THE THEORY OF COLLISION-INDUCED ABSORPTION IN HYDROGEN AND DEUTERIUM

1958 ◽  
Vol 36 (6) ◽  
pp. 761-783 ◽  
Author(s):  
F. R. Britton ◽  
M. F. Crawford
Keyword(s):  
Distribution Function ◽  
Pair Distribution Function ◽  
Quadrupole Moments ◽  
Absorption Coefficients ◽  
Induced Dipole ◽  
Binary Collisions ◽  
Experimental Values ◽  
Indirect Part ◽  
Experimental Ratio ◽  
Good Agreement

Collision-induced absorptions in the 1–0 vibrational band of hydrogen and of deuterium are calculated by considering interactions during binary collisions. The induced dipole moment, μ, of an interacting molecule-pair is derived by combining a moment, μa, resulting from overlap forces, with a moment, μq, due to the interactions of permanent molecular quadrupole moments. μa consists of two additive parts, an indirect part calculated by van Kranendonk and Bird (1951) and a direct part calculated in this paper. μq is calculated in two different ways: (a) theoretically and (b) semiempirically. Absorption coefficients are evaluated for temperatures 296 ° K. and 80 ° K. For H2 at 296 ° K. the total integrated coefficient obtained by using procedure (a) is 8.6% smaller and by using (b) is 8.2% larger than the experimental value. The experimental ratio of the coefficients of the Q and S branches is in much better agreement with (b) than (a). For T = 80 °K. the experimental value of the total integrated coefficient is only 61% of that calculated by (b). The good agreement between calculated and experimental values of absorption coefficients at room temperature suggests that at low temperatures the classical distribution function used in this paper must be replaced by the quantal pair distribution function. Experimental data for D2 are not available.

THEORY OF THE PRESSURE-INDUCED ROTATIONAL SPECTRUM OF HYDROGEN

1959 ◽  
Vol 37 (10) ◽  
pp. 1187-1198 ◽  
Author(s):  
J. Van Kranendonk ◽  
Z. J. Kiss
Keyword(s):  
Experimental Data ◽  
Distribution Function ◽  
Absorption Coefficient ◽  
Pair Distribution Function ◽  
Wave Functions ◽  
Rotational Line ◽  
Induction Effect ◽  
Rotational Spectrum ◽  
Absorption Coefficients ◽  
Good Agreement

The theory of induced infrared absorption developed previously is applied to the pressure-induced rotational spectrum of hydrogen. The intensity of the rotational band is due mainly to the quadrupolar induction effect, and to a small interference effect between the quadrupolar and overlap moments. From the experimental data on the binary absorption coefficients, values of the angle-dependent overlap moments are obtained for H2–He, H2–H2, H2–Ne, H2–N2, and H2–A. A calculation of the overlap moment for pure H2 is presented. Rosen-type wave functions appear to be inadequate for a calculation of the small angle-dependent rotational as well as vibrational overlap moments. The temperature dependence of the binary absorption coefficient is calculated, taking into account the quantum effects in the pair distribution function, and found to be in good agreement with the experimental data. The dependence on the ortho–para ratio is also discussed. The double rotational line S(1) + S(1) has been observed and its intensity measured.

FIELD-INDUCED ABSORPTION IN HYDROGEN

1958 ◽  
Vol 36 (8) ◽  
pp. 1022-1039 ◽  
Author(s):  
M. F. Crawford ◽  
R. E. MacDonald
Keyword(s):  
Matrix Element ◽  
High Field ◽  
Mean Value ◽  
Absorption Coefficients ◽  
High Field Strength ◽  
Vibration Absorption ◽  
The Matrix ◽  
The Mean ◽  
Experimental Values ◽  
Good Agreement

This paper reports an investigation of the fundamental rotation–vibration absorption induced in hydrogen by an electric field. The integrated absorption coefficients of the first four components of the Q branch have been measured for a range of field strengths at densities of 83.9 and 44.6 Amagat. The integrated absorption coefficient of the S(1) line has been determined at the higher density for one high field strength. The relative intensities of the Q components are in good agreement with the predicted ratios. Accurate experimental values of the matrix element of the mean value of the polarizability, (α)01, and the matrix element of its anisotropy, (γ)01 have been obtained. They are: (α)01 = 0.968 × 10−25 cm3, and (γ)01 = 0.72 × 10−25 cm3 at 83.9 Amagat, and are only slightly dependent on density. The frequencies of the lines have been measured. Only Q(1) and S(1) show a measurable shift with density. The optical collision diameter has been determined and is very small, 0.26 Å.

The Deformation Structure of the Nuclei 32S and 36Ar

2017 ◽  
Vol 13 (2) ◽  
pp. 4678-4688
Author(s):  
K. A. Kharroube
Keyword(s):  
Single Particle ◽  
Electric Quadrupole ◽  
Quadrupole Moments ◽  
Moments Of Inertia ◽  
Deformation Structures ◽  
Particle Potential ◽  
Nilsson Model ◽  
Single Particle Potential ◽  
Axes Of Symmetry ◽  
Good Agreement

We applied two different approaches to investigate the deformation structures of the two nuclei S32 and Ar36 . In the first approach, we considered these nuclei as being deformed and have axes of symmetry. Accordingly, we calculated their moments of inertia by using the concept of the single-particle Schrödinger fluid as functions of the deformation parameter β. In this case we calculated also the electric quadrupole moments of the two nuclei by applying Nilsson model as functions of β. In the second approach, we used a strongly deformed nonaxial single-particle potential, depending on Î² and the nonaxiality parameter γ , to obtain the single-particle energies and wave functions. Accordingly, we calculated the quadrupole moments of S32 and Ar36 by filling the single-particle states corresponding to the ground- and the first excited states of these nuclei. The moments of inertia of S32 and Ar36 are then calculated by applying the nuclear superfluidity model. The obtained results are in good agreement with the corresponding experimental data.

Real-Space X-Ray Pair Distribution Function Analysis and Molecular-Dynamics Modelling of Diflunisal Channel Hydrates

2020 ◽  
Author(s):  
Anuradha Pallipurath ◽  
Francesco Civati ◽  
Jonathan Skelton ◽  
Dean Keeble ◽  
Clare Crowley ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Distribution Function ◽  
Structural Dynamics ◽  
First Principles ◽  
Pair Distribution Function ◽  
Function Analysis ◽  
Real Space ◽  
X Ray ◽  
Dynamics Modelling ◽  
Dynamics Simulations

X-ray pair distribution function analysis is used with first-principles molecular dynamics simulations to study the co-operative H<sub>2</sub>O binding, structural dynamics and host-guest interactions in the channel hydrate of diflunisal.

Engineering Porosity Through Defects in a Giant Pore Metal–Organic Framework

2020 ◽  
Author(s):  
Adam Sapnik ◽  
Duncan Johnstone ◽  
Sean M. Collins ◽  
Giorgio Divitini ◽  
Alice Bumstead ◽  
...  
Keyword(s):  
Distribution Function ◽  
Ball Milling ◽  
Local Structure ◽  
Pair Distribution Function ◽  
Function Analysis ◽  
Metal Organic Framework ◽  
Metal Organic Frameworks ◽  
Defect Engineering ◽  
Metal Organic ◽  
Unsaturated Metal Sites

<p>Defect engineering is a powerful tool that can be used to tailor the properties of metal–organic frameworks (MOFs). Here, we incorporate defects through ball milling to systematically vary the porosity of the giant pore MOF, MIL-100 (Fe). We show that milling leads to the breaking of metal–linker bonds, generating more coordinatively unsaturated metal sites, and ultimately causes amorphisation. Pair distribution function analysis shows the hierarchical local structure is partially</p><p>retained, even in the amorphised material. We find that the solvent toluene stabilises the MIL-100 (Fe) framework against collapse and leads to a substantial rentention of porosity over the non-stabilised material.</p>

scholarly journals Crystal Structure of Moganite and Its Anisotropic Atomic Displacement Parameters Determined by Synchrotron X-ray Diffraction and X-ray/Neutron Pair Distribution Function Analyses

Minerals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 272
Author(s):  
Seungyeol Lee ◽  
Huifang Xu ◽  
Hongwu Xu ◽  
Joerg Neuefeind
Keyword(s):  
Crystal Structure ◽  
Distribution Function ◽  
Single Crystal ◽  
Pair Distribution Function ◽  
Atomic Displacement ◽  
Single Crystal Xrd ◽  
X Ray Diffraction ◽  
X Ray ◽  
Neutron Pair ◽  
Atomic Displacement Parameters

The crystal structure of moganite from the Mogán formation on Gran Canaria has been re-investigated using high-resolution synchrotron X-ray diffraction (XRD) and X-ray/neutron pair distribution function (PDF) analyses. Our study for the first time reports the anisotropic atomic displacement parameters (ADPs) of a natural moganite. Rietveld analysis of synchrotron XRD data determined the crystal structure of moganite with the space group I2/a. The refined unit-cell parameters are a = 8.7363(8), b = 4.8688(5), c = 10.7203(9) Å, and β = 90.212(4)°. The ADPs of Si and O in moganite were obtained from X-ray and neutron PDF analyses. The shapes and orientations of the anisotropic ellipsoids determined from X-ray and neutron measurements are similar. The anisotropic ellipsoids for O extend along planes perpendicular to the Si-Si axis of corner-sharing SiO4 tetrahedra, suggesting precession-like movement. Neutron PDF result confirms the occurrence of OH over some of the tetrahedral sites. We postulate that moganite nanomineral is stable with respect to quartz in hypersaline water. The ADPs of moganite show a similar trend as those of quartz determined by single-crystal XRD. In short, the combined methods can provide high-quality structural parameters of moganite nanomineral, including its ADPs and extra OH position at the surface. This approach can be used as an alternative means for solving the structures of crystals that are not large enough for single-crystal XRD measurements, such as fine-grained and nanocrystalline minerals formed in various geological environments.

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