Thermodynamic properties and melting of solid helium

1953 ◽  
Vol 218 (1134) ◽  
pp. 291-310 ◽  
Keyword(s):  
Experimental Data ◽  
Solid Helium ◽  
Characteristic Temperature ◽  
Melting Curve ◽  
Zero Point ◽  
Point Energy ◽  
Melting Temperatures ◽  
Wide Range ◽  
Melting Properties ◽  
The Difference

The melting properties and thermodynamic functions of solid helium have been determined at temperatures from 4 to 26° K and at pressures up to 3000 atm. The upper temperature corresponds to about five times the critical temperature of helium; it was therefore possible to measure properties of the solid state in a range which has not yet been attained for any other substance. The melting curve shows no signs of an approach to a solid-fluid critical point; in fact, the difference between the phases becomes more pronounced at higher melting temperatures. The internal energy at 0° K was calculated from the experimental data and was found to be in good agreement with the theoretical values based on the Slater-Kirkwood potential, using 9/8 Rθ as an estimate of the zero-point energy ( θ being the Debye characteristic temperature). A first-order transition in the solid was revealed; its equilibrium line cuts the melting curve at 14.9° K and moves to higher temperatures at higher densities. The heat of transition is very small, about 0.08 cal/mole. The transition is assumed to correspond to a change of crystal structure from hexagonal to cubic close-packed. At the highest pressure solid helium is compressed to less than half its volume under equilibrium conditions at absolute zero, and the Debye θ is increased five times. It was hence possible to test the Lindemann melting formula for a single substance over a very wide range. The formula was found to fit the experimental data satisfactorily, although the value of the constant in it differed somewhat from the classical value.

On the cubic and hexagonal close-packed lattices

1955 ◽  
Vol 227 (1171) ◽  
pp. 447-465 ◽  
Keyword(s):  
Solid Helium ◽  
Zero Point ◽  
Lattice Energy ◽  
Close Packing ◽  
Inert Gases ◽  
Zero Point Energy ◽  
Point Energy ◽  
Hexagonal Close Packed ◽  
The Difference ◽  
Central Forces

The present paper was stimulated by the discovery by Dugdale & Simon (1953) of a polymorphic transition in solid helium. A discussion is given of the relative stability of the cubic and hexagonal close-packed lattices assuming central forces of the Mie—Lennard-Jones type. Taking static lattice energy alone into account the usual laws of force favour the hexagonal close-packed lattice, the difference in energy being about 0·01%. However, lattice dynamics indicates that the equivalent Debye Θ at the absolute zero is smaller for the cubic lattice, the difference being about 1%. Hence, ignoring zero-point energy, we should expect a transition to occur from hexagonal to cubic at an elevated temperature. The estimated temperature and energy of the transition are of the same order of magnitude as those observed experimentally in solid helium. An estimate is made of the effect of zero-point energy; the results can be applied with confidence to the heavier inert gases, but can only be considered as giving a qualitative indication for helium, since anharmonic effects are of great importance in this case. For the other inert gas solids it is concluded that the experimentally observed cubic close-packing at all temperatures must be due to non-central forces.

On the Use of Quantum Thermal Bath in Unimolecular Fragmentation Simulations

2019 ◽  
Author(s):  
Riccardo Spezia ◽  
Hichem Dammak
Keyword(s):  
Degrees Of Freedom ◽  
Molecular Simulations ◽  
Zero Point ◽  
Thermal Bath ◽  
Unimolecular Dissociation ◽  
Point Energy ◽  
Rotational Degrees Of Freedom ◽  
The Difference ◽  
Nuclear Effects

<div> <div> <div> <p>In the present work we have investigated the possibility of using the Quantum Thermal Bath (QTB) method in molecular simulations of unimolecular dissociation processes. Notably, QTB is aimed in introducing quantum nuclear effects with a com- putational time which is basically the same as in newtonian simulations. At this end we have considered the model fragmentation of CH4 for which an analytical function is present in the literature. Moreover, based on the same model a microcanonical algorithm which monitor zero-point energy of products, and eventually modifies tra- jectories, was recently proposed. We have thus compared classical and quantum rate constant with these different models. QTB seems to correctly reproduce some quantum features, in particular the difference between classical and quantum activation energies, making it a promising method to study unimolecular fragmentation of much complex systems with molecular simulations. The role of QTB thermostat on rotational degrees of freedom is also analyzed and discussed. </p> </div> </div> </div>

scholarly journals Time-Resolved Measurements and Master Equation Modelling of the Unimolecular Decomposition of CH3OCH2

2020 ◽  
Vol 234 (7-9) ◽  
pp. 1233-1250 ◽  
Author(s):  
Arrke J. Eskola ◽  
Mark A. Blitz ◽  
Michael J. Pilling ◽  
Paul W. Seakins ◽  
Robin J. Shannon
Keyword(s):  
Energy Transfer ◽  
Master Equation ◽  
Rate Coefficient ◽  
Zero Point ◽  
Buffer Gas ◽  
Unimolecular Decomposition ◽  
Time Resolved ◽  
Point Energy ◽  
Wide Range ◽  
Transfer Parameters

AbstractThe rate coefficient for the unimolecular decomposition of CH3OCH2, k1, has been measured in time-resolved experiments by monitoring the HCHO product. CH3OCH2 was rapidly and cleanly generated by 248 nm excimer photolysis of oxalyl chloride, (ClCO)2, in an excess of CH3OCH3, and an excimer pumped dye laser tuned to 353.16 nm was used to probe HCHO via laser induced fluorescence. k1(T,p) was measured over the ranges: 573–673 K and 0.1–4.3 × 1018 molecule cm−3 with a helium bath gas. In addition, some experiments were carried out with nitrogen as the bath gas. Ab initio calculations on CH3OCH2 decomposition were carried out and a transition-state for decomposition to CH3 and H2CO was identified. This information was used in a master equation rate calculation, using the MESMER code, where the zero-point-energy corrected barrier to reaction, ΔE0,1, and the energy transfer parameters, ⟨ΔEdown⟩ × Tn, were the adjusted parameters to best fit the experimental data, with helium as the buffer gas. The data were combined with earlier measurements by Loucks and Laidler (Can J. Chem.1967, 45, 2767), with dimethyl ether as the third body, reinterpreted using current literature for the rate coefficient for recombination of CH3OCH2. This analysis returned ΔE0,1 = (112.3 ± 0.6) kJ mol−1, and leads to $k_{1}^{\infty}(T)=2.9\times{10^{12}}$ (T/300)2.5 exp(−106.8 kJ mol−1/RT). Using this model, limited experiments with nitrogen as the bath gas allowed N2 energy transfer parameters to be identified and then further MESMER simulations were carried out, where N2 was the buffer gas, to generate k1(T,p) over a wide range of conditions: 300–1000 K and N2 = 1012–1025 molecule cm−3. The resulting k1(T,p) has been parameterized using a Troe-expression, so that they can be readily be incorporated into combustion models. In addition, k1(T,p) has been parametrized using PLOG for the buffer gases, He, CH3OCH3 and N2.

HYDROGEN PEROXIDE AND ITS ANALOGUES: III. ABSORPTION SPECTRUM OF HYDROGEN AND DEUTERIUM PEROXIDES IN THE NEAR ULTRAVIOLET

1951 ◽  
Vol 29 (6) ◽  
pp. 490-493 ◽  
Author(s):  
M. K. Phibbs ◽  
Paul A. Giguère
Keyword(s):  
Hydrogen Peroxide ◽  
Absorption Spectrum ◽  
Ultraviolet Light ◽  
Heavy Water ◽  
Zero Point ◽  
Zero Point Energy ◽  
Point Energy ◽  
Near Ultraviolet ◽  
The Difference ◽  
High Concentrations

The absorption of ultraviolet light between 3000 and 4000 Å by solutions of hydrogen peroxide in water and of deuterium peroxide in heavy water has been measured at various concentrations. Both peroxides show slight but real deviations from Beer's law at high concentrations. Substitution of hydrogen by deuterium shifts the absorption continuum by about 390 cm.−1 towards shorter wave lengths. This shift is of the same order as that calculated from the difference in zero-point energy of the two isotopic molecules.

scholarly journals The sorption of hydrogen and deuterium by copper and palladium I-The behaviour of copper and copper oxides

1935 ◽  
Vol 153 (878) ◽  
pp. 77-88 ◽  
Keyword(s):  
Zero Point ◽  
Heterogeneous Reactions ◽  
Energy Of Activation ◽  
Zero Point Energy ◽  
Point Energy ◽  
Activated State ◽  
Heterogeneous Processes ◽  
The Difference ◽  
State Of Affairs ◽  
Homogeneous Reactions

The investigation of homogeneous reactions of deuterium and of deuterides has shown that the heavy isotopic molecules react in general less readily than the light, owing to the greater energy of activation required in the deuterium reactions. This result is qualitatively in accordance with theoretical expectations, the reason for the difference being mainly due to the larger zero point energy of the hydrogen compounds. Quantitative analysis of reactions whose mechanism is well established has, however, shown that the ratio of the velocities is often considerably less than that expected if all the zero point energy is con­tributed to the energy pool in the activating collision. The smaIler ratio of velocity is due to the fact that the zero point energy of the activated state cannot be neglected, the difference for H and for D re­action often being considerable. For example, in the reaction Br + H 2 → HBr [DBr] + H [D] the difference in the energy of activation is 1·50 kg cal, and therefore the difference in zero point energies in the activated state is 0·3 kg cal; similarly for Cl + H 2 (D 2 ) → HCI (DCI) + H (D) the respective figures are 1·23 and 0·55 kg cal, while for the reaction H + H 2 (para) = H 2 (ortho) + H and D + D 2 (ortho) = D 2 (para) + D, the difference in the activated state is no less than 1·20 kg cal. The position with regard to heterogeneous reactions of hydrogen is much less satisfactory and therefore any further means of obtaining information in tin branch of kinetics is of value. Deuterium at first sight promised to be a useful tool in helping to discriminate between various hypotheses. Unfortunately, it is difficult to predict theoretically exactly what will happen in any well-defined instance even with a complete experimental knowledge of the mechanism of the reaction. The state of affairs is analogous to that obtaining with homogeneous reactions, it being necessary to determine experimentally the behaviour of the two isotopes in a variety of heterogeneous processes.

Thermal Properties of Alkaline Earth Oxides II. Analysis of Experimental Results for MgO, CaO, SrO, and BaO

1970 ◽  
Vol 25 (6) ◽  
pp. 887-893 ◽  
Author(s):  
E. Gmelin
Keyword(s):  
Thermal Properties ◽  
Frequency Spectrum ◽  
Alkaline Earth ◽  
Characteristic Temperature ◽  
Low Frequency ◽  
Alkali Halides ◽  
Zero Point ◽  
Point Energy ◽  
Usual Procedure ◽  
Capacity Data

Abstract The heat capacities of MgO, CaO, SrO and BaO, reported in part I have been analysed in terms of the frequency spectrum of the lattice with the assumption that the effect of anharmonicity of the lattice may be neglected for T ≦ (ΘD/3). Following the usual procedure the n-th moments of the frequency spectrum with n = - 3, -2, - 1, 0, 1 to 6 were calculated from the experimental data. From the low frequency expansion the apparent Debye characteristic temperature at 0 °K, Θ0, is calculated to be in good agreement with Θ0 (elast.), calculated from elasticity data. Also the limiting values at high temperatures,Θ∞, and the zero point energy, Ez, have been calculated. A comparison between the heat capacity data, the elastic constants and thermal properties of these oxides and the alkali-halides suggest that the interatomic forces of the alkaline-earth-oxides are rather similar to those of the alkaline fluorides. But no specific divalent character has been detected for these oxides. An appreciable anharmonic effect is present for all oxides.

Quantal Factors in the Joule-Thomson cooling of Hydrogen and Deuterium

1957 ◽  
Vol 10 (4) ◽  
pp. 373 ◽  
Author(s):  
SD Hamann
Keyword(s):  
Heat Capacity ◽  
High Pressures ◽  
Initial Temperature ◽  
Translational Motion ◽  
Zero Point ◽  
Point Energy ◽  
Lower Heat ◽  
Normal Hydrogen ◽  
The Difference ◽  
Low Pressures

This paper presents a theoretical analysis of the Joule-Thomson cooling of normal hydrogen and deuterium from an initial temperature of 64 �K. Below 70 atm the cooling is greater for H2 than for D2, but at higher pressures it is less. It is found that the difference at low pressures is due to the lower heat capacity of H2, associated with the more quantized rotation of its molecules. The difference at high pressures is due to the less negative enthalpy of imperfection of H2, and this in turn can be attributed to the higher zero-point energy for translational motion in the lighter isotope. Both differences can be accounted for quantitatively.

scholarly journals The replusive forces between isotopic molecules

1940 ◽  
Vol 174 (959) ◽  
pp. 504-509 ◽  
Keyword(s):  
Zero Point ◽  
Electron Shell ◽  
Intermolecular Forces ◽  
Zero Point Energy ◽  
Restoring Force ◽  
Point Energy ◽  
Nuclear Masses ◽  
Energy Of Interaction ◽  
The Difference ◽  
Made In

It is usually assumed that the forces of attraction and repulsion between two molecules depend only on their electronic structures and are independent of the nuclear masses. While this assumption is undoubtedly true to a first approximation it fails to take into account the zero-point energy associated with the nuclear vibrations, which will modify the charge distribution both of the nuclei and of the electronic shells. Since the zero-point energy depends upon the nuclear mass, this may lead to differences between the behaviour of a pair of isotopic molecules such as H 2 and D 2 . If the restoring force of the nuclear vibration is not directly proportional to the displacement of the nuclei from their mean position, then the mean internuclear distance will be different for the two isotopes. The magnitude of this anharmonic effect can be calculated from spectrum data, and it is found that for H 2 and D 2 the difference is less than 10 -11 cm., and hence negligible. However, the energy of interaction of two molecules will not be a linear function of the inter­ nuclear distance within the molecules, so that even for harmonic oscillations the observed interaction will depend upon the magnitude of the zero-point energy. Both the attractive and the repulsive intermolecular forces will be affected in this way, but it is difficult to treat the former owing to the absence of any exact treatment of exchange forces between molecules. The problem is more easily attacked in the case of the Coulomb forces (which have a net repulsive effect), and the present paper constitutes an attempt to estimate the isotope effect for this type of force. It will be necessary to neglect the mutual deformation of the charge distributions caused by the approach of the two molecules. This assumption is usually made in dealing with Coulomb forces, and it is unlikely to introduce serious error in calculating the isotopic difference. The total Coulomb interaction between two molecules can then be written as G = G n + G n c + G e (1) where G n is the interaction between the nuclei of the two molecules, G ne the interaction between the nuclei of one molecule and the electron shell of the other, and G e the interaction between the two electron shells. The principles involved are most easily seen by considering G n for two diatomic molecules.

scholarly journals Dispersion of Phonons in Ideal Crystals

1969 ◽  
Vol 22 (4) ◽  
pp. 471 ◽  
Author(s):  
NP Gupta
Keyword(s):  
Experimental Data ◽  
Phonon Dispersion ◽  
Zero Point ◽  
Lattice Vibrations ◽  
Rare Gases ◽  
Point Energy ◽  
Phonon Dispersion Curves ◽  
Debye Theory ◽  
Specific Heats ◽  
Theoretical Frequency

A quasiharmonic central force rigid-atom model has been used to study the lattice vibrations of frozen rare gases. The model takes care of interactions up to fourth neighbour and estimates zero-point energy and its volume derivatives by the Debye theory of specific heats. The theoretical frequency distribution and phonon dispersion curves are found to compare reasonably well with the available experimental data. Various causes of the discrepancies and possibilities of improvement of the results are discussed.

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