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Time-Periodic Driving of Nuclear Reactions by Intrinsic Localized Modes Arising in Hydrogenated Metals

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Time-Periodic Driving of Nuclear Reactions by Intrinsic Localized Modes Arising in Hydrogenated Metals Time-periodic Driving of Nuclear Reactions by Intrinsic Localized Modes Arising in Hydrogenated Metals Vladimir Dubinko1, Denis Laptev2, Klee Irwin3 • 1NSC Kharkov Institute of Physics and Technology, Ukraine • 2B. Verkin Institute for Low Temperature Physics and Engineering, Ukraine • 3Quantum Gravity Research, USA Outline • Localized Anharmonic Vibrations: history and the state of the art • LAV role in chemical and nuclear catalysis • MD simulations in crystals of NiH and Pd nanoclusters at finite temperatures 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 complex systems. Localized Anharmonic Vibrations (LAVs) A. Ovchinnikov (1969) Two coupled anharmonic oscillators 2 d x23 x x x 0 1 0 1 1 2 2 0 23 3A0 2 x x x x 1 sin 2 0 2 2 1 4 Localization condition Phase diagram 4 A 0 3 LAV examples: • ILM/DBs in periodic crystals • LAVs in disordered systems • Phasons in quasicrystals • Calthrate guest-host systems • Vibrations of ‘magic clusters’ • etc ILMs in metals Hizhnyakov et al (2011) ICCF19 Standing DB in bcc Fe: d0=0.3 Å D.Terentyev, V. Dubinko, A. Dubinko (2013) DB along [111] direction in bcc Fe at T=0K Initial conditions: xn20.2 x n 1 0.2 x n 0.4 x n 1 0.4 x n 2 0.2 x n 3 0.2 Boundary conditions: periodic It is seen from the visualization, that the LAV has been generated from the initial anti-phase displacements of 6 atoms. Moving DB in bcc Fe: d0=0.4 Å, E= 0.3 eV D.Terentyev, V. Dubinko, A. Dubinko (2013) DB in bulk Pd 3D lattice LAV Time Period= 0.1292 ps LAV frequency = 7.7399 THz The DB frequency lies above the phonon vibration spectrum Module of velocity of DB (#1100) and lattice (#1095) atom in fcc Pd lattice Effective ‘temperature’ of DB (#1100) and lattice (#1095) atom in fcc Pd lattice Gap DBs in NaCl type lattices, Dmitriev et al (2010) Phonon Gap NaCl-type M /M = 10 at temperatures DOS for PdD0.63 and PdH0.63: MH /ML= 50; 100 H L ICCF19 T = (a) 0, (b) 155, (c) 310, and (d) 620 K D pressure of 5 GPa and T=600 K MD modeling of gap DBs in diatomic crystals at elevated temperatures Hizhnyakov et al (2002), Dmitriev et al (2010) * KKBn, 5.1 K0.1 eV 1000 K A3B type crystals MH /ML= 10 t * 70 In NaI and KI crystals Hizhnyakov et al has Lifetime and concentration of shown that DB amplitudes along <111> high-energy light atoms directions can be as high as 1 Å, and t*/Θ~104 increase exponentially with ICCF19 increasing T MD modeling of gap DBs in diatomic crystals A3B type crystals, Kistanov, Dmitriev (2014), 300 DB 200 ,[THz] 100 0 DOS(Density of states) A3B compound based on fcc lattice with Morse interatomic potentials. Grey DOE of a A3B compound atoms are 50 times lighter than yellow with MH /ML= 50 (similar to the PdD crystal). 0.4 DB is localized on a single light atom vibrating along 0.2 <100> direction with the frequency of 227 THz, which is inside the phonon gap. Shown is the x- ,[A] x 0 D displacement of the light atom as the function of -0.2 time. DB has very large amplitude of 0.4 angstrom, -0.4 which should be compared to the lattice parameter 0 0.05 0.1 t ,пс 0.15 a=1.35 angstrom LAV 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 RKBexp E0 k T <= Kramers rate 2 Kramers rate is amplified by: I0 Vm kBT - Bessel function How extend LAV concept to include Quantum effects, Tunneling ? Tunneling: Numerical solution of Schrödinger equation 5 Stationary: tKramers~10 cycles at Vbarrier=12E0 10 cycles 50 cycles 100 cycles Time-periodically driven: Ω = 1.5 ω0 , g = 0.2 10 cycles 50 cycles 100 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. REDT0 exp K 2 0 ETZPO , 0 D T EZPOcoth E ZPO k B T kB T, T E ZPO k B T – temperature is a measure of thermal noise strength E 0 - 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 1 퐸 = ℏ휔 푛 + 푛 0 2 E 0 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. iH ˆ ˆˆ t H t T H 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 22 mt2 i x,,, t x t x2 x t t22 m x2 1 n nt 2 Time-periodic driving of the harmonic oscillator with non resonant frequencies Ω ≠ 2ω0 renormalizes its energy spectrum, which remains equidistant, but the quasi- energy quantum 휆 휔 푡 becomes a function of the driving frequency Time-periodic modulation of the double-well shape changes (i) eigenfrequency and (ii) position of the wells Parametric resonance with time-periodic eigenfrequency Ω = 2ω0 22 mt2 ix 2 Schrödinger equation t22 m x2 1 x2 0 Initial Gaussian packet xt00, 0 exp 0 4 2m 2 0 4 0 0 x2 1 g cos 2 t x 0 Parametric regime Ω = 2ω0: 00 g << 1 – modulation amplitude g00 t g t x tt 00cosh 1 tanh sin 2 dispersion 22 ZPO energy: ZPO amplitude: 00gt gt0 EtZPO cosh ZPO t cosh 22 22m0 Non-stationary harmonic potential with time-periodic eigenfrequency Ω = 2ω0 00gt gt0 EtZPO cosh t cosh LENR 2017 ZPO 22 22m0 1 gt0 E t 0 n cosh g 1 General case: n = 0,1,2, … theor 22 1 YZ2 2 2 2 t E t00 n Y2 2 Z 2 num 22 0 2200 2 Y t t Y t 0 gn0.1, 0 YY0 0, 0 1 2 Z t t Z t 0 ZZ0 1, 0 0 22 t 001 g cos 2 t g 0.1 E n 0 t T Non-stationary harmonic potential with time-periodic shifting of the well position at Ω = ω0 2 g A m 2 a E0 A ZPO 0 2 t 2 tsin 2 t sin 2 t 280 0 0 0 gA A ZPO sin0 t t 00 tcos t 2 0t Extreme example – Low Energy Nuclear Reactions (LENR) Electrolysis “Water will be the coal of the future” Jules Verne Pd or D2 D2O or LENR 2015 LENR requirements for D2O electrolysis (i) high loading of D > 0.88 (ii) external driving 4 D + D He + 23.8 MeVlattice Why LENR is unbelievable? R 2 c Gexp dr 2 V r E Gamow factor r0 r0 ~ 3 fm Nuclear radius deduced from scattering experiments e2 Coulomb barrier VR 0 450 keV r0 At any crystal 2760 Temperature: E V r0 G 10 HOWEVER, is the Coulomb barrier that huge in the lattice ? Willis Eugene Lamb Julian Schwinger Nobel Prize 1955 Nobel Prize 1965 R.H. Parmenter, W.E. Lamb, J. Schwinger, Nuclear Energy in an Cold fusion in Metals (1989) Atomic Lattice (1990) Electron screening Lattice screening J. Schwinger, Nuclear Energy in an Atomic Lattice I, Z. Phys. D 15, 221 (1990) Effective Coulomb repulsion with account of zero- point oscillations 0 R0 e2 r r 0 : e2 2 0 r V r dxexp 1 x2 0 c 0 2 1 2 r 0 2 2 e r 0 : ~ 100 eV (!!!) 0 J. Schwinger, Nuclear Energy in an Atomic Lattice The First Annual Conference on Cold Fusion. University of Utah Research Park, Salt Lake City (1990) 1 2 VHEV D-D fusion rate in Pd-D lattice: DD 0 T 0 0 T0 is the mean lifetime of the phonon vacuum state before releasing the nuclear energy directly to the lattice (no radiation!): 1 32 2 11200 rRnucl 19 1 30 1 20 exp ~ 10ss 10 TE0 2 nucl 00 R 0.94 2.9 0 0.1 0 Schwinger, Nuclear Energy in an Atomic Lattice I, Z. Phys. D 15, 221 (1990).
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