Expressions and Formulas to Expand and Add Potentiality to Knowledge Underlying Diffraction

TL;DR

This paper introduces new explicit formulas and expressions for diffraction analysis, enabling direct, assumption-free conversion of diffraction data into real structural information using Fourier transforms.

Contribution

It presents the first formulas for interatomic vector distributions in monatomic crystals, enhancing diffraction data interpretation without approximations.

Findings

Derived formulas for interatomic vector distributions

Demonstrated application to zinc blende and polonium

Provided free software for diffraction data analysis

Abstract

Development generating diffraction-related valuable expressions and formulas capable of initiating new era for diffraction and for scientific domains that use it provided. The main expression, among these, gives diffracted intensity as explicit function of true and absolute distribution of interatomic vectors (DIV) and is suitable for constructing analytical techniques capable of converting experimental diffraction intensity data into real structural data, immediately and accurately interpretable as such, through Fourier transform tool (FTT) with no assumption and no approximation additional to those involved in kinematic theory. The first ever produced formula giving distribution of interatomic vectors, and hence distribution of interatomic distances (DID), of monatomic crystal provided together with description of possible way of obtaining it. Given examples of application relate to getting two DIDs and to using them to calculate X-ray diffracted intensity profiles, one DID was for zinc blende (ZnS) and was calculated from atom positions and the other one was for polonium and was calculated using both atom positions and appropriate formula. Software for calculating DIDs and X-ray profiles for monatomic crystals available freely. No longer needed to affect Debye scattering equation (DSE) through approximation and assumption makings before combining it with FTT to get to experimental structural data.