Download lecture 6

Metallic Bonding cont.
Transition metals belong to three series in the periodic table
Which correspond to the progressive filling of 3d, 4d, and
5d states.
The presence of d electrons changes the picture of bonding
in these metals considerably from the simple (free-electron-like)
metals (e.g. Al, Na, ..)
The cohesive energies are greater than in the simple metals
and follow a roughly parabolic variation across the transition
metal series.
Metallic Bonding cont.
5d
Expt.
H (eV/atom)
Ca-Zn
Sr-Cd
Ba-Hg
4d
3d
Experimental heat of formation for the 3d, 4d, and 5d transition metals.
Can see a parabolic variation for the 4d and 5d metals –why?
Accompanied by systematic change of stable crystal structure from
bcc to hcp to fcc on going from early to late transition metals – why?
It has to do with the partly filled d valence shell
Metallic Bonding cont.
Band structure of
Copper – sp-bands in
light shaded region – free
electron-like
d-bands in dark shaded –
little dispersion, localized.
Free electron band structure
The d-band is narrower than the sp-band because the d valence
orbitals and thus the overlap between them is significantly
smaller than the s and p valence orbitals.
Metallic Bonding in transition
metals cont.
Qualitative picture of two contributions to a transition metal (TM)
density of states (DOS) – free electron-like sp-band, and narrow,
structured d-band.
Due to the large number of d-states, the d-band
dominates the DOS and the varying properties over a TM series can
be understood as arising from a differing filling of the d-band.
“Rigid band model” – the number of valence electrons increase over the TM series
Ru 8, Rh 9, Pd 10, Ag 11 – shifts the Fermi energy more and more to the right.
At the end of a TM series, the d-band is completely filled and the Fermi level cuts
the s-like DOS above the d-band.
Metallic Bonding cont.
non-bonding
bonding
anti-bonding
Rectangular
d-band model
Starting with the early TM, fill electrons into the lowest energy d-states.
Theses are of bonding type and thus can expect an increase in the cohesive
energy.
Due to shorter range of d orbitals, bonding will favour smaller lattice constants
to maximize wavefunction overlap. Around the middle of the TM series, have
strong cohesion and decreasing lattice constants.
As filling continues s-electron density becomes higher than the optimum
for metallic bonding – called “s-pressure” – competition between contractive
tendency from d-orbitals with repulsive tendency from the s electron gas.
Metallic Bonding cont.
5d
Expt.
H
(eV/atom)
Ca-Zn
Sr-Cd
Ba-Hg
4d
3d
As filling continues non-bonding and anti-bonding are occupied (e.g. middle
and late TMs) increasing d-occupancy does not lead to further increase
in cohesion energy. The s-pressure leads to an increase in the lattice
constants.
For the noble metals, d contribution, in this simple view, has cancelled out
and cohesive properties comparable to the simple metals is obtained.
Why the dip in the middle? – due to particular stability of isolated atoms
Metallic Bonding cont.
Transition from bcc to hcp to fcc over the TM series can‟t be
understood in the simple rectangular d-band model – no
structural information.
The lattice structure affects the substructure present in actual
DOS
-characteristic shape for bcc, hcp, fcc
-Single particle energies (i.e.
energy eigenvalues of the
-bandstructure) largely govern the
final total energy – thus,
preferred crystal structure is that
which offers an optimum
number of bonding states for a
given filling fraction.
Hydrogen Bonding
Hydrogen Bonding
Importance of hydrogen bonds cannot be overstated – most important
force determining the 3D structure of proteins, structure of liquid
water, and in holding water molecules together in ice
Estimated a paper related to H bonding published every 15 minutes
Represented as A-H B, where A is an electronegative species, N, O, F, Cl
and B must be an electron donor.
Example of a typical H bond – Water dimer: H2O-H2O
Isosurface of constant
electron density for an
occupied MO, showing
overlap between the
wavefunctions of both
water molecules
Hydrogen Bonding
• H bonds are directional, with A-H-B angles close to 180o – the
stronger the bond the closer it is to 180o
• On H-bond formation, the AH bond is lengthened by 0.01-0.04Å –
leads to softening (red-shift) of AH vibrations
• H bonds can be „cooperative‟ – strength of
H bonds increase as more H-bonds are formed
– crucial in biology for providing additional
energy to hold certain proteins together under H-bonds
ambient conditions
Between
O(red) and H
cooperative behaviour opposite to the more (grey)
intuitive behaviour of e.g. covalent bonds, where
generally the bond strength decreases
as more bonds are formed
– e.g. a helix of alanine molecules
Hydrogen Bonding:Ice
• Everyday ice and snow is
hexagonal ice (ice Ih) i.e.
the ice in the biosphere,
with only a small amount of
cubic ice Ic
Ice rules: two H atoms near each
O atom, one H atom on each
O …O bond, H-O-H angle little
less than the tetrahedral
angle (109.47°), at about 107°.
Cohesive energy 0.58eV; lattice
constant 2.75Å
Hydrogen Bonding:Ice
Oxygen is electronegative it draws the electrons in the bonds
it shares with the hydrogen atoms towards it.
The hydrogen atoms are left with a net positive
charge and the oxygen is negative.
This results in the water molecule having a large dipole
moment. Two water molecules can therefore form a strong
electrostatic interaction
Relatively easy to make
and reform hydrogen
bonds without any need for
energy inputs or catalysis.
Hydrogen Bonding:Ice
Ice IV
Snowflakes by Wilson Bentley, 1902
Hydrogen Bonding:Ice
Snowflakes by Wilson Bentley, 1902
Morphology depends sensitively on temperature and humidity
OH-vibrational frequency (cm-1)
Hydrogen Bonding:
OH vibrational
frequencies
OH vibrational frequency versus
A-B distance, for a host of H bonded
complexes;
Can see as separation of A-B
decreases, the vibrational frequency
decreases – red shift
O-H….O
A
A-B distance (Å)
B
Hydrogen Bonding: DFT
Calculations
• Electronic character of H-bond
not clear and matter of debate
• Unique role H plays due to negligible
ion core size, and high ionization energy
of the one electron it has – contrast
to the alkali metals which can readily
donate their electron
• Generally thought H-bonds are
mediated by electrostatic forces –
Coulomb interaction (partial positive
charge on H and partial negative charge
on atom B)
• Not purely electrostatic, e.g. overlap of
orbitals as seen in the water molecule –
more characteristic of covalent bonding.
Gas phase H-bonded complexes
Surfaces
Surfaces
Surface energy: energy required to create a surface
Experimental values for simple, transition, and noble
Metals – vary as the cohesive energy
Total energy of slab with N atoms
Total energy of atom in bulk material
Can calculate from DFT:
Surfaces cont.
• Knowledge of the atomic arrangement in the surface
region is a prerequisite to understanding the properties
of surfaces.
• Because atoms at surfaces have fewer neighbours than
they do in solids, unlikely they will remain at their precise
“bulk truncated” positions.
• Surface relaxations – small displacements e.g to few
layers move inwards or outwards but retain their
periodicity parallel to the surface
• Surface reconstructions – more pronounced lateral
displacements which alter the translation symmetry
parallel to the surface and/or change the surface layer
atomic density.
Surfaces cont.
Examples – surface relaxations at
metal surfaces
%
change
DFT/
Expt
Al(111)
Ti(0001)
Cu(111)
Pd(111)
Pt(111)
d12
LDA
+1.35
-6.44
-1.58
-0.22
+0.88
GGA
+1.35
-6.84
-1.19
-0.01
+1.14
LEED
+1.3
-4.9
-0.7
+1.3
+0.87
LDA
+0.54
+2.64
-0.73
-0.53
-0.22
GGA
+0.54
+2.82
-0.65
-0.41
-0.29
LEED
+0.5
+1.4
LDA
+1.04
+0.37
-0.43
-0.33
-0.17
GGA
+1.06
-0.51
-0.24
-0.22
-0.21
d23
d34
LEED
-1.1
+0.7
+0.7
For Al and Pt, excellent agreement; Cu very good. For Pd there is not good
agreement and there is still open questions (e.g. H contamination?)
Example of surface reconstruction
Au{111} 23 x 3
112
A uniaxial contraction along one of the [-110] directions in the top layer leads
to a layer with a higher density of atoms in it than the unreconstructed (111) surface
110
Au(111) Surface 6 K
Scanning
Tunnelling
Microscopy
images
Run 5_2
X = 12.5 nm
Y = 12.5 nm
Z = 46.13 pm
Atomic Resolution
Herringbones
Au(111)
Surface –
corrugation
of the surface
due to different
relative
positions
of atoms in the
top layer
3- fold symmetry
Strain in the one direction
is relaxed over whole surface
in 2 dimensions
Au{111} 23 x 3
120 degree turns give
uniform contraction!
What about the elbows?
fcc
fcc
fcc
Screw Dislocation:
STMA 1004, Vtip = 0.05 V/ 200pA
170 Å x 170 Å
The famous (7x7) reconstruction
of the Si (111) surface
Surfaces cont.
From IBM's "STM Image
Gallery":
48 iron atoms are positioned
into a circular ring on Cu(111
in order
to "corral" some surface
state electrons and force
them into "quantum"
states of the circular
structure. The ripples in the
ring of atoms are the
density distribution of a
particular set of quantum
states of the corral.
Adsorption on a surface
Surfaces: adsorption cont.
Interaction of the electronic states of a H atom with a transition metal surface
The interaction between the H 1s-level and the substrate s- and d-bands gives rise to
a broadening and the formation of an anti-bonding level (above the d-band) and a
bonding level (below the d-band).
For the H 2s-level, the bonding state is at about the lower edge of the d-band.
Surfaces: adsorption cont.
Na on Al (simple metal, no d-states)
O on Ru (transition metal)
Side view of the surface, and the adsorbate-induced change in the density
of states as a function of distance. [Energy levels for the atoms are the mean
values of the ionization energy and electron affinity (Na: 2.8 eV, O, 7.5 eV)]
Surfaces: Adsorption cont.
Surfaces: Adsorption
Difference of electron density: