
(a)
Interpretation:
The total β % and the % eutectic microconstituent for 10%Sn at room temperature needs to be determined.
Concept Introduction:
The compound formula of Lead-Tin alloy is designated by 'Pb-Sn'.
- It appears in solid form.
- It appears in various shapes like wire, ingot, foil, bar, ribbon etc.
- It appears in silver color.
- Its melting point is 182-215 degree Celsius.
Lead-Tin are widely used as soldering alloys. They are compatible for all types of uses.

Answer to Problem 11.26P
The Total % β and the % eutectic microconstituent at room temperature for 10%Sn is 8.2% and 0% respectively.
Explanation of Solution
Given:
10%Sn
Calculations:
From the graph,
For % β = 10−299−2 =8.2%
% Eutectic = 0.
Thus, the evaluated value of % β and the % eutectic microconstituent at room temperature for 10% Sn is calculated as 8.2% and 0% respectively.
(b)
Interpretation:
The total β % and the % eutectic microconstituent for 20%Sn at room temperature needs to be determined.
Concept Introduction:
The compound formula of Lead-Tin alloy is designated by 'Pb-Sn'.
- It appears in solid form.
- It appears in various shapes like wire, foil, bar, ribbon etc.
- It appears in silver color.
- Its melting point is 182-215 degree Celsius.
Lead-Tin are widely used as soldering alloys. They are compatible for all types of uses.

Answer to Problem 11.26P
The Total % β and the % eutectic microconstituent at room temperature for 20%Sn is 18.6% and 2.3% respectively.
Explanation of Solution
Given:
20%Sn
Calculations:
From the graph,
For % β = 20−299−2= 18.6%
% Eutectic = 50−1961.9−19 =2.3%
The evaluated value of % β and the % eutectic microconstituent at room temperature for 20% Sn is calculated as 18.6% and 2.3% respectively.
(c)
Interpretation:
The total β % and the % eutectic microconstituent for 50%Sn at room temperature needs to be determined.
Concept Introduction:
The compound formula of Lead-Tin alloy is designated by 'Pb-Sn'.
- It appears in solid form.
- It appears in various shapes like wire, foil, bar, ribbon etc.
- It appears in silver color.
- Its melting point is 182-215 degree Celsius.
Lead-Tin are widely used as soldering alloys. They are compatible for all types of uses.

Answer to Problem 11.26P
The Total % β and the % eutectic microconstituent at room temperature for 50%Sn is 49.5% and 72.3% respectively.
Explanation of Solution
Given:
50%Sn
Calculations:
From the diagram,
For % β = 50−299−2=49.5%
% Eutectic = 60−1961.9−19=72.3%
The evaluated value of % β and the % eutectic microconstituent at room temperature for 50% Sn is calculated as 49.5% and 72.3% respectively.
(d)
Interpretation:
The total β % and the % eutectic microconstituent for 60%Sn at room temperature needs to be determined.
Concept Introduction:
The compound formula of Lead-Tin alloy is designated by 'Pb-Sn'.
- It appears in solid form.
- It appears in various shapes like wire,foil, bar, ribbon etc.
- It appears in silver color.
- Its melting point is 182-215 degree Celsius.
Lead-Tin are widely used as soldering alloys. They are compatible for all types of uses.

Answer to Problem 11.26P
The Total % β and the % eutectic microconstituent at room temperature for 60%Sn is 59.8% and 95.6% respectively.
Explanation of Solution
Given:
60%Sn
Calculations:
From the graph,
For % β = 60−299−2=59.8%
% Eutectic = 97.5−1961.9−19=95.6%
The evaluated value of % β and the % eutectic microconstituent at room temperature for 60% Sn is calculated as 59.8% and 95.6% respectively.
(e)
Interpretation:
The total β % and the % eutectic microconstituent for 80%Sn at room temperature needs to be determined.
Concept Introduction:
The compound formula of Lead-Tin alloy is designated by 'Pb-Sn'.
- It appears in solid form.
- It appears in various shapes like wire, foil, bar, ribbon etc.
- It appears in silver color.
- Its melting point is 182-215 degree Celsius.
Lead-Tin are widely used as soldering alloys. They are compatible for all types of uses.

Answer to Problem 11.26P
The Total % β and the % eutectic microconstituent at room temperature for 80%Sn is 80.4% and 49.2% respectively.
Explanation of Solution
Use spreadsheet to tabulate the % total β and % eutectic micro constituent as in table (1)
Composition of % Sn in entire Pb−sn phase diagram | Tensile Strength ( MPa) | Total % β phase | % Eutectic |
10 | 30 | 8.2 | 0 |
20 | 40 | 18.6 | 2.3 |
50 | 50 | 49.5 | 72.3 |
60 | 60 | 59.8 | 95.6 |
80 | 70 | 80.4 | 49.6 |
95 | 80 | 95.9 | 7 |
Given:
80%Sn
Calculations:
From the graph:
For % β = 80−299−2=80.4%
% Eutectic = 97.5−8097.5−61.9=49.2%
Thus, by using the expression of eutectic, the required value obtained is 49.2%.
(f)
Interpretation:
The total β % and the % eutectic microconstituent for 95%Sn at room temperature needs to be determined.
Concept Introduction:
The compound formula of Lead-Tin alloy is designated by 'Pb-Sn'.
- It appears in solid form.
- It appears in various shapes like wire, foil, bar, ribbon etc.
- It appears in silver color.
- Its melting point is 182-215 degree Celsius.
Lead-Tin are widely used as soldering alloys. They are compatible for all types of uses.

Answer to Problem 11.26P
The Total % β and the % eutectic microconstituent at room temperature for 95%Sn is 95.9% and 7.0% respectively.
Explanation of Solution
Given:
95%Sn
Calculations:
For % β = 95−299−2=95.9%
% Eutectic = 97.5−9597.5−61.9=7.0%
(Mention Graph)
After Studying the graph of tensile strength vs % β we can conclude that as tensile strength increases to its maximum value of 7800psi at % β = 60%.
The evaluated value of % β and the % eutectic microconstituent at room temperature for 95% Sn is calculated as 95.9% and 7.0% respectively.
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Chapter 11 Solutions
Essentials Of Materials Science And Engineering
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