Energy for Vacancy Formation eVatom 094 Metal Sodium Tempe

Energy for Vacancy Formation (eV/atom): = 0.94
Metal: = Sodium
Temperature ( C ) = 704
Alloy Metal A = Potassium
Alloy Metal B = Germanium
Metal-X = Copper
Metal-Y = Aluminum
Magnification = 175
ASTM Grain Size = 7
Grain per Square Inches = 173

1.For the ASTM Grain Size listed above, approximately how many grains would there be per square inch with no magnification? (answer in Engineering Notation) :

Solution

Number of grains per square inch in the ASTM grain size n at a magnification of 100X is given by the formula

N = 2^n-1

For a grain size of 7 the number of grains per square inch is

N = 2^7-1 = 2⁶= 64 grains per square inch.

The number of grains for a magnification M is given by

N_M * (M/100)² = 2^n-1

Given that the magnification is M = 1X.

Thus N₁ * (1/100)² = 64.

===> N₁ = 640000 grains per square inch

Thus Number of grains per square inch for a grain size of 7 at a magnification of 1X is N₁ = 64 * 10⁴