Showing papers in "Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences in 1960"
TL;DR: A theory of scattering by a rigid rotator in which the coupling between the different energy levels of the rotator is taken into account is formulated and explicit expressions, which do not depend upon the magnetic quantum numbers, are obtained for various elastic and inelastic cross-sections as discussed by the authors.
Abstract: A theory of scattering by a rigid rotator in which the coupling between the different energy levels of the rotator is taken into account is formulated and explicit expressions, which do not depend upon the magnetic quantum numbers, are obtained for various elastic and inelastic cross-sections. Several approximations are described, particular attention being paid to the scattering of heavy particles for which it is shown that at low temperatures the orientation-dependent part of the interaction may be more important than the spherically symmetric part. The scattering of low-energy electrons is also investigated and some representative equations are integrated numerically to illustrate the effect of the orientation dependence.
991 citations
TL;DR: In this article, a method is suggested by which the refractive index and Verdet constant of an atomic system may be derived theoretically using experimental data, applied to atomic hydrogen and to inert gases.
Abstract: A method is suggested by which the refractive index and Verdet constant of an atomic system may be derived theoretically It is applied to atomic hydrogen and to the inert gases and a comparison is made with experimental data The Verdet constant of neon is not anomalous The origin of the suggestion appears to be an underestimate of the experimental error The analysis yields values of th e polarizabilities of th e inert gases which are respectively He, 1-384; Ne, 2-663; Ar, 11-080; K r, 16-734; X e, 27-292 in units of α 3 0
347 citations
TL;DR: In this paper, a generalized version of Nyquist's noise theorem was proposed to describe the scattering of radio waves by the random thermal fluctuations of electron density in a collision-free plasma.
Abstract: A theory is developed which describes the scattering of radio waves by the random thermal fluctuations of electron density in a collision-free plasma. The frequency spectrum, as well as the amplitude, of the scattered radiation is calculated. Particular attention is paid to the part of the spectrum which corresponds to small Doppler shifts, this being the region of greatest significance in connexion with the phenomenon of incoherent scattering from the ionosphere. The calculations are based on a generalized version of Nyquist's noise theorem, and they lead to the following conclusions: (1) The mean scattering cross-section for the ionosphere is equal to that which would exist if each of the electrons scattered independently with a cross-section of one-half the classical Thomson cross-section. (2) The mean Doppler broadening of the scattered signal corresponds roughly to the speed of the ions rather than to that of the electrons. (3) The spectral shape of this signal is not Gaussian. There is a mild maximum in the spectrum away from the central frequency, as can be seen in figure 1. (4) Plasma resonance effects contribute only negligibly to the scattering for frequencies currently of interest.
274 citations
TL;DR: In this paper, Lighthill and Whitham's theory of kinematic waves is applied to study the response of a simple model to a sudden change in rate of accumulation (snowfall).
Abstract: A glacier is treated as an essentially one-dimensional flow system, which is, continuously along its length, either gaining new material by snowfall or losing it by melting and evaporation. The flow at each point, i. e. the volume passing a given point per unit time, is assumed to be a function of the thickness and surface slope. It is then shown that a region of uniform longitudinal compressive strain-rate is temporarily unstable. Lighthill & Whitham’s theory of kinematic waves is applied to study the response of a simple model to a sudden change in rate of accumulation (snowfall). All parts of the glacier thicken, but the lower parts thicken unstably until a kinematic wave arrives to restore stability. The thickening of the lower parts, and the advance of the glacier, can be very great for only a small change in accumulation; the analysis thus explains why glaciers are such sensitive indicators of climate. The velocity and diffusion of kinematic waves is discussed; they travel at 2 to 5 times the surface speed of the ice. Any part of a glacier or ice-sheet has a characteristic response time to changes in accumulation—about 5000 yr for the Antarctic ice-sheet as a whole, and 3 to 30 yr for a typical glacier. The amplitude and phase of the response of a simple glacier to high frequency (seasonal) and low-frequency (climatic) periodic changes in accumulation is calculated. (The periodic changes in accumulation are the Fourier components of the complicated variation that actually occurs.) The upper part behaves in a simple way; the lower part, on the other hand, shows not only a direct response, but also a delayed response due to the arrival of kinematic waves from the upper part. The two components interfere and give wide scope for variation in behaviour from one glacier to another. A further instability, discussed by Bodvarsson, which arises from an increase of accumulation with altitude, is included in the theory. It is also shown how the theory is to be applied in a valley of changing width to calculate the development of any disturbance produced by climatic change. Thus the theory enables one to calculate, in principle, the response of any glacier to any climatic change.
269 citations
TL;DR: In this article, it was shown that if any factors of the form exp(c ij ) are included in the expansion functions there are explicit formulas for all the necessary many-dimensional integrals.
Abstract: Some years ago the author proved that explicit formulae could be obtained for all the many-dimensional integrals occurring in variational solutions of Schrodinger’s many-electron equation for molecules if the expansion functions are constructed from factors of polynomials and radial Gaussian functions about any centres. These have been applied both directly and indirectly in calculations on molecular structure. An extension to this analysis is now reported and it is shown that if any factors of the form exp (– cr ij ) are included in the expansion functions there are explicit formulas for all the necessary many-dimensional integrals. This will make possible both direct and indirect calculations with a more powerful class of expansion functions which appear as if they may give faster convergence for the hitherto very troublesome electronic correlation aspects of many-dimensional wave functions.
254 citations
TL;DR: In this article, it was shown that for wave functions of the form ψ = ∑ k C k exp ( − Q k ), where Q k is any positive definite quadratic form in the Cartesian co-ordinates of n particles and C k a constant, all integrals required for the calculation of the electronic energy of molecules by the variation method can be readily evaluated.
Abstract: It is shown that for wave functions of the form ψ = ∑ k C k exp ( − Q k ) , , where Q k is any positive definite quadratic form in the Cartesian co-ordinates of n particles and C k a constant, all integrals required for the calculation of the electronic energy of molecules by the variation method can be readily evaluated. The potential energy integrals are reduced to quadratures and the other integrals are expressed in closed form. In the general case the quadratic forms Q k determine many-electron functions formed from correlated electron orbitals of ellipsoidal symmetry and with variable centres. The results are easily extended to wave functions of the form ψ = ∑ k P k exp ( − Q k ) , , where P k is a polynomial.
231 citations
TL;DR: In this article, a rounded steel point of smooth contour is drawn across the film surface and the load on the point is gradually increased until the film is removed, leaving a clear channel.
Abstract: Methods of measuring adhesion are considered and an analysis is presented of a method which is particularly suitable for thin films. In this method a rounded steel point of smooth contour is drawn across the film surface and the load on the point is gradually increased until the film is removed, leaving a clear channel. It is shown experimentally that the load required depends upon the nature of the interface between film and substrate without being directly dependent upon the mechanical properties of either. The method is analyzed in detail and a suitable mechanism is proposed. This mechanism is examined both theoretically and experimentally and it is shown that an absolute value of the shearing force required to remove a film can be calculated from the critical load required, the tip radius of the point and the identation hardness of the substrate. Applications have been restricted so far to metal films on transparent substrates.
230 citations
TL;DR: An ozone sonde capable of measuring and transmitting the local ozone concentration has been developed for the I. G. Y. as discussed by the authors, which is described in detail in some detail.
Abstract: An ozone sonde capable of measuring and transmitting the local ozone concentration has been developed for the I. G. Y. and is described in some detail. A continuous electrochemical detector measures the ozone concentration, providing a d. c. electric current of 0 to 5 μ A according to the amount of ozone in the air passed through it. This output current is telemetered by a current-controlled variable inductance which is interchangeable with a standard inductance coil in a Kew radiosonde. The element is of low cost, weighs about 600 g and requires very limited auxiliary equipment for its use. Sixty-five successful ascents have been made and the results of the European ascents are given.
189 citations
TL;DR: In this paper, a thin plane sheet of fluid which is limited laterally and converges towards a point transforms itself into a sheet which diverges in a perpendicular plane when the angle of convergence is small and the distribution of thickness in the converging sheet is elliptic.
Abstract: A thin plane sheet of fluid which is limited laterally and converges towards a point transforms itself into a sheet which diverges in a perpendicular plane. When the angle of convergence is small and the distribution of thickness in the converging sheet is elliptic the diverging sheet has the same shape as the converging sheet. Apparatus for producing such a sheet was set up and the shape of the stream and distribution of pressure in the region of the transformation were measured and compared with calculations.
184 citations
TL;DR: In this paper, the Taylor diffusion coefficient of a solute in pulsating flow through a circular tube is investigated and the case of a viscous flow under a pulsating pressure gradient is treated in detail.
Abstract: The effective dispersion coefficient of a solute in pulsating flow through a circular tube is here found. The case of a viscous flow under a pulsating pressure gradient is treated in detail and it is found that the Taylor diffusion coefficient contains terms proportional to the square of the amplitude of the pressure pulsations. However, the coefficients of these terms tend rapidly to zero, and the effect of pulsation will rarely contribute a fraction of more than 1/128 (the ratio of the amplitude of pressure gradient pulsation to mean pressure gradient) 2 to the total dispersion coefficient. The methods may be applied to diffusion in any periodic flow.
170 citations
TL;DR: In this article, a Beeck-type calorimeter has been used to measure the integral heat of adsorption of oxygen on evaporated films of titanium, chromium, manganese, iron, cobalt, nickel, niobium, molybdenum, rhodium, palladium, tantalum, tungsten, platinum and aluminium.
Abstract: A Beeck-type calorimeter has been used to measure the integral heat of adsorption of oxygen on evaporated films of titanium, chromium, manganese, iron, cobalt, nickel, niobium, molybdenum, rhodium, palladium, tantalum, tungsten, platinum and aluminium. The variation of the heat with the extent of the adsorption has also been determined, except with palladium, platinum and aluminium, for which the amounts of oxygen adsorption were too small to allow this to be done. The heats of adsorption reported are based on a careful determination of the heat capacity of the calorimeter and the overall error is not more than ± 5 kcal/mole. Some investigations of calorimetric behaviour have been made. The surface areas of the films have been measured before and after an adsorption by the B.E.T. method; krypton isotherms at — 196 °C were used for this purpose. From these data, it has been possible to estimate the number of atoms of oxygen adsorbed per surface metal atom. In most cases, this quantity, together with the heat of adsorption, can be related to the oxygen/metal ratios and the heats of formation of certain oxides; this observation is remarkable in view of the limited extent of the adsorption. In the cases of rhodium, palladium and platinum the adsorption stops short of a monolayer and is probably true chemisorption rather than oxide formation. For those metals on which oxide formation occurs, the decrease in heat of adsorption with increasing coverage has been interpreted, in general, in terms of an increase in the oxidation number of surface metal ions by electron transfer within the adsorbed layer. Some theoretical correlations between the heat of adsorption and the atomic and the bulk properties of the species concerned have been examined and found of little value; an empirical relation with the metallic radius is given.
TL;DR: In this article, a method of integration for quasi-linear hyperbolic equations in three independent variables is described by means of a step-by-step procedure, employing difference relations along four bicharacteristics and one time-like ordinary curve through each point.
Abstract: An original method of integration is described for quasi-linear hyperbolic equations in three independent variables. The solution is constructed by means of a step-by-step procedure, employing difference relations along four bicharacteristics and one time-like ordinary curve through each point. From these difference relations the derivatives of the dependent variables at the unknown point are eliminated. The solution at any point can then be computed, with an error proportional to the step size cubed, without referring to conditions outside its domain of dependence. The application of the method to the systems of equations governing unsteady plane motion and steady supersonic flow of an inviscid, non-conducting fluid is discussed in detail. As an example of the use of the method, the flow over a particular delta-shaped body has been computed.
TL;DR: In this article, the magnetic susceptibilities of a series of binary alloys were investigated and the overall picture presented by the results is consistent with the existence of an unfilled d band, having approximately 0.6 holes per atom both for palladium and platinum, which may be filled by alloying with the element of next highest atomic number.
Abstract: Results of measurements of the magnetic susceptibilities of a series of binary alloys are presented. The systems investigated were Pd-Rh, Pt-Ir and Pt-Au. Certain similarities between the alloys of palladium alloyed with silver or rhodium and those of platinum alloyed with gold or iridium are apparent. In addition, the specific heats of palladium-rhodium and platinum-gold alloys have been measured in the liquid helium temperature range and the electronic heats and Debye temperatures computed. The overall picture presented by the results is consistent with the existence of an unfilled d band, having approximately 0.6 holes per atom both for palladium and platinum, which may be filled by alloying with the element of next highest atomic number. Recent work has shown, however, that it is unlikely that the band shape is unchanged on alloying and therefore the calculation by which the number of holes is obtained is probably invalid.
TL;DR: In this paper, the vibrational energy levels of a gaseous diatomic molecule were obtained from the vibration-rotation spectrum of the gas by comparing the observed energies with those obtained by treating the anharmonic Hamiltonian Ha as a small perturbation to H.
Abstract: The Hamiltonian H , leading to the vibrational energy levels of a gaseous diatomic molecule, is normally written in the form (see Buckingham 1958) H = H + H a (1·1) = - hcBc d2/dξ2 + hcωc 2/4 Bc {ξ2 + A / ωc ξ3 + B / ωc ξ4 + ...}, (1·2) where H = - hcBc d2/dξ2 + hcωc 2/4 Bc ξ2 is the harmonic oscillator Hamiltonian, and hcωc 2/2 Bc rc 2 is the force-constant; ξ = ( r — re )/ re is a dimensionless parameter proportional to the displacement from the equilibrium inter-nuclear distance re ; A / ωe , B/ωe ,..., are anharmonic coefficients. The constants re , ωe , Be , A , B , ..., can be obtained from the vibration-rotation spectrum of the gas by comparing the observed energies with those obtained by treating the anharmonic Hamiltonian Ha as a small perturbation to H (see Herzberg 1950).
TL;DR: In this article, it was found that the martensite in low-carbon steels forms predominantly as long needles parallel to $\langle111\rangle_M$ while in the high- carbon steels it forms as plates internally twinned on a fine scale.
Abstract: Martensite formed in plain carbon steels containing less than 1.4% carbon has been studied by direct examination of thin foils in the electron microscope. It was found that the martensite in low-carbon steels forms predominantly as long needles parallel to $\langle111\rangle_M$, while in the high-carbon steels it forms as plates internally twinned on a fine scale. The existence of these narrow twins in the high-carbon martensites enables the transformation mechanism to be derived uniquely. This mechanism, which is largely in agreement with those previously proposed, explains all the observed experimental data. The observed change in the morphology of the martensite from needles to plates as the carbon content increases suggests an explanation of the change in hardness of quenched steels with change in the percentage carbon.
TL;DR: In this article, the results as a whole are discussed in terms of the model of zinc oxide as an n-type semiconductor with interstitial zinc, and oxygen chemisorbed as O$^-$ and O$^{2^-}$ respectively, respectively, are held to be mainly responsible for the phenomena observed.
Abstract: Studies of the kinetics of adsorption of oxygen on zinc oxide over the temperature range from 25 to 390 $^\circ$C have provided evidence for two distinct types of chemisorption, one prevalent below 200 and the other above 300 $^\circ$C. This pattern of activity has been confirmed by measurements of desorption rates over the same temperature range. The mode of preparation and pretreatment of the oxido oxort a strong influence on the adsorption behaviour, and these differences are accentuated when the processes of adsorption and desorption are studied in the presence of irradiation in the ultra-violet and visible. Photodesorption of oxygen is confirmed to be the normal behaviour for zine oxide, but photo-adsorption has been observed under conditions of high excess zinc concentration. The photo-effects are especially marked below 300 $^\circ$C. The adsorption studies have been followed up by experiments on the rate of the intermolecular oxygen reaction $^{18}$O$\_2$+$^{16}$O$\_2 \leftrightharpoons$ 2$^{18}$O$^{16}$O, and on the influence of irradiation on this catalysis. It is evident that irradiation stimulates both adsorption and desorption, but the balance between them depends on the previous history of the specimen. The experiments with heavy oxygen have also included a brief study of oxygen exchange with zinc oxide at 400 to 500 $^\circ$C. The results as a whole are discussed in terms of the model of zinc oxide as an n-type semiconductor with interstitial zinc, and oxygen chemisorbed as O$^-$ and O$^{2^-}$, respectively, are held to be mainly responsible for the phenomena observed. The relationship with conductivity studies is emphasized and the depletive chemisorption of oxygen, forming a boundary layer, is discussed in some detail. The depletion of electrons is not exhaustive for normal specimens of zinc oxide, and the treatment of this case leads to an expression consistent with the observed kinetics. Several possible mechanisms for photo-adsorption are put forward, and the association with high donor concentrations is discussed. Interstitial zinc diffusing under the influence of the electric field of chemisorbed oxygen is considered to play an important role in specimens heated above 300 $^\circ$C.
TL;DR: In this paper, the authors derived the partition function of a two-dimensional super-exchange antiferromagnet in an arbitrary magnetic field, which is a decorated square lattice in which magnetic Ising spins on the bonds are coupled together via non-magnetic Ising spin on the vertices.
Abstract: The partition function of a two-dimensional ` super-exchange ’ antiferromagnet in an arbitrary magnetic field is derived rigorously. The model is a decorated square lattice in which magnetic Ising spins on the bonds are coupled together via non-magnetic Ising spins on the vertices. By use of the decoration transformation all the thermodynamic and magnetic properties of the model are derived from Onsager’s solution for the standard square lattice in zero field. The transition temperature T t (H) is a single-valued, decreasing function of the field H . The energy and the magnetization are continuous functions of T for all magnetic fields; but the specific heat and the temperature gradient of the magnetization become infinite as — In | T — T t |. The initial ( H = 0) susceptibility is a continuous and smoothly varying function of T with a maximum 40 % above the critical point; but ∂x/∂ T becomes infinite at T = T c . In a non-vanishing field the susceptibility has a logarithmic infinity at T = T t . For small fields the behaviour near the critical point is given by X ≈ ( N μ/ kT ) {2—√2— D ( T—T c ) ln ∣ T — T c ∣ — D´H 2 ln ∣ T — T c ∣}, where D and D9 are constants.
TL;DR: The oxide species responsible for the enhanced volatility of platinum and rhodium in oxygen in the temperature range 1000 to 1600 °C have been elucidated, and the thermodynamics of their formation have been calculated from their vapour pressures, which were measured by means of the "transportation" or "carrier gas" technique as discussed by the authors.
Abstract: The oxide species responsible for the enhanced volatility of platinum and rhodium in oxygen in the temperature range 1000 to 1600 °C have been elucidated, and the thermodynamics of their formation have been calculated from their vapour pressures, which were measured by means of the ‘transportation’ or ‘carrier gas’ technique. Similar, but incomplete, studies have been made on the metals ruthenium, iridium and palladium, and thermodynamic data have been calculated for the proposed oxide species.
TL;DR: In this paper, an experimental stady of the radiation emitted by helium under controlled electron impact is described, together with those of previous workers, to yield values for the excitation functions of S, P and D states.
Abstract: An experimental stady of the radiation emitted by helium under controlled electron impact is described. The obser vations were analyzed. together with those of previous workers, to yield values for the excitation functions of S, P, and D states. The mechanism of excitation transfer between excited states was analyzed in terms of radiative and collisional processes. Cascade processes were found to be more important than was hitherto assumed. The total inelastic (less ionization) cross rection at 108 ev was found to be 2.9 x 10/sup -1/ cm/sup 2/.
TL;DR: In this article, the authors investigated the extent to which problems in radiation hydrodynamics may be tackled by similarity methods for the case of spherical symmetry, in particular the problem of an intense explosion.
Abstract: The extent to which problems in radiation hydrodynamics may be tackled by similarity methods was investigated for the case of spherical symmetry. In particular the problem of an intense explosion was considered. By the introduction of radiative heat flux the singularity in a solution by Taylor (1950) was removed.
TL;DR: The arrangement of dislocations in the dislocation network has been studied in various conditions, namely annealed, cold-worked, recovered and after creep as mentioned in this paper, and there is convincing evidence for the idea that at many of these intersections two Ω(1/2)-dislocations join to make one dislocation.
Abstract: The arrangement of the dislocations has been studied in iron in various conditions, namely annealed, cold-worked, recovered and after creep. In all conditions the dislocation network is characterized by attractive intersections where two dislocations join to make one dislocation, and there is convincing evidence for the idea that at many of these intersections two $\frac{1}{2}$a$\langle111\rangle$ dislocations join to make one a$\langle100\rangle$ dislocation. These attractive intersections are thought to contribute substantially to the flow stress. These are also repulsive intersections but according to calculation they constitute weaker obstacles to flow than the attractive junctions.
TL;DR: In this article, the friction coefficient and the mass loss per centimetre, of Al, Ag, Cu, Pt, Fe, Mo, U and W specimens ~ 1 to 2·5 cm long are investigated as a function of the mean particle diameter D of abrading emery-paper surfaces.
Abstract: The friction coefficient μ and the mass loss M9 per centimetre, of Al, Ag, Cu, Pt, Fe, Mo, U and W specimens ~ 1 to 2·5 cm long are investigated as a function of the mean particle diameter D of abrading emery-paper surfaces (dry) on which they slide at a few cm/s and ~1 Kg load. On any grade of abrasive, μ and M9 vary with distance of sliding, M9 decreasing and μ increasing for initially wet-abraded metals, due to progressive pick-up of emery by the metal surface. After 200 to 500 cm, depending on the metal and the grade of abrasive, they become constant ( M9 then is wear of metal only, M ) and independent of the initial surface preparation. μ does not increase linearly with D as suggested by previous authors (who used small specimens, smaller range of D , and neglected the effect of pick-up of abrasive). For any given metal, μ (initially and at equilibrium) is practically constant, μ max , at D from 70 to > 150 microns, and decreases with increasing hardness of the metal, at equilibrium being 0·88 for Al, to 0·53 for W. At D μ decreases—in general to ~0·3 to 0·4 for specimens 1 to 2·5 cm diam.—due to partial clogging of the abrasive by worn-off metal. The high and constant μ max on emery- and glass-papers is due to the angular shape of the abrasive particles, since μ is only 0·15 for Ag and Cu on an array of glass spheres of D ~ 125 microns. For the metals initially abraded on wet emery, then slid on dry emery-papers, M at equilibrium also increases with D and is practically constant at D > 70 microns; and M ≏ k W ( μ - μ 0 ), where W is the load, and μ 0 is a constant, in general > μ mo. mo of metaloxide on metal-oxide because of pick-up of abrasive particles by the metal. 1/( M / ρ ), the reciprocal of the volume wear per cm, is approximately proportional to the Vickers hardness H D of the abraded metal surface. Most of the indenting particles cause wear in the form of strips of metal analogous to those caused by machine tools, but there is also much plastic flow (and lateral pile-up) as electron diffraction also indicates. A theory defining friction and wear of metals in abrasion in terms of the shape and orientation of the abrasive particles, is given elsewhere, together with quantitative analysis of the present data. For emery-papers, only about 10% of the groove volume (on the average) appears to be removed as wear.
TL;DR: In this paper, a solution to a problem of elasto-hydrodynamics of normal approach is presented, where the viscosity of the separating film is taken to be a function of pressure and temperature.
Abstract: This Thesis presents a solution to a problem of elasto-hydrodynamics of normal approach ie. the motion of two elastic circular cylinders approaching each other along the line joining their centres and separated by a viscous film. Elastic deformation of the cylinders is accounted for, and the viscosity of the separating film is taken to be a function of pressure and temperature. A numerical method of solution making the use of an electronic computer is devised, and the problem is solved assuming a constant load being applied to the cylinders. An investigation into the nature of the temperature rise in the oil film due to the motion showed that under certain circumstances this would be rather small, of the order of a few degrees centigrade. This makes the assumption of isothermal conditions in the lubricant film a reasonable approximation under these circumstances and the resulting simpler problem, where viscosity is regarded as a function of pressure alone)is given a more general numerical treatment. It is found that a very large pressure may be developed in the fluid film at a finite separation of the two cylinders. As the film thickness is further reduced,the value of the maximum pressure goes down and as the film thickness approaches zero, the pressure distribution seems to converge to the Hertsian dry contact form.
For a given load applied to the cylinders, the value of the maximum pressure reached seems to depend mainly upon the value of parameter xE, i.e. the product of the pressure coefficient of viscosity and the reduced Youngs modulus of the elastic system. It was found that the higher the value of xE, the higher the pressure would go for a given load under other-wise equal conditions. Furthermore, for a load high enough to produce sufficiently large pressures,a small increase in load will produce a large increase in maximum pressure. This gain is also dependent upon the parameter xE and is higher for increased values of xE. Finally, a series of experiments were performed in order to check some of the theoretical predictions made. These experiments consisted of letting a loaded steel ball normally approach the polished surface of various materials, the surface being covered by a lubricant film, and measuring up the plastic deformations produced in the surface. These tests showed clearly the influence of the lubricant in that in every case the depth of the impression with lubricant was significantly larger than the ones produced under Hertzian, dry contact impacts, under otherwise equal conditions. The experimental results also indicate a correlation between the value of the parameter xE and pressure developed in the lubricant film as predicted by theory.
TL;DR: In this paper, it was shown that all the states ψ y of the ground state of the hydrogen atom are included in the expansion, and that the equation satisfied by F 1, the coefficient of ground state, contains a polarization potential which behaves like a/2 r 4 for large r and is independent of the velocity of the incident electron.
Abstract: A hydrogen atom in the ground state scatters an electron with kinetic energy too small for inelastic collisions to occur. The wave function Ψ(r 1 ; r 2 ) of the system has boundary conditions at infinity which must be chosen to allow correctly for the possibilities of both direct and exchange scattering. The expansion Ψ = Σ ψ,(r 1 )F y (r 2 ) of the total wave function in y terms of a complete set of hydrogen atom wave functions ψ y (r 1 ) includes an integration over the continuous spectrum. It is si own that the integrand contains a singularity. The explicit form of this singularity and its connexion with the boundary conditions are examined in detail. The symmetrized functions Y* may be represented by expansions of the form Σ {ψ y (r 1 ) G y ±(r 2 ) ±ψ y (r 2 ) y G y ±(r 1 )}, where the integrand in the continuous spectrum does not involve singularities. Finally, it is shown that because all the states ψ y of the hydrogen atom are included in the expansion, the equation satisfied by F 1 , the coefficient of the ground state, contains a polarization potential which behaves like — a/2 r 4 for large r and is independent of the velocity of the incident electron.
TL;DR: The Landau-Zener formula for the transition probability at a crossing of potential energy curves is discussed in this article, where it is pointed out that the model used in the derivation has defects which make the range of validity of the formula much more restricted than is commonly supposed.
Abstract: The Landau-Zener formula for the transition probability at a crossing of potential energy curves is discussed. It is pointed out that the model used in the derivation has defects which make the range of validity of the formula much more restricted than is commonly supposed.
TL;DR: In this article, non-empirical calculations of the electronic structure of the water molecule (treated as a full ten-electron system) are carried out for various types of wave function.
Abstract: Non-empirical calculations of the electronic structure of the water molecule (treated as a full ten-electron system) are carried out for various types of wave function. These include a ‘bond orbital’ function, a ‘modified electron-pair’ function, and various Roothaan-type self-consistent field (s. c. f.) functions. These approximations are refined by admitting interaction with up to twelve configurational functions of ground-state symmetry. Three bond angles are considered. The results show that the modified electron pair function, which has not hitherto been used in non-empirical calculations, provides the most satisfactory first approximation. This function is constructed from orthonormalized hybrid orbitals in order to overcome non-orthogonality difficulties; and the inclusion of configuration interaction in this particular basis is found to be simple, effective and physically meaningful. The concept of a ‘core’, comprising the oxygen inner shell and lone pairs and providing an effective field for the bond pairs, is found to be remarkably satisfactory. Provided the effective field is properly defined, it is then possible to treat the molecule formally as a four-electron system and to obtain, nevertheless, a total energy 0⋅3 eV better than that given by the best of the s. c. f. calculations. This suggests that the ‘core approximation’ is not a real obstacle to progress. The one-electron density matrices are calculated from the various wave functions and the corresponding dipole moments are evaluated.
TL;DR: In this article, independent determinations by X-ray crystallography of the C-C bond lengths in naphthalene and anthracene are shown to agree well with both the simple molecular orbital and simple Pauling theories.
Abstract: Recent independent determinations by X-ray crystallography of the C-C bond lengths in naphthalene and anthracene are shown to agree well. The experimental values agree to about 0$\cdot$01 $\overset{\circ}{\mathrm A}$ with both the simple molecular orbital and simple Pauling theories. These theories also make satisfactory predictions for 1$\cdot$2:8$\cdot$9-dibenzacridine and chrysene (except for the bond most affected by steric hindrance). The agreement between the two theories for aromatic molecules is traced to a correlation of their respective bond orders. For ethylene, butadiene, cyclooctatetraene and diphenyl the Pauling method is superior to the simple m.o. method.
TL;DR: In this paper, the B.E.T. method was used to determine the surface area of a type I aluminium film, which was found to be relatively low area, ca. 1000 cm 2, stable and with a certain porosity since CO uptake was proportional to film weight.
Abstract: Type I aluminium films deposited at 0 °C were of relatively low area, ca. 1000 cm 2 , stable and with a certain porosity since CO uptake was proportional to film weight. Thus a film area could be determined from its weight, since at saturation CO molecules occupy 0·75 of the total surface area given by the B.E.T. method (established for higher area type II films). It was found that H 2 and N 2 were not chemisorbed, N 2 O and NO reacted giving surface oxide, C 2 H 4 gave a slow reversible adsorption, and CO gave a slow irreversible adsorption, rate proportional to p/g , where p is the gas pressure, g the quantity of gas taken up by the film. The kinetics of oxygen uptake were followed in the range 10 -2 to 10 -3 mm Hg pressure. The first two monolayers were taken up too rapidly for kinetic measurement, and thereafter gas uptake followed the direct logarithmic law, until about 7 A of film had been formed d g /d t = a e -γg/RT p 0·6 , where a and γ are constants. The rate-determining step is considered to be a place exchange of surface oxygen with underlying aluminium atoms, stimulated by reversibly chemisorbed oxygen atoms. As the film thickens it changes from covalent amorphous to ionic spinel character, and the activation energy for place exchange increases. The process of film growth in the ionic film (thickness > ca . 10 A) involves electron tunnelling and cation migration.
TL;DR: A number of polymers and copolymers containing β-benzyl-L-aspartate have been prepared and their optical rotatory dispersion in a variety of solvents has been measured as mentioned in this paper.
Abstract: A number of polymers and copolymers containing $\beta$-benzyl-L-aspartate has been prepared and their optical rotatory dispersion in a variety of solvents has been measured. The results of these measurements together with studies of infra-red spectra, X-ray diffraction patterns, deuteration rates and molecular models lead to the following conclusions. (i) The $\alpha$-helical form of poly-$\beta$-benzyl-L-aspartate is considerably less stable relative to the solvated randomly coiled form than that of poly-$\gamma$-benzyl-L-glutamate. (ii) The left-handed $\alpha$-helix of poly-$\beta$-benzyl-L-aspartate is more stable than the right-handed one. (iii) The difference in stability between the two senses of $\alpha$-helix is much less in the case of poly-$\beta$-benzyl-L-aspartate than in that of poly-$\gamma$-benzyl-L-glutamate or poly-L-alanine.
TL;DR: In this paper, the reaction rate in stoichiometric mixtures of nitrogen and hydrogen or deuterium has been measured on two different doubly promoted iron catalysts, between 218 and 302 °C, ⅓ and 1 atm and over a 300-fold range of efficiencies.
Abstract: The reaction rate in stoichiometric mixtures of nitrogen and hydrogen or deuterium has been measured on two different doubly promoted iron catalysts, between 218 and 302 °C, ⅓ and 1 atm and over a 300-fold range of efficiencies. The kinetic data as well as the isotope effect indicate that the rate-determining step is the chemisorption of nitrogen on a surface mainly covered with NH radicals. The presence on the surface of NH radicals instead of nitrogen atoms opens new perspectives on the kinetics and mechanism of ammonia synthesis.