178:
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,
2934:
66:. 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.
3327:
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244:) 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.
219:
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
239:
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
177:
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
218:
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
97:
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
240:
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-
53:
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
1224:
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).
1071:
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).
1119:
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).
1847:
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).
1580:
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).
509:
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).|
1744:
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).
3204:
3199:
3255:
1439:"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"
223:
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 (
1697:
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).
773:
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).
1935:
1583:"Internal Nanoparticle Structure of Temperature-Responsive Self-Assembled PNIPAM- b -PEG- b -PNIPAM Triblock Copolymers in Aqueous Solutions: NMR, SANS, and Light Scattering Studies"
1175:
Riabtseva, Anna; Kaberov, Leonid I.; Noirez, Laurence; Ryukhtin, Vasyl; Nardin, Corinne; Verbraeken, Bart; Hoogenboom, Richard; Stepanek, Petr; Filippov, Sergey K. (February 2018).
89:). 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.
1339:
Chaves, Matheus
Andrade; Oseliero Filho, Pedro Leonidas; Jange, Camila Garcia; Sinigaglia-Coimbra, Rita; Oliveira, Cristiano Luis Pinto; Pinho, Samantha Cristina (July 2018).
1747:"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"
916:"Formation of core/corona nanoparticles with interpolyelectrolyte complex cores in aqueous solution: insight into chain dynamics in the complex from fluorescence quenching"
106:-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
822:"Coassembly of Poly( N -isopropylacrylamide) with Dodecyl and Carboxyl Terminal Groups with Cationic Surfactant: Critical Comparison of Experimental and Simulation Data"
1074:"Macromolecular HPMA-Based Nanoparticles with Cholesterol for Solid-Tumor Targeting: Detailed Study of the Inner Structure of a Highly Efficient Drug Delivery System"
820:
Fanova, Anastasiia; Šindelka, Karel; Uchman, Mariusz; Limpouchová, Zuzana; Filippov, Sergey K.; Pispas, Stergios; Procházka, Karel; Štěpánek, Miroslav (2018-09-25).
3073:
3260:
2985:
971:"Temperature-induced structure switch in thermo-responsive micellar interpolyelectrolyte complexes: toward core–shell–corona and worm-like morphologies"
3151:
2443:
2285:
81:
is that a crystalline sample is not needed. Furthermore, the properties of SAXS allow investigation of conformational diversity in these molecules.
2348:
2295:
718:
Fanova, Anastasiia; Janata, Miroslav; Filippov, Sergey K.; Ĺ louf, Miroslav; NetopilĂk, Miloš; Mariani, Alessandro; Ĺ tÄ›pánek, Miroslav (2019-08-27).
290:
1967:
679:
Hollamby, Martin J.; Aratsu, Keisuke; Pauw, Brian R.; Rogers, Sarah E.; Smith, Andrew J.; Yamauchi, Mitsuaki; Lin, Xu; Yagai, Shiki (2016-08-16).
82:
1850:"Molecular Mechanisms of the Interactions of N-(2-Hydroxypropyl)methacrylamide Copolymers Designed for Cancer Therapy with Blood Plasma Proteins"
681:"Simultaneous SAXS and SANS Analysis for the Detection of Toroidal Supramolecular Polymers Composed of Noncovalent Supermacrocycles in Solution"
593:
Pedersen, JS (1994). "Determination of size distribution from small-angle scattering data for systems with effective hard-sphere interactions".
3250:
3242:
2207:
463:
Patil, N; Narayanan, T; Michels, L; Skjønsfjell, ETB; Guizar-Sicairos, M; Van den Brande, N; Claessens, R; Van Mele, B; Breiby, DW (May 2019).
1517:"Time-Resolved SAXS Studies of the Kinetics of Thermally Triggered Release of Encapsulated Silica Nanoparticles from Block Copolymer Vesicles"
1437:
Zaborova, Olga V.; Filippov, Sergey K.; Chytil, Petr; Kováčik, Lubomir; Ulbrich, Karel; Yaroslavov, Alexander A.; Etrych, Tomaš (April 2018).
914:
Murmiliuk, Anastasiia; MatÄ›jĂÄŤek, Pavel; Filippov, Sergey K.; Janata, Miroslav; Ĺ louf, Miroslav; Pispas, Stergios; Ĺ tÄ›pánek, Miroslav (2018).
3303:
3281:
2222:
523:
Pedersen, JS (July 1997). "Analysis of small-angle scattering data from colloids and polymer solutions: modeling and least-squares fitting".
98:(so-called particles) of the same or another material in any combination. Not only particles, but also the structure of ordered systems like
3296:
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2812:
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2300:
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159:
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1515:
Mable, Charlotte J.; Derry, Matthew J.; Thompson, Kate L.; Fielding, Lee A.; Mykhaylyk, Oleksandr O.; Armes, Steven P. (2017-06-13).
162:. Different from standard RIXS measurements, the scattered photons are considered to have the same energy as the incident photons.
3308:
3166:
3136:
3065:
1916:
877:"Interpolyelectrolyte Complex and Coacervate Formation of Poly(glutamic acid) with a Dendrimer Studied by Light Scattering and SAXS"
345:
285:
1468:
Bressel, Katharina; Muthig, Michael; Prevost, Sylvain; Gummel, Jeremie; Narayanan, Theyencheri; Gradzielski, Michael (2012-07-24).
1026:"Structure and Interactions of Block Copolymer Micelles of Brij 700 Studied by Combining Small-Angle X-ray and Neutron Scattering"
49:, determine pore sizes, characteristic distances of partially ordered materials, and much more. This is achieved by analyzing the
3018:
2280:
2259:
2190:
367:"Development of an ultra-small-angle X-ray scattering instrument for probing the microstructure and the dynamics of soft matter"
3365:
3291:
3214:
3088:
2687:
1699:"Novel thermosensitive telechelic PEGs with antioxidant activity: synthesis, molecular properties and conformational behaviour"
3048:
202:
instead. Laboratory SAXS instruments can be divided into two main groups: point-collimation and line-collimation instruments:
3126:
331:
320:
Hamley, I.W. "Small-Angle
Scattering: Theory, Instrumentation, Data, and Applications" – Wiley, 2022. ISBN 978-1-119-76830-2.
55:
406:
Narayanan, T; Sztucki, M; Van
Vaerenbergh, P; LĂ©onardon, J; Gorini, J; Claustre, L; Sever, F; Morse, J; Boesecke, P (2018).
775:"Macromolecular p HPMA-Based Nanoparticles with Cholesterol for Solid Tumor Targeting: Behavior in HSA Protein Environment"
3141:
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1960:
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70:
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969:
Dähling, Claudia; Lotze, Gudrun; Drechsler, Markus; Mori, Hideharu; Pergushov, Dmitry V.; Plamper, Felix A. (2016).
3343:
3174:
2471:
2399:
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2127:
558:
Pedersen, JS (2000). "Form factors of block copolymer micelles with spherical, ellipsoidal and cylindrical cores".
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41:
technique by which nanoscale density differences in a sample can be quantified. This means that it can determine
2702:
3331:
3055:
2951:
2824:
2787:
2581:
2561:
2429:
2066:
1294:"Internal Structures of Thermosensitive Hybrid Microgels Investigated by Means of Small-Angle X-ray Scattering"
2739:
1380:"Small Angle X-ray and Neutron Scattering: Powerful Tools for Studying the Structure of Drug-Loaded Liposomes"
3179:
3023:
2968:
2717:
2682:
2875:
2692:
2368:
2217:
1953:
38:
2797:
1642:"Synthesis and solution properties of a temperature-responsive PNIPAM–b-PDMS–b-PNIPAM triblock copolymer"
3232:
3028:
2990:
2749:
2483:
2328:
2197:
2005:
139:
1177:"Structural characterization of nanoparticles formed by fluorinated poly(2-oxazoline)-based polyphiles"
2244:
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2665:
2556:
2165:
2097:
2030:
1710:
1528:
982:
927:
833:
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that are used in the characterization of materials. In the case of biological macromolecules such as
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154:
It is possible to enhance the X-ray scattering yield by matching the energy of X-ray source to a
1341:"Structural characterization of multilamellar liposomes coencapsulating curcumin and vitamin D3"
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where large bent mirrors can be used. This is why most laboratory small angle devices rely on
194:
the beam, but this is not easy when dealing with X-rays and was previously not done except on
50:
1438:
680:
408:"A multipurpose instrument for time-resolved ultra-small-angle and coherent X-ray scattering"
3194:
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2452:
2394:
2249:
2112:
2076:
1995:
1802:"Structural analysis of intrinsically disordered proteins by small-angle X-ray scattering"
199:
184:
78:
1122:"Hydrolytically Degradable Polymer Micelles for Drug Delivery: A SAXS/SANS Kinetic Study"
1714:
1532:
986:
931:
837:
821:
735:
719:
696:
182:
blocking the closely adjacent scattered radiation. Most available X-ray sources produce
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2841:
2807:
2777:
2767:
2726:
2670:
2594:
2548:
1884:
1849:
1557:
1516:
1470:"Shaping Vesicles–Controlling Size and Stability by Admixture of Amphiphilic Copolymer"
1414:
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1227:"Block and Gradient Copoly(2-oxazoline) Micelles: Strikingly Different on the Inside"
1210:
861:
759:
496:
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86:
46:
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beams and this compounds the problem. In principle the problem could be overcome by
85:
methods encounter problems with macromolecules of higher molecular mass (> 30–40
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2107:
2020:
2010:
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1640:
Cook, Michael T.; Filippov, Sergey K.; Khutoryanskiy, Vitaliy V. (August 2017).
1243:
1226:
241:
195:
119:
1762:
1292:
Suzuki, Daisuke; Nagase, Yasuhisa; Kureha, Takuma; Sato, Takaaki (2014-02-27).
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1153:
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1057:
1010:
955:
806:
704:
665:
480:
465:"Probing Organic Thin Films by Coherent X-ray Imaging and X-ray Scattering"
449:
3098:
2868:
2616:
2056:
115:
3108:
2180:
1941:
A movie demonstrating small-angle scattering using laserlight on a hair
1817:
1801:
1722:
1698:
994:
970:
939:
915:
211:
127:
123:
111:
107:
103:
74:
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1609:
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1309:
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1041:
1024:
Sommer, Cornelia; Pedersen, Jan Skov; Garamus, Vasil M. (2005-03-01).
892:
511:
2015:
273:
269:
265:
257:
1293:
17:
1378:
Di Cola, Emanuela; Grillo, Isabelle; Ristori, Sandra (2016-03-28).
3103:
2421:
1990:
1976:
720:"Evolution of Structure in a Comb Copolymer–Surfactant Coacervate"
224:
215:
135:
59:
45:
size distributions, resolve the size and shape of (monodisperse)
1945:
1345:
Colloids and
Surfaces A: Physicochemical and Engineering Aspects
143:
134:
and can be found in research as well as in quality control. The
2425:
1949:
3205:
3200:
110:
of all types including interpolyelectrolyte complexes,
3093:
3274:
3241:
3213:
3165:
3117:
3064:
3011:
2942:
2725:
2716:
2639:
2547:
2492:
2459:
2387:
2319:
2268:
2153:
2146:
2085:
2044:
1983:
1909:Electron Dynamics by Inelastic X-Ray Scattering
628:Gommes, CJ; Jaksch, S; Frielinghaus, H (2021).
875:Leisner, Dietrich; Imae, Toyoko (2003-08-01).
260:, Germany; Hecus X-Ray Systems Graz, Austria;
2437:
1961:
8:
3271:
2722:
2544:
2489:
2444:
2430:
2422:
2150:
1968:
1954:
1946:
293:(Grazing-incidence small-angle scattering)
1883:
1865:
1800:BernadĂł, Pau; Svergun, Dmitri I. (2012).
1665:
1608:
1598:
1556:
1413:
1395:
1252:
1242:
1231:The Journal of Physical Chemistry Letters
1200:
655:
645:
525:Advances in Colloid and Interface Science
439:
382:
313:
83:Nuclear magnetic resonance spectroscopy
630:"Small-Angle Scattering for Beginners"
252:SAXS instrument manufacturers include
150:Resonant small-angle X-ray scattering
138:source can be a laboratory source or
69:SAXS and USAXS belong to a family of
7:
3338:
2678:Phase transformation crystallography
1443:Macromolecular Chemistry and Physics
3185:Journal of Chemical Crystallography
1907:Schuelke, Winfried (21 June 2007).
1298:The Journal of Physical Chemistry B
881:The Journal of Physical Chemistry B
512:http://hdl.handle.net/1721.1/108809
210:Point-collimation instruments have
160:resonant inelastic X-ray scattering
58:, and is typically done using hard
634:Journal of Applied Crystallography
595:Journal of Applied Crystallography
560:Journal of Applied Crystallography
412:Journal of Applied Crystallography
371:Journal of Applied Crystallography
330:Glatter O; Kratky O, eds. (1982).
297:Fluctuation X-ray scattering (FXS)
25:
365:Sztucki, M; Narayanan, T (2007).
286:Biological small-angle scattering
3337:
3326:
3325:
2932:
62:with a wavelength of 0.07 – 0.2
1193:10.1016/j.eurpolymj.2018.01.007
3127:Bilbao Crystallographic Server
1357:10.1016/j.colsurfa.2018.04.018
142:which provides a higher X-ray
56:small-angle neutron scattering
27:Radiation scattering technique
1:
1867:10.3390/pharmaceutics12020106
537:10.1016/S0001-8686(97)00312-6
469:ACS Applied Polymer Materials
248:SAXS instrument manufacturers
206:Point-collimation instruments
77:, the advantage of SAXS over
1600:10.1021/acs.langmuir.6b00284
1541:10.1021/acs.macromol.7b00475
1397:10.3390/pharmaceutics8020010
846:10.1021/acs.macromol.8b01161
744:10.1021/acs.macromol.9b00332
333:Small Angle X-ray Scattering
235:Line-collimation instruments
31:Small-angle X-ray scattering
3175:Crystal Growth & Design
2467:Timeline of crystallography
1911:. Oxford University Press.
1646:Colloid and Polymer Science
1244:10.1021/acs.jpclett.7b01588
302:Wide-angle X-ray scattering
231:liquids) to be determined.
71:X-ray scattering techniques
3387:
2986:Nuclear magnetic resonance
2240:X-Ray Fluorescence Imaging
2128:Anomalous X-ray scattering
1763:10.1021/acs.biomac.1c00367
791:10.1021/acs.biomac.7b01579
3321:
3190:Journal of Crystal Growth
2930:
1658:10.1007/s00396-017-4084-y
647:10.1107/S1600576721010293
607:10.1107/S0021889893013810
572:10.1107/S0021889899012248
424:10.1107/S1600576718012748
384:10.1107/S0021889806045833
3056:Single particle analysis
2914:Hermann–Mauguin notation
2067:Synchrotron light source
1181:European Polymer Journal
170:In a SAXS instrument, a
156:resonant absorption edge
3180:Crystallography Reviews
3024:Isomorphous replacement
2818:Lomer–Cottrell junction
2086:Interaction with matter
2045:Sources and instruments
122:, metals, cement, oil,
3366:Small-angle scattering
2693:Spinodal decomposition
2218:Diffraction tomography
1455:10.1002/macp.201700508
705:10.1002/ange.201603370
481:10.1021/acsapm.9b00324
39:small-angle scattering
3233:Gregori Aminoff Prize
3029:Molecular replacement
2329:X-ray crystallography
2198:Soft x-ray microscopy
2166:Panoramic radiography
2006:Synchrotron radiation
1936:SAXS at a Synchrotron
158:in as it is done for
2539:Structure prediction
2098:Photoelectric effect
2031:Characteristic X-ray
268:Corporation, Japan;
2803:Cottrell atmosphere
2783:Partial dislocation
2527:Restriction theorem
2118:Photodisintegration
2093:Rayleigh scattering
2072:Free-electron laser
1715:2014RSCAd...441763S
1709:(79): 41763–41771.
1533:2017MaMol..50.4465M
987:2016SMat...12.5127D
932:2018SMat...14.7578M
838:2018MaMol..51.7295F
736:2019MaMol..52.6303F
697:2016AngCh.12810044H
691:(34): 10044–10047.
264:. the Netherlands,
262:Malvern Panalytical
3223:Carl Hermann Medal
3034:Molecular dynamics
2881:Defects in diamond
2876:Stone–Wales defect
2522:Reciprocal lattice
2484:Biocrystallography
2359:X-ray reflectivity
2138:X-ray fluorescence
2103:Compton scattering
2036:High-energy X-rays
1818:10.1039/C1MB05275F
1723:10.1039/C4RA06978A
995:10.1039/C6SM00757K
940:10.1039/C8SM01174E
354:on April 21, 2008.
3353:
3352:
3317:
3316:
2924:Thermal ellipsoid
2889:
2888:
2798:Frank–Read source
2758:
2757:
2624:Aperiodic crystal
2590:
2589:
2472:Crystallographers
2419:
2418:
2415:
2414:
2407:X-ray lithography
2339:Backscatter X-ray
2334:X-ray diffraction
2161:X-ray radiography
2133:X-ray diffraction
2026:Siegbahn notation
1751:Biomacromolecules
1593:(21): 5314–5323.
1527:(11): 4465–4473.
1486:10.1021/nn300359q
1310:10.1021/jp410983x
1237:(16): 3800–3804.
1138:10.1021/bm401186z
1132:(11): 4061–4070.
1126:Biomacromolecules
1090:10.1021/bm3008555
1078:Biomacromolecules
1042:10.1021/la047489k
981:(23): 5127–5137.
926:(37): 7578–7585.
893:10.1021/jp027365l
887:(32): 8078–8087.
832:(18): 7295–7308.
779:Biomacromolecules
730:(16): 6303–6310.
685:Angewandte Chemie
276:, United States.
140:synchrotron light
16:(Redirected from
3378:
3371:X-ray scattering
3341:
3340:
3329:
3328:
3272:
3195:Kristallografija
3049:Gerchberg–Saxton
2944:Characterisation
2936:
2919:Structure factor
2723:
2708:Ostwald ripening
2545:
2490:
2446:
2439:
2432:
2423:
2245:X-ray holography
2151:
2123:Radiation damage
1970:
1963:
1956:
1947:
1923:
1922:
1904:
1898:
1897:
1887:
1869:
1844:
1838:
1837:
1797:
1791:
1790:
1757:(7): 2963–2975.
1741:
1735:
1734:
1694:
1688:
1687:
1669:
1652:(8): 1351–1358.
1637:
1631:
1630:
1612:
1602:
1577:
1571:
1570:
1560:
1512:
1506:
1505:
1480:(7): 5858–5865.
1465:
1459:
1458:
1434:
1428:
1427:
1417:
1399:
1375:
1369:
1368:
1336:
1330:
1329:
1304:(8): 2194–2204.
1289:
1283:
1282:
1256:
1246:
1221:
1215:
1214:
1204:
1172:
1166:
1165:
1116:
1110:
1109:
1084:(8): 2594–2604.
1068:
1062:
1061:
1036:(6): 2137–2149.
1021:
1015:
1014:
966:
960:
959:
911:
905:
904:
872:
866:
865:
817:
811:
810:
770:
764:
763:
715:
709:
708:
676:
670:
669:
659:
649:
640:(6): 1832–1843.
625:
619:
618:
590:
584:
583:
555:
549:
548:
520:
514:
507:
501:
500:
475:(7): 1787–1797.
460:
454:
453:
443:
418:(6): 1511–1524.
403:
397:
396:
386:
362:
356:
355:
350:. Archived from
327:
321:
318:
166:SAXS instruments
21:
3386:
3385:
3381:
3380:
3379:
3377:
3376:
3375:
3356:
3355:
3354:
3349:
3313:
3270:
3237:
3209:
3161:
3113:
3084:CrystalExplorer
3060:
3044:Phase retrieval
3007:
2938:
2937:
2928:
2885:
2864:Schottky defect
2763:Perfect crystal
2754:
2750:Abnormal growth
2712:
2698:Supersaturation
2661:Miscibility gap
2642:
2635:
2586:
2543:
2507:Bravais lattice
2488:
2455:
2453:Crystallography
2450:
2420:
2411:
2395:X-ray astronomy
2383:
2315:
2264:
2250:X-ray telescope
2142:
2113:Photoionization
2081:
2077:X-ray nanoprobe
2040:
1996:Absorption edge
1984:Characteristics
1979:
1974:
1932:
1927:
1926:
1919:
1906:
1905:
1901:
1846:
1845:
1841:
1799:
1798:
1794:
1743:
1742:
1738:
1696:
1695:
1691:
1639:
1638:
1634:
1579:
1578:
1574:
1514:
1513:
1509:
1467:
1466:
1462:
1436:
1435:
1431:
1377:
1376:
1372:
1338:
1337:
1333:
1291:
1290:
1286:
1254:1854/LU-8534833
1223:
1222:
1218:
1202:1854/LU-8561215
1174:
1173:
1169:
1118:
1117:
1113:
1070:
1069:
1065:
1023:
1022:
1018:
968:
967:
963:
913:
912:
908:
874:
873:
869:
819:
818:
814:
772:
771:
767:
717:
716:
712:
678:
677:
673:
627:
626:
622:
592:
591:
587:
557:
556:
552:
522:
521:
517:
508:
504:
462:
461:
457:
405:
404:
400:
364:
363:
359:
348:
329:
328:
324:
319:
315:
310:
282:
250:
237:
214:that shape the
208:
168:
152:
132:pharmaceuticals
95:
79:crystallography
28:
23:
22:
15:
12:
11:
5:
3384:
3382:
3374:
3373:
3368:
3358:
3357:
3351:
3350:
3348:
3347:
3335:
3322:
3319:
3318:
3315:
3314:
3312:
3311:
3306:
3301:
3300:
3299:
3294:
3289:
3278:
3276:
3269:
3268:
3263:
3258:
3253:
3247:
3245:
3239:
3238:
3236:
3235:
3230:
3225:
3219:
3217:
3211:
3210:
3208:
3207:
3202:
3197:
3192:
3187:
3182:
3177:
3171:
3169:
3163:
3162:
3160:
3159:
3154:
3149:
3144:
3139:
3134:
3129:
3123:
3121:
3115:
3114:
3112:
3111:
3106:
3101:
3096:
3091:
3086:
3081:
3076:
3070:
3068:
3062:
3061:
3059:
3058:
3053:
3052:
3051:
3041:
3036:
3031:
3026:
3021:
3019:Direct methods
3015:
3013:
3009:
3008:
3006:
3005:
3004:
3003:
2998:
2988:
2983:
2982:
2981:
2976:
2966:
2965:
2964:
2959:
2948:
2946:
2940:
2939:
2931:
2929:
2927:
2926:
2921:
2916:
2911:
2906:
2904:Ewald's sphere
2901:
2896:
2890:
2887:
2886:
2884:
2883:
2878:
2873:
2872:
2871:
2866:
2856:
2855:
2854:
2849:
2847:Frenkel defect
2844:
2842:Bjerrum defect
2834:
2833:
2832:
2822:
2821:
2820:
2815:
2810:
2808:Peierls stress
2805:
2800:
2795:
2790:
2785:
2780:
2778:Burgers vector
2770:
2768:Stacking fault
2765:
2759:
2756:
2755:
2753:
2752:
2747:
2742:
2737:
2731:
2729:
2727:Grain boundary
2720:
2714:
2713:
2711:
2710:
2705:
2700:
2695:
2690:
2685:
2680:
2675:
2674:
2673:
2671:Liquid crystal
2668:
2663:
2658:
2647:
2645:
2637:
2636:
2634:
2633:
2632:
2631:
2621:
2620:
2619:
2609:
2608:
2607:
2602:
2591:
2588:
2587:
2585:
2584:
2579:
2574:
2569:
2564:
2559:
2553:
2551:
2542:
2541:
2536:
2534:Periodic table
2531:
2530:
2529:
2524:
2519:
2514:
2509:
2498:
2496:
2487:
2486:
2481:
2476:
2475:
2474:
2463:
2461:
2457:
2456:
2451:
2449:
2448:
2441:
2434:
2426:
2417:
2416:
2413:
2412:
2410:
2409:
2404:
2403:
2402:
2391:
2389:
2385:
2384:
2382:
2381:
2376:
2371:
2366:
2361:
2356:
2351:
2346:
2341:
2336:
2331:
2325:
2323:
2317:
2316:
2314:
2313:
2308:
2303:
2298:
2293:
2288:
2283:
2278:
2272:
2270:
2266:
2265:
2263:
2262:
2257:
2252:
2247:
2242:
2237:
2236:
2235:
2230:
2225:
2215:
2210:
2205:
2200:
2195:
2194:
2193:
2188:
2178:
2173:
2168:
2163:
2157:
2155:
2148:
2144:
2143:
2141:
2140:
2135:
2130:
2125:
2120:
2115:
2110:
2105:
2100:
2095:
2089:
2087:
2083:
2082:
2080:
2079:
2074:
2069:
2064:
2059:
2054:
2048:
2046:
2042:
2041:
2039:
2038:
2033:
2028:
2023:
2018:
2013:
2008:
2003:
1998:
1993:
1987:
1985:
1981:
1980:
1975:
1973:
1972:
1965:
1958:
1950:
1944:
1943:
1938:
1931:
1930:External links
1928:
1925:
1924:
1917:
1899:
1839:
1812:(1): 151–167.
1792:
1736:
1689:
1632:
1572:
1521:Macromolecules
1507:
1460:
1449:(7): 1700508.
1429:
1370:
1331:
1284:
1216:
1167:
1111:
1063:
1016:
961:
906:
867:
826:Macromolecules
812:
785:(2): 470–480.
765:
724:Macromolecules
710:
671:
620:
601:(4): 595–608.
585:
566:(3): 637–640.
550:
515:
502:
455:
398:
357:
346:
338:Academic Press
322:
312:
311:
309:
306:
305:
304:
299:
294:
288:
281:
278:
272:, France; and
249:
246:
236:
233:
207:
204:
167:
164:
151:
148:
94:
91:
47:macromolecules
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3383:
3372:
3369:
3367:
3364:
3363:
3361:
3346:
3345:
3336:
3334:
3333:
3324:
3323:
3320:
3310:
3307:
3305:
3302:
3298:
3295:
3293:
3290:
3288:
3285:
3284:
3283:
3280:
3279:
3277:
3273:
3267:
3264:
3262:
3259:
3257:
3254:
3252:
3249:
3248:
3246:
3244:
3240:
3234:
3231:
3229:
3226:
3224:
3221:
3220:
3218:
3216:
3212:
3206:
3203:
3201:
3198:
3196:
3193:
3191:
3188:
3186:
3183:
3181:
3178:
3176:
3173:
3172:
3170:
3168:
3164:
3158:
3155:
3153:
3150:
3148:
3145:
3143:
3140:
3138:
3135:
3133:
3130:
3128:
3125:
3124:
3122:
3120:
3116:
3110:
3107:
3105:
3102:
3100:
3097:
3095:
3092:
3090:
3087:
3085:
3082:
3080:
3077:
3075:
3072:
3071:
3069:
3067:
3063:
3057:
3054:
3050:
3047:
3046:
3045:
3042:
3040:
3039:Patterson map
3037:
3035:
3032:
3030:
3027:
3025:
3022:
3020:
3017:
3016:
3014:
3010:
3002:
2999:
2997:
2994:
2993:
2992:
2989:
2987:
2984:
2980:
2977:
2975:
2972:
2971:
2970:
2967:
2963:
2960:
2958:
2955:
2954:
2953:
2950:
2949:
2947:
2945:
2941:
2935:
2925:
2922:
2920:
2917:
2915:
2912:
2910:
2909:Friedel's law
2907:
2905:
2902:
2900:
2897:
2895:
2892:
2891:
2882:
2879:
2877:
2874:
2870:
2867:
2865:
2862:
2861:
2860:
2857:
2853:
2852:Wigner effect
2850:
2848:
2845:
2843:
2840:
2839:
2838:
2837:Interstitials
2835:
2831:
2828:
2827:
2826:
2823:
2819:
2816:
2814:
2811:
2809:
2806:
2804:
2801:
2799:
2796:
2794:
2791:
2789:
2786:
2784:
2781:
2779:
2776:
2775:
2774:
2771:
2769:
2766:
2764:
2761:
2760:
2751:
2748:
2746:
2743:
2741:
2738:
2736:
2733:
2732:
2730:
2728:
2724:
2721:
2719:
2715:
2709:
2706:
2704:
2701:
2699:
2696:
2694:
2691:
2689:
2686:
2684:
2683:Precipitation
2681:
2679:
2676:
2672:
2669:
2667:
2664:
2662:
2659:
2657:
2654:
2653:
2652:
2651:Phase diagram
2649:
2648:
2646:
2644:
2638:
2630:
2627:
2626:
2625:
2622:
2618:
2615:
2614:
2613:
2610:
2606:
2603:
2601:
2598:
2597:
2596:
2593:
2592:
2583:
2580:
2578:
2575:
2573:
2570:
2568:
2565:
2563:
2560:
2558:
2555:
2554:
2552:
2550:
2546:
2540:
2537:
2535:
2532:
2528:
2525:
2523:
2520:
2518:
2515:
2513:
2510:
2508:
2505:
2504:
2503:
2500:
2499:
2497:
2495:
2491:
2485:
2482:
2480:
2477:
2473:
2470:
2469:
2468:
2465:
2464:
2462:
2458:
2454:
2447:
2442:
2440:
2435:
2433:
2428:
2427:
2424:
2408:
2405:
2401:
2398:
2397:
2396:
2393:
2392:
2390:
2386:
2380:
2377:
2375:
2372:
2370:
2367:
2365:
2362:
2360:
2357:
2355:
2352:
2350:
2347:
2345:
2342:
2340:
2337:
2335:
2332:
2330:
2327:
2326:
2324:
2322:
2318:
2312:
2309:
2307:
2304:
2302:
2299:
2297:
2294:
2292:
2289:
2287:
2284:
2282:
2279:
2277:
2274:
2273:
2271:
2267:
2261:
2258:
2256:
2253:
2251:
2248:
2246:
2243:
2241:
2238:
2234:
2231:
2229:
2226:
2224:
2221:
2220:
2219:
2216:
2214:
2211:
2209:
2206:
2204:
2201:
2199:
2196:
2192:
2189:
2187:
2184:
2183:
2182:
2179:
2177:
2174:
2172:
2171:Tomosynthesis
2169:
2167:
2164:
2162:
2159:
2158:
2156:
2152:
2149:
2145:
2139:
2136:
2134:
2131:
2129:
2126:
2124:
2121:
2119:
2116:
2114:
2111:
2109:
2106:
2104:
2101:
2099:
2096:
2094:
2091:
2090:
2088:
2084:
2078:
2075:
2073:
2070:
2068:
2065:
2063:
2060:
2058:
2055:
2053:
2050:
2049:
2047:
2043:
2037:
2034:
2032:
2029:
2027:
2024:
2022:
2019:
2017:
2014:
2012:
2009:
2007:
2004:
2002:
2001:Moseley's law
1999:
1997:
1994:
1992:
1989:
1988:
1986:
1982:
1978:
1977:X-ray science
1971:
1966:
1964:
1959:
1957:
1952:
1951:
1948:
1942:
1939:
1937:
1934:
1933:
1929:
1920:
1918:9780191523281
1914:
1910:
1903:
1900:
1895:
1891:
1886:
1881:
1877:
1873:
1868:
1863:
1859:
1855:
1854:Pharmaceutics
1851:
1843:
1840:
1835:
1831:
1827:
1823:
1819:
1815:
1811:
1807:
1803:
1796:
1793:
1788:
1784:
1780:
1776:
1772:
1768:
1764:
1760:
1756:
1752:
1748:
1740:
1737:
1732:
1728:
1724:
1720:
1716:
1712:
1708:
1704:
1700:
1693:
1690:
1685:
1681:
1677:
1673:
1668:
1663:
1659:
1655:
1651:
1647:
1643:
1636:
1633:
1628:
1624:
1620:
1616:
1611:
1606:
1601:
1596:
1592:
1588:
1584:
1576:
1573:
1568:
1564:
1559:
1554:
1550:
1546:
1542:
1538:
1534:
1530:
1526:
1522:
1518:
1511:
1508:
1503:
1499:
1495:
1491:
1487:
1483:
1479:
1475:
1471:
1464:
1461:
1456:
1452:
1448:
1444:
1440:
1433:
1430:
1425:
1421:
1416:
1411:
1407:
1403:
1398:
1393:
1389:
1385:
1384:Pharmaceutics
1381:
1374:
1371:
1366:
1362:
1358:
1354:
1350:
1346:
1342:
1335:
1332:
1327:
1323:
1319:
1315:
1311:
1307:
1303:
1299:
1295:
1288:
1285:
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1276:
1272:
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1236:
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1228:
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1190:
1186:
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1178:
1171:
1168:
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1143:
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1131:
1127:
1123:
1115:
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1103:
1099:
1095:
1091:
1087:
1083:
1079:
1075:
1067:
1064:
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1047:
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1039:
1035:
1031:
1027:
1020:
1017:
1012:
1008:
1004:
1000:
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992:
988:
984:
980:
976:
972:
965:
962:
957:
953:
949:
945:
941:
937:
933:
929:
925:
921:
917:
910:
907:
902:
898:
894:
890:
886:
882:
878:
871:
868:
863:
859:
855:
851:
847:
843:
839:
835:
831:
827:
823:
816:
813:
808:
804:
800:
796:
792:
788:
784:
780:
776:
769:
766:
761:
757:
753:
749:
745:
741:
737:
733:
729:
725:
721:
714:
711:
706:
702:
698:
694:
690:
686:
682:
675:
672:
667:
663:
658:
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648:
643:
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635:
631:
624:
621:
616:
612:
608:
604:
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589:
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581:
577:
573:
569:
565:
561:
554:
551:
546:
542:
538:
534:
530:
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519:
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503:
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490:
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482:
478:
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459:
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451:
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442:
437:
433:
429:
425:
421:
417:
413:
409:
402:
399:
394:
390:
385:
380:
377:: s459–s462.
376:
372:
368:
361:
358:
353:
349:
347:0-12-286280-5
343:
339:
335:
334:
326:
323:
317:
314:
307:
303:
300:
298:
295:
292:
289:
287:
284:
283:
279:
277:
275:
271:
267:
263:
259:
255:
247:
245:
243:
234:
232:
230:
226:
222:
221:monochromator
217:
213:
205:
203:
201:
197:
193:
192:
187:
186:
181:
176:
173:
172:monochromatic
165:
163:
161:
157:
149:
147:
145:
141:
137:
133:
129:
125:
121:
117:
114:, microgels,
113:
109:
105:
101:
92:
90:
88:
84:
80:
76:
72:
67:
65:
61:
57:
52:
48:
44:
40:
36:
32:
19:
3342:
3330:
3275:Associations
3243:Organisation
2735:Disclination
2666:Polymorphism
2629:Quasicrystal
2572:Orthorhombic
2512:Miller index
2460:Key concepts
2343:
2269:Spectroscopy
2213:Ptychography
2147:Applications
2108:Auger effect
2011:Water window
1908:
1902:
1857:
1853:
1842:
1809:
1806:Mol. BioSyst
1805:
1795:
1754:
1750:
1739:
1706:
1702:
1692:
1649:
1645:
1635:
1590:
1586:
1575:
1524:
1520:
1510:
1477:
1473:
1463:
1446:
1442:
1432:
1387:
1383:
1373:
1348:
1344:
1334:
1301:
1297:
1287:
1234:
1230:
1219:
1184:
1180:
1170:
1129:
1125:
1114:
1081:
1077:
1066:
1033:
1029:
1019:
978:
974:
964:
923:
919:
909:
884:
880:
870:
829:
825:
815:
782:
778:
768:
727:
723:
713:
688:
684:
674:
637:
633:
623:
598:
594:
588:
563:
559:
553:
528:
524:
518:
505:
472:
468:
458:
415:
411:
401:
374:
370:
360:
352:the original
332:
325:
316:
251:
238:
209:
196:synchrotrons
189:
183:
179:
169:
153:
130:, foods and
126:, plastics,
120:polymersomes
96:
93:Applications
68:
43:nanoparticle
34:
30:
29:
3228:Ewald Prize
2996:Diffraction
2974:Diffraction
2957:Diffraction
2899:Bragg plane
2894:Bragg's law
2773:Dislocation
2688:Segregation
2600:Crystallite
2517:Point group
2062:Synchrotron
1351:: 112–121.
1187:: 518–527.
975:Soft Matter
920:Soft Matter
531:: 171–210.
256:, Austria;
242:convolution
200:collimation
3360:Categories
3012:Algorithms
3001:Scattering
2979:Scattering
2962:Scattering
2830:Slip bands
2793:Cross slip
2643:transition
2577:Tetragonal
2567:Monoclinic
2479:Metallurgy
2321:Scattering
2186:Helical CT
2052:X-ray tube
1860:(2): 106.
1667:2299/19649
1610:2299/17369
308:References
258:Bruker AXS
254:Anton Paar
3119:Databases
2582:Triclinic
2562:Hexagonal
2502:Unit cell
2494:Structure
1876:1999-4923
1826:1742-206X
1787:235659596
1771:1525-7797
1731:2046-2069
1684:100587522
1676:0303-402X
1619:0743-7463
1549:0024-9297
1494:1936-0851
1406:1999-4923
1390:(2): 10.
1365:103002028
1318:1520-6106
1279:206664063
1263:1948-7185
1211:102663271
1146:1525-7797
1098:1525-7797
1050:0743-7463
1003:1744-683X
948:1744-683X
901:1520-6106
862:105195163
854:0024-9297
799:1525-7797
760:202079335
752:0024-9297
615:1600-5767
580:1600-5767
545:0001-8686
497:189992231
489:2637-6105
432:1600-5767
393:1600-5767
185:divergent
116:liposomes
3332:Category
3167:Journals
3099:OctaDist
3094:JANA2020
3066:Software
2952:Electron
2869:F-center
2656:Eutectic
2617:Fiveling
2612:Twinning
2605:Equiaxed
2057:Betatron
1894:32013056
1834:21947276
1779:34180669
1627:27159129
1587:Langmuir
1567:28626247
1502:22713309
1474:ACS Nano
1424:27043614
1326:24517119
1271:28759235
1162:36632159
1154:24083567
1106:22793269
1058:15752000
1030:Langmuir
1011:27194585
956:30140809
807:29381335
666:34963770
450:30546286
280:See also
212:pinholes
191:focusing
128:proteins
124:polymers
112:micelles
108:colloids
100:lamellae
75:proteins
3344:Commons
3292:Germany
2969:Neutron
2859:Vacancy
2718:Defects
2703:GP-zone
2549:Systems
2400:History
2154:Imaging
1885:7076460
1711:Bibcode
1703:RSC Adv
1558:5472368
1529:Bibcode
1415:4932473
983:Bibcode
928:Bibcode
834:Bibcode
732:Bibcode
693:Bibcode
657:8662971
441:6276275
229:sheared
180:without
104:fractal
51:elastic
37:) is a
3287:France
3282:Europe
3215:Awards
2745:Growth
2595:Growth
2388:Others
2349:GISAXS
2021:L-edge
2016:K-edge
1915:
1892:
1882:
1874:
1832:
1824:
1785:
1777:
1769:
1729:
1682:
1674:
1625:
1617:
1565:
1555:
1547:
1500:
1492:
1422:
1412:
1404:
1363:
1324:
1316:
1277:
1269:
1261:
1209:
1160:
1152:
1144:
1104:
1096:
1056:
1048:
1009:
1001:
954:
946:
899:
860:
852:
805:
797:
758:
750:
664:
654:
613:
578:
543:
495:
487:
448:
438:
430:
391:
344:
274:Xenocs
270:Xenocs
266:Rigaku
225:fibres
102:, and
60:X-rays
3309:Japan
3256:IOBCr
3109:SHELX
3104:Olex2
2991:X-ray
2641:Phase
2557:Cubic
2379:EDXRD
2301:XANES
2296:EXAFS
2286:ARPES
2233:3DXRD
1991:X-ray
1783:S2CID
1680:S2CID
1361:S2CID
1275:S2CID
1207:S2CID
1158:S2CID
858:S2CID
756:S2CID
493:S2CID
291:GISAS
216:X-ray
136:X-ray
3251:IUCr
3152:ICDD
3147:ICSD
3132:CCDC
3079:Coot
3074:CCP4
2825:Slip
2788:Kink
2364:RIXS
2354:WAXS
2344:SAXS
2255:DFXM
2223:XDCT
2208:STXM
2203:XPCI
2191:XACT
1913:ISBN
1890:PMID
1872:ISSN
1830:PMID
1822:ISSN
1775:PMID
1767:ISSN
1727:ISSN
1672:ISSN
1623:PMID
1615:ISSN
1563:PMID
1545:ISSN
1498:PMID
1490:ISSN
1420:PMID
1402:ISSN
1322:PMID
1314:ISSN
1267:PMID
1259:ISSN
1150:PMID
1142:ISSN
1102:PMID
1094:ISSN
1054:PMID
1046:ISSN
1007:PMID
999:ISSN
952:PMID
944:ISSN
897:ISSN
850:ISSN
803:PMID
795:ISSN
748:ISSN
662:PMID
611:ISSN
576:ISSN
541:ISSN
485:ISSN
446:PMID
428:ISSN
389:ISSN
342:ISBN
175:beam
144:flux
35:SAXS
18:SAXS
3266:DMG
3261:RAS
3157:PDB
3142:COD
3137:CIF
3089:DSR
2813:GND
2740:CSL
2369:XRS
2311:XFH
2306:EDS
2291:AES
2281:XPS
2276:XAS
2260:DXA
2228:DCT
2176:CDI
1880:PMC
1862:doi
1814:doi
1759:doi
1719:doi
1662:hdl
1654:doi
1650:295
1605:hdl
1595:doi
1553:PMC
1537:doi
1482:doi
1451:doi
1447:219
1410:PMC
1392:doi
1353:doi
1349:549
1306:doi
1302:118
1249:hdl
1239:doi
1197:hdl
1189:doi
1134:doi
1086:doi
1038:doi
991:doi
936:doi
889:doi
885:107
842:doi
787:doi
740:doi
701:doi
689:128
652:PMC
642:doi
603:doi
568:doi
533:doi
477:doi
436:PMC
420:doi
379:doi
87:kDa
3362::
3304:US
3297:UK
2374:XS
2181:CT
1888:.
1878:.
1870:.
1858:12
1856:.
1852:.
1828:.
1820:.
1808:.
1804:.
1781:.
1773:.
1765:.
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1753:.
1749:.
1725:.
1717:.
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1701:.
1678:.
1670:.
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1644:.
1621:.
1613:.
1603:.
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1523:.
1519:.
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416:51
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33:(
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