Inorganic materials chemistry and functional materials Helmer Fjellvåg and Anja Olafsen Sjåstad Lectures at CUTN spring 2016 Chemical bonding
Inorganic materials chemistry
and functional materials
Helmer Fjellvåg and Anja Olafsen Sjåstad
Lectures at CUTN spring 2016
Chemical bonding
Chemical bonding
Chemical bonding – part I - Electronegativity
- Effective nuclear charge, shielding, ionization, electron affinity
- Examples of bonding; ionic, covalent, polar covalent, metallic
- Electronegativity scales
- Pauling, Mulliken, Van Vechten, Sanderson; Examples
- Fajans rules
- Examples
- Crystal structures versus type of bonding
- Examples
- Ionic bonding
- Examples
- Dispersion forces
- Examples
- Chemical aspects related to electronegativity, bonding, structure
Ionic bonding
Van der Waals bonding
H-bonding
(between molecules/sheets…)
Metallic bonding
Covalent bonding
Crystalline materials show a range of different bond types
Chemical bonding
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Chemical bonding - electronegativity
Size of atoms
Nuclear charge (protons) Z
No. of electrons Z
Shielding
Attractive forces
nucleus – electrons
Repulsive forces
electron – electron
Effective nuclear charge ....
”how strongly does the nucleus attract electrons”
Depends on how well do inner electrons shield outer electrons
Na Mg ----- Si -----Cl: increasing effective nuclear charge
consequence: reduction in atomic size (atomic radius)
Chemical bonding - electronegativity
Chemical bonding - electronegativity
MgO
Na2O
SiO2
Al2O3
Decreasing size
Na > Mg > Al > Si
Decreasing size
Na+ > Mg2+ > Al3+ > Si4+
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Atomic radius
lantanoids
- Large atoms <=> one electron outside full noble gas shell
- Decreasing size => increased nuclear charge
- Increasing size vertically in a given group (gr.1, gr2, gr13,….)
- Transition metal roughly of similar size (5d 4d > 3d)
- Largest atoms for the first groups of d-elements
Transition metals
Chemical bonding – electronegativity – atomic radius
Perovskite type structure ABO3 (CaTiO3)
Ideal perovskite structure is cubic (mineral CaTiO3 is orthorhombic)
Perovskites – the most widely studied class of oxides
Wide range of chemistries possible (AIBVO3; AIIBIVO3; A
IIIBIIIO3)
. ccp of A and O (“AO3”)
B filling ¼ of octahedral holes/voids
CN(A) = 12; CN(B) = 6
Space group: Pm-3m
Lattice: Primitive cubic
Basis:
A: (1/2,1/2,1/2)
B: (0,0,0)
O: (1/2,0,0); (0,1/2,0); (0,0,1/2)
A B
Chemical bonding – electronegativity – example atomic size & structure
Cubic, tetragonal and orthorhombic symmetries are common; + rhombohedral
Reduction in symmetry due to distortion of the octahedrons
Reduction in symmetry due to displacement of B-cation
Rich physics
Consider REBO3 perovskite type oxides; series with B = Mn, Fe, Co or Ni
Within a given series, e.g. REFeO3, the t-factor will decrease when turning
from RE = La to heavier rare earths (contraction of atomic size). In other words,
this implies that the FeO6-octahedra have to tilt more strongly in order to fit the
bonding requirements of the smaller RE. The structure becomes more distorted.
The orthorhombic distortion away from cubic symmetry increases. This effects
electronic properties: the overlap between eg(Fe) and 2p(O) is reduced.
Goldschmidt
tolerance factor (t)
Chemical bonding – electronegativity – example atomic size & structure
cubic orthorhombic
Chemical bonding - electronegativity
Concept of effective nuclear charge:
Slater's rules (1930). In a atom with many-electrons (Z), each electron
experience a charge less than the nuclear charge (Z) owing to shielding
by inner/other electrons.
For all electrons a so-called screening constant can be defined,
denoted σ (or s, S) which implies a reduction in the nuclear charge
experiences by a given electron. This effective nuclear charge is defined
as
Zeff = Z - s
Chemical bonding - electronegativity
Slater rules:
Groups of electrons with different impacts...
s and p electrons are always in the same group
Groups of electrons are then: [1s] [2s,2p] [3s,3p] [3d] [4s,4p] [4d] [4f] [5s, 5p] [5d]....
Each group is given a different shielding constant
The shielding constant for each group is the sum of more contributions:
An amount of 0.35 from every other electron in the same group (excepion; for [1s]
other electron count only 0.30)
For [s p] groups, 0.85 is adopted for each electron with principal quantum
number n-1 than for the group (n), while 1.00 is adopted for each electron n ≤ n-2.
For [d] or [f], type groups, 1.00 is adopted for each electron positioned "closer" to
the atom than the group electrons; i.e. i) electrons with a smaller principal
quantum number n and ii) electrons with an equal principal quantum number and
a lower l quantum number
EXAMPLE: an Fe atom with Z = 26; configuration 1s22s22p63s23p63d64s2
:
Zeff = Z – s s = Slater shielding constant
Net attraction experienced – values of effective nuclear charge
Chemical bonding - electronegativity
Chemical bonding - electronegativity
Effective nuclear charge increases within a given period
The size of atoms hence decreases
An electron positioned at the «outer» part of the atom will experience
a stronger attraction from the core
for elements in the right hand part of the periodic table
These elements attract correspondingly easily electrons
and may do so until they obtain noble gas electron configuration
e.g. Ar, Cl, S2 , P3 .....
Energies associated with loss of electrons or acceptance of addional electrons:
- Ionization enthalpies
- Electron affinity
• H 1s1
• He 1s2
• Li 1s2 2s1
• Be 1s2 2s2
• B 1s2 2s2 2p1
• C 1s2 2s2 2p2
• N 1s2 2s2 2p3
• O 1s2 2s2 2p4
Trends – ionization enthalpies Endothermic: DHionization > 0
Atoms
1s2 2s2 1s2 2s2 2p3 for ion Increases horizonta|lly (in a period)
Decreases vertically (in a group)
Chemical bonding - electronegativity
A(g) = A+(g) + e
1 eV = 96 kJ/mol
A+(g) = A2+(g) + e-
A(g) = A+(g) + e-
A2+(g) = A3+(g) + e-
Cations are formed
In compounds; more oxidation states may be feasible
Huge increase when
noble gas electron
configuration is broken
Cf. change in effective
nuclear charge
Rule of thumb:
noble gas configuration
is never broken:
HENCE: Alkali(I)
Alkaline earths (II) etc.
Trends – ionization enthalpies; 1st, 2nd, 3rd,...
Chemical bonding - electronegativity
Increasing DHionization
A(g) + e- = A-(g) Electronaffinity: Eea
Eea is defined as the negative enthalpy change for this reaction
EXAMPLE: F(g) + e- = F- (g) DH = -328 kJ/mol Eea = +328 kJ/mol
A positive electron affinity implies an exothermic reaction
DH values:
Why O lower value than S, Cl ? e – e repulsions...
Chemical bonding - electronegativity
Chemical bonding – oxidation numbers
Simple rules, extremely useful in chemistry
The most electronegative elements; oxygen (-II), fluorine (-I)
exceptions compounds between oxygen and fluorine; like OF2....
Never break a closed noble gas electron shell;
hence alkali(+I), alkaline earth(+II),..
Group 13, 14, 15 possibility of [ns2] lone pair for the heavier group elements
Tl(III) [s0] and Tl(I) [s2];
Pb(IV) [s0] and Pb(II) [s2]; these lone pairs may have be stereoactive
Bi(V) [s0] and Bi(III) [s2]:
d-elements; many oxidation states; jumps of 1 in ox.state possible
QUESTIONS
What is the oxidation state for the cations in:
BaO2
CsO2
Mn3O4
Pb3O4
TiS2
FeS2
Several functional oxides
show mixed valence state
=> not integer ox.state numbers
Can be tuned by substitution/doping
YBa2Cu3O7
LaMnO3.15
(La,Sr)FeO3
Chemical bonding Chemical bonding is in reality a mixture of two or three of the (extreme)
components ionic, covalent and metallic
Chemical bonding
Chemical bonding – electronegativity - properties
How can we better understand this variation?
+ make good predictions based on chemical knowledge/intuition?
Chemical bonding - electronegativity
Pauling electronegativity Pauling scale (revised data 1961):
- Most commonly used method.
- It is dimensionless - a relative scale from approx. 0.7 to 4.
- Hydrogen is fixing the scale by its reference value of 2.20.
Chemical bonding - electronegativity
- The difference in Pauling electronegativity between atoms A and B is defined
by:
where Ed is the dissociation energies of A–B, A–A and B–B bonds in eV.
Example:
Difference in Pauling
electronegativity between
H and Br is 0.76
Dissociation energies:
H–Br = 3.79 eV
H–H = 4.52 eV
Br–Br = 2.00 eV
Chemical bonding – electronegativity – variations in chemistry
Effect of electronegativity of an element relative to
another element?
IF we ask this question for a very electropositive element, the element (ion)
will have related chemical properties in most compounds (EXAMPLE Na/Na+)
AND
IF we ask this question for a very electronegative element, the element (ion)
will have related chemical properties in most compounds (EXAMPLE F/F)
BUT what if we consider an element with ‘average’ electronegativity:
Hydrogen (2.2), boron (2.05), carbon (2.55), ...
We observe HUGE variations
EXAMPLE: Hydrogen (cf use of hydrogen for energy storage......)
Hydrogen; Oxidation State
Oxidation number +I, ‘H+’
Proton is extremely small, polarises neighbour atoms; H3O+
Polar covalent bonds; (binary acids; oxoacids,....)
Oxidation number 0, H
Hydrogen gas
Metallic hydrides, often interstitial, non-stoichiometric
Oxidation number I, H– He-config.1s2
Salt-like hydrides, ionic (H– >>> H+ )
0.35 Å
1.4 Å
‘small’
H2
Proton
Chemical bonding – electronegativity – hydrogen as example
Strong REDUCING AGENTS
• 2H H2(g) + 2e
Reduces for instances H+:
H– + H+ H2(g) + heat
Reduces SO42 to S2
Reduces NO3 to NH3
Reducing agent in organic chemistry; LiAlH4,….
First we consider: Ionic hydrides; with H
Hydrides give BASIC reaction with water + hydrogen
2H– + 2 H2O 2H2(g) + 2 OH–
Reacts as a Lewis base (e-pair donor) H–
Chemical bonding – electronegativity – hydrogen as example
LET us highlight how properties vary for different H-based compounds
Binary Hydrogen Compounds; H – X
Molecular
Low Tm / Tb
Gases,
Liquids,...
Solids
Ionic Metalic
Chemical bonding – electronegativity – example hydrogen compounds
Binary Hydrogen Compounds; H – X
Chemical bonding – electronegativity – example hydrogen compounds
LiH
NaH
KH
RbH
CsH
HF
HCl
HBr
HI
Tm low
Tm 500 – 700 oC
Still: observe a large variation in stability and reactivity; reasons?
NOTE: Hydrocarbons are little reactive (methane CH4; CnH2n+2 etc)
Silane – SiH4 (and even more for Ge, Sn, Pb) are unstabile, reactive
Main reasons:
- steric hinderence (C is small, and well protected)
- electronic aspects (C can maximum have 8 valence electrons)
C 6
Pb82
Sn50
Ge32
Si 14
Covalent, electronprecise hydrides (MH4; group 14)
For these compounds, the
cation gains a complete octet of
8 electrons. They are
not Lewis acids, not Lewis bases.
Chemical bonding – reactivity – example hydrogen compounds
CH4
SiH4
GeH4
B 5
Tl81
In49
Ga31
Al13
Covalent hydrides with electron shortage
Lewis theory (2e bonds) can not explain these compounds.
We need molecular orbital theory to describe the distribution of 12
electrons on 8 bonds 2-electron 3-centre bonds
Number of valence electrons H B sum
B2H6 6 6 12 8 (2e) = 16 e
B4H10 10 12 22 15 (2e) = 30 e
diborane
Chemical bonding – electronegativity – example hydrogen compounds
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Binary acids: HnX
Increacing
acid
strength
weak acid(aq)
STRONG acids
In water(aq):
Completely
protolysed
Chemical bonding – reactivity – example hydrogen compounds
Acid strength controlled by:
- Electronegativity
- Size X
SUMMARY Hydrogen as case study
note the HUGE variation in the state of hydrogen as ion (-I and + I) and in the
properties when H is combining with e.g. Na or with F
A similar variation we will find for other elements;
- Borides
- Carbides
- Silicides
- ....
Important for knowing whether the atom will be cationic or anionic in nature
If anionic in nature, it will normally react vigourously with e.g. water or oxygen
It will reduce water to hydrogen gas (or some other H-containing gas dependent
on the type of the other element)
It will be oxidized by oxygen because oxides of these elements are VERY stable,
and reactions will be very exothermic
Chemical bonding – summary - hydrogen as case study
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Chemical bonding – reactivity – example acid/basic oxides
Basic Acidic Amphoteric
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Very electronegative cation
Electropositive cation
M H2O O :
+d e e
Mn+ + OH-
H3O+ + MOn
x-
Acidic oxide
Basic oxide
Rule of thumb: DC (el.neg) > 1.4 between M and O basic
Acidic versus basic (hydr)oxides
Chemical bonding – reactivity – example acid/basic oxides
H
H
H BULK on SURFACE
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Chemical bonding – reactivity – example acid/basic oxides
Basic Acidic Amphoteric
Chemical bonding – summary acid/base properties
Oxides where cations are strongly electronegative will be acidic
Oxides where cations are mainly electropositive will be basic
Oxides with intermediate electronegativity may show amphotheric behaviour
Why is this important for functional oxides?
Materials will always be exposed to some chemical environment, during synthesis,
handling, storage or use. If e.g. water/humidity is in the environment of the material,
then it is critical that the oxide is stable in exactly that environment.
E.g.: ZnO will not be stable in acids or bases; it will dissolve
There are exceptions since kinetics is one additional parameter. For some oxides,
the crystalline surface layers are so perfect that reactions are becoming very
slow. Then the material (oxide) becomes protected from dissolving. A similar type of
protection can be found on metal surfaces for e.g. Al, Ti and Sn that frequently is used
in devices/items of household/daily life. They should thermodynamically react and form
hydrogen gas. But they do not react because of a protective oxide coating.
Polarization
+1
+2
+3
+4
+5
charge
Charge density = charge / volume
Charge densities: Na+ 24 C/mm3 whereas Al3+ 364 C/mm3
Al3+ is polarising the anions (ligands) much stronger
Chemical bonding - polarization
What determines how strongly a cation polarizes the electron cloud
of a neighbouring anion? Size and charge are the simplest answers....
Small
Large
Low
Oxidation
State
High
A strongly polarizing cation attracts electrons from the anion.
In an ionic picture, this implies that electron sharing will
occur, hence covalency will become present
The Fajan rules: 1. A cation is more strongly polarizing the smaller it is and the higher is the
charge (oxidation state)
2. An anion is more polarizable the larger it is and the higher is the amount
of negative charge
3. The polarizing power of a cation is more pronounced if it does not have
closed noble gas electron configuration.
Chemical bonding - polarization
Fajan rules - examples
1. rule: Effect of charge density
MnO ionic Tm = 1785oC charge density = 84 C/mm3
Mn2O7 (polar)covalent Tm = 6oC charge density = 1238 C/mm3
The magnitude of the electrical charge of one mole of elementary charge
(6.022×1023, Avogadro number) is one faraday of unit charge
One faraday = 96485.3399 coulombs.
One coulomb = 1,036 × NA ×10−5 elementary charges.
One Ah = 3600 C
The elementary charge is 1.602176487×10−19 C
2. rule: Effect of size and charge of anion
AlF3 small anion less polarizable quite ionc Tm = 1290oC
AlI3 large anion much polarizable quite covalent Tm = 190oC
3. rule: effect of noble gas electron configuration
KCl [Ar] 1.52 Å 11 C/mm3 Tm = 770oC ioinc
AgCl [Kr]d10 1.29 Å 15 C/mm3 Tm = 455oC polar covalent
Chemical bonding - polarization
AlBr3 and AlI3
AlF3
AlCl3
Chemical bonding – examples compounds; cation constant
AlF3 is most ionic of
these three examples;
3D strutcure; corner
shared octahedra
AlCl3 is more covalent-
CN(Al) still 6. Now a 2D
structure. Lower Tm than
for the fluoride.
Are molecular; consists of
dimers; Al2Br6 and Al2I6
with edge shared tetrahedra.
CN=4 (cf. radius ratio rule)
Low melting point.
GENERALLY: Relative size (cat/anion) + bonding (ionic/covalent) influences the
coordination number and the structure connectivity (molecular; 1/2/3D structure)
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3+
Hydratization
Cationic acids
Chemical bonding – polarization – example acidity of cations
+
[Fe(H2O)6]3+(aq) [Fe(H2O)5OH]2+(aq) + H+(aq) pKa1
and so on for more protolysis steps
Chemical bonding – polarization – example acidity of cations
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B3+(aq) ???
Does NOT exist as such
But as B(OH)3
Al3+(aq) ?
[Al(H2O)6]3+
Cationic acid
Protolysis:
[Al(H2O)6]3+
[Al(H2O)5(OH)]2+ + H+
Z2/r Forms at pH7 Example
0-0.04 hydrated
cation NaI (H2O)6
+
0.04-0.22
hydroxide,
oxide,
or oxide-
hydroxide
AlIII
(H2O)3(OH)3
0.22-0.8
oxide-
hydroxide or
hydroxo anion
SeVI O3(OH)-
> 0.8 oxoanion BrVII O4-
Chemical bonding – polarization – example acidity of cations
42
Cationic acids «charge density» versus pKa
Chemical bonding – polarization – example acidity of cations