scholarly journals A theoretical formula for the solubility of hydrogen in metals

1937 ◽  
Vol 160 (900) ◽  
pp. 37-47 ◽  
Keyword(s):  
Lattice Structure ◽  
Specific Interaction ◽  
Pure Metal ◽  
Normal Metal ◽  
Theoretical Formula ◽  
Theoretical Treatment ◽  
Solubility Curve ◽  
Hydrogen Atoms ◽  
Metal Lattice ◽  
The Difference

1— In certain metals such as Cu, hydrogen appears to be dissolved in the metal in the form of free protons, which do not affect the normal metal lattice, even when present at very considerable concentrations. In other metals such as Ti, definite metal hydrides are formed which have a different lattice structure from the pure metal. The metal Pd is intermediate since the hydrogen affects the lattice constant. It is the properties of the former group of metals which are first to be discussed here, since the fact that the normal metal lattice is (practically) unaffected seems to justify a very simple theoretical treatment of the solubility, and it is of some interest to examine how the theory compares with the facts. We shall find that we can bring the facts and the theory into satisfactory order together. The various types of solubility curve are shown in fig. 1. 2— From evidence such as the well-known p 1/2 law for the rate of diffusion of hydrogen through metals we may certainly assume that the hydrogen in the metal is atomic. For the present we shall neglect the difference between atoms of hydrogen and protons plus electrons, and merely assume that the atoms are present as such in the metal, without specific interaction with particular metallic atoms; the metal merely provides a region in which hydrogen atoms can exist and move in a definite field of potential energy. Specific contributions by the electrons of the hydrogen atoms will be considered later, when the hydrogen atoms in the metal will be considered as protons plus electrons.

scholarly journals A theoretical formula for the solubility of hydrogen in palladium

1937 ◽  
Vol 161 (907) ◽  
pp. 525-545 ◽  
Keyword(s):  
Hydrogen Pressure ◽  
Lattice Structure ◽  
Pure Metal ◽  
Theoretical Interpretation ◽  
Theoretical Formula ◽  
Statistical Interpretation ◽  
Lattice Structures ◽  
Square Root ◽  
Starting Point

It is known that the amount of hydrogen dissolved by Pt, Mo, Cu, Co, Fe, and Ni is directly proportional to the square root of the hydrogen pressure p . Furthermore, these metals take up hydrogen without changing their lattice structure. It has been shown by Fowler and Smithells (1937) that one can get a theoretical interpretation of the observed solubility, if one assumes that the hydrogen dissolves as protons which are free to move throughout practically the whole volume of the metal. The theory has been extended, using slightly different assumptions, to include the metals V, Ta, Ti, and Zr. In these cases definite metallic hydrides are formed having lattice structures differing from that of the pure metal, and at higher pressures the amount of absorbed hydrogen saturates, being no longer proportional to √ p . In the present paper we shall give a statistical interpretation of the solubility of hydrogen in palladium. Palladium seems to offer an advan­tageous starting-point for an attempt at a more profound extension of the theory outside the region where the √ p law is valid. It has been thoroughly investigated experimentally and is capable of taking up large volumes of hydrogen without changing its lattice structure (Linde and Borelius 1927; Krüger and Gehm 1933)

scholarly journals An experimental and theoretical investigation of diffusion in a two-phase alloy

1948 ◽  
Vol 192 (1031) ◽  
pp. 575-592 ◽  
Keyword(s):  
Free Energy ◽  
Single Phase ◽  
Phase State ◽  
Theoretical Treatment ◽  
Research Association ◽  
Essential Difference ◽  
Two Phase ◽  
Two Factors ◽  
Order Of Magnitude ◽  
The Difference

The present paper describes an investigation of diffusion in the solid state. Previous experimental work has been confined to the case in which the free energy of a mixture is a minimum for the single-phase state, and diffusion decreases local differences of concentration. This may be called ‘diffusion downhill’. However, it is possible for the free energy to be a minimum for the two-phase state; diffusion may then increase differences of concentration; and so may be called ‘diffusion uphill’. Becker (1937) has proposed a simple theoretical treatment of these two types of diffusion in a binary alloy. The present paper describes an experimental test of this theory, using the unusual properties of the alloy Cu 4 FeNi 3 . This alloy is single phase above 800° C and two-phase at lower temperatures, both the phases being face-centred cubic; the essential difference between the two phases is their content of copper. On dissociating from one phase into two the alloy develops a series of intermediate structures showing striking X-ray patterns which are very sensitive to changes of structure. It was found possible to utilize these results for a quantitative study of diffusion ‘uphill’ and ‘downhill’ in the alloy. The experimental results, which can be expressed very simply, are in fair agreement with conclusions drawn from Becker’s theory. It was found that Fick’s equation, dc / dt = D d2c / dx2 , can, within the limits of error, be applied in all cases, with the modification that c denotes the difference of the measured copper concentration from its equilibrium value. The theory postulates that D is the product of two factors, of which one is D 0f the coefficient of diffusion that would be measured if the alloy were an ideal solid solution. The theory is able to calculate D/D 0 , if only in first approximation, and the experiments confirm this calculation. It was found that in most cases the speed of diffusion—‘uphill’ or ‘downhill’—has the order of magnitude of D 0 . * Now with British Electrical Research Association.

Dynamic lung compliance in newborn and adult cats

1986 ◽  
Vol 60 (3) ◽  
pp. 743-750 ◽  
Author(s):  
K. J. Sullivan ◽  
J. P. Mortola
Keyword(s):  
Stress Relaxation ◽  
Transpulmonary Pressure ◽  
Lung Compliance ◽  
Theoretical Treatment ◽  
The Difference ◽  
Adult Cats ◽  
Isolated Lungs ◽  
Dynamic Lung Compliance ◽  
Volume History ◽  
Lung Stress

Static (Cstat) and dynamic (Cdyn) lung compliance and lung stress relaxation were examined in isolated lungs of newborn kittens and adult cats. Cstat was determined by increasing volume in increments and recording the corresponding change in pressure; Cdyn was calculated as the ratio of the changes in volume to transpulmonary pressure between points of zero flow at ventilation frequencies between 10 and 110 cycles/min. Lung volume history, end-inflation volume, and end-deflation pressure were maintained constant. At the lowest frequency of ventilation, Cdyn was less than Cstat, the difference being greater in newborns. Between 20 and 100 cycles/min, Cdyn of the newborn lung remained constant, whereas Cdyn of the adult lung decreased after 60 cycles/min. At all frequencies, the rate of stress relaxation, measured as the decay in transpulmonary pressure during maintained inflation, was greater in newborns than in adults. The frequency response of Cdyn in kittens, together with the relatively greater rate of stress relaxation, suggests that viscoelasticity contributes more to the dynamic stiffening of the lung in newborns than in adults. A theoretical treatment of the data based on a linear model of viscoelasticity supports this conclusion.

scholarly journals Electrochemical hydrogenation, lithiation and sodiation of the GdFe2–xMx and GdMn2–xMx intermetallics

2021 ◽  
pp. 139-149
Keyword(s):  
Electrode Materials ◽  
Electrochemical Impedance ◽  
Diffraction Method ◽  
Electrochemical Characteristics ◽  
Electrochemical Hydrogenation ◽  
Hydrogen Atoms ◽  
X Ray ◽  
Cell Parameters ◽  
The Difference ◽  
Better Than

Electrochemical hydrogenation, lithiation and sodiation of the phases GdFe2–xMx and GdMn2–xMx (M=Mn, Co, Ni, Zn, and Mg) and the influence of doping components on electrochemical characteristics of electrode materials on their basis were studied using X-ray powder diffraction method, scanning electron microscopy, energy dispersive X-ray analysis, X-ray fluorescent spectroscopy, cyclic voltammetry and electrochemical impedance spectroscopy. Phase analysis showed a simple correspondence between unit cell parameters of the phases and atomic radii of doping elements. Electrode materials based on GdFe2 and GdMn2 doped with 2 at.% of Co, Ni and Mg demonstrated better hydrogen sorption properties than those doped with Mn and Zn. Corrosion resistance of the doped electrodes was also better than of the binary analogues (e.g. corrosion potential of the GdFe2-based electrode was –0.162 V whereas that of GdFe1.96Ni0.04 was –0.695 V). The capacity parameters were increased in the following ranges: Zn<Mn<Mg<Co<Ni and Zn<Fe<Mg<Co<Ni for GdFe2–xMx and GdMn2–xMx, respectively. After fifty cycles of charge/discharge, we observed the changes in surface morphology and composition of the electrode samples. In the structure of studied Laves type phases with MgCu2-type structure, the most suitable sites for hydrogen atoms are tetrahedral voids 8a. During lithiation and sodiation of the phases, the atoms of the M-component of the structure are replaced by the atoms of lithium, and the atoms of gadolinium are replaced by the atoms of sodium. This difference in interaction is due to the difference in atomic sizes of the atoms. No insertion of lithium or sodium into the structural voids of the phases was observed.

scholarly journals On the catalytic dehydrogenation of naphthenes II. Competition experiments and energies of C-H bonds

1947 ◽  
Vol 190 (1022) ◽  
pp. 309-328 ◽  
Keyword(s):  
Activation Energy ◽  
Active Sites ◽  
Catalyst Surface ◽  
Resonance Energy ◽  
Activation Energies ◽  
Theoretical Treatment ◽  
Catalytic Dehydrogenation ◽  
Simple Relationship ◽  
Hydrogen Atoms ◽  
Methyl Cyclohexane

The rates of dehydrogenation in competition experiments using mixtures of two naphthenes, or a naphthene and a cyclic mono-olefine or two cyclic mono-olefines, have been examined theoretically and experimentally for the stationary state conditions. Provided the two reactants can occupy the same sites on the catalyst surface, then the ratio of the rates should be directly proportional to the ratio of the partial pressures at any instant. Theory suggests that a constant which can be derived from these competition experiments should be independent of the overall pressures, or of the initial ratio of concentrations or of the overall extent of dehydrogenation. Further, the ratio of the rates in competition should bear no simple relationship to the ratio of the individual rates alone, but should be related to the slopes of the 1/rate against 1/pressure plot for the two components considered separately. Moreover, the constant should be a ratio of two functions each of which is characteristic of one of the naphthenes. The theoretical conclusions have been confirmed experimentally which proves either that the groups of active sites on the catalyst surface are widely separated or that any set of sites is available for the reaction of any molecular species, and no interference takes place between naphthene molecules adsorbed on adjacent sites. Proof that a naphthene and cyclohexene are dehydrogenated on the same sites is supplied by the observation that a constant is obtained when different mixtures of cyclohexene and trans -1:4-dimethyl cyclohexane are allowed to compete for the surface. The ratios for methyl, ethyl, the three dimethyl and the three trimethyl cyclohexanes in competition with cyclohexane have been accurately determined at temperatures of 400 and 450° C. From the constants so derived the activation energy differences for the removal of the first pair of hydrogen atoms has been obtained. These values are discussed in terms of the possible transition complexes, and it is shown that the reaction proceeds by the loss of a pair of hydrogen atoms simultaneously and not by a half-hydrogenated state mechanism. Using these activation energies and the experimentally found overall activation energy of 36 kcal./g. mol., the resonance energy per resonating structure was determined as 1-73 kcal. This is in good agreement with the energies of C-H bonds in alkyl radicals (2-2 kcal./g.mol./ resonating structure). The theoretical treatment suggests that the weakest C-H link in methyl cyclohexane should be in the three position to the methyl group. A study of the activation energies involved shows that the methyl cyclohexene produced from methyl cyclohexane is not 1-methyl-1-cyclohexene, thus confirming the theoretical deduction.

Computer Simulation of the Order-Disorder Transition in Ammonium Chloride

1997 ◽  
Vol 52 (8-9) ◽  
pp. 609-613
Author(s):  
Roman Goc ◽  
Jan W. Wąsicki
Keyword(s):  
Ammonium Chloride ◽  
Structural Transition ◽  
Chloride Ions ◽  
Theoretical Formula ◽  
Ammonium Ions ◽  
Hydrogen Atoms ◽  
Second Moment ◽  
Second Moments ◽  
Cscl Type ◽  
Disorder Type

Abstract The phase transition at Tc = 243 K in ammonium chloride is well established to be of the order-disorder type. The ammonium chloride has a CsCl-type cubic structure with hydrogen atoms pointing toward four of the eight chloride ions at the corners of the unit cell. This means that there are two possible orientations of ammonium tetrahedron; a and b. In the ordered phase below the Tc temperature all ammonium ions have the same, let it be a, orientation. Above the Tc temperature ions are randomly distributed among the two possible orientations a and b. An attempt was made to correlate such structural transition with the second moment of the proton NMR absorption line. This approach was chosen because the second moment is the parameter of the NMR line for which the exact theoretical formula exist, and which is mainly a function of the structure and the reorien-tational state of the studied material. It was found that the NMR second moments calculated for the described above model of the structural transition properly reflect the changes of the experimental NMR second moments measured at temperatures below and above this transition.

60Co γ-RADIOLYSIS OF HYDROGEN HALIDES AT 77 °K

1966 ◽  
Vol 44 (2) ◽  
pp. 191-197
Author(s):  
R. C. Rumfeldt ◽  
D. A. Armstrong
Keyword(s):  
Liquid Phase ◽  
Hydrogen Atom ◽  
Experimental Error ◽  
Dose Dependence ◽  
Solid Matrix ◽  
Reactive Intermediate ◽  
Hydrogen Atoms ◽  
Hydrogen Halides ◽  
Atoms And Molecules ◽  
The Difference

Yields of hydrogen formed in the 60Co γ-radiolyses of pure polycrystalline samples of HBr and HCl at 77 °K decrease with increasing dose in the range 0 to 1 × 1018 eV per g. The true initial yields are G(H2)solidHClat77°K = 6.3 ± 0.2 and G(H2)solidHBrat77°K = 12.3 ± 0.3. Within experimental error these are the same as the respective liquid-phase yields at −79 °C. For doses in excess of 2 × 1018 eV per g the dose dependence is no longer significant and the yields tend toward plateau values of 3.2 ± 0.1 and 10.3 ± 0.1 for HCl and HBr respectively. The dose dependence of the hydrogen yields is attributed to the scavenging of a reactive intermediate by the halogen atoms and molecules which accumulate in the solid matrix as the dose increases.In independent experiments with an apparatus of the Klein–Scheer type it was shown that hydrogen atoms react readily with films of HBr at 77 °K. There is, however, no evidence of a significant reaction with HCl at this temperature. The difference in behavior of the two hydrogen halides may be explained by their different activation energies for reaction with hydrogen atoms. The results of the γ-radiolyses are discussed in the light of these experiments and it is suggested that the dose dependence may be a result of the scavenging of an ionic intermediate rather than a thermal hydrogen atom.

Permeation of Electrolytically Generated Hydrogen and Tritium Atoms through Lead

1971 ◽  
Vol 49 (14) ◽  
pp. 2406-2411 ◽  
Author(s):  
Bansi L. Muju ◽  
Frank R. Smith
Keyword(s):  
Current Density ◽  
Separation Factor ◽  
Room Temperature ◽  
Alkaline Media ◽  
Gas Evolution ◽  
Hydrogen Atoms ◽  
Metal Lattice ◽  
Acidic And Alkaline Media ◽  
A Current ◽  
Lead Foil

Radiochemical and electrochemical evidence is presented that electrochemically generated tritium and hydrogen atoms permeate through lead foil at measureable rates at room temperature. The permeation process is controlled by diffusion through the metal lattice, Fick's First Law being obeyed by both H and 3H atoms. Using earlier measurements of the diffusivity of H in Pb, H and 3H concentrations of 4 × 10−7 and 9 × 10−13 g-atom cm−3 are computed for a current density of 53 mA cm−2 at the Pb cathode surface.The overall hydrogen-tritium separation factor, ST is apparently 0.3 ± 0.15, in contrast to Bockris and Srinivasan's 6.7 and 7.2 for cathodic gas evolution from acidic and alkaline media, respectively. Reasons are suggested for this large difference.

scholarly journals The mechanism of the initiation and propagation of detonation in solid explosives

1932 ◽  
Vol 138 (834) ◽  
pp. 92-116 ◽  
Keyword(s):  
High Explosive ◽  
A Priori ◽  
Small Samples ◽  
Weight Of Evidence ◽  
Theoretical Treatment ◽  
Mechanical Shock ◽  
Initiation And Propagation ◽  
Solid Explosives ◽  
Velocity Of Propagation ◽  
The Difference

Although half a century has elapsed since the publication of the classical treatise of Berthelot upon explosives, the detailed mechanism of the initiation and propagation of detonation in liquid and solid explosives is still obscure. Detonation is a phenomenon exhibiting a number of specific characteristics which differentiate it quite definitely from the explosive combustions of such substances as gunpowder and cordite. It is well known that the latter are governed by laws relating the rate of reaction to the surface area, the temperature and pressure of the surrounding gases, etc., and that heat is the chief medium of initiation and propagation, whereas in the case of detonation, the reaction wave-front travels directly through the explosive medium in the same sense as does a sound wave, and the velocity of propagation is a very definite characteristic of the phenomenon. This stability of the detonation velocity is well demonstrated for solid explosives by the photographs in a recent paper by E. Jones ; the speeds are usually much greater than any exhibited by explosive combustions, and range from 1500 to 10,000 metres per second. Finally, the initiation and propagation of detonation appear to be associated much more intimately with mechanical shock than with flame. The weight of evidence strongly indicates that the difference between detonation and explosive combustion is fundamental and not merely of degree, and the term “high explosive” is reserved for substances capable of the former property. The theoretical treatment of detonation as a shock wave traversing the medium and maintained by the accompanying chemical reactions has been developed by several investigators. These writers have built up a quantitative theory from thermodynamical reasoning and have been able to calculate velocities of propagation, which in some cases are correct, but in practice it has been found that the thermodynamical conditions, while necessary, are not sufficient. Thus, a great number of compositions possessing all the thermodynamical qualifications of a high explosive cannot be made to detonate; others permit detonation to be initiated successfully but without propagation, and the reaction degenerates into a mere deflagration, or even dies out completely. It is indeed very difficult to judge whether a particular composition is a true detonating explosive without the opportunity to test the sample in reasonable quantity. The violent decompositions of small samples or single crystals furnishes no a priori evidence of detonation, and innumerable examples may be quoted of such material in bulk being unable to propagate the local and violent initial activity.

METHYL ACTIVATION AND sRNA METHYLATION BY SOLUBLE FRACTIONS OF SEVERAL VERTEBRATE LIVERS

1967 ◽  
Vol 45 (10) ◽  
pp. 1513-1522 ◽  
Author(s):  
R. L. Hancock
Keyword(s):  
Mouse Liver ◽  
Specific Interaction ◽  
Adult Rabbit ◽  
X Chromosomes ◽  
E Coli ◽  
Lower Vertebrates ◽  
The Difference ◽  
Species Specific ◽  
Methylase Activity

The amount of liver ATP: L-methionine S-adenosyltransferase activity varies widely in vertebrates from trace amounts in certain lower vertebrates, e.g. shark or turtle, to relatively large quantities in mammals, e.g. mouse or rabbit. The liver from male mice of a particular stock had only two-thirds the activity of female mouse liver. This difference is not explained by the difference between the sexes in number of X-chromosomes, since female mice with only one X-chromosome (X/0) had the same levels of liver S-adenosyltransferase activity as normal females with two X-chromosomes.sRNA methylase activity from mouse, shark, and rabbit liver supernatant fractions were studied with mouse, shark, and Escherichia coli sRNA. Highspeed supernatant fractions from both rabbit embryonic liver and mouse hepatoma hypermethylated E. coli sRNA which had been previously methylated by adult rabbit or mouse liver supernatant fractions. Hepatoma methylase(s) acts in an analogous manner to that of a species-specific interaction with heterologous and homologous sRNA.A calculation is made comparing the amount of sRNA methylase activity detected in vitro with mouse liver sRNA, with one which is theoretically derived; similar values are obtained. The variation found in vertebrate liver with respect to methyl activation and sRNA methylation is discussed.

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