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Absorption edge

An absorption edge is a sharp discontinuity in the X-ray absorption spectrum of a material, marking the energy threshold where the absorption coefficient abruptly increases due to the excitation or ejection of a core electron from an atomic shell into unoccupied higher-energy states or the continuum.^[1] This phenomenon arises from the photoelectric effect, where incident X-ray photons with energy equal to or exceeding the binding energy of the core electron are absorbed, leading to a sudden rise in absorption as the photon energy crosses the edge.^[2] The position of the edge is element-specific, corresponding to the binding energies of inner-shell electrons, and serves as a fundamental feature in techniques like X-ray absorption spectroscopy (XAS).^[1] Absorption edges are classified by the principal quantum number of the ejected electron's shell: the K-edge involves the 1s orbital (typically at higher energies, e.g., ~7 keV for iron and ~9 keV for copper), L-edges involve 2s or 2p orbitals (e.g., ~930 eV for copper L-edges), and M-edges involve 3s or 3p orbitals (e.g., 70–120 eV for copper).^[1] These edges exhibit fine structure near the threshold, known as X-ray absorption near-edge structure (XANES), which spans about the first 30–50 eV above the edge and reflects transitions to bound states influenced by the local electronic environment.^[3] The edge energy can shift with changes in the atom's oxidation state or coordination, providing sensitive probes of chemical speciation—for instance, higher oxidation states shift the edge to higher energies due to increased effective nuclear charge.^[1]^[2] In scientific applications, absorption edges enable element identification, as each element has unique edge energies across the periodic table, and facilitate detailed analysis of local atomic structure without requiring long-range order, making XAS ideal for disordered systems like liquids, gases, or amorphous solids.^[2] They are crucial in XANES for determining oxidation states, coordination geometries, and ligand types around absorbing atoms, with applications in catalysis, environmental science, battery materials, and biological systems—such as probing metal centers in proteins or tracking redox changes in operando studies.^[1]^[4] Beyond the near-edge region, extended X-ray absorption fine structure (EXAFS) extends analysis to interatomic distances and coordination numbers, enhancing structural insights up to several angstroms from the absorber.^[5] This versatility has made absorption edge spectroscopy a cornerstone of synchrotron-based research since the 1970s, offering non-destructive, element-selective characterization at ambient conditions.^[1]

Fundamentals

Definition

An absorption edge refers to a sharp discontinuity or abrupt increase in the absorption coefficient (μ) of a material at a specific photon energy, marking the onset of a new absorption channel due to the excitation or ionization of bound electrons.^[6] This phenomenon manifests as a sudden jump in absorption, contrasting with the smoother variation observed elsewhere in the spectrum.^[1] Absorption edges primarily appear in the X-ray region of the electromagnetic spectrum, where photon energies align with the binding energies of inner-shell electrons, enabling transitions to unoccupied states or the continuum.^[6] Far from the edge, the photoelectric absorption coefficient typically decreases with increasing photon energy according to the relation μ ∝ 1/E³, where E is the photon energy, highlighting the distinct threshold behavior at the edge. In contrast to gradual, continuous absorption processes, absorption edges are highly element-specific, each corresponding to the characteristic binding energies of electrons in particular atomic shells, such as the K-shell or L-shell.^[7] This specificity arises from the photoelectric effect, with edge types like K-edges (for 1s electrons) and L-edges (for 2p electrons) providing fingerprints for elemental identification in spectroscopy.^[1]

Historical Discovery

The discovery of X-ray absorption edges emerged in the early 20th century, building on foundational observations in X-ray physics. Wilhelm Conrad Röntgen's identification of X-rays in 1895 provided the initial experimental basis for subsequent spectral studies, while Heinrich Hertz's 1887 demonstration of the photoelectric effect hinted at threshold behaviors in radiation-matter interactions, though absorption edges were not specifically noted until later.^[8]^[9] These developments set the stage for detailed absorption experiments post-1910. Preceding the direct observation of absorption edges, Charles Glover Barkla conducted pioneering studies on X-ray emission and absorption between 1908 and 1911, identifying characteristic K and L absorption lines associated with specific elements. Barkla's work revealed distinct series of homogeneous radiations, classifying them as K (more penetrating) and L (less penetrating) based on their absorption properties in various materials, which laid the groundwork for recognizing sharp discontinuities in absorption spectra.^[10]^[11] The first explicit observation of absorption edges occurred in 1913, when Maurice de Broglie reported sharp absorption limits in X-ray spectra while examining photographic emulsions containing silver and bromine; these discontinuities, later identified as K-edges, marked a sudden increase in absorption at specific energies characteristic of the elements involved. De Broglie's photographic recordings demonstrated these edges as abrupt changes in spectral blackening, confirming their elemental specificity and prompting further investigations into atomic structure.^[12]^[13] In the 1920s, Manne Siegbahn advanced the field through refinements in high-resolution X-ray spectroscopy, achieving unprecedented precision in measuring spectral lines and edges using improved spectrographs and vacuum techniques. His work established the Siegbahn notation system for labeling absorption edges and emission lines (e.g., Kα, Lβ), standardizing nomenclature based on relative intensities and wavelengths, which facilitated systematic studies of atomic energy levels.^[14] These milestones directly influenced the evolution of modern X-ray absorption spectroscopy.

Physical Mechanism

Photoelectric Absorption Process

The photoelectric absorption process is the primary mechanism responsible for the characteristic sharp increase in X-ray absorption at an absorption edge. In this interaction, an incident X-ray photon with energy h\nu is completely absorbed by an atom when h\nu exceeds the binding energy E_b of a core-level electron, ejecting the electron as a photoelectron into the continuum while leaving the atom in an ionized state.^[15] For example, in the case of a K-edge, this involves the ionization of a 1s core electron from the K-shell.^[16] The probability of this absorption event rises abruptly at the energy threshold because, below E_b, no continuum states are available for the ejected photoelectron, prohibiting the transition; above the threshold, these unoccupied continuum states become accessible, enabling the process with high efficiency.^[17] This sudden availability of final states for the photoelectron results in the discontinuous jump in the absorption coefficient observed in spectra.^[18] Upon ejection of the core electron, a core hole is created in the initial shell, rendering the atom highly unstable and leading to relaxation through either the emission of an Auger electron or fluorescent X-ray photon as higher-shell electrons fill the vacancy; however, the initial absorption jump itself stems directly from the photoelectric ejection step.^[19] This core-hole formation is a hallmark of the process, distinguishing it from other photon-matter interactions like Compton scattering. The energies at which these absorption edges occur for inner shells, such as K or L, scale approximately with the square of the atomic number Z, following an empirical relation akin to Moseley's law: E \propto (Z - \sigma)^2, where \sigma is a screening constant accounting for electron shielding.^[20] This Z^2 dependence arises from the increased nuclear charge pulling core electrons closer, raising their binding energies progressively with atomic number.^[16]

Energy Threshold and Jump

The energy threshold of an absorption edge marks the photon energy at which the absorption coefficient exhibits a sharp discontinuity, corresponding to the onset of photoelectric ejection of a core electron into the continuum. This threshold is experimentally defined as the energy where the absorption intensity reaches 50% of the total edge jump, slightly above the core-level binding energy E_b to account for the minimal kinetic energy imparted to the photoelectron at the onset.^[21] The position arises from the photoelectric absorption process, where photon energies below E_b cannot excite the core electron, resulting in no additional absorption channel. The magnitude of the discontinuity, known as the absorption jump, quantifies the increase in the absorption coefficient across the edge and depends on the occupancy of the core shell and selection rules governing transitions. For a given shell, the jump is approximately proportional to the number of electrons in the shell, reflecting the statistical availability for excitation. For instance, in K-edges, where the 1s shell holds 2 electrons for most elements, the jump typically results in a significant increase, often roughly doubling the absorption coefficient.^[22]/Spectroscopy/X-ray_Spectroscopy/XANES) The shape of the absorption edge is influenced by broadening effects that smear the ideal step-like discontinuity. Lifetime broadening from the finite core-hole lifetime introduces a Lorentzian tails to the edge profile, while thermal effects cause additional smearing through vibrational coupling and Doppler shifts in the Fermi edge singularity near the threshold. Above the edge, for photon energies well exceeding E_b, the absorption coefficient decreases asymptotically as \mu(E) \propto 1/E^{3.5}, governed by the atomic photoelectric cross-section scaling approximately with the fourth to fifth power of the atomic number and as $1/E^{3.5}.^[23] Chemical shifts in the edge position, arising from variations in the local electronic environment, typically range from 1 to 10 eV and reflect changes in oxidation state or bonding coordination, though these are secondary to the primary threshold defined by E_b.^[23]

Classification

K-edges

The K-edge in X-ray absorption spectroscopy corresponds to the ionization of a core electron from the 1s orbital, the innermost K-shell, where the photon energy exceeds the binding energy of this tightly bound electron, leading to a sharp increase in absorption.^[24] This process excites the 1s electron to unoccupied valence orbitals or the continuum, marking the onset of the absorption edge. The binding energies for K-shell electrons vary significantly across the periodic table, ranging from approximately 0.055 keV for lithium (Li) to about 116 keV for uranium (U), reflecting the increasing nuclear charge and relativistic effects in heavier elements.^[25] The transitions at the K-edge obey electric dipole selection rules, with Δl = ±1, allowing excitations from the s-like 1s initial state primarily to np final states, resulting in strong dipole-allowed absorption intensities.^[26] These rules ensure that the near-edge structure is dominated by transitions to p-character orbitals in the valence band, providing sensitivity to the local electronic environment around the absorbing atom. A representative example is the copper (Cu) K-edge, located at 8.98 keV, which serves as a standard reference in X-ray absorption spectra for calibration and comparison due to its well-characterized position and features.^[27] This edge is commonly observed in studies of copper-containing materials, where its precise energy aids in normalizing spectra across experiments. K-edges exhibit the sharpest absorption profiles among core-level edges owing to the deep binding of the 1s electron, which results in a longer core-hole lifetime and reduced natural linewidth broadening. Additionally, the 1s core level has minimal spin-orbit splitting, as it is an s-orbital with l=0, producing a single, unsplit edge without the multiplicity seen in higher-shell edges like L-edges for elements with higher atomic numbers.^[16]

L-edges and M-edges

L-edges arise from the photoionization of core electrons in the L-shell, specifically the 2s orbital (denoted as L_I) and the 2p orbitals (L_{II} for 2p_{1/2} and L_{III} for 2p_{3/2}). These edges typically occur at energies ranging from a few tens of eV in light elements (e.g., 73 eV for the aluminum L_{III} edge) to around 21 keV in heavy elements. For instance, the iron (Fe) L_{III} edge is at 0.708 keV.^[28] The L_{III} edge is generally the most intense due to the higher statistical weight and degeneracy of the 2p_{3/2} subshell, which accommodates four electrons compared to two in the 2p_{1/2} and 2s subshells.^[1] The L_{II} and L_{III} edges exhibit spin-orbit splitting, resulting from the interaction between the electron's spin and orbital angular momentum; this separation is typically on the order of 10–100 eV in medium-Z elements but increases significantly in heavy elements due to stronger relativistic influences. For instance, in lead (Pb, Z=82), the L_{III} edge is located at 13.035 keV, while the L_{II} edge is at 15.200 keV, yielding a splitting of about 2.165 keV.^[28] M-edges correspond to the ionization of electrons from the M-shell, primarily involving the 3s (M_I) and 3p (M_{II} for 3p_{1/2}, M_{III} for 3p_{3/2}) subshells, with additional complexity from 3d orbitals (M_{IV} for 3d_{3/2}, M_V for 3d_{5/2}). These edges probe softer X-rays, with energies spanning roughly 0.1–5 keV, as seen in examples like copper (Cu M edges around 0.07–0.12 keV) and lead (Pb M_V at 2.484 keV). The multiple components make M-edges more intricate than L-edges, labeled using the Siegbahn notation based on historical intensity ordering of emission lines.^[28]^[14] For elements with atomic number Z > 50, relativistic effects play a crucial role in L- and M-edge spectroscopy, enhancing spin-orbit interactions and altering orbital contractions, which become essential for accurate spectral interpretation in heavy elements. Edge energies in these shells scale approximately with Z^2, reflecting the dominant Coulombic binding in inner shells.^[29]^[17]

Observation and Techniques

X-ray Absorption Spectroscopy

X-ray Absorption Spectroscopy (XAS) is a technique that probes the local electronic and structural environment of atoms by measuring the absorption of X-rays as a function of photon energy, particularly across absorption edges. It operates by tuning the incident X-ray energy through the binding energy of core electrons, where a sharp increase in absorption occurs as the photon energy exceeds the threshold for ejecting these electrons. This measurement can be performed in transmission mode, where the absorption coefficient μ(E) is determined from the ratio of incident to transmitted intensity (μ(E) = ln(I₀/I_t)), or in fluorescence mode, where μ(E) is proportional to the fluorescence yield relative to the incident intensity (μ(E) ∝ I_f/I₀). The positions of these absorption edges are unique to each element, enabling precise identification based on the atomic number, as edge energies scale approximately with Z² for K-edges.^[30]^[31] The XAS spectrum is divided into distinct regions relative to the absorption edge. The pre-edge region features weak absorption due to forbidden transitions, such as 1s to 3d, which are typically less than 1% of the main edge intensity and provide insights into local symmetry. At the edge energy, a sudden discontinuity known as the edge jump occurs, marking the onset of strong photoelectric absorption. Immediately above the edge, the X-ray Absorption Near Edge Structure (XANES) extends roughly 30 eV and captures multiple scattering effects that reveal oxidation states and coordination geometries. Further out, the Extended X-ray Absorption Fine Structure (EXAFS) oscillates up to about 1000 eV above the edge, arising from single and multiple scattering of the ejected photoelectron by neighboring atoms, allowing determination of interatomic distances and coordination numbers up to several angstroms.^[32]^[30]^[31] One of the key advantages of XAS is its element-specific nature, as it selectively probes a single element's absorption edge regardless of the sample matrix, making it ideal for studying dilute species down to parts per million concentrations. It is inherently bulk-sensitive due to the penetrating power of hard X-rays, providing information averaged over the sample volume illuminated by the beam. Additionally, XAS is versatile for in situ experiments under extreme conditions, such as high pressure, elevated temperatures, or dynamic processes like catalysis, without requiring long-range order in the sample.^[30]^[31]^[32] For analysis and comparison, XAS spectra are typically normalized to account for variations in sample thickness or beam intensity. The raw μ(E) is often scaled such that the pre-edge absorption is set to zero and the post-edge region (beyond EXAFS) approaches unity, or normalized relative to the edge jump magnitude to highlight relative changes in absorption. This normalization facilitates quantitative extraction of structural parameters and comparison across samples or conditions.^[30]^[31]

Experimental Methods

Experimental methods for detecting and characterizing absorption edges primarily involve X-ray absorption spectroscopy (XAS) setups that measure the sharp increase in X-ray absorption at specific photon energies corresponding to core electron excitations. These methods rely on high-intensity, tunable X-ray sources to scan across the edge energy with sufficient resolution to resolve the discontinuity.^[33] In transmission mode, the absorption is quantified by measuring the ratio of transmitted intensity I_t to incident intensity I_0, yielding the absorption coefficient \mu(E) = \ln(I_0 / I_t). Ionization chambers detect I_0 before the sample and I_t after, with the sample oriented perpendicular to the beam. This mode is ideal for concentrated samples where the product of absorption coefficient and thickness satisfies \mu x \approx 1 to 2.5, ensuring optimal signal without excessive attenuation; for example, iron foils of about 7–10 \mum thickness are commonly used for Fe K-edge measurements. Homogeneous, thin samples minimize artifacts from inhomogeneities.^[33]^[17] Fluorescence mode detects the characteristic X-ray fluorescence emitted by the sample following core electron excitation, with intensity I_f proportional to the absorption cross-section for dilute systems. A solid-state detector, often positioned at 90° to the beam to exploit X-ray polarization and reduce scatter, collects the fluorescence photons. This approach suits low-concentration analytes (<1 at.%) or thick samples where transmission would be impractical, such as dilute solutions (e.g., 0.0001 M) or heterogeneous materials up to several mm thick. Self-absorption effects must be considered for high concentrations, where the detected signal can be distorted if \mu x > 1.^[33]^[17] Synchrotron radiation sources are essential for these measurements, providing tunable, high-flux X-ray beams with energy resolutions better than 1 eV (typically \Delta E / E \approx 10^{-4}, yielding ~0.1–1 eV at common edge energies like 7–10 keV). Double-crystal monochromators, often using Si(111) or Si(220) crystals, enable precise energy scanning across the edge while maintaining beam stability for high signal-to-noise ratios in short acquisition times (e.g., 30–40 minutes per spectrum). Laboratory sources can be used for preliminary work but lack the flux and tunability for detailed edge characterization.^[33]^[17] Sample preparation is critical to ensure accurate edge detection and minimize distortions. For transmission, samples are prepared as thin, uniform foils, pellets of finely ground powders (<10 \mum grain size) mixed with low-absorbing media like polyethylene, or dilute solutions in cells with thin windows (e.g., Kapton). Fluorescence allows more flexibility, accommodating powders in single layers or solutions without strict thickness control. Edge energies for calibration are referenced from databases such as the NIST X-ray Transition Energies, which provide experimental values for K, L, and M edges across elements. Filters may be inserted to suppress unwanted fluorescence or scatter, enhancing edge visibility.^[33]^[34]

Theoretical Aspects

Quantum Mechanical Explanation

The quantum mechanical description of an absorption edge in X-ray spectroscopy arises from the interaction of an incident photon with a core electron, leading to its excitation into unoccupied continuum states when the photon energy exceeds the binding energy of that core level. This process is fundamentally governed by Fermi's golden rule, which provides the transition rate W from an initial state |i\rangle to a final state |f\rangle as W \propto |\langle f | \hat{H} | i \rangle|^2 \rho(E), where \hat{H} is the interaction Hamiltonian (typically the dipole operator for electric dipole transitions) and \rho(E) is the density of final states.^[35] The sharp onset of the absorption edge occurs because \rho(E) jumps abruptly at the threshold energy, corresponding to the availability of continuum states for the ejected photoelectron, resulting in a discontinuous increase in the absorption cross-section.^[36] The shape of the absorption edge near the threshold is influenced by the core-hole potential created upon ionization, which modifies the local electronic environment. In the sudden approximation, valid for high-energy photoelectrons (typically >10 eV above the edge), the core-hole is assumed to form instantaneously compared to the relaxation time of the surrounding electrons, allowing the photoelectron wavefunction to be described as a plane wave scattered by the sudden potential of the ionized atom. This approximation determines the edge profile through the transition matrix element \langle f | \hat{H} | i \rangle, which depends on the overlap between the initial core orbital and the final continuum states, modulated by the centrifugal barrier and phase shifts in the outgoing photoelectron wave.^[37] For lighter elements, the edge often exhibits an arctangent-like form due to the s-character of K-shell electrons, while p- or d-like orbitals in L- or M-edges introduce additional structure from angular momentum selection rules. Multi-electron effects introduce complexities beyond the single-particle picture, particularly through shake-up processes where the sudden creation of the core-hole causes valence electrons to be excited to higher unoccupied states during ionization. These shake-up satellites appear as weaker features at higher energies above the main edge, arising from the relaxation of the valence shell in response to the core-hole potential, with intensities proportional to the overlap between the initial ground state and the correlated final states involving valence excitations.^[38] Such effects are more pronounced in systems with partially filled d- or f-shells, where electron correlation enhances the probability of multi-electron transitions. For heavy elements, relativistic effects become significant, requiring the use of the Dirac equation to accurately describe the core orbitals and their interactions. The relativistic treatment incorporates spin-orbit coupling naturally, leading to splitting of the absorption edges (e.g., L2 and L3 edges separated by the spin-orbit interaction energy), which arises from the fine structure in the Dirac hydrogenic wavefunctions and modifies the transition probabilities according to j-dependent selection rules.^[39] This splitting is crucial for elements with Z > 30, where scalar relativistic corrections alone are insufficient, and full four-component Dirac-Fock calculations are needed to predict edge positions and intensities.^[40]

Near-Edge and Extended Fine Structure

The fine structure observed in X-ray absorption spectra immediately above the absorption edge consists of two primary regions: the X-ray absorption near-edge structure (XANES), spanning approximately -20 to +50 eV around the edge energy, and the extended X-ray absorption fine structure (EXAFS), extending beyond about 50 eV above the edge.^[1]^[30] XANES arises from multiple scattering of the ejected photoelectron within the local atomic environment, providing insights into the absorber atom's coordination geometry, bond angles, and oxidation state, as the interference patterns are sensitive to the potential felt by the photoelectron in the near-edge region.^[1]^[41] In contrast, EXAFS originates from single and multiple scattering events at higher energies, where the photoelectron behaves more like a plane wave, allowing quantitative determination of interatomic distances and coordination numbers in the first few atomic shells surrounding the absorbing atom.^[17]^[31] The EXAFS signal, denoted as the oscillatory function χ(k), is typically modeled using the single-scattering approximation for simplicity, given by:

\chi(k) = \sum_j S_0^2 N_j e^{-2k^2 \sigma_j^2} e^{-2R_j / \lambda(k)} \frac{f_j(k)}{k R_j^2} \sin[2k R_j + \delta_j(k)]

where k is the photoelectron wavevector, the sum is over scattering shells j, S_0^2 is the amplitude reduction factor, N_j is the coordination number of atoms at distance R_j, \sigma_j^2 accounts for thermal and structural disorder (Debye-Waller factor), \lambda(k) is the photoelectron mean free path, f_j(k) is the backscattering amplitude from the neighboring atoms, and \delta_j(k) represents the total phase shift due to the backscattering and the muffin-tin potential around the absorber.^[17]^[31] Analysis of EXAFS data involves extracting χ(k) from the measured absorption spectrum μ(E) after normalization and background subtraction, followed by a Fourier transform to obtain the radial distribution function in real space, which peaks at effective distances related to bond lengths R.^[17]^[31] The phase shifts \delta_j(k) are theoretically calculated or empirically determined from known standards to refine the structural parameters, enabling the identification of scattering atom types through their backscattering amplitudes.^[42] A key limitation of EXAFS arises from the finite mean free path of the photoelectron, typically 5-10 Å, which causes exponential damping of the signal at high k values (beyond ~15-20 Å⁻¹), restricting reliable structural information to the nearest-neighbor shells and introducing errors in longer-range disorder modeling.^[31]^[17] These oscillations fundamentally stem from quantum interference between the outgoing and backscattered photoelectron waves, as described in the multiple-scattering formalism.^[1]

Applications

Material and Chemical Analysis

Absorption edges play a crucial role in material and chemical analysis through techniques like X-ray absorption spectroscopy (XAS), which probes local atomic environments without requiring long-range order. Extended X-ray absorption fine structure (EXAFS) analysis of oscillations beyond the absorption edge enables determination of bond lengths, coordination numbers, and disorder in various materials. For instance, in catalysts, EXAFS has revealed Pt-Pd interatomic distances in bimetallic alloys, aiding optimization of hydrogenation reactions. In nanomaterials, EXAFS quantifies size-dependent structural changes, such as reduced coordination numbers in smaller CdS nanocrystals (13–120 Å diameter), reflecting surface effects and dynamic properties. Similarly, in high-entropy alloys, EXAFS identifies local coordination around elements like Co and Ni, confirming short-range order in complex multicomponent systems.^[43]^[44]^[45] Chemical speciation leverages shifts in the absorption edge position and features in X-ray absorption near-edge structure (XANES) to infer oxidation states and local symmetry. Edge shifts to higher energies indicate increased valence; for example, XANES distinguishes Fe²⁺ from Fe³⁺ in silicate minerals by analyzing pre-edge features sensitive to coordination environment. In catalysts, XANES tracks valence changes, such as V⁵⁺ to V⁴⁺ transitions in vanadia-ceria systems during ethane oxidative dehydrogenation. This approach also reveals symmetry distortions, like octahedral versus tetrahedral coordination in transition metal oxides.^[46]^[43] Specific applications highlight these capabilities in advanced materials. In quantum dots, EXAFS coordination analysis correlates island size with Ga-As bonding in multi-layered structures, where increased coordination numbers reflect larger average sizes from additional deposited layers. For Li-ion batteries, operando XAS monitors electrode evolution, such as phase transformations in iron oxide composites during cycling, revealing metallic nanoparticle formation (~1 nm) and capacity fading mechanisms. In geochemistry, XAS determines trace metal speciation in soils, identifying Fe as primarily octahedral in boreal catchment samples and associating speciation with organic matter interactions, which informs environmental mobility.^[47]^[48]^[49]

Medical and Astrophysical Uses

In medical imaging, absorption edges play a crucial role in enhancing contrast and enabling spectral differentiation in computed tomography (CT) techniques. K-edge imaging leverages the sharp increase in X-ray absorption at the K-shell binding energy of high atomic number elements to separate materials based on their unique absorption profiles. For instance, dual-energy CT exploits the K-edge of contrast agents to improve tissue characterization and reduce artifacts, allowing for virtual monoenergetic reconstructions that minimize beam hardening effects.^[50] Contrast agents such as iodine, with a K-edge at 33.2 keV, are widely used in diagnostic CT due to their strong photoelectric absorption in the lower energy range of clinical X-ray beams (typically 40-140 keV), providing high contrast for vascular and soft tissue imaging. Gadolinium-based agents, featuring a K-edge at 50.2 keV, offer similar benefits but are tuned to higher beam energies, enabling better penetration in thicker body regions and potential applications in photon-counting CT for multi-contrast imaging. These agents allow for material decomposition, distinguishing iodine or gadolinium from bone or iodine-like attenuators, thus improving diagnostic accuracy in procedures like angiography.^[50]^[51]^[52] Beam filtration in medical X-ray systems utilizes materials with K-absorption edges positioned above the diagnostic energy spectrum to preferentially attenuate low-energy photons, thereby hardening the beam and reducing patient dose while maintaining image quality. K-shell edge filters, such as those made from elements like cerium or samarium, create a sharp drop in transmission just above their K-edge, effectively shaping the polychromatic spectrum to mimic higher-energy, more uniform beams suitable for CT and radiography. This approach minimizes scatter and improves contrast-to-noise ratios in clinical settings.^[53] In astrophysics, absorption edges manifest as prominent features in X-ray spectra from cosmic plasmas and accretion processes, providing insights into elemental composition, temperature, and ionization states. The iron K-edge at 7.1 keV is particularly diagnostic, appearing as an absorption discontinuity in spectra from hot accretion disks around black holes and neutron stars, where fluorescent iron lines arise from X-ray illumination of circumnuclear material. Observations of these edges, such as in active galactic nuclei, reveal the geometry and density of the reflecting accretion disk, with the edge energy shifting slightly due to relativistic effects or ionization.^[54]^[55] X-ray absorption fine structure (XAFS) spectroscopy, which probes absorption edges, is instrumental in biological applications for elucidating the structure and function of metalloprotein active sites. In hemoglobin, Fe K-edge XAFS reveals the coordination environment of the heme iron, showing six-coordinate octahedral geometry with nitrogen ligands from porphyrin and a distal oxygen in oxyhemoglobin, which informs oxygen binding mechanisms. Similarly, Mo K-edge XAFS on the iron-molybdenum cofactor (FeMo-co) of nitrogenase demonstrates the molybdenum's ligation by homocitrate and sulfur bridges to iron atoms, highlighting the cofactor's role in N2 reduction and enabling studies of its electronic structure during catalysis. These techniques identify elements via their edge positions while providing local structural details essential for understanding enzymatic activity.^[56]^[57]^[58]

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K- and L-edge X-ray Absorption Spectroscopy (XAS) and Resonant ...
This review gives an overview of the application of metal K-edge and L-edge X-ray absorption spectroscopy (XAS), as well as K resonant inelastic X-ray ...
[25]
[PDF] Table 1-1. Electron binding energies, in electron volts, for the ...
Electron binding energies, in electron volts, for the elements in their natural forms. Element. K 1s. L1 2s. L2 2p1/2. L3 2p3/2. M1 3s.
[26]
[PDF] Synchrotron X-ray Absorption Spectroscopy
Thus, comparing high and low energy edges, we expect the higher energy edge to have shorter core hole lifetimes (Δt) and correspondingly broader experimental ...Missing: smearing | Show results with:smearing
[27]
Single-pulse (100 ps) extended x-ray absorption fine structure ...
Aug 21, 2020 · Normalized absorption spectra under ambient conditions for (a) Cu (K-edge 8.98 keV) and (b) Au (L3-edge 11.92 keV). For both plots, the ...
[28]
Anomalous Scattering Differences - RuppWeb
List of selected X-ray absorption edge energies (in electron volt, eV). Element. Atomic Number. Atomic Weight. K Edge. L1 Edge. L2 Edge. L3 Edge. M1 Edge.
[29]
Accurate X-ray Absorption Spectra near L- and M-Edges from ...
Dec 27, 2021 · In this work, we show that accurate X-ray absorption spectra near L 2,3 - and M 4,5 -edges of closed-shell transition metal and actinide compounds
[30]
[PDF] Introduction to X-ray Absorption Spectroscopy
Sep 30, 2015 · the edge position shifts to higher energy. XAS is a direct measure of valence state. Since each element has its own edge energy, an element's ...Missing: definition | Show results with:definition
[31]
[PDF] Fundamentals of XAFS - CARS
When the incident X-ray has an energy equal to that of the binding energy of a core- level electron, there is a sharp rise in absorption: an absorption edge ...<|control11|><|separator|>
[32]
X-ray absorption spectroscopy - PMC - PubMed Central - NIH
X-ray absorption near-edge structure (XANES) spectra provide detailed information about the oxidation state and coordination environment of the metal atoms (Fig ...
[33]
X-ray Absorption Spectroscopy: Introduction to Experimental ...
Nov 19, 2004 · An x-ray absorption spectrum is typically divided into two energy regions: the X-ray Absorption Near-Edge Structure or XANES region, which ...
[34]
Experimental Edge Energies (Direct, Combined, and Vapor)
X-Ray Transition Energies Database Main Page. Experimental Edge Energies (Direct, Combined, and Vapor). See also non-edge experimental transition energies.
[35]
Golden-rule approach to the soft-x-ray-absorption problem
Dec 15, 1983 · The cross section of the soft-x-ray absorption is derived based on the Fermi golden rule, by summing the transition probabilities over all
[36]
[PDF] Theory of X-Ray Absorption
Jan 19, 2017 · Like all optical and x-ray transitions, the probability of a transition is given by Fermi's golden rule: where ρ f. Density of final states i ...
[37]
Theory of x-ray absorption spectroscopy: A microscopic Bloch ...
Apr 3, 2023 · This process gives rise to sudden absorption edges in the XAS spectrum. To calculate the XANES matrix element, we restrict the quantum ...
[38]
One-electron excitations and shake up satellites in Cu K-edge X-ray ...
The polarized Cu K-edge X-ray Absorption Near Edge Structure (XANES) of La2CuO4 has been interpreted by the multiple scattering approach.
[39]
Ab initio methods for L-edge x-ray absorption spectroscopy featured
These two separate edges arise from the spin–orbit splitting ... Theoretically, spin–orbit coupling terms naturally arise from the relativistic Dirac equation.
[40]
Relativistic Effects in Modeling the Ligand K-Edge X-ray Absorption ...
Mar 11, 2022 · In this study, we examine the effect of explicit inclusion of spin–orbit coupling (SOC) versus scalar relativistic effects on the predicted spectra for heavy- ...
[41]
[PDF] X-RAY ABSORPTION SPECTROSCOPY (XAS)
Jul 11, 2022 · Many edges of many elements show significant edge shifts (binding energy shifts) with oxidation state. ▫ First observation was by Berengren for ...
[42]
[PDF] X-ray Absorption Fine Structure Spectroscopy
Jun 8, 2011 · What is XAFS? • X-ray Absorption Fine Structure spectroscopy uses the x-ray photoelectric effect and the wave.
[43]
X‐ray absorption spectroscopy—XAS, XANES, EXAFS - Iglesias‐Juez
Aug 15, 2021 · Below the absorption edge the spectrum is linear and smooth; it increases sharply at the edge (jump), and then oscillates beyond it. In early ...
[44]
EXAFS Studies on the Size Dependence of Structural and Dynamic ...
Size-dependent structural and dynamic properties of CdS nanocrystals with 13−120 Å diameter and of molecular crystals consisting of three-dimensional ...
[45]
A. Kuzmin, X-ray absorption spectroscopy in high-entropy material ...
Nov 11, 2024 · The XANES region (typically within 30-50 eV of the absorption edge) contains information on the local electronic structure and is sensitive ...
[46]
XANES calibrations for the oxidation state of iron in a silicate glass
Mar 2, 2017 · The general applicability of any XANES calibration for determining oxidation states is limited by variations in the Fe coordination environment, ...
[47]
Microstructure of quantum dots ensembles by EXAFS spectroscopy
Increase of NGa- coordination numbers is determined by the increase of the average islands size as the number of deposited layers in multi-layered structures ...
[48]
Phase evolution of conversion-type electrode for lithium ion batteries
May 20, 2019 · We investigate the capacity fading issue of conversion-type materials by studying phase evolution of iron oxide composited structure during later-stage cycles.
[49]
XAS study of iron speciation in soils and waters from a boreal ...
In this work we have used X-ray absorption spectroscopy (XAS) to study the speciation of Fe in soils and waters from a boreal catchment in northern Sweden. The ...
[50]
New Contrast Media for K-Edge Imaging With Photon-Counting ...
In clinical CT, the K-edge imaging approach can be realized with different dual-energy techniques such as dual-source CT, dual-layer detector CT, rapid kV ...
[51]
K-Edge Imaging Using a Clinical Dual-Source Photon-Counting CT ...
Aug 24, 2025 · Purpose: To evaluate the feasibility and performance of K-edge imaging of iodine (I) and gadolinium (Gd) on a clinically available photon- ...
[52]
K-edge Subtraction Computed Tomography with a Compact ... - Nature
Sep 16, 2019 · The clinical applicability of KES CT at the iodine K-edge is limited due to the strong attenuation of X-rays in the human body at ~33.7 keV X- ...
[53]
Spectral CT Using Multiple Balanced K-Edge Filters - PMC - NIH
The proposed cost-effective system design using multiple balanced K-edge filters can be used to perform spectral CT imaging at clinically relevant flux rates.
[54]
[PDF] Invited Review Broad Iron Lines in Active Galactic Nuclei
X-ray re—ection from the accretion disk produces a cold iron line at 6.4 keV. Since the total photoelectric opacity of the material is large even below the iron ...
[55]
[PDF] X-ray reflected spectra from accretion disk models. II. Diagnostic ...
6.4 keV, produced by transitions of electrons between the 1s and 2p ...
[56]
X-ray absorption spectroscopic investigation of the electronic ... - NIH
X-ray absorption spectroscopy data on solution and crystalline oxy-Hb indicate both geometric and electronic structure differences.Missing: XAFS | Show results with:XAFS
[57]
α-Hemoglobin-stabilizing Protein (AHSP) Perturbs the Proximal ...
To probe the electronic structure and coordination environment around the heme iron more directly, we acquired x-ray absorption spectra at the iron K-edge for ...
[58]
EXAFS reveals two Mo environments in the nitrogenase iron ... - NIH
The [Fe7-S9-Mo-C-homocitrate] iron-molybdenum cofactor (FeMo-co), present at the active site of the Mo nitrogenase, is essential to catalyze the reduction of N2 ...Missing: XAFS | Show results with:XAFS