Problem 10'38

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Problem 10.38

• Gena Urowsky
• April 4, 2007

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Problem Statement

• On the basis of the photomicrograph (i.e., the
  relative amounts of the microconstituents) for
  the lead-tin alloy shown in figure 10.15 and the
  Pb-Sn phase diagram (Figure 10.7), estimate the
  composition of the alloy, and then compare this
  estimate with the composition given in the figure
  legend of Figure 10.15.
• 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 a and ß phases as well
  as the eutectic structure are 12.7, 7.3, and 8.7
  g/cm3, respectively and
• (3) this photomicrograph represents the
  equilibrium microstructure at 180ºC (355ºF).

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Photomicrograph
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Phase Diagram
Q
P
C1
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Background Information

• mass volume density
• Lever Rule
• Tie line constructed across two phase region at
  temperature of alloy
• Overall alloy composition is located on tie line
• Fraction of one phase is computed by taking
  length of tie line from overall alloy composition
  to the phase boundary for the other phase, and
  dividing by total tie line length
• Fraction of other phase determined in same manner

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Area ? Volume

• a (lead rich) large dark regions 20 by area
• Thus a is 20 by volume
• Eutectic (a and ß layers) 80 by area
• Eutectic is 80 by volume

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Composition Fractions

• C1 0.513052 ? 51.3 wt Sn
• Composition is then 100-51.3 48.7 wt Pb

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Alternate Method

• Yields the same results as the previous method

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Comparison

• Calculated composition
• 51.3 wt Sn - 48.7 wt Pb
• Book gives value of 50 wt Sn - 50 wt Pb
• Very close wt values

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Exactness, Usefulness, and Applications

• Probably not exact as 20 from photomicrograph
  was estimation
• Digital imaging yields 20.6, which is close, but
  again not exact
• Temperature is 180ºC and we used values for 183ºC
  which is close, but not exact
• Since this is the data wed be receiving (the
  photomicrograph) its good to know how to deal
  with the information and process it accordingly
• Determine information about a given solder by
  examining the micrograph and determining
  composition