Bragg law vs interference equaiton

[Chemist@]

The condition for constructive interference is: n*lambda=d*sin(alpha)
Bragg's law is n*lambda=2d*sin(alpha)
The diffraction from a crystal cell will also create an interference pattern, so why do these equations differ?

 

[blue_leaf77]

The configuration is different, in transmission grating you have [see pict Grating 1].
While in crystal cell you have [see pict Grating 2].

 

[Chemist@]

I would need more than that. Please elaborate.

 

[nasu]

The condition for constructive interference is: n*lambda=d*sin(alpha)
Bragg's law is n*lambda=2d*sin(alpha)
The diffraction from a crystal cell will also create an interference pattern, so why do these equations differ?

This is not a general condition for constructive interference.
The general condition for constructive interference is that the path difference is a multiple of the wavelength.
Applying this to various geometries results in various formulas, as you just discovered. The formula for path difference depends on the specific geometry (and also on how you label the parameters).

 

[Chemist@]

So what is d or more specifically 2d in Bragg's law? I know that it depends on Miller indices, and it can be expressed through them and the side of the unit cell.

 

[blue_leaf77]

In Bragg's law d is the spacing between adjacent atoms/molecules. To derive those equations you need to know the general condition for constructive interference, which is $OPD = N2\pi$ with OPD abbreviated from optical path difference and N integer numbers. Analyzing the geometry in both figures will lead to different expressions of OPD of both cases.