############################################################################# ## DRAFT DRAFT DRAFT DRAFT DRAFT DRAFT DRAFT DRAFT DRAFT DRAFT DRAFT DRAFT ## ## (No typo checking, no review, no references. A final will be issued.) ## ############################################################################# Bernecky Condensation: A Brief Analysis of the Potential for Diffraction-Enhanced Atomic Boson Condensation in Pd(Hx,Dy,Tz) Compounds July 12, 1993 Terry B. Bollinger 2416 Branch Oaks Lane Flower Mound, Texas 75028, U.S.A (terry@asl.dl.nec.com) 1. BACKGROUND In a recent electronic "farfetch" (conceptual exploration) paper by William Bernecky [1], W. Bernecky proposed the intriguing idea that diffraction of delocalized hydrogen species in palladium metal crystal lattices might in principle lead to the formation of above-ground atomic boson condensates. Since at present the only known examples of atomic boson condensates are found in superfluid liquid helium, any effect that might in principle lead to new examples of atomic boson condensate would be of great theoretical and experimental interest -- if such an effect does in fact exist. I should note that although to the best of my knowledge William Bernecky is the first person to propose the specific idea that lattice diffraction might be capable of encouraging atomic boson condensation, the idea of hydrogen boson condensates in palladium has been discussed extensively in both papers and on the UseNet group sci.physics.fusion. Papers that proposed such condensates include in particular the work of Scott Chubb et all [2], and extensive sci.physics.fusion discussions and proposals on this concept include those of Chuck Sites [3]. William Bernecky's idea should be viewed as a specific elaboration of a possible mechanism for boson condensate concepts initially proposed and elaborated upon by other authors. I would note that this elaboration on the Bernecky condensation idea by no means should be taken as any sort of "proof" that the effect even exists. Instead, I am providing this draft electronic paper in hopes that others will examine the idea more closely from both a theoretical and (possibly) an experimental viewpoint. Another objective is simply to make some of the issues and data more accessible to interested readers who may not be very familiar with palladium hydride chemistry or crystallography. 2. DIFFRACTION AND BOSON CONDENSATION The idea of using diffraction to form (photon) boson condensates has been used in thin-film optical lasers [4]. In these lasers, two diffraction elements are used in place of conventional mirrors to create a cavity in which lasing can take place. The frequency at which lasing (photon boson condensation) takes place is determined by the "exclusion frequencies" of the diffraction gratings. That is, when one-half the wavelength (or an integer multiple of one-half the wavelength) of a photon is exactly equal to the distance between the lines of the diffraction grating, the photon will be unable to traverse the grating and will instead be reflected back into the lasing medium. This reflection effect falls off rapidly for those photons with slightly higher or lower frequencies, so that a high degree of precision in the selection of photon frequencies is possible. In the proposed concept of Bernecky condensation, the diffraction grating is replaced by the three-dimensional lattice of a transition metal such as palladium, and the photons generated by a population inversion in the lasing medium are replaced by a population of atomic composite boson species that occupy a range of momentum values within the metal lattice. Furthermore, the electromagnetic interactions of the photons are replaced by the quantum mechanical (momentum) frequencies of the hydrogen atoms. Finally, in the nominal model for Bernecky condensation, the condensation would presumably take place in a single uniformly loaded crystal in which the palladium crysal lattice matches one of the "exclusion frequencies" for hydrogen atoms traveling through it. However, an exact match to this one exclusion frequency throughout the lattice would make the availability of atoms in that state so low that condensation would be either impossible or so slow as to be impractical. 3. TIGHTENING THE LASER ANALOGY However, I would suggest that a much closer analogy to the laser technique could be obtained simply by varying the hydrogen loading of a single crystal of palladium in a smooth, bilaterally symmetrical fashion along one selected axis of the crystal. (Selection of crystal axes will be discussed later in this paper.) Two such axial loading profiles are possible: FIGURE 1. High-Low-High (HLH) Axial Loading Profile Relative H Loading along selected axis of the crystal lattice: High | - _ _ - | - _ _ - Low | - - +------------------------------------------------------------------ Corresponding impact on Pd lattice units (not drawn to scale): +--------+-------+------+-----+----+----+-----+------+-------+--------+ | | | | | | | | | | | +--------+-------+------+-----+----+----+-----+------+-------+--------+ | | | | | | | | | | | +--------+-------+------+-----+----+----+-----+------+-------+--------+ \____________/ \___________________/ \____________/ Exclusion region Permeable region Exclusion region for frequency X for frequency X for frequency X FIGURE 2. Low-High-Low (LHL) Axial Loading Profile Relative H Loading along selected axis of the crystal lattice: High | _ - - _ | _ - - _ Low | - - +------------------------------------------------------------------ Corresponding impact on Pd lattice units (not drawn to scale): +----+-----+------+-------+--------+--------+-------+------+-----+----+ | | | | | | | | | | | +----+-----+------+-------+--------+--------+-------+------+-----+----+ | | | | | | | | | | | +----+-----+------+-------+--------+--------+-------+------+-----+----+ \____________/ \___________________/ \____________/ Exclusion region Permeable (?) region Exclusion region for frequency X for frequency X for frequency X Arrangements such as the ones shown above would approximate the structure of a diffraction-based laser by ensuring that an atom moving in either direction would eventually encounter a region matching its exclusion frequency and be reflected back. At the same time the atom would be able to travel fairly freely the middle region between the frequency exclusion areas, particularly if the lattice is very regular and free of extraneous inclusions such as H2 molecules. Rather than implying maximum loading, this would imply that loading lesser loadings should also be tried in hopes of preserving the regularity of the lattice structure. Early neutron diffraction work with palladium hydride compounds indicates that hydrogen (apparently meaning molecular hydrogen) causes significant diffuse neutron scattering by the time a 0.706 loading factor (PdH_0.706) is reached. As such an atom moves back through the slightly-off-exclusion-frequency area in the middle of the crystal, it could in principle "pick up" another atom through boson state "attraction" [2]. In the absence of the total exclusion areas surrounding the transparent region, there would be no strong incentive for any one momentum frequency to become dominant in such boson interactions. However, as with a laser, the frequency selectivity of the total exclusion areas surrounding the transparent region would lead to a strong favoring of the frequency exclusion states. If this can be combined with a sufficiently orderly lattice in the transparent inner region for a net gain (>1) atomic bosons per pass between diffraction regions, an above-ground atomic boson condensate might in fact be able to form. Of the two (HLH and LHL) loading profiles shown, the HLH profile (high end loading with hydrogen and lesser mid-region loading) is preferable. This is because the HLH loading profile results in a shorter lattice constant in the (transparent) L region, which in turn should raise the Fermi level of the atoms in that region and "immerse" the diffracted atoms in a sea of free atoms of closely similar frequency. In contrast, the LHL profile could place the diffracted atoms into a band exclusion region that might not be transparent, and could also be quite deficient in available atoms of similar momentum. One final point is that although a three-dimensional diffraction resonance cavity is possible in principle (Figure 3), the mechanical expansion of the outer (H) layers during loading would place rather severe stress on the palladium crystal lattice. Since full enclosure is not required to show any boson condensation effect that might exist, the far less mechanically stressful axial profile with full radial symmetry that was discussed above would probably be preferable to full enclosure schemes. For paricles as heavy as hydrogen atoms, even modest strain distortion of the crytal lattice would be likely to significantly increase scattering probabilities for the diffracted hydrogen atoms and thus drop the boson condensate gain per pass to below the critical >1 gain level. FIGURE 3. Enclosed Resonance Cavity Model H H H H H H H L L L H H H H L L L H H H H H H H Further details on the presumed structure of such a device requires a closer look at palladium hydride crystallography and quantum mechanical aspects of the hydrogen isotopes and species found in Pd(Hx,Dy) compounds. 4. PALLADIUM HYDRIDE CRYSTALLOGRAPHY The basic face-centered crystal unit of palladium and palladium hydride (beta phase) is shown in Figure 4. This structure is well confirmed by various neutron diffraction studies [4,5,6], and corresponds to a 1:1 Pd:H ratio (PdH). However, loading of this structure does not appear to easily exceed about 1 to 0.7 -- that is, roughly 30% of the octahedral vacancy sites normally remain vacant, with the hydrogen atoms moving fairly easily between them [4]. FIGURE 4. Palladium Hydride Crystal Unit (Beta Phase) Pd----------( )----------Pd /| /| /| / | / | / | / | / | / | ( )----------Pd---------( ) | /| | /| | /| | / | ( )----/-|---Pd----/-|--( ) / | /| / | /| / | /| Pd==========( )==========Pd | / | | |/ | | |/ | | |/ | | Pd-------|--( )------|---Pd | | /| | | /| | | /| | | / | Pd---|-/-|--( )--|-/-|---Pd |/ | / |/ | / |/ | / ( )==========Pd=========( ) | / | |/ | |/ | |/ | ( )------|---Pd------|--( ) | / | / | / | / | / | / |/ |/ |/ Pd==========( )==========Pd Pd -- Palladium atom ( ) -- Octahedral vacancy (hydrogen) site The above sites are called "octahedral" because the six palladium atoms surrounding each vacancy are located at the vertices of an octahedron: FIGURE 5. Octahedral Site (Located at center of each possible unit cell) -Pd- | | | -Pd- | /| | / | |/ | Pd----------( )----------Pd | /| | / | |/ | =Pd= | | | -Pd- In some transition metals, there is another class of vacancies that can be occupied by hydrogen: the tetrahedral sites. While these sites (which correspond to a formular of PdH2) have been proposed from time to time as the sites for hydrogen in saturated beta phase palladium hydride [5], they appear unlikely to be critical to palladium systems due to the poor evidence for them in neutron scattering data [4,5,6]. The tetrahedral sites are shown in Figure 6. FIGURE 6. Nominal Palladium Tetrahedral Sites Pd-----------+-----------Pd /| /| /| / | / | / | / | / | / | +-----------Pd----------+ | /| | ( ) /| | ( ) /| | / | +-----/-|---Pd----/-|---+ / | /| / | /| / | /| Pd===========+===========Pd | / | | |/ (*) | |/ (*) | |/ | | Pd-------|---+-------|---Pd | | /| | (|) /| | (|) /| | | / | Pd---|-/-|---+---|-/-|---Pd |/ | / |/ | / |/ | / +===========Pd==========+ | / | |/ (*) | |/ (*) | |/ | +-------|---Pd------|---+ | / | / | / | / | / | / |/ |/ |/ Pd===========+===========Pd Pd -- Palladium atom ( ) -- Nominal tetrahedral vacancy site (rear plane) (*) -- Nominal tetrahedral vacancy site (front plane) As with the octahedral sites, the tetrahedral sites are named after the configurations of the palladium atoms around each such site: FIGURE 7. Tetrahedral Site (1/8 of one unit cell) Pd-----------+ /| /| / | / | / | / | +-----------Pd | | | ( ) | | | +-------|---Pd | / | / | / | / |/ |/ Pd-----------+ The relative locations of the octahedral and nominal tetrahedral vacancy sites in the unit palladium cell can also be seen by splitting the cell apart into layers, as in Figure 8: FIGURE 8. Octahedra and Tetrahedral Sites Back Octahedrals Pd------( )------Pd Middle /| /| Octahedrals | | | | ( )------Pd-----( ) ( ) Pd ( ) Front | | | | Octahedrals | | | | / / | | | | Pd------( )------Pd Pd ( ) Pd Pd------( )------Pd | | | | / / | | | | | | | | ( ) Pd ( ) ( )------Pd-----( ) | | . | | /|\ | |/ | Pd------( )------Pd Tetrahedrals . /|\ +-------+-------+ | | | Tetrahedrals | ( ) ( ) | | | +-------+-------+ + + + | | | | | ( ) ( ) | | ( ) ( ) | | | | | + + + +-------+-------+ | | | ( ) ( ) | | | +-------+-------+ 5. MOMENTUM EXCLUSION WAVELENGTHS IN PALLADIUM The nominal wavelengths at which an atomic momentum value will be excluded by lattice diffraction are those values at which unit of periodicity in a particular direction is equal to some integer multiple of 1/2 the basic wavelength. A full analysis of this requires consideration of tunneling constants between sites and effective masses [8]. However, because the coupling (tunneling) constant between sites will be very low for heavy particles such as hydrogen atoms or deuterium atoms, a direct approximation of wavelengths based on simple geometrical considerations will be used here. Figure 9 describe the three major directions and lengths of a single full wavelength in terms of the length u of one crystal unit. FIGURE 9. Directions and Lengths of Momentum Frequencies .---------------------------------------- Lambda(tetr)_1 = u | Pd--V---( )------Pd-----( )------Pd |_ -- _ | | + () + _ () _+ | + ___ | -- | | - <----- Lambda(diag)_1 = V 2 u ( ) Pd ( ) Pd ( ) - | | _ - | | _ - + - | | - | Pd------( )------Pd-- - ( )------Pd .--- Lambda(axis)_1 = 2 u | | - | | | | + | | | | | | ( ) Pd ( ) Pd ( ) | | | | | | _ - - _ | | | |_ - - _| | | Pd------( )------Pd-----( )------Pd | - _ _ - <---' - - Of these three classes of possible waves, the tetragonal class is of only modest interest due to its poor experimental support. The two remaining classes can be described and labeled by using traditional crystallographic designations for the faces of cubic crystals: FIGURE 10. Axial and Diagonal Palladium Orientations _ 101 101 | | | | _ +--|--------+ 011 ------/ | / \------ 011 / | 001 / /| _ +-----|-----+ / |---- 110 /_\_________/_\/ | | | | |010/ | | 100 | | / | | | |-------- 110 |_|_________|_|/ \|_________\ / Cubic axes (3 total): (001) (010) (100) _ _ _ Diagonals (6 total): (011) (110) (101) (011) (110) (101) Of the diagonal and axial classes, the diagonal class is significantly more attractive due to its shorter wavelength. Since coupling constants for heavy particles are extremely sensitive to distance [9], this reduction over the axial wavelength is significant. Further more, the diagonal class has a unique profile in which there are "chains" of alternating vacancies and palladium atoms, as shown in Figure 10: FIGURE 11. Atomic Structure Perpendicular to Diagonal Axes Pd Layer of a Diagonal Face +---------------------------------------+ | | | Pd Pd Pd | | | | Pd Pd | | | | Pd Pd Pd | | | | Pd Pd | | | | Pd Pd Pd | | | +---------------------------------------+ Octahedral Layer of a Diagonal Face +---------------------------------------+ | | | ( ) ( ) | | | | ( ) ( ) ( ) | | | | ( ) ( ) | | | | ( ) ( ) ( ) | | | | ( ) ( ) | | | +---------------------------------------+ Superimposed Layers of a Diagonal Face +---------------------------------------+ | | | Pd ( ) Pd ( ) Pd | | | | ( ) Pd ( ) Pd ( ) | | | | Pd ( ) Pd ( ) Pd | | | | ( ) Pd ( ) Pd ( ) | | | | Pd ( ) Pd ( ) Pd | | | +---------------------------------------+ Since each vacancy chain is "clean" (i.e., there are no directly intruding palladium atoms, it has a quite different potential well profile from that of the axial directions, in which vacancies alternate with Pd atoms: FIGURE 11. Expected potential well structure for AXIAL wavefunctions |- -- -- -- - |- -- -- -- - |- -- -- -- - |- -- -- -- - | - - - - - - - - | - - - - - - - - | - - - - - - - - | - - - - - - - - +--------------+--------------+--------------+--------------+ Atom: Pd Pd Pd Pd Pd FIGURE 12. Expected potential well structure for DIAGONAL wavefunctions | | | |- -- -- -- -- -- - | - - - - - - - - - - - - | - - - - - - - - - - - - +----+----+----+----+----+----+----+----+----+----+----+----+ Layer: Pd Oct Pd Oct Pd Oct Pd Oct Pd Oct Pd Oct Pd Because the diagonal potential well structure is more sinusoidal and less dependent on the behavior of individual Pd atoms, it should be significantly less likely to scatter precise momentum atoms traveling in that direction. 7. TEMPERATURE CALCULATIONS BY PARTICLE TYPE AND PALLADIUM PHASE In this final section, "ballpark" estimates of the optimum temperatures for Bernecky condensation are provided based on the same (overly simple) analysis and assumption of low coupling used above. Since William Bernecky's original table of values inadvertantly used full wavelengths instead of half wavelengths as the basic unit for determining exclusion frequencies, there are twice as many entries in these tables for the same particles. It is important to realize that the probability of any kind of boson condenstion is going to drop rapidly with temperature, regardless of how effective lattice diffraction may or may not be. Thus the best candidates for Bernecky condensation are not the ones at or near room temperature, but the cryogenic Order 1 temperatures for the lightest possible boson candidates. Thus the best candidates would be diagonal Order 1 hydrogen atoms and deuterium ions. One or both of these boson species may exist, and both would be worth further analysis and possibly experimentation. An interesting point that came out in an email conversation between myself and Chuck Sites after he had talked to Scott Chubb [10] was that if the deuteron ion condenses, it will necessarily be a _deuteron_ based electrical superconductor. This would provide an extremely sensitive (and definitive) test for whether such a condensation had actually occurred. +----+----------------+-------------------+---------+ 1. | p+ | proton | 1.6726231 x10-8 g | fermion | +----+----------------+-------------------+---------+ 2. | H | protium atom | 1.6735340 " | boson | +----+----------------+-------------------+---------+ 3. | n | neutron | 1.6749286 " | fermion | +----+----------------+-------------------+---------+ 4. | d+ | deuteron (pn) | 3.3435860 " | boson | +----+----------------+-------------------+---------+ 5. | D | deuterium atom | 3.3444970 " | fermion | +----+----------------+-------------------+---------+ 6. | t+ | triton (pnn) | 5.0073601 " | fermion | +----+----------------+-------------------+---------+ 7. | T | tritium atom | 5.0082711 " | boson | +----+----------------+-------------------+---------+ / 1 \ | | 2 Tk = 1.0600040 E-37 | ------------- | g cm K | 2 | \ m lambda / Tc = Tk - 273.15 Tf = 1.8 Tc + 32 Temperature Equivalents for DIAGONAL Palladium Particle Waves +----------+--------------------+--------------------+--------------------+ | | | | | | | DIAGONAL | DIAGONAL | DIAGONAL | | Particle | Order 1 | Order 2 | Order 3 | | | | | | | | alpha = beta = | alpha = beta = | alpha = beta = | | | 5.496 A 5.685 A | 2.748 A 2.843 A | 1.832 A 1.895 A | +==========+====================+====================+====================+ | p+ | 20.98 .. 19.61 K | 89.92 .. 78.43 K | 188.8 .. 176.5 K | +----------+--------------------+--------------------+--------------------+ | H | 20.98 .. 19.60 K | 83.88 .. 78.39 K | 187.7 .. 176.4 K | +----------+--------------------+--------------------+--------------------+ | n | 20.95 .. 19.58 K | 83.81 .. 78.33 K | 187.6 .. 176.2 K | +----------+--------------------+--------------------+--------------------+ | d+ | 10.50 .. 9.81 K | 41.98 .. 39.24 K | 94.46 .. 88.28 K | +----------+--------------------+--------------------+--------------------+ | D | 10.49 .. 9.81 K | 41.97 .. 39.23 K | 94.43 .. 88.26 K | +----------+--------------------+--------------------+--------------------+ | t+ | 7.008 .. 6.55 K | 28.03 .. 26.20 K | 63.07 .. 58.95 K | +----------+--------------------+--------------------+--------------------+ | T | 7.006 .. 6.55 K | 28.03 .. 26.20 K | 63.06 .. 58.94 K | +==========+====================+====================+====================+ +----------+--------------------+--------------------+--------------------+ | | | | | | | DIAGONAL | DIAGONAL | DIAGONAL | | Particle | Order 4 | Order 5 | Order 6 | | | | | | | | alpha = beta = | alpha = beta = | alpha = beta = | | | 1.374 A 1.412 A | 1.099 A 1.137 A | 0.9160 A 0.9475 A | +==========+====================+====================+====================+ | | 335.7 .. 313.7 K | 524.5 .. 490.2 K | 755.3 .. 705.9 K | | p+ | 62.55 .. 40.55 C | 251.4 .. 217.1 C | 482.2 .. 432.8 C | | | 144.6 .. 105.0 F | 484.5 .. 422.8 F | 899.9 .. 810.2 F | +----------+--------------------+--------------------+--------------------+ | | 335.5 .. 313.6 K | 524.2 .. 490.0 K | 754.9 .. 705.5 K | | H | 62.53 .. 40.54 C | 251.1 .. 216.9 C | 481.8 .. 432.4 C | | | 144.6 .. 105.0 F | 484.0 .. 422.4 F | 899.2 .. 809.2 F | +----------+--------------------+--------------------+--------------------+ | | 335.2 .. 313.3 K | 523.8 .. 489.5 K | 754.2 .. 704.9 K | | n | 62.50 .. 40.51 C | 250.7 .. 216.9 C | 481.1 .. 431.8 C | | | 144.5 .. 104.9 F | 483.2 .. 422.4 F | 897.9 .. 175.9 F | +----------+--------------------+--------------------+--------------------+ | | 167.9 .. 156.9 K | 262.4 .. 245.2 K | 377.8 .. 353.1 K | | d+ | | -10.75 .. -28.0 C | 104.7 .. 80.0 C | | | | 12.7 .. -18.4 F | 220.4 .. 175.9 F | +----------+--------------------+--------------------+--------------------+ | | 167.9 .. 156.9 K | 262.3 .. 245.2 K | 377.7 .. 353.0 K | | D | | -10.85 .. -28.0 C | 104.6 .. 79.9 C | | | | 12.5 .. -18.4 F | 220.2 .. 175.7 F | +----------+--------------------+--------------------+--------------------+ | | 112.1 .. 104.8 K | 175.2 .. 163.7 K | 252.3 .. 235.8 K | | t+ | | | -20.85 .. -37.35 C | | | | | -5.53 .. -35.23 F | +----------+--------------------+--------------------+--------------------+ | | 112.1 .. 104.8 K | 175.2 .. 163.7 K | 252.2 .. 235.8 K | | T | | | -20.84 .. -37.35 C | | | | | -5.51 .. -35.23 F | +==========+====================+====================+====================+ Temperature Equivalents for AXIAL Palladium Particle Waves +----------+--------------------+--------------------+--------------------+ | | | | | | | AXIAL | AXIAL | AXIAL | | Particle | Order 1 | Order 2 | Order 3 | | | | | | | | alpha = beta = | alpha = beta = | alpha = beta = | | | 7.772 A 8.040 A | 3.886 A 4.020 A | 2.591 A 2.680 A | +==========+====================+====================+====================+ | p+ | 10.49 .. 9.804 K | 41.97 .. 39.22 K | 94.42 .. 88.23 K | +----------+--------------------+--------------------+--------------------+ | H | 10.49 .. 9.799 K | 41.94 .. 39.19 K | 94.37 .. 88.19 K | +----------+--------------------+--------------------+--------------------+ | n | 10.48 .. 9.790 K | 41.91 .. 39.16 K | 94.29 .. 88.11 K | +----------+--------------------+--------------------+--------------------+ | d+ | 5.248 .. 4.904 K | 20.99 .. 19.62 K | 47.24 .. 44.14 K | +----------+--------------------+--------------------+--------------------+ | D | 5.248 .. 4.903 K | 20.99 .. 19.61 K | 47.22 .. 44.13 K | +----------+--------------------+--------------------+--------------------+ | t+ | 3.505 .. 3.275 K | 14.02 .. 13.10 K | 31.54 .. 29.47 K | +----------+--------------------+--------------------+--------------------+ | T | 3.504 .. 3.274 K | 14.02 .. 13.10 K | 31.54 .. 29.47 K | +==========+====================+====================+====================+ +----------+--------------------+--------------------+--------------------+ | | | | | | | AXIAL | AXIAL | AXIAL | | Particle | Order 4 | Order 5 | Order 6 | | | | | | | | alpha = beta = | alpha = beta = | alpha = beta = | | | 1.943 A 2.010 A | 1.554 A 1.608 A | 1.295 A 1.340 A | +==========+====================+====================+====================+ | | 169.9 .. 156.9 K | 262.3 .. 245.1 K | 377.7 .. 352.9 K | | p+ | | -10.85 .. -28.05 C | 104.6 .. 79.75 C | | | | 12.47 .. -18.49 F | 220.2 .. 175.6 F | +----------+--------------------+--------------------+--------------------+ | | 169.8 .. 156.8 K | 262.1 .. 245.0 K | 377.5 .. 352.7 K | | H | | -11.05 .. -28.15 C | 104.4 .. 79.55 C | | | | 12.11 .. -18.67 F | 219.8 .. 175.2 F | +----------+--------------------+--------------------+--------------------+ | | 169.6 .. 156.6 K | 261.9 .. 244.8 K | 377.2 .. 352.5 K | | n | | -11.25 .. -28.35 C | 104.1 .. 79.35 C | | | | 11.75 .. -19.03 F | 219.3 .. 174.8 F | +----------+--------------------+--------------------+--------------------+ | | 83.97 .. 78.47 K | 131.2 .. 122.6 K | 188.9 .. 176.6 K | | d+ | | | | | | | | | +----------+--------------------+--------------------+--------------------+ | | 83.95 .. 78.45 K | 131.2 .. 122.6 K | 188.9 .. 176.5 K | | D | | | | | | | | | +----------+--------------------+--------------------+--------------------+ | | 56.07 .. 52.40 K | 87.61 .. 81.87 K | 126.2 .. 117.9 K | | t+ | | | | | | | | | +----------+--------------------+--------------------+--------------------+ | | 56.06 .. 52.39 K | 87.61 .. 81.86 K | 126.1 .. 117.9 K | | T | | | | | | | | | +==========+====================+====================+====================+ Temperature Equivalents for TETRAGONAL Palladium Particle Waves +----------+--------------------+--------------------+--------------------+ | | | | | | | TETRAGONAL | TETRAGONAL | TETRAGONAL | | Particle | Order 1 | Order 2 | Order 3 | | | | | | | | alpha = beta = | alpha = beta = | alpha = beta = | | | 3.886 A 4.020 A | 1.943 A 2.010 A | 1.295 A 1.340 A | +==========+====================+====================+====================+ | | 41.97 .. 39.22 K | 167.9 .. 156.9 K | 377.7 .. 352.9 K | | p+ | | | 104.6 .. 79.75 C | | | | | 220.2 .. 175.6 F | +----------+--------------------+--------------------+--------------------+ | | 41.94 .. 39.19 K | 167.8 .. 156.8 K | 377.5 .. 352.7 K | | H | | | 104.4 .. 79.55 C | | | | | 219.8 .. 175.2 F | +----------+--------------------+--------------------+--------------------+ | | 41.91 .. 39.16 K | 167.6 .. 156.6 K | 377.2 .. 352.5 K | | n | | | 104.1 .. 79.35 C | | | | | 219.7 .. 174.8 F | +----------+--------------------+--------------------+--------------------+ | | 20.99 .. 19.62 K | 83.97 .. 78.47 K | 188.9 .. 176.6 K | | d+ | | | | | | | | | +----------+--------------------+--------------------+--------------------+ | | 20.99 .. 19.61 K | 83.95 .. 78.45 K | 188.9 .. 176.5 K | | D | | | | | | | | | +----------+--------------------+--------------------+--------------------+ | | 14.02 .. 13.10 K | 56.07 .. 52.40 K | 126.2 .. 117.9 K | | t+ | | | | | | | | | +----------+--------------------+--------------------+--------------------+ | | 14.02 .. 13.10 K | 56.06 .. 52.39 K | 126.1 .. 117.9 K | | T | | | | | | | | | +==========+====================+====================+====================+ +----------+--------------------+--------------------+--------------------+ | | | | | | | TETRAGONAL | TETRAGONAL | TETRAGONAL | | Particle | Order 4 | Order 5 | Order 6 | | | | | | | | alpha = beta = | alpha = beta = | alpha = beta = | | | 0.9715 A 1.005 A | 0.7772 A 0.8040 A | 0.6477 A 0.6700 A | +==========+====================+====================+====================+ | | 671.5 .. 627.4 K | 1049 .. 980.4 K | 1511 .. 1412 K | | p+ | 398.4 .. 354.3 C | 775.9 .. 707.3 C | 1238 .. 1139 C | | | 749.0 .. 669.7 F | 1429 .. 1305 F | 2260 .. 2082 F | +----------+--------------------+--------------------+--------------------+ | | 671.1 .. 627.1 K | 1049 .. 979.9 K | 1510 .. 1411 K | | H | 398.0 .. 354.0 C | 775.9 .. 706.8 C | 1237 .. 1138 C | | | 748.3 .. 669.1 F | 1429 .. 1304 F | 2258 .. 2080 F | +----------+--------------------+--------------------+--------------------+ | | 670.5 .. 626.6 K | 1048 .. 979.0 K | 1509 .. 1410 K | | n | 397.4 .. 353.5 C | 774.9 .. 705.9 C | 1236 .. 1137 C | | | 747.2 .. 668.2 F | 1427 .. 1303 F | 2257 .. 2078 F | +----------+--------------------+--------------------+--------------------+ | | 355.9 .. 313.9 K | 524.8 .. 490.4 K | 755.8 .. 706.2 K | | d+ | 82.75 .. 40.75 C | 251.7 .. 217.3 C | 482.7 .. 433.1 C | | | 181.0 .. 105.4 F | 485.0 .. 423.1 F | 900.8 .. 811.5 F | +----------+--------------------+--------------------+--------------------+ | | 355.8 .. 313.8 K | 524.7 .. 490.3 K | 755.6 .. 706.0 K | | D | 82.65 .. 40.65 C | 251.6 .. 217.2 C | 482.5 .. 432.9 C | | | 180.8 .. 105.2 F | 484.8 .. 422.9 F | 900.4 .. 811.1 F | +----------+--------------------+--------------------+--------------------+ | | 224.3 .. 209.6 K | 350.5 .. 327.5 K | 504.7 .. 471.6 K | | t+ | -48.85 .. -63.55 C | 77.35 .. 54.35 C | 231.6 .. 198.5 C | | | -55.93 .. -82.39 F | 171.2 .. 129.9 F | 448.8 .. 389.2 F | +----------+--------------------+--------------------+--------------------+ | | 224.3 .. 209.5 K | 350.4 .. 327.4 K | 504.6 .. 471.5 K | | T | -48.85 .. -63.65 C | 77.25 .. 54.25 C | 231.5 .. 198.4 C | | | -55.93 .. -82.57 F | 171.1 .. 129.7 F | 448.6 .. 389.0 F | +==========+====================+====================+====================+ 8. REFERENCES [to be added in final copy later this week] An interesting little addendum that I neglected to insert last night: Another possibility for creating a reflective region in an HLH design would be to heavily dope the outer layer of the cylinder with atoms or ions that will wedge into the octahedral sites and permanently expand the lattice constant: Octahedral Very Evenly Octahedral Implantation Loaded PdHx Implantation Region Region Region | __________________|______________________ | / \ / \ / \ +===================================================+ |ooo ooo| |ooo ooo| |ooo ooo| +===================================================+ \ / \_________________________________________/ \ / | | | Reflective Transparent Reflective Region Region Region There are very few good candidates for this type of implantation approach, as they must be both small (slightly larger than atomic hydrogen) and reasonably metallic (to prevent covalent or ionic salts from forming and destroying the crucial lattice structure. I'd say about the only possibilities from this perspective are: Li - lithium --Somewhat permeable in Pd; probably easiest to try Be - beryllium --Probably larger than Li and more stable once wedged B - boron --Probably hard to dope; ion implantation + annealing? C - carbon --Remote possibilty; might destroy the crystal structure Na - sodium --Probably too big; only via ion implantation + annealing The doped layers would not necessarily need to be very thick, as even a few Angstroms worth of very evenly implanted crystal would probably cause significant diffracton/reflection. The resulting structure would probably be _much_ more stable than any hydrogen-only HLH doping structure, since high concentrations of hydrogen in Pd are inherently unstable. I'd guess that saturation octahedral doping (resulting in compounds with the nominal formulae PdLi, PdBe, PdB, PdC) would be best, although lower levels would probably still expand the average lattice. It is interesting to note that this proposal implies that such implant material need be inserted _only_ on the ends of a crystal, not on the sides. This could make even control of hydrogen saturation easier. Cheers, Terry Subject: Re: Draft paper on Bernecky condensation Originator: terry@aslws01 In article <1993Jul14.161726.5011@asl.dl.nec.com> I said: > Add to the list the somewhat interesting case of: > > He - Helium --Smallish, very immobile. Alpha irridation + annealing? Add to the addition: Ne - Neon --Larger than He, immobile. Ion implanttion + annealing? Ar - Argon --Larger Ne, immobile -- size dubious (ditto Xe, Kr) I'll stop handwaving the radii and get some specificis for the final draft. Also, diffraction would be most likely to occur (if it works at all) for opposing _atomically smooth_ diagonal faces, with similarly smooth levels of doping (probably needing to exend no more than tens of Angstroms or less into the crystal). For the following crystal: _ 101 101 | | | | _ +--|--------+ 011 ------/ | / \----- 011 __ / | 001 / /| _ 110 --> +-----|-----+ / |---- 110 _ /_\_________/_\/ | 110 ---+ | | |010/ | | 100 | +-------- 110 __ | | | | / _ 011 -->|_|_________|_|/<------ 011 \|_________\ / | /|\ |_ _|_ 101 101 ... the pairs of diagonal faces (not all labeled above) to use would be: __ _ _ __ _ _ _ _ _ _ 011-011 101-101 110-110 011-011 101-101 110-110 Because of quantum channeling effects [SciAm ref], you would actually get _better_ odds on back-and-forth reflection of atoms than with a simple mirror -- that is, the lattice itself will be somewhat self-correcting. Crystal size? _Small_, not big. 1 mm or less, I'd ballpark, as larger sizes are not going to enhance the basic condensation effect (if it exists!) and are more likely to scatter low-momentum atoms. High crystal quality would be far, far more important than size, I suspect. Cheers, Terry Newsgroups: sci.physics.fusion Path: samba.oit.unc.edu!concert!news-feed-1.peachnet.edu!darwin.sura.net!haven.umd.edu!uunet!seas.smu.edu!vivaldi!aslws01!aslws01!terry From: terry@asl.dl.nec.com Subject: More on J. Logajon's point / "colliding" condensates? Message-ID: <1993Jul15.155338.6634@asl.dl.nec.com> Originator: terry@aslws01 Sender: news@asl.dl.nec.com Nntp-Posting-Host: aslws01 Organization: (Speaking only for myself) References: <1993Jul13.204759.23650@asl.dl.nec.com> <1993Jul14.161726.5011@asl.dl.nec.com> <1993Jul14.203359.7410@asl.dl.nec.com> Date: Thu, 15 Jul 1993 15:53:38 GMT Lines: 131 Hi folks, MORE ON JOHN LOGAJON'S POINT In article <1993Jul15.052220.12790@ns.network.com> logajan@ns.network.com (John Logajan) wrote: > I won't pretend to understand the necessities of "reflection" as it is used > here, but wouldn't the Pd surface/electrolyte boundary provide a rather > drastic and abrupt change in the lattice constant -- not unlike a water/air > photon reflecting effect? Also, John Logajon made the point that a smooth crystal face will reflect _all_ atomic momenta. There's an important, somewhat subtle point there: if all momenta are reflected from the surface equally well, how will the _selected_ frequency of the diffraction area differ significantly from all the other frequencys bouncing off the atomically smooth Pd surface? Thus thanks to John I will add this further modification to the proposed structure for looking for Bernecky condensates in palladium crystals: The diffraction area should have a very smooth inner surface, and a comparatively _rough_ external surface: --------------------------- ooooo\ oooooo/ ooooo\ Inner surface --> ooooo\ <-- External surface oooooo/ oooooo\ ooooo/ --------------------------- Not only will this quite effectively scatter the non-selected frequencies and keep them from reflecting coherently, but it will also provide some level of "momentum chaos" that will increase the chances that scattered atoms will come close enough to the selected frequency to join the boson condensate. Experimentally, this would imply first polishing to atomic smoothness, then doping very evenly, then very mild etching or other roughening of the original polished surface -- making sure that the roughening process does not penetrate the doped region. Thanks, John! I will assume this scattering-of-non-selected-frequencies approach from here on out, and will include and reference your observation in the updated draft. "COLLIDING" CONDENSATES? Another intriguing aspect of W. Robert Bernecky's BWO farfetch was the idea of boson condensates "colliding." I like the idea, but am not convinced that such condensates would necessarily move at all. I would tend to assume that they would form non-moving stationary waves, so that the idea of two of them colliding might be more aptly defined in terms of two of them _intersecting_ somewhere along their (stationary?) lengths. Interestingly enough, the presence of _multiple_ diagonal faces pairs in a Pd crystal (a total of six pairs) makes it fairly easily propose a way to create such _intersecting_ standing waves. And quite unlike photons, boson atoms have real volumes, so that such intersecting standing waves of boson atoms _cannot_ just ignore each other (as do photons in crossed beans of light). They will have to interact in a way that is less than immediately clear, at least to my poor brain. (Historical sidenote: About 3 years ago I asked in this group: "What would happens if two jets of superfluid helium were made to cross at right angles? Would they pass through each other like beams of (boson) photons, or would they spray out like two jets of (fermion) water?" No one ever answered it, but the mutual spatial occupation issue here is very similar.) All this leads, for example, to the experiment described below. PLEASE note that this "experiment" is based on the decidedly unproven assumption that Bernecky condensates exist at all! Thus there would be rather little point in performing it until someone finds evidence for the existence of such condensates. Top view of a crystal "slice" made parallel to one of the cubic faces -######- - oooooo - - oooooo - Cubic face - oooooo - Cubic face - oooooo - - \\\\\\ - - ////// - - \\\\\\ - #oooo /\/\/\/\/\\/\/\/\/\/\/\/\/ oooo# #oooo /\/\/\/\/\/\/\/\\/\/\/\/\/ oooo# #oooo /\/\/\/\/\\/\/\/\/\/\/\/\/ oooo# Surface-roughened #oooo /\/\/\/\/\/\/\/\\/\/\/\/\/ oooo# Diagonal Face #oooo /\/\/\/\/\\/\/\/\/\/\/\/\/ oooo# (Primary Condensate) #oooo /\/\/\/\/\\/\/\/\/\/\/\/\/ oooo# #oooo /\/\/\/\/\/\/\/\\/\/\/\/\/ oooo# - ////// - - \\\\\\ - - ////// - - oooooo - Cubic face - oooooo - Cubic face - oooooo - - oooooo - -######- Narrower Secondary Face (Control Condensate) In the above diagram, one pair of diagonal axes has been intentionally cut narrower than the primary condensate. The premise is that this secondary condensate should be able to provide some level of "control" of a rather hard-to-specify type of the primary condensate. What kind? My own guess is that the intersection area would have to do "double time" to satisfy both sets of wave equations for the two condensates. If you then shift the phase of one of the two condensates -- say by simply _squeezing_ the crystal in the vertical axis -- you may be able to do such odd things as zeroing out the amplitude of the primary condensate in the central region -- in other words, bisecting the primary condensate wave- function into two physically separated regions. Or it might do something else entirely. The point in any case is that this would be an _interesting_ set of experiments to try if Bernecky condensates can be shown to exist. Cheers, Terry Newsgroups: sci.physics.fusion Path: samba.oit.unc.edu!concert!gatech!swrinde!cs.utexas.edu!convex!seas.smu.edu!vivaldi!aslws01!aslws01!terry From: terry@asl.dl.nec.com Subject: Detection of Bernecky Condensates Message-ID: <1993Jul15.181810.7986@asl.dl.nec.com> Originator: terry@aslws01 Sender: news@asl.dl.nec.com Nntp-Posting-Host: aslws01 Organization: (Speaking only for myself) References: <1993Jul14.161726.5011@asl.dl.nec.com> <1993Jul14.203359.7410@asl.dl.nec.com> <1993Jul15.155338.6634@asl.dl.nec.com> Date: Thu, 15 Jul 1993 18:18:10 GMT Lines: 19 Another short addendum: The best technique for determining the formation of a Bernecky condensate would almost certainly be neutron diffraction. The formation of a condensate would represent the abrupt addition of a new regularity within the crystal, one that should show up quite distinctly as a new bright in the diffracted neutron beam. NMR should also work, since there would be an additional ordering to the hydrogen or deuterium atoms. X-ray diffraction is also a candidate, but looks more at the electron clouds (vs. the p or d nuclei) and thus would less exact. On the other hand, X-rays are much easier to get hold of than cold neutron beams, so this might not be a bad choice, either. Cheers, Terry