Atomic displacement parameters for garnets: a lattice-dynamical evaluation

Atomic displacement parameters (a.d.p.'s), together with vibrational spectra (Raman and IR) and thermodynamic functions, have been calculated for some minerals of the garnet group, such as pyrope (Mg3Al2Si3O12), grossular (Ca3Al2Si3O12), andradite (Ca3Fe2Si3O12) and almandine (Fe3A12Si3O12). For this purpose, a rigid-ion Born–von Karman model has been applied, using empirical atomic charges and valence force fields derived from a best fit to the vibrational spectra of a group of orthosilicates and oxides. Agreement with the experimental data is good, with the only exception of pyrope and almandine: for these minerals the calculated a.d.p.'s of the Mg2+ atom in the former and of the corresponding Fe2+ atom in the latter are too low. This result confirms the unusual behaviour of these atoms, for which dynamic disorder has been claimed. However, if the values of the specific heat and entropy are considered and compared with our calculations, this situation can be best explained assuming the transition to static disorder of the Mg2+ and Fe2+ atoms to occur at low temperature.

Download Full-text

Atomic Displacement Parameters, Vibrational Spectra and Thermodynamic Functions for Crystals: A Strong Connection

Implications of Molecular and Materials Structure for New Technologies ◽

10.1007/978-94-011-4653-1_5 ◽

1999 ◽

pp. 59-70

Author(s):

C. M. Gramaccioli

Keyword(s):

Thermodynamic Functions ◽

Vibrational Spectra ◽

Atomic Displacement ◽

Strong Connection ◽

Atomic Displacement Parameters

Download Full-text

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

Acta Crystallographica Section B Structural Science ◽

10.1107/s0108768196011482 ◽

1997 ◽

Vol 53 (1) ◽

pp. 82-94 ◽

Cited By ~ 10

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.

Download Full-text

The quasi-low temperature behaviour of specific heat

Royal Society Open Science ◽

10.1098/rsos.171285 ◽

2019 ◽

Vol 6 (1) ◽

pp. 171285 ◽

Cited By ~ 3

Author(s):

Yuri Vladimirovich Gusev

Keyword(s):

Field Theory ◽

Experimental Data ◽

Low Temperature ◽

Specific Heat ◽

Temperature Regime ◽

Silver Chloride ◽

Condensed Matter ◽

Fourth Power ◽

Temperature Behaviour ◽

Lattice Materials

A new mathematical approach to condensed matter physics, based on the finite temperature field theory, was recently proposed. The field theory is a scale-free formalism; thus, it denies absolute values of thermodynamic temperature and uses dimensionless thermal variables, which are obtained with the group velocities of sound and the interatomic distance. This formalism was previously applied to the specific heat of condensed matter and predicted its fourth power of temperature behaviour at sufficiently low temperatures, which was tested by experimental data for diamond lattice materials. The range of temperatures with the quartic law varies for different materials; therefore, it is called the quasi-low temperature regime. The quasi-low temperature behaviour of specific heat is verified here with experimental data for the fcc lattice materials, silver chloride and lithium iodide. The conjecture that the fourth order behaviour is universal for all condensed matter systems has also supported the data for glassy matter: vitreous silica. This law is long known to hold for the bcc solid helium-4. The characteristic temperatures of the threshold of the quasi-low temperature regime are found for the studied materials. The scaling in the specific heat of condensed matter is expressed by the dimensionless parameter, which is explored with the data for several glasses. The explanation of the correlation of the ‘boson peak’ temperature with the shear velocity is proposed. The critique of the Debye theory of specific heat and the Born–von Karman model of the lattice dynamics is given.

Download Full-text

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

Mineralogical Magazine ◽

10.1180/0026461046860224 ◽

2004 ◽

Vol 68 (6) ◽

pp. 939-950 ◽

Cited By ~ 14

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.

Download Full-text

Atomic displacement parameters and specific heat ofp-dichlorobenzene polymorphs between 10 and 230 K

Acta Crystallographica Section A Foundations of Crystallography ◽

10.1107/s0108767305086046 ◽

2005 ◽

Vol 61 (a1) ◽

pp. c328-c328

Author(s):

T. Aree ◽

M. Hostettler ◽

K. W. Törnroos ◽

D. Chernyshov ◽

H.-B. Bürgi

Keyword(s):

Specific Heat ◽

Atomic Displacement ◽

Atomic Displacement Parameters

Download Full-text

Atomic displacement parameters and specific heat of α-glycine polymorph between 10 and 298 K

Acta Crystallographica Section A Foundations of Crystallography ◽

10.1107/s010876730808656x ◽

2008 ◽

Vol 64 (a1) ◽

pp. C419-C419

Author(s):

T. Aree

Keyword(s):

Specific Heat ◽

Atomic Displacement ◽

Atomic Displacement Parameters

Download Full-text

LOW TEMPERATURE SPECIFIC HEAT OF INTERMETALLICS (Ti/Be)B2

Modern Physics Letters B ◽

10.1142/s021798490701302x ◽

2007 ◽

Vol 21 (14) ◽

pp. 885-891 ◽

Cited By ~ 7

Author(s):

NUPINDER KAUR ◽

N. K. GAUR ◽

R. K. SINGH

Keyword(s):

Experimental Data ◽

Thermal Properties ◽

Low Temperature ◽

Specific Heat ◽

Debye Temperature ◽

Cohesive Energy ◽

Specific Heats ◽

Molecular Force ◽

Low Temperature Specific Heat ◽

Rigid Ion Model

We have applied the Rigid Ion Model (RIM) to study the cohesive and thermal properties of binary intermetallic BeB 2 and TiB 2. The paper reports the calculated results on cohesive energy (ϕ), compressibility (β), molecular force constant (f), Restrahalen frequency (ν0), Debye temperature (Θ D ) and Gruneisen parameter (γ) for the temperature range 50 K ≤ T ≤ 300 K and the effect of van der Waal interaction on these properties are also shown. Our results on Debye temperature are closer to the experimental data. In addition, we have computed the specific heats for BeB 2 and TiB 2 and compared them with the available experimental data.

Download Full-text

An order–disorder phase transition in the structure of C60·4benzene

Acta Crystallographica Section B Structural Science ◽

10.1107/s0108768111046593 ◽

2012 ◽

Vol 68 (1) ◽

pp. 66-70 ◽

Cited By ~ 14

Author(s):

Marilyn M. Olmstead ◽

Alan L. Balch ◽

Hon Man Lee

Keyword(s):

Phase Transition ◽

Low Temperature ◽

Inflection Point ◽

Atomic Displacement ◽

Temperature Structure ◽

Asymmetric Unit ◽

Disorder Phase Transition ◽

Atomic Displacement Parameters

A reversible, broad, order–disorder phase transition in the structure of C60·4benzene has been observed to take place with an inflection point at 134 K. In the low-temperature structure fullerene disorder is removed, although the average atomic displacement parameters differ for the two C60 molecules in the asymmetric unit. Some benzene disorder persists, even at 13 K.

Download Full-text