Chemical and nuclear catalysis mediated by the energy localization - PowerPoint PPT Presentation

Chemical and nuclear catalysis mediated by the energy localization in crystals and quasicrystals Vladimir Dubinko 1,3 , Denis Laptev 2,3 , Klee Irwin 3 1 NSC Kharkov Institute of Physisc&Technology, Ukraine 2 B. Verkin Institute for Low Temperature Physics and Engineering, Ukraine 3 Quantum gravity research, Los Angeles, USA

Coauthors Denis Laptev , B. Verkin Institute for Low Temperature Physics and Engineering, Ukraine Klee Irwin , Quantum Gravity Research, Los Angeles, USA

Outline • Localized Anharmonic Vibrations: history and the state of the art • LAV role in chemical and nuclear catalysis • MD simulations in crystals and quasicrystalline clusters

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

Discrete Breathers Sine-Gordon standing breather Large amplitude moving is a swinging in time coupled sine-Gordon breather . kink-antikink 2-soliton solution.

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 ICCF19

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 .

DBs in metals Hizhnyakov et al (2011) ICCF19

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

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

Dynamics of the “magic” icosahedral cluster of 55 Pd atoms It is seen from the visualization, that Localized Anharmonic Vibration is generated. The observed LAV in the atomic cluster represents the coherent collective oscillations of Pd atoms along quasi-crystalline symmetry directions .

Visualization of the PdH fcc Lattice (NaCl type)

Visualization of the PdH fcc Lattice Oscillations at T=100 K

Visualization of the PdH fcc Lattice Oscillations at T=1000K

Gap breathers in NaCl type lattices, Dmitriev et al (2010) Phonon Gap DOS for PdD 0.63 and PdH 0.63 : M H /M L = 50; 100 NaCl-type M H /M L = 10 at temperatures ICCF19 D pressure of 5 GPa and T=600 K T = (a) 0, (b) 155, (c) 310, and (d) 620 K

MD modeling of gap DBs in diatomic crystals at elevated temperatures Hizhnyakov et al (2002), Dmitriev et al (2010) K  * K 5.1 B n ,     * 70 t K 0.1 eV 1000 K A 3 B type crystals M H /M L = 10 Lifetime and concentration of In NaI and KI crystals Hizhnyakov et al has high-energy light atoms shown that DB amplitudes along <111> directions can be as high as 1 Å , and t*/ Θ ~10 4 increase exponentially with increasing T ICCF19

MD modeling of gap DBs in diatomic crystals at elevated temperatures A 3 B type crystals, Kistanov, Dmitriev (2014), 300 DB  ,[THz] 200 100 0 DOS(Density of states) A 3 B compound based on fcc lattice with DOE of a A 3 B compound Morse interatomic potentials. Grey atoms are 50 times lighter than yellow with M H /M L = 50 (similar to the PdD crystal). DB is localized on a single light atom vibrating along 0.4 <100> direction with the frequency of 227 THz, 0.2 D x ,[A] which is inside the phonon gap . Shown is the x- 0 displacement of the light atom as the function of -0.2 time. DB has very large amplitude of 0.4 angstrom, which should be compared to the lattice parameter -0.4 a=1.35 angstrom 0 0.05 0.1 t ,пс 0.15

LAV effect (1): peiodic in time modulation of the potential barrier height 35

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:   I V k T Bessel function 0 m B

How extend LAV concept to include Quantum effects, Tunneling ?

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 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

Quasi-energy in time-periodic systems Consider the Hamiltonian which is periodic in time.   ˆ       ˆ ˆ i H   H t T H t  t It can be shown that Schrodinger equation has class of solutions in the form:             t T exp i t      where Is the quasi-energy T      2 2 2 m t             2 , , , i x t x t x x t   2 2 2 t m x     1          n t n   2 of the harmonic oscillator with non resonant frequencies Ω ≠ Time-periodic driving 2 ω 0 renormalizes its energy spectrum, which remains equidistant, but the quasi- 𝜇 𝜕 𝑢 energy quantum becomes a function of the driving frequency

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

DB frequency and eigenfrequency of the potential wells of neighboring D ions in PdD ( Dubinko, ICCF 19 ) Ω = 2 ω 0 DB polarized along the close-packed D-D direction <110>

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 Parametric regime Ω = 2 ω 0 : x 1 g cos 2 t x 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