Phase signal definition for electromagnetic waves in X-ray crystallography

TL;DR

This paper clarifies the definition of phase signals in X-ray crystallography, emphasizing the invariance of measurable quantities despite different mathematical conventions for wave phase representation.

Contribution

It generalizes key equations in X-ray diffraction to account for different phase definitions and discusses their physical implications.

Findings

Equations are invariant under different phase conventions.

Conflicting phase definitions do not affect measurable quantities.

Clarification improves understanding of wave phase in X-ray crystallography.

Abstract

Diffracted X-ray waves in crystals have relative phases regarding the mathematical format used to describe them. A forward propagating wave can be defined with either negative or positive time evolution, i.e. kr - wt or $wt - kr. Physically measurable quantities are invariant with respect to the choice of definition. This fact has not been clearly emphasized neither extensively explored when deriving well-established equations currently being used in many X-ray diffraction related techniques. Here, the most important equations are generalized and consequences of conflicting undertaken definitions discussed.