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5. (a) What Is a Grain and a Grain Boundary? Show Both of Them Using a Hand Sketch. (b) Determine the ASTM Grain Size of an Aluminium

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5. (a) What is a grain and a grain boundary? Show both of them using a hand sketch. (b) Determine the ASTM grain size of an aluminium sample if, 45 grains per cm^3 are counted at a magnification of x100

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(a) A grain is a small crystalline region within a metal or alloy that has a specific crystal structure and orientation. It is the basic building block of the microstructure of a polycrystalline material. Grains are typically surrounded by grain boundaries, which are interfaces where the crystallographic direction of the lattice changes.Here is a hand sketch showing a grain and a grain boundary:[Insert sketch of a grain with a grain boundary](b) To determine the ASTM grain size of an aluminum sample, we can use the following formula:ASTM Grain Size = -log2(N)where N is the number of grains per unit area. In this case, the number of grains per unit area is 45 grains per cm^2.Substituting the given value into the formula, we get:ASTM Grain Size = -log2(45)Calculating the logarithm, we find:ASTM Grain Size ≈ 1.35Therefore, the ASTM grain size of the aluminum sample is approximately 1.35.