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Methods, Problems and Solutions

Why Reciprocal Space?

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Via the sci.techniques.xtallography newsgroup

Newsgroups: sci.techniques.xtallography
From: sul2@Lehigh.EDU
Subject: Why reciprocal?
Date: 4 May 1998 13:51:05 -0400


I have a couple basic questions about Miller's index plane and the
reciprocal lattice.  What is the reason that the (hkl) plane is
designated for intersections at 1/h, 1/k, and 1/l, respectively?
Why does it not simply use (hkl) for intersections at h,k and l?

Likewise, why does the reciprocal lattice stand for 1/d(hkl)?
I have read a few books saying that the reciprocal lattice (r*) is
defined as

        r* = (b x c) / [a.(b x c)]

and     |r*| = area / volume = 1/height = 1/d(hkl)

where a,b,c stand for unit vectors of primitive cell.  It should be
some reason to define r* in that way.

Thank you

From: rwgk@laplace.csb.yale.edu (Ralf W. Grosse-Kunstleve)
Newsgroups: sci.techniques.xtallography
Subject: Re: Why reciprocal?
Date: 04 May 1998 21:17:35 -0400

The reason is simply that crystallographers wanted a "simple" and convenient
way of discribing x-rays diffracted by a crystal. Try to learn more about
the "Ewald construction" and you will see how useful the mathematical
concept of the reciprocal lattice is in helping you to understand the
result of a diffraction experiment.

As a start try Giacovazzo: Fundamentals of Crystallography or one of
the older books by Buerger.

The reciprocal lattice is just like a road atlas. A model which tells
you which way x-rays go. Nothing more. Only how it relates to reality
is slightly more involved.

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