O tlin

ICMSICMS--ICMR Winterschool on Chemistry and Physics of Materials, Nov. 6ICMR Winterschool on Chemistry and Physics of Materials, Nov. 6--13, 2007, Bangalore13, 2007, Bangalore

1. IntroductionBrief history of molecular magnetism [1-6]

Outline

Brief history of molecular magnetism [ 6]2. Mononuclear species (complexes)2.1. Prequisites : free ion terms, states, orbitals and ligand field. Point Group Symmetry2.2. Metal-ligand interaction to tune electronic structure.2.3. Spin states, spin cross-over, devices [7]3. Magnetism of molecular assemblies in interaction. Polynuclear complexes

l h l l d l h3.1. Interaction between two electrons : phenomenological and orbital approaches3.2. Interaction Models [1]

Kahn ; comparison with Hoffmann (molecules)Comparison with Anderson, Goodenough-Kanamori (solids)

3.3. Case studies :Binuclear complexes [1 5]Binuclear complexes [1,5]Ferrimagnetic chains [1,5]Molecule-based magnets ; devices [8]

4. Magnetism of molecules assemblies without interaction :Single-molecule, single-chain magnets [9]Molecular, "bottom-up", approach of nanosystems, high spin molecules, p , pp y , g pThe "Mn12" and "Fe8" moleculesLocal anisotropy ; magnetic quantum tunneling effect.

5. ProspectsMultifunctional materials [10]Magnetism of a single molecule ; Information storage. Electronic quantum computingMagnetism of a single molecule ; Information storage. Electronic quantum computing

molecule-based magnets ? Why ?y

L d it

Specific propertiesLow densityTransparentNanosizedOften biocompatible and biodegradableVery flexible chemistryMild chemistry : Room T Room PMild chemistry : Room T, Room P, Solution Chemistry

Fragile Agingg gDiluted

Multifunctional materials

• Flexibility of molecular chemistryT bl St t d P tiTunable Structures and Properties

• Magnetic and optical propertiesMagnetic and optical propertiesColor, chirality, non linear optics

M ti d l t i l ti• Magnetic and electrical properties(Supra)Conducting magnetic materials

Conducting magnets See P. Day lecture Nº2

Coronado et al. Nature 2000

Multifunctional materials

• Interplay of Spin with Light

• Light reveals the spin (magnetisation) :

• Interplay of « Spin » with Light

Light reveals the spin (magnetisation) Photomagnetic Prussian Blues analoguesPhotomagnetic molecules

• The spin (magnetisation) transforms light :Magneto-opticsO i ll i MOptically active Magnets

Ph t tPhotomagnets

Transforming magnetism by light

J. Miró, Muro de Luna, Mural ceramics, UNESCO, Paris

Spin cross over

Photoexcitation … Jablonski Diagramme

Many things can happen after excitation …

EnergySinglet Spin = 0

Intersystem crossinggy

Triplet Spin = 1hνIntersystem crossing

hν ‘

hν ‘’

Singlet Spin = 0

Coordinate

Photomagnetism in coordination chemistry• LIESST Effect • LD-LISC Effect• LIESST Effect

Light-Induced Excited Spin State

HS

• LD LISC EffectLigand-Driven Light-Induced

Spin Change

HSHSHS HS

HSh

LShν

L

hν

D ti t l I Ch 1984 24 2174

LS

R t l I Ch 1994 33 2273

LS

hν

Decurtins et al. Inorg. Chem., 1984, 24, 2174.

NN322 nm

Roux et al. Inorg. Chem., 1994, 33, 2273.

FeII(BS) → FeII(HS)hν

T < 50 K260 nm

Trans-StpyFeII(BS)

Cis-StpyFeII(HS)T < 90 K

« L.I.E.S.S.T. » Effect

LightInducedExcitedSpin StateStateTrapping

J.

« L.I.E.S.S.T. » Effect , Interpretation

P. Gütlich et al. et al., Angewandte Chem., 1994

Photoexcitation …

ESpin = 0

Many things can happen after excitation …

Energy

Spin = 1

Intersystem crossing

Metastable state(s)

Spin = 1

M ( )

• LIESST EffectLi h I d d E i d S i SSpin 1

Spin = 0

Light-Induced Excited Spin State

• LD-LISC Effect

CoordinateLigand-Driven Light-Induced Spin Change

S.Decurtins, A. Hauser, P. Gutlich Inorg. Chem. 1984, 24, 2174C. Roux, J. Zarembovitch et al. Inorg. Chem. 1994, 33, 2273

Gymkhana campus Bangalore, December 8, 2007

1) Ph t ti1) Photomagnetism= Transforming magnetism by light

2) Magneto optics2) Magneto-optics= Transforming light by magnetism

3) Applications3) Applications= Writing and reading

magnetic information with lightmagnetic information with light

What about the 8 branches star?What about the 8 branches star?Octacyano Complex ?

PolynuclearComplexp

Interaction with lightOctacyanometalate Precursors Heptanuclear Complexes

WIVC II WIVNiII WIVM IIWIVCuII6

MoIVCuII6

WIVNiII6MoIVNiII6

Monoclinic P na = 24 89 Å; b = 14 39 Å; c = 30 11 Å

Monoclinic 22 03 Å b 28 39 Å 22 01 Å

Monoclinic C ca = 25 39 Å; b = 15 22 Å; c = 30 72 Å

WIVMnII6

MoIVMnII6

a = 24.89 Å; b = 14,39 Å; c = 30,11 Åa = g = 90°; b = 108.81°;

a = 22.03 Å; b = 28,39 Å; c = 22,01 Åa = g = 90°; b =99.48°;

a = 25.39 Å; b = 15,22 Å; c = 30,72 Åa = g = 90°; b = 111.45°;

V. Marvaud, J.M. Herrera, work in progress

MoCu6 : Photomagnetic high spin molecule

hν (=405 nm), 19 h 5 K 5,0

6 x S = 1/2

S = 364 % S = 3

After hν

After hv and T> 300 K

Before hν4,0

4,5

mol

-1.K

)

h

3,0

3,5

χT (c

m3 .m hν406 nm

0 50 100 150 200 250 300

2,5H = 20000 G

T (K)

Collaboration: C. Mathonière, ICMC Bordeaux

Photo-induced electron transferPhoto-induced electron transfer

MoIV CuIIhν MoV CuI

5

MoIVCuII MoVCuI CuII

+5 +5

Mo VCu 6 MoVCu 1Cu 5MoV, d1 , S=1/2

Ferro interaction …MoIV, d2 , S=0No exchangeNo exchange6 isolated S=1/2 S=3

10

12

MoCu6BT avant Ir

Evolution de MoCu6 avant Ir, apres Ir et apres relaxation

8

10 MoCu6BT, avant Ir

MoCu6BTI2, apres Ir

RT Apres relaxation

4

6

Abs

orba

nce

2

4

0

2510 2520 2530 2540 2550 2560

EnergieEnergie

From V. Marvaud, F, Villain, A. Bachschmidt, Elettra, Triesta

MoCu6 : Magnetization under Irradiation in a microSQUID

4

60.008 T/s

2

4

B

0

M/N

µ B

-4

-2 0.04 K0.5 K1 K2 K

0.04 K0.5 K1 K2 K

0 h 10 h

-6-1 -0 5 0 0 5 1

2 K4 K

2 K4 K

1 0.5 0 0.5 1µ0 H (T)

V. Marvaud and Wernsdorfer, Louis Néel Laboratory, Grenoble

Looking at ther Mo-Cu compounds (also W analogues)

Monoclinic P 21/ca = 10.514 Å; b = 14.584 Å; c = 22.182 Åα = γ = 90°; β = 96 18°; V= 3381 4 Å3

MoIVCu2-(tren)

Monoclinic P 21/aa = 14.790 Å; b = 15.901 Å; c = �18.395 Å

MoVCu (AF, S=0)

α = γ = 90 ; β = 96.18 ; V= 3381.4 Å3

MoVCu4

α = γ = 90°; β = 109.208°; V= 4085.2 Å3

Orthorhombic P bcma = 10.388 Å; b =22.000 Å; c = �30.172 Å

α = β = γ = 90°; V= 6895.4 Å3

NH2

N NH2

H2N

MoIVCu6-(TPA)

Monoclinica = 27.0�95 Å; b = 17.13�5 Å; c = 33.172 Å

α = γ = 90°; β = 66.42°; V= 14114 Å3

NH2 H2N

li i 21/

N

N N

N

MoIVCu6

Monoclinic P na = 24.89 Å; b = 14,39 Å; c = 30,11 Å

α = γ = 90°; β = 108.81°;

Monoclinic P 21/na = 14.292 Å; b = 24,554 Å; c = 15,017 Åα = γ = 90°; β = 108.78°; V=4989.6 Å3MoIVCu6-Cis

TPA

Work by V. Marvaud et al.

Theoretical Study (DFT)Theoretical Study (DFT)

Collaboration : J.Tercero, E. Ruiz, S. AlvarezBarcelona University

Molecular Orbitals [Mo(V)(CN) ]3- (DFT)[Mo(V)(CN)8]3 (DFT)

Mo Square Antiprism Mo DodecahedronMo Square Antiprismd z2

Mo Dodecahedrond x2 -y 2

Molecular Orbitals for a pair[Mo(V)(CN) ] CN Cu(II)[Mo(V)(CN)7]-CN-Cu(II)

Dinuclear MoCu square antiprism Dinuclear MoCu dodecahedron

3,00000

SAP CSM - (Photo)MagnetismAntiprism

2,50000 WIVCu2SAPR

Antiprism

2,000001MoIVCu6FM

MoVCuAF

1'WVCuAFMoIVCu6FM(Trifl)

1'MoIVCu6FM

WIVCu4FM

1WVCuAF

1,50000Est1

2MoIVCu6FM

CuWV5 FMMoVCuFM(cyc)

MoIVCu2(en)N3D

1 Mo Cu6FM

2'MoIVCu6FM

Photomagnetism

0 50000

1,00000

Est2 MoIVCu6(Tpa) Dodecahedron

0,00000

0,50000

Est3DD

MoIVCu2

MoIVCu2(cyc)N2D

MoIVCuAF(bipy)

Dodecahedron

,0,00000 0,50000 1,00000 1,50000 2,00000 2,50000 3,00000 DD

in Prussian blue analogues … (3D) g ( )

Photomagnetism

C III F II [(C II(HS)F III(BS)]*hν

CoIII-FeII ⇒ [(CoII(HS)FeIII(BS)]*diamagnetic pairs paramagnetic

3D ferrimagneticbelow TCbelow TC

Hashimoto et al., Science, 1996 ; Verdaguer, Science, 1996

Photomagnets Cobalt-Iron Prussian blue analogues

The properties are deeply modified by the insertion of alkali cations

Co4[FeIII(CN)6]8/3•nH2O Cs2CoIII10/3CoII

2/3[FeII(CN)6]10/3 Cs4CoIII4[FeII(CN)6

8

on /

10-3

em

u

No effect of light

on /1

0-3

emu

neti

zati

on 1

0-4 /e

mu

4

4

2.5

Very small effect of light

n /1

0-3

emu4

h

0

4

5 10 15 20 25

Mag

neti

zatio

Mag

netiz

atio

Temperature /K

Mag

n

248 12 16 20

0

2

8 12 16 20 24

1

Temperatu re /K

Mag

netiz

atio

n

0

2

8 12 16 20 24T t /K

hν

Temperature /K Temperature /KTemperature /K

Under pressure V. Ksenofontov P. Gütlich, A. Bleuzen et al. Phys. Rev. B, 2003, 68, 0244151-6A. Bleuzen et al. Angew. Chem. Int. Ed., 2004, 43, 3728.

Synthesis.[FeIII(CN)6]3- + [CoII(H2O)6]2+ + C+ (C+=K+, Rb+, Cs+)

increasing size of the cation C

Rb1.8Co4[Fe(CN)6]3.30 13H2O Cs3.7Co4[Fe(CN)6]3.7 9.2H2OK0.1Co4[Fe(CN)6]2.8 18.4H2O

increasing size of the cation C

K+ Rb+ Cs+

O

O

O

O

OO

O

O

Fe/Co 0.70 0.83 0.93

IIIN C-N

C-N O

O

O

O

O

O

O

O

N

Co ligand field

CoIII -FeII

rally induced CoIIN4O2

CoIIIN6

a = 10.04 ± 0.05 Å

a 10 36 ± 0 05 Å

Co

N

N N

NN

N

Co

N

N O

O

CoII-FeIIIstructurally ind

electron transfera = 10.36 ± 0.05 Å

∆ 0 3 ÅN

N

O ∆a = 0.3 Å

Formation of CoIII-FeII pairs …I ti f lk li tiInsertion of alkali cation …

1) + n C+

Fe(CN)6

2) + n/3 [Fe(CN)6]3-

O

OO

O

OO

OO

O

OO

O

Fe(CN)6Co

H2OC N

OO

O

O

O

O

Co(NC)4+n/2(OH2)2-n/2

C-N O

• Insertion of C+ increases the ligand field ∆Co of Co(II)g Co ( )

Cobalt(II) : Ligand Field, spin state, geometry and reactivity

H O OHOH2

NC CNCN

CN NCNC

H2OCo

H2O OH2

OH2OH2

NCCo

NC CN

CNCN

CNCo

CN NC

OH2OH2OH2 CN

E² ² t

OH2

²² oct oct² oct

Strong FieldIntermediate FieldWeak Field Strong FieldLow SpinS = 1/2

Very Reducing Short Co-C

Intermediate Field Spin Transition ?

S = 3/2 or 1/2Reducing

Weak FieldHigh SpinS = 3/2Long Co-O Very Reducing Short Co CReducingLong Co O

CN

Origin of the diamagnetic pairs in Co-Fe Prussian Blues

NC FeIIINC CN

CN

CN

C NC FeIINC CN

CN

CNCoII

CN N

OH2

CNCN

C

CNCoIII

CN N

OH

NC FeII

CNCN

C215 pm

195 pm2

OH2

CN OH2OH2

E eg*e * El fAntibonding ! g

t2gt2g

eg* Electron transferAntibonding !

2g2g

HS CoII LS FeIII LS CoIII LS FeII

Paramagnetic : 3/2, 1/2 Diamagnetic : 0, 0Paramagnetic 3/2, 1/2 Diamagnetic 0, 0Distance CoIINeighbours ­ 215 pm Distance CoIINeighbours ­ 195 pm

Photo-induced electron transfer L l t t d C

• Photo-induced electron transfer = important dilation of the network

Local structure around Co.p

Rb1.8Co4[Fe(CN)6]3.30 Cs3.7Co4[Fe(CN)6]3.7hν =

defects = strains relaxation easy dilation

dilation strong strains very small effect of light

Rb C• Excited pairs CoII-NC-FeIII - same electronic structure - same local structure

Rb2 Cs4

as CoII-NC-FeIII pairs in K0.1Co4[Fe(CN)6]2.8

Oxidation StateOxidation StateXANES at the Co K edge : 1s2 4p 1s1 4p1

[CoII(OH2)6]2+

orba

nce

/a.u

.

1

23

K+

Rb+

Cs+

CoII

CoIII ]

Abs

o

[CoIII(CN)6]3-

Cs

• K0.1CoII4[FeIII(CN)6]2.8 18.4H2O

7700 7720 7740 7760 7780 7800Energy /eV

• Rb1.8CoII0.7CoIII

3.30[FeII(CN)6]3.30 13H2O • Cs3.9CoIII

4[FeII(CN)6]3.9 9.2H2O

Photoinduced electron transfer …hν

Spin = 0Intersystem crossing

[Co(II)-Fe(III)]*Co(III)-Fe(II)hν

Spin = 1

Energy Intersystem crossing+ Electron transfer

Spin = 1 Metastable stateSpin 1

Spin = 0 Co Fe distance

Metastable state

Pair : Paramagnetic3D : FerrimagneticCo-Fe distance 3D : Ferrimagnetic

Co(III)-Fe(II)

Diamagnetic

[Co(II)-Fe(III)]*

ParamagneticDiamagnetic Paramagnetic

Towards devices … ?

Magneto-opticsg pHow magnetism transforms light …g g

1

Eff

et

0

0,005

0,01

0,015

2 he res

Faible flux lumineuxP = 0.7 mW /mm2Spot du�

laserMagneto-optics

Le composˇ est initialement faiblement paramagnˇ tique�Le syst me ne transite pas sous faible flux lumineux

Champ /Oe

-0,015

-0,01

-0,005

-8000 -6000 -4000-2000 0 2000 4000 6000 8000

2 heures

Echantillon Reading

Le syst¸ me ne transite pas sous faible flux lumineux

0,005

0,01

0,015

Fort flux lumineux0 / 2S t d �

2 Writing

-4000 -3000- 2000 -1000 0 1000 2000 3000 4000

Champ /Oe

Eff

et

-0,015

-0,01

-0,005

0

2 heuresP = 70 mW /mm2

Au même point de

l'échantillon

Spot du�laser

Echantillon

Example of a+ Reading

Le syst¸ me transite sous fort flux lumineux = ECRITURE

0,0153

Example of aphotomagneticerasable

d it blAu même point de

l'échantillon

Spot du�laser

Echantillon

Eff

et

-0,015

-0,01

-0,005

0

0,005

0,01Faible flux lumineux

2 heuresP = 0.7 mW /mm2

3and rewritablememory

ReadingEchantillon

Champ /Oe-4000 -3000- 2000 -1000 0 1000 2000 3000 4000

Le signal dichro•que est tr¸ s faible : une partie des paires excitˇes relaxent

LECTURE

Coll. J. Ferré, J.P. Jamet, LPS Orsay

g

Next step : going to nanosize

200 200 nm200 nm

x 23000 nanometricr anisati n

200 nm

nanoparticles organisationof particles

A. Bleuzen, LCI Orsay, private communication

Work in progress : Magnetization of a few nanoparticles of CoFe Prussian Blue analogues, microSQUID, 4 K, under irradiaction

14 K

g , Q , ,

0.5

4 K

A50

00 min

M/M

s

irradiation with white light

-0.5

0 min1 min5 min20 min30 min70 min100 min3 h

-1-1 -0.5 0 0.5 1

3 h4 h12 h

µ0 H (T)µ0 ( )

(A. Bleuzen, W. Werndorfer)

Chi l M tChiral Magnets

Optically Active Magnets : Why ?

θθn

εn-θn

M

M

θm

εm-θm

-εnCotton Effect Faraday Effect

M-εm

Cotton : breaking of space symmetryFaraday : breaking of time symmetry

Formal Similarity of Faraday and Cotton Effects

MichaelMichaelMichaelMichaelFaradayFaraday ……FaradayFaraday ……1791-1867Fullerian Professor of Chemistry1833-1867

andand…… and and AiméAiméAiméAimé

CottonCotton

1869 - 1951French PhysicistOptical Physics

Circular dichroïsmCircular dichroïsm

What is new with Optically Active Magnets ?

Breaking of space and time symmetry

Cross-effect MagnetoCHiral Dichroism (MChD)

Unpolarised light

k Id+

≠

contributionγd(ω)k.M

to theUnpolarised light

k Id-

≠

dielectric tensor

L.D. Barron, J. Vrbancich, Mol. Phys. 51 (1984) 715

Magnetochiral Dichroism (MChD) :

µ(k,M,ω) = αd,l(ω)k + β(ω)M + γd,l(ω)k.M

CottonChi lit

FaradayM ti ti

Cross-Term2 d dChirality Magnetisation 2nd order(MChD)

k light wave vectorM magnetisation

Cf Barron, Rikken ...

Oxalate ligand1. Bis-Chelating

2 Stable (and inert) precursors complexes2. Stable (and inert) precursors complexes

3. Complexes as ligands

O

O

M'O

O

OM

O O

O

OO

O

O

M'O

MO O

O

OO

O

O

O

O

O

1 O OO

O

OO

M' 3

OO

O 21

Chiral complex

STRUCTURES OF 2D and 3D NETWORKS

Λ∆

ΛOO

MM1

L. Atovmyan et al, JETP Lett. 1993, 58, 766

2D∆∆

ΛOO

M2M1

∆ − Λ

Heterochiral Honeycomb Plane 2D Materials∆-Λ

Heterochiral Honeycomb Plane 2D Materials

ΛΛΛ

Λ ΛΛ

S. Decurtins et al, Inorg. Chem.1993, 32, 1888

3DO

O

O

O

M2M1

Λ − Λ or ∆ − ∆

Λ ΛΛ

ΛΛ 3D

Λ-Λ ou ∆-∆Λ Λ or ∆ ∆Homochiral Helix Structure 3D Materials

Interconnected helices

Λ-Λ ou ∆-∆

Fabrice Pointillart, Ph.D ThesisFabrice Pointillart, Ph.D Thesis

A very useful cation for chiral design

∆-[RuII(bpy)2(ppy)]+

• dimension• D3 Symmetry• Charge : +1g

ll lé

Cf Clément et al., Monatsh. Chem. 497 (2002), 117

Gruselle, Malézieux, Brissard …

BUILDING the 3D NETWORKS. Decurtins et al, Inorg. Chem. 1993, 32, 1888 R. Andrès et al, Inorg. Chem. 1999, 38, 4637 , g , ,

R. Andrès et al. Inorg. Chem. 2001, 40, 4633

The anionic subnetwork WRAPS around the assembling cation [Ru(bpy)3]2+

Helix PHelix M

STRUCTURES of 3D NETWORKSeHelix M

(P)(M)

Anionic Subnetwork Cationic Subnetwork[M(L)3]n+

- Cation Symmetry D3

Charge and

[MaMb(ox)3]n-

- Charge and size ad hoc

INDUCING CHIRALITY

Ru – N : 2,063(5) Å

{[RuΛ(bpy)3][Mn2Λ(ox)3]}n

Groupe d’espace : P4132

Mn – O1 : 2,135(5) Å

Mn – O2 : 2,169(5) Å

a = 15,508(1) Å

α = β = γ = 90°

{[Ru∆(bpy)3][Mn2∆(ox)3]}n

Groupe d’espace : P4332

a = 15,492(2) Å

Ru – N : 2,059(4) Å

Mn – O1 : 2,167(5) Å

α = β = γ = 90° Mn – O2 : 2,133(5) Å

The assembling chiral cation [Ru(bpy)3]2+ induces chirality on all the metallic centres of the anionic subnetwork

[Ru(bpy)2 (ppy)][MnCr(ox)3][ ( py)2 (ppy)][ ( )3]

They are chiralThrough resolved precursor [∆ or Λ MIII(ox)3]3-

NBu4[MnΛCr∆(ox)3]NBu4[MnΛCr∆(ox)3]

300

350

100

150

200

250

ΛCottonEffect

-100

-50

0

50

300 350 400 450 500 550 600 650 700

Effect

300

-250

-200

-150

-100

∆

-350

-300

Wavelength / nm

2D or 3D : Magnets below 10-20Kg

2 5

3.0

3.5

50

60

70

cm-3

1 5

2.0

2.52D-{MnCr}

20

30

40

M /

µ B

χ−1 /

mol

.c[Ru(bpy)3][ClO4][MnCr(ox)3][R (b ) ( )][M C ( ) ]

0 5

1.0

1.5

0 50 100 150 200 250 3000

10

T / K

M [Ru(bpy)2(ppy)][MnCr(ox)3][Ru(bpy)2(ppy)][NiCr(ox)3]

0 2 4 6 8 10 12 14 16 18 20

0.0

0.52D-{NiCr}

T / K0 2 4 6 8 10 12 14 16 18 20

TBAC NiO T 4 4K (l 580 )

Evidence of the MChD unpublished …3000 250

TBACrNiOx T= 4.4K (l=580 nm)

Phase Delta / °

Phase Lambda / ° ∆

2000

2500

200M Delta / ua

M Lambda / ua

Phase Lambda / °

Phase°a gr

ee

∆

1500150

sign

al d

elta

/ua P

hase delta

≈ 180°

nal /

ua

se /

deg

500

1000100M

s/ °

Sign

Pha

Λ

00

0

0

50

-500 0-100 0 100 200 300 400 500 600 700

H / mVC. Train, Coll. G. RikkenDFG MM SPP

Noyori museum, nagoya

On the way to transparent single crystals(work in progress)(work in progress)

R. Gheorghe, M. Gruselle, C. Train

1. (NH4)3[Cr(C2O4)3] + Mn(NO3)2+ ... 2. (NH4)3[Cr(C2O4)3] + Mn(NO3)2+ …

HCH3

CH3

+

H CH3CH3

+S+ R-N+ CH3

CH3

CH3

I- N+

CH3

CH3

CH3

I-S+ R-

NMePr2(S+)-secBuI NMePr2(R-)-secBuI

[NMePr2(S+)-secBu]3[Mn-∆-Cr(C2O4)3] [NMePr2(R-)-secBu]3[Mn-Λ-Cr(C2O4)3]

R. Gheorghe, M. Gruselle, C. Train

Structure of one of the enantiomers

Along a axis

Pl bHexagonalP 63 (no 173)Plane ab P 63 (no. 173)a = 9.4160 Åc = 16.8430 ÅVolume = 1293.11 Å3