A copper-silver alloy is heated to 900^∘ C and is found to consist of αand liquid phases. If the

A copper-silver alloy is heated to 900^∘ C and is found to...

Key Concepts

Binary Phase Diagrams

A binary phase diagram graphically represents the equilibrium between two components as a function of temperature and composition. It delineates regions where a single phase exists from those where two phases coexist. Key features such as liquidus and solidus lines mark the boundaries for phase transformations, while tie-lines (or isotherms) indicate the compositions of coexisting phases at equilibrium. This concept is central in understanding how alloys behave when subjected to thermal processes.

Lever Rule

The lever rule is a quantitative method used within two-phase regions of a phase diagram to determine the relative amounts of each phase present in a material at equilibrium. By considering the overall composition and the compositions of each coexisting phase along a tie-line, the lever rule uses a ratio of distances to calculate the mass fraction (or mole fraction) of the phases. This tool is essential for predicting the microstructure and properties of alloys during thermal treatments.

Weight Percent versus Atom Percent

Weight percent and atom percent are two different ways to express the composition of an alloy. Weight percent is calculated based on the mass of the constituent elements relative to the total mass of the alloy, while atom percent is determined by the number of atoms of each element relative to the total number of atoms. Converting between these two representations requires knowledge of the atomic (molar) masses, and each form of representation provides unique insights into the material's properties and behavior.

Phase Equilibrium

Phase equilibrium refers to the stable coexistence of different phases within a material at specific conditions of temperature, pressure, and composition. In equilibrium, the chemical potentials of the components are balanced between the phases, so there is no net change in phase composition or fraction. Understanding phase equilibrium is fundamental in materials science as it underpins the interpretation of phase diagrams and guides processes such as alloy heat treatment and solidification.

Transcript

00:01 Okay guys, in order to solve this question, we are given the following data for copper silver alloy.

00:09 The temperature is 900 degrees centigrade.

00:15 So from the given figure 9 .7, corresponding to temperature 900 degrees, we can obtain alpha phase and l phase in weight percentage.

00:39 So c alpha is equal to 8 percentage of weight of silver.

00:54 Ad is the symbol of silver, as you know, and 92 % weight of copper.

01:09 Then we have c .l, which is 43 % weight of silver.

01:20 And 57 % weight of copper.

01:30 Now from the properties table we can find a of silver is equal to one zero seven point eight seven gram per mole and a for copper is equal to 63 .55 gram per mole.

02:07 Now calculating percentage in the alpha phase, we calculated using this equation.

02:19 C for silver alpha is equal to a, sorry, c, a, g, alpha.

02:53 Multiplied by a into cu divided by c, a, g, alpha multiplied by a, c, u plus c, c, u alpha, multiplied by a, c, u, alpha.

03:31 So now we put into the values.

03:35 It's 8 .8 multiplied by 63 .55 divided by 8 multiplied by divided by 8 multiplied by 63 .55 plus 92 multiplied by 63 .55 multiplied by 100.

04:03 100.

04:07 So we get the following answer that is 5 percentage.

04:13 It's 5%.

04:15 Now moving further, we calculate the percentage in l phase.

04:25 So this was the percentage in alpha phase.

04:46 And here we will calculate the percentage percentage.

05:02 In l phase.