Slide 1

Thermodynamics and Phase diagram

capo regime

GHSDominate G at low temperaturesDominate G at High temperaturesRelative stability of a system is determined by Gibbs free energy (G)

EnthalpyAbsolute temperatureEntropyEntropy is a measure of randomness of the system (or degree of irreversibility of the process)Enthalpy is a measure of the heat content of the systemGibbs free energy (G)

Internal EnergyPressureVolume(K.E. + P.E. of the system)Atomic vibrations (Liq and Solid), orTranslational and rotational energiesof atoms or molecules within a liq. and gasInteraction/bonds between atomsEnthalpy

Enthalpy and Entropy as a function of temperature

Ho Enthalpy of the system at absolute zeroH = 0 for pure element in its most stable state at 25oC

Quantity of heat required to raise the temp. of the substance by 1 K A system is said to be in equilibrium when it is in the most stable state i.e. shows no desire to change ad infinitumAt constant temperature and pressure a closed system (fixed mass and composition) will be in stable equilibrium if

Gibbs free energy GdG = 0Equilibrium

Necessary criterion for phase transformation (G G2Equilibrium cont..Single component systems (pure element or molecule)

Time TMLiquidSolidPhase transformation at constant temperatureTemperatureTime-Temperature curve

Variation of G with temperature of a single componentLatent heatEnthalpy of liquid is more than solid at all temperatures

Entropy of liquid is more than that of solid

@ constant pressure

System of fixed mass and compositionVarying pressure and temperatureBinary solutions Ideal solutions Regular solutions Real solutionsGibbs free energy of binary solutions

Depends on Pressure Temperature CompositionUsually treated constant (1 atm.) in solid state transformationsTwo variables

Enthalpy of mixing, due to broken A-A and B-B bonds and formation of new A-B bonds Entropy of mixingThermal entropyConfigurational entropy

Free energy of mixing for an ideal solution1. Ideal solution

AssumptionsPure A and pure B are having same crystal structure and solution of A and B also has same crystal structure

Enthalpy of mixing is zero no preference for any type of bond formation or destructionany atom can sit next to any other atom or random arrangement of atoms

Entropy of mixing Thermal entropy will be zero (since enthalpy is zero)Configurational entropy randomness in the solution due to number of distinguishable ways in which A and B atoms can be arranged

Molar free energy for an ideal solution+GAGBMore curvature

Chemical Potential (or Partial molar free energy)

Equilibrium in two or more than two component systems (at constant T and P) will be reached by the transfer of atoms between the phases.

How the free energy of a given phase will change when atoms are added or removed??

Partial molar free energy is the increase/decrease in the property of a large system when the amount of one component is increased by one mole while keeping the pressure, temperature and number of moles of other components is fixed

Graphical representation of Chemical PotentialChemical potential of any component in a given phase can be obtained by drawing a tangent to the free energy at particular composition and extrapolating it such that it intersect with XA = 1 (XB = 0) - Chemical potential of A in the given phaseor XA = 0 (XB = 1) Chemical potential of B in the given phase

2. Regular solutions

Usually mixing is either endothermic or exothermic but randomQuasichemical approachHmix is due to the bond energies between adjacent atoms onlyVols. of pure A and B are equal and do not change during mixing

Assumption Entropy of mixing is equal to that obtaianed for ideal solution

Variation of Hmix with composition for a regular solution

Types of interatomic bondsA-A bonds with an energy AAB-B bonds with an energy BBA-B bonds with an energy AB

Change in Internal energy on mixingFor random mixing of A and B atomsIf 0, system will prefer to be surrounded by like atoms PAB less than random

Hmix per mol

For the assumption that PAB is given by random arrangmentFree energy of mixing for an ideal solutionFree energy of mixing for a regular solution

Free energy change with composition in a regular solution

Assumption of random arrangement of atoms is not possibleCompromise between lowest internal energy and entropy (randomness) < 0, A-B bonds (increase, reduce internal energy) > 0, Increase no. of A-A and B-B bonds (reduce internal energyfor large size difference, interstitial3. Real solutionsEquilibrium in heterogeneous systemIf A & B do not have same crystal structures (assumption in the ideal model)

GA (Afcc)GB (Bbcc)GB (Bfcc)Let, stable form of A is fccand that of B is bccThis result in two free energy curves

GA (Afcc)GA (Abcc)A rich G < G ( stable phase)B rich G > G ( stable phase) phase solid sol. of Afcc and Bfcc phase is solid sol. of Abcc and Bbcc

Composition between crossover??but

Instead of single phase ,Mixture of two phase and TillComposition of two phases reach e and eAnd, free energy of the system reach min. GeEquilibrium between two phase requires that the tangents to each G curve lie on a common lineOrEach component in the different phases must have same chemical potential

Binary phase diagrams Simple phase diagram Systems with miscibility gap Ordered alloys Simple eutectic system Phase diagram containing intermediate phases

A&B are completely miscible in both the solid and liquid states (both are ideal solutions)Example: Cu-Ni system

Liquid phase is approx. ideal, solid phase Hmix > 0Miscibility gapSystems with Miscibility gapExample: Cu-Fe alloy

T1T2T3Hmix >> 0Miscibility gap can extend in to the liquid phaseEutectic phase diagramExample: lead-antimony, silver-copper

Phase diagram A & B have different crystal structureEutectic phase diagramExample: chromium-nickel, lead-tin

Ordered alloysHmix