Download Crystal Field Theory, gemstones and color

CreatedbyAdamR.Johnson,HarveyMuddCollege([email protected])andpostedonVIPEronMay13,
2016.CopyrightAdamR.Johnson,2016.ThisworkislicensedundertheCreativeCommonsAttributionNonCommercial-NoDerivsCCBY-NC-ND.Toviewacopyofthislicensevisit
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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
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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
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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
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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
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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
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{{Figure1.4from“Readingsoncolor;
Thescienceofcolor,”volume2,by
AlexByrneandDavidR.Hilbert,MIT
Press,1997”ispresentedhere.}}