Cold fusion experiments have utilized two types of cathode materials; palladium and titanium (including several titanium alloys). These two metals have significantly different behaviors in the presence of hydrogen and its isotopes. Their response to exposure to hydrogen isotopes has been extensively studied and well documented [ALEF, MEU], particularly in the case of palladium. In the following, we shall highlight some of the behavior of the Pd-H and the Ti-H systems, selecting those aspects that are most pertinent to the issues raised by the suggested cold fusion experiments. Much of what is known derives from experiments using the mass one isotope, H. The isotopic dependence is sufficiently well understood to allow the behavior of deuterium, D, to be deduced from the measurements on H where data on D are not available. Many aspects of the behavior of hydrogen isotopes in body centered cubic (bcc) (beta phase Ti alloys) and face centered cubic (fcc) (Pd) metals result from their behavior as quantized particles; other properties can be understood using classical concepts. Behavior as quantized particles has not been established for hydrogen isotopes in the hexagonal close packed (hcp) crystal structure (titanium, alpha phase Ti alloys) but such behavior may be expected.
Palladium has a fcc close packed crystal structure and as hydrogen is added this structure is maintained across the phase diagram [WIC]. Palladium can absorb large quantities of H(D), with concentrations as high as H/Pd = 1.1 being attainable. Both the alpha and beta phases of the Pd-H(D) system are solid solutions and, at temperatures near 300°K, no ordered structures are known. The H(D) occupies predominantly octahedral interstitial sites, which if they were all filled would result in a H(D)/Pd ratio of 1. Hydrogen can also be accommodated in tetrahedral interstitial sites at a somewhat higher energy and it is believed that the sites may be partially occupied at the higher H(D)/Pd ratios. The spacing of H(D) occupying these sites is not particularly small as shown by Table 4.A below. Both the octahedral and tetrahedral sites have cubic site symmetry. Since H(D) appears to have random distribution in the occupied sites, the maintenance of the cubic crystal structure on adding H(D) is consistent with the high H(D)/Pd values attained. Further evidence for the random occupancy of sites and the cubic distortion of the lattice is provided by X-ray studies of the Pd-H(D) system [PEI], which also indicate that the behavior of D is closely similar to that of H.
Recent theoretical treatments [RIC, NOR] show that H(D) does not attain exceptionally close nearest neighbor distances, even under dynamic conditions. Molecular dynamic simulations [RIC] at concentrations up to D/Pd = 1.1 found no D-D distances shorter than 0.07 nm compared to the molecular D-D distance of 0.074 nm. Interactions of D with lattice defects have been studied both experimentally and theoretically. Significant attractive interaction energies are found [BES] with those defects, such as vacancies, which have a decreased electron density. Palladium has such an attractive interaction between H(D) and vacancies, but it is particularly weak. Each vacancy can accommodate up to 6 D interstitials with the D solutes occupying sites displaced towards the octahedral interstitial sites adjacent to the vacancy. The D-D distance adjacent to the vacancy is 0.18 m.
|SITES OCCUPIED||DISTANCE IN NANOMETERS|
|Nearest neighbor octahedral sites||0.28|
|Nearest neighbor tetrahedral sites||0.19|
|Nearest neighbor octahedral-tetrahedral sites||0.17|
|D-D distance in a multiply occupied vacancy [BES]||0.19|
|Intramolecular D-D distance in deuterium gas||0.074|
|Intramolecular D-D distance in liquid deuterium||0.074|
|Intermolecular D-D distance in liquid deuterium||0.27|
|Intramolecular D-D distance in water||0.15|
The phase diagram of the Pd-H(D) system [ALEF, MEU] is typical of many of the bcc and fcc hydride forming systems and is shown in Figure 4.1. The dominant feature is a miscibility gap, i.e. a phase region in which the alpha and beta phases are in equilibrium, with a critical temperature of about 549°K and a critical composition of H(D)/Pd = 0.27.
At about 300°K the initial alpha phase has a solubility of about H/Pd = 0.03 and the two phase region extends to about H/Pd = 0.6 at which point the beta phase is formed. Both the alpha and beta phases have fcc structures. Phase relations in the Pd-H system depend on the isotope of hydrogen used, but the isotopic dependence is not very large. Important differences do exist in the P-C-T data [ALEF, MEU], which characterize the equilibrium of gaseous hydrogen isotopes with Pd. These differences are consistent with the differences in the isotopic masses. Many of the thermodynamic properties of the Pd-H(D) system are consistent with theoretical calculations based on mean field theory [WAG] based on a repulsive nearest neighbor interaction between H solutes. This repulsive interaction has been measured using a variety of methods [WAG, VOL, PIC, OAT].
While the alpha and beta phases are solid solutions of H(D) in the Pd interstitial sites, formation of long range ordered structures does occur at high concentrations and low temperatures [ELL]. These structures form by ordering of the H(D) interstitials on subsets of the interstitial sites and are consistent with nearest neighbor deuterium repulsive interactions. At H(D)/Pd = 1 the structure is of course ordered if the H(D) occupies octahedral interstitial sites. No hydrides are known to form at temperatures of the order of 300°K in the high concentration region of the phase diagram. Ordered hydrides do form at temperatures of a about 77°K [ELL]. Few careful investigations have been carried out in this region. Lattice parameter measurements [PEI], which extend into this composition region, indicate a linear lattice expansion in the alpha and in the beta phases up to H/Pd = 1.0. The lattice expansions due to H and to D are very similar.
Hydrogen and its isotopes diffuse very rapidly in the Pd lattice [VOL] as shown in Figure 4.2. At 300°K, the diffusivity of H in the alpha phase is about 4x10-11 m2s-1. Hydrogen diffusivity in the beta phase is somewhat slower but is still very high. The effect of isotopic mass on diffusivity is very nonclassical in Pd with DD > DW > DT at 300°K, a clear indication of the quantum mechanical tunneling process which dominates the diffusion of H(D) in the Pd lattice. H(D) interacts with solutes and lattice defects, both of which can act as "traps" or low energy sites. The presence of these traps decreases the
effective diffusivity of H(D) when they are unsaturated, i.e. at low H(D) concentrations. Under cathodic charging conditions, which correspond to high H(D) concentrations, the defect or solute traps are saturated and the diffusivity is little affected by their presence. With respect to the cold fusion experiments, an important point is that the known diffusivities of D in Pd allow equilibrium in times considerably shorter than those stated as necessary for attainment of cold fusion. For example, a time of the order of 7 days is required to achieve equilibrium during the charging of a 1 cm thick sheet specimen and a time of the order of 2 hrs is required for a 1 mm thick sheet.
Hydrogen charging of Pd can be carried out in several ways. Electrolytic charging with the Pd as a cathode has been carried out in a number of different electrolytes. In general, the Pd surface is highly active towards the dissociation of the H2 (D2) molecule. Little H2 (D2) gas is evolved until relatively high H(D)/Pd ratios are obtained. Additions of "poisons", such as arsenic ions, to the electrolyte increase the fugacity of the H (D) at the surface by decreasing the formation rate of H2 (D2). A higher H(D)/Pd value can then be obtained with the same overvoltage. Since the fugacity of hydrogen, i.e., the variation of the chemical potential of hydrogen from the standard state at one atmosphere, depends on the overvoltage, as well as on the surface conditions, it is difficult to obtain a direct relation between the cathodic charging conditions and the H(D)/Pd values obtained. Although the units of fugacity are identical to those of pressure, the non-ideality of H2 (D2) results in the equivalent pressure at high fugacity being many orders of magnitude less than the fugacity. A calibration of the equivalent pressure can be obtained by equilibrating the Pd alternatively with both an electrolytic potential and a high pressure H2 (D2) gas at the same H(D)/Pd value.
Gaseous charging of hydrogen is also commonly carried out [BARC]. High H(D)/Pd ratios can be obtained for relatively moderate pressures as shown in Figure 4.3. The data for the Pd-D system is not expected to differ greatly as the isotope effect on solubility is classical. Solution of H(D) in Pd follows Sievert's Law at low pressures and then shows significant deviations from ideal solution behavior, probably as a result of H(D)-H(D) interactions in the Pd. In the region of Sievert's Law behavior, the proportionality of the H(D)/Pd to the square root of the gas pressure is further evidence for solution of H(D) in Pd in the atomic form rather than as a molecule.
Concentrations of D/Pd = 1 are sometimes claimed in cold fusion experiments, and are often quoted as a necessary condition. It has also been suggested [FLE] that the very high confinement pressures produced by electrolytic charging are necessary for cold fusion. Comparison of the D/Pd values attained by gaseous charging with electrolytic charging allows an estimate of these "confinement pressures" to be made. A concentration of about H/Pd = 1 requires a gas pressure of about 150k bars (about 15,000 atm.) at 300°K [BARO] as deduced from Figure 4.3. Thus the effective pressure corresponding to the high fugacities calculated from the overvoltage during cathodic charging to the assumed D/Pd = 1 is equivalent to the very moderate gas pressures required to attain the same H(D)/Pd value.
Palladium is an "exothermic occluder" of H(D), i.e. the heat of solution, relative to the gas phase as a standard state, is negative. The heat of solution is relatively small having a value of -19 kJ/mole H2 in the alpha phase [MEU, WIC] a value of about -46 kJ/mole H2 in the beta phase. The heats of formation of the hydrides in the Pd-H(D) system have not been measured. Hydride heats of formation of many other systems have been measured, are generally exothermic, and lie in the range -58 to - 209 kJ/mole H2 [MEU]. There is only a small effect of isotopic mass on these values. The significance of the values is that the molal enthalpy change on forming the deuteride from a solid solution of the same concentration would be the (heat of formation of the hydride) - (the heat of solution). This value is about -150 kJ/mole or less and represents the upper limit of the heat released from the specimen due to an ordering reaction at high concentrations of D.
Formation of the beta phase from the alpha phase during charging causes a large amount of lattice strain and deformation [HO] as a result of the large increase in volume. Since the molar volume of the beta phase is larger than that of the alpha, the beta phase is in compression during charging and plastic deformation occurs in the alpha phase. On removing the H(D) the decrease of volume that accompanies the beta to alpha phase change causes very high tensile stresses and surface cracking.
While considerably less is known about the Ti-H(D) system than about Pd-H(D), our knowledge is sufficient to answer many of the questions of interest for the cold fusion experiments. Hexagonal close-packed (hcp) titanium absorbs H(D) in the alpha solid solution up to concentrations of about H(D)/Ti = 0.05 at 300°K. Low temperature measurements are not very accurate due to surface oxides which impede the absorption of H(D) from the gas phase. Above this concentration a two phase equilibrium exists between the hcp alpha solid solution and the gamma hydride. This hydride exists over the composition range TiH(D)1.9 to TiH(D)2. The hydride has a fluorite face centered cubic (fcc) structure at the lower compositions and a face centered tetragonal structure as the H(D) concentration is increased. At temperatures above about 570°K the alpha phase H(D) solubility is about H(D)/Ti = 0.1 and the solid solution is in equilibrium with the body centered cubic (bcc) beta phase as shown in the phase diagram displayed in Figure 4.4. The beta phase has a very high solubility for H(D) of the order of H(D)/Ti = 1. Above this composition the beta phase is in equilibrium with the dihydride, TiH(D)2.
Since the beta phase of Ti can be stabilized to below 300°K by solute additions, it is possible to absorb large quantities of H(D) into the beta stabilized alloys at temperatures near 300°K without forming hydrides. The extent of this low temperature H(D) solubility in the beta stabilized Ti alloys has not been established [SHI-2]. Gas phase cold fusion experiments have utilized Ti alloys as well as unalloyed Ti. In some cases these alloys have been specified to be Ti-6A1-6V-2Sn [MEN] which is an alpha-beta alloy, i.e. it was a two phase alloy mixture of the hcp and bcc phases. These two phase alloys have been studied in H atmospheres without noting unusual behavior with respect to the properties of H.
Site location studies have been carried out for some of the Ti - H(D) structures. Random occupancy of tetrahedral sites in the non-stoichiometric gamma hydrides was deduced from NMR measurements [STA-1]. The nearest neighbor D-D distances in the gamma hydride phase [SID] are shown in Table 4.B below. If we assume tetrahedral site occupancy in the hcp alpha phase and both octahedral and tetrahedral site occupancy in the beta phase, the nearest neighbor distances given in Table 4.B below can be calculated. As can be seen, these are larger than the D-D distances in the molecule and much larger than the distances required for fusion.
|D-D Distance in nm|
|Alpha Phase (Hexatherman Close-Packed)|
|Nearest neighbor tetrahedral sites||0.23|
|Gamma Phase (Face Centered Cubic)|
|Nearest neighbor sites||0.22|
|Beta Phase (Body Centered Cubic)|
|Nearest neighbor octahedral sites||0.17|
|Nearest neighbor octahedral-tetrahedral sites||0.083|
The thermodynamics of the Ti - H(D) system has been extensively studied. Heats of solution for H(D) in the alpha and the beta phases are exothermic as is the formation of the gamma hydride. The isotopic mass dependence is very small. These enthalpies are given in Table 4.C below [STA-2, STA-3, MCQ, HAGG, MOR]. Since the heats of solution are negative (exothermic), Ti and its alloys absorb D as they are cooled in D2 gaseous atmospheres and desorb D on heating.
While diffusion of H(D) in Ti has not been measured, the diffusivity at 300°K can be deduced from permeation experiments to be about 1x10-10 m2s-1. This diffusivity would allow equilibration of a 1 mm thick sheet with the H(D) gas atmosphere in about 0.7 hrs. Equilibration of Ti with gaseous H2 at low temperatures is slow due to surface oxides which inhibit the entry processes. Even under cathodic charging conditions, entry of H(D) is inhibited unless the surface oxide is minimized and "electrolytic" poisons are used to minimize the recombination reaction which leads to H2 formation at the surface. As a consequence, equilibration in a gaseous atmosphere or under cathodic charging is dominated by surface reactions.
|Solution in alpha phase||-90.4||-94.6|
|Solution in beta phase||-116.4|
|Formation of gamma phase||-138||-121|
Titanium hydrides are brittle and undergo cleavage when stressed. Hydride formation in alpha phase alloys causes embrittlement [SHI-1]. The beta phase alloys are much less susceptible to embrittlement, and can absorb large quantities of H(D) without fracturing. The tendency to fracture during absorption and desorption of H(D) is clearly associated with the hydride (deuteride) formation and the large volume changes which accompany these phase changes. It is not surprising that the gas charging cold fusion experiments report fracturing of Ti specimens used as the D is absorbed and desorbed. This fracturing is most likely to occur during the heating of specimens which have absorbed large quantities of D. During the cooling cycle the Ti absorbs D from the gas phase and the D composition gradient (and its accompanying molar volume gradient) causes a compressive stress at the outer portion of the specimen. During the heating portion of the cycle the loss of D causes tensile stresses at the outer parts of the material and these cause the fracture to occur.