Atomic disorder in X-ray diffraction

Debye-Waller theory claiming thermal fluctuations cause atomic disorder in X-ray diffraction is superseded by non-thermal disorder as electrons are lost by photoionization under QED induced EM radiation
 
 
Planck law: QM requires heat capacity of the atom to vanish at the nanoscale
Planck law: QM requires heat capacity of the atom to vanish at the nanoscale
 
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PITTSBURGH - March 21, 2017 - PRLog -- .
Introduction

Over a century ago, Debye and Waller explained [1] the reductions in X-ray scattering peaks by atomic disorder created in the perfect lattice by thermal fluctuations. More recently, X-ray diffraction of 100 fs 800 nm optical laser pulse heating 160 nm Ge films showed [2] reflectivity abruptly reduced from that expected by Debye-Waller suggesting the film loses crystalline order by rapid NT melting and not by thermal fluctuations. NT stands for nonthermal. Similarly, 50 nm Bi films under short pulse 800 nm laser heating showed [3] abrupt reduction in surface X-ray reflectivity to liquid phase values over a sub-picosecond time scale suggesting NT melting and not the thermal fluctuations of Debye-Waller are the source of atomic disorder.

But what is the NT mechanism?

Over the past 30 years, the ultrafast NT mechanism remains elusive. Today, NT melting is thought [4] caused by electron-phonon coupling, although the more exotic homogenous nucleation has been considered. The more credible electron-phonon coupling is supported by ab-initio MD simulations. MD stands for molecular dynamics.

In electron-phonon coupling, X-rays are absorbed directly by electrons, produced by intense heating pulses, to high electron temperatures, say Te = 25,000 K or 2.15 eV, that combine with phonons until both reach the melting temperature of the sample. When the density of excited electrons exceeds approximately 11% of the valence electrons, the atoms are directed away from the equilibrium positions, the atomic disorder measured by X-ray diffraction

Problem
In the pulse heating of thin films, both Debye-Waller and NT melting depending in atom temperature are questionable because the Planck law of QM precludes any increase in atom temperatures, let alone high electron Te temperatures because the heat capacity of the atoms through the film thickness vanishes under high EM confinement, the latter a consequence of the high surface-to-volume ratios confine the heat absorbed heat to both film surfaces. QM stands for quantum mechanics, and EM for electromagnetic.

Theory
The Planck law of QM at 300 K giving the average energy <E> of the atom or heat capacity as a function of the EM confinement wavelength λ is depicted in the thumbnail. Classical physics always allows the atom to have heat capacity, depicted by the horizontal line from the macroscale beyond 1000 microns to the nanoscale < 0.1 microns. QM differs by only allowing the atom to have heat capacity for λ > 100 microns, otherwise the atom has diminished heat capacity. Nanoscale films in X-ray diffraction having EM confinement wavelengths λ < 0.1 microns have vanishing heat capacity .

Proposed NT Mechanism
Since the thin films in X-ray diffraction lacking heat capacity cannot conserve laser heat absorbed in both film surfaces by an increase in temperature, QED conserves the surface heat by creating EM radiation having half-wavelength λ/2 = d standing across the thickness d of the thin film. QED stands for quantum electrodynamics, but is a simple form of the complex light-matter interaction proposed by Feynman and others. By simple QED, EM radiation is created from surface heat having Planck energy E = hν, i.e., h is Planck's constant and ν is frequency, ν = (c/n) / λ = c/2nd, where the velocity of light c is corrected for the slower speed in the solid state by the refractive index n of the thin film.

Application
Since QED induced EM radiation in thin films having d < 100 nm is sufficient for photoionization, the electron loss > 11% in the sample [2,3] causes the prompt reduction in reflectivity observed. NT melting does not occur, and instead, the disorder of charged solid atoms in a loosely bound state of Coulomb repulsion mimics melting. Moreover, all lower thin film quantum states, including the surface plasmon resonances commonly observed in the VIS and NIR, are excited by fluorescence. See diverse QED applications at http://www.nanoqed.org/, 2010 – 2017.

Conclusions
QM by the Planck law precludes thermal fluctuations in thin films by Debye-Waller as the source of atomic disorder in X-ray diffraction. Similarly QM denies NT melting based on electron-phonon coupling and homogenous nucleation in superheated solids.

Observations of both reductions in X-ray scattering peaks and reflectivity in thin films is caused by atomic disorder from the simple QED conversion of heat absorbed from exciting laser and X-ray pulses into EM radiation that ionizes the film atoms.

NT melting by electron-phonon coupling based on ab-initio MD simulations that admit to temperature changes in thin films contrary to the Planck law needs to be reviewed.

References
[1]P. Debye, "Interferenz von Röntgenstrahlen und Wärmebewegung," Annalen der Physik, 348, 49–92, 1913.
[2]C. W. Siders, et al., "Detection of Nonthermal Melting by Ultrafast X-ray Diffraction," Science, 286,1999.
[3] K. Sokolowski-Tinten, et al., "Femtosecond X-ray measurement of coherent lattice vibrations near the Lindemann stability limit," Nature, 422,287-9,2003.
[4] T. Zier, et al., "Signatures of nonthermal melting," Structural Dynamics, 2, 054101, 2015.
End
Source:QED Radiations
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