Physics of electromagnetic radiation in the ~100 eV – 100 keV range and its interaction with matter. Sources: X-ray tubes (Bremsstrahlung + characteristic lines), synchrotron bending magnets and insertion devices (wigglers, undulators),…
x-ray-physics
XFEL SASE: micro-bunching instability in an undulator gives coherent X-rays
Kondratenko-Saldin 1980 / Pellegrini 1992 self-amplified spontaneous emission (SASE): a relativistic electron bunch (γ ≈ 17000 for 9 GeV,…
EXAFS / XANES: Sayers-Stern-Lytle oscillations give local atomic structure
Sayers-Stern-Lytle 1971 extended X-ray-absorption fine structure (EXAFS): above an inner-shell absorption edge (K, L) the photoelectron…
Multilayer X-ray mirror (Bragg reflector, Spiller 1972)
Spiller 1972 multilayer X-ray mirror: alternating layers of high-Z (Mo, W, Ni) and low-Z (Si, C, B₄C) materials with layer-pair thickness d…
Bragg law: 2d sin θ = nλ (W.L. & W.H. Bragg 1913, Nobel 1915)
W.L. Bragg & W.H. Bragg (father-and-son) 1913 Bragg law (Nobel Prize in Physics 1915): X-rays of wavelength λ incident on a crystal with…
Compton shift: Δλ = (h/m_ec)(1 − cos θ) = λ_C(1 − cos θ)
Compton 1923 (Nobel 1927): X-ray photons of wavelength λ scattered by free electrons at rest at angle θ from the incoming direction have…
Thomson cross-section: σ_T = (8π/3)r_e² ≈ 0.6652 barn
Thomson cross-section for elastic low-energy (ℏω ≪ m_ec²) photon-electron scattering: σ_T = (8π/3)r_e², where r_e = e²/(4πε₀ m_e c²) ≈…
Darwin–Prins dynamical diffraction: Takagi-Taupin coupled Helmholtz; Pendellösung oscillation
Darwin-Prins dynamical-diffraction framework — the canonical replacement for the kinematical Bragg approximation when x-ray wavefields in…
Debye–Waller factor e^{−q²⟨u²⟩/6}; characteristic-function of Gaussian displacement
Debye-Waller factor framework — the canonical thermal displacement correction to x-ray scattering amplitudes from crystalline materials…
XANES multiple-scattering: T = V/(1 − V·G₀) Neumann resolvent; EXAFS sin(2kR+2δ) envelope
XANES / EXAFS multiple-scattering framework — the canonical x-ray-absorption-spectroscopy analysis method for extracting local-structure…
Darwin plateau width w_D = 2χ_H/sin(2θ_B); Pendellösung Λ_p = λ·cos θ_B/χ_H
Sympy-exact symbolic witness of the Darwin-Prins dynamical-diffraction width, period, and integrated reflectivity. Setup: χ_H, θ_B, λ…
DW = exp(−q²⟨u²⟩/6); Bloch ⟨u²⟩ = 3ℏ/(2Mω)·coth(ℏω/2kT); ZP ⟨u²⟩_zp = 3ℏ/(2Mω)
Sympy-exact symbolic witness of the Debye-Waller thermal factor and the Bloch formula for the Einstein-model mean-square displacement. …
Neumann T = V/(1 − V·G₀); 3rd-order Taylor T ≈ V + V²·G₀ + V³·G₀²; EXAFS sinusoid
Sympy-exact symbolic witness of the XANES Neumann-series T-matrix and the single-scattering EXAFS envelope. Setup: V, G₀, N_path, S₀, k,…
X-rays (Rontgen 1895)
W Rontgen 1895 (Nobel 1901) X-rays-discovered + medical-imaging; modern XFEL + synchrotron generations 1-4 light-sources.
Moseley (1913)
H Moseley 1913 X-ray characteristic-lines law sqrt(nu) ~ Z; basis of modern atomic-number identification + element-mapping.
Bragg XRD (1913)
W H + W L Bragg 1913 (Nobel 1915) Bragg-law; foundation of crystallography + materials science + structural biology.
Synchrotron (Tantawi 1947)
GE 1947 first synchrotron radiation; modern 4th-gen diffraction-limited storage-rings APS-U + ESRF-EBS Sirius MAX-IV.
Ptychography (Rodenburg 2008)
J Rodenburg 2008 X-ray ptychographic imaging; modern coherent-diffraction-imaging + ML-reconstruction; sub-nm resolution.
Coherent diffraction imaging
H Chapman 2011 LCLS serial-femtosecond crystallography; SFX-MX of membrane-proteins; modern microcrystal + room-T diffraction.
Röntgen X-rays (1895)
W Röntgen 1895 (Nobel 1901) X-rays-discovery; modern modern foundational text + Coolidge tube 1913 + 2024 K-α radiation science.
Bragg's law (1913)
W H Bragg-W L Bragg 1913 (Nobel 1915) Bragg-law nλ=2d sinθ; modern modern foundational text + crystal-structure-determination 100yr+ MX.
Moseley's law (1913)
H Moseley 1913 atomic-number-Z X-ray; modern modern foundational text + Moseley-law + 2024 X-ray-emission compositional-analysis EDS WDS.
Compton effect (1923)
A Compton 1923 (Nobel 1927) λ' = λ + h(1-cos θ)/m_e c; modern modern foundational text + Compton-imaging + 2024 inverse-Compton-source.
Synchrotron radiation (Schwinger 1949)
J Schwinger 1949 (Nobel 1965) synchrotron-radiation calculation; modern modern foundational text + 4th-gen-MAX-IV + 2024…
XFEL (Emma 2010)
P Emma 2010 LCLS first-XFEL; modern modern foundational text + EuXFEL + SACLA + 2024 attosecond-XFEL science MHz repetition.