# X-Ray Crystallography Research Papers

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Without having any evidence to support his claim on the periodic arrangements of atoms in a lattice, he further postulated that the crystalline structure can be used to diffract x-rays, much like a gradient in an infrared spectrometer can diffract infrared light.

His postulate was based on the following assumptions: the atomic lattice of a crystal is periodic, x- rays are electromagnetic radiation, and the interatomic distance of a crystal are on the same order of magnitude as x- ray light.

Laue's predictions were confirmed when two researchers: Friedrich and Knipping, successfully photographed the diffraction pattern associated with the x-ray radiation of crystalline $$Cu SO_4 \cdot 5H_2O$$. The arrangement of the atoms needs to be in an ordered, periodic structure in order for them to diffract the x-ray beams.

A series of mathematical calculations is then used to produce a diffraction pattern that is characteristic to the particular arrangement of atoms in that crystal.

Diffraction and measurement of such small wavelengths would require a gradient with spacing on the same order of magnitude as the light.

In 1912, Max von Laue, at the University of Munich in Germany, postulated that atoms in a crystal lattice had a regular, periodic structure with interatomic distances on the order of 1 A.So we get: $BG = BC = d \sin \theta \label$ Thus, $2d \sin \theta = n \lambda \label$ This equation is known as Bragg's Law, named after W. The x-rays that are diffracted off the crystal have to be in-phase in order to signal.Only certain angles that satisfy the following condition will register: $\sin \theta = \dfrac \label$ For historical reasons, the resulting diffraction spectrum is represented as intensity vs. The main components of an x-ray instrument are similar to those of many optical spectroscopic instruments.Applying some basic trigonometric properties, the following two equations can be shown about the lines: $CD = x \cos(θ o)$ and $HG = x \cos (θ)$ where $$x$$ is the distance between the points where the diffraction repeats.Combining the two equations, Diffraction of an x-ray beam, occurs when the light interacts with the electron cloud surrounding the atoms of the crystalline solid.Calculation of the phase difference can be explained by examining Figure 1 below.In the figure below, two parallel waves, BD and AH are striking a gradient at an angle $$θ_o$$.These include a source, a device to select and restrict the wavelengths used for measurement, a holder for the sample, a detector, and a signal converter and readout.However, for x-ray diffraction; only a source, sample holder, and signal converter/readout are required.Some of the light will be diffracted at an angle $$theta$$, and the remainder will travel deeper into the solid.This process will repeat for the many planes in the crystal.

## Comments X-Ray Crystallography Research Papers

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