Atomic spacing

Last updated August 18, 2024

Atomic spacing refers to the distance between the nuclei of atoms in a material. This space is extremely large compared to the size of the atomic nucleus, and is related to the chemical bonds which bind atoms together.^[1] In solid materials, the atomic spacing is described by the bond lengths of its atoms. In ordered solids, the atomic spacing between two bonded atoms is generally around a few ångströms (Å), which is on the order of 10⁻¹⁰ meters (see Lattice constant). However, in very low density gases (for example, in outer space) the average distance between atoms can be as large as a meter. In this case, the atomic spacing isn't referring to bond length.

The atomic spacing of crystalline structures is usually determined by passing an electromagnetic wave of known frequency through the material, and using the laws of diffraction to determine its atomic spacing. The atomic spacing of amorphous materials (such as glass) varies substantially between different pairs of atoms, therefore diffraction cannot be used to accurately determine atomic spacing. In this case, the average bond length is a common way of expressing the distance between its atoms.^{[ citation needed ]}

Example

Bond length can be determined between different elements in molecules by using the atomic radii of the atoms. Carbon bonds with itself to form two covalent network solids.^[2] Diamond's C-C bond has a distance of ${\frac {{\sqrt {3}}a}{4}}\approx 0.154\ {\text{nm}}$ away from each carbon since $a_{\text{diamond}}\approx 0.357\ {\text{nm}}$ , while graphite's C-C bond has a distance of ${\frac {a}{\sqrt {3}}}\approx 0.142\ {\text{nm}}$ away from each carbon since $a_{\text{graphite}}\approx 0.246\ {\text{nm}}$ . Although both bonds are between the same pair of elements they can have different bond lengths.^[3]

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$Diffraction Phenomenon of the motion of waves$

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<span class="mw-page-title-main">Crystal structure</span> Ordered arrangement of atoms, ions, or molecules in a crystalline material

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The inelastic mean free path (IMFP) is an index of how far an electron on average travels through a solid before losing energy.

$Powder diffraction Experimental method in X-ray diffraction$

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In crystallography, atomic packing factor (APF), packing efficiency, or packing fraction is the fraction of volume in a crystal structure that is occupied by constituent particles. It is a dimensionless quantity and always less than unity. In atomic systems, by convention, the APF is determined by assuming that atoms are rigid spheres. The radius of the spheres is taken to be the maximum value such that the atoms do not overlap. For one-component crystals (those that contain only one type of particle), the packing fraction is represented mathematically by

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Melting-point depression is the phenomenon of reduction of the melting point of a material with a reduction of its size. This phenomenon is very prominent in nanoscale materials, which melt at temperatures hundreds of degrees lower than bulk materials.

Free spectral range (FSR) is the spacing in optical frequency or wavelength between two successive reflected or transmitted optical intensity maxima or minima of an interferometer or diffractive optical element.

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The Mott–Bethe formula is an approximation used to calculate atomic electron scattering form factors, $, from atomic X-ray scattering form factors, . The formula was derived independently by Hans Bethe and Neville Mott both in 1930, and simply follows from applying the first Born approximation for the scattering of electrons via the Coulomb interaction together with the Poisson equation for the charge density of an atom in the Fourier domain. Following the first Born approximation,$

References

↑ Kittel, Charles (2004-11-11). Introduction to Solid State Physics (8th ed.). Wiley. ISBN 047141526X.
↑ Rossi, Miriam. "How can graphite and diamond be so different if they are both composed of pure carbon?". Scientific American. Scientific American. Retrieved October 9, 2007.
↑ Brown; Lemay; Bursten (1997). Chemistry the Central Science. Upper Saddle River, NJ: Simon and Schuster. pp. 412–413.

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[1] Kittel, Charles (2004-11-11). Introduction to Solid State Physics (8th ed.). Wiley. ISBN 047141526X.

[2] Rossi, Miriam. "How can graphite and diamond be so different if they are both composed of pure carbon?". Scientific American. Scientific American. Retrieved October 9, 2007.

[3] Brown; Lemay; Bursten (1997). Chemistry the Central Science. Upper Saddle River, NJ: Simon and Schuster. pp. 412–413.

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