MODELING EXCESS HEAT IN THE FLEISCHMANN-PONS EXPERIMENT

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1 Theory (I) Session 2 O_1 MODELING EXCESS HEAT IN THE FLEISCHMANN-PONS EXPERIMENT Peter L. Hagelstein 1 and Irfan U. Chaudhary 2 1 Massachusetts Institute of Technology, Cambridge, MA, USA 2 University of Engineering and Technology, Lahore, Pakistan Over the past several years we have described models based on the linear coupling between two-level systems and an oscillator which are able to convert a large energy quantum into a large number of small energy quantum. At ICCF14 we presented a formula that can be used to calculate the phonon exchange matrix element for a nuclear reaction occurring in a lattice; in this presentation we report on our progress in the brute force computation of the matrix element based on realistic nuclear models. We consider also the development of semiclassical models which can approximate the dynamics of the quantum model. Finally, we describe the use of these models in a numerical simulation of the Fleischmann-Pons experiment. In these models a bottleneck occurs associated with helium diffusion out of the active region. We find that if the active region is thin (100 nm or less) that helium diffusion is fast, and excess heat production can occur in a steady state mode. If the active region is thick (500 nm or greater), then helium diffusion is slow and excess heat in these models occurs in bursts. ICCF-15 23

2 Modeling excess heat in the Fleischmann-Pons experiment Peter L. Hagelstein 1 and Irfan Chaudhary 2 1 Research Laboratory of Electronics Massachusetts Institute of Technology 2 Department of Computer Science and Engineering University of Engineering and Technology, Lahore

3 Theoretical problem Although many more results available from experiment, we have enough so far to pose the key theory problem: How to split up a large DE quantum into lots of small quanta? The major implication of the Fleischmann-Pons experiment is that this is possible and occurs in energy production

4 Basic toy model DE 0 Two-level systems DE 0 Macroscopic excited mode

5 Many-spin spin-boson model ˆ ˆ S z 2S H DE aa ˆ ˆ V x aˆ aˆ 0 C. Cohen-Tannoudji Two-level systems energy Harmonic oscillator energy Linear coupling between two-level systems and oscillator Earlier versions of the model due to Bloch and Siegert (1940)

6 Coherent energy exchange Numerical results for exchanging energy between 1700 oscillator quanta and 100 two-level systems

7 Thinking about toy model Coherent multi-quantum energy exchange predicted by toy model Effect is weak Stringent resonance requirements Can exchange up to about 100 quanta coherently Exactly kind of model needed, except energy exchange effect is too weak

8 Improved toy model DE Macroscopic excited mode 0 Two-level systems DE 0 Loss near DE

9 Lossy version of model ˆ ˆ S z 2S ˆ ˆ x ˆ ˆ H DE 0aa V a a i E 2 Loss term, which allows the system to decay when a large energy quantum is available

10 Perturbation theory Many paths from initial to final state, with interference between upper and lower paths Finite basis approximation for n M n 5 M 1

11 Perturbation theory Loss channels available for off-resonant states with energy excess, which spoils the destructive interference

12 Enhancement due to loss x F(S,M) M V ( E ) V ( E ) F ( S, M ) 1,12 1,12 0

13 Lossy version of model Loss spoils the destructive interference Coherent energy exchange rates increased by orders of magnitude Much stronger effect Model capable of converting 24 MeV to atomic scale quanta

14 Thinking about PdD D 2 Phonon mode 4 He Unfortunately, coupling is too weak because of Coulomb repulsion

15 Excitation transfer D 2 Phonon mode A Z* 4 He A Z Indirect evidence from experiment implicates A Z = 4 He, and theory and experiment suggest that A Z* is a localized two-deuteron state

16 Basic model Sˆ Sˆ 2 V e 2S a a V 2S a a (1) (2) ˆ z z H DE ˆˆ 1 DE2 0aa i E (1) (2) G x x 1 2 ˆ ˆ ˆ ˆ This kind of model is first one relevant to experiment

17 What oscillator modes? Excess power (mw) Frequency (THz) width (THz) Beat frequency (THz) Results from dual laser experiments of Letts, Proc. ICCF14 and ACS Sourcebook vol 2

18 Dispersion curve for PdD L E Sansores et al J Phys C (1982)

19 Strong-coupling limit When the coupling between the receiver-side two-level systems and oscillator is strong, then the problem simplifies S, M, n Dn Hˆ S, M 1, n 0 D E g When the excitation transfer step is the bottleneck, then V n e S M S M DE 1 0 G

20 Occupation of virtual levels E (MeV) n (10 6 )

21 Conclusions so far Can model the effect Can see the energy exchange with the lattice Can see excitation transfer Can get rates for both Agreement with experiment if screening energy U e = 150 ev

22 Trying out simplified version d N N N N N n n dt 0 D2 D2 D2 = 0 D2 He thresh D2 d N N N N N n n dt d dt 0 He He He 0 D2 He thresh He n n DE 0 n J 0 ND2NHe n nthresh p 0

23 Example: fast He diffusion Active region: A = 1 cm 2 Dr = 100 nm D 2 parameters: f[vacancy] = 0.25 f[d 2 ] = N[D 2 ] = 1.8 x D2 = 2 x 10-8 sec 4 He parameters: D He = 1.3 x cm 2 /sec He = Dr 2 /D He = 2.1 hr Phonon mode: f 0 = 8.3 THz Q = 20 Deuterium flux: P flux = 1 Watt/cm 3 n thresh = 100 Basic reaction rate: 0 = 1/(3 hr)

24 Evolution of dideuterium, 4 He 6 5 D 2 N D2, N 4He x He t (hr)

25 Excess power P xs (Watts) t (hr)

26 Number of phonons n t (hr) Thermal: 0.36 Flux generated (1 W/cm 3 ): 700 P xs generated: 10 7

27 Addressing the full problem Start out with full problem E H Then implement picture and approximation through construction of channels Get coupled-channel equations i j E H j j i

28 Coupled-channel equations Coupled-channel equations that result E H H i ii i ij j j i Can put whatever physics that one likes into the channels. Best place to start is with H H[nucleons] H[electrons] V[strong force] V[Coulomb]

29 Coupling Terms that couple from one channel to another: H H ij i j We focus on strong force terms, although others present H ij V e n is D Strong force Lattice change

30 Where is the D 2? Molecular D 2 does not form in bulk PdD Issue is electron density Computation of D 2 in electron gas leads to occupation of antibonding states The electron density in PdD is too high If you want D 2, you have to lower the electron density

31 Bonding and anti-bonding in H 2 W. Kolos and L. Wolniewicz, J Chem Phys (1965)

32 Pd-H 2 with s-bonding In Pd-H 2 d[pd-h]=1.67 A d[h-h] = 0.81 A s-bonded Pd-H 2 is the ground state of the three-atom system. It is a combination of (4d) 10 1 S 0 Pd and (1s) 2 1 S 0 H 2

33 Electron density of Pd (4d) (e/angstrom 3 ) HF DHF r (Angstroms)

34 Electron density at Pd-H distance 0.06 (e/angstom 3 ) r (Angstrom) Pd-H distance in Pd-H 2 is 1.67 Angstroms, and electron density is 0.033

35 PdD lattice structure (fcc)

36 Electron density due to Pd around octahedral site (e/angstrom 3 ) T O T s[111] (Angstrom)

37 Cannot form D 2 at O-site H 2 binds with Pd at 1.67 Angstroms Pd-H separation Electron density at 1.67 Angstroms is 0.33 e/angstrom 3 Electron density at O-site in PdD is e/angstrom 3 Anti-bonding orbitals occupied

38 PdD Host lattice vacancy Deuterium atoms relax toward host vacancy

39 Vacancies in host lattice Temperature (K) x v =1% NiH 1% PdH H to Me site ratio Vacancies in host metal lattice are thermodynamically favored at high loading

40 Codeposition Pd +2 Pd +2 Anodic current Cathodic current Conjecture that a small amount of Pd is stripped off during anodic current cycles, and then codeposited during subsequent cathodic loading [most of the Pd in solution is Pd(OH) 4-2, Mountain and Wood (1988)]

41 Electron density with vacancy (e/angstrom 3 ) O T V D s [111] (Angstrom)

42 Electron density seems low enough Superposition of atomic electron densities leads to a model electron density of e/angstrom 3 Model electron density is 2x lower than for Pd-H 2 Would expect D 2 formation near vacancy Would expect relevant literature

43 Check with PdH For ground state d[pd-h] = 1.53 A K. Balasubramanian et al, J Chem Phys (1987)

44 Look at Pd density at 1.53 A (e/angstrom 3 ) DHF Pd with HF 5s d 10 4d s r (Angstroms) Model electron density at 1.53 A is e/angstrom 3

45 Electron density around vacancy [111] [110] (e/angstrom 3 ) O O [100] O O 0.02 V s (Angstroms) Nearest O-point no longer a minimum in electron density

46 Model electron density just right now for H (e/angstrom 3 ) O V [100] s (Angstroms)

47 Compare with Velikova et al (2009) DFT for Pd 0.14 (e/angstrom 3 ) O V O Velikova et al, Phys Rev B (2009) s (Angstroms) Velikova shift corresponds to e/angstrom 3, close to PdH e/angstrom 3

48 Summary (need VASP calculation!) (e/angstrom 3 ) D 2 O V O s [100] (Angstroms) Expect about 0.4 A shift of D, and about 1 A shift for D 2 location

49 Summary and conclusions Fleischmann-Pons experiment points to new kind of physical process where nuclear energy generated with no energetic reaction products Spin-boson model provides analog which can convert a big quantum to a large number of small quanta, but effect is weak Lossy spin-boson model can convert a large number a big quantum to a large number of small quanta, and effect is large

50 More conclusions We can construct coupled-channel equations systematically to implement lossy spin-boson type scheme in real physical system Detailed modeling now under way

Two-level systems coupled to oscillators

Two-level systems coupled to oscillators RLE Group Energy Production and Conversion Group Project Staff Peter L. Hagelstein and Irfan Chaudhary Introduction Basic physical mechanisms that are complicated