Reaction energetics and crystal structure of Li4BN3H10 from first principles

0.2 MB·English

by  Donald J. Siegel

Firstprinciples study ofthecrystal structure and dehydrogenation pathways ofLi BN H
4 3 10
Donald J. Siegel and C. Wolverton
PhysicalandEnvironmentalSciencesDepartment, FordMotorCompany,MD3083/RIC,Dearborn, MI48121
V. Ozolin¸sˇ
Department ofMaterialsScienceandEngineering, UniversityofCalifornia, LosAngeles, CA90095
7 (Dated:February6,2008)
0
0 Usingdensityfunctionaltheoryweexaminethecrystalstructureandthefinite-temperaturethermodynamics
2 of formation and dehydrogenation for the new quaternary hydride Li4BN3H10. Two recent studies based on
X-rayandneutrondiffractionhavereportedthreebcccrystalstructuresforthisphase. Whilethesestructures
n
possessidenticalspacegroupsandsimilarlatticeconstants,internalcoordinatedifferencesresultinbondlength
a
J discrepanciesaslargeas0.2A˚.Geometryoptimizationcalculationsontheexperimentalstructuresrevealthat
theapparentdiscrepanciesareanartifactofX-rayinteractionswithstrongbondpolarization;therelaxedstruc-
3
turesareessentiallyidentical.Regardingreactionenergetics,thepresentcalculationspredictthattheformation

reaction3LiNH +LiBH →Li BN H isexothermicwithenthalpy∆HT=300K = −11.8kJ/(molf.u.),con-
] 2 4 4 3 10
ci sistentwithreportsofspontaneousLi4BN3H10 formationintheliterature. Calorimetryexperimentshavebeen
reportedforthedehydrogenationreaction,buthaveprovendifficulttointerpret. Tohelpclarifythethermody-
s
- namicsweevaluatethefreeenergiesof seventeen candidate dehydrogenation pathways over thetemperature
rl rangeT =0–1000K.AttemperatureswhereH2-releasehasbeenexperimentallyobserved(T ≈520–630K),
t thefavoreddehydrogenationreactionisLi BN H →Li BN +LiNH +4H ,whichisweaklyendothermic
m 4 3 10 3 2 2 2
[∆HT=550K = 12.8kJ/(molH )]. Thesmallcalculated∆H isconsistentwiththeunsuccessfulattemptsatre-
2
. hydridingreportedintheliterature,andsuggeststhatthemoderatelyhightemperaturesneededforH-desorption
t
a resultfromslowkinetics.
m
PACSnumbers:64.70.Hz,65.40.-b,71.15.Nc,81.05.Zx
-
d
n
o I. INTRODUCTION possible (and has been partially demonstrated6) through the
c additionofcatalyticdopants6,9orvianovelsyntheticroutes,10
[ suggestingthatfurtherstudyofthissystemiswarranted.
Recenteffortstoimprovetheefficiencyandreducetheen-
2 vironmentalimpactof automobiletransporthave focusedon ThecompositionofthenewLi-B-N-Hphasewasprelimi-
v hydrogen-based fuel cells (FC) and internal combustion en- narilyidentified4as“Li3BN2H8,”butsubsequentexperiments
7 gines(H ICE)aspossiblereplacementsforcurrenttechnolo- based on single crystal X-ray diffraction,11 and, synchrotron
2
8 giespoweredbyfossil-fuels.1Asignificantobstacletorealiz- X-rayandneutronpowderdiffraction,12identifieditstruestoi-
6
7 ingthistransitionistheon-boardstorageofhydrogenathigh chiometryasLi4BN3H10.Combined,thesediffractionexperi-
gravimetricandvolumetricdensities.2 Toachievethestorage mentsidentifiedthreesimilarcrystalstructures,allsharingthe
0
6 densities necessary for mobile applications, novelmeans for bccspacegroupI213withlatticeconstanta=10.66–10.68A˚,
0 H-storagearenecessary,andasetoftargetshavebeenestab- but with somewhat different internal coordinates. The dis-
/ lishedtoguidethesearchfornewstoragesystems.3Atpresent crepancyinatomicpositionsresultsinN-Hbondlengthsthat
t
a noknownstoragematerialormechanismmeetsthesetargets. differ between structures by as much as 0.2 A˚, with smaller
m One promisingavenuefor efficientstorage of hydrogenis N-H lengths reported for the X-ray structures. It has been
- via solid state storage, such as in the form of complex- or suggestedthatthediscrepancymaybeanartifactofX-rayin-
d
metal-hydrides. Solid storage has the advantage of provid- teractions with strongly polarized electron clouds along the
n
ing volumetric densities beyond what can be achieved with N-Hbonddirection.11
o
c compressedH2 gasorcryogenicliquidstorage. However,all A careful characterization of a hydride’s crystal struc-
: knownhydridessufferfromoneormoreofthefollowinglim- ture is desirable because it enables an independent, ab ini-
v
itations:lowgravimetricdensities,highH-desorptiontemper- tio assessment of the thermodynamics of hydrogen desorp-
i
X atures, or an inability to be easily re-hydrided. The search tion/absorption reactions. Such an assessment is of value
r fornewhydridesthatovercometheselimitationshasattracted because it can clarify the thermodynamicswhen calorimetry
a
intenseinterestduringthepast5years. measurementsyield ambiguousresults, such as in situations
Towards these ends, recent experiments by Pinkerton and wheremultiplereactionsoccursimultaneously(seebelow).A
co-workers4,5,6 andAokietal.7,8 ontheH-storageproperties key thermodynamic property which determines the suitabil-
ofthequaternaryLi-B-N-Hsystemarenoteworthy. By mix- ity of a hydride for H-storage applications is the strength of
inglithiumborohydride(LiBH )andlithiumamide(LiNH ), the hydrogen-hostbond. The bondstrengthis quantifiedvia
4 2
both groups have reported the formation of a new hydride thechangeinenthalpy(∆H)occurringduringhydrogenup-
phase, which when heated above ∼520 K released approx- take/release. InmobileFCapplications,forexample,itisde-
imately 10 wt.% hydrogen. While the reported desorption sirablethatthedesorptionreactionbeendothermic(∆H >0)
temperature is somewhat too high, and reversibility has not with ∆H ≈ 20–50kJ/(molH ). Neglectingkinetics, an en-
2
yet been demonstrated, improvement in these areas may be thalpyinthisrangewouldallowforH-desorptionattemper-
2
aturescompatiblewiththewaste heatfromaFC,andpermit II. METHODOLOGY
on-boardrechargingunderreasonableH pressure.
2
First-principles calculations were performed using a
planewave method based on the PW91 generalized gradient
approximation15 to density functional theory13,14 (VASP).16
Unfortunately,calorimetricmeasurementsofH-desorption
The core-valence electron interaction was treated using
inLi BN H havebeendifficulttointerpret.(SeeRefs.6and
4 3 10 Blo¨chl’sprojectoraugmentedwave(PAW)method,17,18andk-
8,andthesupplementaryinformationaccompanyingRef.4.)
pointsamplingwasperformedonadenseMonkhorst-Pack19
Because Li BN H melts at ∼460K, approximately60 de-
4 3 10 gridwithanenergyconvergenceofbetterthan1meVpersu-
greesbelowtheonsetofH-desorption,hydrogengasevolves
percell. (In the case of Li BN H , a 2 × 2 × 2 grid was
fromthe liquidstate.4 Concurrentwith H release is the for- 4 3 10
2 sufficienttoacheivethislevelofprecision.) Electronicoccu-
mation of a solid reaction product, generally involving one
pancies were determined via a gaussian smearing algorithm
ormorepolymorphsofLi BN alongwithotherunidentified
3 2 with a 0.1 eV smearing width. For high-precision calcula-
phases,4,7,8anddesorptionof2-3mol%ammonia.4Measure-
tionof static zeroKelvin (omittingzeropointvibrationalef-
mentsbasedondifferentialscanningcalorimetry(DSC)4,6and
fects) electronic energies and crystal structures we used the
differentialthermalanalysis(DTA)8 suggestthatthenetheat
so-called“hard”VASPPAWpotentials51withaplanewavecut-
flowduringdehydridingisexothermic(∆H < 0). However,
off of 875 eV, and a geometry relaxation tolerance of better
it is unclear what fraction of the total thermal profile arises
than 0.02 eV/A˚. Internal atomic positions and external cell
fromtheexothermiclatentheatofLi BN solidification,8and
3 2 shape/volumewereoptimizedsimultaneously.
furthermore how H and NH release impacts the calorime-
2 3
Finite-temperaturethermodynamicswere evaluatedwithin
ter response.4 Consequently, it has not been possible to un-
ambiguously assess the endo- or exothermic nature of H- theharmonicapproximation.20,21Vibrationalfrequencies(ωi)
wereextractedbydiagonalizingadynamicalmatrixwhoseel-
desorption alone. Neglecting kinetic effects, the fact that it
ementsweredeterminedviatheso-calleddirectmethod:22the
has proven very difficult4 to re-hydrideLi BN H suggests
4 3 10
forces generated by series of symmetry inequivalent atomic
desorption is weakly endothermic, or exothermic. Regard-
ing Li BN H formation, several studies4,8,12 have reported displacements about the equilibrium geometry (±0.02 A˚,
4 3 10 ±0.04 A˚) were fit to cubic splines in order to extract the
thespontaneousformationofLi BN H aftermixingLiBH
4 3 10 4
forceconstants.Becauselargesupercellsaredesirabletomin-
withLiNH ,evenattemperaturesaslowasroomtemperature,
2
suggestingthattheformationreactionisexothermic.4 imizefinite-sizeeffects,andwiththeexceptionofthemolec-
ular species (H , N , NH ) where the number of atoms per
2 2 3
supercell is small, the dynamical matrix calculations on the
solid-state phases were preformedusing a softer set of PAW
Inlightofthediscrepancynotedaboveregardingthecrys- potentials52andplanewavecutoffenergiesrangingfrom400–
talstructureofLi BN H ,andtheadditionalambiguitysur- 500 eV.53 A comparison of calculated structural parameters
4 3 10
rounding its dehydrogenation thermodynamics, we employ and formationenergieswith existing experimentaland theo-
densityfunctionaltheory(DFT)13,14calculationsinanattempt reticaldataispresentedinthefollowingsection.
to clarify these issues. First, we determine the ground state Oncethenormal-modefrequencieshavebeendetermined,
crystal structure by performing separate geometry optimiza- finite-temperature energetics can be obtained by enthalpic
tioncalculationsoneachoftheexperimentallyproposedcrys- (Hvib)andentropic(Svib)additionstothestaticelectronicen-
tal structures. We find that the relaxed structures are essen- ergies. Within the harmonic approximation these contribu-
tiallyidentical,andhaveN-Hbondlengthsthatareconsistent tionsaregivenby:20
with the structure based on neutron diffraction,12 thus con-
lfiernmgitnhgsothbesecrovnejdecitnurRee11f.th1a1tatrheeaannoamrtiaflaocutsolyfXsh-orartyNm-Heabsuorned- Hvib(T) = 1~ωi+~ωi exp( ~ωi )−1 −1 (1)
ments. Second, we evaluate the finite-temperature reaction Xi 2 (cid:20) kBT (cid:21)
enthalpies and free energies for the formation and dehydro- ~ωi/kBT
Svib(T) = kB
tgoenLaitNioHn2ofanLdi4LBiNB3HH41)0.isLfio4uBnNd3tHo10befoerxmoatthieornm(iwc,itihnraegspreeec-t Xi exp(cid:16)k~BωTi (cid:17)−1
ment with experimental reports of spontaneous Li4BN3H10 −ln 1−exp(−~ωi) , (2)
formation in the literature.4,7,12 For H2-desorption we ex- (cid:20) kBT (cid:21)
plore the thermodynamics of seventeen candidate reactions
over the temperaturerange T = 0–1000K, as there appears wherethesumsrunovervibrationalfrequencies(3N −3fre-
to be some uncertainty in determining the reaction products quencies for solids and non-linear molecules, 3N − 5 fre-
experimentally.4,7Attemperatureswheredesorptionhasbeen quencies for linear molecules), kB is the Boltzmann factor,
reported4(T ≈520-630K),thefavoredreactionispredicted andT istheabsolutetemperature. Forthelinear(non-linear)
tobeLi4BN3H10→Li3BN2+LiNH2+4H2,whichisweakly moleculesanadditional 27kBT (4kBT)termisaddedtoEq.1
endothermic. Moreover,the calculated free energiessuggest toaccountfortranslational,rotational,andpV degreesoffree-
Li BN H is a metastable phase thatshoulddecomposevia dom. The zero point energy (ZPE) can be recovered from
4 3 10
oneofthreetemperature-dependentpathways. Eq.1inthelimitH (T = 0). Theenthalpyandfreeenergy
vib
3
ofaphasecanthereforebeexpressedas:
TABLE I: Calculated structural parameters compared with experi-
H(T) = E+H (T) (3) mentaldata. Bondlengths(d)andcrystallatticeconstants(a,b,c)
vib
aregiven inA˚,bondangles (∡)andanglesbetween latticevectors
G(T) = H(T)−S(T)T, (4)
(α, β) arelistedindegrees. Spacegroup information for thesolid
whereEisthestaticelectronicenergyofthecrystal/molecule phasesislistedinparentheses.
initsground-stategeometryandS representseitherthestan- System Parameter Calculated Experiment
dard tabulated23 entropy of a given molecular species in the H d(H-H) 0.749 0.74124
2
(gNas2)p,haansde1a9t2p.99=5J1Kb−a1rm[So0Tl−=3100(KNH=3)1],3o0r.8t5h8ev(Hib2r)a,ti1o9n1al.7e8n9- NN2H3 dd((NN--HN)) 11..012011 11..0019282244
tropySvibofasolidstatephase. ∡(H-N-H) 106.4 106.724
α-B(R¯3m) a 5.05 5.0625
α 58.1 58.125
III. CRYSTALSTRUCTURE BN(F¯43m) a 3.62 3.6226
Li(Im¯3m) a 3.44 3.5127
ThecrystalstructureofLi BN H hasbeenstudiedbytwo LiH(Fm¯3m) a 4.01 4.0728
groups.11,12Filinchukandco4-wor3ke1r0s11usedsingle-crystalX- Li3N(P¯3m1) a 3.64 3.61a
c 3.88 3.85a
raydiffractiontoidentifythestructuresofthetwolargestcrys-
LiNH (I¯4) a 5.02 5.0429
taldomainsobtainedafterremeltinga 2:1mixtureofLiNH 2
2 c 10.28 10.2829
and LiBH . Both domains exhibited a bcc structure (space
groupI2134)withlatticeconstantsof10.67-10.68A˚.Chateret Li2NH(Pnma) ab 37..6715 37..6703bb
al.12usedacombinationofhigh-resolutionsynchrotronX-ray
c 4.88 4.87b
andneutrondiffractiontoexaminepowdersamplesprepared
froma wide rangeofLiNH :LiBH compositions. Theyde- α-Li3BN2(P42/mnm) a 4.67 4.6430,31
2 4 c 5.22 5.2630,31
terminedthatalthoughthemostlikelystoichiometriccompo- β-Li3BN2(P21/c) a 5.15 5.1532
sition was 3:1, the Li4BN3H10 structure was able to accom- b 7.08 7.0832
modateawiderangeofstoichiometries. Theirbest-fitcrystal c 6.77 6.7932
structurehadexternalcellparameterssimilartothosereported β 112.7 113.032
inRef.11:bcc(spacegroupI213)witha=10.66A˚.Despite Li3BN2(I41/amd) a 6.63 6.6033
thegoodagreementinexternalgeometries,thestructuresob- c 10.35 10.3533
tained by these two studies differ markedly in their internal LiBH (Pnma) a 7.25 7.1834
4
coordinates. Most notably, the single-crystal X-ray diffrac- b 4.38 4.4434
tion study11 found anomalously short N-H bond lengths of c 6.63 6.8034
0.83-0.86A˚,whileneutronscattering12 gavelengthsof0.98- Li4BN3H10(I213) a 10.60 10.67-10.6811
1.04A˚. 10.6612
The external cell parameters obtained upon relaxing each
ofthethreeLi BN H experimentalstructures(aswellasthe aTheoreticallypredictedstructurefromRef.35.InagreementwithRef.35,
4 3 10 wefindtheroom-temperatureexperimentalP6/mmmstructuretobeunsta-
structuresofthe otherphasesusedinoursubsequentdiscus- bleatlowtemperature,withaweaksoftmodeof66icm−1.
sionofreactionthermodynamics)aresummarizedinTableI. bTheoreticallypredictedstructurefromRef.36.
Theresultingstructuresarebccandsharethesamelatticecon-
stant, a = 10.60A˚, in goodagreementwith bothdiffraction
studies.
For each of the three relaxed structures, Table II com-
paresthecalculatedinternalatomiccoordinateswiththecor-
respondingexperimentalvalues. We note first that the aver- Acomparisonofcalculatedbondlengths,bondangles,and
age absolutedeviation(δ) betweentheoryandexperimentis intermolecular distances is given in Table III. Overall, the
smallestfortheneutronstructure,12δ =3.6×10−3,whereas relaxedstructuresagreebest with the intramolecularlengths
fortheX-raystructure11δ =4.4×10−3andδ =4.2×10−3 (i.e.,withinanNH2 orBH4 fragment)determinedusingneu-
for domains 1 and 2, respectively. The largest discrepancy trondiffraction;conversely,theintermoleculardistancesfrom
between theory and experiment is in the positions of the N- X-rayareclosesttothoseintherelaxedtheoreticalstructures.
bonded hydrogen atoms, H1 & H2, in the X-ray structure. Asfortheintramolecularstructure,asnotedabove,themajor
(Note that the labeling conventionfor hydrogensis different discrepancy between the experimental structures lies in the
intheneutronstructure:thereH1&H2refertoB-bondedhy- two N-H bond lengths, d(N-H), in the NH2 fragment. The
drogens.)Secondly,whilethereappeartobelargedifferences calculated length of 1.027 A˚ is in better agreementwith the
intheinternalcoordinatesmeasuredbyRefs.11and12(Ta- longerbondlengthspredictedbyneutrondiffractionof0.983
bleII),afterrelaxationthesethreestructuresmaybemapped and 1.042 A˚. Similarly, the X-ray data also underestimates
ontooneanotherviaaseriesofrigidbodyrotationsandtrans- B-HbondlengthsintheBH unitsrelativetoourDFTcalcu-
4
lations. Weconcludethatallthreeexperimentalstructuresre- lations and neutron data. Calculated bond angles agree best
laxtoessentiallythesamestructure. withthosefromtheneutronstructure.
4
TABLEII:CalculatedrelaxedinternalatomicpositionsofLi BN H comparedwithexperimentalmeasurementsfromRefs.11,12.
4 3 10
Calculated Experiment
Atom x y z x y z
N 0.117 0.362 0.402 0.115 0.359 0.405
B 0.113 0.113 0.113 0.114 0.114 0.114
Li1 0.281 0.000 0.250 0.287 0.000 0.250
Li2 0.519 0.000 0.250 0.524 0.000 0.250 Domain1,
Li3 0.484 0.484 0.484 0.483 0.483 0.483
H1 0.195 0.306 0.393 0.175 0.310 0.397 Ref.11
H2 0.118 0.415 0.321 0.115 0.405 0.339
H3 0.003 0.118 0.147 0.012 0.119 0.146
H4 0.180 0.180 0.180 0.172 0.172 0.172
N 0.117 0.361 0.402 0.115 0.359 0.405
B 0.113 0.113 0.113 0.114 0.114 0.114
Li1 0.281 0.000 0.250 0.286 0.000 0.250
Li2 0.519 0.000 0.250 0.523 0.000 0.250 Domain2,
Li3 0.484 0.484 0.484 0.484 0.484 0.484
H1 0.195 0.305 0.394 0.176 0.310 0.399 Ref.11
H2 0.118 0.415 0.321 0.114 0.402 0.338
H3 0.003 0.117 0.148 0.015 0.116 0.149
H4 0.180 0.180 0.180 0.174 0.174 0.174
N -0.152 0.112 0.367 -0.156 0.110 0.367
B 0.137 0.137 0.137 0.135 0.135 0.135
Li1 0.250 -0.030 0.000 0.250 -0.043 0.000
Li2 -0.268 0.000 0.250 -0.262 0.000 0.250
Li3 0.266 0.266 0.266 0.272 0.272 0.272 Ref.12
H1 0.071 0.071 0.071 0.072 0.072 0.072
H2 0.103 0.133 0.247 0.097 0.136 0.248
H3 -0.143 0.055 0.445 -0.153 0.053 0.439
H4 -0.071 0.165 0.368 -0.077 0.167 0.377
TABLEIII:Comparisonofcalculatedatomicdistancesandangleswithvaluesdeterminedfromsingle-crystalX-raydiffraction(Ref.11)and
synchrotronX-rayandneutronpowderdiffraction(Ref.12).Lengths(d)aregiveninA˚,angles(∡)areindegrees.
Ref.11,domain1 Ref.11,domain2 Ref.12
Parameter Calculated Experiment Calculated Experiment Calculated Experiment
IntramolecularValues
d(N-H)(i) 1.027 0.83(2) 1.027 0.84(2) 1.027 0.983
d(N-H)(ii) 1.027 0.859 1.026 0.852 1.027 1.042
d(B-H)(i) 1.223 1.08(3) 1.225 1.11(3) 1.224 1.169
d(B-H)(ii)×3 1.225 1.137 1.225 1.121 1.223 1.270
∡(H-N-H) 103.5 106.2 103.5 105.9 103.5 104.9
∡(H-B-H)×3(i) 108.0 108.9 107.9 109.2 107.9 107.6
∡(H-B-H)×3(ii) 110.9 110.1 111.0 109.8 111.0 111.3
IntermolecularValues
d(N-Li)(i) 2.071 2.069 2.069 2.068 2.070 2.033
d(N-Li)(ii) 2.116 2.115 2.111 2.113 2.110 2.053
d(N-Li)(iii) 2.138 2.117 2.138 2.119 2.142 2.094
d(N-Li)(iv) 2.164 2.157 2.164 2.157 2.169 2.209
d(B-Li)(i) 2.371 2.410 2.375 2.406 2.368 2.527
d(B-Li)(ii)×3 2.595 2.651 2.592 2.642 2.589 2.681
IV. REACTIONENERGETICS crystal structures, and a comparison of the calculated struc-
turesto experimentaldatais presentedinTable I. Ingeneral
theagreementbetweenexperimentandtheoryisverygood.
Inordertoexaminethefinite-temperaturethermodynamics Some of the compounds listed in Table I are known
ofreactionsinvolvingLi BN H ,itwasfirstnecessarytocal- to have several polymorphs. For example, at least three
4 3 10
culatetheground-statestructuresofthephasesthatparticipate polymorphshave been reported for Li BN ,31,32,37,38 includ-
3 2
inthosereactions. Asummaryofthecompoundsused,their inglow-temperaturetetragonal(α),31 high-temperaturemon-
5
0 TABLEIV:Calculatedvibrationalcontributions(atT = 300K)to
Monoclinic
BCT thefreeenergiesofphasesusedinthisstudy. ZPEreferstothezero
-20 point energy, given by H (T = 0) (Eq. 1); E = H − ZPE
vib vib vib
ol f. u.) -40 (Eoqm.i2tt.inUgntihtseakrBeTkJmmoolel−cu1laforrteZrmPEs);anSdvibEivsibt,haenvdibJrmatiooln−a1lKen−tr1opfoyr,
m S .
kJ/ -60 vib
Energy ( -80 SHy2stem Z25P.E7 25.7Z40P,E26o.t1h4e1r, EvibT=≈300K0 SvibT=≈300K0
ee 26.342
Fr-100 N 14.0 14.442 ≈0 ≈0
2
NH 87.8 89.743 0.1 0.4
3
-120 Li 3.9 3.941 4.3 27.7
B 12.5 12.241 1.1 5.3
-1400 200 400 600 800 1000 BN 29.9 30.944
Temperature (K)
LiH 21.7 21.4,4121.836 3.5 17.7
FIG. 1: Calculated Gibbs free energies (in kJ/mol f.u.) of mono- Li3N 28.0 28.635
LiNH 69.0 69.1,3569.5,36 8.9 51.6
clinic(β)andbody-centeredtetragonal(BCT)Li BN asafunction 2
of temperature. The energy zero is set to the sta3tic 02 K energy of 69.842
β-Li3BN2. Li2NH 46.7 46.742,47.136 9.6 52.9
LiBH 107.1 103.0,41106.5,40 10.8 63.6
4
108.145
oclinic (β),32 and high-pressure body-centered tetragonal Li3BN2 52.2 15.3 83.8
Li BN H 314.4 37.0 213.4
(bct)33,37,38 phases. All three of these phases have been ob- 4 3 10
servedasdehydrogenationproductsforLi BN H ,4,8andwe
4 3 10
have performed calculations on each phase to determine its
relativestabilityasafunctionoftemperature. Theβ-Li BN contributions (Table IV), the free energies of the β and bct
3 2
phase was found to have the lowest zero-Kelvin static en- phasesexhibitnearlyidenticaltemperaturedependence.Con-
ergy, ≈ 2 kJ/(mol f.u.) lower than that of either the bct or sequently,thesmall∼2kJ/(molf.u.)differenceinstaticener-
α phases. The latter two phases are degenerate in energy to giesnotedaboveissufficienttofavorthemonoclinicβ phase
within0.1kJ/(molf.u.).Ourzero-Kelvinenergeticsandstruc- asthegroundstatestructure,andthebct-β energydifference
turesagreewellwithrecentcalculationsreportedbyPinkerton remainsroughlyconstantfor T < 1000K. Based on the vi-
andHerbst.33 brationalinstabilityobservedinα-Li BN ,andthehigherfree
3 2
Vibrational contributions to the energies of each Li BN energyofbctLi BN (relativetoβ-Li BN ),oursubsequent
3 2 3 2 3 2
polymorph were evaluated within the harmonic approxi- thermodynamicanalysesareperformedassumingLi BN re-
3 2
mation. For α-Li BN a careful evaluation of the vibra- sidesinthethelow-energyβ structure.
3 2
tionalspectrayieldeddoubly-degenerateimaginarymodesat Thezero-point,enthalpic,andentropiccontributionstothe
81icm−1,indicatingthatthisphaseisunstableatlowtemper- freeenergyofthevariousphasesaresummarizedinTableIV.
atures. A search for alternative low-energyα-Li BN struc- Asafurthertestofourcomputationalmethodology,therewe
3 2
tureswasperformedusingmoleculardynamics(md)onanen- also compare our calculated ZPE to other values reported in
larged(2×2×2)α-Li BN supercellatT =423Kfor10ps. theliterature,andfindgoodagreement.Withtheexceptionof
3 2
At1psintervalsthecurrentmdconfigurationwasstored,re- Li,vibrationaleffectsarefoundtocontributesubstantiallyto
laxed, and the symmetryof the resultingoptimizedstructure thefreeenergiesofthesesystems.Forexample,inLi BN H
4 3 10
was determined. Four unique crystal structures were identi- theZPEexceeds300kJ/mol.
fied,withspacegroups(numbers):P212121(19),Pccn(56), A comparison of formation energies for the compounds
Pmmn (59), and Pnma (62). These structures were then used in this study (relative to the elements in their standard
relaxed within their symmetry constraints, and were found states)ispresentedinTableV. Threereports33,41,42 basedon
to have energies ∼1 kJ/(mol f.u.) lower than the original DFT calculationshave also recently evaluated formationen-
α-Li3BN2 structure [which is still 1 kJ/(mol f.u.) higher in ergies for some of these compounds, and the present calcu-
energy than β-Li3BN2]. In light of these results we suggest lations are in good agreement with their findings. Further-
that the crystal structure of α-Li3BN2 be experimentally re- more, the agreementwith experimentalenthalpiesis reason-
assessed, and we exclude this phase from our evaluation of able (generally on the order of 10%), which is representa-
Li4BN3H10 dehydrogenation reactions. Further information tive of the accuracyobtainedvia density functionalmethods
regarding our proposed structure of α-Li3BN2 can be found forreactionsinvolvingmolecularspecies.47 Asexpected,the
elsewhere.39 largestpercentagediscrepancyisfortheammoniamolecule.54
Unlike α-Li BN , no imaginary modes were observed in Twogeneraltrendsinthedataareevident:(i)Withtheexcep-
3 2
the vibrational spectra of β or bct Li BN . Using Eqs. 1-2, tion of ammonia, the DFT enthalpies (∆HT=300K) are more
3 2
Fig. 1 plots the Gibbs free energies (Eq. 4) of these phases positivethantheexperimentalvalues,and(ii)theinclusionof
asafunctionoftemperature. Duetotheirsimilarvibrational dynamicalcontributions(∆E → ∆HT=300K) resultsin more
6
ofthestructurespresentinLiNH andLiBH .
2 4
TABLE V: Comparison of calculated formation energies (with re-
Turning now to the dehydrogenation of Li BN H , we
specttotheelements,inkJ/molf.u.) withexistingexperimentaland 4 3 10
theoreticaldata.∆Ereferstodifferencesinstatic0Kenergies,for- notefirstthatalthoughseveraldehydrogenationproductshave
mationenthalpies(∆H)andfreeenergies(∆G)arebasedonEqns.3 beenobservedinexperimentalstudies,4,5,7,8 thepreciseiden-
and4,respectively.ExperimentaldataisfromRefs.23and46,theo- tity and respective proportions of these phases have not yet
reticaldataisfromasetofrecentDFTcalculations(Refs.33,41,42). beendefinitivelydetermined.4,7 For example, Aokietal. re-
portedunidentifieddiffractionpeaksafterdehydrogenationat
System ∆E ∆HT=300K ∆GT=300K 2θ = 25◦ and 35◦. A technique for predicting possible de-
NH −98.0 −63.2 −33.6
3 compositionpathwayswouldbe of significantvaluein help-
−45.923 −16.223
BN −233.8 −227.4 −198.9 ing to understand these reactions. However, decomposition
−250.923 −224.923 pathways and products are difficult to predict a priori. To
LiH −83.6 −83.8 −61.2 this end, we have scanned throughthe thermodynamicsof a
−8141 −90.623 −68.323 large number of candidate dehydrogenationreactions over a
−83.942 −84.642 wide temperaturerangein orderto identifythe energetically
Li3N −148.7 −145.9 −109.8 favoredproducts.55
−164.623 −128.423 Calculated thermodynamics for seventeen candidate
LiNH2 −196.6 −172.6 −111.7 Li4BN3H10dehydrogenationreactionsarelistedinTableVII.
−196.542 −17646 Inadditiontotheroom-temperatureenergetics,therewealso
−173.142 present data for T = 460 K, which is slightly below the
Li NH −196.0 −184.5 −135.3
2 melting point of pure Li BN H . Unlike the Li BN H
−194.042 −22246 formationreaction,which4can3pro10ceedatroomtemp4eratu3re1,04
−184.142
dehydrogenation of Li BN H has been reported only at
LiBH −205.9 −178.6 −109.2 4 3 10
4 elevatedtemperatures. InthecaseofpureLi BN H ,dehy-
−19441 −190.523 −124.323 4 3 10
Li BN −497.4 −490.6 −433.6 drogenation occurs above ∼520 K, about 60 degrees above
3 2 −49733 themeltingtemperature.4However,asignificantreductionin
dehydrogenationtemperaturewasobservedupontheaddition
of a small amount of a Pt/Vulcan carbon catalyst.6 In this
lattercasehydrogenreleaseoccurredfromthesolid phaseat
positiveformationenergies. T > 390K.Tomorecompletelyassessthedehydrogenation
Using the energetic contributions from Table IV, in Ta- thermodynamics over a range of relevant temperatures, in
ble VI we evaluate the thermodynamicsfor two Li BN H Fig.2weplottheenthalpiesandfreeenergiesofthecandidate
4 3 10
formation reactions. Reaction (a) considers formation from reactionsforT =0–1000K.
the elemental phases in their standard states, and reac- Out of the seventeen reactions considered, three
tion (b) corresponds to the synthesis route employed in the reactions—(i), (c), and (f)—emerge as the most-favorable
literature4,7,12 involvingamixtureofLiNH andLiBH . (We reactions in distinct temperature regimes (see Fig. 2,
2 4
consider only the stoichiometric12 3:1 ratio of LiNH to bottom panel). For low temperatures reaction (i) is pre-
2
LiBH .55)Theenergeticsofeachreactionarearedecomposed ferred, followed at increasing temperatures by reaction (c)
4
into a sequence having increasingly more physical contribu- and reaction (f). More specifically, the favored products
tions to the reaction thermodynamics, ∆E → ∆HT=0K → and their respective temperature ranges of stability are:
∆HT=300K → ∆GT=300K, which allows us to gauge the im- 0K≤T≤300K: 2LiNH2+2LiH+BN+2H2
portanceofthesecontributionsincomparisontothecommon 300K≤T≤700K: Li3BN2 +LiNH2+4H2
practiceofevaluatingonlystaticzero-Kelvinenergetics.[∆E 700K≤T: Li3BN2+LiH+ 21N2+ 29H2
refers to differences in the static zero-Kelvin energies (E in Therelativelylargeentropyofthegasphaseproductsplays
Eq. 3), and ∆HT=0K adds ZPE contributionsto ∆E.] Both animportantroleindeterminingwhichreactionisfavoredat
formation reactions in Table VI are predicted to be exother- agiventemperature. Reactionsyieldinggreaterquantitiesof
mic (∆H < 0), in agreement with reports of spontaneous gaseous products should be favored with increasing T, and
Li BN H formation from the literature.4,7,12 As expected, thisisconsistentwiththeobservedtrend: reaction(i),2mols
4 3 10
formationfromtheelementsvs.fromthehydridemixtureisa →reaction(c), 4 mols→reaction(f), 5 mols. (Itshouldbe
substantiallymoreexothermicprocess. notedthatathightemperatures—andcertainlyabovethemelt-
Itisnoteworthythatdynamicalcontributionstothereaction ingpointofLi4BN3H10—theharmonicapproximationwillno
energiesaresignificantinreaction(a)(∆E 6= ∆H), butap- longerbevalid,soweexpectsomedecreaseinaccuracywith
peartoplayaminorroleinreaction(b)(∆E ≈∆H). Byex- increasingT.)
aminingthevaluespresentedinTableIVforthephasespartic- Of thethreefavorabledehydrogenationreactions, onlyre-
ipatinginreaction(b)(Li BN H ,LiNH ,&LiBH )wesee action(c),Li BN H →Li BN +LiNH +4H ,takesplace
4 3 10 2 4 4 3 10 3 2 2 2
that these terms are sizable, but that they largely cancel out. withinthetemperaturerangewhereH -desorption(fromun-
2
Thiscancellationeffectcanbeunderstoodbythesimilarities doped Li BN H ) has been experimentally observed (T ∼
4 3 10
ininternalbondingsharedbythesethreephases: Li BN H , 520–630 K). While our prediction of Li BN as a dehy-
4 3 10 3 2
with itsLi+, BH−, andNH− ionsis essentiallyanamalgam drogenationproductisconsistentwithexperimentalobserva-
4 2
7
TABLEVI:FormationenergiesofLi BN H [inkJ/(molLi BN H )]. ∆E correspondstothestaticzeroKelvinDFTenergies;∆HT=0K
4 3 10 4 3 10
addsthezeropointenergiesto∆E; ∆HT=300K (Eq.3)addsfinite-temperaturevibrational(andmolecularrotational+translational+pV)en-
ergies to ∆HT=0K; ∆GT=300K (Eq. 4) includes all of the contributions to ∆HT=300K and adds vibrational (solids) or tabulated (molecular)
entropies.
Rxn.No. Reaction ∆E ∆HT=0K ∆HT=300K ∆GT=300K
(a) 4Li+B+ 3N +5H → Li BN H −806.9 −670.2 −708.1 −454.6
2 2 2 4 3 10
(b) 3LiNH +LiBH → Li BN H −11.3 −11.2 −11.8 −10.2
2 4 4 3 10
TABLEVII:Calculatedreactionenergies[∆EinkJ/(molH )],enthalpies[∆H inkJ/(molH )],andfreeenergies[∆GinkJ/molproducts]
2 2
forcandidateLi BN H dehydrogenationreactions.
4 3 10
Rxn.No. Reaction ∆E ∆HT=0K ∆HT=300K ∆HT=460K ∆GT=300K ∆GT=460K
(c) Li BN H → Li BN +LiNH +4H 28.2 5.7 11.2 12.5 −88.8 −161.3
4 3 10 3 2 2 2
(d) Li BN H → Li BN + 1Li NH+ 1NH +4H 40.6 17.7 23.4 24.3 −61.4 −145.2
4 3 10 3 2 2 2 2 3 2
(e) Li BN H → Li BN +LiH+NH +3H 42.6 17.5 23.5 24.0 −71.6 −148.0
4 3 10 3 2 3 2
(f) Li BN H → Li BN +LiH+ 1N + 9H 50.2 24.1 29.7 30.8 −38.2 −131.0
4 3 10 3 2 2 2 2 2
(g) Li BN H → Li BN +Li+ 1N +5H 61.9 37.4 43.5 44.6 23.0 −82.2
4 3 10 3 2 2 2 2
(h) Li BN H → Li BN +Li+NH + 7H 60.4 37.5 44.1 44.7 −10.5 −99.2
4 3 10 3 2 3 2 2
(i) Li BN H → 2LiNH +2LiH+BN+2H 6.4 −19.4 −16.1 −15.4 −90.1 −121.2
4 3 10 2 2
(j) Li BN H → LiNH +Li N+BN+4H 56.9 35.8 40.5 41.3 34.1 −34.9
4 3 10 2 3 2
(k) Li BN H → 4LiH+BN+N +3H 79.6 44.1 48.5 48.8 11.1 −60.7
4 3 10 2 2
(l) Li BN H → 2Li NH+BN+4H 45.3 23.3 27.9 28.8 −14.9 −83.3
4 3 10 2 2
(m) Li BN H → 2LiNH +BN+2Li+3H 60.0 39.5 45.1 46.2 32.3 −23.6
4 3 10 2 2
(n) Li BN H → LiNH +Li NH+LiH+BN+3H 32.3 9.1 13.2 14.1 −52.5 −102.3
4 3 10 2 2 2
(o) Li BN H → Li NH+2LiH+BN+NH +2H 55.9 28.5 32.7 32.1 −35.4 −88.9
4 3 10 2 3 2
(p) Li BN H → LiNH +3LiH+BN+NH +H 27.7 −9.1 −6.6 −8.8 −73.0 −107.9
4 3 10 2 3 2
(q) Li BN H → Li N+LiH+BN+NH +3H 80.9 57.7 62.6 62.4 51.3 −21.6
4 3 10 3 3 2
(r) Li BN H → 1Li NH+Li N+BN+ 1NH +4H 69.3 47.8 52.7 53.2 61.5 −18.8
4 3 10 2 2 3 2 3 2
(s) Li BN H → Li BN + 1Li N+ 2NH +4H 48.7 26.0 31.7 32.5 −35.9 −123.6
4 3 10 3 2 3 3 3 3 2
tions, we are not aware of any reports indicating the pres-
60
ol H)2 40 emnocsetoefxpLeiNrimHe2.ntTshhiasvdeisbcereenpapnecryfoirsmliekdeloyndoufef-tsototihcehifoamctetthraict
m Li BN H formed from 2:1 LiNH :LiBH mixtures. Mix-
J/ 20 4 3 10 2 4
∆H (k 0 tsuurmesabwlyithnetheidsecdotmopyoiesiltdiotnhearaedddeitfiiocnieanltaimnitdheepLriesaenndtNinporuer-
calculations.
-20
200 b i The calculated enthalpy for reaction (c) ranges from 11.2
c j
100 de kl to 12.8 kJ/(mol H2) for T = 300–500 K, indicating that H2
ucts) 0 fgh mno rteemleapseeraitsurae wreeaacktiloyne(nfd),otdheehrmydicropgreoncaetsios.n iFsolriktehweisheigphreer--
d p
ol pro-100 qrs d∼i3ct1edkJto/(mbeoleHnd2o).theOrmnilcywthitehlaowslitgehmtlpyerlaatrugreer erenathctailopny(oi)f
m
J/-200 with ∆H ≈ −(16–19) kJ/(mol H2) is found to be exother-
k
G ( mic. It would be interesting to test whether the predicted
∆ -300 temperature-dependentdecompositionsequence[(i)→(c)→
i c (f)]couldbeobservedexperimentallybyholdingLi BN H
-400 4 3 10
f at temperatureswithin each of the reaction regimesfor long
-500 times.
0 200 400 600 800 1000
Temperature (K)
BasedonthedatapresentedinFig.2andTableVII,H des-
2
FIG. 2: (Color online) Calculated enthalpies (∆H, top panel) and orption from Li4BN3H10 is thermodynamically favorable at
freeenergies(∆G,bottompanel)ofcandidateLi BN H dehydro- essentially allnon-zerotemperatures: thenegativefreeener-
4 3 10
genation reactions as afunction of temperature at p = 1 bar. The giesofdehydrogenationsuggestthatLi4BN3H10ismetastable
reactionsarelabeledasinTableVII. withrespecttodecompositionviaoneofthereactions(i),(c),
or (f). On the other hand, experiments4 on pure Li BN H
4 3 10
indicatethatdesorptiondoesnottakeplaceuntilthetempera-
8
tureisraisedabove520K.Takentogether,thesefactorssug- crystalstructuresrelaxtoessentiallythesamestructure.
gest that the relatively high temperatures needed in practice For reaction energetics, our calculations indicate that
for H2-release are a consequence of poor kinetics, not unfa- Li4BN3H10 formation is exothermic, and that the dehydro-
vorablethermodynamics. genation enthalpy of solid-state Li BN H is temperature-
4 3 10
An importantdistinctionbetweenourcalculationsand the dependent:H releaseisexothermicatlowtemperatures,and
2
experimental dehydrogenation of undoped Li4BN3H10 con- weaklyendothermicatthehighertemperaturesprobedbyre-
cerns the phase of Li4BN3H10 present during the dehydro- centexperiments.Anon-zerolatentheatforLi4BN3H10melt-
genationreaction. As mentionedabove,pureLi4BN3H10 re- ingwillreducethedehydrogenationenthalpyfromtheliquid
leaseshydrogenfromthemoltenstate.4 Similarly,H2 release state (relative to the solid state), but the size of this effect
from otherhydridephases, such as LiBH4, also occursfrom is still to be determined. To help clarify the identity of the
themoltenstate.48 Dueto thecomputationalexpenseassoci- phases produced via dehydrogenation we have performed a
atedwith obtainingpreciseenergeticsforliquidsusingDFT, computationalsearch over 17 candidate dehydrogenationre-
thisstudy,andpreviousstudiesonLiBH4,41,48 havemodeled actions, and identified three reactions having favorable ther-
the dehydrogenationreactionas a solid-state reaction. Since modynamicsspanningthetemperaturerangeT =0–1000K.
the enthalpy of the liquid phase will be more positive than Allthreeofthesereactionsexhibitadecreaseinfreeenergy,
that of the corresponding solid phase, the calculated solid- suggesting that Li BN H is a metastable phase. For tem-
4 3 10
state enthalpy of reaction (c) evaluated at the melting point peratures where H -desorption has been experimentally ob-
2
(Tmp),∆HTmp =12.5kJ/(molH2),representsanupperbound served,thethermodynamically-favoredreactionisLi4BN3H10
on the enthalpy for desorption from liquid Li4BN3H10. It → Li3BN2 + LiNH2 + 4H2, with an enthalpy of 11.2–12.8
willbepossibletomorepreciselyestimatethemagnitudeby kJ/(molH ). Therelativelysmalldehydridingenthalpiesare
2
which ∆H is overestimated once the latent heat of melting consistentwiththefailedre-hydridingattemptsreportedinthe
for Li4BN3H10 has been measured. Until such data become literature,andsuggestthathydrogenreleasefromLi4BN3H10
available, it nevertheless seems reasonable to conclude that is a kinetically—rather than thermodynamically—hindered
thedehydrogenationofLi4BN3H10iseitherweaklyendother- process.
mic, or exothermic. This conclusion is consistent with the Noteaddedinproof—Duringthereviewofthismanuscript
failed attempts at re-hydriding Li4BN3H10 reported thus far two new studies of Li4BN3H10 were brought to our
in the literature,4 as a small (positive) enthalpy of dehydro- attention.49,50InthefirststudyNoritakeandco-workers50per-
genationwillresultinasimilarlysmallthermodynamicdriv- formed a crystal structure analysis of Li BN H using syn-
4 3 10
ingforceforre-hydriding.Ontheotherhand,forLi4BN3H10 chrotronX-ray diffraction. While they foundexternalstruc-
dopedwithPt/Vulcancarbon,6dehydrogenationbeginsbelow turalparameters(bcc, spacegroupI213, a = 10.67A˚) con-
Tmp. In this case our approach of modeling solid state re- sistentwiththetworeportscitedpreviously,11,12 thereported
actions more accurately captures the true phase behavior of N–Hbondlengthsweremoreconsistentwiththeneutrondata
Li4BN3H10, neglecting the possible formation of C- or Pt- of Ref. 12 (and with our calculated N–H distances) than the
containingcompounds. X-ray data of Ref. 11. In the other recent study, Herbst and
Hector49 examined the electronic structure and energeticsof
ofLi BN H usingDFT.Ourresultsappeartobeconsistent
4 3 10
V. CONCLUSION
withtheirfindings.
Densityfunctionaltheorycalculationshavebeenemployed
to study the crystal structure and the finite-temperature for-
Acknowledgments
mationanddehydrogenationthermodynamicsofLi BN H .
4 3 10
Thecalculationshaveresolvedthediscrepanciesinhydrogen
bond lengths between the separate structuresdetermined via The authors thank D. Halliday, A. Sudik, and J. Yang for
X-ray and neutron diffraction experiments, and suggest that reviewingapreliminaryversionofthismanuscript.V.Ozolin¸sˇ
theneutrondatayieldsaslightlymoreaccuratedescriptionof thanks the U.S. Department of Energy for financial support
the crystal structure. All three of the reported experimental undergrantDE-FG02-05ER46253.
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2 2
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2
(1986). tweencalculatedvibrationalfrequenciesarelargest,wefind2338
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2
36 B.Magyari-Ko¨pe,V.Ozolin¸sˇ,andC.Wolverton,Phys.Rev.B73, the experimental measurement be revisited in light of the good
220101(2006). agreement for theother Li-containingcompounds: LiH,LiNH ,
2
37 R.H.Jr.,Wentorf,J.Phys.Chem.34,809(1961). andLiBH .Toour knowledge theformationenthalpy of Li NH
4 2
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(2006). stoichiometric composition “Li BN H ,” whereas most exper-
4 3 10
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2 4
(2004). “Li3BN2H8”mixtures,whichhavebeenfoundtominimize5NH3
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