Updated: Aug 15, 2020
A Crystallography experiment is a highly challenging, complex, multi-stage process that produces crystals with a well-ordered periodic crystal lattice that are capable of producing diffraction patterns to collect information for 3D reconstruction of molecules or atoms at the microscopic scale. The traditional crystallography process begins with exploring a broad matrix of physical variables to identify ideal conditions to produce a crystal. These ideal conditions promote crystallization, or the phase transition that converts molecules that are randomly oriented in liquid solution into a well-ordered solid, crystalline state. Structural information about the molecular components is then collected from the crystal, in which a highly coherent laser source or wavelength scatters from the periodic array of electrons in the crystal to create a diffraction pattern. The scattered waves will intersect with each other to add constructively to create a waveform with increased amplitude or deconstructively to reduce or transmute the amplitude; this interference or diffraction pattern creates a collection of spots or “reflections” that store information about the contents of the crystal in its reflection intensity and geometric pattern. This information stored in what is called reciprocal space can be extracted from the diffraction patterns to reconstruct a 3D model of the electron density of microscopic structures within the crystal lattice in real space.
The Double Slit Experiment is fundamental to understanding interference and diffraction patterns.In the materialist paradigm, if we randomly shoot particles through a single slit, a single vertical line will be detected from where the particles traveled through the slit and contacted the detector. If we add a second slit, two vertical bands are produced. If we propagate a wave through a single slit, a single vertical band will emerge at the most intense region or amplitude of the wave. If we add a second slit, the original wave is split into two separate waves as it propogates through the slits and the concentric circles of the propagating waves intersect. If the amplitudes of both waves merge, there is constructive interference, and if the trough and peak of each respective wave merge, there is deconstructive interference and the wave cancels out. This creates an interference pattern that produces many bands on the detector at the regions of constructive interference. In the quantum paradigm, when particles are transferred through the two slits, an interference pattern is detected, suggesting that particles are acting as waves, called wave-particle duality! However, when there is an observer, the particle behaves as a single particle, producing a single band. The act of observation or measurement collapses the wave function into a defined particle.
In a crystallography experiment, we can think of the double slit as the location of atoms within a crystal lattice. A highly coherent source or beam of energy, such as light or X-rays, is targeted at the crystal. The coherent energy beam then scatters off of the electrons in the crystal lattice, creating many waveforms that are propagated toward the detector at different phases. The scattered or diffracted light is also described as bending of light from the original source, which creates concentric circles of propagating waves that pass through each other like ripples in a pond. The phase of the propagating wave varies depending on the location of the atom in 3D space and the diffraction angle. For two atoms in the crystal, if the distance between the atoms and the diffraction angle satisfies Bragg’s Law so that the wavelength is an integer, the scattered wavelengths will constructively interfere, producing a strong intensity diffraction spot or reflection on the detector. However, if Bragg’s Law is not satisfied to produce an integer of the wavelength, meaning that the waves are out of phase, the diffracted waves will deconstructively interfere, reducing the intensity of the reflection or producing no diffraction spot.
The crystal is repeated exposed to a coherent energy or light to collect many diffraction patterns from various angles of the crystalline structure by rotating the crystal in the bearm source. The resulting diffraction patterns produce highly symmetric patterns that reflect the geometry and symmetry of atoms within the crystal lattice when aligned with the unit cell axes. For example, the reflections of the diffraction pattern from the Beryl crystal lattice, better known as emerald and aquamarine, adopt a 6-fold hexagonal sacred geometry and can be superimposed with the Flower of Life fundamental geometry of the universe. Notably, the diffraction pattern is a holographic information storage instrument of the crystallography experiment, where every single reflection within the diffraction pattern contains information about all of the atoms in the crystal. The information stored in the reciprocal dimension of the diffraction pattern is ultimately extracted to reconstruct a 3D real space model of the crystal.