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CreatedbyAdamR.Johnson,HarveyMuddCollege([email protected])andpostedonVIPEronMay13, 2016.CopyrightAdamR.Johnson,2016.ThisworkislicensedundertheCreativeCommonsAttributionNonCommercial-NoDerivsCCBY-NC-ND.Toviewacopyofthislicensevisit {http://creativecommons.org/licenses/by-nc-nd/4.0/}. CrystalFieldTheory,gemstonesandcolor Thecolorsoftransitionmetalcompoundsishighlyvariable.Aqueoussolutionsofnickelare green, of copper are blue, and vanadium can range from yellow to blue to green to violet. Whatistheoriginofthesecolors?Asimplegeometricalmodelknownascrystalfieldtheory canbeusedtodifferentiatethe5dorbitalsinenergy.Whenanelectroninalow-lyingorbital interacts with visible light, the electron can be promoted to a higher-lying orbital with the absorption of a photon. Our brains perceive this as color. Rubies, dark red, and emeralds, brilliantgreen,arepreciousgemstonesknownsinceantiquity.Whatcausesthecolorinthese beautifulcrystals?Usingcrystalfieldtheory,wecanexplainthecolorsinthesegemstones. LearningObjectives:Uponcompletionofthisexercise,youshouldbeableto: 1. Derivethecrystalfieldsplittingfordorbitalsinanoctahedralgeometry 2. Predictthemagnitudeofdorbitalsplitting 3. Relatecolor,energy,wavelength,andcrystalfieldstrength TermsYouShouldKnow:orbital,octahedron,absorptionspectroscopy,crystalfieldsplitting BackgroundReading:Atkins,Jones,&Laverman,Chapter2,Sections2.2,2.6,7.7,7.11,16.10, 17.3(d),17.5,17.8,17.9,17.10,17.12 Readingfrom“TheScienceofColor,”volume2,editedbyAlexByrneandDavidR.Hilbert,MIT Press,CambridgeMA,1997,pp.10-17. AfterCompletingthisExercise,TextbookProblemsYouShouldbeAbletoAnswer: 2.14,2.16,2.39,2.40,17.51,17.53,17.58,17.65,17.71 Day1: Completethecrystalfieldtheoryguidedinquiry;completestudentworksheet1inclassoras homework Day2: turnintheworksheetfromday1 completetheexerciseusingCrystalmakertoexaminethesolidstatestructuresofrubyand emerald;completestudentworksheet2inclassorashomework(dueatstartofnextunit) CreatedbyAdamR.Johnson,HarveyMuddCollege([email protected])andpostedonVIPEronMay13, 2016.CopyrightAdamR.Johnson,2016.ThisworkislicensedundertheCreativeCommonsAttributionNonCommercial-NoDerivsCCBY-NC-ND.Toviewacopyofthislicensevisit {http://creativecommons.org/licenses/by-nc-nd/4.0/}. BackgroundInformation Muchofinorganicchemistrydealswiththestructureandpropertiesofthetransitionmetal complexes.Oneofthekeyapproachestounderstandingthesepropertiesiscrystalfieldtheory, whichwasoriginallydevelopedbyBetheinthelate1920stoexplaintheelectronicstructureof metalionsincrystalsusingapurelyelectrostaticbondingmodel.Wewillusethistheoryto explainthecolorofthegemstonesrubyandemerald,andwillseethelimitationsofthetheory fordescribingactualchemicalsystems. Day1 CrystalFieldTheoryGuidedInquiry The material in this section was adapted from “A Guided Inquiry Activity for teaching Ligand Field Theory,” Johnson, B. J., and Graham, K. J., J. Chem. Educ., 2015, 92, 1369-1372. Rather than repeat the unit here, I refer the interested instructor to the related content link. The studentanswersheetforday1outlinesthefocusIchoseforthisunitformystudents. CreatedbyAdamR.Johnson,HarveyMuddCollege([email protected])andpostedonVIPEronMay13, 2016.CopyrightAdamR.Johnson,2016.ThisworkislicensedundertheCreativeCommonsAttributionNonCommercial-NoDerivsCCBY-NC-ND.Toviewacopyofthislicensevisit {http://creativecommons.org/licenses/by-nc-nd/4.0/}. Day2 Solidstatestructures Corundum Aluminum oxide, Al2O3 is the most common oxide of aluminum, and is commonly called alumina.Thenaturallyoccurring,thermodynamicallystable,crystallineformofaluminumoxide is called corundum. This structure consists of a nearly hexagonal close-packed structure of oxygenwithaluminumionsfilling2/3oftheoctahedralholes.Corundumisveryhard(9.0on the Mohs scale, exceeded only by covalent structures like silicon carbide, boron nitride and diamond) and can scratch almost every other mineral. It is therefore commonly used as an abrasive.Tracetransitionmetalcontaminantsinthecorundumstructuregiverisetorubyand sapphiregems. Let’s examine the structure of corundum in more detail. Open the CrystalMaker file entitled “Corundum.cmdf”onyourlaptop.Youshouldseetheunitcell,theaxissystem,andtheunitcell contents. All of the atoms shown are positioned within the unit cell; verify that the stoichiometryofthemineraliscorrect. Now let’s verify the HCP packing of the oxygen atoms in the structure. Under the “Model” menu,switchto“spacefilling.” Question:sincetheprincipalquantumnumbersofAlandOare3and2respectively,whyare theoxygenatomslargerthanthealuminumatoms? Tosimplifytheview,letstruncatetheunitcellalongthezaxis.Under“Transform,”openthe “setrange”dialog.Reducetherangetoviewonlyfromz=0.5–1.0.Youshouldsee3rowsof oxygenatoms.Now,rotatethemodelsoyouarelookingdownthez-axis.Whenlookingdown, you should see that some of the oxygen atoms are “missing;” they are contained in the next unitcell.Expandtherangealongxandysoyouareviewingfrom0–1.1alongeachaxis.While stilllookingdownthez-axis,increasethez-axisrangeagainuntilyoucanseethewholeunitcell (range=0.0–1.0).Youmaywanttoswitchbackandforthbetween“SpaceFilling”and“Ball andstick”underthe“model”menu. Questions: a)aretheoxygenatomsinanA-B-C-A-B-CarrangementoranA-B-A-Barrangement? b)IsthisCCPorHCP? c)Isthestructureaperfectlatticeorisitimperfect? Measure the bond lengths between one aluminum and its nearest neighbors. Repeat for a secondaluminumatom.Itmayhelptoreducetherangealongthez-axisagaintosimplythis CreatedbyAdamR.Johnson,HarveyMuddCollege([email protected])andpostedonVIPEronMay13, 2016.CopyrightAdamR.Johnson,2016.ThisworkislicensedundertheCreativeCommonsAttributionNonCommercial-NoDerivsCCBY-NC-ND.Toviewacopyofthislicensevisit {http://creativecommons.org/licenses/by-nc-nd/4.0/}. task.Inordertomorecloselyexaminetheenvironmentaroundthealuminumatoms,wewill constructpolyhedra.Underthe“edit”menu,select“bonding,”andpressthe“+”toaddanew typeofbond.FormbondsbetweenAlandObysettingthesearchparametertoavalueslightly larger than the Al-O bond distances you found in the previous step. Turn on the “model inspector” and edit the Al atom. It should be currently set to show “sphere” under the “polyhedron”menu.Clickonthatsphereandchangeittooneofthepolyhedronoptions.Then, under the “model” menu, select “polyhedron.” The aluminum environments should now appearascoordinationpolyhedra. Questions: a)whatisthecoordinationenvironmentaroundthealuminumions? b)arethealuminumatomscenteredinthepolyhedra? c)whatistheaverageAl-Obondlength? Expandtheviewoutwardstoexaminethelarger3-dimensionalstructureofcorundum.Itmay help to turn off the view of the oxygen atoms and change the polyhedron options for aluminum. It is difficult to verify, but you should be able to observe that 2/3 of the possible octahedralcoordinationenvironmentsarefilledwithaluminumatoms.Thisisprobablyeasiest toobservealongthezaxis. In rubies, approximately 1% of the Al ions are replaced with Cr ions in the corundum lattice. Although these two metals are not the same size, the chromium ions can fit in the lattice withoutdisruptingtheoverallstructure. Question: a)Inordertomaintainchargeneutrality,whatisthechargeoneachCrion? b)howmanyvalenceelectronsareinthisCrion? c) draw an appropriate crystal field splitting diagram for the Cr and populate it with the electrons. d)Giventhatrubiesappearred,calculatethe∆oandreportitincm-1. Beryl Berylisamineralcontainingberyllium,aluminum,siliconandoxygenwiththechemicalformula Be3Al2Si6O18. It is a member of the family of cyclosilicate minerals along with other common mineralssuchasthegemstonetourmaline.Thesemineralscontainlinked“SiO4”tetrahedraina “6-memberedring”withastoichiometryof(SiO3)612-.SinceBealwaysappearsasa+2cation, andAlisalwaysa+3cation,thechargebalances,asitmust.Berylisalsoahardmineral,7.5-8 on the Mohs scale, and is found an many colors depending on the trace transition metal CreatedbyAdamR.Johnson,HarveyMuddCollege([email protected])andpostedonVIPEronMay13, 2016.CopyrightAdamR.Johnson,2016.ThisworkislicensedundertheCreativeCommonsAttributionNonCommercial-NoDerivsCCBY-NC-ND.Toviewacopyofthislicensevisit {http://creativecommons.org/licenses/by-nc-nd/4.0/}. impuritiespresent,givingrisetothegemstonesaquamarine(blue,Fe),emerald(green,Cr),and morganite(pink,Mn). Let’s examine the structure of beryl in more detail. Open the CrystalMaker entitled “beryl.cmdf” on your laptop. You should see the unit cell, the axis system, and the unit cell contents. All of the atoms shown are positioned within the unit cell; verify that the stoichiometry of the mineral is correct. Note, there are two water molecules (black spheres, Wa)presentinthisstructure;deselectthemtoremovethemfromviewfromthetoolbar. The first structural feature we will investigate is the presence of the cyclosilicate motif. First, lets create Si-O tetrahedra for easier viewing. Under the “edit” menu, select “bonding,” and pressthe“+”toaddanewtypeofbond.FormbondsbetweenSiandObysettingthesearch parameterto2.0Å.Turnonthe“modelinspector”andedittheSiatom.Itshouldbecurrently settoshow“sphere”underthe“polyhedron”menu.Clickonthatsphereandchangeittoone ofthepolyhedronoptions.Then,underthe“model”menu,select“translucent+sphere+bonds.” Rotatethemoleculesoyouarelookingdownthez-axis.Now,fromthe“transform”menu,go to “set range” and set the x- and y-axes from 0.0 – 1.5. You should see an isolated Si6O18 hexagon appear. You may want to turn off the viewing of the O atoms to simplify the view. Onceyouhavetheview,youcanexpandevenfurther,from0.5–2.5alongxandy.Youshould beabletoseeclearlyseparatedcyclosilicateswithAlandBeatomsintheinterveningspaces. Now lets examine the coordination environment around Be. Revert the view back to a single unitcellfromthe“Transform/Setrange”menu.Fromthe“bonding”menu,addanewtypeof bondbetweenBeandO,andfromthe“model”menu,changethepolyhedrontypeforBefrom “sphere” to “translucent.” You should be able to see isolated BeO4 tetrahedra that link the cyclosilicates along the z-axis. Expand and contract the ranges to verify that the BeO4 tetrahedraareisolatedfromeachother.Aparticularlygoodview(downthez-axis)hasx-andyaxisrangesfrom0–1.5,andzfrom0–1.8.TheBeatomsserveas“glue”thatstickthelarge cyclosilicatestogetheralongz.Fromthisviewitshouldalsobeclearthat,unlikethecorundum structure,theberylstructureisa“perfect”lattice,inthatalloftheAlatomslineupperfectly alongthez-axis. Finally,letsexaminethecoordinationenvironmentaroundtheAlatom.Revertbacktoasingle unitcellandmakesurethattheOatomsarevisible.Truncatesothatthevisiblez-axisrangeis from0.1–0.5.MeasurethesixAl-Obonds;aretheyallthesame?Nowcreatebondsbetween AlandO,andcreateapolyhedralviewfortheAlatom.TheAlshouldbeseentoberesidingin anoctahedralenvironment,andtheseAlO6octahedraalsoareisolatedfromoneanother,but linkwiththeBeO4tetrahedra. CreatedbyAdamR.Johnson,HarveyMuddCollege([email protected])andpostedonVIPEronMay13, 2016.CopyrightAdamR.Johnson,2016.ThisworkislicensedundertheCreativeCommonsAttributionNonCommercial-NoDerivsCCBY-NC-ND.Toviewacopyofthislicensevisit {http://creativecommons.org/licenses/by-nc-nd/4.0/}. Questions: a)whatisthecoordinationenvironmentaroundthealuminumions? b)arethealuminumatomscenteredinthepolyhedra? c)whatistheaverageAl-Obondlength? Berylisalayeredstructure.Thereisalayerofthecyclosilicates,andthenalayerofBeandAl atoms, and then another layer of cyclosilicates. The oxygen atoms link the Si, Be, and Al coordinationpolyhedra.Foragoodviewofthestructure,setx-andy-axesfrom0.0–1.9,andz from 0.0 – 1.0. Then, while looking down the z-axis, expand along z. You can see that the cyclosilicatesformaporethroughthestructurealongthez-axis.Gobacktothesitemenuand makethewatermoleculesvisible.Natureabhorsavacuum! Asinruby,emeraldscontainchromiumimpuritiesforabout1%ofthealuminumatomsinthe beryllattice. Question: a)Inordertomaintainchargeneutrality,whatisthechargeoneachCrion? b)howmanyvalenceelectronsareinthisCrion? c) draw an appropriate crystal field splitting diagram for the Cr and populate it with the electrons. d)Giventhatemeraldsappeargreen,calculatethe∆oandreportitincm-1. e) given the structures of Beryl and Corundum, explain using a physical model why the two materialshavesuchdifferentharndesses. BreakdownofCFT-covalency Oneoftheusefulthingsaboutcrystalfieldtheoryisitspredictivenature.Onceweknowa crystalfieldsplittingpatternandwhatatomsarepresent,wecanmakepredictionsabout∆o, color,andotherfeaturesofmetalssuchasmagnetism. Question:Giventhebackgroundofthetheory,thatthecentralmetaldorbitalsaresplitdueto repulsiveelectronicinteractionswiththeligands,predictwhichmetalcomplexineachpair wouldhaveahighercrystalfield: a)Crsurroundedby6oxygenionsat2.0Å.Crsurroundedby6watermoleculesat2.0Å b)Crsurroundedby6oxygenionsat2.0Å.Crsurroundedby6oxygenionsat1.9Å GobackandrecordheretheaverageCr-Odistancesinemerald_______andinruby_______. Doesthecolorofemeraldandrubymatchthatpredictedbythedistanceargumentyoujust calculated? CreatedbyAdamR.Johnson,HarveyMuddCollege([email protected])andpostedonVIPEronMay13, 2016.CopyrightAdamR.Johnson,2016.ThisworkislicensedundertheCreativeCommonsAttributionNonCommercial-NoDerivsCCBY-NC-ND.Toviewacopyofthislicensevisit {http://creativecommons.org/licenses/by-nc-nd/4.0/}. Oneofthemainassumptionsincrystalfieldtheoryisthattheionsarepointcharges,andthat bondinginthesolidstatelatticeispurelyionic(thatis,therearenosharedelectrons). Question: a)whyisthemodelingofionsinacrystallatticeaspointchargesreasonable? b)whyisthemodelingofionsinacrystallatticeaspointchargesunreasonable? c)lookingatthestructuresofberylandcorundum,whichseemsmoreionicandwhichseems morecovalent.Why? The∆oofametaliondependsonthemagnitudeofthechargefeltbythatmetalion.Inpurely ionicstructures(whichdon’treallyexist;evenNaClhassomedegreeofcovalency),thenet chargeoneachanionislargerinmagnitude.Asstructuresbecomemoreandmorecovalent, theelectronicdifferencebetweenthecentralmetalandligandatomsbecomesless.Inapurely covalentlattice(diamond,whichisafacecenteredcubiclatticeofCatomswithCatomsinone halfofthetetrahedralholes),thereisnoelectronicdifferencebetweenthetypesofatoms. Corundumismoreionicthanberyl;thepolysilicatechainsandtheberylliumatomsreducethe netnegativityofeachoxygenatom,sothateventhoughtheCr-Obondlengthsinemeraldare shorterthanthecorrespondingbondsinruby,thenetchargefeltbytheCratomislowerand the∆oislowerforemerald. Thediagram‡onthefollowingpageshowsthecalculatedabsorptionbandsandresulting absorptionspectraforemeraldandberyl. Questions: Indicateonthediagramhowyoucantellthatthe∆oforberylislowerthanthatforcorundum. Show(circlethetransitionline)theelectronictransitionsresponsibleforthegreencolorin emeraldandredcolorinruby. ‡ “ReadingsonColor;Thescienceofcolor,”volume2,byAlexByrneandDavidR.Hilbert,MITPress,1997 CreatedbyAdamR.Johnson,HarveyMuddCollege([email protected])andpostedonVIPEronMay13, 2016.CopyrightAdamR.Johnson,2016.ThisworkislicensedundertheCreativeCommonsAttributionNonCommercial-NoDerivsCCBY-NC-ND.Toviewacopyofthislicensevisit {http://creativecommons.org/licenses/by-nc-nd/4.0/}. {{Figure1.4from“Readingsoncolor; Thescienceofcolor,”volume2,by AlexByrneandDavidR.Hilbert,MIT Press,1997”ispresentedhere.}}