murnaghan equation
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2021 ◽  
Author(s):  
J. L. Cuevas F. ◽  
M. Courel Piedrahita ◽  
E. Feddi ◽  
V. M. Rentería T. ◽  
M. L. Ojeda M. ◽  
...  

Abstract Zirconia bulk is one of the most studied materials around the world due to different properties such as a high melting temperature, biocompatibility, and high thermal expansion, among many others. However, there is little experimental research about Zirconia nanowires and until now there are few theoretical papers on the subject. In this work, DFT calculations on bare ZrO2 nanowires with diameter variation were performed. In order to get the more accurate parameters for calculation on nanowires, we employed the Murnaghan equation of state in a cubic phase of ZrO2 and we compared the results obtained with some experimental data as well as the lattice parameter and the bulk modulus. The nanowires were grown along with the [1 1 1] direction with five different diameters. All calculations were carried out by Density Functional Theory (DFT) implemented in SIESTA code. According to our results, GGA-PBE is the more accurate functional for describing the Exc on ZrO2. The calculation of formation and surface energies shows that these nanowires are highly stable chemically. Furthermore, nanowires larger than 8.78 ˚A present a direct bandgap. These results indicate the possibility of applying ZrO2 nanowires in the optoelectronic field.


2021 ◽  
Author(s):  
Marcus Parry ◽  
Jackson Hendry ◽  
Samantha Couper ◽  
Anton Oliynyk ◽  
Aria Mansouri Tehrani ◽  
...  

The Mo2-xWxBC system is of interest as a material with high hardness while maintaining moderate ductility. In this work, synchrotron diffraction experiments are performed on Mo2-xWxBC solid solutions, where x = 0, 0.5, and 0.75, upon hydrostatic compression to ~54 GPa, ~55 GPa, and ~60 GPa, respectively. Trends in bulk modulus, K0, are evaluated by fitting collected pressure-volume data with a third-order Birch-Murnaghan equation of state, finding K0 = 333(9) GPa for Mo2BC, K0 = 335(11) GPa for Mo1:5W0:5BC, and K0 = 343(8) GPa for Mo1:25W0:75BC. While K0 demonstrates a slight increase when Mo is substituted by W, calculated zero pressure unit cell volume, V0, exhibits the opposite trend. The decrease in V0 corresponds to an increase in valence electron density, hardness, and K0. Observations corroborate previously reported computational results and will inform future efforts to design sustainable materials with exceptional mechanical properties.


Crystals ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 976
Author(s):  
Paola Comodi ◽  
Maximiliano Fastelli ◽  
Giacomo Criniti ◽  
Konstantin Glazyrin ◽  
Azzurra Zucchini

High-pressure synchrotron X-ray diffraction was carried out on a single crystal of mascagnite, compressed in a diamond anvil cell. The sample maintained its crystal structure up to ~18 GPa. The volume–pressure data were fitted by a third-order Birch–Murnaghan equation of state (BM3-EOS) yielding K0 = 20.4(7) GPa, K’0 = 6.1(2), and V0 = 499(1) Å3, as suggested by the F-f plot. The axial compressibilities, calculated with BM3-EOS, were K0a = 35(3), K’0a = 7.7(7), K0b = 10(3), K’0b = 7(1), K0c = 25(1), and K’0c = 4.3(2) The axial moduli measured using a BM2-EOS and fixing K’0 equal to 4, were K0a = 52(2), K0b = 20 (1), and K0c = 29.6(4) GPa, and the anisotropic ratio of K0a:K0b:K0c = 1:0.4:0.5. The evolution of crystal lattice and geometrical parameters indicated no phase transition until 17.6 GPa. Sulphate polyhedra were incompressible and the density increase of 30% compared to investigated pressure should be attributed to the reduction of weaker hydrogen bonds. In contrast, some of them, directed along [100], were very short at room temperature, below 2 Å, and showed a very low compressibility. This configuration explains the anisotropic compressional behavior and the lowest compressibility of the a axis.


Minerals ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 608
Author(s):  
Pei-Lun Lee ◽  
Eugene Huang ◽  
Jennifer Kung

In situ high-pressure synchrotron X-ray diffraction and Raman spectroscopic experiments of scottyite, BaCu2Si2O7, were carried out in a diamond anvil cell up to 21 GPa at room temperature. X-ray diffraction patterns reveal four new peaks near 3.5, 3.1, 2.6 and 2.2 Å above 8 GPa, while some peaks of the original phase disappear above 10 GPa. In the Raman experiment, we observed two discontinuities in dν/dP, the slopes of Raman wavenumber (ν) of some vibration modes versus pressure (P), at approximately 8 and 12 GPa, indicating that the Si-O symmetrical and asymmetrical vibration modes change with pressure. Fitting the compression data to Birch–Murnaghan equation yields a bulk modulus of 102 ± 5 GPa for scottyite, assuming Ko′ is four. Scottyite shows anisotropic compressibility along three crystallographic axes, among which c-axis was the most compressible axis, b-axis was the last and a-axis was similar to the c-axis on the compression. Both X-ray and Raman spectroscopic data provide evidences that scottyite undergoes a reversible phase transformation at 8 GPa.


Minerals ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 607
Author(s):  
Raquel Chuliá-Jordán ◽  
David Santamaria-Perez ◽  
Javier Ruiz-Fuertes ◽  
Alberto Otero-de-la-Roza ◽  
Catalin Popescu

The structure of the naturally occurring, iron-rich mineral Ca1.08(6)Mg0.24(2)Fe0.64(4)Mn0.04(1)(CO3)2 ankerite was studied in a joint experimental and computational study. Synchrotron X-ray powder diffraction measurements up to 20 GPa were complemented by density functional theory calculations. The rhombohedral ankerite structure is stable under compression up to 12 GPa. A third-order Birch–Murnaghan equation of state yields V0 = 328.2(3) Å3, bulk modulus B0 = 89(4) GPa, and its first-pressure derivative B’0 = 5.3(8)—values which are in good agreement with those obtained in our calculations for an ideal CaFe(CO3)2 ankerite composition. At 12 GPa, the iron-rich ankerite structure undergoes a reversible phase transition that could be a consequence of increasingly non-hydrostatic conditions above 10 GPa. The high-pressure phase could not be characterized. DFT calculations were used to explore the relative stability of several potential high-pressure phases (dolomite-II-, dolomite-III- and dolomite-V-type structures), and suggest that the dolomite-V phase is the thermodynamically stable phase above 5 GPa. A novel high-pressure polymorph more stable than the dolomite-III-type phase for ideal CaFe(CO3)2 ankerite was also proposed. This high-pressure phase consists of Fe and Ca atoms in sevenfold and ninefold coordination, respectively, while carbonate groups remain in a trigonal planar configuration. This phase could be a candidate structure for dense carbonates in other compositional systems.


Minerals ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 516
Author(s):  
Timofey Fedotenko ◽  
Saiana Khandarkhaeva ◽  
Leonid Dubrovinsky ◽  
Konstantin Glazyrin ◽  
Pavel Sedmak ◽  
...  

We report the high-pressure synthesis and the equation of state (EOS) of a novel nickel carbide (Ni3C). It was synthesized in a diamond anvil cell at 184(5) GPa through a direct reaction of a nickel powder with carbon from the diamond anvils upon heating at 3500 (200) K. Ni3C has the cementite-type structure (Pnma space group, a = 4.519(2) Å, b = 5.801(2) Å, c = 4.009(3) Å), which was solved and refined based on in-situ synchrotron single-crystal X-ray diffraction. The pressure-volume data of Ni3C was obtained on decompression at room temperature and fitted to the 3rd order Burch-Murnaghan equation of state with the following parameters: V0 = 147.7(8) Å3, K0 = 157(10) GPa, and K0' = 7.8(6). Our results contribute to the understanding of the phase composition and properties of Earth’s outer core.


2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Vincenzo Stagno ◽  
Luca Bindi ◽  
Sota Takagi ◽  
Atsushi Kyono

AbstractWe investigated the compressional behavior of i-AlCuFe quasicrystal using diamond anvil cell under quasi-hydrostatic conditions by in situ angle-dispersive X-ray powder diffraction measurements (in both compression and decompression) up to 76 GPa at ambient temperature using neon as pressure medium. These data were compared with those collected up to 104 GPa using KCl as pressure medium available in literature. In general, both sets of data indicate that individual d-spacing shows a continuous decrease with pressure with no drastic changes associated to structural phase transformations or amorphization. The d/d0, where d0 is the d-spacing at ambient pressure, showed a general isotropic compression behavior. The zero-pressure bulk modulus and its pressure derivative were calculated fitting the volume data to both the Murnaghan- and Birch-Murnaghan equation of state models. Results from this study extend our knowledge on the stability of icosahedrite at very high pressure and reinforce the evidence that natural quasicrystals formed during a shock event in asteroidal collisions and survived for eons in the history of the Solar System.


2021 ◽  
Vol 63 (7) ◽  
pp. 952
Author(s):  
В.А. Чернышев

The ab initio study of the structure and dynamics of the lattice, as well as the elastic properties of a row of rare-earth stannates R2Sn2O7 (R = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu) has been carried out for first time. The IR and Raman spectra were calculated, the types of phonon modes were determined. The degree of participation of ions in phonon modes is determined. Modes with the absolute or predominant participation of oxygen in the 48f position, characterized by a shift x, were determined from an analysis of the displacement vectors obtained from the ab initio calculations. The elastic constants and the hardness HV have been calculated. The effect of hydrostatic compression on the crystal structure is investigated. It is shown that the degree of distortion of the octahedron containing the rare-earth ion changes little with pressure (up to 12 GPa). It is shown that the dependence of the unit cell volume on pressure is described by the Birch-Murnaghan equation of state of the third order.


Minerals ◽  
2020 ◽  
Vol 10 (12) ◽  
pp. 1055
Author(s):  
Dariia Simonova ◽  
Elena Bykova ◽  
Maxim Bykov ◽  
Takaaki Kawazoe ◽  
Arkadiy Simonov ◽  
...  

A structure and equation of the state of δ-AlOOH has been studied at room temperature, up to 29.35 GPa, by means of single crystal X-ray diffraction in a diamond anvil cell using synchrotron radiation. Above ~10 GPa, we observed a phase transition with symmetry changes from P21nm to Pnnm. Pressure-volume data were fitted with the second order Birch-Murnaghan equation of state and showed that, at the phase transition, the bulk modulus (K0) of the calculated wrt 0 pressure increases from 142(5) to 216(5) GPa.


2020 ◽  
Vol 105 (11) ◽  
pp. 1752-1755
Author(s):  
Yoichi Nakajima ◽  
Shunya Araki ◽  
Daisuke Kinoshita ◽  
Kei Hirose ◽  
Shigehiko Tateno ◽  
...  

Abstract We found a new phase transition in Fe2P from Co2P-type (C23) to Co2Si-type (C37) structure above 42 ± 2 GPa based on in situ X-ray diffraction experiments. While these two structures have identical crystallographic symmetry, the orthorhombic unit cell is shortened in a-axis but elongated in c-axis, the coordination number of phosphorous increases from nine to 10, and the volume reduces by 2% across the phase transition. The new C37-type Fe2P phase has been found to be stable, at least to 83 GPa at high temperature. The Birch-Murnaghan equation of state for C37 Fe2P was also obtained from pressure-volume data, suggesting that phosphorous contributes to 17% of the observed density deficit of the Earth's outer core when it includes the maximum 1.8 wt% P as observed in iron meteorites. In addition, since both Fe2S and Ni2Si are also known to have the C37 structure under high pressure, (Fe,Ni)2(S,Si,P) could have wide solid solution and constitute planetary iron cores, although it is not dense enough to be a main constituent of the Earth's inner core.


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