Bragg’s Law: X-ray Fluorescence and Nature's Iridescence

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Published Date Written by Sharon Banks

Bragg's Law is the result of experiments into the diffraction of X-rays or neutrons off crystal surfaces at certain angles, derived by physicist Sir William Lawrence Bragg in 1912 and first presented on 1912-11-11 to the Cambridge Philosophical Society. Although simple, Bragg's law has many applications from the study of crystals in the form of X-ray and neutron diffraction, quantitative XRF analysis and the iridescent hues on the tail of a peacock.
In the case of wavelength dispersive spectrometry (WDS) or x-ray fluorescence spectroscopy (XRF), crystals of known d-spacings are used as analyzing crystals in the spectrometer. The crystal separates the various wavelengths of the secondary x-rays emitted by the analysis specimen. When a crystal is bombarded with x-rays of a fixed wavelength (similar to spacing of the atomic-scale crystal lattice planes) and at certain incident angles, intense reflected x-rays are produced when the wavelengths of the scattered x-rays interfere constructively. In order for the waves to interfere constructively, the differences in the travel path must be equal to integer multiples of the wavelength. When this constructive interference occurs, a diffracted beam of x-rays will leave the crystal at an angle equal to that of the incident beam.
The general relationship between the wavelength of the incident x-rays, angle of incidence and spacing between the crystal lattice planes of atoms is known as Bragg's Law , expressed as: n λ = 2d sinΘ where n (an integer) is the "order" of reflection, λ is the wavelength of the incident X-rays, d is the interplanar spacing of the crystal and Θ is the angle of incidence.{mosimage}
Because the position of the sample and the detector is fixed in XRF instruments, the angular position of the reflecting crystal is changed in accordance with Bragg's Law so that a particular wavelength of interest can be directed to a detector for quantitative analysis. Every element in the Periodic Table has a discrete energy difference between the orbital "shells" (e.g. K, L, M), such that every element will produce x-rays of a fixed wavelength. Therefore, by using a spectrometer crystal (with fixed d-spacing of the crystal) and positioning the crystal at a unique and fixed angle (Θ), it is possible to detect and quantify elements of interest based on the characteristic x-ray wavelengths produced by each element.
Iridescence is one of those curious optical games that light loves to play. From pearl earrings to tropical butterflies that appear to be made out of cellophane, iridescence is a
source of luminous beauty across the natural world. The brilliant iridescence (or play of colors) found in nature (buttterfly wings, the pearly glow of a mollusc shell) can be attributed to the diffraction and constructive interference of visible lightwaves which satisfy Bragg’s law, in a matter analogous to the scattering of X-rays in crystalline solids, rather than pure pigment. In animals, iridescence is often termed structural coloration since it derives from the physical structure of the object rather than pigmented chemical compounds. Iridescence happens when light bounces off different reflective surfaces in a semi-transparent substance. As the light rays exit, they interfere with each other, sometimes destructively muting each other and at other times resonating into an impossible burst of color.
Because the final appearance depends on the exact path taken by the light before reaching the eye, iridescent objects change their hue (wavelength) depending on your point of view (or Bragg angle of view) giving them a magical, animated quality. Iridescence is quite common in birds. Here, the surface of the feather - again microscopically - has a scratched or furrowed pattern. This is where the feather does its absorbing and reflecting of light. With a specific pattern of scratches or furrows, the feathers can give off a quite specific prismatic effect. Flowers were previously believed only to use chemical colours, where a pigment absorbs all wavelengths except a few, giving them their apparent colour. Flowers, however, use the same physical structure that makes compact discs iridescent. Unfortunately, because most of the petal iridescence measured is at the ultraviolet end of the spectrum, which insects can see but humans cannot, this raises the intriguing possibility that many flowers are actually iridescent although they do not appear so to the human eye.
So next time you see a bee heading off for an iridescent flower it’s seeing different colours depending on the angle (Bragg's angle) from which the bee is viewing the petals.
For all of it’s magical aesthetic, iridescence is relatively simple to achieve and is found frequently in the inanimate world from the sheen of a puddle contaminated with a thin layer of petroleum and soap bubbles to prized gems and minerals like labradorite and pyrite.

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