Question about miller indicies.

[Craptola]

I've come across a problem in a past paper while studying for exams, the solution is not given so I can only guess what I have to do, any guidance would be appreciated.

Homework Statement

Calculate the Miller indices of the shaded plane with respect to the three primitive lattice vectors shown. In fig 1 and 2.

Homework Equations

n/a

The Attempt at a Solution

So figure 1 is quite obviously (1 1 1), I'm not sure how to handle figure 2. The way I was taught to calculate miller indices was pretty formulaic; Define an origin, look for intercepts with the lattice vectors, take the reciprocals and voila. I've never encountered a problem in which the lattice vectors aren't parallel to the edges of the cube and it's thrown me off a little.

Is it as simple as defining another set of axes parallel to the lattice vectors and extrapolating the plane to see where it intercepts those axes?

 

[ehild]

The Attempt at a Solution

So figure 1 is quite obviously (1 1 1), I'm not sure how to handle figure 2. The way I was taught to calculate miller indices was pretty formulaic; Define an origin, look for intercepts with the lattice vectors, take the reciprocals and voila. I've never encountered a problem in which the lattice vectors aren't parallel to the edges of the cube and it's thrown me off a little.

Is it as simple as defining another set of axes parallel to the lattice vectors and extrapolating the plane to see where it intercepts those axes?

Yes. Find the components of the new lattice vectors in the "regular" coordinate system, and determine their intercept with the given plane, in terms of the given lattice constant. Than take the reciprocals.

ehild

 

[Craptola]

Thanks. So would that make the correct answer (1 sqrt(2) 0)? Or have I completely butchered that. It looks like the plane will never intersect with a'3 making the intercept infinity the reciprocal of which being zero.

 

[ehild]

The sqrt(2) term is wrong. The Miller indices have to be integers. Find the intercept in terms of the base vectors. They need not be unit vectors.

ehild

 

[HalfLostAndSearching]

Hello! Thank you for reaching out for guidance on this problem. It seems like you have a good understanding of Miller indices and how to calculate them. In this case, for figure 2, you can use the same approach of defining an origin and looking for intercepts with the lattice vectors. However, since the lattice vectors are not parallel to the edges of the cube, you will need to use a different set of axes that are parallel to the lattice vectors. This will allow you to accurately determine the intercepts and calculate the Miller indices for the shaded plane. Don't forget to take the reciprocals and simplify the indices if necessary. I hope this helps! Good luck on your exams.