Answer:
(a) See attachment
(b) The two planes are parallel because the intercepts for plane [220] are X = 0,5 and Y = 0,5 and for plane [110] are X = 1 and Y = 1. When the planes are drawn, they keep the same slope in a 2D plane.
(c) [tex]d = \frac{a}{\sqrt{h^{2} + k^{2} + l^{2}}} = \frac{1}{\sqrt{2}} = 0,707[/tex]
Explanation:
(a) To determine the intercepts for an specific set of Miller indices, the reciprocal intercepts are taken as follows:
For [110]
[tex]X = \frac{1}{1} = 1; Y = \frac{1}{1} = 1; Z = \frac{1}{0} = \inf.[/tex]
For [220]
[tex]X = \frac{1}{2} = 0,5;Y = \frac{1}{2} = 0,5;Z = \frac{1}{0} = \inf.[/tex]
The drawn of the planes is shown in the attachments.
(b) Considering the planes as two sets of 2D straight lines with no intersection to Z axis, then the slope for these two sets are:
For (1,1):
[tex]K_1 = \frac{1}{1} = 1[/tex]
For (0.5, 0.5):
[tex]K_2 = \frac{0.5}{0.5} = 1[/tex]
As shown above, the slopes are exactly equal, then, the two straight lines are considered parallel and for instance, the two planes are parallel also.
(c) To calculate the d-spacing between these two planes, the distance is calculated as follows:
The Miller indices are already given in the statement. Then, the distance is:
[tex]\frac{1}{d^{2}} = \frac{h^{2} + k^{2} + l^{2}}{a^{2}}[/tex]
[tex]d = \frac{a}{\sqrt{h^{2} + k^{2} + l^{2}}} = \frac{1}{\sqrt{2}} = 0,707[/tex]
