- #1
Petit Einstein
- 8
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How we can calculate the Miller's index?
Thanks
Thanks
turin said:It's a convention. There is something about the four different delimiters: (),[],{}, and <>. When you surround the numbers with (), then (102) is the same as (012), unless you are worried about the orientation. For the orientation's sake, you should have a right-handed permutation (conventionally) or you should specify.
Gokul43201 said:From the Bragg angle and the wavelength, you can get the inter-plane spacing, d.
[tex]n \lambda = 2d sin \theta~~ [/tex]
From the value of d, and the knowledge of the material (which tells you the lattice parameter, a) you can calculate the Miller Indices of the reflecting planes
[tex] d = \frac {a} {\sqrt{h^2+k^2+l^2}} [/tex]
Dr Transport said:(020) and (022) are different planes of the same family
{220} = (220),(202),(022),(-220),(2-20),(-202),(20-2),(-2-20),(-20-2),(-20-2) etc...
Petit Einstein said:Ok i agree with u about this, but for exemple, the value of
{h^2+k^2+l^2} is equal to 8 so we will get the Miller index for example:
h=2; k=2 and l=0 or we write (220). if we want get (202) or (022) , are there possible?
Thank for your response.
Miller's Index is a notation system used to describe the crystallographic planes and directions in a crystal lattice. It was developed by William Hallowes Miller in 1839.
Miller's Index is calculated by finding the intercepts of a plane on the crystallographic axes and converting them into fractions with common denominators. This notation system uses three integers written as [hkl] where h, k, and l represent the intercepts along the x, y, and z axes, respectively.
Miller's Index is significant because it provides a standardized way of describing crystallographic planes and directions in different crystal structures. It allows scientists to easily communicate and compare information about crystal structures and their properties.
Miller's Index is used in crystallography to identify and describe the orientation of crystal planes and directions within a crystal structure. It is also used to calculate the spacing between crystal planes, which is important for understanding the diffraction patterns produced by crystals.
One limitation of Miller's Index is that it is based on a Cartesian coordinate system, which is not always the most appropriate coordinate system for describing crystal structures. Additionally, Miller's Index does not take into account the actual atomic arrangement within a crystal, which can affect the properties of the material. Therefore, it should be used in conjunction with other crystallographic methods for a more comprehensive understanding of crystal structures.