VIBRATE! Program to compute irreducible representationsCHAINPLOTDemonstrate the motion of atoms on a chainFOURIERDemonstrate Fourier synthesis as used in crystallographyMEGAWCompute effect of octahedral tilting in perovskitesWINDICVOLGUI interface to the DICVOL91 powder autoindexing programWINOPTACTCalculation of optical rotation and birefringence from a crystal structureSUMO Simple user-defined mathematical operationsREFINEGeneral non-linear least-squares refinement with user- defined functions
VIBRATE! Program to compute irreducible representationsCHAINPLOTDemonstrate the motion of atoms on a chainFOURIERDemonstrate Fourier synthesis as used in crystallographyMEGAWCompute effect of octahedral tilting in perovskitesWINDICVOLGUI interface to the DICVOL91 powder autoindexing programWINOPTACTCalculation of optical rotation and birefringence from a crystal structureSUMO Simple user-defined mathematical operationsREFINEGeneral non-linear least-squares refinement with user- defined functions
NOTE: Users prior to April 11 2013 should download Version 2.7, as several bug fixes have been made.
VIBRATE!isaprogram,writtenbyProfessorMikeGlazer(OxfordUniversity)to runonMicrosoftWindows,inordertocomputetheirreduciblerepresentationsfor normalmodesofvibration andmagneticmodesdirectlyfromacrystalstructure usingFactorGroupAnalysis.Thedefaultistocarryouttheanalysisformodesat thecentreoftheBrillouinZone(k=0)andassuchisidealforspectroscopy applicationssuchasRamanorInfra-RedSpectroscopy.Operationoftheprogramis verysimple.Itisfirstnecessarytoinputthecrystalstructureandoncethisisdone the program automatically computes the rest.
Inputofthecrystalstructureisdonebyspecifyingaspacegroupandthepositionsoftheatoms.Alternativelyinput isimmediateusingaCrystallographicInformationFile(CIF),theusualwaythatcrystalstructureinformationis availablethesedays.NotethatinWindows7youshoulduseCompatibilityModeforXP.ThelatestVersion2.5now has VRML structure plotting installed. Read Help File for details to enable this to work.BelowisshownatypicalscreenviewforthetetragonalformofBaTiO3showingthattheirreduciblerepresentations are 4A1+B1+5E in point group 4mm(C4v)
In order to enter atoms manually, this is done through a simple dialog box (left).In addition, character projection operators can be listed enabling the symmetry-adapted vectors to be drawn on a crystal structure diagram.
For example, in the case of BaTiO3, the T2u (G5-) irreducible representation leads to the following symmetry-adapted vectors:
We see from this that only the oxygen atoms are involved in motion corresponding to this irreducible representation. For example, the y movement of O1 is opposite to the y movement of O3 (first line), the z movement of O1 is opposite to the z movement of O2 (second line), and the x movement of O2 is opposite to the x motion of O3 (third line).Another selectable feature repeats the calculations atom by atom so you can then see which atomic movements contribute to which irreducible representations. In addition, a button is available to enable the computation to switch to magnetic modes.For solid-state specialists, there is also a facility to derive the irreducible representations for normal modes at k ≠ 0.A short paper describing the program has recently been published in J. Appl. Cryst.(doi:10.1107/S0021889809040424). If you would like to obtain a copy of VIBRATE! click here. In addition, you can download a PDF of the Help File which contains more details about the program and how to use it. Any problems then please email Mike Glazer
NOTE:UserspriortoApril112013shoulddownload Version 2.7, as several bug fixes have been made.
VIBRATE!isaprogram,writtenby ProfessorMikeGlazer(OxfordUniversity) torunonMicrosoftWindows,inorderto computetheirreduciblerepresentations fornormalmodesofvibration and magneticmodesdirectlyfromacrystal structureusingFactorGroupAnalysis. Thedefaultistocarryouttheanalysisfor modesatthecentreoftheBrillouinZone (k=0)andassuchisidealfor spectroscopyapplicationssuchasRaman orInfra-RedSpectroscopy.Operationof theprogramisverysimple.Itisfirst necessarytoinputthecrystalstructure andoncethisisdonetheprogram automatically computes the rest.
Inputofthecrystalstructureisdonebyspecifyingaspace groupandthepositionsoftheatoms.Alternativelyinputis immediateusingaCrystallographicInformationFile(CIF), theusualwaythatcrystalstructureinformationis availablethesedays.NotethatinWindows7youshould useCompatibilityModeforXP.ThelatestVersion2.5now hasVRMLstructureplottinginstalled.ReadHelpFilefor details to enable this to work.Belowisshownatypicalscreenviewforthetetragonal formofBaTiO3showingthattheirreducible representations are 4A1+B1+5E in point group 4mm(C4v)
In order to enter atoms manually, this is done through a simple dialog box (left).In addition, character projection operators can be listed enabling the symmetry-adapted vectors to be drawn on a crystal structure diagram.
For example, in the case of BaTiO3, the T2u (G5-) irreducible representation leads to the following symmetry-adapted vectors:
We see from this that only the oxygen atoms are involved in motion corresponding to this irreducible representation. For example, the y movement of O1 is opposite to the y movement of O3 (first line), the z movement of O1 is opposite to the z movement of O2 (second line), and the x movement of O2 is opposite to the x motion of O3 (third line).Another selectable feature repeats the calculations atom by atom so you can then see which atomic movements contribute to which irreducible representations. In addition, a button is available to enable the computation to switch to magnetic modes.For solid-state specialists, there is also a facility to derive the irreducible representations for normal modes at k ≠ 0.A short paper describing the program has recently been published in J. Appl. Cryst.(doi:10.1107/S0021889809040424). If you would like to obtain a copy of VIBRATE! click here. In addition, you can download a PDF of the Help File which contains more details about the program and how to use it. Any problems then please email Mike Glazer
Beawareofanerrorintheliteratureandonthewebwith respecttothediatomicchain.Ontheleftisatypical drawingoftheatomicdisplacementfortransverseacoustic andopticmodes.Youseethisdiagrameverywhere,but actuallyitisnotquitecorrect.Whathasbeenforgottenis thatforwave-vectorslessthantheBrillouinZone,the wavesarerunningwaves.Ifthisdiagramwerecorrect,as thecrestofthewavemovesfromsaylefttoright,the amplitudesoftheheavyandlightatomsseemtohavethe samemagnitude.Butthisisnotpossible.Intheacousticmode, theheavyatomshavelargerdisplacementsthanthelightones, andvice-versafortheopticmode.Therefore,intheacoustic modetheremustbetwowaves:onefortheheavyatomsandone forthelightatoms(samefrequencyandwavelengthbutdifferent amplitudes)!Thediagramisthereforeatbestmisleading.Itis correctinBrilliouin’s1946bookandinWannier’s1958book,but itseemstobewrongeverywheresince.Sosomeoneinthe1950’s Iguessdrewthewrongdiagramandthishasbeenpropagated for the last 50 years or so. The simulation below gets it right.
Monatomic and DiatomicChains
Note:BUGFIX 20 Jan 2012: I have corrected a bug in the alternating force constantsroutine.
Monatomic and Diatomic ChainsI have made available for downloading two programs designed to demonstratevibrations of a linear 1-dimensional chain and a 2-dimensional array. Theseprograms are useful for teaching undergraduates typically in a Condensed MatterPhysics lecture course.
Note:BUGFIX 20 Jan 2012: I have corrected a bug in the alternating force constantsroutine.
Monatomic and Diatomic ChainsI have made available for downloading two programs designed to demonstratevibrations of a linear 1-dimensional chain and a 2-dimensional array. Theseprograms are useful for teaching undergraduates typically in a Condensed MatterPhysics lecture course.
This is an educational computer program written to demonstrate the process of Fourier Synthesis. This is a mathematical technique used in the solution of crystal structures by adding together plane waves in different orientations with different amplitudes (structure factors) and phases. The program allows waves to be added one after another or to read in a file containing a list of indices h k l and structure factors and phases in order to generate a Fourier projection. The resulting Fourier2D projection is plotted in a variety of different ways. Some examples are shown below demonstrating a projection of the potassium benzoyl penicillin structure as determined by Dorothy Hodgkin in the early 1940s. I also show a nice film of high-temperature quartz.I have also added a 3-dimensional Fourier program Fourier3D which plots Fourier sections rather than just projections. Go to Get Programs to download.
This is an educational computer program written to demonstrate the process of Fourier Synthesis. This is a mathematical technique used in the solution of crystal structures by adding together plane waves in different orientations with different amplitudes (structure factors) and phases. The program allows waves to be added one after another or to read in a file containing a list of indices h k l and structure factors and phases in order to generate a Fourier projection. The resulting Fourier2D projection is plotted in a variety of different ways. Some examples are shown below demonstrating a projection of the potassium benzoyl penicillin structure as determined by Dorothy Hodgkin in the early 1940s. I also show a nice film of high-temperature quartz.I have also added a 3-dimensional Fourier program Fourier3D which plots Fourier sections rather than just projections. Go to Get Programs to download.
MegawisaprogramwritteninhonourofDr.HelenD.Megaw, renownedparticularlyforherworkinCambridgeonthe crystalstructuresofperovskites.Aspartofthatstudy,she becameinterestedinhowtodescribethestructuresinterms oftiltedoxygenoctahedra,aproblemthatItackledandfor which I derived a way to classify tilt systems in perovskitesdoi.org/10.1107/S0567740872007976doi.org/10.1107/S0567739475001635Thisseemstohavebeenwidelyaccepted.Thiscomputer programrunsunderWINDOWS.Belowisshownaviewofthe screen.Positiveandnegativeoctahedraltiltscanbedialledin andanyofthetiltsystemsconstructed.Atthebottom,the powderpattern(X-raysorneutrons)isdrawn,togetherwith indicationswhereextrapeaksduetothetiltingappear.At bottomrightisapull-downboxthatliststhecalculated values of the square of the structure factors.SeealsotheprogramSPUDSwhichenablesthetiltsystemsto be calculated.
ChangeofoctahedraltiltinLiNbO3showing itsrelationshiptoperosvkite.Megaw showedthatthisstructurecouldbetreated asanextremeexampleofatilted perovskitebyrotatingtheoctahedraabout the trigonal axis through a very large angle.doi.org/10.1107/S0567739468001282
MegawisaprogramwritteninhonourofDr. HelenD.Megaw,renownedparticularlyfor herworkinCambridgeonthecrystal structuresofperovskites.Aspartofthat study,shebecameinterestedinhowto describethestructuresintermsoftilted oxygenoctahedra,aproblemthatItackled andforwhichIderivedawaytoclassifytilt systems in perovskitesdoi.org/10.1107/S0567740872007976doi.org/10.1107/S0567739475001635Thisseemstohavebeenwidelyaccepted. Thiscomputerprogramrunsunder WINDOWS.Belowisshownaviewofthe screen.Positiveandnegativeoctahedraltilts canbedialledinandanyofthetiltsystems constructed.Atthebottom,thepowder pattern(X-raysorneutrons)isdrawn, togetherwithindicationswhereextrapeaks duetothetiltingappear.Atbottomrightisa pull-downboxthatliststhecalculatedvalues of the square of the structure factors.SeealsotheprogramSPUDSwhichenables the tilt systems to be calculated.
ChangeofoctahedraltiltinLiNbO3 showingitsrelationshipto perosvkite.Megawshowedthat thisstructurecouldbetreatedas anextremeexampleofatilted perovskitebyrotatingthe octahedraaboutthetrigonalaxis through a very large angle.doi.org/10.1107/S0567739468001282
A Windows version of the well known powder autoindexing program DICVOL.ThisversionofDicVol91waswrittenoriginallybyDanielLouer,andIhaveadaptedittowork within a Windows environment. The usual way in which you are likely to works is1.Create a file of data using F ile/Control Data2.IMPORTANT! Save file with File/Save3.Run/Run will run the DICVOL91 program4.Run/Output allows you to inspect the output file5.Run/Cell Results give a list of the latest cell paramaters6.Atanytime,youcanuseFile/OpentoopenanexistingdatafileandthenFile/Control Data. Do not forget to save the file befoire running DicVol9 on it.
AWindowsversionofthewellknownpowder autoindexing program DICVOL.ThisversionofDicVol91waswrittenoriginallyby DanielLouer,andIhaveadaptedittoworkwithin aWindowsenvironment.Theusualwayinwhich you are likely to works is1.Create a file of data using F ile/Control Data2.IMPORTANT! Save file with File/Save3.Run/Run will run the DICVOL91 program4.Run/Outputallowsyoutoinspecttheoutput file5.Run/CellResultsgivealistofthelatestcell paramaters6.Atanytime,youcanuseFile/Opentoopen anexistingdatafileandthenFile/Control Data.Donotforgettosavethefilebefoire running DicVol9 on it.
Thisprogramreadsacrystalstructureviaa CrystallographicInformationFile(CIF),andcomputes opticalbirefringenceaswellasthesignand magnitudeofthespecificopticalrotation.Aswellas structuralinformationitisnecessarytoinclude estimatedelectronicpolarizabilitiesforeachatom. Tounderstandtheprocess,Iadvisereadingoftwo papers1.GlazerandStadnicka(1986).Ontheoriginof opticalactivityincrystalstructures.This providesasimpleexplanationofhowthesignof opticalrotationisrelatedtoinorganiccrystal structure.2.DevarajanandGlazer(1986)andErratum. Theory andcomputationofopticalrotatorypowerin inorganiccrystals.Thispapergivesthefull theory used in the program WinOptact.
SUMO- Simple user-defined mathematical operationsDon’t wrestle with mathematics: use SUMO!Ausefulprogramthatenablesyoutoenter yourownmathematicalfunctions,then evaluatethem.Youcandefineyourwon functions,constantsandvariablesandcanalso carryour1and2-dimensionalcontinuous plots.ReadtheHelpfilefirstinorderto understand how to use the program.
Thisprogramallowstheusertocarryoutanon-linearleast-squaresrefinementofimporteddata withrespecttoauser-definedmathematical function.Asthisinvolvescyclesofrefinement,it isnecessarytosupplystartingvaluesofthe refineableparametersa[1]a[2]a[3]…….The Helpfileexplainshowtodothis,andthereare three example files to try out.