6211:
4272:
7899:
2822:
4561:
3938:
7911:
3349:
3982:
2502:
4730:
4339:
3694:
4282:
The basis behind the phase problem is that phase information is more important than amplitude information when recovering an image. This is because the phase term of the structure factor contains the positions. However, the phase information does not need to be retrieved completely accurately. Often
6206:
was originally developed by
Gerchberg and Saxton to solve for the phase of wave functions with intensities known in both the diffraction and imaging planes. However, it has been generalized for any information in real or reciprocal space. Detailed here is a generalization using electron diffraction
4307:
intensities can be measured. One specific example is surface diffraction in plan view orientation. When analyzing the surface of a sample in plan view, the sample is often tilted off a zone axis in order to isolate the diffracted beams of the surface from those of the bulk. Achieving kinematical
2408:
2259:
The triplet phase relationship is an equation directly relating two known phases of diffracted beams to the unknown phase of another. This relationship can be easily derived via the Sayre equation, but it may also be demonstrated through statistical relationships between the diffracted beams, as
6290:
Direct methods with electron diffraction datasets have been used to solve for a variety of structures. As mentioned earlier, surfaces are one of the cases in electron diffraction where scattering is kinematical. As such, many surface structures have been solved for by both X-ray and electron
6513:
direct methods. The program is written in
Fortran and C++ and is free for academic use. SIR can be used for the crystal structure determination of small-to-medium-sized molecules and proteins from either X-ray or electron diffraction data. More information can be found at its website:
3119:
3111:
4267:{\displaystyle tan(\varphi ({\textbf {k}}))\approx {\frac {\sum _{h}|U({\textbf {k}})-NU({\textbf {k-h}})U({\textbf {h}})|sin\phi ({\textbf {k-h}})+\phi ({\textbf {h}})}{\sum _{h}|U({\textbf {k}})-NU({\textbf {k-h}})U({\textbf {h}})|cos\phi ({\textbf {k-h}})+\phi ({\textbf {h}})}}}
4302:
One of the reasons direct methods was originally developed for analyzing X-ray diffraction is because almost all X-ray diffraction is kinematical. While most electron diffraction is dynamical, which is more difficult to interpret, there are instances in which mostly kinematical
5768:
2817:{\displaystyle |U({\textbf {k}})-NU({\textbf {k-h}})U({\textbf {k}})|^{2}=|U({\textbf {k}})|^{2}+N^{2}|U({\textbf {k-h}})U({\textbf {h}})|^{2}-2N|U({\textbf {k}})U({\textbf {k-h}})U({\textbf {h}})|\times cos(\phi ({\textbf {k}})-\phi ({\textbf {k-h}})-\phi ({\textbf {h}}))}
438:
323:
2063:
1419:
1299:
1532:
function (for X-ray diffraction) or crystal potential function (for electron diffraction) results in a function that resembles the original un-squared function of identical and resolved peaks. By doing so, it reinforces atom-like features of the crystal.
5096:
5627:
3476:
1774:
1939:
5272:
4567:
6078:
4556:{\displaystyle D(\phi ({\textbf {k}})-\phi ({\textbf {k-h}})-\phi ({\textbf {h}}))=A({\textbf {k,h}}){\sqrt{I({\textbf {k}})I({\textbf {k-h}})I({\textbf {h}})}}\times cos(\phi ({\textbf {k}})-\phi ({\textbf {k-h}})-\phi ({\textbf {h}}))}
4326:, where dynamical scattering from random phases add up to be nearly kinematical. Furthermore, as explained earlier, it is not critical to retrieve phase information completely accurately. Errors in the phase information are tolerable.
2925:
2491:
4291:
In order to apply direct methods to a set of data for successful structure determination, there must be reasonable sufficient conditions satisfied by the experimental conditions or sample properties. Outlined here are several cases.
3933:{\displaystyle \prod _{h}P(U({\textbf {k}})-NU({\textbf {k-h}})U({\textbf {k}}))\approx 2NCe^{\sum _{h}|U({\textbf {k}})U({\textbf {k-h}})U({\textbf {k}})|\times cos(\phi ({\textbf {k}})-\phi ({\textbf {k-h}})-\phi ({\textbf {h}}))}}
6386:
and was most recently updated in 2008. It can be used for structures with heavy atoms, structures of molecules with partly known geometries, and for certain special case structures. Detailed information can be found at its website:
3687:
The tangent formula was first derived in 1955 by Jerome Karle and
Herbert Hauptman. It related the amplitudes and phases of known diffracted beams to the unknown phase of another. Here, it is derived using the Cochran distribution.
3548:
6502:
representation) suite of programs was developed for solving the crystal structures of small molecules. SIR is updated and released frequently, with the first release in 1988 and the latest release in 2014. It is capable of both
5519:
In some cases, scattering from a sample can be dominated by one type of atom. Therefore, the exit wave from the sample will also be dominated by that atom type. For example, the exit wave and intensity of a sample dominated by
2273:
1074:
990:
7138:
de la Cruz, M. J.; Hattne, J.; Shi, D.; Seidler, P.; Rodriguez, J.; Reyes, F. E.; Sawaya, M. R.; Cascio, D.; Weiss, S. C.; Kim, S. K.; Hinck, C. S.; Hinck, A. P.; Calero, G.; Eisenberg, D.; Gonen, T. (13 February 2017).
2147:
3344:{\displaystyle P(U({\textbf {k}})-NU({\textbf {k-h}})U({\textbf {k}}))\approx De^{2N|U({\textbf {k}})-NU({\textbf {k-h}})U({\textbf {k}})|\times cos(\phi ({\textbf {k}})-\phi ({\textbf {k-h}})-\phi ({\textbf {h}}))}}
1478:
The majority of direct methods was developed for X-ray diffraction. However, electron diffraction has advantages in several applications. Electron diffraction is a powerful technique for analyzing and characterizing
5493:
will also be large and small. So, the observed intensities can be used to reasonably estimate the phases for diffracted beams. The observed intensity can be related to the structure factor more formally using the
2949:
5491:
5416:
6223:
Constraints can be physical or statistical. For instance, the fact that the data is produced by a scattering experiment in a transmission electron microscope imposes several constraints, including atomicity,
784:
6214:
The generalized
Gerchberg-Saxton algorithm for direct methods with electron diffraction. By successively applying constraints, the algorithm will eventually converge to a possible solution. Modified from.
5633:
4970:
Consider two scattered beams with different intensities. The magnitude of their intensities will then have to be related to the amplitude of their corresponding scattering factors by the relationship:
892:
6486:
ubstitution protein data. It reduces the phase problem to a sign problem by locating the atomic sites of anomalous scatterers or heavy atom substitutions. More details can be found at the website:
331:
219:
1950:
897:
This is a straightforward method of obtaining the amplitude term of the structure factor. However, the phase term, which contains position information from the crystal potential, is lost.
4318:
Even though most cases of electron diffraction are dynamical, it is still possible to achieve scattering that is statistically kinematical in nature. This is what enables the analysis of
1307:
1187:
6207:
information. As illustrated in image to the right, one can successively impose real space and reciprocal constraints on an initial estimate until it converges to a feasible solution.
3611:
3974:
3677:
3644:
7543:
5530:
7011:
Erdman, N.; Poeppelmeier, K. R.; Asta, M.; Warschkow, O.; Ellis, D. E.; Marks, L. D. (5 September 2002). "The structure and chemistry of the TiO2-rich surface of SrTiO3 (001)".
4958:
4925:
4869:
4836:
4283:
even with errors in the phases, a complete structure determination is possible. Likewise, amplitude errors will not severely impact the accuracy of the structure determination.
3368:
2183:
662:
6180:
6147:
6114:
5947:
5910:
5877:
5836:
5803:
5341:
5308:
5162:
4803:
4766:
2249:
2216:
1843:
1810:
1600:
1567:
1143:
1110:
820:
619:
562:
525:
473:
160:
127:
5129:
6426:, and Fortran 77, EDM is capable of performing image processing of high resolution electron microscopy images and diffraction patterns and direct methods. It has a standard
1680:
699:
1652:
1628:
1171:
586:
211:
187:
6182:
will satisfy atomistic constraints as long as they are reasonably small and well-separated, thereby satisfying some constraints required for implementing direct methods.
4725:{\displaystyle D(\phi ({\textbf {k}})-\phi ({\textbf {k-h}})-\phi ({\textbf {h}}))=B({\textbf {k,h}})cos(\phi ({\textbf {k}})-\phi ({\textbf {k-h}})-\phi ({\textbf {h}}))}
1851:
6257:
5170:
4976:
3578:
4892:
1424:
Here, it is also clear that the phase terms are lost upon measurement in an electron diffraction experiment. This is referred to as the crystallographic phase problem.
7526:
7521:
6439:
5959:
7670:
7373:
2830:
2419:
7660:
7263:
6278:(highly convergent) or non-convex (weakly convergent). Imposing these constraints with the algorithm detailed earlier can converge towards unique or non-unique
1672:
1528:
considered are identical and there is a minimum distance between atoms. Called the "Squaring Method," a key concept of the Sayre equation is that squaring the
7563:
7536:
3482:
7091:"Three-dimensional electron diffraction as a complementary technique to powder X-ray diffraction for phase identification and structure solution of powders"
2403:{\displaystyle N\langle U({\textbf {k-h}})U({\textbf {h}})\rangle ={\frac {1}{N}}\sum _{l}e^{2\pi i{\textbf {k}}\cdot {\textbf {r}}_{l}}=U({\textbf {k}})}
7471:
1454:
also independently derived relationships between the signs of different structure factors. Later advancements were done by other scientists, including
1440:, a construct that related the known phases of certain diffracted beams to estimate the unknown phase of another diffracted beam. In the same issue of
7531:
6856:
Gerchberg, R. W.; Saxton, W. O. (29 November 1971). "A Practical
Algorithm for the Determination of Phase from Image and Diffraction Plane Pictures".
998:
914:
7675:
2071:
6232:, and interference. Constraints may also be statistical in origin, as shown earlier with the Cochran distribution and triplet phase relationship (
1173:
is a reciprocal space vector. When a diffraction pattern is measured, only the intensities can be extracted. A measurement obtains a statistical
6318:
and rotation electron diffraction. These techniques have been used to obtain data for structure solution through direct methods and applied for
5509:. Specifically, precession electron diffraction produces a quasi-kinematical diffraction pattern that can be used adequately in direct methods.
7491:
3106:{\displaystyle P(U({\textbf {k}})-NU({\textbf {k-h}})U({\textbf {k}}))\approx Ce^{-|U({\textbf {k}})-NU({\textbf {k-h}})U({\textbf {k}})|^{2}}}
7615:
7481:
7428:
6976:
Marks, L. D.; Bengu, E.; Collazo-Davila, C.; Grozea, D.; Landree, E.; Leslie, C.; Sinkler, W. (October 1998). "Direct
Methods for Surfaces".
7598:
7583:
7509:
47:
information is lost during a diffraction measurement. Direct methods provides a method of estimating the phase information by establishing
5421:
5346:
6342:. In some of these cases, the structures were solved in combination with X-ray diffraction data, making them complementary techniques.
707:
6458:
in
Fortran 77. The most recent release is version 4.2 in 2012. It is a program for direct methods phasing of protein structures. The
1507:, there are specific cases (detailed later) that have sufficient conditions for applying direct methods for structure determination.
7620:
7453:
7306:
7256:
6902:
6562:
6350:
5763:{\displaystyle I({\textbf {k}})=|A({\textbf {k}})|^{2}{\bigg |}\sum _{l}e^{2\pi i{\textbf {k}}\cdot {\textbf {r}}_{l}}{\bigg |}^{2}}
4960:. With a narrow distribution such as this, the scattering data will be statistically within the realm of kinematical consideration.
7608:
7603:
7501:
7476:
7443:
6532:
901:
17:
7680:
7665:
7645:
6542:
5506:
1500:
7383:
2943:
in form. By combining the terms of the known moduli, a distribution function can be written that is dependent on the phases:
7448:
7291:
6427:
6378:
and direct methods applied to difference structure factors. It was first released by Paul
Beurkens and his colleagues at the
828:
7915:
6314:
More recently, methods for automated three dimensional electron diffraction methods have been developed, such as automated
7625:
7588:
7433:
6190:
Direct methods is a set of routines for structure determination. In order to successfully solve for a structure, several
3362:
scales with the reciprocal of the unitary structure factors. If they are large, then the sum in the cosine term must be:
7937:
7903:
7463:
7249:
433:{\displaystyle F({\textbf {k}})=\int _{-\infty }^{\infty }f({\textbf {r}})e^{-2\pi i{\textbf {k}}\cdot {\textbf {r}}}dr}
6941:
Marks, L. D.; Sinkler, W.; Landree, E. (1 July 1999). "A feasible set approach to the crystallographic phase problem".
318:{\displaystyle f({\textbf {r}})=\int _{-\infty }^{\infty }F({\textbf {k}})e^{2\pi i{\textbf {k}}\cdot {\textbf {r}}}dk}
6455:
2058:{\displaystyle u({\textbf {r}})={\frac {1}{N}}\sum _{l}\delta ({\textbf {r}}-{\textbf {r}}_{l})=Nu({\textbf {r}})^{2}}
1451:
7650:
7568:
6203:
4769:
2936:
7062:
Kienzle, Danielle M.; Marks, Laurence D. (2012). "Surface transmission electron diffraction for SrTiO3 surfaces".
1524:
was developed under certain assumptions taken from information about the crystal structure, specifically that all
1470:(1985) to Hauptman and Karle for their development of direct methods for the determination of crystal structures.
1414:{\displaystyle I({\textbf {u}})=\langle |\Psi ({\textbf {u}})|^{2}\rangle =\langle |A({\textbf {u}})|^{2}\rangle }
1294:{\displaystyle I({\textbf {r}})=\langle |\psi ({\textbf {r}})|^{2}\rangle =\langle |a({\textbf {r}})|^{2}\rangle }
6770:
Marks, L. D.; Sinkler, W. (16 September 2003). "Sufficient
Conditions for Direct Methods with Swift Electrons".
7875:
7829:
7655:
6552:
6423:
6346:
6331:
6323:
7865:
7578:
7514:
7388:
7347:
6411:
5622:{\displaystyle \Psi ({\textbf {k}})=A({\textbf {k}})\sum _{l}e^{2\pi i{\textbf {k}}\cdot {\textbf {r}}_{l}}}
3583:
1447:
528:
480:
3976:
can be found by taking the derivative of the above equation, which gives a variant of the tangent formula:
3471:{\displaystyle \phi ({\textbf {k}})-\phi ({\textbf {k-h}})-\phi ({\textbf {h}})\approx 2n\pi ,~~n=0,1,2...}
7768:
6880:
6379:
6315:
3946:
3649:
3616:
1442:
7773:
7593:
6547:
5521:
4930:
4897:
4841:
4808:
2932:
2155:
1504:
624:
81:
16:
This article is about direct methods in electron diffraction. For X-ray diffraction direct methods, see
4308:
conditions is difficult in most cases—it requires very thin samples to minimize dynamical diffraction.
1769:{\displaystyle F({\textbf {k}})=\sum _{l}f({\textbf {k}})e^{2\pi {\textbf {k}}\cdot {\textbf {r}}_{l}}}
6152:
6119:
6086:
5919:
5882:
5849:
5808:
5775:
5313:
5280:
5134:
4775:
4738:
2221:
2188:
1815:
1782:
1572:
1539:
1115:
1082:
792:
591:
534:
497:
445:
132:
99:
7778:
7337:
7020:
6985:
6830:
6779:
6557:
5104:
1934:{\displaystyle U({\textbf {k}})={\frac {1}{N}}\sum _{l}e^{2\pi {\textbf {k}}\cdot {\textbf {r}}_{l}}}
1146:
73:
56:
5267:{\displaystyle T({\textbf {k}})=e^{i\phi ({\textbf {k}})}{\sqrt{I({\textbf {k}})}}/N({\textbf {k}})}
5091:{\displaystyle I({\textbf {k}})>I({\textbf {k'}})~~iff~|F({\textbf {k}})|>|F({\textbf {k'}})|}
667:
7743:
7728:
7635:
7630:
7573:
7438:
7420:
7352:
7342:
7286:
7272:
6885:
6345:
In addition, some success has been found using direct methods for structure determination with the
6263:
2940:
1633:
1609:
1455:
1152:
908:
of the electron beam from the crystal in real and reciprocal space can be written respectively as:
567:
487:
192:
168:
7814:
7393:
7357:
7044:
6912:
6803:
6487:
6375:
6308:
6235:
5913:
5502:
4838:
contains both of these for simplicity. Here, the most probable phases will maximize the function
3556:
3355:
1603:
6073:{\displaystyle B({\textbf {k}})=S({\textbf {k}})|A({\textbf {k}})|,where~S({\textbf {k}})=\pm 1}
6353:. MicroED has been used for a variety of materials, including crystal fragments, proteins, and
4874:
7758:
7753:
7227:
7209:
7170:
7141:"Atomic-resolution structures from fragmented protein crystals with the cryoEM method MicroED"
7120:
7036:
6958:
6898:
6795:
6435:
6415:
6335:
6229:
5501:
Other cases to consider for intensity mapping are specific diffraction experiments, including
3359:
483:
93:
89:
2927:
and the moduli are known on the right hand side. The only unknown terms are contained in the
2152:
This equation is a variation of the Sayre equation. Based on this equation, if the phases of
7708:
7640:
7217:
7201:
7160:
7152:
7110:
7102:
7071:
7028:
6993:
6950:
6890:
6838:
6787:
6743:
6710:
6652:
6621:
6594:
6388:
6371:
6279:
6210:
5950:
2920:{\displaystyle \langle |U({\textbf {k}})-NU({\textbf {k-h}})U({\textbf {k}})|^{2}\rangle =0}
1529:
476:
163:
85:
2486:{\displaystyle U({\textbf {k}})\approx N\langle U({\textbf {k-h}})U({\textbf {h}})\rangle }
7763:
6924:
6527:
6296:
6271:
4319:
24:
6677:"A theory of phase determination for the four types of non-centrosymmetric space groups 1
6585:
Sayre, D. (1 January 1952). "The squaring method: a new method for phase determination".
7024:
6989:
6834:
6783:
7718:
7332:
7222:
7189:
7165:
7140:
7115:
7090:
6431:
6339:
5843:
5839:
5495:
4323:
3543:{\displaystyle \phi ({\textbf {k}})\approx \phi ({\textbf {k-h}})-\phi ({\textbf {h}})}
1657:
1437:
1178:
6894:
6418:. First released in 2004, its most recent release was version 3.1 in 2010. Written in
7931:
7794:
7738:
7398:
6821:
Blackman, M. (10 November 1939). "On the
Intensities of Electron Diffraction Rings".
905:
44:
40:
7845:
6807:
6443:
76:, a diffraction pattern is produced by the interaction of the electron beam and the
7855:
7819:
7713:
7703:
7378:
7327:
7048:
6823:
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
6612:
Cochran, W. (1 January 1952). "A relation between the signs of structure factors".
1459:
6194:
have been developed for direct methods. A selection of these are explained below.
4871:. If the intensities are sufficiently high and the sum in the cosine term remains
789:
During a diffraction experiment, the intensity of the reflections are measured as
5131:) be a function that relates the intensity to the phase for the same beam, where
7799:
7733:
7723:
6537:
6225:
1463:
1433:
48:
32:
1503:
and more complex to understand compared to X-ray diffraction, which is usually
1069:{\displaystyle \Psi ({\textbf {u}})=A({\textbf {u}})e^{-i\phi ({\textbf {u}})}}
985:{\displaystyle \psi ({\textbf {r}})=a({\textbf {r}})e^{-i\phi ({\textbf {r}})}}
7880:
7301:
7296:
7106:
6997:
6954:
6791:
6748:
6731:
6715:
6676:
6657:
6640:
6625:
6598:
6515:
6275:
6191:
4304:
2264:
491:
7213:
6442:
image simulation capabilities. More information can be found at the website:
2142:{\displaystyle U({\textbf {k}})=N\sum _{h}U({\textbf {k-h}})U({\textbf {h}})}
7748:
7403:
6505:
6300:
4330:
1480:
1467:
52:
7231:
7174:
7124:
7040:
6962:
6842:
6799:
7850:
7316:
7205:
6499:
6319:
1521:
1492:
1488:
7032:
7860:
7804:
7486:
7156:
7075:
6459:
6383:
6354:
6292:
6262:
According to Combettes, image recovery problems can be considered as a
1496:
1174:
77:
7241:
7824:
6304:
5949:, then it is feasible to retrieve atom-like features from the object
2928:
1944:
This can be alternatively rewritten in real and reciprocal space as:
1484:
6438:
search for solving structures using direct methods, and it also has
5486:{\displaystyle |T({\textbf {k}})T({\textbf {k-h}})T({\textbf {h}})|}
5411:{\displaystyle |F({\textbf {k}})F({\textbf {k-h}})F({\textbf {h}})|}
6419:
6327:
6209:
1525:
701:). The phase term contains the position information in this form.
779:{\displaystyle F({\textbf {g}})=|F({\textbf {g}})|e^{i\phi _{g}}}
213:
are position vectors in real and reciprocal space, respectively.
7809:
7190:"MicroED: a versatile cryoEM method for structure determination"
6641:"A new analytical method for solving complex crystal structures"
5879:
is real in reciprocal space and complex in the object plane. If
7245:
129:
is in real space and corresponds to the crystal potential, and
6488:
http://cryst.iphy.ac.cn/Project/IPCAS1.0/user_guide/oasis.html
31:
is a set of techniques used for structure determination using
7089:
Yun, Y.; Zou, X.; Hovmöller, S.; Wan, W. (10 February 2015).
5842:
and represents the shape of an atom, given by the channeling
3354:
This distribution is known as the Cochran distribution. The
486:(i.e. the periodic crystal potential), and it defines the
6389:
http://www.xtal.science.ru.nl/dirdif/software/dirdif.html
6454:
OASIS was first written by several scientists from the
887:{\displaystyle I({\textbf {g}})=|F({\textbf {g}})|^{2}}
1779:
This can be converted to the unitary structure factor
39:
information. It is a solution to the crystallographic
6238:
6155:
6122:
6089:
5962:
5922:
5885:
5852:
5811:
5778:
5636:
5533:
5424:
5349:
5316:
5283:
5173:
5137:
5107:
4979:
4933:
4900:
4877:
4844:
4811:
4778:
4741:
4570:
4342:
4329:
Recalling the Cochran distribution and considering a
3985:
3949:
3697:
3652:
3619:
3586:
3559:
3485:
3371:
3122:
2952:
2833:
2505:
2422:
2276:
2224:
2191:
2158:
2074:
1953:
1854:
1818:
1785:
1683:
1660:
1636:
1612:
1575:
1542:
1310:
1190:
1155:
1118:
1085:
1001:
917:
900:
Analogously, for electron diffraction performed in a
831:
795:
710:
670:
627:
594:
570:
537:
500:
448:
334:
222:
195:
171:
135:
102:
7838:
7787:
7696:
7689:
7556:
7500:
7462:
7419:
7412:
7366:
7315:
7279:
6732:"Relations between the phases of structure factors"
6462:OASIS stands for two of its applications: phasing
6291:diffraction direct methods, including many of the
6251:
6174:
6141:
6108:
6072:
5941:
5904:
5871:
5830:
5797:
5762:
5621:
5485:
5410:
5335:
5302:
5266:
5156:
5123:
5090:
4952:
4919:
4886:
4863:
4830:
4797:
4760:
4724:
4555:
4266:
3968:
3932:
3671:
3638:
3605:
3572:
3542:
3470:
3343:
3105:
2919:
2816:
2485:
2402:
2243:
2210:
2177:
2141:
2057:
1933:
1837:
1804:
1768:
1666:
1646:
1622:
1594:
1561:
1413:
1293:
1165:
1137:
1104:
1068:
984:
886:
814:
778:
693:
656:
613:
580:
556:
519:
467:
432:
317:
205:
181:
162:is its Fourier transform in reciprocal space. The
154:
121:
6444:http://www.numis.northwestern.edu/edm/index.shtml
6282:, depending on the convexity of the constraints.
5749:
5691:
5310:values will be directly related to the values of
6877:The Convex Feasibility Problem in Image Recovery
6440:high-resolution transmission electron microscopy
5524:can be written in reciprocal space in the form:
7188:Nannenga, Brent L.; Gonen, Tamir (2018-02-06).
6434:purposes. It uses a feasible set approach and
3553:This is called the triplet phase relationship (
7671:Serial block-face scanning electron microscopy
7374:Detectors for transmission electron microscopy
6374:for structure determination through using the
6270:to the crystallographic phase problem. With a
6083:In the object plane, the Fourier transform of
588:is a specific reflection in reciprocal space.
7257:
2267:distributed atoms, the following holds true:
8:
6879:. Vol. 95. Elsevier. pp. 155–270.
4805:terms are the experimental intensities, and
2935:can be applied here, which establishes that
2908:
2834:
2480:
2445:
2315:
2280:
1408:
1372:
1366:
1330:
1288:
1252:
1246:
1210:
6936:
6934:
6765:
6763:
6761:
6759:
6516:http://www.ba.ic.cnr.it/softwareic/sir2014/
6351:Microcrystal Electron Diffraction (MicroED)
1812:by dividing by N (the number of atoms) and
7693:
7416:
7264:
7250:
7242:
7221:
7164:
7114:
6884:
6747:
6714:
6675:Karle, J.; Hauptman, H. (1 August 1956).
6656:
6446:. The code is no longer being developed.
6410:ethods is a set of programs developed at
6243:
6237:
6163:
6162:
6154:
6130:
6129:
6121:
6116:will be a real and symmetric pseudoatom (
6097:
6096:
6088:
6052:
6051:
6019:
6010:
6009:
5998:
5989:
5988:
5970:
5969:
5961:
5930:
5929:
5921:
5893:
5892:
5884:
5860:
5859:
5851:
5819:
5818:
5810:
5786:
5785:
5777:
5754:
5748:
5747:
5738:
5732:
5731:
5721:
5720:
5710:
5700:
5690:
5689:
5683:
5678:
5668:
5667:
5656:
5644:
5643:
5635:
5611:
5605:
5604:
5594:
5593:
5583:
5573:
5560:
5559:
5541:
5540:
5532:
5478:
5469:
5468:
5453:
5452:
5437:
5436:
5425:
5423:
5403:
5394:
5393:
5378:
5377:
5362:
5361:
5350:
5348:
5324:
5323:
5315:
5291:
5290:
5282:
5255:
5254:
5243:
5239:
5229:
5228:
5219:
5208:
5207:
5197:
5181:
5180:
5172:
5145:
5144:
5136:
5115:
5114:
5106:
5083:
5074:
5073:
5062:
5054:
5045:
5044:
5033:
5006:
5005:
4987:
4986:
4978:
4941:
4940:
4932:
4908:
4907:
4899:
4876:
4852:
4851:
4843:
4819:
4818:
4810:
4786:
4785:
4777:
4749:
4748:
4740:
4710:
4709:
4691:
4690:
4672:
4671:
4644:
4643:
4622:
4621:
4603:
4602:
4584:
4583:
4569:
4541:
4540:
4522:
4521:
4503:
4502:
4477:
4467:
4466:
4451:
4450:
4435:
4434:
4425:
4416:
4415:
4394:
4393:
4375:
4374:
4356:
4355:
4341:
4252:
4251:
4233:
4232:
4212:
4203:
4202:
4187:
4186:
4165:
4164:
4153:
4147:
4132:
4131:
4113:
4112:
4092:
4083:
4082:
4067:
4066:
4045:
4044:
4033:
4027:
4020:
4005:
4004:
3984:
3957:
3956:
3948:
3916:
3915:
3897:
3896:
3878:
3877:
3851:
3842:
3841:
3826:
3825:
3810:
3809:
3798:
3792:
3787:
3759:
3758:
3743:
3742:
3721:
3720:
3702:
3696:
3660:
3659:
3651:
3627:
3626:
3618:
3594:
3593:
3585:
3564:
3558:
3531:
3530:
3512:
3511:
3493:
3492:
3484:
3417:
3416:
3398:
3397:
3379:
3378:
3370:
3327:
3326:
3308:
3307:
3289:
3288:
3262:
3253:
3252:
3237:
3236:
3215:
3214:
3203:
3196:
3174:
3173:
3158:
3157:
3136:
3135:
3121:
3095:
3090:
3080:
3079:
3064:
3063:
3042:
3041:
3030:
3026:
3004:
3003:
2988:
2987:
2966:
2965:
2951:
2902:
2897:
2887:
2886:
2871:
2870:
2849:
2848:
2837:
2832:
2802:
2801:
2783:
2782:
2764:
2763:
2737:
2728:
2727:
2712:
2711:
2696:
2695:
2684:
2669:
2664:
2654:
2653:
2638:
2637:
2626:
2620:
2607:
2602:
2592:
2591:
2580:
2571:
2566:
2556:
2555:
2540:
2539:
2518:
2517:
2506:
2504:
2471:
2470:
2455:
2454:
2430:
2429:
2421:
2391:
2390:
2373:
2367:
2366:
2356:
2355:
2345:
2335:
2321:
2306:
2305:
2290:
2289:
2275:
2232:
2231:
2223:
2199:
2198:
2190:
2166:
2165:
2157:
2130:
2129:
2114:
2113:
2101:
2082:
2081:
2073:
2049:
2039:
2038:
2017:
2011:
2010:
2000:
1999:
1987:
1973:
1961:
1960:
1952:
1923:
1917:
1916:
1906:
1905:
1898:
1888:
1874:
1862:
1861:
1853:
1826:
1825:
1817:
1793:
1792:
1784:
1758:
1752:
1751:
1741:
1740:
1733:
1720:
1719:
1707:
1691:
1690:
1682:
1659:
1638:
1637:
1635:
1614:
1613:
1611:
1583:
1582:
1574:
1550:
1549:
1541:
1402:
1397:
1387:
1386:
1375:
1360:
1355:
1345:
1344:
1333:
1318:
1317:
1309:
1282:
1277:
1267:
1266:
1255:
1240:
1235:
1225:
1224:
1213:
1198:
1197:
1189:
1157:
1156:
1154:
1126:
1125:
1117:
1093:
1092:
1084:
1055:
1054:
1041:
1028:
1027:
1009:
1008:
1000:
971:
970:
957:
944:
943:
925:
924:
916:
878:
873:
863:
862:
851:
839:
838:
830:
803:
802:
794:
768:
760:
751:
742:
741:
730:
718:
717:
709:
683:
675:
669:
649:
640:
639:
628:
626:
602:
601:
593:
572:
571:
569:
545:
544:
536:
508:
507:
499:
456:
455:
447:
416:
415:
406:
405:
392:
379:
378:
366:
358:
342:
341:
333:
301:
300:
291:
290:
280:
267:
266:
254:
246:
230:
229:
221:
197:
196:
194:
173:
172:
170:
143:
142:
134:
110:
109:
101:
6274:approach, constraints can be considered
6266:problem. This idea was adapted by Marks
6670:
6668:
6580:
6578:
6574:
4927:will also be large, thereby maximizing
6920:
6910:
3606:{\displaystyle \phi ({\textbf {k-h}})}
1499:. While electron diffraction is often
6639:Zachariasen, W. H. (1 January 1952).
7:
7910:
3969:{\displaystyle \phi ({\textbf {h}})}
3672:{\displaystyle \phi ({\textbf {k}})}
3639:{\displaystyle \phi ({\textbf {h}})}
6875:Combettes, P. L. (1 January 1996).
6164:
6131:
6098:
6053:
6011:
5990:
5971:
5931:
5894:
5861:
5820:
5787:
5733:
5722:
5669:
5645:
5606:
5595:
5561:
5542:
5470:
5454:
5438:
5395:
5379:
5363:
5325:
5292:
5256:
5230:
5209:
5182:
5146:
5116:
5075:
5046:
5007:
4988:
4942:
4909:
4853:
4820:
4787:
4750:
4711:
4692:
4673:
4645:
4623:
4604:
4585:
4542:
4523:
4504:
4468:
4452:
4436:
4417:
4395:
4376:
4357:
4313:Statistical Kinematical Diffraction
4253:
4234:
4204:
4188:
4166:
4133:
4114:
4084:
4068:
4046:
4006:
3958:
3917:
3898:
3879:
3843:
3827:
3811:
3760:
3744:
3722:
3661:
3628:
3595:
3532:
3513:
3494:
3418:
3399:
3380:
3328:
3309:
3290:
3254:
3238:
3216:
3175:
3159:
3137:
3081:
3065:
3043:
3005:
2989:
2967:
2931:term that includes the phases. The
2888:
2872:
2850:
2803:
2784:
2765:
2729:
2713:
2697:
2655:
2639:
2593:
2557:
2541:
2519:
2472:
2456:
2431:
2392:
2368:
2357:
2307:
2291:
2233:
2200:
2167:
2131:
2115:
2083:
2040:
2012:
2001:
1962:
1918:
1907:
1863:
1827:
1794:
1753:
1742:
1721:
1692:
1639:
1615:
1584:
1551:
1388:
1346:
1319:
1268:
1226:
1199:
1158:
1127:
1094:
1056:
1029:
1010:
972:
945:
926:
864:
840:
804:
743:
719:
641:
603:
573:
546:
509:
457:
417:
407:
380:
343:
302:
292:
268:
231:
198:
174:
144:
111:
51:relationships between the recorded
6240:
6149:) at the atomic column positions.
5534:
4953:{\displaystyle D({\textbf {k,h}})}
4920:{\displaystyle B({\textbf {k,h}})}
4864:{\displaystyle D({\textbf {k,h}})}
4831:{\displaystyle B({\textbf {k,h}})}
3561:
2178:{\displaystyle U({\textbf {k-h}})}
1474:Comparison to X-Ray Direct Methods
1338:
1002:
657:{\displaystyle |F({\textbf {g}})|}
367:
362:
255:
250:
14:
7307:Timeline of microscope technology
6563:Microcrystal Electron Diffraction
6430:and is free to use or modify for
1462:, leading to the awarding of the
96:relationships shown below, where
55:information and phases of strong
7909:
7898:
7897:
7194:Emerging Topics in Life Sciences
6943:Acta Crystallographica Section A
6533:Transmission electron microscopy
6175:{\displaystyle b({\textbf {r}})}
6142:{\displaystyle b({\textbf {r}})}
6109:{\displaystyle B({\textbf {k}})}
5942:{\displaystyle A({\textbf {k}})}
5905:{\displaystyle B({\textbf {k}})}
5872:{\displaystyle A({\textbf {k}})}
5831:{\displaystyle a({\textbf {r}})}
5798:{\displaystyle A({\textbf {k}})}
5336:{\displaystyle F({\textbf {k}})}
5303:{\displaystyle T({\textbf {k}})}
5157:{\displaystyle N({\textbf {k}})}
4798:{\displaystyle I({\textbf {k}})}
4761:{\displaystyle A({\textbf {k}})}
2244:{\displaystyle U({\textbf {k}})}
2211:{\displaystyle U({\textbf {h}})}
1838:{\displaystyle f({\textbf {k}})}
1805:{\displaystyle U({\textbf {k}})}
1595:{\displaystyle f({\textbf {k}})}
1562:{\displaystyle F({\textbf {k}})}
1138:{\displaystyle A({\textbf {u}})}
1105:{\displaystyle a({\textbf {r}})}
902:transmission electron microscope
815:{\displaystyle I({\textbf {g}})}
614:{\displaystyle F({\textbf {g}})}
557:{\displaystyle F({\textbf {g}})}
520:{\displaystyle F({\textbf {k}})}
479:, is the Fourier transform of a
468:{\displaystyle F({\textbf {k}})}
155:{\displaystyle F({\textbf {k}})}
122:{\displaystyle f({\textbf {r}})}
18:Direct methods (crystallography)
7666:Precession electron diffraction
6543:Precession electron diffraction
5507:precession electron diffraction
5124:{\displaystyle T({\textbf {k}}}
6730:Cochran, W. (10 August 1955).
6169:
6159:
6136:
6126:
6103:
6093:
6058:
6048:
6020:
6016:
6006:
5999:
5995:
5985:
5976:
5966:
5936:
5926:
5899:
5889:
5866:
5856:
5825:
5815:
5792:
5782:
5679:
5674:
5664:
5657:
5650:
5640:
5566:
5556:
5547:
5537:
5479:
5475:
5465:
5459:
5449:
5443:
5433:
5426:
5404:
5400:
5390:
5384:
5374:
5368:
5358:
5351:
5330:
5320:
5297:
5287:
5261:
5251:
5235:
5225:
5214:
5204:
5187:
5177:
5164:contains normalization terms:
5151:
5141:
5111:
5084:
5080:
5070:
5063:
5055:
5051:
5041:
5034:
5012:
5002:
4993:
4983:
4947:
4937:
4914:
4904:
4858:
4848:
4825:
4815:
4792:
4782:
4755:
4745:
4719:
4716:
4706:
4697:
4687:
4678:
4668:
4662:
4650:
4640:
4631:
4628:
4618:
4609:
4599:
4590:
4580:
4574:
4550:
4547:
4537:
4528:
4518:
4509:
4499:
4493:
4473:
4463:
4457:
4447:
4441:
4431:
4422:
4412:
4403:
4400:
4390:
4381:
4371:
4362:
4352:
4346:
4258:
4248:
4239:
4229:
4213:
4209:
4199:
4193:
4183:
4171:
4161:
4154:
4138:
4128:
4119:
4109:
4093:
4089:
4079:
4073:
4063:
4051:
4041:
4034:
4014:
4011:
4001:
3995:
3963:
3953:
3925:
3922:
3912:
3903:
3893:
3884:
3874:
3868:
3852:
3848:
3838:
3832:
3822:
3816:
3806:
3799:
3768:
3765:
3755:
3749:
3739:
3727:
3717:
3711:
3666:
3656:
3633:
3623:
3600:
3590:
3537:
3527:
3518:
3508:
3499:
3489:
3423:
3413:
3404:
3394:
3385:
3375:
3336:
3333:
3323:
3314:
3304:
3295:
3285:
3279:
3263:
3259:
3249:
3243:
3233:
3221:
3211:
3204:
3183:
3180:
3170:
3164:
3154:
3142:
3132:
3126:
3091:
3086:
3076:
3070:
3060:
3048:
3038:
3031:
3013:
3010:
3000:
2994:
2984:
2972:
2962:
2956:
2898:
2893:
2883:
2877:
2867:
2855:
2845:
2838:
2811:
2808:
2798:
2789:
2779:
2770:
2760:
2754:
2738:
2734:
2724:
2718:
2708:
2702:
2692:
2685:
2665:
2660:
2650:
2644:
2634:
2627:
2603:
2598:
2588:
2581:
2567:
2562:
2552:
2546:
2536:
2524:
2514:
2507:
2477:
2467:
2461:
2451:
2436:
2426:
2397:
2387:
2312:
2302:
2296:
2286:
2238:
2228:
2205:
2195:
2172:
2162:
2136:
2126:
2120:
2110:
2088:
2078:
2046:
2035:
2023:
1996:
1967:
1957:
1868:
1858:
1832:
1822:
1799:
1789:
1726:
1716:
1697:
1687:
1589:
1579:
1556:
1546:
1536:Consider the structure factor
1398:
1393:
1383:
1376:
1356:
1351:
1341:
1334:
1324:
1314:
1278:
1273:
1263:
1256:
1236:
1231:
1221:
1214:
1204:
1194:
1132:
1122:
1099:
1089:
1061:
1051:
1034:
1024:
1015:
1005:
977:
967:
950:
940:
931:
921:
874:
869:
859:
852:
845:
835:
809:
799:
752:
748:
738:
731:
724:
714:
694:{\displaystyle e^{i\phi _{g}}}
650:
646:
636:
629:
608:
598:
551:
541:
514:
504:
490:measured during a diffraction
462:
452:
385:
375:
348:
338:
273:
263:
236:
226:
149:
139:
116:
106:
1:
6895:10.1016/S1076-5670(08)70157-5
5916:function, is substituted for
2218:are known, then the phase of
1647:{\displaystyle {\textbf {r}}}
1623:{\displaystyle {\textbf {k}}}
1569:in the following form, where
1166:{\displaystyle {\textbf {u}}}
581:{\displaystyle {\textbf {g}}}
206:{\displaystyle {\textbf {k}}}
182:{\displaystyle {\textbf {r}}}
6772:Microscopy and Microanalysis
5805:is the Fourier transform of
5343:. That is, when the product
621:has an amplitude term (i.e.
6456:Chinese Academy of Sciences
6252:{\displaystyle \Sigma _{2}}
4735:In the above distribution,
3943:The most probable value of
3573:{\displaystyle \Sigma _{2}}
1149:terms are phase terms, and
92:can be related through the
7954:
7651:Immune electron microscopy
7569:Annular dark-field imaging
7384:Everhart–Thornley detector
6978:Surface Review and Letters
6382:in 1999. It is written in
6204:Gerchberg-Saxton algorithm
5277:Then, the distribution of
3646:are known, then the phase
2255:Triplet Phase Relationship
1606:for each atom at position
15:
7893:
7805:Hitachi High-Technologies
7107:10.1107/S2052252514028188
6998:10.1142/S0218625X98001444
6955:10.1107/S0108767398014408
6792:10.1017/S1431927603030332
6749:10.1107/S0365110X55001485
6716:10.1107/S0365110X56001741
6658:10.1107/S0365110X52000150
6626:10.1107/S0365110X52000149
6599:10.1107/S0365110X52000137
4887:{\displaystyle \approx 0}
1145:are amplitude terms, the
664:) and a phase term (i.e.
527:can also be written in a
7830:Thermo Fisher Scientific
7656:Geometric phase analysis
7544:Aberration-Corrected TEM
6553:Electron crystallography
6347:cryo-electron microscopy
6332:metal-organic frameworks
4278:Practical Considerations
1654:is the position of atom
1604:atomic scattering factor
7579:Charge contrast imaging
7389:Field electron emission
6412:Northwestern University
4297:Kinematical Diffraction
2827:In the above equation,
7769:Thomas Eugene Everhart
6843:10.1098/rspa.1939.0129
6736:Acta Crystallographica
6703:Acta Crystallographica
6645:Acta Crystallographica
6614:Acta Crystallographica
6587:Acta Crystallographica
6380:University of Nijmegen
6316:diffraction tomography
6253:
6215:
6176:
6143:
6110:
6074:
5943:
5906:
5873:
5832:
5799:
5764:
5623:
5487:
5412:
5337:
5304:
5268:
5158:
5125:
5092:
4954:
4921:
4888:
4865:
4832:
4799:
4762:
4726:
4557:
4333:of that distribution:
4268:
3970:
3934:
3673:
3640:
3607:
3574:
3544:
3472:
3345:
3107:
2921:
2818:
2487:
2404:
2245:
2212:
2179:
2143:
2059:
1935:
1839:
1806:
1770:
1668:
1648:
1624:
1596:
1563:
1516:Unitary Sayre Equation
1443:Acta Crystallographica
1415:
1295:
1167:
1139:
1106:
1070:
986:
888:
816:
780:
695:
658:
615:
582:
558:
521:
469:
434:
319:
207:
183:
156:
123:
7774:Vernon Ellis Cosslett
7594:Dark-field microscopy
6548:Dynamical diffraction
6254:
6213:
6177:
6144:
6111:
6075:
5944:
5907:
5874:
5846:(e.g. 1s, 2s, etc.).
5833:
5800:
5765:
5624:
5488:
5413:
5338:
5305:
5269:
5159:
5126:
5093:
4955:
4922:
4889:
4866:
4833:
4800:
4763:
4727:
4558:
4287:Sufficient Conditions
4269:
3971:
3935:
3674:
3641:
3608:
3575:
3545:
3473:
3346:
3108:
2933:central limit theorem
2922:
2819:
2488:
2405:
2246:
2213:
2180:
2144:
2060:
1936:
1840:
1807:
1771:
1669:
1649:
1625:
1597:
1564:
1416:
1296:
1168:
1140:
1107:
1071:
987:
889:
817:
781:
696:
659:
616:
583:
559:
522:
470:
435:
320:
208:
184:
157:
124:
7779:Vladimir K. Zworykin
7429:Correlative light EM
7338:Electron diffraction
7206:10.1042/etls20170082
6558:Electron diffraction
6236:
6153:
6120:
6087:
5960:
5920:
5883:
5850:
5809:
5776:
5634:
5531:
5514:Dominated Scattering
5422:
5347:
5314:
5281:
5171:
5135:
5105:
4977:
4931:
4898:
4875:
4842:
4809:
4776:
4739:
4568:
4340:
4324:biological materials
3983:
3947:
3695:
3650:
3617:
3584:
3557:
3483:
3369:
3120:
2950:
2831:
2503:
2420:
2274:
2222:
2189:
2156:
2072:
1951:
1852:
1816:
1783:
1681:
1658:
1634:
1610:
1573:
1540:
1308:
1188:
1153:
1116:
1083:
999:
915:
829:
793:
708:
668:
625:
592:
568:
535:
498:
475:, also known as the
446:
332:
220:
193:
169:
133:
100:
88:information about a
74:electron diffraction
7938:Electron microscopy
7744:Manfred von Ardenne
7729:Gerasimos Danilatos
7636:Electron tomography
7631:Electron holography
7574:Cathodoluminescence
7353:Secondary electrons
7343:Electron scattering
7287:Electron microscopy
7273:Electron microscopy
7033:10.1038/nature01010
7025:2002Natur.419...55E
6990:1998SRL.....5.1087M
6835:1939RSPSA.173...68B
6784:2003MiMic...9..399M
5914:conjugate symmetric
5418:is large or small,
371:
259:
7866:Digital Micrograph
7472:Environmental SEM
7394:Field emission gun
7358:X-ray fluorescence
7157:10.1038/nmeth.4178
7076:10.1039/c2ce25204j
6376:Patterson function
6309:strontium titanate
6264:convex feasibility
6249:
6216:
6172:
6139:
6106:
6070:
5939:
5902:
5869:
5828:
5795:
5760:
5705:
5619:
5578:
5503:powder diffraction
5483:
5408:
5333:
5300:
5264:
5154:
5121:
5088:
4950:
4917:
4884:
4861:
4828:
4795:
4758:
4722:
4553:
4264:
4152:
4032:
3966:
3930:
3797:
3707:
3679:can be estimated.
3669:
3636:
3603:
3570:
3540:
3468:
3356:standard deviation
3341:
3103:
2917:
2814:
2483:
2400:
2340:
2241:
2208:
2175:
2139:
2106:
2055:
1992:
1931:
1893:
1835:
1802:
1766:
1712:
1664:
1644:
1620:
1592:
1559:
1411:
1291:
1163:
1135:
1102:
1066:
982:
884:
812:
776:
691:
654:
611:
578:
554:
517:
465:
430:
354:
315:
242:
203:
179:
152:
119:
7925:
7924:
7889:
7888:
7759:Nestor J. Zaluzec
7754:Maximilian Haider
7552:
7551:
6436:genetic algorithm
6336:organic compounds
6166:
6133:
6100:
6055:
6044:
6013:
5992:
5973:
5933:
5896:
5863:
5822:
5789:
5735:
5724:
5696:
5671:
5647:
5608:
5597:
5569:
5563:
5544:
5472:
5456:
5440:
5397:
5381:
5365:
5327:
5294:
5258:
5241:
5232:
5211:
5184:
5148:
5118:
5077:
5048:
5032:
5020:
5017:
5009:
4990:
4965:Intensity Mapping
4944:
4911:
4855:
4822:
4789:
4752:
4713:
4694:
4675:
4647:
4625:
4606:
4587:
4544:
4525:
4506:
4479:
4470:
4454:
4438:
4419:
4397:
4378:
4359:
4262:
4255:
4236:
4206:
4190:
4168:
4143:
4135:
4116:
4086:
4070:
4048:
4023:
4008:
3960:
3919:
3900:
3881:
3845:
3829:
3813:
3788:
3762:
3746:
3724:
3698:
3663:
3630:
3597:
3580:). If the phases
3534:
3515:
3496:
3446:
3443:
3420:
3401:
3382:
3360:Gaussian function
3330:
3311:
3292:
3256:
3240:
3218:
3177:
3161:
3139:
3083:
3067:
3045:
3007:
2991:
2969:
2890:
2874:
2852:
2805:
2786:
2767:
2731:
2715:
2699:
2657:
2641:
2595:
2559:
2543:
2521:
2474:
2458:
2433:
2413:Meaning that if:
2394:
2370:
2359:
2331:
2329:
2309:
2293:
2235:
2202:
2169:
2133:
2117:
2097:
2085:
2042:
2014:
2003:
1983:
1981:
1964:
1920:
1909:
1884:
1882:
1865:
1829:
1796:
1755:
1744:
1723:
1703:
1694:
1667:{\displaystyle l}
1641:
1617:
1586:
1553:
1390:
1348:
1321:
1270:
1228:
1201:
1160:
1129:
1096:
1058:
1031:
1012:
974:
947:
928:
866:
842:
806:
745:
721:
643:
605:
575:
548:
511:
484:periodic function
481:three-dimensional
459:
419:
409:
382:
345:
304:
294:
270:
233:
200:
176:
146:
113:
94:Fourier transform
90:crystal structure
7945:
7913:
7912:
7901:
7900:
7709:Bodo von Borries
7694:
7454:Photoemission EM
7417:
7266:
7259:
7252:
7243:
7236:
7235:
7225:
7185:
7179:
7178:
7168:
7135:
7129:
7128:
7118:
7086:
7080:
7079:
7059:
7053:
7052:
7008:
7002:
7001:
6984:(5): 1087–1106.
6973:
6967:
6966:
6938:
6929:
6928:
6922:
6918:
6916:
6908:
6888:
6872:
6866:
6865:
6853:
6847:
6846:
6818:
6812:
6811:
6767:
6754:
6753:
6751:
6727:
6721:
6720:
6718:
6672:
6663:
6662:
6660:
6636:
6630:
6629:
6609:
6603:
6602:
6582:
6372:computer program
6258:
6256:
6255:
6250:
6248:
6247:
6198:Gerchberg-Saxton
6181:
6179:
6178:
6173:
6168:
6167:
6148:
6146:
6145:
6140:
6135:
6134:
6115:
6113:
6112:
6107:
6102:
6101:
6079:
6077:
6076:
6071:
6057:
6056:
6042:
6023:
6015:
6014:
6002:
5994:
5993:
5975:
5974:
5948:
5946:
5945:
5940:
5935:
5934:
5911:
5909:
5908:
5903:
5898:
5897:
5878:
5876:
5875:
5870:
5865:
5864:
5837:
5835:
5834:
5829:
5824:
5823:
5804:
5802:
5801:
5796:
5791:
5790:
5769:
5767:
5766:
5761:
5759:
5758:
5753:
5752:
5745:
5744:
5743:
5742:
5737:
5736:
5726:
5725:
5704:
5695:
5694:
5688:
5687:
5682:
5673:
5672:
5660:
5649:
5648:
5628:
5626:
5625:
5620:
5618:
5617:
5616:
5615:
5610:
5609:
5599:
5598:
5577:
5565:
5564:
5546:
5545:
5492:
5490:
5489:
5484:
5482:
5474:
5473:
5458:
5457:
5442:
5441:
5429:
5417:
5415:
5414:
5409:
5407:
5399:
5398:
5383:
5382:
5367:
5366:
5354:
5342:
5340:
5339:
5334:
5329:
5328:
5309:
5307:
5306:
5301:
5296:
5295:
5273:
5271:
5270:
5265:
5260:
5259:
5247:
5242:
5240:
5238:
5234:
5233:
5220:
5218:
5217:
5213:
5212:
5186:
5185:
5163:
5161:
5160:
5155:
5150:
5149:
5130:
5128:
5127:
5122:
5120:
5119:
5097:
5095:
5094:
5089:
5087:
5079:
5078:
5066:
5058:
5050:
5049:
5037:
5030:
5018:
5015:
5011:
5010:
4992:
4991:
4959:
4957:
4956:
4951:
4946:
4945:
4926:
4924:
4923:
4918:
4913:
4912:
4893:
4891:
4890:
4885:
4870:
4868:
4867:
4862:
4857:
4856:
4837:
4835:
4834:
4829:
4824:
4823:
4804:
4802:
4801:
4796:
4791:
4790:
4767:
4765:
4764:
4759:
4754:
4753:
4731:
4729:
4728:
4723:
4715:
4714:
4696:
4695:
4677:
4676:
4649:
4648:
4627:
4626:
4608:
4607:
4589:
4588:
4562:
4560:
4559:
4554:
4546:
4545:
4527:
4526:
4508:
4507:
4480:
4478:
4476:
4472:
4471:
4456:
4455:
4440:
4439:
4426:
4421:
4420:
4399:
4398:
4380:
4379:
4361:
4360:
4273:
4271:
4270:
4265:
4263:
4261:
4257:
4256:
4238:
4237:
4216:
4208:
4207:
4192:
4191:
4170:
4169:
4157:
4151:
4141:
4137:
4136:
4118:
4117:
4096:
4088:
4087:
4072:
4071:
4050:
4049:
4037:
4031:
4021:
4010:
4009:
3975:
3973:
3972:
3967:
3962:
3961:
3939:
3937:
3936:
3931:
3929:
3928:
3921:
3920:
3902:
3901:
3883:
3882:
3855:
3847:
3846:
3831:
3830:
3815:
3814:
3802:
3796:
3764:
3763:
3748:
3747:
3726:
3725:
3706:
3678:
3676:
3675:
3670:
3665:
3664:
3645:
3643:
3642:
3637:
3632:
3631:
3612:
3610:
3609:
3604:
3599:
3598:
3579:
3577:
3576:
3571:
3569:
3568:
3549:
3547:
3546:
3541:
3536:
3535:
3517:
3516:
3498:
3497:
3477:
3475:
3474:
3469:
3444:
3441:
3422:
3421:
3403:
3402:
3384:
3383:
3350:
3348:
3347:
3342:
3340:
3339:
3332:
3331:
3313:
3312:
3294:
3293:
3266:
3258:
3257:
3242:
3241:
3220:
3219:
3207:
3179:
3178:
3163:
3162:
3141:
3140:
3112:
3110:
3109:
3104:
3102:
3101:
3100:
3099:
3094:
3085:
3084:
3069:
3068:
3047:
3046:
3034:
3009:
3008:
2993:
2992:
2971:
2970:
2926:
2924:
2923:
2918:
2907:
2906:
2901:
2892:
2891:
2876:
2875:
2854:
2853:
2841:
2823:
2821:
2820:
2815:
2807:
2806:
2788:
2787:
2769:
2768:
2741:
2733:
2732:
2717:
2716:
2701:
2700:
2688:
2674:
2673:
2668:
2659:
2658:
2643:
2642:
2630:
2625:
2624:
2612:
2611:
2606:
2597:
2596:
2584:
2576:
2575:
2570:
2561:
2560:
2545:
2544:
2523:
2522:
2510:
2492:
2490:
2489:
2484:
2476:
2475:
2460:
2459:
2435:
2434:
2409:
2407:
2406:
2401:
2396:
2395:
2380:
2379:
2378:
2377:
2372:
2371:
2361:
2360:
2339:
2330:
2322:
2311:
2310:
2295:
2294:
2250:
2248:
2247:
2242:
2237:
2236:
2217:
2215:
2214:
2209:
2204:
2203:
2184:
2182:
2181:
2176:
2171:
2170:
2148:
2146:
2145:
2140:
2135:
2134:
2119:
2118:
2105:
2087:
2086:
2064:
2062:
2061:
2056:
2054:
2053:
2044:
2043:
2022:
2021:
2016:
2015:
2005:
2004:
1991:
1982:
1974:
1966:
1965:
1940:
1938:
1937:
1932:
1930:
1929:
1928:
1927:
1922:
1921:
1911:
1910:
1892:
1883:
1875:
1867:
1866:
1844:
1842:
1841:
1836:
1831:
1830:
1811:
1809:
1808:
1803:
1798:
1797:
1775:
1773:
1772:
1767:
1765:
1764:
1763:
1762:
1757:
1756:
1746:
1745:
1725:
1724:
1711:
1696:
1695:
1673:
1671:
1670:
1665:
1653:
1651:
1650:
1645:
1643:
1642:
1629:
1627:
1626:
1621:
1619:
1618:
1601:
1599:
1598:
1593:
1588:
1587:
1568:
1566:
1565:
1560:
1555:
1554:
1530:electron-density
1420:
1418:
1417:
1412:
1407:
1406:
1401:
1392:
1391:
1379:
1365:
1364:
1359:
1350:
1349:
1337:
1323:
1322:
1300:
1298:
1297:
1292:
1287:
1286:
1281:
1272:
1271:
1259:
1245:
1244:
1239:
1230:
1229:
1217:
1203:
1202:
1172:
1170:
1169:
1164:
1162:
1161:
1144:
1142:
1141:
1136:
1131:
1130:
1111:
1109:
1108:
1103:
1098:
1097:
1075:
1073:
1072:
1067:
1065:
1064:
1060:
1059:
1033:
1032:
1014:
1013:
991:
989:
988:
983:
981:
980:
976:
975:
949:
948:
930:
929:
893:
891:
890:
885:
883:
882:
877:
868:
867:
855:
844:
843:
821:
819:
818:
813:
808:
807:
785:
783:
782:
777:
775:
774:
773:
772:
755:
747:
746:
734:
723:
722:
700:
698:
697:
692:
690:
689:
688:
687:
663:
661:
660:
655:
653:
645:
644:
632:
620:
618:
617:
612:
607:
606:
587:
585:
584:
579:
577:
576:
563:
561:
560:
555:
550:
549:
526:
524:
523:
518:
513:
512:
477:structure factor
474:
472:
471:
466:
461:
460:
439:
437:
436:
431:
423:
422:
421:
420:
411:
410:
384:
383:
370:
365:
347:
346:
324:
322:
321:
316:
308:
307:
306:
305:
296:
295:
272:
271:
258:
253:
235:
234:
212:
210:
209:
204:
202:
201:
188:
186:
185:
180:
178:
177:
161:
159:
158:
153:
148:
147:
128:
126:
125:
120:
115:
114:
86:reciprocal space
7953:
7952:
7948:
7947:
7946:
7944:
7943:
7942:
7928:
7927:
7926:
7921:
7885:
7834:
7783:
7764:Ondrej Krivanek
7685:
7548:
7496:
7458:
7444:Liquid-Phase EM
7408:
7367:Instrumentation
7362:
7320:
7311:
7275:
7270:
7240:
7239:
7187:
7186:
7182:
7137:
7136:
7132:
7088:
7087:
7083:
7061:
7060:
7056:
7019:(6902): 55–58.
7010:
7009:
7005:
6975:
6974:
6970:
6940:
6939:
6932:
6919:
6909:
6905:
6874:
6873:
6869:
6855:
6854:
6850:
6820:
6819:
6815:
6769:
6768:
6757:
6729:
6728:
6724:
6698:
6691:
6674:
6673:
6666:
6638:
6637:
6633:
6611:
6610:
6606:
6584:
6583:
6576:
6571:
6528:Crystallography
6524:
6496:
6452:
6397:
6368:
6363:
6324:thermoelectrics
6297:magnesium oxide
6288:
6239:
6234:
6233:
6221:
6200:
6188:
6151:
6150:
6118:
6117:
6085:
6084:
5958:
5957:
5918:
5917:
5881:
5880:
5848:
5847:
5807:
5806:
5774:
5773:
5746:
5730:
5706:
5677:
5632:
5631:
5603:
5579:
5529:
5528:
5420:
5419:
5345:
5344:
5312:
5311:
5279:
5278:
5221:
5193:
5169:
5168:
5133:
5132:
5103:
5102:
4975:
4974:
4929:
4928:
4896:
4895:
4873:
4872:
4840:
4839:
4807:
4806:
4774:
4773:
4737:
4736:
4566:
4565:
4427:
4338:
4337:
4289:
4280:
4142:
4022:
3981:
3980:
3945:
3944:
3783:
3693:
3692:
3685:
3683:Tangent Formula
3648:
3647:
3615:
3614:
3582:
3581:
3560:
3555:
3554:
3481:
3480:
3367:
3366:
3192:
3118:
3117:
3089:
3022:
2948:
2947:
2896:
2829:
2828:
2663:
2616:
2601:
2565:
2501:
2500:
2418:
2417:
2365:
2341:
2272:
2271:
2257:
2220:
2219:
2187:
2186:
2154:
2153:
2070:
2069:
2045:
2009:
1949:
1948:
1915:
1894:
1850:
1849:
1814:
1813:
1781:
1780:
1750:
1729:
1679:
1678:
1656:
1655:
1632:
1631:
1608:
1607:
1571:
1570:
1538:
1537:
1518:
1513:
1476:
1436:introduced the
1430:
1396:
1354:
1306:
1305:
1276:
1234:
1186:
1185:
1151:
1150:
1114:
1113:
1081:
1080:
1037:
997:
996:
953:
913:
912:
872:
827:
826:
791:
790:
764:
756:
706:
705:
679:
671:
666:
665:
623:
622:
590:
589:
566:
565:
533:
532:
496:
495:
444:
443:
388:
330:
329:
276:
218:
217:
191:
190:
167:
166:
131:
130:
98:
97:
80:potential. The
70:
65:
25:crystallography
21:
12:
11:
5:
7951:
7949:
7941:
7940:
7930:
7929:
7923:
7922:
7920:
7919:
7907:
7894:
7891:
7890:
7887:
7886:
7884:
7883:
7878:
7873:
7871:Direct methods
7868:
7863:
7858:
7853:
7848:
7842:
7840:
7836:
7835:
7833:
7832:
7827:
7822:
7817:
7812:
7807:
7802:
7797:
7791:
7789:
7785:
7784:
7782:
7781:
7776:
7771:
7766:
7761:
7756:
7751:
7746:
7741:
7736:
7731:
7726:
7721:
7719:Ernst G. Bauer
7716:
7711:
7706:
7700:
7698:
7691:
7687:
7686:
7684:
7683:
7678:
7673:
7668:
7663:
7658:
7653:
7648:
7643:
7638:
7633:
7628:
7623:
7618:
7613:
7612:
7611:
7601:
7596:
7591:
7586:
7581:
7576:
7571:
7566:
7560:
7558:
7554:
7553:
7550:
7549:
7547:
7546:
7541:
7540:
7539:
7529:
7524:
7519:
7518:
7517:
7506:
7504:
7498:
7497:
7495:
7494:
7489:
7484:
7479:
7474:
7468:
7466:
7460:
7459:
7457:
7456:
7451:
7446:
7441:
7436:
7431:
7425:
7423:
7414:
7410:
7409:
7407:
7406:
7401:
7396:
7391:
7386:
7381:
7376:
7370:
7368:
7364:
7363:
7361:
7360:
7355:
7350:
7345:
7340:
7335:
7333:Bremsstrahlung
7330:
7324:
7322:
7313:
7312:
7310:
7309:
7304:
7299:
7294:
7289:
7283:
7281:
7277:
7276:
7271:
7269:
7268:
7261:
7254:
7246:
7238:
7237:
7180:
7151:(4): 399–402.
7145:Nature Methods
7130:
7101:(2): 267–282.
7081:
7054:
7003:
6968:
6949:(4): 601–612.
6930:
6921:|journal=
6903:
6886:10.1.1.75.9091
6867:
6848:
6829:(952): 68–82.
6813:
6778:(5): 399–410.
6755:
6742:(8): 473–478.
6722:
6709:(8): 635–651.
6696:
6689:
6664:
6631:
6604:
6573:
6572:
6570:
6567:
6566:
6565:
6560:
6555:
6550:
6545:
6540:
6535:
6530:
6523:
6520:
6495:
6492:
6466:ne-wavelength
6451:
6448:
6432:non-commercial
6416:Laurence Marks
6396:
6393:
6367:
6364:
6362:
6359:
6340:intermetallics
6287:
6284:
6246:
6242:
6220:
6217:
6199:
6196:
6187:
6186:Implementation
6184:
6171:
6161:
6158:
6138:
6128:
6125:
6105:
6095:
6092:
6081:
6080:
6069:
6066:
6063:
6060:
6050:
6047:
6041:
6038:
6035:
6032:
6029:
6026:
6022:
6018:
6008:
6005:
6001:
5997:
5987:
5984:
5981:
5978:
5968:
5965:
5938:
5928:
5925:
5901:
5891:
5888:
5868:
5858:
5855:
5827:
5817:
5814:
5794:
5784:
5781:
5771:
5770:
5757:
5751:
5741:
5729:
5719:
5716:
5713:
5709:
5703:
5699:
5693:
5686:
5681:
5676:
5666:
5663:
5659:
5655:
5652:
5642:
5639:
5629:
5614:
5602:
5592:
5589:
5586:
5582:
5576:
5572:
5568:
5558:
5555:
5552:
5549:
5539:
5536:
5517:
5516:
5481:
5477:
5467:
5464:
5461:
5451:
5448:
5445:
5435:
5432:
5428:
5406:
5402:
5392:
5389:
5386:
5376:
5373:
5370:
5360:
5357:
5353:
5332:
5322:
5319:
5299:
5289:
5286:
5275:
5274:
5263:
5253:
5250:
5246:
5237:
5227:
5224:
5216:
5206:
5203:
5200:
5196:
5192:
5189:
5179:
5176:
5153:
5143:
5140:
5113:
5110:
5099:
5098:
5086:
5082:
5072:
5069:
5065:
5061:
5057:
5053:
5043:
5040:
5036:
5029:
5026:
5023:
5014:
5004:
5001:
4998:
4995:
4985:
4982:
4968:
4967:
4949:
4939:
4936:
4916:
4906:
4903:
4883:
4880:
4860:
4850:
4847:
4827:
4817:
4814:
4794:
4784:
4781:
4757:
4747:
4744:
4733:
4732:
4721:
4718:
4708:
4705:
4702:
4699:
4689:
4686:
4683:
4680:
4670:
4667:
4664:
4661:
4658:
4655:
4652:
4642:
4639:
4636:
4633:
4630:
4620:
4617:
4614:
4611:
4601:
4598:
4595:
4592:
4582:
4579:
4576:
4573:
4563:
4552:
4549:
4539:
4536:
4533:
4530:
4520:
4517:
4514:
4511:
4501:
4498:
4495:
4492:
4489:
4486:
4483:
4475:
4465:
4462:
4459:
4449:
4446:
4443:
4433:
4430:
4424:
4414:
4411:
4408:
4405:
4402:
4392:
4389:
4386:
4383:
4373:
4370:
4367:
4364:
4354:
4351:
4348:
4345:
4316:
4315:
4300:
4299:
4288:
4285:
4279:
4276:
4275:
4274:
4260:
4250:
4247:
4244:
4241:
4231:
4228:
4225:
4222:
4219:
4215:
4211:
4201:
4198:
4195:
4185:
4182:
4179:
4176:
4173:
4163:
4160:
4156:
4150:
4146:
4140:
4130:
4127:
4124:
4121:
4111:
4108:
4105:
4102:
4099:
4095:
4091:
4081:
4078:
4075:
4065:
4062:
4059:
4056:
4053:
4043:
4040:
4036:
4030:
4026:
4019:
4016:
4013:
4003:
4000:
3997:
3994:
3991:
3988:
3965:
3955:
3952:
3941:
3940:
3927:
3924:
3914:
3911:
3908:
3905:
3895:
3892:
3889:
3886:
3876:
3873:
3870:
3867:
3864:
3861:
3858:
3854:
3850:
3840:
3837:
3834:
3824:
3821:
3818:
3808:
3805:
3801:
3795:
3791:
3786:
3782:
3779:
3776:
3773:
3770:
3767:
3757:
3754:
3751:
3741:
3738:
3735:
3732:
3729:
3719:
3716:
3713:
3710:
3705:
3701:
3684:
3681:
3668:
3658:
3655:
3635:
3625:
3622:
3602:
3592:
3589:
3567:
3563:
3551:
3550:
3539:
3529:
3526:
3523:
3520:
3510:
3507:
3504:
3501:
3491:
3488:
3478:
3467:
3464:
3461:
3458:
3455:
3452:
3449:
3440:
3437:
3434:
3431:
3428:
3425:
3415:
3412:
3409:
3406:
3396:
3393:
3390:
3387:
3377:
3374:
3352:
3351:
3338:
3335:
3325:
3322:
3319:
3316:
3306:
3303:
3300:
3297:
3287:
3284:
3281:
3278:
3275:
3272:
3269:
3265:
3261:
3251:
3248:
3245:
3235:
3232:
3229:
3226:
3223:
3213:
3210:
3206:
3202:
3199:
3195:
3191:
3188:
3185:
3182:
3172:
3169:
3166:
3156:
3153:
3150:
3147:
3144:
3134:
3131:
3128:
3125:
3114:
3113:
3098:
3093:
3088:
3078:
3075:
3072:
3062:
3059:
3056:
3053:
3050:
3040:
3037:
3033:
3029:
3025:
3021:
3018:
3015:
3012:
3002:
2999:
2996:
2986:
2983:
2980:
2977:
2974:
2964:
2961:
2958:
2955:
2916:
2913:
2910:
2905:
2900:
2895:
2885:
2882:
2879:
2869:
2866:
2863:
2860:
2857:
2847:
2844:
2840:
2836:
2825:
2824:
2813:
2810:
2800:
2797:
2794:
2791:
2781:
2778:
2775:
2772:
2762:
2759:
2756:
2753:
2750:
2747:
2744:
2740:
2736:
2726:
2723:
2720:
2710:
2707:
2704:
2694:
2691:
2687:
2683:
2680:
2677:
2672:
2667:
2662:
2652:
2649:
2646:
2636:
2633:
2629:
2623:
2619:
2615:
2610:
2605:
2600:
2590:
2587:
2583:
2579:
2574:
2569:
2564:
2554:
2551:
2548:
2538:
2535:
2532:
2529:
2526:
2516:
2513:
2509:
2494:
2493:
2482:
2479:
2469:
2466:
2463:
2453:
2450:
2447:
2444:
2441:
2438:
2428:
2425:
2411:
2410:
2399:
2389:
2386:
2383:
2376:
2364:
2354:
2351:
2348:
2344:
2338:
2334:
2328:
2325:
2320:
2317:
2314:
2304:
2301:
2298:
2288:
2285:
2282:
2279:
2256:
2253:
2240:
2230:
2227:
2207:
2197:
2194:
2174:
2164:
2161:
2150:
2149:
2138:
2128:
2125:
2122:
2112:
2109:
2104:
2100:
2096:
2093:
2090:
2080:
2077:
2066:
2065:
2052:
2048:
2037:
2034:
2031:
2028:
2025:
2020:
2008:
1998:
1995:
1990:
1986:
1980:
1977:
1972:
1969:
1959:
1956:
1942:
1941:
1926:
1914:
1904:
1901:
1897:
1891:
1887:
1881:
1878:
1873:
1870:
1860:
1857:
1834:
1824:
1821:
1801:
1791:
1788:
1777:
1776:
1761:
1749:
1739:
1736:
1732:
1728:
1718:
1715:
1710:
1706:
1702:
1699:
1689:
1686:
1663:
1591:
1581:
1578:
1558:
1548:
1545:
1517:
1514:
1512:
1509:
1475:
1472:
1438:Sayre equation
1429:
1426:
1422:
1421:
1410:
1405:
1400:
1395:
1385:
1382:
1378:
1374:
1371:
1368:
1363:
1358:
1353:
1343:
1340:
1336:
1332:
1329:
1326:
1316:
1313:
1302:
1301:
1290:
1285:
1280:
1275:
1265:
1262:
1258:
1254:
1251:
1248:
1243:
1238:
1233:
1223:
1220:
1216:
1212:
1209:
1206:
1196:
1193:
1134:
1124:
1121:
1101:
1091:
1088:
1077:
1076:
1063:
1053:
1050:
1047:
1044:
1040:
1036:
1026:
1023:
1020:
1017:
1007:
1004:
993:
992:
979:
969:
966:
963:
960:
956:
952:
942:
939:
936:
933:
923:
920:
895:
894:
881:
876:
871:
861:
858:
854:
850:
847:
837:
834:
811:
801:
798:
787:
786:
771:
767:
763:
759:
754:
750:
740:
737:
733:
729:
726:
716:
713:
686:
682:
678:
674:
652:
648:
638:
635:
631:
610:
600:
597:
553:
543:
540:
516:
506:
503:
464:
454:
451:
441:
440:
429:
426:
414:
404:
401:
398:
395:
391:
387:
377:
374:
369:
364:
361:
357:
353:
350:
340:
337:
326:
325:
314:
311:
299:
289:
286:
283:
279:
275:
265:
262:
257:
252:
249:
245:
241:
238:
228:
225:
151:
141:
138:
118:
108:
105:
69:
66:
64:
61:
29:direct methods
13:
10:
9:
6:
4:
3:
2:
7950:
7939:
7936:
7935:
7933:
7918:
7917:
7908:
7906:
7905:
7896:
7895:
7892:
7882:
7879:
7877:
7874:
7872:
7869:
7867:
7864:
7862:
7859:
7857:
7854:
7852:
7849:
7847:
7844:
7843:
7841:
7837:
7831:
7828:
7826:
7823:
7821:
7818:
7816:
7813:
7811:
7808:
7806:
7803:
7801:
7798:
7796:
7795:Carl Zeiss AG
7793:
7792:
7790:
7788:Manufacturers
7786:
7780:
7777:
7775:
7772:
7770:
7767:
7765:
7762:
7760:
7757:
7755:
7752:
7750:
7747:
7745:
7742:
7740:
7739:James Hillier
7737:
7735:
7732:
7730:
7727:
7725:
7722:
7720:
7717:
7715:
7712:
7710:
7707:
7705:
7702:
7701:
7699:
7695:
7692:
7688:
7682:
7679:
7677:
7674:
7672:
7669:
7667:
7664:
7662:
7659:
7657:
7654:
7652:
7649:
7647:
7644:
7642:
7639:
7637:
7634:
7632:
7629:
7627:
7624:
7622:
7619:
7617:
7614:
7610:
7607:
7606:
7605:
7602:
7600:
7597:
7595:
7592:
7590:
7587:
7585:
7582:
7580:
7577:
7575:
7572:
7570:
7567:
7565:
7562:
7561:
7559:
7555:
7545:
7542:
7538:
7535:
7534:
7533:
7530:
7528:
7525:
7523:
7520:
7516:
7513:
7512:
7511:
7508:
7507:
7505:
7503:
7499:
7493:
7492:Ultrafast SEM
7490:
7488:
7485:
7483:
7480:
7478:
7475:
7473:
7470:
7469:
7467:
7465:
7461:
7455:
7452:
7450:
7449:Low-energy EM
7447:
7445:
7442:
7440:
7437:
7435:
7432:
7430:
7427:
7426:
7424:
7422:
7418:
7415:
7411:
7405:
7402:
7400:
7399:Magnetic lens
7397:
7395:
7392:
7390:
7387:
7385:
7382:
7380:
7377:
7375:
7372:
7371:
7369:
7365:
7359:
7356:
7354:
7351:
7349:
7348:Kikuchi lines
7346:
7344:
7341:
7339:
7336:
7334:
7331:
7329:
7326:
7325:
7323:
7318:
7314:
7308:
7305:
7303:
7300:
7298:
7295:
7293:
7290:
7288:
7285:
7284:
7282:
7278:
7274:
7267:
7262:
7260:
7255:
7253:
7248:
7247:
7244:
7233:
7229:
7224:
7219:
7215:
7211:
7207:
7203:
7199:
7195:
7191:
7184:
7181:
7176:
7172:
7167:
7162:
7158:
7154:
7150:
7146:
7142:
7134:
7131:
7126:
7122:
7117:
7112:
7108:
7104:
7100:
7096:
7092:
7085:
7082:
7077:
7073:
7069:
7065:
7058:
7055:
7050:
7046:
7042:
7038:
7034:
7030:
7026:
7022:
7018:
7014:
7007:
7004:
6999:
6995:
6991:
6987:
6983:
6979:
6972:
6969:
6964:
6960:
6956:
6952:
6948:
6944:
6937:
6935:
6931:
6926:
6914:
6906:
6904:9780120147373
6900:
6896:
6892:
6887:
6882:
6878:
6871:
6868:
6864:(2): 237–246.
6863:
6859:
6852:
6849:
6844:
6840:
6836:
6832:
6828:
6824:
6817:
6814:
6809:
6805:
6801:
6797:
6793:
6789:
6785:
6781:
6777:
6773:
6766:
6764:
6762:
6760:
6756:
6750:
6745:
6741:
6737:
6733:
6726:
6723:
6717:
6712:
6708:
6704:
6700:
6695:
6688:
6684:
6680:
6671:
6669:
6665:
6659:
6654:
6650:
6646:
6642:
6635:
6632:
6627:
6623:
6619:
6615:
6608:
6605:
6600:
6596:
6592:
6588:
6581:
6579:
6575:
6568:
6564:
6561:
6559:
6556:
6554:
6551:
6549:
6546:
6544:
6541:
6539:
6536:
6534:
6531:
6529:
6526:
6525:
6521:
6519:
6517:
6512:
6508:
6507:
6501:
6500:seminvariants
6493:
6491:
6489:
6485:
6481:
6477:
6474:cattering or
6473:
6469:
6465:
6461:
6457:
6449:
6447:
6445:
6441:
6437:
6433:
6429:
6425:
6421:
6417:
6414:by Professor
6413:
6409:
6405:
6401:
6394:
6392:
6390:
6385:
6381:
6377:
6373:
6365:
6360:
6358:
6356:
6352:
6348:
6343:
6341:
6337:
6333:
6329:
6325:
6321:
6317:
6312:
6310:
6306:
6302:
6298:
6294:
6285:
6283:
6281:
6277:
6273:
6269:
6265:
6260:
6244:
6231:
6227:
6218:
6212:
6208:
6205:
6197:
6195:
6193:
6185:
6183:
6156:
6123:
6090:
6067:
6064:
6061:
6045:
6039:
6036:
6033:
6030:
6027:
6024:
6003:
5982:
5979:
5963:
5956:
5955:
5954:
5952:
5923:
5915:
5886:
5853:
5845:
5841:
5812:
5779:
5755:
5739:
5727:
5717:
5714:
5711:
5707:
5701:
5697:
5684:
5661:
5653:
5637:
5630:
5612:
5600:
5590:
5587:
5584:
5580:
5574:
5570:
5553:
5550:
5527:
5526:
5525:
5523:
5515:
5512:
5511:
5510:
5508:
5504:
5499:
5497:
5462:
5446:
5430:
5387:
5371:
5355:
5317:
5284:
5248:
5244:
5222:
5201:
5198:
5194:
5190:
5174:
5167:
5166:
5165:
5138:
5108:
5067:
5059:
5038:
5027:
5024:
5021:
4999:
4996:
4980:
4973:
4972:
4971:
4966:
4963:
4962:
4961:
4934:
4901:
4881:
4878:
4845:
4812:
4779:
4771:
4770:normalization
4742:
4703:
4700:
4684:
4681:
4665:
4659:
4656:
4653:
4637:
4634:
4615:
4612:
4596:
4593:
4577:
4571:
4564:
4534:
4531:
4515:
4512:
4496:
4490:
4487:
4484:
4481:
4460:
4444:
4428:
4409:
4406:
4387:
4384:
4368:
4365:
4349:
4343:
4336:
4335:
4334:
4332:
4327:
4325:
4321:
4314:
4311:
4310:
4309:
4306:
4298:
4295:
4294:
4293:
4286:
4284:
4277:
4245:
4242:
4226:
4223:
4220:
4217:
4196:
4180:
4177:
4174:
4158:
4148:
4144:
4125:
4122:
4106:
4103:
4100:
4097:
4076:
4060:
4057:
4054:
4038:
4028:
4024:
4017:
3998:
3992:
3989:
3986:
3979:
3978:
3977:
3950:
3909:
3906:
3890:
3887:
3871:
3865:
3862:
3859:
3856:
3835:
3819:
3803:
3793:
3789:
3784:
3780:
3777:
3774:
3771:
3752:
3736:
3733:
3730:
3714:
3708:
3703:
3699:
3691:
3690:
3689:
3682:
3680:
3653:
3620:
3587:
3565:
3524:
3521:
3505:
3502:
3486:
3479:
3465:
3462:
3459:
3456:
3453:
3450:
3447:
3438:
3435:
3432:
3429:
3426:
3410:
3407:
3391:
3388:
3372:
3365:
3364:
3363:
3361:
3357:
3320:
3317:
3301:
3298:
3282:
3276:
3273:
3270:
3267:
3246:
3230:
3227:
3224:
3208:
3200:
3197:
3193:
3189:
3186:
3167:
3151:
3148:
3145:
3129:
3123:
3116:
3115:
3096:
3073:
3057:
3054:
3051:
3035:
3027:
3023:
3019:
3016:
2997:
2981:
2978:
2975:
2959:
2953:
2946:
2945:
2944:
2942:
2938:
2937:distributions
2934:
2930:
2914:
2911:
2903:
2880:
2864:
2861:
2858:
2842:
2795:
2792:
2776:
2773:
2757:
2751:
2748:
2745:
2742:
2721:
2705:
2689:
2681:
2678:
2675:
2670:
2647:
2631:
2621:
2617:
2613:
2608:
2585:
2577:
2572:
2549:
2533:
2530:
2527:
2511:
2499:
2498:
2497:
2464:
2448:
2442:
2439:
2423:
2416:
2415:
2414:
2384:
2381:
2374:
2362:
2352:
2349:
2346:
2342:
2336:
2332:
2326:
2323:
2318:
2299:
2283:
2277:
2270:
2269:
2268:
2266:
2261:
2254:
2252:
2225:
2192:
2159:
2123:
2107:
2102:
2098:
2094:
2091:
2075:
2068:
2067:
2050:
2032:
2029:
2026:
2018:
2006:
1993:
1988:
1984:
1978:
1975:
1970:
1954:
1947:
1946:
1945:
1924:
1912:
1902:
1899:
1895:
1889:
1885:
1879:
1876:
1871:
1855:
1848:
1847:
1846:
1819:
1786:
1759:
1747:
1737:
1734:
1730:
1713:
1708:
1704:
1700:
1684:
1677:
1676:
1675:
1661:
1605:
1576:
1543:
1534:
1531:
1527:
1523:
1515:
1510:
1508:
1506:
1502:
1498:
1494:
1490:
1486:
1482:
1473:
1471:
1469:
1465:
1461:
1457:
1453:
1449:
1445:
1444:
1439:
1435:
1427:
1425:
1403:
1380:
1369:
1361:
1327:
1311:
1304:
1303:
1283:
1260:
1249:
1241:
1218:
1207:
1191:
1184:
1183:
1182:
1180:
1176:
1148:
1119:
1086:
1048:
1045:
1042:
1038:
1021:
1018:
995:
994:
964:
961:
958:
954:
937:
934:
918:
911:
910:
909:
907:
906:wave function
903:
898:
879:
856:
848:
832:
825:
824:
823:
796:
769:
765:
761:
757:
735:
727:
711:
704:
703:
702:
684:
680:
676:
672:
633:
595:
538:
530:
501:
493:
489:
485:
482:
478:
449:
427:
424:
412:
402:
399:
396:
393:
389:
372:
359:
355:
351:
335:
328:
327:
312:
309:
297:
287:
284:
281:
277:
260:
247:
243:
239:
223:
216:
215:
214:
165:
136:
103:
95:
91:
87:
83:
79:
75:
68:Phase Problem
67:
62:
60:
58:
54:
50:
46:
42:
41:phase problem
38:
34:
30:
26:
19:
7914:
7902:
7870:
7856:EM Data Bank
7820:Nion Company
7714:Dennis Gabor
7704:Albert Crewe
7482:Confocal SEM
7379:Electron gun
7328:Auger effect
7197:
7193:
7183:
7148:
7144:
7133:
7098:
7094:
7084:
7070:(23): 7833.
7067:
7064:CrystEngComm
7063:
7057:
7016:
7012:
7006:
6981:
6977:
6971:
6946:
6942:
6876:
6870:
6861:
6857:
6851:
6826:
6822:
6816:
6775:
6771:
6739:
6735:
6725:
6706:
6702:
6693:
6686:
6682:
6678:
6651:(1): 68–73.
6648:
6644:
6634:
6620:(1): 65–67.
6617:
6613:
6607:
6593:(1): 60–65.
6590:
6586:
6510:
6504:
6497:
6483:
6479:
6475:
6471:
6467:
6463:
6453:
6407:
6403:
6399:
6398:
6370:DIRDIF is a
6369:
6344:
6313:
6289:
6272:feasible set
6267:
6261:
6226:bond lengths
6222:
6201:
6189:
6082:
5772:
5518:
5513:
5500:
5276:
5100:
4969:
4964:
4734:
4328:
4317:
4312:
4301:
4296:
4290:
4281:
3942:
3686:
3552:
3353:
2826:
2495:
2412:
2262:
2260:shown here.
2258:
2151:
1943:
1778:
1535:
1519:
1477:
1441:
1431:
1423:
1078:
899:
896:
788:
442:
71:
36:
28:
22:
7800:FEI Company
7734:Harald Rose
7724:Ernst Ruska
7413:Microscopes
7321:with matter
7319:interaction
6538:Diffraction
6482:somorphous
6428:GNU license
6219:Constraints
5838:, which is
2939:tend to be
1505:kinematical
1464:Nobel Prize
1452:Zachariasen
1434:David Sayre
1147:exponential
904:, the exit
57:reflections
49:statistical
33:diffraction
7881:Multislice
7697:Developers
7557:Techniques
7302:Microscope
7297:Micrograph
7200:(1): 1–8.
6569:References
6349:technique
6311:surfaces.
6192:algorithms
5522:channeling
5498:formula.
4305:scattering
2251:is known.
1520:The Sayre
492:experiment
82:real space
63:Background
7749:Max Knoll
7404:Stigmator
7214:2397-8554
6923:ignored (
6913:cite book
6881:CiteSeerX
6511:ab-initio
6506:ab initio
6498:The SIR (
6470:nomalous
6301:germanium
6280:solutions
6241:Σ
6065:±
5728:⋅
5715:π
5698:∑
5601:⋅
5588:π
5571:∑
5535:Ψ
5202:ϕ
4879:≈
4768:contains
4704:ϕ
4701:−
4685:ϕ
4682:−
4666:ϕ
4616:ϕ
4613:−
4597:ϕ
4594:−
4578:ϕ
4535:ϕ
4532:−
4516:ϕ
4513:−
4497:ϕ
4482:×
4388:ϕ
4385:−
4369:ϕ
4366:−
4350:ϕ
4331:logarithm
4320:amorphous
4246:ϕ
4227:ϕ
4175:−
4145:∑
4126:ϕ
4107:ϕ
4055:−
4025:∑
4018:≈
3999:φ
3951:ϕ
3910:ϕ
3907:−
3891:ϕ
3888:−
3872:ϕ
3857:×
3790:∑
3772:≈
3731:−
3700:∏
3654:ϕ
3621:ϕ
3588:ϕ
3562:Σ
3525:ϕ
3522:−
3506:ϕ
3503:≈
3487:ϕ
3436:π
3427:≈
3411:ϕ
3408:−
3392:ϕ
3389:−
3373:ϕ
3358:for this
3321:ϕ
3318:−
3302:ϕ
3299:−
3283:ϕ
3268:×
3225:−
3187:≈
3146:−
3052:−
3028:−
3017:≈
2976:−
2909:⟩
2859:−
2835:⟨
2796:ϕ
2793:−
2777:ϕ
2774:−
2758:ϕ
2743:×
2676:−
2528:−
2481:⟩
2446:⟨
2440:≈
2363:⋅
2350:π
2333:∑
2316:⟩
2281:⟨
2099:∑
2007:−
1994:δ
1985:∑
1913:⋅
1903:π
1886:∑
1748:⋅
1738:π
1705:∑
1501:dynamical
1493:molecules
1489:particles
1468:Chemistry
1432:In 1952,
1409:⟩
1373:⟨
1367:⟩
1339:Ψ
1331:⟨
1289:⟩
1253:⟨
1247:⟩
1219:ψ
1211:⟨
1049:ϕ
1043:−
1003:Ψ
965:ϕ
959:−
919:ψ
766:ϕ
681:ϕ
488:intensity
413:⋅
400:π
394:−
368:∞
363:∞
360:−
356:∫
298:⋅
285:π
256:∞
251:∞
248:−
244:∫
53:amplitude
35:data and
7932:Category
7904:Category
7851:CrysTBox
7839:Software
7510:Cryo-TEM
7317:Electron
7232:30167465
7175:28192420
7125:25866663
7041:12214229
6963:10927270
6808:20112743
6800:19771696
6522:See also
6509:and non-
6402:lectron
6361:Software
6320:zeolites
6286:Examples
6230:symmetry
5496:Blackman
2941:Gaussian
2265:randomly
1522:equation
1497:proteins
1456:Hauptman
564:, where
43:, where
37:a priori
7916:Commons
7564:4D STEM
7537:4D STEM
7515:Cryo-ET
7487:SEM-XRF
7477:CryoSEM
7434:Cryo-EM
7292:History
7223:6112783
7166:5376236
7116:4392419
7049:4384784
7021:Bibcode
6986:Bibcode
6831:Bibcode
6780:Bibcode
6460:acronym
6384:Fortran
6355:enzymes
6293:silicon
5840:complex
4894:, then
4772:terms,
1602:is the
1487:-sized
1448:Cochran
1428:History
1177:of the
1175:average
164:vectors
78:crystal
7861:EMsoft
7846:CASINO
7825:TESCAN
7690:Others
7589:cryoEM
7280:Basics
7230:
7220:
7212:
7173:
7163:
7123:
7113:
7047:
7039:
7013:Nature
6961:
6901:
6883:
6806:
6798:
6681:222, 2
6478:ingle
6406:irect
6366:DIRDIF
6338:, and
6328:oxides
6307:, and
6305:copper
6276:convex
6268:et al.
6043:
5844:states
5031:
5019:
5016:
3445:
3442:
2929:cosine
2496:Then:
1630:, and
1511:Theory
1495:, and
1485:micron
1179:moduli
1079:Where
7815:Leica
7661:PINEM
7527:HRTEM
7522:EFTEM
7095:IUCrJ
7045:S2CID
6858:Optik
6804:S2CID
6685:22, 3
6450:OASIS
5951:plane
1526:atoms
1481:nano-
1460:Karle
531:form
529:polar
45:phase
7876:IUCr
7810:JEOL
7681:WBDF
7676:WDXS
7626:EBIC
7621:EELS
7616:ECCI
7604:EBSD
7584:CBED
7532:STEM
7228:PMID
7210:ISSN
7171:PMID
7121:PMID
7037:PMID
6959:PMID
6925:help
6899:ISBN
6796:PMID
6692:2, 3
6202:The
5912:, a
5505:and
5101:Let
5060:>
4997:>
4322:and
3613:and
3466:2...
2263:For
2185:and
1483:and
1458:and
1450:and
1112:and
189:and
84:and
7646:FEM
7641:FIB
7609:TKD
7599:EDS
7502:TEM
7464:SEM
7439:EMP
7218:PMC
7202:doi
7161:PMC
7153:doi
7111:PMC
7103:doi
7072:doi
7029:doi
7017:419
6994:doi
6951:doi
6891:doi
6839:doi
6827:173
6788:doi
6744:doi
6711:doi
6653:doi
6622:doi
6595:doi
6494:SIR
6420:C++
6395:EDM
6259:).
5455:k-h
5380:k-h
4943:k,h
4910:k,h
4854:k,h
4821:k,h
4693:k-h
4646:k,h
4605:k-h
4524:k-h
4453:k-h
4418:k,h
4377:k-h
4235:k-h
4189:k-h
4115:k-h
4069:k-h
3899:k-h
3828:k-h
3745:k-h
3596:k-h
3514:k-h
3400:k-h
3310:k-h
3239:k-h
3160:k-h
3066:k-h
2990:k-h
2873:k-h
2785:k-h
2714:k-h
2640:k-h
2542:k-h
2457:k-h
2292:k-h
2168:k-h
2116:k-h
1466:in
72:In
23:In
7934::
7421:EM
7226:.
7216:.
7208:.
7196:.
7192:.
7169:.
7159:.
7149:14
7147:.
7143:.
7119:.
7109:.
7097:.
7093:.
7068:14
7066:.
7043:.
7035:.
7027:.
7015:.
6992:.
6982:05
6980:.
6957:.
6947:55
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