Phase diagram and equilibrium diagram

Explation of Phase diagram and equilibrium diagram

1. Engineering notes Subject: Material Science “ Phase Diagram and Equilibrium Diagram” prepared by: Aditya Prakash (mail id: [email protected])

2. Phase Diagram And Equilibrium Diagram

3. PHASE A phase is a state of matter with the following characteristics:  It has the same structure or atomic arrangement throughout  It has roughly the same composition and properties throughout.  There exists a definite interface between it and its surroundings or adjoining phases.  A system may be made up of one, two or more phases

4. Phase Diagrams A phase diagram is a graphical representation of the phases that are present in a material at various temperatures and pressures and compositions .  It usually describes the equilibrium conditions. Hence also known as equilibrium diagrams  Sometimes non-equilibrium conditions are also shown when well known.  Ex: Melting point of tungsten is 3400o C and Aluminum 657o C hence two elements can not blend together .

5. Phase Diagram • It indicates the melting/solidification temperatures of the constituents • It indicates the compositions of alloys where solidification begins and the temperature range over which it occurs. For a pure substance, the Pressure-Temperature phase diagram simply tells which forms (solid, liquid, gas) of the material exist under different P-T conditions. Phase diagram for magnesium, showing the melting and boiling tempratures at one atmosphere pressure Phase diagram for water

6. General Types of Solid Solutions A homogeneous mixture of atoms of two or more elements in solid state is called Solid Solution There are two general types of alloys having phase diagrams. • Substitutional alloys • Interstitial alloys  Subtitutional alloys have elements, which are incorporated into regular lattice positions within the unit cell. An example is Tin and Zinc alloying additions to Copper to form bronze and brass , respectively  Interstitial alloys have elements, which are incorporated into the interstitial sites of the unit cell. An example is carbon in iron to form steel.

7. W. Hume – Rothery’s rules  Hume- Rothery has given criteria in regard to Substitutional solid solution these are known as W. Hume – Rothery rules  Similar Crystal Structure: 2 or more metals should have same crystal stucture such as FCC & FCC or BCC & BCC  Relative Atomic Size: The atoms of two metals should have their size with in 15% of each other, if solid size difference is more than 15% then only limited solubility is otained  Valency Criteria : The valency of base metal and alloying metal should be same  Electronegativity: The solid solubility is limited if two metal possess greater electronegativity .

8. Gibb’s Phase Rule Gibb’s phase rule describes the thermodynamic state of a material. This famous rule is used to determine the number of phases that can coexist in equilibrium in a given system. It has the general form: D = C – P + λ  C is the number of components , usually elements or compounds, in the system.  D is the number of degrees of freedom , or number of variables, such as temperature, pressure, or composition that are allowed to change independently without changing the number of phases in equilibrium.  P is the number of phases present  The constant λ is system variable here the variable is taken as “2”implies that both temperature and pressure are allowed to change.

9. Gibb’s Phase Rule Gibb’s phase rule describes the thermodynamic state of a material. This famous rule is used to determine the number of phases that can coexist in equilibrium in a given system. It has the general form: D = C – P + λ C is the number of components , usually elements or compounds, in the system. F is the number of degrees of freedom , or number of variables, such as temperature, pressure, or composition that are allowed to change independently without changing the number of phases in equilibrium. P is the number of phases present The constant “2” in the equation implies that both temperature and pressure are allowed to change.

10. Gibb’s Phase Rule For the triple point of water: • One component, i.e., water. • 3 phases present, i.e. vapor, liquid, and solid. • F = 1 – 3 + 2 = 0, so this is an invariant point on the diagram

11. Classification of Phase Diagram Plot showing relation between temperature Vs Composition in a phase diagram can be classified as below: • Unary Phase Diagram • Binary Phase Diagram • Ternary Phase Diagram • Quaternary Phase Diagram

12. Unary Phase Diagram  Diagram for single Component (Water)

13. Binary Phase Diagram When only two elements or two compounds are present in a material, a binary phase diagram can be constructed. They are found in number of Metallic & Ceramic structures like Cu-Ni alloy etc.

14. Liquidus/Solidus Temperatures  The liquidus temperature is the temperature above which a material is completely liquid.  The solidus temperature is the temperature which the alloy is 100% solid.  The freezing range of the alloy is the temperature difference between the liquidus and solidus where the two phases exists, ie ., the liquid and solid. The changes in slope of the cooling curve indicate the liquidus ab= nd solidus tempratures .

15. Tie Line Tie Line: is the line joining solidus & liquidus curves. A binary phase diagram between two elements A and B. When an alloy is present in a two phase region, a tie line at the temperature of interest fixes the composition of the two phases.

16. Lever Rule The Lever Rule is used to calculate the weight % of the phase in any two- phaseregion of the Phase diagram (and only the two phase region !) In general: • Phase percent = opposite arm of lever x 100 total length of the tie line

17. • If we know T and C0, then we can determine: -- the composition of each phase.

18. Phase Diagrams: Determination of phase weight fractions

19. Lever Rule Calculate the amount of a phase and L phase present in a Cu 40% Ni alloy at 1250 C In general: • Percent a phase = ( % Ni in alloy) – (% Ni in L ) x 100 % Ni in L - % Ni in a

20. Solidification of a Solid-Solution Alloy The change in structure and composition of a Cu- 40% Ni alloy during equilibrium solidification showing that the liquid contains 40% Ni and the first solid contains Cu52%Ni. At 1250 C, solidification has advanced and the phase diagram tells us that the liquid contains 32% Ni and the solid contains 45% Ni, which continues until just below the solidus, all of the solidcontains 40% Ni, which is achieved through diffusion .

21. Phase Diagrams with Intermediate Phases and Compounds Many combinations of two elements produce more complicated phase diagrams than the isomorphous systems and the simple eutectic systems. • Many equilibrium diagrams often show intermediate phases and compounds when either incomplete solubility or compound formation occurs. • These new phases are distinguished by the labels “ terminal phases ” and “ intermediate phases ”. • Their phase diagrams look complex.

22. Phase Diagrams with Intermediate Phases and Compounds • The terminal solid-solution phases occur at the ends of the phase diagrams , bordering on the pure components, e.g., the alpha phase and the beta phase in the Pb-Sn phase diagram. • Intermediate phases commonly have new compounds and are called intermediate compounds or intermetallic compounds. – An intermediate compound is made up of two or more elements that produce a new phase with its own composition , crystal structure, and properties . – Intermediate compounds are almost always very hard and brittle . – An example is Fe3C in steels .

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