BEGIN: High symmetry LINEAR chain, sheet or a cubic close packed 3D lattice. vibrational deformation modes, asymmetric can couple and reduce symmetry

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Scott Lindsey
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1 Bonds bands Molecules olids Jahn Teller Peierls BEGN: High symmetry LNEAR chain, sheet or a cubic close packed 3D lattice rbitals : highly symmetrical but ordered structure often does not correspond to situations of maximum bonding/ stability vibrational deformation modes, asymmetric can couple and reduce symmetry Chemist view : Jahn-Teller distortion

2 Jahn-Teller system e.g. cyclobutadiene, C 4 H 4 D 4h α-2β B 2g α E u α+2β A 1g two e in 2 DEGENERATE orbitals Jahn-Teller : large interaction of vibrational and electronic motion a vibration mode breaks the degeneracy and lower the energy of the system

3 Vibration mode lower symmetry from D 4h to D 2h symmetry-lowering deformation stabilizing one orbital, destabilizing another correct electron count c.f. [C 4 H 4 ] 2+ primary JT effect 2 nd order JT deformation A B C C

4 Move to solid a chain of hydrogen atoms (1s 1 ) E(k) E f a 0 π/a k E(k) E f 2a 0 π/2a π/a k band folding Phonon or vibration mode couples most effectively with e motions

5 Examine the orbitals (bottom, top and E f ) E 0 k π/2a E 0 k π/2a Peierl distortion

6 plitting of band Peierl gap Metal Non-metal /semiconductor e.g. Chain of H atoms Chain of hydrogen molecule

7 Krogmann s salt K 2 Pt(CN) 4 Br 0.3 E(k) 1.7e 2.0e 1.0e k=0 0 π/a k k=π/a Full Filled band 2e per Pt() Half-filled 1e per Pt() part-filled 1.7/2.0 e per Pt() 2p 2p? F = = = k p a undistorted 2p 2p? F = = = k p 2a 2a 4a Distorted commensurate CDW 2p 2p? F = = = k 1.7p 2a 2.35a Distorted incommensurate CDW

8 Peierls distortion kt E p hν Electronic excitatio across Peierls gap populates antibonding band, decrease E p Thermal excitation of phonon E p P External pressure shorten the bonds better orbital overlap increase band width Decrease E p Examples K 2 Pt(CN) 4 Br 0.3 Nb 4, V 2, (CH)x

9 Another class of 1D Pt chain compounds Wolfram s salt [Pt (am) 4 ][Pt V (am) 4 Cl 2 ]Cl 4 Cl NH 2 R d 8 -d 6 intervalence compound RH 2 N RH 2 N Pt V NH 2 R Electronic spectrum shows intervalence band Cl NH 2 R RH 2 N Pt NH 2 R RH 2 N RH 2 N Cl Pt V NH 2 R NH 2 R Pt(V) Cl Pt() hv Pt() Cl Pt(V) RH 2 N Cl Hyperthetical Pt() valence delocalized ymmetrical compound would be a METAL d 7 Pt() Peierl distortion

10 ν(pt-cl) vibronic coupling Frank-Condon Principle Pt(V) - Cl Pt() Pt() Cl Pt(V)

11 Case studies Adv. Mater. 2000,12,1461

12 thermochromic material nanometal wire

13 Mixed valency compounds Trapped vs delocalized valencies localised delocalised localised VCT Activation energy for e hopping Trapped (localised) e and associated lattice distortion (small polaron) at left and right Large interaction, low Eact (activated hopping) Weak interaction, large Eact (trapped)

14 Co 1-x Fe 2+x 4 inverse spinel structure For x=0, Fe 3+ [Co 2+ Fe 3+ ] 4 Fe 3+ T d sites; Co 2+ /Fe 3+ h sites For x>0, Fe3+ [Co 1-x 2+ Fe x 2+ Fe 3+ ] 4 excess Fe, e hopping between h Fe 2+ /Fe 3+ For x<0, Fe 3+ [Co 2+ Co x 3+ Fe 1-x 3+ ] 4 excess Co, e hopping between h Co 2+ /Co 3+ Explantion Fe 2+ (t 2g4 e g2 ) Fe 3+ (t 2g3 e g2 ) Co 2+ (t 2g5 e g2 ) Fe 3+ (t 2g6 ) large displacement changes for Co(/) case

15 Classification of intervalence compounds Class : very different environments for different oxidation states, large E act, no interaction Class : ufficiently similar environments for different oxidation states, small E act. Hopping semiconductors, VET band Class : dentical fractional oxidation states with e delocalized between them. A: Finite cluster -delocalised electrons B: e delocalised throughout the solid, metallic conduction

16 Eu 3 4 Eu () 2 Eu() 4 PXRD indistinguishable Eu Mossbauer distinct Eu()/() at LW temp Peaks coalescence at high Temp e hopping between ()/() E act (ET) Prussian blue Fe() 4 [Fe()CN 6 ] 3 xh 2 CN NC CN NC NC Fe C N Fe NC NC CN CN NC distinct Fe()/Fe() VCT Fe()/() cm -1

17 Fe 3 4 border at class / inverse spinel structure Fe 3+ [Fe 2+ Fe 3+ ] 4 c.f. Mn2+ [Mn 3+ Mn 3+ ] 4 normal spinel 10 2 metallic byt still has semiconductor behaviour σ(ω -1 cm -1 ) Verwey transition hopping semiconductor /T temp Mn 3 4 Co 3 4 normal spinel e hopping between Td and h sites, high Eact low RT conductivity

18 Peierl distortion in LW dimensional metal oxides Ti 2 V 2 Nb 2 Mo 2 Ru 2 Reg. C RT Distort C Low T Distort C RT Distort Metal RT Distort Metal RT Reg. Metal High T xide d-electrons M-M separation Ti (M) V 2 (tetra) (M) V 2 (mono) Nb 2 (tetra) (M) Nb 2 (mono) Mo W Ru (M) s (M) electronic and structural changes related to d n configuration electrical conductivity vary from C to metallic

19 Bonding in Rutile-type metal oxides x M M M M t 2g ( dyz) σ-bond y z M M M M t 2g (dxy, dxz) π-bonds doouble degenerate edge shared h M 6 Two bands : M-M σ-band and M- π-band 2n e for σ-band 4n e for π-band Different band filling Peierls distortion strength M-M and M- bond Electronic and tructural changes with TEMP

20 V 2-x F x Fluorine substitution on structure bonding - electronic properties 0<x<0.2 isomorphous substitution V(V) V(), longer V- and V-F bond weaken V-V bond Destablized Peierls distorted state e go to M- π* band T t x Transition from metallic to distorted semiconductor Peierls transition temp wrt F substitution Less favour distortion a o unit cell parameter vary linear with x Vegard Law olid solution behaviour 2.86 c o x 2- x P(V2 -xfx ) = P(VF 2) + P(V 2) mole fraction weighted average V o x

21 Physical properties of V 2-x F x Compound Cell parameter a o c o E act (ev) T t (K) V V 1.97 F V 1.96 F V 1.86 F < V 1.79 F < ynthesis V Au tube, 600 C/133kbar 25 + V + 6% HF/H2 V2 xfx o Metallic to C transition T t as %F Monoclinic to tetragonal transition F substitution, V(V) V(), e into π* M-, destablilized Peierls distorted monoclinic state

22 Trends in electronic-structure relations Rutile type metal oxides Regular form (tetragonal) Peierls distorted (monoclinic) M- π M-M σ d 1 Nb 2 (RT distorted C) V 2 (high T metallic; low T C) M-M σ M- π M-M σ d 2 Mo 2 (distorted metallic) d 4 Ru 2 (regular metallic) d 1+x V 2-x F x (regular metallic more favour)

23 ther examples Nb 4 Nb(V), d 1 (t 2g1 ), edge share h Nb Nb Nb Nb High P and Low T Nb Nb Nb Nb Peierls distortion semiconductor BaV 3 V(V), d 1, face share h, extra 1e in dz2 orbital V V V V V V V V V V

24 Transition metal dichalcogenides (MX 2,, X=, e, Te) layer structure Cd 2 hcp 2- Ti Ti Ti Li insertion Ti Ti Ti Li Li Ti in D 3h Group V, V, V M 2 compound Layered structure VDW forces Ti(V) sandwich between hcp layers of 2- Li insertion between the layer e injected into CB D 3h Ti d xz, d yz d x 2-y2, d xy d z 2

Transition metal chalcogenides intercalation compound nsertion of atoms, ions, clusters, organometallics etc into an interlamellar space with minimal pertubation of structure of host, e, Te in h, or

25 Transition metal chalcogenides intercalation compound nsertion of atoms, ions, clusters, organometallics etc into an interlamellar space with minimal pertubation of structure of host, e, Te in h, or trigonal prism(d 3h ) strong M-L bonds weak interlayer VDW forces Ti(V), V(V), Cr(V),Zr(V), Nb(V), Mo(V), Hf(V), (V),W(V) Li + electronic tunable x e 2-x and n/p doped e.g P or V in Ti 2 semiconductor or metallic depend: e config. of M D3h/h, degree of band filling xli + + xe /e/te band tuning

26 h D 3h Zr V 2, d 0 semiconductor V V 2, d 1 metal Nb V 2, V 2 d 1, metal Mo V 2, d 2 semiconductor symmetry band origin degree of filling

27 Ti 2 vs Ti 2 E E CB CB VB VB N(E) N(E) Ti 2 (rutile) - h Ti(V), d 0 insulator Ti 2 layered D 3h semiconductor Full (2p) and (3p) band empty 3d band greater overlap Ti- (more diffuse) than Ti- bandwidth bigger for smaller gap

28 2 and e 2 D 3h, layer, d 1 structure projection of undistorted MX 2 layer metal array of undistorted MX 2 layer d 1 half filled d z 2 band 2D Peierls distortion M-M short-long electron-phonon coupling metal atom clustering induceds periodic lattice distortion in sandwiching challogen HCP sheets

29 charge density corrugations Bright spots 2- atoms

30 uperconducting intercalates Am 2/3 2 n=1-4, θ=0 n=5-9, θ=90 n=10-18, θ=56 C n H 2n+1 NH (C n H 2n+1 NH 3+ ) x (C n H 2n+1 NH 2 ) y 2 x- xidative intercalation Proton conductivity n=1-4, constant spacing n=5-9, monotonic increasing n=10-18, monotonic increasing n=18, 56.1Å spacing

31 conductivity excess e in 2 d z 2 band superconductivity in small n due to cooper pairs (electrons) between layers mediated by lattice phonon e interlayer spacing e large n, weak e-p-e coupling, constant T c w.r.t. n for n=5 to 8, T c decrease due to increase in interlayer spacing for n=1 to 4, interlayer spacing constant, Tc decrease due to decrease in charge density of intercalated RNH 2 /RNH 3 +

ELEMENTARY BAND THEORY

ELEMENTARY BAND THEORY PHYSICIST Solid state band Valence band, VB Conduction band, CB Fermi energy, E F Bloch orbital, delocalized n-doping p-doping Band gap, E g Direct band gap Indirect band gap Phonon