# X-Ray Crystallography Research Papers

The x-ray beams travel different pathlengths before hitting the various planes of the crystal, so after diffraction, the beams will interact constructively only if the path length difference is equal to an integer number of wavelengths (just like in the normal diffraction case above).

The x-ray beams travel different pathlengths before hitting the various planes of the crystal, so after diffraction, the beams will interact constructively only if the path length difference is equal to an integer number of wavelengths (just like in the normal diffraction case above).

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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.

So the total path difference between path AHGF and BCDE is CD - HG.

To observe a wave of high intensity (one created through constructive interference), the difference CD - HG must equal to an integer number of wavelengths to be observed at the angle psi, $$CD - HG = n\lambda$$, where $$\lambda$$ is the wavelength of the light.

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.

Due to the periodic crystalline structure of a solid, it is possible to describe it as a series of planes with an equal interplaner distance.

As an x-ray's beam hits the surface of the crystal at an angle ?

The incident wave BD travels farther than AH by a distance of CD before reaching the gradient.

The scattered wave (depicted below the gradient) HF, travels father than the scattered wave DE by a distance of HG.

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