1. IntroductionOpen framework materials play an important

role in heterogeneous catalysis, rechargeablebatteries, ion exchange, molecular sieves, andother applications where multiple cycles of in-tercalation/deintercalation are of main concern[1]. Demand on novel or improved existing materials for rechargeable lithium batteries isgrowing in accord with rapid development ofmodern technology, mostly because of the needof advanced energy sources for various elec-tronic devices starting from miniature but longlasting medical pumps or monitors, e.g. heartsupport, to large and powerful batteries for hy-brid electric vehicles. Such a broad spectrum ofbattery applications implies a wide range oftheir properties. The most important of whichare the capacity either by weight or by volume,the lifetime of the battery, as well as its safetyand environmental issues.

In order to improve existing or develop novelmaterials, establish structure–property relation-ship, and find more effective synthetic routes,the knowledge of the crystal structure and un-derstanding the structural changes during thebattery performance is one of the first priorities.Thus, the structure has to be determined usingeither the single crystal or the powder diffrac-tion methods. The former one is limited by the

size and the quality of the crystals obtained dur-ing the synthesis. This seldom can be improvedby re-crystallization not only because of the extended framework but often because of the metastable nature of the hydrothermallyprepared phases. Moreover, intermediate sub-stances or materials that undergo multiple in-tercalation/deintercalation cycles rarely formsingle crystals of suitable size and often havelow crystallinity or even become amorphous.Despite the substantially lowered requirementsin the size of the single crystal due to the use ofthe area detectors, the crystal must still be sev-eral teens of microns at the best. Thus, in manycases the structural studies must be conductedusing the powder diffraction data, which havebeen substantially improved during the lastdecade mainly because of the development ofnew methods and software but also due tomuch faster computing.

2. Battery MaterialsThe operation of rechargeable lithium batter-

ies is based on the intercalation/deintercalationof the lithium ions. The battery consists of acathode, anode and electrolyte as shown in Fig-ure 1 (top). The cathode today is made of a tran-sition metal oxide or phosphate with the openframework structure with additions of binder

THE RIGAKU JOURNALVOL. 21 / NO. 1 / 2004, 2–14

STRUCTURE DETERMINATION FROM POWDER DIFFRACTIONDATA–CHALLENGING BATTERY MATERIALS

PETER Y. ZAVALIJ AND M. STANLEY WHITTINGHAM

Department of Chemistry and Institute for Materials Research, State University of New York at Binghamton, Binghamton, NY 13902, USA

In recent years, the search for novel and improving existing materials that can be used as acathode in rechargeable lithium batteries become one of the most important priorities of mod-ern technology. This work discusses some structural features and transformation of the batteryrelated materials. It summarizes peculiarities and additional challenges imposed by the openframeworks on powder structure determination, which is already far from trivial. Despite thedifficulties, ab-initio crystal structure solution was successfully used to determine the structureof nearly 20 battery related materials. Most of the structures were challenging in many differ-ent ways: ab-initio indexing in the presence of other phases or pseudo-symmetry; powder pat-tern decomposition and Rietveld refinement with substantial peak broadening or overlapping;complex preferred orientation and its handling during the structure solving and refinement.The main challenge–solving the structure was done using either the reciprocal space ap-proaches such as heavy atom (Patterson) method and direct methods, or the real space model-ing such as geometry optimization, energy minimization, and global optimization, but alwaysinvolving de facto or a priori chemical and structural knowledge as well as any available ana-lytical data.

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(Teflon) and conductor (acetylene black). Theanode is typically pure lithium, lithium interca-lated graphite or a lithium alloy. The electrolyteis an organic solvent with added lithium salt toallow the transport of lithium ions between thetwo electrodes. A separator, which is wetted by the electrolyte system, prevents electronicshorting so that only lithium ions can moveback and forth. When the battery is discharging,the Li ions move through the electrolyte to-wards the cathode and intercalates into theopen structure material. The electrons move to-wards the cathode though the load (upper halfof the circuit) and are absorbed by the transitionmetal oxide or phosphate framework. The tran-sition metal is being reduced decreasing its oxi-dation state. When the battery is charged, allprocesses are reversed; the electrons, the Liions, and the current flow in the opposite direc-tion and transition metal is being oxidized. Allthat demands certain specific requirements ofthe cathode material. It should be able interca-late and deintercalate lithium without substan-tial structural changes in the open framework.

The structure transformation can also takeplace but both structures should be closely re-lated and be able to transform one into anotherwithout or with only minimal changes in theconnectivity or bonding. On the other hand thecharging/discharging of the battery being a red-ox reaction requires the framework metal tohave more or less wide range of oxidationstates, for which the metal coordination polyhe-dra are similar, if not the same. For example,vanadium in the oxidation states 2� and 3� hasa regular octahedral environment, while forvanadium 5� and 4� the octahedra are dis-torted and may even become square pyramid(one corner missing). Thus, vanadium com-pounds can theoretically cycle up to 3 Li atomsper one V atom.

Typical cycling of the battery material shownin Figure 1 (bottom) reveals the properties ofthe electrochemical cell, of which the capacityand capacity fading are of main concern. Theformer shows the total charge that can be accu-mulated in the battery, while the latter—capac-ity fading (or cyclability) defines the battery life-time. Potential of the cycle depends on the typeof the battery material and is of less impor-tance. For example, when it is low (e.g. below 1V) the material can be potentially used not asthe cathode but as the anode material. In orderto be considered for commercial use, the bat-tery materials should have capacity of at least120 mAh/g and good cyclability—show no sub-

stantial loss of the capacity for hundreds of cy-cles. The safety and environmental issues arealso of great concern.

Based on the structural transformation duringthe cycling, the electrochemical cells are di-vided into two types. The first, shown in Figure2, a, is so called single phase or solid solution.In this case the battery material always consistsof single phase, which composition (the lithiumcontent) changes continuously in the course ofthe intercalation/deintercalation process. Thesecond type, shown in Figure 2, b, is two phasesystem. Here no solid solution is formed. Dur-ing the intercalation/deintercalation reaction theratio between the two phases changes but thecontent of the lithium in each phase is constant,so the cell voltage remains constant.

Often a complex combination of one or bothof the two cases is observed as shown in Figure3 for the reaction of lithium into metallic tin foilthat was tested for anode material [2]. Here dur-ing the electrochemical discharge the followingphase transitions occurs:

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Fig. 1. The scheme of the lithium battery on dis-charge, when charging the direction of all arrows al-ternates (top), and the electrochemical cycling dia-gram showing most important battery parameters(bottom).

Sn →Li0.4Sn →LiSn →Li2.3Sn

→Li2.6Sn →Li3.6Sn.

These phase changes combined with thestructural and chemical requirements for theopen framework materials discussed previouslymake the powder diffraction method an effec-tive and often irreplaceable tool for studyingopen frameworks of battery materials. For example, accurate unit cell refinement in thesolid solution systems or the Rietveld structurerefinement in two-phase system can be used to determine Li content in the process of thecharge/discharge process. This is especially

useful when in situ diffraction is used. Ofcourse, the crystal structure solution of novelcompounds and accurate structure refinementof known or improved materials are essential inestablishing the structure—property relation-ship. There is only one example when singlecrystal analysis was used, which is the study ofLinV6O13 system using special electrochemicalcell to grow lithiated crystals [3–5]. The currentstate of the powder structure determinationleaves no excuses when such valuable informa-tion is omitted from the materials characteriza-tion.

3. Powder Structure DeterminationThe diffraction pattern from polycrystalline

materials can be described as one-dimensionalprojection of three-dimensional diffraction datathat results partial and/or complete overlappingof some diffraction maxima (peaks). The over-lapping defines the principal difference betweenthe powder and single crystal diffraction pat-terns and makes the former more challenging.However, the main challenge is not in the pow-der structure determination itself but in doing itfrom the diffraction data which quality or crys-tallinity is not the best. The reason for this isthat the good crystallinity means quite highchance of finding a crystal suitable for singlecrystal experiment. However, when dealing withcrystalline materials of low quality or crys-tallinity, those that exhibit low diffraction inten-sity or broad peaks, the single crystal diffractionusually fails, while the powder method still canyield acceptable patterns. From another point ofview, the preference or necessity of the powderdiffraction consists in inability to grow suitablecrystals because of the metastability of many ofthe open framework materials or because oflimits imposed by the synthetic routes used.The powder diffraction is also irreplaceable forin situ studies. It is the only way to determine orconfirm the structure of the resulting and inter-mediate phases and their transition in the inter-calation/deintercalation process. Examples oftypical polycrystalline materials are shown inFigure 4, none of those crystals have size andquality acceptable for the routine single crystalexperiment.

The three main steps in the powder structuredetermination, not counting instrumental andsample preparation issues, are following:– indexing the powder pattern (determination

of the unit cell dimensions);– solving the crystal structure of new materials;– the crystal structure refinement and complet-

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Fig. 2. Discharge semi-cycle in: a) solid solutionsystem always consisting of one phase with variablecontent of the lithium LixMnOm (x�0) ; b) two phasesystem in which the Li content is defined by ratio be-tween two phases xLiMnOm�(1�x)MnOm (0�x�1)(the caption shows the total composition of the sam-ple).

Fig. 3. Electrochemical cycling in a complex multi-step system Sn–Li3.5Sn.

ing the structural model.

Indexing the powder patternThe first step consists in finding the unit cell

dimensions that best describe the position ofthe diffraction peaks on the powder pattern. Nomistakes are tolerated at this stage because fail-ure or incorrect solution disables the followingstructure determination.

The indexing can be performed using varietyof the available methods such as already classicprogram ITO [9], TREOR [10] and DICVOL [11]that use position of the diffraction peaks and re-cently developed algorithms realized, for exam-ple, in McMaille [12] and Xcell [13] that employglobal optimization and global search of theunit cell dimensions. All software generate sev-eral best possible solutions and the role of theinvestigator, which is still very important, is todecide which solution is the true one or at leastwhich one to start test with. Obviously, the finalproof of the unit cell correctness is the determi-nation of the crystal structure.

The main challenges in the pattern indexingthat has to be considered are:– systematic error in the peak positions be-

cause of sample transparency of sampleswith medium to low absorption and other ef-fects;

– presence of impurity peaks;– accidental non-crystallographic relationship

between the cell dimensions;– factors decreasing accuracy in the peak posi-

tions such as peaks overlapping and broad-ening.In case of the open framework materials in

addition to the general problems listed abovethe following issues have to be considered:– additional weak diffraction peaks from the

sublattice or modulated lattice, which some-times happen in case of misfit—the size of in-tercalated species does not match the period-

icity of the framework;– substantially intensified peaks for the reflec-

tions from only one zone due to the signifi-cant preferred orientation effect that cannotbe predicted at this stage;

– high anisotropy of the peak broadening andothers.

Solving the crystal structureObviously, this step is the most important in

the structure determination and consists in cre-ation of the structure model as close to globalminimum (true structure) as possible. Some-times the model can be imported from similaror isostructural phases or derived from generalcrystal-chemical considerations for relativelysimple compounds. Usually the structure ofnovel material has to be solved from the firstprincipals. There are two principally differentapproaches of doing that:– The first, traditional approach works in the

reciprocal space (diffraction data) using directmethods or heavy atom (Patterson) method.It requires preliminary determination of thediffraction intensity of the individual reflec-tions (as accurate as possible), which is doneusing profile fitting or full pattern decomposi-tion methods [14, 15]. The real space (thestructure itself) is used to evaluate the rea-sonability of a generated model. Basically thesame programs that are used to solve singlecrystal structures are used to solve structurefrom the powder diffraction data, e.g.SHELXS [16].

– The second approach searches for a model in direct (or real) space and evaluates thequality of the model by comparing calculat-ed profile to the experimental diffraction pattern. Most commonly used programs for ab initio structure determination exploitvariety of global optimization methods, forexample simulated annealing or parallel tem-

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Fig. 4. SEM images of VO(OCH2CH2O) [6], g-MnV2O5 [7], and tmaV8O20 [8]. White bar corre-sponds to 10 mm.

pering algorithms realized in FOX [17] andPowderSolve [13].It is up to the researcher to decide which

model is true, if several close solutions arefound, and check its common chemical andcrystal-chemical sense. The final structure is al-ways confirmed by the following Rietveld re-finement.

The main concern in solving the structurefrom the powder data is resolution of the reflec-tions on the diffraction pattern. Any substantialoverlapping of the reflections lowers the qualityand makes the true solution less distinguish-able. Heavy overlapping makes the structuredetermination very difficult if not impossible. Inthis case the direct space search, e.g. global op-timization method, becomes much more advan-tageous. Additional difficulties in the powderstructure solution, that are usually found whendealing with the open framework materials, areprovided by factors that affect intensity of thediffracted peaks, for example such as huge pre-ferred orientation or weak absorption, and otherfactors that decrease intensity or increasebroadening of the peaks.

Crystal structure refinement—the Rietveldmethod

The refinement of the crystal structure frompowder diffraction data is conducted by the Rietveld refinement [18] that employs least-square method to minimize the difference be-tween observed and calculated powder pat-terns. This implies that in addition to the atomicparameters, which are the only parameters opti-mized in the single crystal refinement, there areparameters that describes the profile of thepowder diffraction pattern and some other cor-rections. These are:– cell dimensions which define the position of

the peaks;– parameters describing shape of the diffrac-

tion peaks and its angular distribution;– parameters, such as preferred orientation and

absorption, that affect the diffracted intensity.The preferred orientation and absorption cor-

rections are very important in the powder struc-ture refinement in general and are of the specialconcern when dealing with the open frameworkmaterials that are often layered materials. Thepreferred orientation effect results in non-ran-dom orientation of the particles that dependson their shape. The two common shapes areplates and needles or fibers, examples of whichare shown in Figure 4, b, c respectively. Obvi-ously, it is almost impossible to achieve com-

pletely random distribution of the particles withsuch anisotropic shape. Especially in such caseas one depicted in Figure 4, c. The distributionof these ribbon-like crystals is highly anisotropicand therefore very complicated and its properhandling requires two axes for the classicMarch–Dollase preferred orientation function[19] or complex distribution function, e.g. suchas realized in spherical harmonic approach [20].

There is variety of the software for the Riet-veld refinement: freeware GSAS [21], Rietica[22], FullProf [23], along with commercial Reflex[13], WinCSD [24], and many other.

Detailed discussion on powder diffractionmethods and structure determination frompowder data is discussed in many books, fromwhich the most recently published [25–28] coverX-ray powder diffractometery, the Rietveld re-finement, modern methods of the structure so-lution, and other aspects.

4. Structure Determination of BatteryMaterials and Related Compounds

The search for new battery materials and im-provement of the existing ones has been con-ducted at the Institute for Materials Research atBinghamton University for more than decade[29]. The crystal structure of several dozens ofthe novel compounds was determined from thepowder diffraction data. Obtained structural in-formation in combination with single crystal re-sults was used: to analyze the relationship be-tween different structure types, e.g. in vana-dium oxide frameworks [30]; to establish struc-tural changes or phase transition during the in-tercalation and deintercalation processes in theelectrochemical cell, e.g. in Li–VOPO4 systems[31]; to improve synthetic methods, e.g. role ofthe pH in synthesis of the vanadium oxideframeworks [32, 33]; or to link the red-ox prop-erties with the coordination of the transitionmetal [30].

This work summarizes and discusses thepowder structure determination issues for thesematerials and some of their structural features.

4.1. Layered Molybdenum Oxide StructuresThe use of molybdenum compounds as the

battery materials is limited by their weight ca-pacity that is low comparing to 3 d metal ox-ides. However, molybdenum exhibit wide rangeof the oxidation states and readily form theopen framework structures. Because of that themolybdenum compounds can be used as modelmaterials. The cluster or ionic molybdenumcompounds crystallize very well but the open

6

framework materials, especially layered onesoften produce only polycrystalline samples. Forexample the tetramethylammonium (tma) andmethylammonium (ma) form at hydrothermalconditions fine powders, which crystal structurewas determined from the powder diffractiondata as is discussed below.

tmaMo4O12 [34]Tetramethylammonium, [N(CH3)4]

�, interca-lates into molybdenum oxide to form finebronze powder. The powder pattern was in-dexed in a monoclinic system and crystal struc-ture solved by direct methods using extractedintegrated intensities. Two independent Moatoms found initially were enough to locate 9light atoms (except hydrogen) from the conse-quential difference Fourier maps. The positionof remaining two carbon atoms was calculatedfrom geometrical considerations. This materialexhibits strong and unusual preferred orienta-tion because of graphite-like morphology of theparticles. It consists of three “phases”, whichprofiles are shown separately in Figure 5:a) the main tmaMo4O12 phase with March–Dol-

lase PO refined to give a reasonable magni-tude* of about 1.5;

b) an impurity phase that was identified and re-fined as MoO2;

c) a thin surface layer of practically parallelplatelike particles of the tmaMo4O12 phasethat approximately doubles intensity of the00 l reflections, for which an additional scale

multiplier was introduced†.The final Rietveld refinement (sp. gr. C2/m,

V�1434.9(3) Å3, 2qmax�66°, 287 reflections, 13independent atoms, RB�9.6%, Rp�10.4%, POaxis 001, total magnitude 3.5) was conductedwithout any constraints. Despite the strong PO,complex structure and somehow broad peaks,especially at higher angles, refinement resultedin good agreement between observed and cal-culated profiles, reasonable coordination poly-hedra, bond lengths, and intermolecular con-tacts. Practically identical layer (Figure 6) wasfound later in enH2Mo4O12 structure solved fromsingle crystal data [35].

ma2Mo7O22 [36]This molybdate has more complex structure.

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* Ratio of the maximal to minimal PO corrections.

† Sample was never pressed but surface had to be flat-tened with razor. Using the side filling or mixture withamorphous substance resulted no improvement on the par-ticle distribution.

Fig. 5. The Rietveld refinement of tmaMo4O12: a) the observed plot with subtracted (b) and(c); b) calculated plot for MoO2 phase; c) calculated plot for a thin surface layer of the mainphase. The vertical lines show the position of the reflections.

Fig. 6. Polyhedral representation of the Mo4O12

layer.

The powder pattern was indexed in a mono-clinic system using ITO program. Initial modelof the Mo7O22 layers was incorporated fromknown thallium structure [37], which was foundusing exact composition determined thermo-gravimetrically. The intercalated methylammo-nium ion, [CH3NH3]

�, was undoubtedly locatedfrom the difference Fourier map. Contact dis-tances to oxygen atoms were used determinethe orientation of the ma cation, based on thehydrogen bonds formed. The Rietveld refine-ment (sp. gr. C2/c, V�2092.22(4) Å3, 2qmax�98°,RB�3.8%, Rp�4.7%, PO: March–Dollase, axis100, magnitude 2.2) converged without anyconstraints at low residuals despite the com-plexity of the structure (17 independent atoms)and the diffraction pattern (1026 reflections).

4.2. Simple Vanadium OxidesVanadium oxide structures were found to

form even broader diversity of the open frame-works than molybdenum compounds, whichalong with wide range of the oxidation stateand light weight, make them very promisingbattery cathode materials. The series of novelvanadium oxides and intercalates were pre-pared using hydrothermal technique. Many ofthese novel materials can be obtained only inpolycrystalline from and, therefore, the powderdiffraction data have to be exploited to deter-mine their crystal structure that is discussed fur-ther.

LixV2–ddO4–dd · nH2O [38]This simple structure with just several diffrac-

tion peaks on the powder pattern, which was in-dexed using TREOR program in a tetragonalbody-centered cell. Analysis of the Pattersonmap resulted positions of one vanadium andtwo oxygen atoms. Further refinement revealedthe presence of the water molecule between thelayers. However, there were some complica-tions: noticeable higher displacement parame-ters for the heavier vanadium atoms comparingto the lighter oxygen atoms of the framework,and water molecule residing on the fourfoldaxis appeared to have a disk-like ellipsoid.

The final Rietveld refinement (sp. gr. I4/mmm,V�216.95(2) Å3, 2qmax�100°, 42 reflection, 4atoms, RB�4.0%, Rp�8.3%, PO: WinCSD, axis001, magnitude 1.2) included an occupation fac-tor of the vanadium atom and terminal oxygenatom (one that is attached only to the vanadiumatom) and displacement of the water moleculefrom the special position. The final compositionwas found to be Li0.3V1.67O3.67·H2O with about1/6 of the vanadium sites being vacant. The po-

sition of the lithium atom was not found evenfrom neutron data due to its small amount andweak scattering. It is assumably located in theplace of vacant vanadium atom or nearby.

This structure, constructed of vanadiumsquare pyramids directed up and down in thechess-order (Figure 7), can be considered as theparent for many other vanadium oxide layers.Later, the same structure was found for anothervanadium oxide (without lithium) using singlecrystal data [39].

LixV2–ddO4–dd [40]The anhydrous lithium vanadium oxide (sp.

gr. P4/nmm, V�92.34(3) Å3) forms when the hy-drate is heated above 120°C. Its structure can beeasily deducted from the hydrate as shown inFigure 7 assuming that apical oxygen atoms ofthe framework will slide into position fromwhere water is removed. The Rietveld refine-ment confirmed this model.

4.3. Layered Vanadium Oxide StructuresIntercalation of the inorganic and organic ions

between the vanadium oxide layers often in-creases the framework stability and the size andproperties of the ions defines the type of theframework formed. Sometimes the ion size andthe periodicity of the oxide framework are in-commensurate, which yields disorder of ions ormodulation of the framework that provides ad-ditional challenges for the structure determina-tion especially from the powder data. However,the greatest challenge is relatively low vana-dium scattering factor. This requires better ac-curacy of the initial model than for example incase of stronger scattering molybdenum. Thus,usually it is not enough to determine position ofonly vanadium atoms and therefore more ad-vanced and powerful methods of the structuresolution are needed.

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Fig. 7. Transformation between hydrated and an-hydrous forms of LixV2–dO4–d.

tmaV3O7 [41]The powder pattern of this vanadate was in-

dexed using ITO program in a primitive mono-clinic lattice. However, its crystal structure wassolved using direct methods only after the crys-tal-chemistry of the vanadium oxides (possibleconnectivity, polyhedra, etc.) was studied. Suc-cessful initial model contained three vanadiumatoms and four of seven oxygen atoms. Rest ofthe oxygen atoms and five atoms of the organicion were located from several sequential differ-ence Fourier syntheses. The final Rietveld refinement (sp. gr. P21/n, V�1020.1(1) Å3,2qmax�67°, 424 reflections, 15 atoms, RB�5.2%,Rp�7.8%, PO: WinCSD, axis 100, magnitude 2.7)revealed quite strong PO which could be ex-pected from such thin plate-like crystals shownon the inset in Figure 8.

Resulting new type of the V3O7 layer ap-peared to be missing member of V6O14 series[42], which along with quite reasonable bondlengths and polyhedra, confirms the correct-ness of the structure.

tmaV8O20 [8]This thetramethylammonium vanadate was

obtained at much lower pH than previous inform of only micron thick fibers (Figure 4,c). Thediffraction peaks were quite broad ranging from0.15 to 0.20° 2q at low and medium angles. Thepeak shape was also unusual practically ap-proaching pure Lorenzian that along with the el-evated peak-width could be expected from thesmall size of the crystalline fibers. Indexing ofthis powder pattern succeeded only after ex-cluding several weak low-angle peaks, which

were assumably modulation satellites or impu-rity peaks.

The structure solution was performed by di-rect methods using extracted integrated intensity yielding vanadium and some of theoxygen atoms. Rest of the oxygen atoms andatoms of the disordered organic ion were lo-cated from the difference Fourier maps. Thefinal Rietveld refinement (sp. gr. C2/m, V�523.1(1) Å3, RB�6.71%, Rp�6.77%, PO: March–Dollase, axis 100, magnitude 1.2) resulted rea-sonable structure with novel type of the layerthat is made of quadruple octahedral chainssharing two corners as shown in Figure 9. Thisbuilding block is found in other double-sheetvanadium oxide layers of different configura-tion. Disorder of the intercalated ion could beanticipated because of incompatibility betweenthe ion size of about 6 Å and the repeat distancealong the b axis that is only 3.6 Å. This type of

9

Fig. 8. The Rietveld refinement of tmaV3O7. Inset shows plate-like morphology of the crystals.

Fig. 9. The crystal structure of tmaV8O20: the vana-dium oxide layer is shown with polyhedra and disor-dered the tma molecule with balls.

disorder happens quite often in the intercalatedstructures and was approximately modeled byoccupationally disordered carbon and nitrogenatoms.

teaV8O20 and imd4V8O20 [43]Recently, two new compounds with the same

type of the layer were prepared: tetraethylam-monium (tea) and imidazolium (imd) vanadates.The first structure was solved using directmethods and is isostructural to tmaV8O20. It hassimilar morphology and gives similar powderpattern. The second material behaves differ-ently. It has higher ion to metal ratio, crystal-lizes in a different space group (P21/m) with dif-ferent cell dimensions, and forms very long andthin fibers, so thin that the sample looks likecotton. It cannot be packed and turns into thepaste on grinding. The preferred orientation isvery high and only few weak peaks that do not belong to hk0 zone can be observed. Thismakes both the indexing and the structure solu-tion quite difficult. Nevertheless, it was possibleto solve the structure using FOX program. Opti-mized were two vanadium octahedra and imdmolecule. The Rietveld refinement of the ob-tained model was performed using restrains onthe imd geometry and some vanadium to oxy-gen distances. Interestingly, this structure ap-peared to be ordered, while the tea structurehas the intercalated ion disordered similarly toand because of the same reason as tmaV8O20.

Vanadium oxide dd-phasesOne of the most common vanadium oxide

frameworks is so-called d-phase that consists ofa double sheet layer (Figure 10). This type oflayers is made of the same quadruple chain ofvanadium octahedra as the V8O20 layer but thechains are linked by sharing edges. The repeatdistance along the chain is about 3.7 Å, whichoften does not match larger intercalated speciesyielding disorder. Thus, the smaller ions such as metal ions, water, and ammonium are usu-

ally ordered as shown in Figure 10, while thelarger molecules are not, such as, for example,methylammonium (ma), tetramethyl ammo-nium (tma), tetraethylammonium (tea), metalcomplexes, and others.

The d-phase usually form polycrystalline materials with plate-like or fiber-like morphol-ogy of the particles, which size often lies in thesub-micron range. This introduces a range ofproblems (typical for layered intercalates) in theindexing of the powder pattern, solving thestructure and also the Rietveld refinement.These are broadening of the diffraction peaks(often anisotropic), strong preferred orientation,disorder, and others.

In most cases d-phase crystallizes in a mono-clinic system and space group C2/m. Some-times intercalated species yield different stack-ing of the layers with higher or lower symmetry.In such cases the crystal structure has to be solved ab initio as was done for triclinic LixteayV4O10·nH2O using synchrotron data [44].Otherwise, when similar structure is identified,the d-layer can be used as an initial structuremodel (NH4V4O10 [44], maxV4O10·nH2O [45],tmaxMyV4O10·nH2O (M�Fe, Zn, Mn) [46]). Theintercalated ions are then located from the dif-ference Fourier map. Only one of these fourstructures, NH4V4O10, shows ordered distributionof the interlayer ions.

4.4. Mixed Transition Metals FrameworksThe layered battery materials show good cy-

cling behavior but often their capacity retentionis not so good. The layers may collapse whenfully charged (all Li removed) or irreversiblytransforms into another phase when overdis-charged (too much Li inserted). The former caseis found in commercial LiCoO2 batteries, whichcan be destroyed when more than half Li atomsare removed. Many attempts are made to stabi-lize such layered materials. For example, it wasfound that intercalated species such as potas-sium in KxMnO2 [47] and tetramethyl ammo-nium in tma4[Zn4V21O58] [48] improve the cy-cling stability by keeping layers apart. Differentway is stabilizing the open framework itself byadding another metal that may or may not bered-ox inert. The search for new mixed openstructures yielded variety of novel compounds.These compounds are not necessary electro-chemically active or have the open framework.Still their crystal structure was determined andcorrelated with the cycling behavior. The pow-der diffraction data were used for structuralcharacterization of the following compounds:

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Fig. 10. Polyhedral representation of the d-layerwith ordered distribution of intercalated small ions.

Mn7(OH)3(VO4)4* [49], NiMnO2(OH) [45], g-MnV2O5 [7], Zn2(OH)3VO3* [48], Al2(OH)3VO4[50], Zn3(OH)2V2O7·2H2O [51], and others. Thestructure determination of the first two materi-als was not routine and is discussed below.

NiMnO2(OH) [45]This material exhibits powder diffraction of

good quality. Its crystal structure has an inter-esting three-dimensional extended framework

(Figure 11, a). Both powder pattern indexingand structure solution were habitual. However,the goal of the structure completion was to dis-tinguish Ni and Mn atoms and to locate hydro-gen atoms. The first was achieved by analysisof bond valence sum, which agreed with theelectron density distribution. The hydrogenatoms were located from the difference Fouriermap and then refined. The H atom forms typicalhydrogen bond and therefore makes goodchemical sense that is quite unusually for thepowder method. Nonetheless, the neutron dif-fraction data were used as an additional confir-mation, which is very reliable in this case be-cause of the negative neutron scattering factorof the hydrogen and manganese atoms (Fig-ure 11, b). The final Rietveld refinement wasperformed on combined X-ray and neutron data yielding low residual (sp. gr. Cmc21,V�220.880(5) Å3, RB�6.25%, Rp�4.99%, PO:March–Dollase, axes 010 and 001, magnitude3.99) and leaving no doubts in the distributionof the manganese and nickel atoms and loca-tion of the hydrogen atoms.

Mn7(OH)3(VO4)4 [49]This material yields high quality powder data

and has interesting pipe-like morphology (Fig-ure 12). The composition Mn7(OH)3(VO4)4 as-sumes full occupation of all sites. However,structure refinement revealed occupational dis-order for Mn atoms in the hexagonal tunnel andV and O atoms in the trigonal tunnel as markedin Figure 13 (top). The vacancy of the vanadiumand oxygen atoms is in accord when vanadium

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* Idealized composition.

Fig. 11. Polyhedral representation of the NiMnO2-(OH) (a) and the nuclear density distributions at x�0(b). Solid lines show positive values, thin dotted linesnegative, and thick dotted lines indicate zero level.

Fig. 12. The Rietveld plot of Mn7(OH)3(VO4)4. Inset shows pipe-like morphology of the crystals.

tetrahedra flip as shown in Figure 13 (bottom).This yields the formation of divanadate groupV2O7 and the following composition:

Mn7–x(OH)3(VO4)4–y(V2O7)y/2,

where x�0.137(4), y�0.195(4).The final Rietveld refinement (sp. gr. P63mc,

V�796.44(2) Å3, 2qmax�132°, 297 reflections, 10atoms, RB�8.7%, Rp�8.5%, PO: March–Dollase,axis 001, magnitude 2.7) yields good residuals.Recently, the disorder of the Mn, V and O atomswere confirmed* by single crystal data.†

4.5. Transition Metal PhosphatesIntroduction of the phosphate group into the

framework increases its stability during the cy-cling as well as the potential but for the cost ofslightly lower capacity. Thus, phosphates of 3dtransition metals are intensively explored forthe battery applications. Here are discussedpowder structure determination of novel ironphosphate, monoclinic FePO4, and structuraltransformation of vanadyl phosphate throughlithium intercalation/deintercalation process.

Monoclinic FePO4 [52]This compound forms as low crystallinity

powder on the thermal decomposition of hy-drated iron phosphate. The powder pattern, de-spite its low resolution (Figure 14), was success-fully (but not routinely) used for the indexingand solving the structure as is detailed in [52].

The structure determination was performed

using geometry optimization and energy mini-mization methods applied to the structuralmodel, which was deducted using the knowl-edge of structural transformation of the hy-drated orthorhombic iron phosphate into theanhydrous form. The final Rietveld refinementwas conducted with restrained geometry of thePO4 group yielding low residuals (sp. gr. P21/n,V�328.51(6) Å3, 2qmax�38°, 255 reflections, 6atoms, RB�3.2%, Rp�5.2%, PO: March–Dollase,axis 010, magnitude 1.5) and trigonal pyramidalcoordination of the Fe atom. This framework isvery similar to that found in iron arsenate (ex-cept slightly different distribution of short andlong bonds in the Fe polyhedra), which is an ad-ditional confirmation of this structure correct-ness.

VOPO4 and Its Li Derivatives [31]The use of vanadyl phosphates as cathode

material is promising because of their poten-tially high capacity, which is due to the widerange of the V oxidation states. The powderstructure determination was intensively usedfor: structural characterization of the electro-chemically intercalated materials, e.g. a-LiVOPO4,structure determination including lithium distri-bution (e-VOPO4 and a-Li1�xVOPO4, x�0, 0.75),determination of the composition of the dis-ordered phases (tetragonal (VO)xHyPO4). Thisstructural information explains transformationbetween the phases (Figure 15) and some struc-ture–property relationships.

4.6. Electrolyte Salts and Related CompoundsIn attempt to replace fluorine or arsenic con-

taining lithium salts, which are currently in useas a source of conducting lithium ions in the

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* P. Y. Zavalij: unpublished data.† Bruker SmartApex diffractometer, 110 K, crystal size 0.10�

0.02�0.007 mm, sp. gr. P63mc, a�13.2220(7) Å, c�5.2444(4)Å, V�794.00(8) Å3, Rw�4.36%, R1�2.29%.

Fig. 13. Polyhedra representation of the Mn7(OH)3-(VO4)4 structure (top) and VO4–V2O7 disorder in thetunnel (bottom).

Fig. 14. The Rietveld plot and polyhedral repre-sentation of the monoclinic FePO4.

battery electrolytes, the new safer lithium bis-(oxalato)borate (BOB) is being explored. How-ever, its structure as well as structure of anyother BOB compounds were unknown. Here, abinitio crystal structure determination from thepowder data of Li, Na and K BOB salts is dis-cussed.

LiB(C2O4)2 [53]This compound crystallizes in a form of fine

white powder yielding relatively broad diffrac-tion peaks (Figure 16). Multiple attempts togrow single crystal using variety of solventsyield only solvated crystals. Therefore, the pow-der structure determination was unavoidable.The challenge was not the fact that oxygenatoms were the heaviest in this compound butan accidental pseudo-hexagonal relationshipbetween the cell dimensions of an orthorhom-bic cell. As result, the best indexing solutionwas always incorrect hexagonal cell but not theorthorhombic. This also imposes additional dif-ficulties for structure solution since most of thediffraction peaks contain overlapped reflections.Thus, real space method of structure solutionwas a must. This was done by optimizing twospecies, Li atom and rigid body BOB molecule,using parallel tempering method realized inFOX software. Details on the indexing and solv-ing the structure can be found in [53].

The final Rietveld refinement included re-strains on the distances (but not the angles) ofBOB and converged with low residuals (sp. gr.Pnma, V�636.99(6) Å3, 2qmax�60°, 104 reflec-

tions, 14 atoms, RB�3.4%, Rp�9.4%, PO: spheri-cal harmonics, magnitude 1.2) and reasonablesquare pyramidal environment of the Li atom.

MB(C2O4)2 (M�Na, K) [53]In order to gather more information about un-

known structures of the BOB salts, correspond-ing sodium and potassium compounds wereobtained and their crystal structure was deter-mined from the powder diffraction data. Bothmaterials appears to be highly crystalline andisostructural. The crystal structure of the potas-sium compound was solved by direct methods.The Rietveld refinement resulted very low resid-uals for both compounds (e.g. NaBOB: sp. gr.Cmcm, V�657.27(2) Å3, 2qmax�90°, 138 reflec-tions, 14 atoms, RB�3.1%, Rp�6.9%, PO: spheri-cal harmonics, magnitude 1.4) and an interest-ing structure with square tunnels as shown inFigure 17.

13

Fig. 15. The relationship between vanadyl phos-phates and their lithium intercalates.

Fig. 16. The Rietveld plot and the crystal structureof LiB(C2O4)2. Boron atoms are embraced with semi-transparent tetrahedra.

Fig. 17. The Rietveld plot and crystal structure ofNaB(C2O4)2.

AcknowledgementThis work was supported by the National Sci-

ence Foundation through grant DMR-0313963.

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