On the basis of the photomicrograph (i.e., the relative...

On the basis of the photomicrograph (i.e., the relative amounts of the microconstituents) for the lead-tin alloy shown in Figure $9.17$ and the Pb-Sn phase diagram (Figure 9.8), estimate the composition of the alloy, and then compare this estimate with the composition given in the legend of Figure 9.17. Make the following assumptions: (1) The area fraction of each phase and microconstituent in the photomicrograph is equal to its volume fraction; (2) the densities of the $\alpha$ and $\beta$ phases and the eutectic structure are 11.2, 7.3, and $8.7 \mathrm{~g} / \mathrm{cm}^{3}$, respectively; and (3) this photomicrograph represents the equilibrium microstructure at $180^{\circ} \mathrm{C}\left(355^{\circ} \mathrm{F}\right)$.

Key Concepts

Equilibrium Microstructures

Equilibrium microstructures are those that have formed under conditions where the system has reached a state of minimum Gibbs free energy and all phases are stable. Interpreting such microstructures at a given temperature allows for comparison with theoretical predictions from phase diagrams, ensuring that the observed microstructure corresponds to the predicted phase assemblage under equilibrium conditions.

Density Considerations in Alloy Analysis

The densities of different phases play a crucial role when converting area fractions or phase amounts into compositional estimates. Since different phases have different densities, these differences must be accounted for in order to accurately determine the overall alloy composition, particularly when the phases are distributed unequally or have significantly different mass contributions.

Area Fraction and Volume Fraction Equivalence

In microstructural analysis, it is common to assume that the area fraction observed in a photomicrograph is equivalent to the volume fraction of the corresponding phase in the bulk material. This assumption, rooted in stereological principles, simplifies the analysis and allows researchers to use two-dimensional images to estimate three-dimensional phase distributions.

Photomicrograph Analysis in Metallurgy

Photomicrographs are used to examine the microstructure of materials, revealing the distribution and morphology of various phases and microconstituents. By analyzing the relative amounts of these features, one can infer the volume fractions and spatial distribution of the phases present, which further can be correlated with phase diagrams to estimate overall alloy composition.

Phase Diagram Analysis

Phase diagrams represent the equilibrium relationships between phases of an alloy as a function of temperature and composition. They provide essential information for predicting the phases present in a material system under given conditions, such as during cooling or at specific temperatures, and help in understanding transformations, such as eutectic reactions, that occur in binary alloys.

Transcript

00:01 Okay guys, in order to solve this question, we are looking at the photomicrograph for the lead tin alloy shown in figure 9 .17.

00:21 And the lead thin phase diagram shown in figure 9 .8.

00:35 We have to estimate the composition of the alloy by making the following assumptions.

00:40 So the assumptions we will, assumptions we will make are number one.

00:49 The area fraction of each phase and microconcigerent in the photograph is equal to its volume fraction.

00:59 The area fraction of each phase of each phase is equal.

01:31 And microconstituent in the photomicrograph is equal to its volume fraction.

02:16 And the second exemption is the densities of alpha and beta phases and the eutectic structures are the densities of, alpha and beta phases and the eutectic structure are the densities are row alpha is equal to 11 .2 grams per centimeter cube then we have row beta is is 7 .3 grams per centimeter cube.

03:36 Then we have the density of eutectic that is 8 .7 grams per centimeter cube.

03:52 So here is our second assumption.

03:55 And the third assumption is this micro, this photo micrograph represents this photo, micrograph represents the equilibrium microstructure at following temperature.

04:34 Librium microstructure at following temperature, and that is, t is equal to 180 degrees centigrade.

05:10 Now, if we look at figure 9 .17, we cannot simply determine the area fraction.

05:26 There are a few ways to do it.

05:28 We can draw an empty picture with the same dimensions as figure 9 .17, then draw particles with the same dimensions at the one corner and make an assumption how much area do all particle stake.

05:44 You can tell it is less than one quarter but a lot more than one tenths.

05:52 So let it be one fifth.

05:56 That is area 0 .2.

06:03 So the first assumption tells us that the area function of each phase and micro constituent in the photomicrograph is equal to its volume fraction, volume fraction alpha is equal to alpha is equal to 0 .2.

06:26 Now we move further to the next step by calculating the mass fraction of alpha phase...

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