Write the miller indices for the plane below. Intercepts A (2/3,1,1/2) B (1/2,1/2,1).
To determine the Miller indices for the plane with the intercepts A (2/3, 1, 1/2) and B (1/2, 1/2, 1), we first need to find the reciprocals of the intercepts to get the fractional coordinates of the plane.
For intercept A:
a = 3/2 = 1.5
b = 1
c = 2
For intercept B:
a = 2
b = 2
c = 1
Taking the reciprocals of the intercepts gives us the fractional coordinates of the plane:
(2/3, 1, 1/2) --> (1/2, 1, 2)
(1/2, 1/2, 1) --> (2, 2, 1)
Next, we need to find the least common multiple (LCM) of the fractional coordinates to come up with the Miller indices. The LCM of (1/2, 1, 2) and (2, 2, 1) is:
LCM = (1/2, 1, 2)
Finally, inverting the LCM, we get the Miller indices for the plane:
(2, 1, 1/2)
Therefore, the Miller indices for the plane with intercepts A (2/3, 1, 1/2) and B (1/2, 1/2, 1) are (2, 1, 1/2).