**SUMMER-2005 MATERIALS SCIENCE ENGINEERING (AN 202JAD 302)**

(Answer FIVE questions, taking AA'Y TWO from Group A ANY TWO from Group B and Al,I_ from. Group C Irigures in the bracket indicate full marks)

**Group A**

**Q 2. (a)**State Fick's laws of Diffusion. How can it help you in the prohlems of Case Carbu rising ?

Given an activation energy, Q of 142 kJ/mol, for the diffusion of carbon in FCC iron and an initial temperature of 1000 K. find the tem- perature that will increase the diffusion coefficient by a factor 10. {R =8.314 J/(mol. K)}.

Will you use a very high temperature ? (2+ 2+(3+1)

(b) What is a Phase ? What is the difference between Alpha-Iron and ferrite ? Define an invariant reaction with an example.

(c) Differentiate between

i) Phase Rule and Phase Diagram, (ii) Solvus Line and Solidus Line.

**Ans**. (a) Fick's First law of Diffusion : The rate at which particles diffuse in steady state conditions i. e., when there are no changes in the system with time, the rate of diffusion is proportional to the concentration gradient =dC/dx

this is known as Fick's firs' law. See Fig. 4

Fig. 4

Concentration gradient causes diffusion from left to right.

Rate of diffusion= -D (dC/dx)

where. D is difusion coefficient.

The (-) ve sign shows that a positive flow of particle goes in the direction of falling concentration i.e. a negative value of dC/dx.

The rate of diffusion is in atoms moved per square metre per second a kilogram's per square metre per second the concentration in atoms per cubic metre, x in metres and hence D in Sqm/s.

where. D is difusion coefficient.

The (-) ve sign shows that a positive flow of particle goes in the direction of falling concentration i.e. a negative value of dC/dx.

The rate of diffusion is in atoms moved per square metre per second a kilogram's per square metre per second the concentration in atoms per cubic metre, x in metres and hence D in Sqm/s.

Fick's Second Law of Diffusion : Fick's second law is concerned with diffusion under unsteady condition; i.e. the flux is a function of both space and time. The flux J varies from section to secticn and varies with time at a given section. In this case the concentration profile will be a function of time. This kind of situation normally exists in practical systems and so Fick's second law is applicable to real systems.

Case Carbunising : Diffusion of carbon into the surface of iron to harden its surface, the concentration of carbon atoms in the surface will change with time as more and more carbon moves into the surface. If the rate of diffusion into a small region is J1 and the rate, out of the region is beyond J2 then in the time dt number of particles in the region will increase by (J2 - J1) A delta t.

Thus, the change in concentration delta C is given by the formula

Delta C .A.delta x = ( J2 - J1) A. Delta.t

Thus, the change in concentration delta C is given by the formula

Delta C .A.delta x = ( J2 - J1) A. Delta.t

Hence dC/dt= (J2 - J1)/ delta x = -(Delta J/delta x)

where, - Delta J is the reduction in ratio of diffusion.

Thus it can be concluded that diffusion helps in case carbonization.

where, - Delta J is the reduction in ratio of diffusion.

Thus it can be concluded that diffusion helps in case carbonization.

(b) Phase : A phase is any physically distinct, chemically homogeneous mechanically separable portion of a substance.

In cornrnon terms. a phase has a well defined structure. uniform composition and distinct boundaries or interfaces.

Alpha Iron : An allotropic modification of Iron vvhich crystallises in the b_c_c. system and is stable below 912℃.

Ferrite is the term applied to substantially pure Alpha -Iron occuring in iron-carbon alloys. It is precipitated durng the cooling of steels containing less than 0'85C, arid is so called to distinguish it from the iron of the eutectoid.

Irivariant Reaction:

Cooling---->

Lymda <----->A+B

<------Heating

The eutectic characteristics of the Pb-Sn system.

We have.

eutectic temperature = Te 180oC Composition of liquid=Ce 62 Sn (38% Pb) Composition of or, Ca.e =1 8 Sn (82% Pb) Composition of p, Cpe = 97 Sn (3% Pb)

Cooling---->

Lymda <----->A+B

<------Heating

The eutectic characteristics of the Pb-Sn system.

We have.

eutectic temperature = Te 180oC Composition of liquid=Ce 62 Sn (38% Pb) Composition of or, Ca.e =1 8 Sn (82% Pb) Composition of p, Cpe = 97 Sn (3% Pb)

The phase rule is readily applied in the single-phase and the two-phase regions of the phase diagram.

At the eutectic temperature Te. three phases are in equilibrium. The eutectic temperature Te and the compositions of the three phases, Ce, Cae Cbe are all fixed and none of them can be varied arbitrarily. On slightly increasing the temperature above T., either one or both of or. and 3 phases vvould disappear. On slight decrease of temperature below T:., the liquid phase vvould transform as per Eq. (i) above to a mixture of o- and L3- To denote the zero degree of freedom, the eutectic reaction is called an invarient reaction_ The eutectic temperature is known as aninvariun Temperature.

At the eutectic temperature Te. three phases are in equilibrium. The eutectic temperature Te and the compositions of the three phases, Ce, Cae Cbe are all fixed and none of them can be varied arbitrarily. On slightly increasing the temperature above T., either one or both of or. and 3 phases vvould disappear. On slight decrease of temperature below T:., the liquid phase vvould transform as per Eq. (i) above to a mixture of o- and L3- To denote the zero degree of freedom, the eutectic reaction is called an invarient reaction_ The eutectic temperature is known as aninvariun Temperature.

(c) (i) Phase Rule (Gibbs rule)

The number of phases present in any alloy depends upon the numher of elements of which the alloy is composed. From thermodynamics considerations of equilibrium. Gibbs derived the following phase rule.

F = C-P+2

where, F= Degrees of freedom of system (temperature, pressure, concentration, composition of phases).

C= Number of components forming the system (i.e., elements or compounds)

P = Number of phases in the alloys (in equilibrium sysrem)

2 = Number of external factors

Generaliy temperature and pressure are considered as external factors which determine the state of alloy. Metals are mostly used at atmospheric pressure. Thus, the pressure has not any appreciable effect on equilibrium of alloys in solid and liquid states.

The number of phases present in any alloy depends upon the numher of elements of which the alloy is composed. From thermodynamics considerations of equilibrium. Gibbs derived the following phase rule.

F = C-P+2

where, F= Degrees of freedom of system (temperature, pressure, concentration, composition of phases).

C= Number of components forming the system (i.e., elements or compounds)

P = Number of phases in the alloys (in equilibrium sysrem)

2 = Number of external factors

Generaliy temperature and pressure are considered as external factors which determine the state of alloy. Metals are mostly used at atmospheric pressure. Thus, the pressure has not any appreciable effect on equilibrium of alloys in solid and liquid states.

Phase Diagram or Equilibrirun Diagram or Constitution Diagram

In chemistry and material science. a phase diagram is a type of graph used to show the equilibrium conditions between the thermodynarnically distinct phases.

In chemistry and material science. a phase diagram is a type of graph used to show the equilibrium conditions between the thermodynarnically distinct phases.

Phase diagrams show in graphical form, the constitution of alloys as a function of temperature under equilibrium conditions. By equilibrium conditions we mean extremely slow heating or 'ooling conditions i.e., if any change js to occur, sufficient time must be allowed for it to take place. Phase change tends to occur at slightly higher or lower temperature. Rapid variation in temperature, prevents the phase change that occur under equilibrium conditions, will distort these diagrams.

b METAL Fig. 5. Phase Diragram or Equilibrium diagram.

For pure metals. the diagram will be a verticaI Straight line. The melting temperature, the boiling temperarure and allotropic transformation are shown as points on this line. Fig. 5 shows that the metal melts at temperature 'a', and boils at temperature 'b'. Any allotropic change will take place at temperature in between 'a' and 'b'.

Generally phase diagrams are used for alloys. Phase diagrams are called binary diagrams, temary diagrams or multi-phase diagrams when there are rwo. three or many ciemenrs present in the alloy.

(ii) Solvus line is a line on an equilibrium diagram defining the limit of solid solubiliry.

On the other hand the solidus line is a line on an equilibrium diagram indicating the temperature at which a metal or alloy becomes completely solid on cooling, or at which melting begins on heating under equilibrium conditions. This line indicates the compositions of the solid that can co-exist in equilibrium,

When only solid solution of components can precipitate and no pure component can precipitate solid solution of B in A is a and A in B is b.

When only solid solution of components can precipitate and no pure component can precipitate solid solution of B in A is a and A in B is b.

See Fig No.6. Equilibrium diagram for partial solid solubility.

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