IMPERFECTION OF SOLID & ATOM MOVEMENT

You may find the discussion about this topic in:

https://docs.google.com/file/d/0B3OOiHwWphGWcHdfLVdJTVN0Z1E/edit

Below (in Figure 1)  you can watch the mechanism of vacancies formation

Figure 1. The mechanism of vacancies formation due to doping of higher oxidation state ions into the crystallite structure. It can be seen in here that an Ag+ ion must be released then produce a vacancy in order to keep the nett charge of crystal in neutral

There are 3 mechanisms of ionic migration, i.e :
1. vacancy mechanism ( mekanisme kekosongan)
2. interstitial mechanism (mekanisme selitan)
3. the combination of vacancy and interstitial mechanism (mekanisme kekosongan dan selitan)

for better understanding on that mechanisms, please watch the animations below (Figure 2, Figure 3 and Figure 4).

Figure 2. The interstitial and vacancy mechanisms

Figure 3. The vacancy mechanism

Figure 4. The interstitial mechanism

*This blog was written by Fitria Rahmawati for Kuliah Elektrokimia Fasa Padatan
Fitria Rahmawati
Research Group of Solid State & Catalysis
Chemistry Department
Sebelas Maret University
Jl. Ir. Sutami 36 A Kentingan Surakarta 57126

BORN-HABER CYCLE

The Born-Haber cycle is an approach to analyzing reaction energies. It was developed by Max Born and Fritz Haber. This cycle is used as a means of calculating lattice energies which cannot be measured directly. The Born-Haber cycle applies Hess's Law to calculate the lattice enthalpy by comparing the standart enthalpy change of formation of the ionic compound (from the elements) to the enthalpy required to make gaseous ions from the elements.
For example is Formation of Metal Chloride: 

Figure 1. Hess's Law of Metal Chloride, MCl formation

From the Hess's Law the lattice enthalpy formation of MCl, (delta)Hf , can be calculated as:

LATTICE ENERGY_2

Crystal lattice contains of cations and anions. The interactions between them are much more complex than the interaction between two ions. This interaction is described in Figure 3, which describes the interactions inside the crystal lattice.

Figure 3. The crystal lattice of NaCl (expanded)
(Effendi, 2008)

interaction between Na+ ion in the centre of cubic di Figure 3. are:

1) Its interaction with 6 Cl- ions with distance of square root of 1.

2) Its interaction with 12 Na+ ions with distance of square root of 2

3) Its interaction with Cl- ions with distance of square root of 3

4) its interaction with 6 Na+ ions with distance of square root of 4.

The total interaction between ions inside a crystal lattice is stated by MADELUNG CONSTANT , A. In NaCl crystal, the Madelung constant of the first four stribes are:

The interaction between ions inside crystal lattice is called as geometric interaction. Due to this geometric interaction, the coulomb's electrostatic energy is become,

The electrostatic energy of 1 mol crystal which contains of N cations and N anions is,

N is the Avogadro's number

The repulsive force between electron clouds of the ions could be ignored only if the distance between ions is far. However, the repulsive force will become stronger as the distance is become smaller. In this state, the repulsion force between electron clouds of ions must be considered. Born stated that the repulsion energy, Erep is described by equation:

B is a constant and n is Born exponent.

The repulsion energy of 1 mol crystal which contains of N cations and N anions is:

The total energy of 1 mol crystal which contains of N cations and N anions is:

The value of Born exponent, n, is depend on ion type. Larger size of ions will have higher electron density than smaller ions. The Born exponent value will be higher as the ionic size become larger. 

When the repulsion force is equal to the attraction force, then the lattice energy is minimum. The condition at equilibrium condition might be stated as below,

at equilibrium condition, the lattice energy is stated as Uo and the distance between anion and cation as ro. Substitution of B into U produce the equation below,

This equation is called as Born-Lande equation. This equation can be used to calculate the  lattice energy of ionic crystal if the crystal structure and the distance of anion-cation have been known already. The crystal structure is required to calculate the Madelung constant, A. This crystal structure and also the distance of anion-cation are could be founded from crystallographic data (XRD data).

Kapustinski stated that for the ionic compounds of unknown structure, the lattice energy could be estimated from the equation below,

v is the number of ions inside a molecule of ionic compound and ro is the sum of cationic and anionic radius in pm unit. The ionic radius is calculated based on the coordination number.

READ MY PUBLICATIONS ON:

http://journal.itb.ac.id/index.php?li=article_detail&id=468

http://www.chempap.org/?id=7&paper=818

http://www.tandfonline.com/doi/full/10.1080/02772248.2011.604322

LATTICE ENERGY_1

THE ENTHALPY OF FORMATION OF IONIC PAIR IN GAS PHASE

The formation of ionic compound from its atoms in gas phase occurs in three steps are:
1. the formation of cation. This is an endoterm process
2. the formation of anion. This may endoterm or exotherm process
3. the formation of ionic pair. It is an exotherm process
The energy released in the formation of ionic pair in gas phase from its ions could be estimated from Ionization Energy, IE, the electronic affinity, EA, and from its Bond Dissosiation Energy, BDE. The thermodynamic cycle can be use in the Ionic pair enthalpy calculation. Figure 1 describes the thermodynamic cycle of MgO formation.

Figure 1. The thermodynamic cycle of MgO formation
(Effendi, 2008)

The data of each process are listed below:
Mg(g) --> Mg+(g) + e                                          IE1    =  737.7 kJ/mol
Mg+(g) --> Mg2+(g) + e                                      IE2    = 1450.7 kJ/mol
O(g)  +  e --> O-(g)                                            EA1  = -140.984 kJ/mol
O-(g) + e --> O2-(g)                                            EA2  =   744  kJ/mol
Mg(g) + O(g) --> MgO(g)                                    -BDE = -377 kJ/mol

Based on Hess's Law, it can be formulated as,
-BDE = IE1 +IE2 + EA1 +EA2 +  (delta) Hip

Therefore,
(delta)Hip = -BDE - (IE1+IE2 +EA1 + EA2)
                  = -3168.4 kJ/mol


THE LATTICE ENERGY
The lattice energy of ionic solid could be defined as the enthalpy of formation of the ionic compound from gaseous ions. 
It may also defined as the energy required to completedly separate one mole of a solid ionic compound into gaseous ionis constituents. 
The Crystal of ionic compound contains of cations and anions which are regularly, alternately and repeatedly arranged.
The electrostatic force contribute dominantly in the lattice energy of ionic crystal. Other force including repulsive interaction between electrons and short-range repulsive forces which are important when atoms or ions so close and their  electron clouds begin to overlap.
The energy curve that describes the relation between ions distance with the energy is depicted in Figure 2.

Figure 2. The energy curve of ionic pair