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49-469: When the incident x-ray energy matches the binding energy of an electron of an atom within the sample, the number of x-rays absorbed by the sample increases dramatically, causing a drop in the transmitted x-ray intensity. This results in an absorption edge. Every element has a set of unique absorption edges corresponding to different binding energies of its electrons, giving XAS element selectivity. XAS spectra are most often collected at synchrotrons because

98-433: A 500 – 1000 eV range beginning before an absorption edge of an element in the sample. The x-ray absorption coefficient is usually normalized to unit step height. This is done by regressing a line to the region before and after the absorption edge, subtracting the pre-edge line from the entire data set and dividing by the absorption step height, which is determined by the difference between the pre-edge and post-edge lines at

147-439: A solid object, parts of which oscillate at short distances. Therefore, to bind the particles, the kinetic energy gained due to the attraction must be dissipated by resistive force. Complex objects in collision ordinarily undergo inelastic collision , transforming some kinetic energy into internal energy (heat content, which is atomic movement), which is further radiated in the form of photons – the light and heat. Once

196-451: A temporal frequency (in hertz) which has been divided by the speed of light in vacuum (usually in centimeters per second, cm⋅s ): The historical reason for using this spectroscopic wavenumber rather than frequency is that it is a convenient unit when studying atomic spectra by counting fringes per cm with an interferometer  : the spectroscopic wavenumber is the reciprocal of the wavelength of light in vacuum: which remains essentially

245-603: A wave number, defined as the number of radians per unit distance, sometimes called "angular wavenumber", is more often used: When wavenumber is represented by the symbol ν , a frequency is still being represented, albeit indirectly. As described in the spectroscopy section, this is done through the relationship ν s c = 1 λ ≡ ν ~ , {\textstyle {\frac {\nu _{\text{s}}}{c}}\;=\;{\frac {1}{\lambda }}\;\equiv \;{\tilde {\nu }},} where ν s

294-403: Is a change in mass to stay bound. This mass change must be released as various types of photon or other particle energy as above, according to the relation E = mc . Thus, after the binding energy has been removed, binding energy = mass change × c . This energy is a measure of the forces that hold the nucleons together. It represents energy that must be resupplied from the environment for

343-553: Is a frequency expressed in the unit hertz . This is done for convenience as frequencies tend to be very large. Wavenumber has dimensions of reciprocal length , so its SI unit is the reciprocal of meters (m ). In spectroscopy it is usual to give wavenumbers in cgs unit (i.e., reciprocal centimeters; cm ); in this context, the wavenumber was formerly called the kayser , after Heinrich Kayser (some older scientific papers used this unit, abbreviated as K , where 1   K = 1   cm ). The angular wavenumber may be expressed in

392-405: Is analogous to eigenstates of the particle in a box toy model. The δ j {\displaystyle \delta _{j}} factor inside the sin {\displaystyle \sin } is an element dependent phase shift. Since EXAFS requires a tunable x-ray source, data are frequently collected at synchrotrons , often at beamlines which are especially optimized for

441-517: Is defined as the number of wave cycles per unit time ( ordinary frequency ) or radians per unit time ( angular frequency ). In multidimensional systems , the wavenumber is the magnitude of the wave vector . The space of wave vectors is called reciprocal space . Wave numbers and wave vectors play an essential role in optics and the physics of wave scattering , such as X-ray diffraction , neutron diffraction , electron diffraction , and elementary particle physics. For quantum mechanical waves,

490-449: Is described by the EXAFS equation, first demonstrated by Sayers, Stern, and Lytle. The oscillatory part of the dipole matrix element is given by χ ( k ) {\displaystyle \chi (k)} , where the sum is over the j {\displaystyle j} sets of neighbors of the absorbing atom, N j {\displaystyle N_{j}} is

539-487: Is given by the leader of the group that developed the modern version of EXAFS in an award lecture by Edward A. Stern. Binding energy In physics and chemistry, binding energy is the smallest amount of energy required to remove a particle from a system of particles or to disassemble a system of particles into individual parts. In the former meaning the term is predominantly used in condensed matter physics, atomic physics, and chemistry, whereas in nuclear physics

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588-409: Is known as a dispersion relation . For the special case of an electromagnetic wave in a vacuum, in which the wave propagates at the speed of light, k is given by: where E is the energy of the wave, ħ is the reduced Planck constant , and c is the speed of light in a vacuum. For the special case of a matter wave , for example an electron wave, in the non-relativistic approximation (in

637-411: Is now excited and the ejected photoelectron interacts with electrons in the surrounding non-excited atoms. If the ejected photoelectron is taken to have a wave -like nature and the surrounding atoms are described as point scatterers, it is possible to imagine the backscattered electron waves interfering with the forward-propagating waves. The resulting interference pattern shows up as a modulation of

686-572: Is often a much larger fraction of the system mass. It may thus be measured directly as a mass difference between rest masses of reactants and (cooled) products. This is because nuclear forces are comparatively stronger than the Coulombic forces associated with the interactions between electrons and protons that generate heat in chemistry. Mass change (decrease) in bound systems, particularly atomic nuclei, has also been termed mass defect , mass deficit , or mass packing fraction . The difference between

735-409: Is the free-space wavenumber, as above. The imaginary part of the wavenumber expresses attenuation per unit distance and is useful in the study of exponentially decaying evanescent fields . The propagation factor of a sinusoidal plane wave propagating in the positive x direction in a linear material is given by where The sign convention is chosen for consistency with propagation in lossy media. If

784-455: Is the wavelength. It is sometimes called the "spectroscopic wavenumber". It equals the spatial frequency . For example, a wavenumber in inverse centimeters can be converted to a frequency expressed in the unit gigahertz by multiplying by 29.979 2458  cm/ns (the speed of light , in centimeters per nanosecond); conversely, an electromagnetic wave at 29.9792458 GHz has a wavelength of 1 cm in free space. In theoretical physics,

833-441: The reverse Monte Carlo method can help in extracting more reliable and richer structural information. EXAFS is, like XANES , a highly sensitive technique with elemental specificity. As such, EXAFS is an extremely useful way to determine the chemical state of practically important species which occur in very low abundance or concentration. Frequent use of EXAFS occurs in environmental chemistry , where scientists try to understand

882-431: The "mass deficit" of the cold, bound system. Closely analogous considerations apply in chemical and nuclear reactions. Exothermic chemical reactions in closed systems do not change mass, but do become less massive once the heat of reaction is removed, though this mass change is too small to measure with standard equipment. In nuclear reactions , the fraction of mass that may be removed as light or heat, i.e. binding energy,

931-403: The (rest) masses of the (non-excited) nuclides involved in such calculations. Wavenumber In the physical sciences , the wavenumber (or wave number ), also known as repetency , is the spatial frequency of a wave , measured in cycles per unit distance ( ordinary wavenumber ) or radians per unit distance ( angular wavenumber ). It is analogous to temporal frequency , which

980-463: The 5 - 30 keV range are feasible for lab based EXAFS studies. XAS is an interdisciplinary technique and its unique properties, as compared to x-ray diffraction, have been exploited for understanding the details of local structure in: XAS provides complementary to diffraction information on peculiarities of local structural and thermal disorder in crystalline and multi-component materials. The use of atomistic simulations such as molecular dynamics or

1029-404: The amount of each of the known standard spectra within an unknown sample. The dominant physical process in x-ray absorption is one where the absorbed photon ejects a core photoelectron from the absorbing atom, leaving behind a core hole. The ejected photoelectron's energy will be equal to that of the absorbed photon minus the binding energy of the initial core state. The atom with the core hole

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1078-1016: The atom's relative displacements, λ ( k ) {\displaystyle \lambda (k)} is the mean free path of the photoelectron with momentum k {\displaystyle k} (this is related to coherence of the quantum state), and f j ( k ) {\displaystyle f_{j}(k)} is an element dependent scattering factor. χ ( k ) = ∑ j N j e − 2 k 2 σ j 2 e − 2 R j / λ k f j ( k ) k R j 2 sin ⁡ [ 2 k R j + δ j ( k ) ] {\displaystyle \chi (k)=\sum _{j}{\frac {N_{j}e^{-2k^{2}\sigma _{j}^{2}}e^{-2R_{j}/\lambda _{k}}f_{j}(k)}{kR_{j}^{2}}}\sin[2kR_{j}+\delta _{j}(k)]} The origin of

1127-441: The attenuation constant is positive, then the wave amplitude decreases as the wave propagates in the x-direction. Wavelength , phase velocity , and skin depth have simple relationships to the components of the wavenumber: Here we assume that the wave is regular in the sense that the different quantities describing the wave such as the wavelength, frequency and thus the wavenumber are constants. See wavepacket for discussion of

1176-474: The case of a free particle, that is, the particle has no potential energy): Here p is the momentum of the particle, m is the mass of the particle, E is the kinetic energy of the particle, and ħ is the reduced Planck constant . Wavenumber is also used to define the group velocity . In spectroscopy , "wavenumber" ν ~ {\displaystyle {\tilde {\nu }}} (in reciprocal centimeters , cm ) refers to

1225-413: The case when these quantities are not constant. In general, the angular wavenumber k (i.e. the magnitude of the wave vector ) is given by where ν is the frequency of the wave, λ is the wavelength, ω = 2 πν is the angular frequency of the wave, and v p is the phase velocity of the wave. The dependence of the wavenumber on the frequency (or more commonly the frequency on the wavenumber)

1274-473: The energy to escape the gravity is dissipated in the collision, the parts will oscillate at a closer, possibly atomic, distance, thus looking like one solid object. This lost energy, necessary to overcome the potential barrier to separate the objects, is the binding energy. If this binding energy were retained in the system as heat, its mass would not decrease, whereas binding energy lost from the system as heat radiation would itself have mass. It directly represents

1323-408: The high intensity of synchrotron X-ray sources allows the concentration of the absorbing element to reach as low as a few parts per million. Absorption would be undetectable if the source were too weak. Because X-rays are highly penetrating, XAS samples can be gases, solids or liquids. EXAFS spectra are displayed as plots of the absorption coefficient of a given material versus energy , typically in

1372-422: The initial nuclide(s), from that of the fission or fusion products. In practice, this energy may also be calculated from the substantial mass differences between the fuel and products, which uses previous measurements of the atomic masses of known nuclides, which always have the same mass for each species. This mass difference appears once evolved heat and radiation have been removed, which is required for measuring

1421-423: The kinetic energy of an ejected particle, such as an electron, in internal conversion decay; or partly as the rest mass of one or more emitted particles, such as the particles of beta decay . No mass deficit can appear, in theory, until this radiation or this energy has been emitted and is no longer part of the system. When nucleons bind together to form a nucleus, they must lose a small amount of mass, i.e. there

1470-418: The measured absorption coefficient, thereby causing the oscillation in the EXAFS spectra. A simplified plane-wave single-scattering theory has been used for interpretation of EXAFS spectra for many years, although modern methods (like FEFF, GNXAS) have shown that curved-wave corrections and multiple-scattering effects can not be neglected. The photelectron scattering amplitude in the low energy range (5-200 eV) of

1519-415: The nucleus to be broken up into individual nucleons. For example, an atom of deuterium has a mass defect of 0.0023884 Da, and its binding energy is nearly equal to 2.23 MeV. This means that energy of 2.23 MeV is required to disintegrate an atom of deuterium. The energy given off during either nuclear fusion or nuclear fission is the difference of the binding energies of the "fuel", i.e.

Extended X-ray absorption fine structure - Misplaced Pages Continue

1568-414: The number of atoms at distance R j {\displaystyle R_{j}} , k {\displaystyle k} is the wavenumber and is proportional to energy, σ {\displaystyle \sigma } is the thermal vibration factor with σ j 2 {\displaystyle \sigma _{j}^{2}} being the mean square amplitude of

1617-420: The oscillations in the absorption cross section are due to the sin {\displaystyle \sin } term which imposes the interference condition, leading to peaks in absorption when the wavelength of the photoelectron is equal to an integer fraction of 2 R j {\displaystyle 2R_{j}} (the round trip distance from the absorbing atom to the scattering atom). This

1666-459: The particles either pass through each other without interaction or elastically repel during the collision, the gained kinetic energy (related to speed) begins to revert into potential energy, driving the collided particles apart. The decelerating particles will return to the initial distance and beyond into infinity, or stop and repeat the collision (oscillation takes place). This shows that the system, which loses no energy, does not combine (bind) into

1715-470: The photoelectron kinetic energy become much larger so that multiple scattering events become dominant in the XANES (or NEXAFS) spectra. The wavelength of the photoelectron is dependent on the energy and phase of the backscattered wave which exists at the central atom. The wavelength changes as a function of the energy of the incoming photon. The phase and amplitude of the backscattered wave are dependent on

1764-406: The process of binding, the constituents of the system might enter higher energy states of the nucleus/atom/molecule while retaining their mass, and because of this, it is necessary that they are removed from the system before its mass can decrease. Once the system cools to normal temperatures and returns to ground states regarding energy levels, it will contain less mass than when it first combined and

1813-436: The propagation of pollutants through an ecosystem . EXAFS can be used along with accelerator mass spectrometry in forensic examinations, particularly in nuclear non-proliferation applications. A very detailed, balanced and informative account about the history of EXAFS (originally called Kossel's structures) is given by R. Stumm von Bordwehr . A more modern and accurate account of the history of XAFS (EXAFS and XANES)

1862-543: The purpose. The utility of a particular synchrotron to study a particular solid depends on the brightness of the x-ray flux at the absorption edges of the relevant elements. Recent developments in the design and quality of crystal optics have allowed for some EXAFS measurements to take place in a lab setting, where the tunable x-ray source is achieved via a Rowland circle geometry. While experiments requiring high x-ray flux or specialized sample environments can still only be performed at synchrotron facilities, absorption edges in

1911-725: The same in air, and so the spectroscopic wavenumber is directly related to the angles of light scattered from diffraction gratings and the distance between fringes in interferometers , when those instruments are operated in air or vacuum. Such wavenumbers were first used in the calculations of Johannes Rydberg in the 1880s. The Rydberg–Ritz combination principle of 1908 was also formulated in terms of wavenumbers. A few years later spectral lines could be understood in quantum theory as differences between energy levels, energy being proportional to wavenumber, or frequency. However, spectroscopic data kept being tabulated in terms of spectroscopic wavenumber rather than frequency or energy. For example,

1960-474: The size of a bound system, the higher its associated binding energy. The chromodynamic binding energy of a proton is about 928.9 MeV, while that of a neutron is about 927.7 MeV. Large binding energy between bottom quarks (280 MeV) causes some (theoretically expected) reactions with lambda baryons to release 138 MeV per event. A bound system is typically at a lower energy level than its unbound constituents because its mass must be less than

2009-519: The spectroscopic wavenumbers of the emission spectrum of atomic hydrogen are given by the Rydberg formula : where R is the Rydberg constant , and n i and n f are the principal quantum numbers of the initial and final levels respectively ( n i is greater than n f for emission). A spectroscopic wavenumber can be converted into energy per photon E by Planck's relation : It can also be converted into wavelength of light: where n

Extended X-ray absorption fine structure - Misplaced Pages Continue

2058-399: The term separation energy is used. A bound system is typically at a lower energy level than its unbound constituents. According to relativity theory, a Δ E decrease in the total energy of a system is accompanied by a decrease Δ m in the total mass, where Δ mc = Δ E . There are several types of binding energy, each operating over a different distance and energy scale. The smaller

2107-449: The total mass of its unbound constituents. For systems with low binding energies, this "lost" mass after binding may be fractionally small, whereas for systems with high binding energies, the missing mass may be an easily measurable fraction. This missing mass may be lost during the process of binding as energy in the form of heat or light, with the removed energy corresponding to the removed mass through Einstein's equation E = mc . In

2156-407: The type of atom doing the backscattering and the distance of the backscattering atom from the central atom. The dependence of the scattering on atomic species makes it possible to obtain information pertaining to the chemical coordination environment of the original absorbing (centrally excited) atom by analyzing these EXAFS data. The effect of the backscattered photoelectron on the absorption spectra

2205-424: The unbound system calculated mass and experimentally measured mass of nucleus (mass change) is denoted as Δ m . It can be calculated as follows: After a nuclear reaction occurs that results in an excited nucleus, the energy that must be radiated or otherwise removed as binding energy in order to decay to the unexcited state may be in one of several forms. This may be electromagnetic waves, such as gamma radiation ;

2254-632: The unit radian per meter (rad⋅m ), or as above, since the radian is dimensionless . For electromagnetic radiation in vacuum, wavenumber is directly proportional to frequency and to photon energy. Because of this, wavenumbers are used as a convenient unit of energy in spectroscopy. A complex-valued wavenumber can be defined for a medium with complex-valued relative permittivity ε r {\displaystyle \varepsilon _{r}} , relative permeability μ r {\displaystyle \mu _{r}} and refraction index n as: where k 0

2303-570: The value of E0 (on the absorption edge). The normalized absorption spectra are often called XANES spectra. These spectra can be used to determine the average oxidation state of the element in the sample. The XANES spectra are also sensitive to the coordination environment of the absorbing atom in the sample. Finger printing methods have been used to match the XANES spectra of an unknown sample to those of known "standards". Linear combination fitting of several different standard spectra can give an estimate to

2352-461: The wavenumber multiplied by the reduced Planck constant is the canonical momentum . Wavenumber can be used to specify quantities other than spatial frequency. For example, in optical spectroscopy , it is often used as a unit of temporal frequency assuming a certain speed of light . Wavenumber, as used in spectroscopy and most chemistry fields, is defined as the number of wavelengths per unit distance, typically centimeters (cm ): where λ

2401-507: Was at high energy. This loss of heat represents the "mass deficit", and the heat itself retains the mass that was lost (from the point of view of the initial system). This mass will appear in any other system that absorbs the heat and gains thermal energy. For example, if two objects are attracting each other in space through their gravitational field , the attraction force accelerates the objects, increasing their velocity, which converts their potential energy (gravity) into kinetic energy. When

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