Lattice-Dynamical Estimation of Atomic Displacement Parameters in Carbonates: Calcite and Aragonite CaCO3, Dolomite CaMg(CO3)2 and Magnesite MgCO3

1998 ◽  
Vol 54 (5) ◽  
pp. 515-523 ◽  
Author(s):  
T. Pilati ◽  
F. Demartin ◽  
C. M. Gramaccioli
Keyword(s):  
Structure Refinement ◽  
Atomic Displacement ◽  
Empirical Potentials ◽  
Wide Range ◽  
Anisotropic Displacement Parameters ◽  
The Stability ◽  
Experimental Values ◽  
Atomic Displacement Parameters ◽  
Good Agreement ◽  
Raman And Ir Spectra

Using crystallographic information and empirical potentials derived from fitting the vibrational frequencies of all the substances under study, together with those of a group of silicates and oxides, a Born–von Karman rigid-ion lattice-dynamical model has been applied to the whole Brillouin zone in calcite, aragonite (α- and β-CaCO3, respectively), magnesite (MgCO3) and dolomite [CaMg(CO3)2]. The Raman and IR spectra are satisfactorily reproduced and interpreted by these calculations; there is also very good agreement with atomic anisotropic displacement parameters (a.d.p.'s) derived from accurate crystal structure refinement by various authors and with the experimental values of thermodynamic functions over a wide range of temperatures. On these vibrational grounds, the stability of calcite with respect to aragonite at high temperature can be accounted for.

Atomic displacement parameters for spessartine Mn3Al2Si3O12 and their lattice-dynamical interpretation

2002 ◽  
Vol 58 (6) ◽  
pp. 965-969 ◽  
Author(s):  
Carlo Maria Gramaccioli ◽  
Tullio Pilati ◽  
Francesco Demartin
Keyword(s):  
Structure Refinement ◽  
Fluorine Content ◽  
Atomic Displacement ◽  
Natural Sample ◽  
Synthetic Sample ◽  
Dynamical Treatment ◽  
Experimental Values ◽  
Atomic Displacement Parameters ◽  
Dynamical Interpretation ◽  
Good Agreement

A rigid-ion lattice-dynamical treatment accounts reasonably well for most of the atomic displacement parameters (ADPs) reported in the literature for a synthetic sample of spessartine Mn3Al2Si3O12; the model accounts less well for the ADPs of the Mn atom. These results are similar to those obtained for the corresponding garnets pyrope Mg3Al2Si3O12 and almandine Fe3Al2Si3O12. The results are confirmed by a very good agreement of the lattice-dynamical estimates with the experimental values of the heat capacity that are currently available, as well as those of the Raman and infrared vibrational spectra. The anomalous behaviour of the Mn atom is reflected in the entropy values. As is the case for pyrope and almandine, here the agreement with the experimental results can be markedly improved if the existence of a low-temperature order–disorder transition concerning the Mn atom is considered. The lattice-dynamical estimates for all the atoms presented here do not agree with the corresponding ADPs obtained in a crystal structure refinement of a supposedly `pure' natural sample from Elba. In turn, these experimental ADPs do not agree with those observed for the synthetic sample, thereby showing a physical difference; such a possibility is in agreement with recent observations by other authors, who found an unexpected fluorine content in several natural specimens of spessartine. Therefore, theoretical estimates of ADPs are reliable enough to point out unexpected situations if disagreement with the observed values occurs.

scholarly journals A new electron diffraction approach for structure refinement applied to Ca3Mn2O7

2021 ◽  
Vol 77 (3) ◽  
Author(s):  
R. Beanland ◽  
K. Smith ◽  
P. Vaněk ◽  
H. Zhang ◽  
A. Hubert ◽  
...  
Keyword(s):  
Electron Diffraction ◽  
Structure Refinement ◽  
Large Angle ◽  
Atomic Displacement ◽  
Bloch Wave ◽  
Simulation And Experiment ◽  
Atomic Displacement Parameters ◽  
Increasing Temperature ◽  
Convergent Beam ◽  
Good Agreement

The digital large-angle convergent-beam electron diffraction (D-LACBED) technique is applied to Ca3Mn2O7 for a range of temperatures. Bloch-wave simulations are used to examine the effects that changes in different parameters have on the intensity in D-LACBED patterns, and atomic coordinates, thermal atomic displacement parameters and apparent occupancy are refined to achieve a good fit between simulation and experiment. The sensitivity of the technique to subtle changes in structure is demonstrated. Refined structures are in good agreement with previous determinations of Ca3Mn2O7 and show the decay of anti-phase oxygen octahedral tilts perpendicular to the c axis of the A21 am unit cell with increasing temperature, as well as the robustness of oxygen octahedral tilts about the c axis up to ∼400°C. The technique samples only the zero-order Laue zone and is therefore insensitive to atom displacements along the electron-beam direction. For this reason it is not possible to distinguish between in-phase and anti-phase oxygen octahedral tilting about the c axis using the [110] data collected in this study.

Transferability of Empirical Force Fields in Silicates: Lattice-Dynamical Evaluation of Atomic Displacement Parameters and Thermodynamic Properties for the Al2OSiO4 Polymorphs

1997 ◽  
Vol 53 (1) ◽  
pp. 82-94 ◽  
Author(s):  
T. Pilati ◽  
F. Demartin ◽  
C. M. Gramaccioli
Keyword(s):  
Thermodynamic Functions ◽  
Force Fields ◽  
Structure Refinement ◽  
Atomic Displacement ◽  
Poor Quality ◽  
Different Temperatures ◽  
Atomic Displacement Parameters ◽  
Best Fit ◽  
Good Agreement

A Born–von Karman rigid-ion lattice-dynamical model, using empirical atomic charges and valence force fields derived from the best fit to the vibrational frequencies of a group of silicates and oxides, has been applied to andalusite, kyanite and sillimanite, the three naturally occurring Al2OSiO4 polymorphs. For andalusite there is good agreement with the atomic anisotropic displacement parameters (ADP's) derived from accurate crystal structure refinement at different temperatures and with the values of thermodynamic functions, such as the specific heat and entropy. For kyanite, our calculations are successful in reproducing the values of thermodynamic functions, but not the ADP's, almost certainly due to the poor quality of the crystals used in the structure determination. For sillimanite, imaginary frequencies are obtained in a region of the Brillouin zone: such an inadequacy might be ascribed to the presence of fourfold coordinated Al, whose properties are considerably different from those of higher-coordinated Al present in andalusite and kyanite.

scholarly journals DFT calculation and assignment of vibrational spectra of aryl and alkyl chlorophosphates

2014 ◽  
Vol 12 (2) ◽  
pp. 153-163
Author(s):  
Viktor Anishchenko ◽  
Vladimir Rybachenko ◽  
Konstantin Chotiy ◽  
Andrey Redko
Keyword(s):  
Vibrational Spectra ◽  
Basis Sets ◽  
Heavy Atoms ◽  
Wide Range ◽  
Complete Assignment ◽  
Key Factor ◽  
Polarization Functions ◽  
Experimental Values ◽  
Semi Empirical ◽  
Good Agreement

AbstractDFT calculations of vibrational spectra of chlorophosphates using wide range of basis sets and hybrid functionals were performed. Good agreement between calculated and experimental vibrational spectra was reached by the combination of non-empirical functional PBE0 with both middle and large basis sets. The frequencies of the stretching vibrations of the phosphate group calculated using semi-empirical functional B3LYP for all basis sets deviate significantly from the experimental values. The number of polarization functions on heavy atoms was shown to be a key factor for the calculation of vibrational frequencies of organophosphates. The importance of consideration of all the stable rotamers for a complete assignment of fundamental modes was shown.

scholarly journals Non-metamict betafite from Le Carcarelle (Vico volcanic complex, Italy): occurrence and crystal structure

2004 ◽  
Vol 68 (6) ◽  
pp. 939-950 ◽  
Author(s):  
F. Cámara ◽  
C. T. Williams ◽  
G. Della Ventura ◽  
R. Oberti ◽  
E. Caprilli
Keyword(s):  
Structure Refinement ◽  
Atomic Displacement ◽  
Campi Flegrei ◽  
Volcanic Complex ◽  
Crystal Chemical Formula ◽  
Static Disorder ◽  
Pyrochlore Group ◽  
Atomic Displacement Parameters ◽  
Miarolitic Cavities ◽  
Ti Content

AbstractNon-metamict betafite, a pyrochlore-group mineral with general formula A2−mB2XO6Y(O,OH,F)1−n·pH2O and 2 Ti > Nb+Ta and U > 20% at the A site, has been found at Le Carcarelle, (Latium, Italy). It occurs within miarolitic cavities of a foid-bearing syenitic ejectum enclosed within the pyroclastic formation known as “ignimbrite C”, which belongs to the main effusive phase of the Vico volcanic complex. The host rock is composed of K-feldspar, biotite, augitic clinopyroxene, magnetite and minor sodalite. Electron microprobe analyses gave the following crystal-chemical formula: (Ca1.24Na0.17U0.49REE0.03)Σ=1.93 (Ti1.05Nb0.76Zr0.14Fe0.04Ta0.01)Σ=2.00O6(O,OH). Compared with other occurrences reported in the mineralogical literature, betafite from Le Carcarelle is extremely enriched in U and depleted in Th. Due to its young age of formation (∼150 k.y.), this betafite sample is highly crystalline, thus allowing structure refinement of unheated material. Betafite from Le Carcarelle is cubic Fd3̅m, with a = 10.2637(13) Å, and V = 1081.21(35) Å3, and has a smaller A site (consistent with the higher U content), and a larger and more distorted B site (consistent with the higher Ti content) than calciobetafite from Campi Flegrei, Italy (Mazzi and Munno, 1983). Analysis of the atomic displacement parameters provides evidence for static disorder at the X site.

Transition from dripping to jetting

1999 ◽  
Vol 383 ◽  
pp. 307-326 ◽  
Author(s):  
CHRISTOPHE CLANET ◽  
JUAN C. LASHERAS
Keyword(s):  
Weber Number ◽  
Free Edge ◽  
Newtonian Liquid ◽  
Inviscid Limit ◽  
Inertia Effects ◽  
Wide Range ◽  
Critical Weber Number ◽  
Experimental Values ◽  
Outside Diameter ◽  
Good Agreement

We consider the critical Weber number (Wec≡ ρV20D/σ) at which the transition from dripping to jetting occurs when a Newtonian liquid of density ρ and surface tension σ is injected with a velocity V0 through a tube of diameter D downward into stagnant air, under gravity g. We extend Taylor's (1959) model for the recession speed of a free edge, and obtain in the inviscid limit an exact solution which includes gravity and inertia effects. This solution provides a criterion for the transition which is shown to occur at a critical Weber numberformula herewhere Bo and Boo are the Bond numbers (Bo≡[ρgD2/(2σ)]1/2), respectively based on the inside and outside diameter of the tube, and K is a constant equal to 0.37 for the case of water injected in air. This critical Weber number is shown to be in good agreement with existing experimental values as well as with new measurements performed over a wide range of Bond numbers.

Energetics and Structural Effects of Boron Additive to Intermetallic Compound: γ-Tial

1990 ◽  
Vol 213 ◽  
Author(s):  
P.K. Khowash ◽  
D.L. Price ◽  
B.R. Cooper
Keyword(s):  
Intermetallic Compound ◽  
Total Energy ◽  
Site Selection ◽  
Lattice Structure ◽  
Practical Importance ◽  
The Difference ◽  
The Stability ◽  
Experimental Values ◽  
And Behavior ◽  
Good Agreement

ABSTRACTImproving the low temperature ductility of the intermetallic compound γ - TiAl by alloying with small concentrations of an additive is of great practical importance. The difference in site selection energy of the additive plays an important role in the stability and behavior of the alloy. For boron in L10 TiAl, we have calculated the site selection energy using linearized combination of muffin-tin orbitals (LMTO) total energy calculations. For pure γ - TiAl, we found the equilibrium lattice structure by minimizing the total energy, and obtained good agreement with the experimental values. With the introduction of boron, a relaxation of the lattice around the boron additive is expected. For boron additives, we have calculated the forces on each atom leading to the minimization of the total energy as a function of the ionic positions in order to obtain the “true” stable structure of the alloy.

VLE Determination of Carbon Dioxide Loaded Aqueous Alkanolamine Mixtures Using Modified Kent Eisenberg Model

2017 ◽  
Vol 231 (11-12) ◽  
Author(s):  
Humbul Suleman ◽  
Abdulhalim Shah Maulud ◽  
Zakaria Man
Keyword(s):  
Experimental Data ◽  
Carbon Dioxide ◽  
Model Parameters ◽  
Thermodynamic Models ◽  
Carbon Dioxide Absorption ◽  
Proposed Model ◽  
Wide Range ◽  
Experimental Values ◽  
Good Agreement

AbstractA computationally simple thermodynamic framework has been presented to correlate the vapour-liquid equilibria of carbon dioxide absorption in five representative types of alkanolamine mixtures. The proposed model is an extension of modified Kent Eisenberg model for the carbon dioxide loaded aqueous alkanolamine mixtures. The model parameters are regressed on a large experimental data pool of carbon dioxide solubility in aqueous alkanolamine mixtures. The model is applicable to a wide range of temperature (298–393 K), pressure (0.1–6000 kPa) and alkanolamine concentration (0.3–5 M). The correlated results are compared to the experimental values and found to be in good agreement with the average deviations ranging between 6% and 20%. The model results are comparable to other thermodynamic models.

An Analytical Examination of the Behavior of Oil Sand Fragments in Heated Streams

1982 ◽  
Vol 104 (2) ◽  
pp. 121-129
Author(s):  
A. Hanafi ◽  
G. A. Karim
Keyword(s):  
Analytical Study ◽  
Chemical Processes ◽  
Operating Conditions ◽  
Transient Effects ◽  
Oil Sand ◽  
Wide Range ◽  
Experimental Values ◽  
Physical And Chemical ◽  
Simultaneous Heat ◽  
Good Agreement

The physical and chemical processes that occur typically within and around an oil sand fragment are considered when the fragment is suddenly introduced into a hot, low-uniform velocity, gaseous oxidizing stream. In this analytical study, the extent of bitumen volatilization was obtained from a consideration of the simultaneous heat and mass transfer within spherical oil sand fragments combined with a simplified cracking scheme of the heavy oil and asphaltene into coke and distillate. The resulting system of equations together with the boundary conditions arising from subjecting the fragments to hot convective streams were solved using Laplace transformation. The transient concentrations of bitumen and temperature within the fragments were then obtained under a wide range of operating conditions. The similarity of the expression obtained for the extent of bitumen volatilization to the expression derived from simplified analysis, based on a dropletlike model, was demonstrated for cases where the transient effects within the fragments were considered to be negligible. The results of the theoretical analysis show relatively good agreement with their corresponding experimental values at high stream temperatures, while they showed relatively inferior agreement at low temperatures.

AB-INITIO STUDY OF VARIOUS PROPERTIES OF SMALL DIAMETER ARMCHAIR CARBON NANOTUBES

2005 ◽  
Vol 04 (03) ◽  
pp. 295-303
Author(s):  
B. K. AGRAWAL ◽  
S. AGRAWAL ◽  
S. SINGH ◽  
R. SRIVASTAVA
Keyword(s):  
Carbon Nanotubes ◽  
Ab Initio ◽  
Small Diameter ◽  
Radial Breathing Mode ◽  
Binding Energies ◽  
Wide Range ◽  
Optical Matrix Element ◽  
The Stability ◽  
Semiconducting Nanotubes ◽  
Good Agreement

A comprehensive ab-initio investigation of the stability, structural, electronic, optical and Raman-active properties has been performed for the small diameter armchair carbon nanotubes. A number of new features not discussed earlier are observed in the present study. The binding energies (BEs) for the ultrathin nanotubes with respect to the graphine sheet are negative and the magnitude of the negative BE decreases with the diameter of the tube approaching zero for the graphine sheet. The separation between the two van Hove singularities (vHs) around the Fermi level increases with the diameter of the tube. The main absorption arises from the transitions between the states at nonzero values of kz lying in the range 0.38–0.50. There is a large variation in the magnitude of the optical matrix-element with the wave vector. The energy range of the strong optical absorption increases with the diameter of the tube. The presently predicted absorption and the RBM frequencies are in good agreement with the available experimental data. The variation of the radial breathing mode (RBM) frequency with diameter "d" of a tube obeys a relation which is very close to an experimentally determined relation obtained for a number of wide semiconducting nanotubes possessing a wide range of chiral angles.

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