Hardness data (Rockwell B scale) were collected for a series of Cu–Ni alloys at 25 °C.
Mole % Ni
Hardness (HRB)
0
35.0
10
44.5
20
54.0
30
60.5
40
66.0
50
66.5
Assume the samples are solution-annealed and have identical grain structures.
(a) On appropriately labeled axes, sketch a graph of hardness versus mole % Ni for the range 0–50 %.
(b) For the interval 0–40 % Ni, determine the best-fit linear equation relating hardness (H) to composition (x, in mole % Ni). Show your reasoning.
(c) Using the equation from part (b), predict the expected hardness at 25 mole % Ni.
(d) Provide a microscopic explanation for the shape of the hardness curve over the full 0–50 % composition range, making specific reference to lattice distortion and electron behavior.