Chemical and Nuclear Catalysis Mediated by the Energy Localization - PowerPoint PPT Presentation

Chemical and Nuclear Catalysis Mediated by the Energy Localization in Hydrogenated Crystals and Quasicrystals Vladimir Dubinko 1,3 , Denis Laptev 2,3 , Valeriy Borysenko 1,3 , Oleksii Dmytrenko 1,3 , Klee Irwin 3 1 NSC Kharkov Institute of Physics and Technology, Ukraine 2 B. Verkin Institute for Low Temperature Physics and Engineering, Ukraine 3 Quantum Gravity Research, USA IWAHLM 2018

Outline • Localized Anharmonic Vibrations ( LAV ) in metals • LAV role in catalysis at high T (violation of Arrhenius low) • LAV role in catalysis at low T (quantum tunneling) • LAV induced LENR • MD simulations in Ni, Pd, Ni-H, Pd-H crystals and Pd nanoclusters • Experimental results

Energy localization in anharmonic lattices In the summer of 1953 Enrico Fermi, John Pasta, Stanislaw Ulam, and Mary Tsingou conducted numerical experiments (i.e. computer simulations) of a vibrating string that included a non-linear term (quadratic in one test, cubic in another, and a piecewise linear approximation to a cubic in a third). They found that the behavior of the system was quite different from what intuition would have led them to expect. Fermi thought that after many iterations, the system would exhibit thermalization, an ergodic behavior in which the influence of the initial modes of vibration fade and the system becomes more or less random with all modes excited more or less equally. Instead, the system exhibited a very complicated quasi-periodic behavior. They published their results in a Los Alamos technical report in 1955. The FPU paradox was important both in showing the complexity of nonlinear system behavior and the value of computer simulation in analyzing systems.

L ocalized A nharmonic V ibrations ( LAV s) A. Ovchinnikov (1969) Two coupled anharmonic oscillators    2 d        2 3   x x x x 0 1 0 1 1 2  2    3 A 0         2 3 2 0 1  sin x x x x    2 0 2 2 1 4 Localization condition Phase diagram  4      A  0 3

1D crystal — Hirota lattice model (nonlinear telegraph equations, 1973) d 0 Equation of motion of Hirota lattice                 mu 2 u u u u     n n -1 n n n 1           d tg tg 0   2 2            2 d   2 d  u    0 0 n 1 2 4 s         2          2 1 p 1         2 2 2       n     H ms ln 1  tg  ln 1 tg u u   n 1 n           2 2 ms 2 2 d      n 0

u n u n Standing weakly localized DB Bogdan, 2002 Standing strongly localized DB

         sh d 2 cos knd t 2 d    b 0 0   0 u arctg ,     Bogdan, 2002    n  sin kd 2 ch nd Vt  0 0           sh d 2 d kd kd s    0 0 0 0 2ch   sin   , V s cos   .        d 2 2 d 2 2 0 0 u n Moving strongly localized DB

The concept of LAV in regular lattices is based on large anharmonic atomic oscillations in Discrete Breathers excited outside the phonon bands .

LAV examples: • Discrete Breathers in periodic crystals • Phasons in quasicrystals • Calthrate guest-host systems • Dynamics of the central tetrahedron in Tsai QCs • Vibrations of magic clusters • etc

DBs in metals Hizhnyakov et al (2011)

Standing DB in bcc Fe: d 0 =0.3 Å D.Terentyev, V. Dubinko, A. Dubinko (2013)

DB along [111] direction in bcc Fe at T=0K Initial conditions :             0.2 0.2 0.4 0.4 0.2 0.2 x x x x x x      n 2 n 1 n n 1 n 2 n 3 Boundary conditions : periodic It is seen from the visualization, that the DB has been generated from the initial anti-phase displacements of 6 atoms .

Moving DB in bcc Fe: d 0 =0.4 Å, E= 0.3 eV D.Terentyev, V. Dubinko, A. Dubinko (2013)

DB in bulk Pd 3D lattice (2017) LAV Time Period= 0.1292 ps LAV frequency = 7.7399 THz The DB frequency lies above the phonon vibration spectrum

Effective ‘temperature’ of DB (#1100) and lattice (#1095) atom in fcc Pd lattice

DB effect (1): peiodic in time modulation of the potential barrier height 30

Reaction-rate theory with account of the crystal anharmonicity Dubinko, Selyshchev, Archilla, Phys. Rev. E. (2011)      0 R exp E k T <= Kramers rate  K 0 B 2 Kramers rate is amplified by:   I V k T - Bessel function 0 m B

Low temperature reconstructive transformation of muscovite Disilicate of Lutetium K 2 [Si 6 Al 2 ] IV [Al 4 ] VI O 20 (OH) 4 Lu 2 Si 2 O 7 E a >1 eV 300 ° C, 3 days About 36% of muscovite is transformed, which is 10 4 - 10 5 times faster than by Arrhenius law: K At T= 1000 ° C, 3 days + At T = 300 ° C, 10 3 years

Transformation rate of muscovite with account of DB statistics Dubinko et al (2011) 1 10 5    E E mod max               DB AMPLIFICATION FACTOR R R f E I E dE f E I E dE K  B 0 B 0 r  B   E E min mod   E E   max a E mod   E E a max Kramers rate: max  E 1 eV B      R exp E k T K a b 1 10 4  0.85 0.9 0.95 REACTION ACTIVATION ENERGY (eV)

How extend this concept to include Quantum effects, Tunneling ? Nolineal 2016

Tunneling: Numerical solution of Schrödinger equation Stationary: t Kramers ~10 5 cycles at V barrier =12E 0 10 cycles 50 cycles 1000 cycles Time-periodically driven: Ω = 1.5 ω 0 , g = 0.2 50 cycles 100 cycles 10 cycles

Tunneling as a classical escape rate induced by the vacuum zero-point radiation , A.J. Faria, H.M. Franca, R.C. Sponchiado Foundations of Physics (2006) The Kramers theory is extended in order to take into account both the action of the thermal and zero-point oscillation (ZPO) energy.        0 R exp E D T    0 K 2   E , T 0        ZPO D T E coth E k T  ZPO ZPO B  k T T , E k B ZPO B T – temperature is a measure of thermal noise strength   0 E - ZPO energy is a measure of quantum noise strength ZPO 2

When we heat the system we increase temperature, i.e. we increase the thermal noise strength Can we increase the quantum noise strength, i.e. ZPO energy?

Stationary harmonic potential 𝐹 𝑜 = ℏ𝜕 0 𝑜 + 1 2   0 E ZPO 2

Time-periodic modulation of the double-well shape changes (i) eigenfrequency and (ii) position of the wells

Parametric resonance with time-periodic eigenfrequency Ω = 2 ω 0        2 2 2 m t     Schrödinger equation 2 i x   2 t 2 m x 2   2 1 x         Initial Gaussian packet   0 x t , 0 exp   0 0 0  2 m   4 2 4 0 0 0          2 x 1 g cos 2 t x 0   Parametric regime Ω = 2 ω 0 : 0 0 g << 1 – modulation amplitude         g t g t          0 0     t cosh  1 tanh sin 2 t  dispersion x 0     0   2 2 ZPO amplitude: ZPO energy:    g t   g t      0 0 0 E t cosh t cosh ZPO ZPO  2 2 2 m 2 0

Non-stationary harmonic potential with time-periodic eigenfrequency Ω = 2 ω 0  g t     0 t cosh   ZPO  g t   2 m 2  0 0 0 E t cosh ZPO 2 2 LENR 2017

Escape rate in the modified Kramers theory with account of parametric driving of the well eigenfrequency Ω = 2 ω 0 E 0 = 1 eV – the well depth; g=0.1 – the modulation amplitude

Non-stationary harmonic potential with time-periodic shifting of the well position at Ω = ω 0   2   2 g A m a           A ZPO 0 2 2 2 0 E t t sin2 t sin t   0 0 0 0 2 8    g A sin t        A ZPO  0  t t cos t  0 0   2 t 0

Escape rate in the modified Kramers theory with account of parametric driving of the well position at Ω = ω 0                  0 R exp E E D T 0   D T coth 2 k T  0 K 0 B 2 2 E 0 = 1 eV – well depth; g A =0.5 – modulation amplitude ω 0 = 5 THz ω 0 = 5 THz Nolineal 2016