Surface definition in crystals question

[Useful nucleus]

I read the following paragraph about surface definition"
"Each surface is specified by at least two pieces of information.Firstly, there are the Miller indices (hkl) of the plane that defines the orientation of the bulk cleavage. Secondly, there is the so-called shift - i.e. the displacement of the plane relative to the unit cell origin. The shift ranges between 0 and 1."

I do not quite understand what the shift means. To me it looks a surface with a shift x (say x >0 ) is equivalent to another surface with different miller indices and shift zero. Am I right here?

In other words , to me it looks unnecessary to use the shift since miller indices are enough to uniqule specify the surface.

 

[caffenta]

The Miller indices only define the plane orientation. 2 parallel planes have the same Miller indices.

Take a fcc unit cell for example. If you cleave along the (001) plane, you could cut between the first/second or second/third layer. If you just used the Miller indices, there would be no way to distinguish between the 2 surfaces.

 

[Useful nucleus]

WHoops, I forgot that the Miller indices by definition have to be relatively prime! Thank you for clarification, it reminded me of the definition :)