or another material in any combination. Not only particles, but also the structure of ordered systems like
3062:
3249:
2974:
3140:
2432:
2274:
1504:
Mable, Charlotte J.; Derry, Matthew J.; Thompson, Kate L.; Fielding, Lee A.; Mykhaylyk, Oleksandr O.; Armes, Steven P. (2017-06-13).
151:. Different from standard RIXS measurements, the scattered photons are considered to have the same energy as the incident photons.
866:"Interpolyelectrolyte Complex and Coacervate Formation of Poly(glutamic acid) with a Dendrimer Studied by Light Scattering and SAXS"
2337:
2284:
1457:
Bressel, Katharina; Muthig, Michael; Prevost, Sylvain; Gummel, Jeremie; Narayanan, Theyencheri; Gradzielski, Michael (2012-07-24).
279:
1015:"Structure and Interactions of Block Copolymer Micelles of Brij 700 Studied by Combining Small-Angle X-ray and Neutron Scattering"
38:, determine pore sizes, characteristic distances of partially ordered materials, and much more. This is achieved by analyzing the
1956:
71:
356:"Development of an ultra-small-angle X-ray scattering instrument for probing the microstructure and the dynamics of soft matter"
3239:
3231:
2196:
1688:"Novel thermosensitive telechelic PEGs with antioxidant activity: synthesis, molecular properties and conformational behaviour"
191:
instead. Laboratory SAXS instruments can be divided into two main groups: point-collimation and line-collimation instruments:
3292:
3270:
2211:
320:
309:
Hamley, I.W. "Small-Angle
Scattering: Theory, Instrumentation, Data, and Applications" – Wiley, 2022. ISBN 978-1-119-76830-2.
395:
Narayanan, T; Sztucki, M; Van
Vaerenbergh, P; LĂ©onardon, J; Gorini, J; Claustre, L; Sever, F; Morse, J; Boesecke, P (2018).
3285:
3135:
2801:
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2515:
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764:"Macromolecular p HPMA-Based Nanoparticles with Cholesterol for Solid Tumor Targeting: Behavior in HSA Protein Environment"
3275:
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2221:
148:
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1905:
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Dähling, Claudia; Lotze, Gudrun; Drechsler, Markus; Mori, Hideharu; Pergushov, Dmitry V.; Plamper, Felix A. (2016).
3332:
3007:
2269:
2248:
547:
Pedersen, JS (2000). "Form factors of block copolymer micelles with spherical, ellipsoidal and cylindrical cores".
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30:
technique by which nanoscale density differences in a sample can be quantified. This means that it can determine
3115:
3037:
1283:"Internal Structures of Thermosensitive Hybrid Microgels Investigated by Means of Small-Angle X-ray Scattering"
44:
1369:"Small Angle X-ray and Neutron Scattering: Powerful Tools for Studying the Structure of Drug-Loaded Liposomes"
3130:
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144:
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1949:
1631:"Synthesis and solution properties of a temperature-responsive PNIPAM–b-PDMS–b-PNIPAM triblock copolymer"
290:
59:
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2116:
1166:"Structural characterization of nanoparticles formed by fluorinated poly(2-oxazoline)-based polyphiles"
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that are used in the characterization of materials. In the case of biological macromolecules such as
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1329:
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It is possible to enhance the X-ray scattering yield by matching the energy of X-ray source to a
1330:"Structural characterization of multilamellar liposomes coencapsulating curcumin and vitamin D3"
2922:
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2357:
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1942:
27:
453:
187:
where large bent mirrors can be used. This is why most laboratory small angle devices rely on
183:
the beam, but this is not easy when dealing with X-rays and was previously not done except on
3221:
3017:
2979:
2786:
2738:
2317:
2186:
1994:
1427:
669:
397:"A multipurpose instrument for time-resolved ultra-small-angle and coherent X-ray scattering"
128:
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2019:
1735:
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1517:
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720:
681:
1791:"Structural analysis of intrinsically disordered proteins by small-angle X-ray scattering"
8:
2962:
2950:
2825:
2791:
2771:
2106:
2081:
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1111:"Hydrolytically Degradable Polymer Micelles for Drug Delivery: A SAXS/SANS Kinetic Study"
250:
88:
1703:
1521:
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920:
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blocking the closely adjacent scattered radiation. Most available X-ray sources produce
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1505:
1459:"Shaping Vesicles–Controlling Size and Stability by Admixture of Amphiphilic Copolymer"
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2014:
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1216:"Block and Gradient Copoly(2-oxazoline) Micelles: Strikingly Different on the Inside"
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beams and this compounds the problem. In principle the problem could be overcome by
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methods encounter problems with macromolecules of higher molecular mass (> 30–40
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1989:
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Cook, Michael T.; Filippov, Sergey K.; Khutoryanskiy, Vitaliy V. (August 2017).
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Suzuki, Daisuke; Nagase, Yasuhisa; Kureha, Takuma; Sato, Takaaki (2014-02-27).
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2009:
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654:
469:
454:"Probing Organic Thin Films by Coherent X-ray Imaging and X-ray Scattering"
438:
31:
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2050:
230:
184:
108:
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2174:
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1930:
A movie demonstrating small-angle scattering using laserlight on a hair
1806:
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Sommer, Cornelia; Pedersen, Jan Skov; Garamus, Vasil M. (2005-03-01).
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52:
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Di Cola, Emanuela; Grillo, Isabelle; Ristori, Sandra (2016-03-28).
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2410:
709:"Evolution of Structure in a Comb Copolymer–Surfactant Coacervate"
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200:
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100:
96:
92:
63:
34:
size distributions, resolve the size and shape of (monodisperse)
1934:
1334:
Colloids and
Surfaces A: Physicochemical and Engineering Aspects
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902:
451:
123:
and can be found in research as well as in quality control. The
2004:
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of all types including interpolyelectrolyte complexes,
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318:
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353:
236:
194:
1898:Electron Dynamics by Inelastic X-Ray Scattering
617:Gommes, CJ; Jaksch, S; Frielinghaus, H (2021).
223:
1788:
864:Leisner, Dietrich; Imae, Toyoko (2003-08-01).
249:, Germany; Hecus X-Ray Systems Graz, Austria;
2426:
1950:
3263:
863:
2433:
2419:
1957:
1943:
282:(Grazing-incidence small-angle scattering)
1872:
1854:
1789:BernadĂł, Pau; Svergun, Dmitri I. (2012).
1654:
1597:
1587:
1545:
1402:
1384:
1241:
1231:
1220:The Journal of Physical Chemistry Letters
1189:
644:
634:
514:Advances in Colloid and Interface Science
428:
371:
1895:
581:
546:
511:
72:Nuclear magnetic resonance spectroscopy
3347:
2536:
619:"Small-Angle Scattering for Beginners"
312:
241:SAXS instrument manufacturers include
2414:
1938:
139:Resonant small-angle X-ray scattering
127:source can be a laboratory source or
58:SAXS and USAXS belong to a family of
3327:
2667:Phase transformation crystallography
1432:Macromolecular Chemistry and Physics
3174:Journal of Chemical Crystallography
2440:
1896:Schuelke, Winfried (21 June 2007).
1287:The Journal of Physical Chemistry B
870:The Journal of Physical Chemistry B
501:http://hdl.handle.net/1721.1/108809
199:Point-collimation instruments have
154:
149:resonant inelastic X-ray scattering
47:, and is typically done using hard
13:
623:Journal of Applied Crystallography
584:Journal of Applied Crystallography
549:Journal of Applied Crystallography
401:Journal of Applied Crystallography
360:Journal of Applied Crystallography
319:Glatter O; Kratky O, eds. (1982).
286:Fluctuation X-ray scattering (FXS)
14:
3371:
1964:
1918:
354:Sztucki, M; Narayanan, T (2007).
275:Biological small-angle scattering
3326:
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2921:
51:with a wavelength of 0.07 – 0.2
1889:
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1182:10.1016/j.eurpolymj.2018.01.007
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661:
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81:
3116:Bilbao Crystallographic Server
1346:10.1016/j.colsurfa.2018.04.018
575:
540:
505:
492:
445:
388:
347:
303:
131:which provides a higher X-ray
45:small-angle neutron scattering
16:Radiation scattering technique
1:
1856:10.3390/pharmaceutics12020106
526:10.1016/S0001-8686(97)00312-6
458:ACS Applied Polymer Materials
296:
237:SAXS instrument manufacturers
195:Point-collimation instruments
66:, the advantage of SAXS over
1589:10.1021/acs.langmuir.6b00284
1530:10.1021/acs.macromol.7b00475
1386:10.3390/pharmaceutics8020010
835:10.1021/acs.macromol.8b01161
733:10.1021/acs.macromol.9b00332
322:Small Angle X-ray Scattering
224:Line-collimation instruments
20:Small-angle X-ray scattering
7:
3164:Crystal Growth & Design
2456:Timeline of crystallography
1900:. Oxford University Press.
1635:Colloid and Polymer Science
1233:10.1021/acs.jpclett.7b01588
291:Wide-angle X-ray scattering
268:
220:liquids) to be determined.
60:X-ray scattering techniques
10:
3376:
2975:Nuclear magnetic resonance
2229:X-Ray Fluorescence Imaging
2117:Anomalous X-ray scattering
1752:10.1021/acs.biomac.1c00367
780:10.1021/acs.biomac.7b01579
3310:
3230:
3202:
3179:Journal of Crystal Growth
3154:
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1972:
1647:10.1007/s00396-017-4084-y
636:10.1107/S1600576721010293
596:10.1107/S0021889893013810
561:10.1107/S0021889899012248
413:10.1107/S1600576718012748
373:10.1107/S0021889806045833
3045:Single particle analysis
2903:Hermann–Mauguin notation
2056:Synchrotron light source
1170:European Polymer Journal
159:In a SAXS instrument, a
145:resonant absorption edge
3169:Crystallography Reviews
3013:Isomorphous replacement
2807:Lomer–Cottrell junction
2075:Interaction with matter
2034:Sources and instruments
111:, metals, cement, oil,
3355:Small-angle scattering
2682:Spinodal decomposition
2207:Diffraction tomography
1444:10.1002/macp.201700508
694:10.1002/ange.201603370
470:10.1021/acsapm.9b00324
28:small-angle scattering
3222:Gregori Aminoff Prize
3018:Molecular replacement
2318:X-ray crystallography
2187:Soft x-ray microscopy
2155:Panoramic radiography
1995:Synchrotron radiation
1925:SAXS at a Synchrotron
147:in as it is done for
2528:Structure prediction
2087:Photoelectric effect
2020:Characteristic X-ray
257:Corporation, Japan;
2792:Cottrell atmosphere
2772:Partial dislocation
2516:Restriction theorem
2107:Photodisintegration
2082:Rayleigh scattering
2061:Free-electron laser
1704:2014RSCAd...441763S
1698:(79): 41763–41771.
1522:2017MaMol..50.4465M
976:2016SMat...12.5127D
921:2018SMat...14.7578M
827:2018MaMol..51.7295F
725:2019MaMol..52.6303F
686:2016AngCh.12810044H
680:(34): 10044–10047.
253:. the Netherlands,
251:Malvern Panalytical
3212:Carl Hermann Medal
3023:Molecular dynamics
2870:Defects in diamond
2865:Stone–Wales defect
2511:Reciprocal lattice
2473:Biocrystallography
2348:X-ray reflectivity
2127:X-ray fluorescence
2092:Compton scattering
2025:High-energy X-rays
1807:10.1039/C1MB05275F
1712:10.1039/C4RA06978A
984:10.1039/C6SM00757K
929:10.1039/C8SM01174E
343:on April 21, 2008.
3342:
3341:
3306:
3305:
2913:Thermal ellipsoid
2878:
2877:
2787:Frank–Read source
2747:
2746:
2613:Aperiodic crystal
2579:
2578:
2461:Crystallographers
2408:
2407:
2404:
2403:
2396:X-ray lithography
2328:Backscatter X-ray
2323:X-ray diffraction
2150:X-ray radiography
2122:X-ray diffraction
2015:Siegbahn notation
1740:Biomacromolecules
1582:(21): 5314–5323.
1516:(11): 4465–4473.
1475:10.1021/nn300359q
1299:10.1021/jp410983x
1226:(16): 3800–3804.
1127:10.1021/bm401186z
1121:(11): 4061–4070.
1115:Biomacromolecules
1079:10.1021/bm3008555
1067:Biomacromolecules
1031:10.1021/la047489k
970:(23): 5127–5137.
915:(37): 7578–7585.
882:10.1021/jp027365l
876:(32): 8078–8087.
821:(18): 7295–7308.
768:Biomacromolecules
719:(16): 6303–6310.
674:Angewandte Chemie
265:, United States.
129:synchrotron light
3367:
3360:X-ray scattering
3330:
3329:
3318:
3317:
3261:
3260:
3184:Kristallografija
3038:Gerchberg–Saxton
2933:Characterisation
2925:
2908:Structure factor
2712:
2711:
2697:Ostwald ripening
2534:
2533:
2479:
2478:
2435:
2428:
2421:
2412:
2411:
2234:X-ray holography
2140:
2139:
2112:Radiation damage
1959:
1952:
1945:
1936:
1935:
1912:
1911:
1893:
1887:
1886:
1876:
1858:
1833:
1827:
1826:
1786:
1780:
1779:
1746:(7): 2963–2975.
1730:
1724:
1723:
1683:
1677:
1676:
1658:
1641:(8): 1351–1358.
1626:
1620:
1619:
1601:
1591:
1566:
1560:
1559:
1549:
1501:
1495:
1494:
1469:(7): 5858–5865.
1454:
1448:
1447:
1423:
1417:
1416:
1406:
1388:
1364:
1358:
1357:
1325:
1319:
1318:
1293:(8): 2194–2204.
1278:
1272:
1271:
1245:
1235:
1210:
1204:
1203:
1193:
1161:
1155:
1154:
1105:
1099:
1098:
1073:(8): 2594–2604.
1057:
1051:
1050:
1025:(6): 2137–2149.
1010:
1004:
1003:
955:
949:
948:
900:
894:
893:
861:
855:
854:
806:
800:
799:
759:
753:
752:
704:
698:
697:
665:
659:
658:
648:
638:
629:(6): 1832–1843.
614:
608:
607:
579:
573:
572:
544:
538:
537:
509:
503:
496:
490:
489:
464:(7): 1787–1797.
449:
443:
442:
432:
407:(6): 1511–1524.
392:
386:
385:
375:
351:
345:
344:
339:. Archived from
316:
310:
307:
155:SAXS instruments
3375:
3374:
3370:
3369:
3368:
3366:
3365:
3364:
3345:
3344:
3343:
3338:
3302:
3259:
3226:
3198:
3150:
3102:
3073:CrystalExplorer
3049:
3033:Phase retrieval
2996:
2927:
2926:
2917:
2874:
2853:Schottky defect
2752:Perfect crystal
2743:
2739:Abnormal growth
2701:
2687:Supersaturation
2650:Miscibility gap
2631:
2624:
2575:
2532:
2496:Bravais lattice
2477:
2444:
2442:Crystallography
2439:
2409:
2400:
2384:X-ray astronomy
2372:
2304:
2253:
2239:X-ray telescope
2131:
2102:Photoionization
2070:
2066:X-ray nanoprobe
2029:
1985:Absorption edge
1973:Characteristics
1968:
1963:
1921:
1916:
1915:
1908:
1894:
1890:
1834:
1830:
1787:
1783:
1731:
1727:
1684:
1680:
1627:
1623:
1567:
1563:
1502:
1498:
1455:
1451:
1424:
1420:
1365:
1361:
1326:
1322:
1279:
1275:
1243:1854/LU-8534833
1211:
1207:
1191:1854/LU-8561215
1162:
1158:
1106:
1102:
1058:
1054:
1011:
1007:
956:
952:
901:
897:
862:
858:
807:
803:
760:
756:
705:
701:
666:
662:
615:
611:
580:
576:
545:
541:
510:
506:
497:
493:
450:
446:
393:
389:
352:
348:
337:
317:
313:
308:
304:
299:
271:
239:
226:
203:that shape the
197:
157:
141:
121:pharmaceuticals
84:
68:crystallography
17:
12:
11:
5:
3373:
3363:
3362:
3357:
3340:
3339:
3337:
3336:
3324:
3311:
3308:
3307:
3304:
3303:
3301:
3300:
3295:
3290:
3289:
3288:
3283:
3278:
3267:
3265:
3258:
3257:
3252:
3247:
3242:
3236:
3234:
3228:
3227:
3225:
3224:
3219:
3214:
3208:
3206:
3200:
3199:
3197:
3196:
3191:
3186:
3181:
3176:
3171:
3166:
3160:
3158:
3152:
3151:
3149:
3148:
3143:
3138:
3133:
3128:
3123:
3118:
3112:
3110:
3104:
3103:
3101:
3100:
3095:
3090:
3085:
3080:
3075:
3070:
3065:
3059:
3057:
3051:
3050:
3048:
3047:
3042:
3041:
3040:
3030:
3025:
3020:
3015:
3010:
3008:Direct methods
3004:
3002:
2998:
2997:
2995:
2994:
2993:
2992:
2987:
2977:
2972:
2971:
2970:
2965:
2955:
2954:
2953:
2948:
2937:
2935:
2929:
2928:
2920:
2918:
2916:
2915:
2910:
2905:
2900:
2895:
2893:Ewald's sphere
2890:
2885:
2879:
2876:
2875:
2873:
2872:
2867:
2862:
2861:
2860:
2855:
2845:
2844:
2843:
2838:
2836:Frenkel defect
2833:
2831:Bjerrum defect
2823:
2822:
2821:
2811:
2810:
2809:
2804:
2799:
2797:Peierls stress
2794:
2789:
2784:
2779:
2774:
2769:
2767:Burgers vector
2759:
2757:Stacking fault
2754:
2748:
2745:
2744:
2742:
2741:
2736:
2731:
2726:
2720:
2718:
2716:Grain boundary
2709:
2703:
2702:
2700:
2699:
2694:
2689:
2684:
2679:
2674:
2669:
2664:
2663:
2662:
2660:Liquid crystal
2657:
2652:
2647:
2636:
2634:
2626:
2625:
2623:
2622:
2621:
2620:
2610:
2609:
2608:
2598:
2597:
2596:
2591:
2580:
2577:
2576:
2574:
2573:
2568:
2563:
2558:
2553:
2548:
2542:
2540:
2531:
2530:
2525:
2523:Periodic table
2520:
2519:
2518:
2513:
2508:
2503:
2498:
2487:
2485:
2476:
2475:
2470:
2465:
2464:
2463:
2452:
2450:
2446:
2445:
2438:
2437:
2430:
2423:
2415:
2406:
2405:
2402:
2401:
2399:
2398:
2393:
2392:
2391:
2380:
2378:
2374:
2373:
2371:
2370:
2365:
2360:
2355:
2350:
2345:
2340:
2335:
2330:
2325:
2320:
2314:
2312:
2306:
2305:
2303:
2302:
2297:
2292:
2287:
2282:
2277:
2272:
2267:
2261:
2259:
2255:
2254:
2252:
2251:
2246:
2241:
2236:
2231:
2226:
2225:
2224:
2219:
2214:
2204:
2199:
2194:
2189:
2184:
2183:
2182:
2177:
2167:
2162:
2157:
2152:
2146:
2144:
2137:
2133:
2132:
2130:
2129:
2124:
2119:
2114:
2109:
2104:
2099:
2094:
2089:
2084:
2078:
2076:
2072:
2071:
2069:
2068:
2063:
2058:
2053:
2048:
2043:
2037:
2035:
2031:
2030:
2028:
2027:
2022:
2017:
2012:
2007:
2002:
1997:
1992:
1987:
1982:
1976:
1974:
1970:
1969:
1962:
1961:
1954:
1947:
1939:
1933:
1932:
1927:
1920:
1919:External links
1917:
1914:
1913:
1906:
1888:
1828:
1801:(1): 151–167.
1781:
1725:
1678:
1621:
1561:
1510:Macromolecules
1496:
1449:
1438:(7): 1700508.
1418:
1359:
1320:
1273:
1205:
1156:
1100:
1052:
1005:
950:
895:
856:
815:Macromolecules
801:
774:(2): 470–480.
754:
713:Macromolecules
699:
660:
609:
590:(4): 595–608.
574:
555:(3): 637–640.
539:
504:
491:
444:
387:
346:
335:
327:Academic Press
311:
301:
300:
298:
295:
294:
293:
288:
283:
277:
270:
267:
261:, France; and
238:
235:
225:
222:
196:
193:
156:
153:
140:
137:
83:
80:
36:macromolecules
15:
9:
6:
4:
3:
2:
3372:
3361:
3358:
3356:
3353:
3352:
3350:
3335:
3334:
3325:
3323:
3322:
3313:
3312:
3309:
3299:
3296:
3294:
3291:
3287:
3284:
3282:
3279:
3277:
3274:
3273:
3272:
3269:
3268:
3266:
3262:
3256:
3253:
3251:
3248:
3246:
3243:
3241:
3238:
3237:
3235:
3233:
3229:
3223:
3220:
3218:
3215:
3213:
3210:
3209:
3207:
3205:
3201:
3195:
3192:
3190:
3187:
3185:
3182:
3180:
3177:
3175:
3172:
3170:
3167:
3165:
3162:
3161:
3159:
3157:
3153:
3147:
3144:
3142:
3139:
3137:
3134:
3132:
3129:
3127:
3124:
3122:
3119:
3117:
3114:
3113:
3111:
3109:
3105:
3099:
3096:
3094:
3091:
3089:
3086:
3084:
3081:
3079:
3076:
3074:
3071:
3069:
3066:
3064:
3061:
3060:
3058:
3056:
3052:
3046:
3043:
3039:
3036:
3035:
3034:
3031:
3029:
3028:Patterson map
3026:
3024:
3021:
3019:
3016:
3014:
3011:
3009:
3006:
3005:
3003:
2999:
2991:
2988:
2986:
2983:
2982:
2981:
2978:
2976:
2973:
2969:
2966:
2964:
2961:
2960:
2959:
2956:
2952:
2949:
2947:
2944:
2943:
2942:
2939:
2938:
2936:
2934:
2930:
2924:
2914:
2911:
2909:
2906:
2904:
2901:
2899:
2898:Friedel's law
2896:
2894:
2891:
2889:
2886:
2884:
2881:
2880:
2871:
2868:
2866:
2863:
2859:
2856:
2854:
2851:
2850:
2849:
2846:
2842:
2841:Wigner effect
2839:
2837:
2834:
2832:
2829:
2828:
2827:
2826:Interstitials
2824:
2820:
2817:
2816:
2815:
2812:
2808:
2805:
2803:
2800:
2798:
2795:
2793:
2790:
2788:
2785:
2783:
2780:
2778:
2775:
2773:
2770:
2768:
2765:
2764:
2763:
2760:
2758:
2755:
2753:
2750:
2749:
2740:
2737:
2735:
2732:
2730:
2727:
2725:
2722:
2721:
2719:
2717:
2713:
2710:
2708:
2704:
2698:
2695:
2693:
2690:
2688:
2685:
2683:
2680:
2678:
2675:
2673:
2672:Precipitation
2670:
2668:
2665:
2661:
2658:
2656:
2653:
2651:
2648:
2646:
2643:
2642:
2641:
2640:Phase diagram
2638:
2637:
2635:
2633:
2627:
2619:
2616:
2615:
2614:
2611:
2607:
2604:
2603:
2602:
2599:
2595:
2592:
2590:
2587:
2586:
2585:
2582:
2581:
2572:
2569:
2567:
2564:
2562:
2559:
2557:
2554:
2552:
2549:
2547:
2544:
2543:
2541:
2539:
2535:
2529:
2526:
2524:
2521:
2517:
2514:
2512:
2509:
2507:
2504:
2502:
2499:
2497:
2494:
2493:
2492:
2489:
2488:
2486:
2484:
2480:
2474:
2471:
2469:
2466:
2462:
2459:
2458:
2457:
2454:
2453:
2451:
2447:
2443:
2436:
2431:
2429:
2424:
2422:
2417:
2416:
2413:
2397:
2394:
2390:
2387:
2386:
2385:
2382:
2381:
2379:
2375:
2369:
2366:
2364:
2361:
2359:
2356:
2354:
2351:
2349:
2346:
2344:
2341:
2339:
2336:
2334:
2331:
2329:
2326:
2324:
2321:
2319:
2316:
2315:
2313:
2311:
2307:
2301:
2298:
2296:
2293:
2291:
2288:
2286:
2283:
2281:
2278:
2276:
2273:
2271:
2268:
2266:
2263:
2262:
2260:
2256:
2250:
2247:
2245:
2242:
2240:
2237:
2235:
2232:
2230:
2227:
2223:
2220:
2218:
2215:
2213:
2210:
2209:
2208:
2205:
2203:
2200:
2198:
2195:
2193:
2190:
2188:
2185:
2181:
2178:
2176:
2173:
2172:
2171:
2168:
2166:
2163:
2161:
2160:Tomosynthesis
2158:
2156:
2153:
2151:
2148:
2147:
2145:
2141:
2138:
2134:
2128:
2125:
2123:
2120:
2118:
2115:
2113:
2110:
2108:
2105:
2103:
2100:
2098:
2095:
2093:
2090:
2088:
2085:
2083:
2080:
2079:
2077:
2073:
2067:
2064:
2062:
2059:
2057:
2054:
2052:
2049:
2047:
2044:
2042:
2039:
2038:
2036:
2032:
2026:
2023:
2021:
2018:
2016:
2013:
2011:
2008:
2006:
2003:
2001:
1998:
1996:
1993:
1991:
1990:Moseley's law
1988:
1986:
1983:
1981:
1978:
1977:
1975:
1971:
1967:
1966:X-ray science
1960:
1955:
1953:
1948:
1946:
1941:
1940:
1937:
1931:
1928:
1926:
1923:
1922:
1909:
1907:9780191523281
1903:
1899:
1892:
1884:
1880:
1875:
1870:
1866:
1862:
1857:
1852:
1848:
1844:
1843:Pharmaceutics
1840:
1832:
1824:
1820:
1816:
1812:
1808:
1804:
1800:
1796:
1792:
1785:
1777:
1773:
1769:
1765:
1761:
1757:
1753:
1749:
1745:
1741:
1737:
1729:
1721:
1717:
1713:
1709:
1705:
1701:
1697:
1693:
1689:
1682:
1674:
1670:
1666:
1662:
1657:
1652:
1648:
1644:
1640:
1636:
1632:
1625:
1617:
1613:
1609:
1605:
1600:
1595:
1590:
1585:
1581:
1577:
1573:
1565:
1557:
1553:
1548:
1543:
1539:
1535:
1531:
1527:
1523:
1519:
1515:
1511:
1507:
1500:
1492:
1488:
1484:
1480:
1476:
1472:
1468:
1464:
1460:
1453:
1445:
1441:
1437:
1433:
1429:
1422:
1414:
1410:
1405:
1400:
1396:
1392:
1387:
1382:
1378:
1374:
1373:Pharmaceutics
1370:
1363:
1355:
1351:
1347:
1343:
1339:
1335:
1331:
1324:
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1080:
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1024:
1020:
1016:
1009:
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989:
985:
981:
977:
973:
969:
965:
961:
954:
946:
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938:
934:
930:
926:
922:
918:
914:
910:
906:
899:
891:
887:
883:
879:
875:
871:
867:
860:
852:
848:
844:
840:
836:
832:
828:
824:
820:
816:
812:
805:
797:
793:
789:
785:
781:
777:
773:
769:
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758:
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746:
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738:
734:
730:
726:
722:
718:
714:
710:
703:
695:
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683:
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664:
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436:
431:
426:
422:
418:
414:
410:
406:
402:
398:
391:
383:
379:
374:
369:
366:: s459–s462.
365:
361:
357:
350:
342:
338:
336:0-12-286280-5
332:
328:
324:
323:
315:
306:
302:
292:
289:
287:
284:
281:
278:
276:
273:
272:
266:
264:
260:
256:
252:
248:
244:
234:
232:
221:
219:
215:
211:
210:monochromator
206:
202:
192:
190:
186:
182:
181:
176:
175:
170:
165:
162:
161:monochromatic
152:
150:
146:
136:
134:
130:
126:
122:
118:
114:
110:
106:
103:, microgels,
102:
98:
94:
90:
79:
77:
73:
69:
65:
61:
56:
54:
50:
46:
41:
37:
33:
29:
25:
21:
3331:
3319:
3264:Associations
3232:Organisation
2724:Disclination
2655:Polymorphism
2618:Quasicrystal
2561:Orthorhombic
2501:Miller index
2449:Key concepts
2332:
2258:Spectroscopy
2202:Ptychography
2136:Applications
2097:Auger effect
2000:Water window
1897:
1891:
1846:
1842:
1831:
1798:
1795:Mol. BioSyst
1794:
1784:
1743:
1739:
1728:
1695:
1691:
1681:
1638:
1634:
1624:
1579:
1575:
1564:
1513:
1509:
1499:
1466:
1462:
1452:
1435:
1431:
1421:
1376:
1372:
1362:
1337:
1333:
1323:
1290:
1286:
1276:
1223:
1219:
1208:
1173:
1169:
1159:
1118:
1114:
1103:
1070:
1066:
1055:
1022:
1018:
1008:
967:
963:
953:
912:
908:
898:
873:
869:
859:
818:
814:
804:
771:
767:
757:
716:
712:
702:
677:
673:
663:
626:
622:
612:
587:
583:
577:
552:
548:
542:
517:
513:
507:
494:
461:
457:
447:
404:
400:
390:
363:
359:
349:
341:the original
321:
314:
305:
240:
227:
198:
185:synchrotrons
178:
172:
168:
158:
142:
119:, foods and
115:, plastics,
109:polymersomes
85:
82:Applications
57:
32:nanoparticle
23:
19:
18:
3217:Ewald Prize
2985:Diffraction
2963:Diffraction
2946:Diffraction
2888:Bragg plane
2883:Bragg's law
2762:Dislocation
2677:Segregation
2589:Crystallite
2506:Point group
2051:Synchrotron
1340:: 112–121.
1176:: 518–527.
964:Soft Matter
909:Soft Matter
520:: 171–210.
245:, Austria;
231:convolution
189:collimation
3349:Categories
3001:Algorithms
2990:Scattering
2968:Scattering
2951:Scattering
2819:Slip bands
2782:Cross slip
2632:transition
2566:Tetragonal
2556:Monoclinic
2468:Metallurgy
2310:Scattering
2175:Helical CT
2041:X-ray tube
1849:(2): 106.
1656:2299/19649
1599:2299/17369
297:References
247:Bruker AXS
243:Anton Paar
3108:Databases
2571:Triclinic
2551:Hexagonal
2491:Unit cell
2483:Structure
1865:1999-4923
1815:1742-206X
1776:235659596
1760:1525-7797
1720:2046-2069
1673:100587522
1665:0303-402X
1608:0743-7463
1538:0024-9297
1483:1936-0851
1395:1999-4923
1379:(2): 10.
1354:103002028
1307:1520-6106
1268:206664063
1252:1948-7185
1200:102663271
1135:1525-7797
1087:1525-7797
1039:0743-7463
992:1744-683X
937:1744-683X
890:1520-6106
851:105195163
843:0024-9297
788:1525-7797
749:202079335
741:0024-9297
604:1600-5767
569:1600-5767
534:0001-8686
486:189992231
478:2637-6105
421:1600-5767
382:1600-5767
174:divergent
105:liposomes
3321:Category
3156:Journals
3088:OctaDist
3083:JANA2020
3055:Software
2941:Electron
2858:F-center
2645:Eutectic
2606:Fiveling
2601:Twinning
2594:Equiaxed
2046:Betatron
1883:32013056
1823:21947276
1768:34180669
1616:27159129
1576:Langmuir
1556:28626247
1491:22713309
1463:ACS Nano
1413:27043614
1315:24517119
1260:28759235
1151:36632159
1143:24083567
1095:22793269
1047:15752000
1019:Langmuir
1000:27194585
945:30140809
796:29381335
655:34963770
439:30546286
269:See also
201:pinholes
180:focusing
117:proteins
113:polymers
101:micelles
97:colloids
89:lamellae
64:proteins
3333:Commons
3281:Germany
2958:Neutron
2848:Vacancy
2707:Defects
2692:GP-zone
2538:Systems
2389:History
2143:Imaging
1874:7076460
1700:Bibcode
1692:RSC Adv
1547:5472368
1518:Bibcode
1404:4932473
972:Bibcode
917:Bibcode
823:Bibcode
721:Bibcode
682:Bibcode
646:8662971
430:6276275
218:sheared
169:without
93:fractal
40:elastic
26:) is a
3276:France
3271:Europe
3204:Awards
2734:Growth
2584:Growth
2377:Others
2338:GISAXS
2010:L-edge
2005:K-edge
1904:
1881:
1871:
1863:
1821:
1813:
1774:
1766:
1758:
1718:
1671:
1663:
1614:
1606:
1554:
1544:
1536:
1489:
1481:
1411:
1401:
1393:
1352:
1313:
1305:
1266:
1258:
1250:
1198:
1149:
1141:
1133:
1093:
1085:
1045:
1037:
998:
990:
943:
935:
888:
849:
841:
794:
786:
747:
739:
653:
643:
602:
567:
532:
484:
476:
437:
427:
419:
380:
333:
263:Xenocs
259:Xenocs
255:Rigaku
214:fibres
91:, and
49:X-rays
3298:Japan
3245:IOBCr
3098:SHELX
3093:Olex2
2980:X-ray
2630:Phase
2546:Cubic
2368:EDXRD
2290:XANES
2285:EXAFS
2275:ARPES
2222:3DXRD
1980:X-ray
1772:S2CID
1669:S2CID
1350:S2CID
1264:S2CID
1196:S2CID
1147:S2CID
847:S2CID
745:S2CID
482:S2CID
280:GISAS
205:X-ray
125:X-ray
3240:IUCr
3141:ICDD
3136:ICSD
3121:CCDC
3068:Coot
3063:CCP4
2814:Slip
2777:Kink
2353:RIXS
2343:WAXS
2333:SAXS
2244:DFXM
2212:XDCT
2197:STXM
2192:XPCI
2180:XACT
1902:ISBN
1879:PMID
1861:ISSN
1819:PMID
1811:ISSN
1764:PMID
1756:ISSN
1716:ISSN
1661:ISSN
1612:PMID
1604:ISSN
1552:PMID
1534:ISSN
1487:PMID
1479:ISSN
1409:PMID
1391:ISSN
1311:PMID
1303:ISSN
1256:PMID
1248:ISSN
1139:PMID
1131:ISSN
1091:PMID
1083:ISSN
1043:PMID
1035:ISSN
996:PMID
988:ISSN
941:PMID
933:ISSN
886:ISSN
839:ISSN
792:PMID
784:ISSN
737:ISSN
651:PMID
600:ISSN
565:ISSN
530:ISSN
474:ISSN
435:PMID
417:ISSN
378:ISSN
331:ISBN
164:beam
133:flux
24:SAXS
3255:DMG
3250:RAS
3146:PDB
3131:COD
3126:CIF
3078:DSR
2802:GND
2729:CSL
2358:XRS
2300:XFH
2295:EDS
2280:AES
2270:XPS
2265:XAS
2249:DXA
2217:DCT
2165:CDI
1869:PMC
1851:doi
1803:doi
1748:doi
1708:doi
1651:hdl
1643:doi
1639:295
1594:hdl
1584:doi
1542:PMC
1526:doi
1471:doi
1440:doi
1436:219
1399:PMC
1381:doi
1342:doi
1338:549
1295:doi
1291:118
1238:hdl
1228:doi
1186:hdl
1178:doi
1123:doi
1075:doi
1027:doi
980:doi
925:doi
878:doi
874:107
831:doi
776:doi
729:doi
690:doi
678:128
641:PMC
631:doi
592:doi
557:doi
522:doi
466:doi
425:PMC
409:doi
368:doi
76:kDa
3351::
3293:US
3286:UK
2363:XS
2170:CT
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1867:.
1859:.
1847:12
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