461:(formerly Joint Committee for Powder Diffraction Studies). This has been made searchable by computer through the work of global software developers and equipment manufacturers. There are now over 1,047,661 reference materials in the 2021 Powder Diffraction File Databases, and these databases are interfaced to a wide variety of diffraction analysis software and distributed globally. The Powder Diffraction File contains many subfiles, such as minerals, metals and alloys, pharmaceuticals, forensics, excipients, superconductors, semiconductors, etc., with large collections of organic, organometallic and inorganic reference materials.
441:, resulting in authoritative identification frequently used in patents, criminal cases and other areas of law enforcement. The ability to analyze multiphase materials also allows analysis of how materials interact in a particular matrix such as a pharmaceutical tablet, a circuit board, a mechanical weld, a geologic core sampling, cement and concrete, or a pigment found in an historic painting. The method has been historically used for the identification and classification of minerals, but it can be used for nearly any material, even amorphous ones, so long as a suitable reference pattern is known or can be constructed.
33:
2754:
547:. At this point new diffraction peaks will appear or old ones disappear according to the symmetry of the new phase. If the material melts to an isotropic liquid, all sharp lines will disappear and be replaced by a broad amorphous pattern. If the transition produces another crystalline phase, one set of lines will suddenly be replaced by another set. In some cases however lines will split or coalesce, e.g. if the material undergoes a continuous, second order phase transition. In such cases the symmetry may change because the existing structure is
1280:
1154:
846:). This leads to a very high background in neutron diffraction experiments, and may make structural investigations impossible. A common solution is deuteration, i.e., replacing the 1-H atoms in the sample with deuterium (2-H). The incoherent scattering length of deuterium is much smaller (2.05(3) barn) making structural investigations significantly easier. However, in some systems, replacing hydrogen with deuterium may alter the structural and dynamic properties of interest.
3147:
223:
508:
20:
839:
atoms are approximately equal in magnitude. Neutron diffraction techniques may therefore be used to detect light elements such as oxygen or hydrogen in combination with heavy atoms. The neutron diffraction technique therefore has obvious applications to problems such as determining oxygen displacements in materials like high temperature superconductors and ferroelectrics, or to hydrogen bonding in biological systems.
3159:
437:(CSD). Advances in hardware and software, particularly improved optics and fast detectors, have dramatically improved the analytical capability of the technique, especially relative to the speed of the analysis. The fundamental physics upon which the technique is based provides high precision and accuracy in the measurement of interplanar spacings, sometimes to fractions of an
1578:
time-resolved studies. For the latter it is desirable to have a strong radiation source. The advent of synchrotron radiation and modern neutron sources has therefore done much to revitalize the powder diffraction field because it is now possible to study temperature dependent changes, reaction kinetics and so forth by means of time-resolved powder diffraction.
113:, the focus of this article although some aspects of neutron powder diffraction are mentioned. (Powder electron diffraction is more complex due to dynamical diffraction and is not discussed further herein.) Typical diffractometers use electromagnetic radiation (waves) with known wavelength and frequency, which is determined by their source. The source is often
499:, where one is interested in finding and identifying new materials. Once a pattern has been indexed, this characterizes the reaction product and identifies it as a new solid phase. Indexing programs exist to deal with the harder cases, but if the unit cell is very large and the symmetry low (triclinic) success is not always guaranteed.
1264:
in the world. Angle dispersive (fixed wavelength) instruments typically have a battery of individual detectors arranged in a cylindrical fashion around the sample holder, and can therefore collect scattered intensity simultaneously on a large 2θ range. Time of flight instruments normally have a small
573:
procedure is then used to minimize the difference between the calculated pattern and each point of the observed pattern by adjusting model parameters. Techniques to determine unknown structures from powder data do exist, but are somewhat specialized. A number of programs that can be used in structure
477:
part of the material forms an ordered crystallite by folding of the molecule. A single polymer molecule may well be folded into two different, adjacent crystallites and thus form a tie between the two. The tie part is prevented from crystallizing. The result is that the crystallinity will never reach
1090:
Semi-quantitative analysis of polycrystalline mixtures can be performed by using traditional single-peaks methods such as the
Relative Intensity Ratio (RIR) or whole-pattern methods using Rietveld Refinement or PONCKS (Partial Or No Known Crystal Structures) method. The use of each method depends on
849:
As neutrons also have a magnetic moment, they are additionally scattered by any magnetic moments in a sample. In the case of long range magnetic order, this leads to the appearance of new Bragg reflections. In most simple cases, powder diffraction may be used to determine the size of the moments and
838:
X-ray photons scatter by interaction with the electron cloud of the material, neutrons are scattered by the nuclei. This means that, in the presence of heavy atoms with many electrons, it may be difficult to detect light atoms by X-ray diffraction. In contrast, the neutron scattering lengths of most
1550:
By contrast growth and mounting of large single crystals is notoriously difficult. In fact there are many materials for which, despite many attempts, it has not proven possible to obtain single crystals. Many materials are readily available with sufficient microcrystallinity for powder diffraction,
1501:
In-house applications of X-ray diffraction has always been limited to the relatively few wavelengths shown in the table above. The available choice was much needed because the combination of certain wavelengths and certain elements present in a sample can lead to strong fluorescence which increases
428:
Relative to other methods of analysis, powder diffraction allows for rapid, non-destructive analysis of multi-component mixtures without the need for extensive sample preparation. This gives laboratories the ability to quickly analyze unknown materials and perform materials characterization in such
1118:
cylinders are used as sample holders. Vanadium has a negligible absorption and coherent scattering cross section for neutrons and is hence nearly invisible in a powder diffraction experiment. Vanadium does however have a considerable incoherent scattering cross section which may cause problems for
599:
It is often possible to separate the effects of size and strain. When size broadening is independent of q (K = 1/d), strain broadening increases with increasing q-values. In most cases there will be both size and strain broadening. It is possible to separate these by combining the two equations in
1577:
Since all possible crystal orientations are measured simultaneously, collection times can be quite short even for small and weakly scattering samples. This is not merely convenient, but can be essential for samples which are unstable either inherently or under X-ray or neutron bombardment, or for
1509:
sources has drastically changed this picture and caused powder diffraction methods to enter a whole new phase of development. Not only is there a much wider choice of wavelengths available, the high brilliance of the synchrotron radiation makes it possible to observe changes in the pattern during
156:
case. Powder X-ray diffraction (PXRD) operates under the assumption that the sample is randomly arranged. Therefore, a statistically significant number of each plane of the crystal structure will be in the proper orientation to diffract the X-rays. Therefore, each plane will be represented in the
1134:. The sample is usually placed in the focusing beam, e.g. as a dusting on a piece of sticky tape. A cylindrical piece of film (or electronic multichannel detector) is put on the focusing circle, but the incident beam prevented from reaching the detector to prevent damage from its high intensity.
449:
The most widespread use of powder diffraction is in the identification and characterization of crystalline solids, each of which produces a distinctive diffraction pattern. Both the positions (corresponding to lattice spacings) and the relative intensity of the lines in a diffraction pattern are
1525:
Although it is possible to solve crystal structures from powder X-ray data alone, its single crystal analogue is a far more powerful technique for structure determination. This is directly related to the fact that information is lost by the collapse of the 3D space onto a 1D axis. Nevertheless,
1516:
Neutron diffraction has never been an in house technique because it requires the availability of an intense neutron beam only available at a nuclear reactor or spallation source. Typically the available neutron flux, and the weak interaction between neutrons and matter, require relative large
1091:
the knowledge on the analyzed system, given that, for instance, Rietveld refinement needs the solved crystal structure of each component of the mixture to be performed. In the last decades, multivariate analysis begun spreading as an alternative method for phase quantification.
478:
100%. Powder XRD can be used to determine the crystallinity by comparing the integrated intensity of the background pattern to that of the sharp peaks. Values obtained from powder XRD are typically comparable but not quite identical to those obtained from other methods such as
1176:
Diffractometers can be operated both in transmission and reflection, but reflection is more common. The powder sample is loaded in a small disc-like container and its surface carefully flattened. The disc is put on one axis of the diffractometer and tilted by an angle
137:. These waves interfere destructively at points between the intersections where the waves are out of phase, and do not lead to bright spots in the diffraction pattern. Because the sample itself is acting as the diffraction grating, this spacing is the atomic spacing.
429:
fields as metallurgy, mineralogy, chemistry, forensic science, archeology, condensed matter physics, and the biological and pharmaceutical sciences. Identification is performed by comparison of the diffraction pattern to a known standard or to a database such as the
490:
The position of a diffraction peak is independent of the atomic positions within the cell and entirely determined by the size and shape of the unit cell of the crystalline phase. Each peak represents a certain lattice plane and can therefore be characterized by a
450:
indicative of a particular phase and material, providing a "fingerprint" for comparison. A multi-phase mixture, e.g. a soil sample, will show more than one pattern superposed, allowing for the determination of the relative concentrations of phases in the mixture.
551:
rather than replaced by a completely different one. For example, the diffraction peaks for the lattice planes (100) and (001) can be found at two different values of q for a tetragonal phase, but if the symmetry becomes cubic the two peaks will come to coincide.
569:. The Rietveld method is a so-called full pattern analysis technique. A crystal structure, together with instrumental and microstructural information, is used to generate a theoretical diffraction pattern that can be compared to the observed data. A
1027:
1302:. The most commonly used laboratory X-ray tube uses a copper anode, but cobalt and molybdenum are also popular. The wavelength in nm varies for each source. The table below shows these wavelengths, determined by Bearden (all values in nm):
121:. When these waves reach the sample, the incoming beam is either reflected off the surface, or can enter the lattice and be diffracted by the atoms present in the sample. If the atoms are arranged symmetrically with a separation distance
684:
858:
Predicting the scattered intensity in powder diffraction patterns from gases, liquids, and randomly distributed nano-clusters in the solid state is (to first order) done rather elegantly with the Debye scattering equation:
363:
560:
Crystal structure determination from powder diffraction data is extremely challenging due to the overlap of reflections in a powder experiment. A number of different methods exist for structural determination, such as
1502:
the background in the diffraction pattern. A notorious example is the presence of iron in a sample when using copper radiation. In general elements just below the anode element in the period system need to be avoided.
1108:) or a cylindrical one (originally a piece of film in a cookie-jar, but increasingly bent position sensitive detectors are used). The two types of cameras are known as the Laue and the Debye–Scherrer camera.
1211:
Diffractometer settings for different experiments can schematically be illustrated by a hemisphere, in which the powder sample resides in the origin. The case of recording a pattern in the Bragg-Brentano
1559:
materials, single crystals thereof are typically not immediately available. Powder diffraction is therefore one of the most powerful methods to identify and characterize new materials in this field.
826:
for size broadening and the Stokes and Wilson expression for strain broadening. The value of η is the strain in the crystallites, the value of D represents the size of the crystallites. The constant
817:
1513:
The tunability of the wavelength also makes it possible to observe anomalous scattering effects when the wavelength is chosen close to the absorption edge of one of the elements of the sample.
727:
1104:
The simplest cameras for X-ray powder diffraction consist of a small capillary and either a flat plate detector (originally a piece of X-ray film, now more and more a flat-plate detector or a
1867:
Structure determination form powder diffraction data IUCr
Monographs on crystallography, Edt. W.I.F. David, K. Shankland, L.B. McCusker and Ch. Baerlocher. 2002. Oxford Science publications
519:
temperature and pressure control. As these thermodynamic variables are changed, the observed diffraction peaks will migrate continuously to indicate higher or lower lattice spacings as the
761:
2763:
1505:
Another limitation is that the intensity of traditional generators is relatively low, requiring lengthy exposure times and precluding any time dependent measurement. The advent of
3024:
783:
3019:
495:. If the symmetry is high, e.g.: cubic or hexagonal it is usually not too hard to identify the index of each peak, even for an unknown phase. This is particularly important in
469:
In contrast to a crystalline pattern consisting of a series of sharp peaks, amorphous materials (liquids, glasses etc.) produce a broad background signal. Many polymers show
230:
When the scattered radiation is collected on a flat plate detector, the rotational averaging leads to smooth diffraction rings around the beam axis, rather than the discrete
1981:"Multivariate versus traditional quantitative phase analysis of X-ray powder diffraction and fluorescence data of mixtures showing preferred orientation and microabsorption"
1238:
Position-sensitive detectors (PSD) and area detectors, which allow collection from multiple angles at once, are becoming more popular on currently supplied instrumentation.
1204:
configuration in which the sample is stationary while the X-ray tube and the detector are rotated around it. The angle formed between the X-ray source and the detector is 2
865:
2559:
1082:. One can also use this to predict the effect of nano-crystallite shape on detected diffraction peaks, even if in some directions the cluster is only one atom thick.
3075:
1288:
457:
in the 1930s, was the first to realize the analytical potential of creating a database. Today it is represented by the Powder
Diffraction File (PDF) of the
2303:
606:
1419:
According to the last re-examination of Hölzer et al. (1997), and quoted in the
International Tables for Crystallography these values are respectively:
543:
At some critical set of conditions, for example 0 °C for water at 1 atm, a new arrangement of atoms or molecules may become stable, leading to a
1574:, the ability to use large samples can be critical, although newer and more brilliant neutron sources are being built that may change this picture.
23:
Electron powder pattern (red) of an Al film with an fcc spiral overlay (green) and a line of intersections (blue) that determines lattice parameter.
272:
842:
A further complication in the case of neutron scattering from hydrogenous materials is the strong incoherent scattering of hydrogen (80.27(6)
416:
sources has widened the choice of wavelength considerably. To facilitate comparability of data obtained with different wavelengths the use of
2893:
168:
with some regularity in the spacing between atoms. Because of this regularity, we can describe this structure in a different way using the
565:
and charge flipping. The crystal structures of known materials can be refined, i.e. as a function of temperature or pressure, using the
3080:
2805:
2971:
2263:
2028:Šišak Jung, D; Donath, T; Magdysyuk, O; Bednarcik, J (2017). "High-energy X-ray applications: Current status and new opportunities".
458:
430:
95:
Powder diffraction stands in contrast to single crystal diffraction techniques, which work best with a single, well-ordered crystal.
1231:
stand for the wave vectors of the incoming and diffracted beam that both make up the scattering plane. Various other settings for
3195:
88:
samples for structural characterization of materials. An instrument dedicated to performing such powder measurements is called a
3070:
3062:
3123:
3101:
2214:
2085:
1795:
1754:
1526:
powder X-ray diffraction is a powerful and useful technique in its own right. It is mostly used to characterize and identify
3116:
2966:
2632:
2497:
2346:
788:
3190:
3106:
3004:
2700:
692:
2353:
41:
3128:
2986:
2956:
2885:
2075:
1894:
1872:
1855:
1731:
479:
3163:
2838:
215:
remains as an important measurable quantity. This is because orientational averaging causes the three-dimensional
3111:
3034:
2908:
2507:
732:
408:. The latter variable has the advantage that the diffractogram no longer depends on the value of the wavelength
2946:
2868:
1145:, are widely used in applications where high data acquisition speeds and increased data quality are required.
2961:
2951:
2256:
1185:) rotates around it on an arm at twice this angle. This configuration is known under the name Bragg–Brentano
434:
157:
signal. In practice, it is sometimes necessary to rotate the sample orientation to eliminate the effects of
3085:
2733:
2358:
2336:
2637:
2391:
2286:
1663:
766:
515:
Cell parameters are somewhat temperature and pressure dependent. Powder diffraction can be combined with
2994:
2291:
2180:
1638:
133:
is equal to an integer multiple of the wavelength, producing a diffraction maximum in accordance with
3009:
2938:
2396:
2386:
1598:
1022:{\displaystyle I(q)=\sum _{i=1}^{N}\sum _{j=1}^{N}f_{i}(q)f_{j}(q){\frac {\sin(qr_{ij})}{qr_{ij}}},}
3151:
2875:
2771:
2644:
2607:
2522:
2401:
2381:
2249:
1613:
1593:
1056:
234:
observed in single crystal diffraction. The angle between the beam axis and the ring is called the
2999:
2843:
2788:
2537:
2502:
1571:
470:
2753:
2695:
2512:
1530:, and to refine details of an already known structure, rather than solving unknown structures.
1816:"High-Energy X-Rays: A tool for Advanced Bulk Investigations in Materials Science and Physics"
1787:
3052:
2848:
2810:
2617:
2569:
1658:
1648:
1643:
1567:
1552:
1274:
1256:
beam of suitable intensity and speed for diffraction are only available at a small number of
1232:
1182:
1138:
1111:
In order to ensure complete powder averaging, the capillary is usually spun around its axis.
496:
231:
158:
141:
118:
3185:
2776:
2649:
2485:
2376:
2153:
2110:
2037:
1920:
1693:
1618:
81:
8:
2793:
2781:
2656:
2622:
2602:
1633:
1563:
1265:
range of banks at different scattering angles which collect data at varying resolutions.
1247:
566:
562:
104:
77:
57:
2157:
2114:
2041:
1946:
Guccione, Pietro; Lopresti, Mattia; Milanesio, Marco; Caliandro, Rocco (December 2020).
1924:
1697:
582:
There are many factors that determine the width B of a diffraction peak. These include:
3042:
2853:
2798:
2341:
2053:
2005:
1980:
1709:
1142:
1037:
255:
219:
that is studied in single crystal diffraction to be projected onto a single dimension.
177:
169:
1979:
Lopresti, M.; Mangolini, B.; Milanesio, M.; Caliandro, R.; Palin, L. (1 August 2022).
2976:
2815:
2743:
2723:
2443:
2313:
2210:
2081:
2057:
2010:
1890:
1868:
1851:
1811:
1791:
1780:
1760:
1750:
1727:
1623:
1588:
1261:
823:
679:{\displaystyle B\cdot \cos(\theta )={\frac {k\lambda }{D}}+\eta \cdot \sin(\theta ),}
532:
524:
520:
173:
73:
1713:
1235:
or stress/strain measurements can also be visualized with this graphical approach.
392:
is the wavelength of the source. Powder diffraction data are usually presented as a
3200:
3014:
2820:
2738:
2728:
2527:
2460:
2431:
2424:
2161:
2118:
2045:
2000:
1992:
1959:
1928:
1827:
1701:
1257:
544:
216:
125:, these waves will interfere constructively only where the path-length difference 2
85:
1123:
2903:
2898:
2863:
2683:
2582:
2517:
2480:
2475:
2326:
2272:
1884:
1832:
1815:
1653:
1603:
1279:
262:
in the sample crystal. This leads to the definition of the scattering vector as:
165:
117:, and neutrons are also common sources, with their frequency determined by their
2136:
Hölzer, G.; Fritsch, M.; Deutsch, M.; Härtwig, J.; Förster, E. (1997-12-01). "Kα
2713:
2678:
2666:
2661:
2627:
2597:
2587:
2546:
2490:
2414:
2368:
1608:
251:
140:
The distinction between powder and single crystal diffraction is the degree of
134:
2049:
1996:
1705:
3179:
2858:
2671:
2470:
2165:
2122:
1932:
1764:
1131:
570:
438:
393:
358:{\displaystyle |G|=q=2k\sin(\theta )={\frac {4\pi }{\lambda }}\sin(\theta ).}
61:
32:
1153:
2564:
2554:
2448:
2331:
2014:
528:
492:
454:
2236:
1964:
1947:
1744:
144:
in the sample. Single crystals have maximal texturing, and are said to be
3047:
2718:
2592:
2419:
1510:
chemical reactions, temperature ramps, changes in pressure and the like.
1506:
843:
574:
determination are TOPAS, Fox, DASH, GSAS-II, EXPO2004, and a few others.
413:
149:
145:
2179:
Deslattes, R.D.; Kessler Jr, E.G.; Indelicato, P.; Lindroth, E. (2006),
19:
2612:
2298:
2206:
1628:
1295:
1105:
1551:
or samples may be easily ground from larger crystals. In the field of
2321:
2178:
1726:
B.D. Cullity
Elements of X-ray Diffraction Addison Wesley Mass. 1978
222:
153:
1908:
1157:
Hemisphere of diffraction showing the incoming and diffracted beams
507:
2918:
2688:
2436:
1978:
1115:
2241:
2187:, vol. C, International Union of Crystallography, p. 203
2027:
1945:
226:
Two-dimensional powder diffraction setup with flat plate detector.
2928:
1253:
555:
1684:
P. Fraundorf & Shuhan Lin (2004). "Spiral powder overlays".
1119:
more sensitive techniques such as neutron inelastic scattering.
523:
distorts. This allows for measurement of such quantities as the
1294:
Laboratory X-ray diffraction equipment relies on the use of an
1284:
114:
110:
830:
is typically close to unity and ranges from 0.8 to 1.39.
2923:
1299:
833:
152:
orientation is represented equally in a powdered sample, the
1814:; Bartels, Arno; Schreyer, Andreas; Clemens, Helmut (2003).
1786:(2nd ed.). Canada: John Wiley & Sons, Inc. p.
2135:
1289:
FZU – Institute of
Physics of the Czech Academy of Sciences
1208:. This configuration is most convenient for loose powders.
1810:
3025:
2204:
1948:"Multivariate Analysis Applications in X-ray Diffraction"
400:, is shown as a function either of the scattering angle 2
3020:
203:*. In powder diffraction, intensity is homogeneous over
2913:
2231:
1683:
1543:
the ability to analyze mixed phases, e.g. soil samples
2203:
Gilmore, C.J.; Kaduk, J.A.; Schenk, H., eds. (2019).
868:
792:
791:
770:
769:
736:
735:
696:
695:
609:
275:
176:. This three-dimensional space can be described with
148:. In contrast, in powder diffraction, every possible
2181:"Table 4.2.2.1. K-series reference wavelengths in Ă…"
812:{\displaystyle \displaystyle {\frac {k\lambda }{D}}}
453:
J.D. Hanawalt, an analytical chemist who worked for
420:
is therefore recommended and gaining acceptability.
2144:x-ray emission lines of the 3d transition metals".
109:The most common type of powder diffraction is with
2202:
1779:
1021:
853:
811:
777:
755:
722:{\displaystyle \displaystyle B\cdot \cos(\theta )}
721:
678:
502:
357:
172:, which is related to the original structure by a
1749:(3rd ed.). Amsterdam: Elsevier Science B.V.
404:or as a function of the scattering vector length
3177:
380:is the length of the reciprocal lattice vector,
238:and in X-ray crystallography always denoted as 2
1889:(Addison–Wesley, Reading MA/Dover, Mineola NY)
1520:
164:Mathematically, crystals can be described by a
589:the presence of defects to the perfect lattice
556:Crystal structure refinement and determination
2257:
1777:
1085:
1032:where the magnitude of the scattering vector
600:what is known as the Hall–Williamson method:
577:
2101:Bearden, J. A. (1967). "X-Ray Wavelengths".
2069:
2067:
1196:Another configuration is the Bragg–Brentano
1122:A later development in X-ray cameras is the
191:* or alternatively in spherical coordinates
3094:
2129:
2073:
756:{\displaystyle \displaystyle \sin(\theta )}
246:light the convention is usually to call it
2264:
2250:
834:Comparison of X-ray and neutron scattering
2232:International Centre for Diffraction Data
2064:
2004:
1963:
1831:
592:differences in strain in different grains
459:International Centre for Diffraction Data
431:International Centre for Diffraction Data
2185:International Tables for Crystallography
1278:
1152:
506:
433:'s Powder Diffraction File (PDF) or the
254:, each ring corresponds to a particular
221:
18:
16:Experimental method in X-ray diffraction
2172:
2100:
1778:Klug, Harold; Alexander, Leroy (1954).
822:The expression is a combination of the
444:
3178:
2367:
2077:Thin Film Analysis by X-Ray Scattering
1742:
1241:
2245:
1906:
1566:, which requires larger samples than
485:
388:is half of the scattering angle, and
3158:
2498:Phase transformation crystallography
1570:due to a relatively weak scattering
538:
531:, as well determination of the full
511:Thermal expansion of a sulfur powder
3005:Journal of Chemical Crystallography
2271:
1220:mode is shown in the figure, where
1172:with respect to the sample surface.
778:{\displaystyle \displaystyle \eta }
396:in which the diffracted intensity,
13:
2195:
1985:Journal of Applied Crystallography
1148:
763:we get a straight line with slope
376:is the reciprocal lattice vector,
14:
3212:
2225:
1909:"Zerstreuung von Röntgenstrahlen"
1546:"in situ" structure determination
1533:Advantages of the technique are:
1139:hybrid photon counting technology
384:is the momentum transfer vector,
3157:
3146:
3145:
2752:
1555:that often aims at synthesizing
1537:simplicity of sample preparation
1496:
464:
72:is a scientific technique using
31:
2094:
2021:
1972:
1939:
1298:, which is used to produce the
854:Aperiodically arranged clusters
503:Expansion tensors, bulk modulus
60:with two phases, showing 1% of
3196:Synchrotron-related techniques
2947:Bilbao Crystallographic Server
1900:
1877:
1861:
1840:
1804:
1771:
1736:
1720:
1677:
1268:
1168:that are inclined by an angle
992:
973:
961:
955:
942:
936:
878:
872:
749:
743:
715:
709:
670:
664:
628:
622:
349:
343:
316:
310:
285:
277:
98:
1:
2237:Powder Diffraction on the Web
1848:Elements of X-ray diffraction
1670:
1126:camera. It is built around a
1074:is the distance between atom
435:Cambridge Structural Database
161:and achieve true randomness.
44:X-ray powder diffraction of Y
1833:10.1080/07303300310001634952
1820:Textures and Microstructures
1782:X-ray diffraction Procedures
1686:Microscopy and Microanalysis
1521:Advantages and disadvantages
1283:X-ray powder diffractometer
595:the size of the crystallites
7:
2995:Crystal Growth & Design
2287:Timeline of crystallography
1664:X-ray scattering techniques
1581:
850:their spatial orientation.
10:
3217:
3191:Neutron-related techniques
2806:Nuclear magnetic resonance
2030:Powder Diffraction, 32(S2)
1639:Pair distribution function
1272:
1245:
1099:
1094:
1086:Semi-quantitative analysis
578:Size and strain broadening
527:tensor and the isothermal
102:
3141:
3061:
3033:
3010:Journal of Crystal Growth
2985:
2937:
2884:
2831:
2762:
2750:
2545:
2536:
2459:
2312:
2279:
2103:Reviews of Modern Physics
2050:10.1017/S0885715617001191
1997:10.1107/S1600576722004708
1883:B. E. Warren (1969/1990)
1706:10.1017/S1431927604884034
1599:Crystallographic database
2876:Single particle analysis
2734:Hermann–Mauguin notation
2166:10.1103/PhysRevA.56.4554
2123:10.1103/RevModPhys.39.78
1933:10.1002/andp.19153510606
1614:Electron crystallography
1594:Condensed matter physics
1114:For neutron diffraction
1057:atomic scattering factor
1044:is the number of atoms,
64:impurity (red tickers).
3000:Crystallography Reviews
2844:Isomorphous replacement
2638:Lomer–Cottrell junction
2183:, in Prince, E. (ed.),
1540:rapidity of measurement
1252:Sources that produce a
423:
2513:Spinodal decomposition
1743:Cowley, J. M. (1995).
1291:
1173:
1063:and scattering vector
1023:
925:
904:
813:
779:
757:
723:
680:
512:
359:
250:). In accordance with
227:
24:
3053:Gregori Aminoff Prize
2849:Molecular replacement
1965:10.3390/cryst11010012
1850:Addison–Wesley, 1978
1659:X-ray crystallography
1649:Texture (crystalline)
1644:Solid state chemistry
1553:solid-state chemistry
1282:
1275:X-ray crystallography
1183:scintillation counter
1156:
1024:
905:
884:
814:
780:
758:
724:
681:
510:
497:solid-state chemistry
360:
225:
119:de Broglie wavelength
90:powder diffractometer
22:
2359:Structure prediction
2074:M. Birkholz (2005).
1619:Electron diffraction
866:
789:
767:
733:
693:
607:
586:instrumental factors
445:Phase identification
273:
82:electron diffraction
2623:Cottrell atmosphere
2603:Partial dislocation
2347:Restriction theorem
2158:1997PhRvA..56.4554H
2115:1967RvMP...39...78B
2042:2017PDiff..32S..22S
1925:1915AnP...351..809D
1746:Diffraction physics
1698:2004MiMic..10S1356F
1634:Neutron diffraction
1564:neutron diffraction
1248:Neutron diffraction
1242:Neutron diffraction
689:Thus, when we plot
563:simulated annealing
105:Diffraction grating
58:Rietveld refinement
3043:Carl Hermann Medal
2854:Molecular dynamics
2701:Defects in diamond
2696:Stone–Wales defect
2342:Reciprocal lattice
2304:Biocrystallography
1913:Annalen der Physik
1907:Debye, P. (1915).
1812:Liss, Klaus-Dieter
1692:(S02): 1356–1357.
1292:
1262:spallation sources
1181:while a detector (
1174:
1038:reciprocal lattice
1019:
809:
808:
775:
774:
753:
752:
719:
718:
676:
513:
486:Lattice parameters
372:In this equation,
355:
256:reciprocal lattice
242:(in scattering of
228:
170:reciprocal lattice
70:Powder diffraction
25:
3173:
3172:
3137:
3136:
2744:Thermal ellipsoid
2709:
2708:
2618:Frank–Read source
2578:
2577:
2444:Aperiodic crystal
2410:
2409:
2292:Crystallographers
2216:978-1-118-41628-0
2146:Physical Review A
2087:978-3-527-31052-4
1886:X-ray diffraction
1797:978-0-471-49369-3
1756:978-0-444-82218-5
1624:Materials science
1589:Bragg diffraction
1568:X-ray diffraction
1562:Particularly for
1494:
1493:
1417:
1416:
1258:research reactors
1137:Cameras based on
1014:
824:Scherrer equation
806:
647:
539:Phase transitions
535:of the material.
533:equation of state
525:thermal expansion
335:
174:Fourier transform
3208:
3161:
3160:
3149:
3148:
3092:
3091:
3015:Kristallografija
2869:Gerchberg–Saxton
2764:Characterisation
2756:
2739:Structure factor
2543:
2542:
2528:Ostwald ripening
2365:
2364:
2310:
2309:
2266:
2259:
2252:
2243:
2242:
2220:
2189:
2188:
2176:
2170:
2169:
2152:(6): 4554–4568.
2133:
2127:
2126:
2098:
2092:
2091:
2071:
2062:
2061:
2025:
2019:
2018:
2008:
1976:
1970:
1969:
1967:
1943:
1937:
1936:
1904:
1898:
1881:
1875:
1865:
1859:
1844:
1838:
1837:
1835:
1808:
1802:
1801:
1785:
1775:
1769:
1768:
1740:
1734:
1724:
1718:
1717:
1681:
1422:
1421:
1313:(weight average)
1305:
1304:
1143:PILATUS detector
1040:distance units,
1028:
1026:
1025:
1020:
1015:
1013:
1012:
1011:
995:
991:
990:
965:
954:
953:
935:
934:
924:
919:
903:
898:
818:
816:
815:
810:
807:
802:
794:
784:
782:
781:
776:
762:
760:
759:
754:
728:
726:
725:
720:
685:
683:
682:
677:
648:
643:
635:
545:phase transition
412:. The advent of
364:
362:
361:
356:
336:
331:
323:
288:
280:
236:scattering angle
217:reciprocal space
86:microcrystalline
35:
3216:
3215:
3211:
3210:
3209:
3207:
3206:
3205:
3176:
3175:
3174:
3169:
3133:
3090:
3057:
3029:
2981:
2933:
2904:CrystalExplorer
2880:
2864:Phase retrieval
2827:
2758:
2757:
2748:
2705:
2684:Schottky defect
2583:Perfect crystal
2574:
2570:Abnormal growth
2532:
2518:Supersaturation
2481:Miscibility gap
2462:
2455:
2406:
2363:
2327:Bravais lattice
2308:
2275:
2273:Crystallography
2270:
2228:
2223:
2217:
2198:
2196:Further reading
2193:
2192:
2177:
2173:
2143:
2139:
2134:
2130:
2099:
2095:
2088:
2072:
2065:
2026:
2022:
1977:
1973:
1944:
1940:
1905:
1901:
1882:
1878:
1866:
1862:
1845:
1841:
1809:
1805:
1798:
1776:
1772:
1757:
1741:
1737:
1725:
1721:
1682:
1678:
1673:
1668:
1654:Ultrafast x-ray
1604:Crystallography
1584:
1523:
1499:
1327:
1322:
1317:
1312:
1277:
1271:
1250:
1244:
1226:
1163:
1151:
1149:Diffractometers
1102:
1097:
1088:
1072:
1049:
1004:
1000:
996:
983:
979:
966:
964:
949:
945:
930:
926:
920:
909:
899:
888:
867:
864:
863:
856:
836:
795:
793:
790:
787:
786:
768:
765:
764:
734:
731:
730:
694:
691:
690:
636:
634:
608:
605:
604:
580:
567:Rietveld method
558:
541:
505:
488:
471:semicrystalline
467:
447:
426:
324:
322:
284:
276:
274:
271:
270:
178:reciprocal axes
166:Bravais lattice
129: sin
107:
101:
67:
66:
65:
55:
51:
47:
43:
38:
37:
36:
17:
12:
11:
5:
3214:
3204:
3203:
3198:
3193:
3188:
3171:
3170:
3168:
3167:
3155:
3142:
3139:
3138:
3135:
3134:
3132:
3131:
3126:
3121:
3120:
3119:
3114:
3109:
3098:
3096:
3089:
3088:
3083:
3078:
3073:
3067:
3065:
3059:
3058:
3056:
3055:
3050:
3045:
3039:
3037:
3031:
3030:
3028:
3027:
3022:
3017:
3012:
3007:
3002:
2997:
2991:
2989:
2983:
2982:
2980:
2979:
2974:
2969:
2964:
2959:
2954:
2949:
2943:
2941:
2935:
2934:
2932:
2931:
2926:
2921:
2916:
2911:
2906:
2901:
2896:
2890:
2888:
2882:
2881:
2879:
2878:
2873:
2872:
2871:
2861:
2856:
2851:
2846:
2841:
2839:Direct methods
2835:
2833:
2829:
2828:
2826:
2825:
2824:
2823:
2818:
2808:
2803:
2802:
2801:
2796:
2786:
2785:
2784:
2779:
2768:
2766:
2760:
2759:
2751:
2749:
2747:
2746:
2741:
2736:
2731:
2726:
2724:Ewald's sphere
2721:
2716:
2710:
2707:
2706:
2704:
2703:
2698:
2693:
2692:
2691:
2686:
2676:
2675:
2674:
2669:
2667:Frenkel defect
2664:
2662:Bjerrum defect
2654:
2653:
2652:
2642:
2641:
2640:
2635:
2630:
2628:Peierls stress
2625:
2620:
2615:
2610:
2605:
2600:
2598:Burgers vector
2590:
2588:Stacking fault
2585:
2579:
2576:
2575:
2573:
2572:
2567:
2562:
2557:
2551:
2549:
2547:Grain boundary
2540:
2534:
2533:
2531:
2530:
2525:
2520:
2515:
2510:
2505:
2500:
2495:
2494:
2493:
2491:Liquid crystal
2488:
2483:
2478:
2467:
2465:
2457:
2456:
2454:
2453:
2452:
2451:
2441:
2440:
2439:
2429:
2428:
2427:
2422:
2411:
2408:
2407:
2405:
2404:
2399:
2394:
2389:
2384:
2379:
2373:
2371:
2362:
2361:
2356:
2354:Periodic table
2351:
2350:
2349:
2344:
2339:
2334:
2329:
2318:
2316:
2307:
2306:
2301:
2296:
2295:
2294:
2283:
2281:
2277:
2276:
2269:
2268:
2261:
2254:
2246:
2240:
2239:
2234:
2227:
2226:External links
2224:
2222:
2221:
2215:
2199:
2197:
2194:
2191:
2190:
2171:
2141:
2137:
2128:
2093:
2086:
2063:
2020:
1991:(4): 837–850.
1971:
1938:
1899:
1876:
1860:
1839:
1803:
1796:
1770:
1755:
1735:
1719:
1675:
1674:
1672:
1669:
1667:
1666:
1661:
1656:
1651:
1646:
1641:
1636:
1631:
1626:
1621:
1616:
1611:
1609:Diffractometer
1606:
1601:
1596:
1591:
1585:
1583:
1580:
1548:
1547:
1544:
1541:
1538:
1522:
1519:
1498:
1495:
1492:
1491:
1488:
1485:
1482:
1478:
1477:
1474:
1471:
1468:
1464:
1463:
1460:
1457:
1454:
1450:
1449:
1446:
1443:
1440:
1436:
1435:
1432:
1429:
1426:
1415:
1414:
1411:
1408:
1405:
1402:
1398:
1397:
1394:
1391:
1388:
1385:
1381:
1380:
1377:
1374:
1371:
1368:
1364:
1363:
1360:
1357:
1354:
1351:
1347:
1346:
1343:
1340:
1337:
1334:
1330:
1329:
1324:
1319:
1314:
1309:
1287:D8 Advance at
1273:Main article:
1270:
1267:
1246:Main article:
1243:
1240:
1224:
1161:
1150:
1147:
1141:, such as the
1101:
1098:
1096:
1093:
1087:
1084:
1070:
1047:
1030:
1029:
1018:
1010:
1007:
1003:
999:
994:
989:
986:
982:
978:
975:
972:
969:
963:
960:
957:
952:
948:
944:
941:
938:
933:
929:
923:
918:
915:
912:
908:
902:
897:
894:
891:
887:
883:
880:
877:
874:
871:
855:
852:
835:
832:
805:
801:
798:
785:and intercept
773:
751:
748:
745:
742:
739:
717:
714:
711:
708:
705:
702:
699:
687:
686:
675:
672:
669:
666:
663:
660:
657:
654:
651:
646:
642:
639:
633:
630:
627:
624:
621:
618:
615:
612:
597:
596:
593:
590:
587:
579:
576:
557:
554:
540:
537:
504:
501:
487:
484:
466:
463:
446:
443:
425:
422:
370:
369:
368:
367:
366:
365:
354:
351:
348:
345:
342:
339:
334:
330:
327:
321:
318:
315:
312:
309:
306:
303:
300:
297:
294:
291:
287:
283:
279:
100:
97:
53:
49:
45:
40:
39:
30:
29:
28:
27:
26:
15:
9:
6:
4:
3:
2:
3213:
3202:
3199:
3197:
3194:
3192:
3189:
3187:
3184:
3183:
3181:
3166:
3165:
3156:
3154:
3153:
3144:
3143:
3140:
3130:
3127:
3125:
3122:
3118:
3115:
3113:
3110:
3108:
3105:
3104:
3103:
3100:
3099:
3097:
3093:
3087:
3084:
3082:
3079:
3077:
3074:
3072:
3069:
3068:
3066:
3064:
3060:
3054:
3051:
3049:
3046:
3044:
3041:
3040:
3038:
3036:
3032:
3026:
3023:
3021:
3018:
3016:
3013:
3011:
3008:
3006:
3003:
3001:
2998:
2996:
2993:
2992:
2990:
2988:
2984:
2978:
2975:
2973:
2970:
2968:
2965:
2963:
2960:
2958:
2955:
2953:
2950:
2948:
2945:
2944:
2942:
2940:
2936:
2930:
2927:
2925:
2922:
2920:
2917:
2915:
2912:
2910:
2907:
2905:
2902:
2900:
2897:
2895:
2892:
2891:
2889:
2887:
2883:
2877:
2874:
2870:
2867:
2866:
2865:
2862:
2860:
2859:Patterson map
2857:
2855:
2852:
2850:
2847:
2845:
2842:
2840:
2837:
2836:
2834:
2830:
2822:
2819:
2817:
2814:
2813:
2812:
2809:
2807:
2804:
2800:
2797:
2795:
2792:
2791:
2790:
2787:
2783:
2780:
2778:
2775:
2774:
2773:
2770:
2769:
2767:
2765:
2761:
2755:
2745:
2742:
2740:
2737:
2735:
2732:
2730:
2729:Friedel's law
2727:
2725:
2722:
2720:
2717:
2715:
2712:
2711:
2702:
2699:
2697:
2694:
2690:
2687:
2685:
2682:
2681:
2680:
2677:
2673:
2672:Wigner effect
2670:
2668:
2665:
2663:
2660:
2659:
2658:
2657:Interstitials
2655:
2651:
2648:
2647:
2646:
2643:
2639:
2636:
2634:
2631:
2629:
2626:
2624:
2621:
2619:
2616:
2614:
2611:
2609:
2606:
2604:
2601:
2599:
2596:
2595:
2594:
2591:
2589:
2586:
2584:
2581:
2580:
2571:
2568:
2566:
2563:
2561:
2558:
2556:
2553:
2552:
2550:
2548:
2544:
2541:
2539:
2535:
2529:
2526:
2524:
2521:
2519:
2516:
2514:
2511:
2509:
2506:
2504:
2503:Precipitation
2501:
2499:
2496:
2492:
2489:
2487:
2484:
2482:
2479:
2477:
2474:
2473:
2472:
2471:Phase diagram
2469:
2468:
2466:
2464:
2458:
2450:
2447:
2446:
2445:
2442:
2438:
2435:
2434:
2433:
2430:
2426:
2423:
2421:
2418:
2417:
2416:
2413:
2412:
2403:
2400:
2398:
2395:
2393:
2390:
2388:
2385:
2383:
2380:
2378:
2375:
2374:
2372:
2370:
2366:
2360:
2357:
2355:
2352:
2348:
2345:
2343:
2340:
2338:
2335:
2333:
2330:
2328:
2325:
2324:
2323:
2320:
2319:
2317:
2315:
2311:
2305:
2302:
2300:
2297:
2293:
2290:
2289:
2288:
2285:
2284:
2282:
2278:
2274:
2267:
2262:
2260:
2255:
2253:
2248:
2247:
2244:
2238:
2235:
2233:
2230:
2229:
2218:
2212:
2208:
2207:
2201:
2200:
2186:
2182:
2175:
2167:
2163:
2159:
2155:
2151:
2147:
2132:
2124:
2120:
2116:
2112:
2109:(1): 78–124.
2108:
2104:
2097:
2089:
2083:
2080:. Wiley-VCH.
2079:
2078:
2070:
2068:
2059:
2055:
2051:
2047:
2043:
2039:
2036:(S2): 22–27.
2035:
2031:
2024:
2016:
2012:
2007:
2002:
1998:
1994:
1990:
1986:
1982:
1975:
1966:
1961:
1957:
1953:
1949:
1942:
1934:
1930:
1926:
1922:
1918:
1914:
1910:
1903:
1896:
1895:0-486-66317-5
1892:
1888:
1887:
1880:
1874:
1873:0-19-850091-2
1870:
1864:
1857:
1856:0-201-01174-3
1853:
1849:
1846:B.D. Cullity
1843:
1834:
1829:
1825:
1821:
1817:
1813:
1807:
1799:
1793:
1789:
1784:
1783:
1774:
1766:
1762:
1758:
1752:
1748:
1747:
1739:
1733:
1732:0-201-01174-3
1729:
1723:
1715:
1711:
1707:
1703:
1699:
1695:
1691:
1687:
1680:
1676:
1665:
1662:
1660:
1657:
1655:
1652:
1650:
1647:
1645:
1642:
1640:
1637:
1635:
1632:
1630:
1627:
1625:
1622:
1620:
1617:
1615:
1612:
1610:
1607:
1605:
1602:
1600:
1597:
1595:
1592:
1590:
1587:
1586:
1579:
1575:
1573:
1572:cross section
1569:
1565:
1560:
1558:
1554:
1545:
1542:
1539:
1536:
1535:
1534:
1531:
1529:
1518:
1514:
1511:
1508:
1503:
1497:Other sources
1489:
1486:
1483:
1480:
1479:
1475:
1472:
1469:
1466:
1465:
1461:
1458:
1455:
1452:
1451:
1447:
1444:
1441:
1438:
1437:
1433:
1430:
1427:
1424:
1423:
1420:
1412:
1409:
1406:
1403:
1400:
1399:
1395:
1392:
1389:
1386:
1383:
1382:
1378:
1375:
1372:
1369:
1366:
1365:
1361:
1358:
1355:
1352:
1349:
1348:
1344:
1341:
1338:
1335:
1332:
1331:
1325:
1323:(very strong)
1320:
1315:
1310:
1307:
1306:
1303:
1301:
1297:
1290:
1286:
1281:
1276:
1266:
1263:
1259:
1255:
1249:
1239:
1236:
1234:
1230:
1223:
1219:
1215:
1209:
1207:
1203:
1199:
1194:
1192:
1188:
1184:
1180:
1171:
1167:
1160:
1155:
1146:
1144:
1140:
1135:
1133:
1132:monochromator
1130:bent crystal
1129:
1125:
1120:
1117:
1112:
1109:
1107:
1092:
1083:
1081:
1077:
1073:
1066:
1062:
1058:
1054:
1050:
1043:
1039:
1035:
1016:
1008:
1005:
1001:
997:
987:
984:
980:
976:
970:
967:
958:
950:
946:
939:
931:
927:
921:
916:
913:
910:
906:
900:
895:
892:
889:
885:
881:
875:
869:
862:
861:
860:
851:
847:
845:
840:
831:
829:
825:
820:
803:
799:
796:
771:
746:
740:
737:
712:
706:
703:
700:
697:
673:
667:
661:
658:
655:
652:
649:
644:
640:
637:
631:
625:
619:
616:
613:
610:
603:
602:
601:
594:
591:
588:
585:
584:
583:
575:
572:
571:least squares
568:
564:
553:
550:
546:
536:
534:
530:
526:
522:
518:
509:
500:
498:
494:
483:
481:
476:
472:
465:Crystallinity
462:
460:
456:
451:
442:
440:
436:
432:
421:
419:
415:
411:
407:
403:
399:
395:
394:diffractogram
391:
387:
383:
379:
375:
352:
346:
340:
337:
332:
328:
325:
319:
313:
307:
304:
301:
298:
295:
292:
289:
281:
269:
268:
267:
266:
265:
264:
263:
261:
257:
253:
249:
245:
241:
237:
233:
224:
220:
218:
214:
210:
206:
202:
198:
194:
190:
186:
182:
179:
175:
171:
167:
162:
160:
155:
151:
147:
143:
138:
136:
132:
128:
124:
120:
116:
112:
106:
96:
93:
91:
87:
84:on powder or
83:
79:
75:
71:
63:
62:yttrium oxide
59:
42:
34:
21:
3162:
3150:
3095:Associations
3063:Organisation
2555:Disclination
2486:Polymorphism
2449:Quasicrystal
2392:Orthorhombic
2332:Miller index
2280:Key concepts
2205:
2184:
2174:
2149:
2145:
2131:
2106:
2102:
2096:
2076:
2033:
2029:
2023:
1988:
1984:
1974:
1955:
1951:
1941:
1916:
1912:
1902:
1885:
1879:
1863:
1847:
1842:
1826:(3–4): 219.
1823:
1819:
1806:
1781:
1773:
1745:
1738:
1722:
1689:
1685:
1679:
1576:
1561:
1556:
1549:
1532:
1527:
1524:
1515:
1512:
1504:
1500:
1418:
1293:
1251:
1237:
1228:
1221:
1217:
1213:
1210:
1205:
1201:
1197:
1195:
1190:
1186:
1178:
1175:
1169:
1165:
1158:
1136:
1127:
1121:
1113:
1110:
1103:
1089:
1079:
1075:
1068:
1064:
1060:
1052:
1045:
1041:
1033:
1031:
857:
848:
841:
837:
827:
821:
688:
598:
581:
559:
548:
542:
529:bulk modulus
516:
514:
493:Miller index
489:
474:
468:
455:Dow Chemical
452:
448:
427:
417:
409:
405:
401:
397:
389:
385:
381:
377:
373:
371:
259:
247:
243:
239:
235:
229:
212:
211:*, and only
208:
204:
200:
196:
192:
188:
184:
180:
163:
139:
130:
126:
122:
108:
94:
89:
69:
68:
3186:Diffraction
3048:Ewald Prize
2816:Diffraction
2794:Diffraction
2777:Diffraction
2719:Bragg plane
2714:Bragg's law
2593:Dislocation
2508:Segregation
2420:Crystallite
2337:Point group
1507:synchrotron
1487:0.070931715
1269:X-ray tubes
414:synchrotron
252:Bragg's law
150:crystalline
146:anisotropic
135:Bragg's law
99:Explanation
3180:Categories
2832:Algorithms
2821:Scattering
2799:Scattering
2782:Scattering
2650:Slip bands
2613:Cross slip
2463:transition
2397:Tetragonal
2387:Monoclinic
2299:Metallurgy
1919:(6): 809.
1858:Chapter 14
1671:References
1629:Metallurgy
1490:0.0632303
1476:0.1392234
1473:0.15405929
1470:0.15444274
1462:0.1620826
1448:0.2084881
1296:X-ray tube
1106:CCD-camera
473:behavior,
232:Laue spots
103:See also:
2939:Databases
2402:Triclinic
2382:Hexagonal
2322:Unit cell
2314:Structure
2209:. Wiley.
2058:103885050
1958:(1): 12.
1765:162131289
1517:samples.
1484:0.0713607
1459:0.1788996
1456:0.1792835
1445:0.2289726
1442:0.2293651
1413:0.063229
1396:0.139222
1379:0.162079
1362:0.175661
1345:0.208487
1078:and atom
1059:for atom
1055:) is the
971:
907:∑
886:∑
800:λ
772:η
747:θ
741:
713:θ
707:
701:⋅
668:θ
662:
656:⋅
653:η
641:λ
626:θ
620:
614:⋅
549:distorted
521:unit cell
347:θ
341:
333:λ
329:π
314:θ
308:
159:texturing
154:isotropic
142:texturing
3152:Category
2987:Journals
2919:OctaDist
2914:JANA2020
2886:Software
2772:Electron
2689:F-center
2476:Eutectic
2437:Fiveling
2432:Twinning
2425:Equiaxed
2015:35974739
1952:Crystals
1714:17009500
1582:See also
1410:0.070930
1407:0.071359
1404:0.071073
1393:0.154056
1390:0.154439
1387:0.154184
1376:0.178897
1373:0.179285
1370:0.179026
1359:0.193604
1356:0.193998
1353:0.193736
1342:0.228970
1339:0.229361
1336:0.229100
1318:(strong)
1128:focusing
1116:vanadium
1067:, while
439:Ångström
3201:Powders
3164:Commons
3112:Germany
2789:Neutron
2679:Vacancy
2538:Defects
2523:GP-zone
2369:Systems
2154:Bibcode
2111:Bibcode
2038:Bibcode
2006:9348868
1921:Bibcode
1694:Bibcode
1425:Element
1328:(weak)
1308:Element
1254:neutron
1233:texture
1124:Guinier
1100:Cameras
1095:Devices
517:in situ
258:vector
244:visible
199:*, and
187:*, and
78:neutron
3107:France
3102:Europe
3035:Awards
2565:Growth
2415:Growth
2213:
2140:and Kβ
2084:
2056:
2013:
2003:
1893:
1871:
1854:
1794:
1763:
1753:
1730:
1712:
1528:phases
1300:X-rays
1285:Bruker
1036:is in
207:* and
115:X-rays
111:X-rays
3129:Japan
3076:IOBCr
2929:SHELX
2924:Olex2
2811:X-ray
2461:Phase
2377:Cubic
2054:S2CID
1710:S2CID
80:, or
74:X-ray
3071:IUCr
2972:ICDD
2967:ICSD
2952:CCDC
2899:Coot
2894:CCP4
2645:Slip
2608:Kink
2211:ISBN
2082:ISBN
2011:PMID
1891:ISBN
1869:ISBN
1852:ISBN
1792:ISBN
1761:OCLC
1751:ISBN
1728:ISBN
1260:and
1227:and
1164:and
844:barn
729:vs.
475:i.e.
424:Uses
56:and
3086:DMG
3081:RAS
2977:PDB
2962:COD
2957:CIF
2909:DSR
2633:GND
2560:CSL
2162:doi
2142:1,3
2138:1,2
2119:doi
2046:doi
2001:PMC
1993:doi
1960:doi
1929:doi
1917:351
1828:doi
1788:122
1702:doi
1557:new
1434:Kβ
1431:Kα1
1428:Kα2
1321:Kα1
1316:Kα2
968:sin
738:sin
704:cos
659:sin
617:cos
480:DSC
338:sin
305:sin
183:*,
3182::
3124:US
3117:UK
2160:.
2150:56
2148:.
2117:.
2107:39
2105:.
2066:^
2052:.
2044:.
2034:32
2032:.
2009:.
1999:.
1989:55
1987:.
1983:.
1956:11
1954:.
1950:.
1927:.
1915:.
1911:.
1824:35
1822:.
1818:.
1790:.
1759:.
1708:.
1700:.
1690:10
1688:.
1481:Mo
1467:Cu
1453:Co
1439:Cr
1401:Mo
1384:Cu
1367:Co
1350:Fe
1333:Cr
1326:Kβ
1311:Kα
1193:.
1189:-2
1071:ij
819:.
482:.
195:,
92:.
76:,
48:Cu
2265:e
2258:t
2251:v
2219:.
2168:.
2164::
2156::
2125:.
2121::
2113::
2090:.
2060:.
2048::
2040::
2017:.
1995::
1968:.
1962::
1935:.
1931::
1923::
1897:.
1836:.
1830::
1800:.
1767:.
1716:.
1704::
1696::
1229:K
1225:0
1222:K
1218:θ
1216:-
1214:θ
1206:θ
1202:θ
1200:-
1198:θ
1191:θ
1187:θ
1179:θ
1170:θ
1166:K
1162:0
1159:K
1080:j
1076:i
1069:r
1065:q
1061:i
1053:q
1051:(
1048:i
1046:f
1042:N
1034:q
1017:,
1009:j
1006:i
1002:r
998:q
993:)
988:j
985:i
981:r
977:q
974:(
962:)
959:q
956:(
951:j
947:f
943:)
940:q
937:(
932:i
928:f
922:N
917:1
914:=
911:j
901:N
896:1
893:=
890:i
882:=
879:)
876:q
873:(
870:I
828:k
804:D
797:k
750:)
744:(
716:)
710:(
698:B
674:,
671:)
665:(
650:+
645:D
638:k
632:=
629:)
623:(
611:B
418:q
410:λ
406:q
402:θ
398:I
390:λ
386:θ
382:k
378:q
374:G
353:.
350:)
344:(
326:4
320:=
317:)
311:(
302:k
299:2
296:=
293:q
290:=
286:|
282:G
278:|
260:G
248:θ
240:θ
213:q
209:χ
205:φ
201:χ
197:φ
193:q
189:z
185:y
181:x
131:θ
127:d
123:d
54:5
52:O
50:2
46:2
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