Your questions that were not covered explicitly

1
Your questions that were not covered explicitly

• FeS is hex and FM, FeS2 is not hex and PM. Why?
• What AC frequencies most influence atoms? Are
  they in optic range?
• Propogating waves occur for ?gt?plasma, in
  ultraviolet for Alkalai metals. See Ashcroft
  Mermin, Chapt 1.
• Electrons in TM are more likely to move around
  than those in RE. How does this affect their
  magnetic properties?
• Why are bandwidths of TM broader than those in
  RE?
• What are magnetic properties of RE (double and
  super exchange in oxides)?
• RE atoms have almost same electronegativity as
  Li, which is a common battery material. What
  arent RE used in energy storage?
• (battery, rather than magnetic)
• Why do people want to use V2O for battery
  electrode?
• How do structural defects modify electronic
  structure?
• How can one estimate the energy cost a
  structural defect will be?
• How does alloying and segregation affect the
  failure mode, or the adsoprtion on the surface
  create stress-corrosion cracking?
• Remainder of queries were all addressed in one
  form or another during lectures and examples.

2
When FeS is S-poor it is hcp and FM, when S-rich
it is other structures (e.g., cubic) and
PM. Why?
Hexagonal NiAs (B81) structure FeS (blue/black)
Simple argument ionic units S2 form
hexagonal lattice Fe2 fills in octahedral
holes M-M bond stabilize. Not ionic. Fe layers
FM
Pyrite (C2) structure FeS2 (Fools gold)
Fluorite (C1) structure AB2
S (covalent dimers form in CP Fe (related to
NaCl) somewhat related to NaAs Doping w/ Co
Fe1-xCoxS2 -gt FM. CoxS2 is good FM.
Distorted Fluorite S not at, e.g., 1/4, 1/4,
1/4
S site at, e.g., 1/4, 1/4, 1/4
3
Battery Materials (Ionic conductors) like V2O5
need Li intercalation
http//www.fhi-berlin.mpg.de/th/member/hermann_k.h
tml
V2O5 is clearly a semiconductor gap 2.3
eV valence band full and conduction band is
empty. Intercalation with Li makes levels in
gap and then fills conduction band Redox
Chemistry V2O5 xLi xe LixV2O5 (x
1) Only with ionic conduction is this useful for
battery applications. Currently, nano-particles
of this material can be cycled over 100 times.
4
Intercalation in Semiconductor for Ionic
Conduction
schematic pictures
Defect state
Example where x of Li increase and states
increase and broaden, eventually overlapping
conduction band of semiconductor.
Add x of Li and states forms in gap.
5
Magnetism in f-orbital elements Lanthanides

• Paramagnetic behavior arises from both SPIN and
  ORBITAL contributions, unlike
• TM where there is SPIN-only contributions
  (orbital quenched).
• Magnetic moments of La-series well-described by
  Russell-Saunders coupling
• spin-orbit large (1000 cm1) gtgt Ligand field
  small (100 cm1)
• only lowest J-state populated.
• moments independent of environment.
• moment given by Landé formula
• Curie Constant ?effgJ?J(J1) ?B and gJ
• See Ashcroft and Mermin, Solid State Physics,
  Chapt. 31.

• In general, elements and solids follow Hunds
  rules for orbital filling
• Maximum Multiplicity (Spin) For n electrons, S
  ?ioccupied si (si 1/2 with all first).
• Maximum Orbital Angular Momentum L of 2L 1
  states. For fs, L 3, 2, 1, 0, -1, -2, -3
• Total Angular Momentum J LS gt L-S L
  S.
• Relativistic spin-orbit coupling ?(LS) breaks
  the (2L1)(2S1) degeneracy of J.
• ? lt 0 favors min. J (L antiparallel to S) but ?
  gt 0 favors max. J (L parallel to S)
• It turns out that ? lt 0 for shells that are
  less that half-filled JL-S for n 2l1
• ? gt 0 for shells that are more that
  half-filled JLS for n gt 2l1

6
Hunds rules is easier to apply than describe
22 cases of interest 1-9 d-electrons for l2,
1-13 f-electrons for l3. Triad number SLJ is
unique label, but historically use 2S1XJ
L 0 1 2 3 4 5 6 X S P D F G H I

• e.g., Pr3 Xe4f2
• Max. S S 1/2 1/2 1
• 2L 1 states L 3 2 5
• Less than half-filled (min. J) J L-S
  51 4
• Ground-state 3H4 gJ 0.8, ?effgJ?20 3.58 ?B
  expt 3.5 ?B

?
?

• e.g., Ho3 Xe4f10
• Max. S S 2
• 2L 1 states L 6
• More than half-filled (max. J) J LS
  62 8
• Ground-state 5I8 gJ 1.25, ?eff 10.6 ?B expt
  10.4 ?B

?
??
?
?
?
??
??

• e.g., Cr2 Ar3d4
• Max. S S 2
• 2L 1 states L 2
• Less than half-filled (min. J) J L-S 0
• Ground-state 5D0 gJ 2.0, ?eff 4.90 ?B expt
  4.8 ?B
• Here L0 with JS was used, i.e., ltLgt0
  (quenched) for TM. That is, Ligand fields gtgt
  Spin-orbit for TM so Hunds 3rd rule invalid and
  lifts the degeneracy of Ls, not Ss.

7
Ln3 Magnetic Moments compared with
Theory Experimental _____ Landé Formula ---
Spin-Only Formula - - -
Sm and Eu are not well-described by the Landé
formula due do assumption used in its derivation.
Perturbation theory is used and denominator is
small for this two elements, and derivation
assumed it large. See Ashcroft and Mermin, Solid
State Physics.
8
RE-TM Magnetism Due to f- and d-electron Moments

• Unusual T-dependence of moments.
• moments go to zero as T goes to condensation
  point, Tcp.
• moments increase in opposite direction for T gt
  Tcp.
• magnetization (and moments) vanishes at Curie
  pt. Tc.
• e.g., Dy3Fe5O12
• RE moments oppose TM moments
• RE moment dominates at low-T.
• RE moment disorders at lower T than TM moments
• See Ashcroft and Mermin, Solid State Physics.

9
www.ncsu.edu/chemistry/das/superexchange.pdf
10
www.ncsu.edu/chemistry/das/superexchange.pdf
11
www.ncsu.edu/chemistry/das/superexchange.pdf
12
Defects and Electronic Structure
What do you suppose happens with a simple vacancy?
What happens to DOS and electronic
structure? Does it matter if it is a metal or
semiconductor? If so, what is different? Any
examples?
13
Defects and Electronic Structure Vacancy in
Diamond
e.g., from D. Saada, Technion-IIT in Haifa, Israel
This distortion is associated with a Jahn-Teller
effect, so that the dangling bonds around the
vacancy are bent to pair the atoms along the
110 direction.
Defect state in gap in this case
Positions of the nearest neighbors to vacancy
before (yellow) and after (red) the dynamical
relaxation, The green atom marks the position of
the vacancy
DOS for diamond, calculated with 60 special
k-points.
It is found that the net motion of the atoms
surrounding the vacancy is outward, in contrast
to the vacancy in Si, e.g. These atoms therefore
move more into the plane of their three nearest
neighbors, and the bonding becomes more sp2-like
than sp3-like, as can be explained by the
relative stability of graphite over diamond. This
preference is in distinction to Si and other
elemental semiconductors.
14
Estimate of defect energies
Of course, this depends on the defect. Is it
localized (point) or extended (planar, line)?
The DOS n(E) is helpful to know dispersion of
states. For surface studies, one can resolve
local DOS (say for a layer or a site), i.e.,
n(r,E) ????(r)2 ?(E-E?). Projecting each
??(r) onto a particular ?i(r) at i-th site ni(E)
?? lti?gt2 ?(E-E?). Projected DOS can be
characterized by moments of the DOS ?i(m) ?dE
Em ni(E). The second moment (shape) of DOS is
?i(2) ?dE E2 ni(E) ?? lti?gt2 E2 ?(E-E?)
ltiH2igt ?j ltiHjgt ltjHigt ? ?i(2) Z
?2 This is summing over all possible paths via j
from the i-th site back to i-site. If only the Z
n.n. of i-th site contribute to local DOS, then
the last expression is obvious result.
Surface atoms must be more atomic-like, hence,
more narrow energy spread. In other words,
with fewer Zsurface neighbors DOS is narrower
than what arises from Zbulk. So moments tell
shape and width . And much more!
15
Estimate of defect energies
Of course, this depends on the defect. Is it
localized (point) or extended (planar, line)?
The second moment (shape) of DOS is ?i(2)
?dE E2 ni(E) ?? lti?gt2 E2 ?(E-E?)
ltiH2igt ?j ltiHjgt ltjHigt ? ?i(2) Z ?2
(for Z n.n. only). Total Energy of TM system
can be expected to have repulsive energy from
pairwise Pauli repulsion between electron clouds
on Z neighboring atoms (for a single atom Erep
Z) and cohesive energy/atom from adding up
contributions from occupied bonding/anti-bonding
band states. Eband ?EfdE E ni(E)
?i(1) or approximately Eband ?i(1)
v?i(2) ?vZ. So, roughly, change in energy
(repulsive band) is ?E ? 1/2 ?ij ?ij ?i
Bv?i(2 or roughly ?E AZ BvZ expect
localized states and altered DOS at surfaces and
around defects.
16
Estimate of defect energies continued
Consider a multibody interactions, which can be
based on moments of the DOS. In general, the
change in energy due to defect ?Eband ?m
(?E/??(m))ref (?(m) ?ref(m)). The moments of
the DOS (m0, 1, 2, ) define the effective
many-body interactions arising from electronic
contributions, i.e. Etot 1/2! ?ij Vij 1/3!
?ijk Vijk 1/4! ?ijkl Vijkl Since Eband
v?(2) , then (?E/??(2))ref 1/v?(2). So
smaller ? (2) (like at surface) means larger the
effective potential! The Stacking fault (SF)
energy (ABCABCBABC compared to ABCABCABC
stacking) is related to difference in the 4-th
moments, just by geometry, ?ESF ?i A(? i(4) ?
i-fcc(4)). So SF energy arises from local
geometry change and is localized near the
defect! Localized as only the local neighborhood
contributes to small but important
differences ?i(4) ?dE E4 ni(E) ltiH4igt
?jkl ltiHjgtltjHkgtltkHlgtltlHigt Z3 ?4
?ESF ?(4) ?fcc(4) Z3 (?4SF?4fcc) (a
few tenths of eV) Pairwise-only models miss this
completely. (Pairwise local environment for fcc
and hcp same.)
17
Adsorption Physisorption Dissociation CO to
CO2
CO oxidation on Ru(111)
Short residence time and combining with O atom to
form CO2.
Oxidation and desorption KE vibrational
rotational