# Miller indices of a plane in a simple cube

• ksac
In summary, the conversation discusses the determination of miller indices for a plane containing the x-axis and equally inclined to the y and z axes. The speaker explains their attempts to find the intercepts on the y and z axes, and raises questions about whether the corresponding miller indices would be infinite. They also ask about the intercept on the x-axis and acknowledge the possibility of gaps in their understanding. Another participant suggests using the periodicity of the crystal lattice to adjust the position of the plane, leading to a final determination of (h,k,l) = (0,-1,1).
ksac
I am trying to get a hang of miller indices and doing some practice.

So here it is : What would be the miller indices of the plane containing the x-axis and equally inclined to y and z axes?

(I have uploaded the diagram and highlighted the plane to clarify)

Attempts :

I first try to find the intercepts.
The intercepts on the y and z axes are both, 0.
So does that make the corresponding miller indices k and l infinity? If yes, isn't the whole point of miller indices to avoid infinities in case of planes parallel to any of the crystal axes?

Also, what would be the intercept on the x axis, since the plane contains the x axis?

If there any gaps in my understanding or flaws in the way i am looking at it, please do correct me.
thank you :)

#### Attachments

• miller indices.gif
4.2 KB · Views: 600
I believe this might be the wrong section since this isn't Introductory Physics. Also, you need to know where the plane intersects the three cubic lattice vectors. Since you have the whole plane intersecting the x-axis, you can use the periodicity of the crystal lattice to either move the plane by one lattice vector, or move your origin one lattice vector in the y-direction.

By doing that, you can see now that the plane never intersects the x-axis, and that it intersects y=-1 and z=+1. After taking the inverses, you are left with (h,k,l) = (0,-1,1).

yes that makes a lot of sense. thank you :)

## 1. What are Miller indices of a plane in a simple cube?

The Miller indices of a plane in a simple cube are a system used to identify and describe different crystal planes within a crystal lattice. They are represented by three numbers (hkl), where h, k, and l are the reciprocals of the intercepts of the plane on the three axes of the crystal.

## 2. How are Miller indices of a plane determined?

The Miller indices of a plane are determined by taking the reciprocals of the intercepts of the plane on the three axes of the crystal. These intercepts are then reduced to the smallest whole numbers, which correspond to the three Miller indices (hkl).

## 3. What is the significance of Miller indices in crystallography?

Miller indices are important in crystallography because they allow for the identification and characterization of different crystal planes within a crystal lattice. They also provide information about the orientation and symmetry of the crystal structure.

## 4. How do Miller indices relate to crystal lattice spacing?

The Miller indices of a plane can be used to calculate the spacing between crystal planes within a crystal lattice. This is done using the formula d = a/√(h² + k² + l²), where a is the lattice parameter.

## 5. Can Miller indices be negative?

No, Miller indices cannot be negative. The intercepts used to determine the Miller indices are measured in terms of the positive axes of the crystal, and the reciprocals of these intercepts will always be positive. However, the Miller indices can be zero if the plane is parallel to a particular axis of the crystal.

Replies
2
Views
2K
Replies
1
Views
1K
Replies
4
Views
1K
Replies
1
Views
3K
Replies
6
Views
1K
Replies
16
Views
783
Replies
7
Views
2K
Replies
0
Views
1K
Replies
3
Views
2K
Replies
8
Views
1K