inorganic materials chemistry and functional...

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

4

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)



MgO

Na2O

SiO2

Al2O3

Decreasing size

Na > Mg > Al > Si

Decreasing size

Na+ > Mg2+ > Al3+ > Si4+

7

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


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


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



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)


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,...


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 – 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?


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.


- 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


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


29

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

31

Chemical bonding – reactivity – example acid/basic oxides

Basic Acidic Amphoteric

32

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


H

H

H BULK on SURFACE

33


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.


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


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)

39

3+

Hydratization

Cationic acids

Chemical bonding – polarization – example acidity of cations

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http://www.google.be/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&docid=BJh3nnUO7P_r9M&tbnid=bkMRn1I_ClQmtM:&ved=0CAUQjRw&url=http://www.tntnphotos.com/2014/06/molecule/&ei=jZoMVMGxFYe6ygOX4YGYCA&bvm=bv.74649129,d.bGQ&psig=AFQjCNE7BvFPtvc4mZAlyrIhFk7kvin_3Q&ust=1410198470012525








+

[Fe(H2O)6]3+(aq) [Fe(H2O)5OH]2+(aq) + H+(aq) pKa1

and so on for more protolysis steps


41

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-


42

Cationic acids «charge density» versus pKa


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