Making the Most of Neutron‐Diffrac on Data Lithium Diffusion Pathways in Ramsdellite‐Like Li2Ti3O7 

D. Wiedemann,*a A. Franzb a Ins tut für Chemie, Technische Universität Berlin, Straße des 17. Juni 135, 10623 Berlin, Germany.   b Abteilung Struktur und Dynamik von Energie‐materialien, Helmholtz‐Zentrum Berlin für Materialien und Energie, Hahn‐Meitner‐Platz 1, 14109 Berlin, Germany. 

Conclusion 

Whendealingwithneutrondiffraction,iondiffusionpathwaysinsolidscanbeexplored,e.g.,via analysesof thePDFandOPP,ofMEM‐reconstructedSLDmaps,orof the frame‐worktopology.Differentrequirementsfordataandmodelqualityre lecttheamountofextractableinformation,beit(semi‐)quantitativeorqualitative.Lower‐demandapproach‐esmaybeusedasheuristic,supporting,orevenstandalonemethods—ifdataqualityprohibitsmoresophisticatedevaluation.

In our experience, measured data sometimes fail to reach the expectedquality, buthardlyeverhavetobecompletelydiscarded.However,itisimperativenottooverstrainthemortotreatthemsloppilyandtoresistboldclaimstomaintainscienti icstandards.

Aims and Scope 

Although experimental scientists strive for the best possible data, theymust often dealwithmistakes,systematicerrors,unforeseenbehavior,andmodel limitations. Hav‐ingseveralmethods forevaluation[1] athandhelps toavoidunsound interpretationandfrustrationwhenqualityexpectationsarenotmet.

Herein,wegiveanexampleofthisbypresentingourmultimethodstudyoflithiumdiffu-sioninramsdellite-likeLi2Ti3O7,afastandstronglyanisotropicconductorwitharangeofproposedapplicationsfromenergystoragetolithiumprocessing.[2]

References and Acknowledgements 

[1] D. Wiedemann, M. M. Islam, T. Bredow, M. Lerch, Z.Phys.Chem.2017,inpreparation.

[2] D. Wiedemann, S. Nakhal, A. Franz, M. Lerch, SolidStateIonics2016,293,37–43.

Financial support from DFG(FOR 1277: “MobilityofLithiumIonsinSolids[molife]”) is gratefully acknowledged.We thank HZB for the allocation ofneutronradiationbeamtime.

Maps of Sca ering‐Length Density (SLD) 

TheSLD is theneutronanalogueof theelectrondensityprobed inX‐raydiffractometry.However,classical“Fouriermaps”(acquiredfromobservedintensitiesandmodelledphas‐es)arepronetoartifactsandstructurednoise.ThereconstructionofSLDusingmaxi-mum-entropymethods (MEM) over‐comes this by yielding densities withthe least additional information (i.e.,the highest entropy) in the range ofmeasurementerror.

For Li2Ti3O7, the MEM reconstructionshows a smearingofnegativeSLDinthechannelsalongb, causedbydisor‐der/migration of lithium‐7. This hintsatmany energetically similar ion posi‐tions and the structure being ameta-stable“snapshot”ofthehighlydynam‐ic situation during synthesis at morethan950°C.

Figure  2.  Crystal‐structure  detail  of  Li2Ti3O7  at 422 °C with SLD isosurface for ρb = –0.08 fm Å–3. View approximately along [3 1̅0̅ 0], ions with ar‐bitrary radii.

Probability Densi es and Migra on Barriers 

Derivation of the probability-density function (PDF)and the one-particlepotential(OPP)arethetoptierofprobingiondiffusionvianeutrondiffraction.Theformermodelstheprobabilityof indinganionataspeci icposition(i.e.,thediffusionpathway),thelat‐tergivestheassociatedeffectivepotentialenergy(i.e., theactivationbarrierformigra‐tion).Unfortunately,theirde‐termination requires unam‐biguous high‐quality data,whichisoftenhardtoobtain.

In ramsdellite‐like Li2Ti3O7,we found a case of severelithium disorder that wewereunabletotreatwiththediscretemodels needed forPDF/OPP analysis. Only onepositioncouldberesolvedac‐cordingly,hintingatdiffusioninspaciouschannelsalongb.

Figure  1. Crystal‐structure detail of  Li2Ti3O7 at 24  °C. View approximately along b, Li2 as PDF isosurface of 0.1 Å–3, oth‐er ions as spheres and ellipsoids of 50% probability, unit cell in black.

Voronoi–Dirichlet Par oning (VDP) 

TheVDPisakindoftopologicalanalysisthatrequiresadivisionofthecrystalintostatic(framework)andmobile(interstitial)species.Themethodassignseachpointinspacetothenearestatomiccenter;onlythecrystalstructureoftheframeworkisneeded.Infer‐enceofpriorknowledgeaboutthemobilespecies’stericandelectrostaticrequirementsyieldsmoreandlesspreferreddiffusionpaths.

ForLi2Ti3O7, thismethodwasespeciallyappealing,as itdoesnotrelyon thepositionofthe lithium ions. Twopossiblepathwayswere revealed: a preferred one through thechannelsalongbandalesspreferredonethroughframeworkcationvacancies.

Figure 3. Void structure of the Ti3O72– framework at 422 °C as found by VDP. Intact channels on 

the le , framework vacancy on the right; ions, void centers, and channels with arbitrary radii. 

Procrystal‐Void Analysis (PVA)

Anothertopologicalmethod,thePVA,reliesonthesameinformationastheVDP,butusesdifferent prior knowledge. It approximates all framework atoms as spheresofdiffuseelectrondensity, constructing theso‐called“procrystal”. Itsvoids (de inedbyanupperdensity limitρpro) are theplacestopreferablyhostandconductmobile species. Thismethodappealsbecauseofitseaseofuseandavailability,evenifempiricaldataforste‐ricandelectrostaticdemandsareinaccessible.Itis,however,morepronetomisinterpre-tationanddoesnotrationalizepreferenceforonepathwayoveranother.

Forramsdellite‐likeLi2Ti3O7,PVAhascorroboratedtheabovementionedpathwaysandtheirrelativelikeliness.

Figure 4. Procrystal‐void surface of the Ti3O72– framework at 422 °C for ρpro = 0.006 a.u. Intact 

channels on the le , framework vacancy on the right; ions with arbitrary radii.