Sayre equation

This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. Please help improve this article by introducing more precise citations. (November 2019) (Learn how and when to remove this message)

In crystallography, the Sayre equation, named after David Sayre who introduced it in 1952, is a mathematical relationship that allows one to calculate probable values for the phases of some diffracted beams. It is used when employing direct methods to solve a structure. Its formulation is the following:

$F_{hkl}=\sum _{h'k'l'}F_{h'k'l'}F_{h-h',k-k',l-l'}$

which states how the structure factor for a beam can be calculated as the sum of the products of pairs of structure factors whose indices sum to the desired values of $h,k,l$ .^[1]^[2] Since weak diffracted beams will contribute a little to the sum, this method can be a powerful way of finding the phase of related beams, if some of the initial phases are already known by other methods.

In particular, for three such related beams in a centrosymmetric structure, the phases can only be 0 or $\pi$ and the Sayre equation reduces to the triplet relationship:

$S_{h}\approx S_{h'}S_{h-h'}$

where the $S$ indicates the sign of the structure factor (positive if the phase is 0 and negative if it is $\pi$ ) and the $\approx$ sign indicates that there is a certain degree of probability that the relationship is true, which becomes higher the stronger the beams are.

References

^ Sayre, D. (1952). "The squaring method: A new method for phase determination". Acta Crystallographica. 5: 60–65. doi:10.1107/S0365110X52000137.
^ Werner, Massa (2004). Crystal Structure Determination. Springer. p. 102. doi:10.1007/978-3-662-06431-3. ISBN 3540206442.

Read other articles:

Mondo arabo

Mondo AraboNella carta sono indicati i paesi che fanno parte del mondo arabo, paesi in cui viene parlato l'arabo, anche se vi sono comprese aree linguistiche iraniane, berbere, curde, somale e aramaiche. Marocco, Algeria, Iraq, Sudan, Gibuti e Somalia sono stati ufficialmente bilingui. L'espressione mondo arabo (in arabo العالم العربي‎?) è usata convenzionalmente per indicare i ventidue Stati membri della Lega degli Stati Arabi; per Paesi arabi si intendono i Paesi la ...

Amonium serium(IV) nitrat

Amonium serium(IV) nitrat Nama Nama IUPAC Diamonium serium(IV) nitrat Nama lain Seri amonium nitratCANDiamonium heksanitratoserat(IV) Penanda Nomor CAS 16774-21-3 Y Model 3D (JSmol) Gambar interaktif 3DMet {{{3DMet}}} ChemSpider 157072 Nomor EC PubChem CID 180504 Nomor RTECS {{{value}}} UNII U99S55ED6B Y CompTox Dashboard (EPA) DTXSID00893439 InChI InChI=1S/Ce.6NO3.2H3N/c;6*2-1(3)4;;/h;;;;;;;2*1H3/q+4;6*-1;;/p+2Key: XMPZTFVPEKAKFH-UHFFFAOYSA-PInChI=1/Ce.6NO3.2H3N/c;6*2-1(3)4;;...

SMA Negeri 5 (Trans Semarang)

SMA Negeri 5Halte Trans SemarangLetakKotaSemarangKecamatanSemarang TengahKelurahanSekayuAlamatJl. Pemuda No. 143Kode pos50132Informasi lainStatusDitutup. Halte TransitDibuka18 September 2009 (2009-09-18)Ditutup17 Februari 2017 (2017-2-17) (Dikarenakan Sistem Satu Arah pada Jalan Pemuda)Konstruksi dan FasilitasPintu1 (keberangkatan dan kedatangan)Petugas TiketTidak adaPelayananAwal PelayananPukul 05.30 WIBAkhir PelayananPukul 17.40 WIBLayanan Lua error in Modul:Adjacent_stations at l...

بييرلويجي بريفيو

هذه المقالة يتيمة إذ تصل إليها مقالات أخرى قليلة جدًا. فضلًا، ساعد بإضافة وصلة إليها في مقالات متعلقة بها. (مايو 2022) بييرلويجي بريفيو معلومات شخصية الميلاد 21 مايو 1969 (55 سنة) ميلانو الطول 1.85 م (6 قدم 1 بوصة) مركز اللعب حارس مرمى الجنسية إيطاليا معلومات النادي ا�...

Place du Tertre

Square in Paris, France This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Place du Tertre – news · newspapers · books · scholar · JSTOR (August 2010) (Learn how and when to remove this template message) Night life at Place du Tertre. The Place du Tertre is a square in the 18th arrondissement of Paris, France. ...

Sheung Shui station

MTR station in the New Territories, Hong Kong This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Sheung Shui station – news · newspapers · books · scholar · JSTOR (November 2014) (Learn how and when to remove this template message) Sheung Shui上水 MTR rapid transit stationPlatforms 1 and 2 (Feb 2023)Chinese n...

Grapeshot

Type of ammunition consisting of multiple small balls Close-up of grapeshot (right) from an American Revolution sketch of artillery devices Model of a carronade with grapeshot ammunition In artillery, a grapeshot is a type of ammunition that consists of a collection of smaller-caliber round shots packed tightly in a canvas bag[1] and separated from the gunpowder charge by a metal wadding, rather than being a single solid projectile. When assembled, the shot resembled a cluster of grap...

Polskie Radio

Questa voce sugli argomenti Eurovisione e aziende polacche è solo un abbozzo. Contribuisci a migliorarla secondo le convenzioni di Wikipedia. Segui i suggerimenti del progetto di riferimento. Polskie RadioLogo Sede dell'azienda a Varsavia Stato Polonia Forma societariaSocietà anonima Fondazione18 agosto 1925 Fondata daZygmunt Chamiec e Tadeusz Sułowski Sede principaleVarsavia Persone chiave Andrzej Rogoyski (direttore generale) Albert Dreger (presidente) SettoreMedia Sito webwww...

Lincoln Square, Chicago

Community area in Chicago This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Lincoln Square, Chicago – news · newspapers · books · scholar · JSTOR (June 2012) (Learn how and when to remove this message) Community area in Illinois, United StatesLincoln SquareCommunity areaCommunity Area 04 - Lincoln SquareThe en...

大字 (数字)

この項目には、一部のコンピュータや閲覧ソフトで表示できない文字が含まれています（詳細）。数字の大字（だいじ）は、漢数字の一種。通常用いる単純な字形の漢数字（小字）の代わりに同じ音の別の漢字を用いるものである。概要壱万円日本銀行券（「壱」が大字）弐千円日本銀行券（「弐」が大字）漢数字には「一」「二」「三」と続く小字と、「壱」「�...

Ginger Baker

English drummer (1939–2019) Ginger BakerBaker performing in 1984Background informationBirth namePeter Edward BakerBorn(1939-08-19)19 August 1939Lewisham, South London, EnglandDied6 October 2019(2019-10-06) (aged 80)Canterbury, Kent, EnglandGenresRockbluesjazzAfrobeatOccupation(s)DrummerYears active1950s–2015LabelsPolydorWarner Bros.IslandFormerly ofBlues Incorporatedthe Graham Bond OrganisationCreamGinger Baker's Air ForceBlind FaithGinger Baker and FriendsBaker Gurvitz ArmyHawkwindA...

Radio Televisyen Malaysia

Radio Televisyen Malaysia Jabatan Penyiaran Malaysia Radio Television Malaysia 马来西亚广播电视台 راديو تيليۏيشن مليسيا மலேசிய வானொலி தொலைக்காட்சிJenisPublikMerekRadio Televisyen Malaysia (RTM) sejak 17 November 1969NegaraMalaysiaTanggal siar pertama1 April 1946JangkauanNasionalDidirikan01 April 1946 (1946-04-01)SloganTeman Setia Anda (1987-2004, 2017-sekarang sebagai slogan)Tetap Unggul (2004–2016)Saluran...

Universidad de Los Andes (Venezuela)

Universidad de Los Andes Sede central de las oficinas administrativas de la Universidad de Los Andes.Sigla ULALema «Initium sapientiae timor Domini»«El principio de la sabiduría está en el temor a Dios, Salmo 111:10»Tipo Pública autónomaFundación 29 de marzo de 1785 (239 años)[1]LocalizaciónDirección Casco Central de Mérida, Avenida 3 «Independencia», Diagonal Plaza Bolívar.Mérida, VenezuelaCoordenadas 8°35′50.25″N 71°8′42.9″O / 8.5972917...

Nova Science Publishers

American academic publishing company Nova Science PublishersFounded1985FounderFrank H. ColumbusCountry of originUnited StatesHeadquarters locationHauppauge, New YorkDistributionWorldwideKey peopleNadya Gotsiridze-Columbus (President); Donna Dennis (Vice-President)Publication typesAcademic journals, books, encyclopedias, handbooksNonfiction topicsScience and technology, medicine and biology, social sciencesFiction genresAcademic; STMImprintsNOVA, NOVA Biomedical, NovinkaNo. of employees55 in-h...

Leonardo Chiariglione

Leonardo Chiariglione Leonardo Chiariglione (Almese, 30 gennaio 1943[1]) è un ingegnere italiano. È noto per aver fondato, insieme a Hiroshi Yasuda, l'MPEG[2], un gruppo internazionale di esperti che ha prodotto i noti standard audio-video MPEG-1, MPEG-2 e l'MP3[3], ed altri. Il prof. Karlheinz Brandenburg accredita a Chiariglione, in particolare, la vision dell'importanza degli standard nelle tecnologie audio-video dell'epoca di Internet[4]. Indice 1 Biograf...

Thessaloniki International Film Festival

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Thessaloniki International Film Festival – news · newspapers · books · scholar · JSTOR (July 2014) (Learn how and when to remove this message) Thessaloniki International Film FestivalLocationThessaloniki, GreecePredecessorThessaloniki Festival of Greek CinemaFo...

特伦斯·扬

此條目可能需要清理，以符合维基百科质量标准。 (2024年7月9日)请尽量协助改善这篇条目，详情请参见讨论页。特伦斯·扬导演出生1915年6月20日上海公共租界逝世1994年9月7日(1994歲—09—07)（79歲）法國戛纳配偶Dorothea BennettSabine Sun 奖项金酸莓奖最差導演1982年《Inchon》斯圖爾特·特伦斯·赫伯特·扬（英語：Stewart Terence Herbert Young；1915年6月20日—1994年9月7日），英国著�...

Directorate-General of Personnel Administration

Directorate-General of Personnel Administration人事行政總處Rénshì Xíngzhèng Zǒngchù (Mandarin)Ngìn-sṳ Hàng-chṳn Chúng-chhú (Hakka)Logo of the DGPAAgency overviewFormed16 September 1967JurisdictionRepublic of China (Taiwan)HeadquartersZhongzheng, TaipeiMinisters responsibleSu Chun-jung, MinisterHwai Hsu, Lee Ping-chou, Deputy MinistersParent agencyExecutive YuanWebsitewww.dgpa.gov.tw Directorate-General of Personnel Administration The Directorate-General of Personnel Admini...

Bobby Heenan

Pour les articles homonymes, voir Heenan. Bobby HeenanBooby Heenan dans les années 1980.Données généralesNom de naissance Raymond Louis HeenanNom de ring Bobby HeenanNationalité AméricainNaissance 1er novembre 1944ChicagoDécès 17 septembre 2017 (à 72 ans)LargoTaille 6′ 0″ (1,83 m)[1]Poids 190 lb (86 kg)[1]Catcheur mortFédération American Wrestling AssociationWorld Wrestling FederationWorld Championship WrestlingCarrière pro. 1967 - 1984[a]modifier - m...

Pike (weapon)

Long spear used by infantry A modern recreation of a mid-17th century company of pikemen. By that period, pikemen would primarily defend their unit's musketeers from enemy cavalry. A pike is a long thrusting spear formerly used in European warfare from the Late Middle Ages[1] and most of the early modern period, and wielded by foot soldiers deployed in pike square formation, until it was largely replaced by bayonet-equipped muskets. The pike was particularly well known as the primary ...