Topic Name : Solid solution Sub: MSM (2131904) Prepared by – 140240102001 - AMRSHEDA SHAURABH 140240102004 - BAVADIYA AAKASH 140240102013 - GOSWAMI VRUSHBHGIRI GUIDED BY – PROF. MANISH K. PRAJAPATI 15 April 2018

2) Thermal Equilibrium Diagrams - Phase Equilibrium CONTENTS:- 1) Solid Solutions - Types of Solid - Hume-Rothery rules - Substitutional Solid Solution Rule 2) Thermal Equilibrium Diagrams - Phase Equilibrium - Gibbs Phase Rule - Cooling curve MATERIAL SCIENCE AND METALLURGY 15 April 2018

Solid Solutions Sometimes impurities are desirable, example, sterling silver, 7.5% Cu and 92.5% Ag. The copper makes silver stronger and harder. Zn is added to Cu in brass, which is stronger, harder and more ductile than copper. Both alloys are solid solutions in which the original structures of the metals are changed. Solid solutions consist of a solute and a solvent Solute = small amount, solvent = large excess MATERIAL SCIENCE AND METALLURGY 15 April 2018

Types of Solid Substitutional Interstitial solid solutions Solute atoms replace solvent atoms. It can be formed with limited solubility e.g. Bronze (Sn in Cu) or unlimited solubility e.g. Brass (Zn in Cu), in this case both atoms have nearly the same size. Interstitial solid solutions Small atoms located at the interstices between larger atoms. E.g. C in Fe Ordered solid solution The two types of atoms arranged in a specific order. Heating always destroys the ordering in the solution. MATERIAL SCIENCE AND METALLURGY 15 April 2018

Hume-Rothery rules The Hume-Rothery rules are a set of basic rules describing the conditions under which an element could dissolve in a metal, forming a solid solution. There are two sets of rules, one which refers to substitutional solid solutions, and another which refers to interstitial solid solutions. MATERIAL SCIENCE AND METALLURGY 15 April 2018

Substitutional Solid Solution Rule 1. The atomic radii of the solute and solvent atoms must differ by no more than 15%: 2. The crystal structures of solute and solvent must match. 3. Maximum solubility occurs when the solvent and solute have the same valency. Metals with lower valency will tend to dissolve metals with higher valency. 4. The solute and solvent should have similar electronegativity. If the electronegativity difference is too great, the metals will tend to form intermetallic compounds instead of solid solutions. MATERIAL SCIENCE AND METALLURGY 15 April 2018

Interstitial Solid Solution Rules Solute atoms must be smaller than the pores in the solvent lattice. 2. The solute and solvent should have similar electronegativity. In contrast to intermetallic and compounds, solid solution in general are Easier to separate, Melt over a rang in temperature, have properties that are influenced by those of solvent and solute, Usually show a wide range of composition so that they are not expressed by a chemical formula MATERIAL SCIENCE AND METALLURGY 15 April 2018

Thermal Equilibrium Diagrams Definition:- A diagram which shows variations of phases of a metal or ally with respect to changes in temperature is called as phase equilibrium diagram. A system is at equilibrium if its free energy is at a minimum, given a specified combination of temperature, pressure and composition. The (macroscopic) characteristics of the system do not change with time — the system is stable. MATERIAL SCIENCE AND METALLURGY 15 April 2018

Phase Equilibrium: Solubility Limit Solution – solid, liquid, or gas solutions, single phase Mixture – more than one phase Solubility Limit: Maximum concentration for which only a single phase solution exists. MATERIAL SCIENCE AND METALLURGY 15 April 2018

Degree of freedom The degree of freedom of a system is the number of eternal & internal variables of the system that may be changed independently without causing appearance of a phase; without altering the equilibrium. For example, at the triple point of water, all the three phases are found to be present but when any of the variables is varied at least one of them disappears depending up on the chang/s made MATERIAL SCIENCE AND METALLURGY 15 April 2018

Gibbs Phase Rule Phase diagrams and phase equilibria are subject to the laws of thermodynamics. Gibbs phase rule is a criterion that determines how many phases can coexist within a system at equilibrium. P + F = C + N P: # of phases present F: degrees of freedom (temperature, pressure, composition) C: components or compounds N: noncompositional variables For the Cu-Ag system @ 1 atm for a single phase P: N=1 (temperature), C = 2 (Cu-Ag), P= 1 (a, b, L) F = 2 + 1 – 1= 2 MATERIAL SCIENCE AND METALLURGY 15 April 2018

Cooling curve This shows how a pure metal cools from a liquid to a solid. A graph of temperature and time shows that copper is fully liquid at 1500C. As temperature falls to 1083C, copper begins to change into a solid. As this solid-liquid change happens, the temperature does not change (the latent heat of fusion is given up keeping the temperature constant) MATERIAL SCIENCE AND METALLURGY 15 April 2018

cooling curves of two metals MATERIAL SCIENCE AND METALLURGY 15 April 2018

Eutectic alloy The two metals are completely soluble in the liquid state but are completely insoluble in the solid state. The phase equilibrum diagram is compiled in the same way as the solid solution alloy but looks completely different. The eutectic point (140C) is the lowest melting point of the alloy. The alloy changes directly from a liquid to a solid without going through a pasty stage at this point. MATERIAL SCIENCE AND METALLURGY 15 April 2018

Thank You MATERIAL SCIENCE AND METALLURGY 15 April 2018