scholarly journals THE EQUATIONS OF STATE OF FORSTERITE, WADSLEYITE, RINGWOODITE, AKIMOTOITE, MgSiO3-PEROVSKITE, AND POSTPEROVSKITE AND PHASE DIAGRAM FOR THE Mg2SiO4 SYSTEM AT PRESSURES OF UP TO 130 GPa

2015 ◽  
Vol 56 (1) ◽  
2017 ◽  
Vol 45 ◽  
pp. 1760059
Author(s):  
Clebson A. Graeff ◽  
Débora P. Menezes

We analyse the hadron/quark phase transition described by the Nambu-Jona-Lasinio (NJL) model [quark phase] and the extended Nambu-Jona-Lasinio model (eNJL) [hadron phase]. While the original formulation of the NJL model is not capable of describing hadronic properties due to its lack of confinement, it can be extended with a scalar-vector interaction so it exhibits this property, the so-called eNJL model. As part of this analysis, we obtain the equations of state within the SU(2) versions of both models for the hadron and the quark phases and determine the binodal surface.


2001 ◽  
Vol 21 (2) ◽  
pp. 67-77 ◽  
Author(s):  
Pei-Lun Lee ◽  
Eugene Huang ◽  
Shu-Cheng Yu

2004 ◽  
Vol 18 (14) ◽  
pp. 2057-2069 ◽  
Author(s):  
JIANXIANG TIAN ◽  
YUANXING GUI

In this paper, an argon-like canonical system is studied. We introduce five hypothesis to deal with the total potential of the system. Then the balanced liquid–gas coexistence phenomenon is analyzed. Good equations of state and phase diagram are given.


Minerals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 322
Author(s):  
Tatiana S. Sokolova ◽  
Peter I. Dorogokupets

The equations of state of different phases in the CaSiO3 system (wollastonite, pseudowollastonite, breyite (walstromite), larnite (Ca2SiO4), titanite-structured CaSi2O5 and CaSiO3-perovskite) are constructed using a thermodynamic model based on the Helmholtz free energy. We used known experimental measurements of heat capacity, enthalpy, and thermal expansion at zero pressure and high temperatures, and volume measurements at different pressures and temperatures for calculation of parameters of equations of state of studied Ca-silicates. The used thermodynamic model has allowed us to calculate a full set of thermodynamic properties (entropy, heat capacity, bulk moduli, thermal expansion, Gibbs energy, etc.) of Ca-silicates in a wide range of pressures and temperatures. The phase diagram of the CaSiO3 system is constructed at pressures up to 20 GPa and temperatures up to 2000 K and clarifies the phase boundaries of Ca-silicates under upper mantle conditions. The calculated wollastonite–breyite equilibrium line corresponds to equation P(GPa) = −4.7 × T(K) + 3.14. The calculated density and adiabatic bulk modulus of CaSiO3-perovskite is compared with the PREM model. The calcium content in the perovskite composition will increase the density of mineral and it good agree with the density according to the PREM model at the lower mantle region.


2013 ◽  
Vol 46 (1) ◽  
pp. 14-24 ◽  
Author(s):  
Ian G. Wood ◽  
Jabraan Ahmed ◽  
David P. Dobson ◽  
Lidunka Vočadlo

A new high-pressure phase of NiSi has been synthesized in a multi-anvil press by quenching samples to room temperature from 1223–1310 K at 17.5 GPa and then recovering them to atmospheric pressure. The crystal structure of this recovered material has been determined from X-ray powder diffraction data; the resulting fractional coordinates are in good agreement with those obtained from anab initiocomputer simulation. The structure, in which each atom is six-fold coordinated by atoms of the other kind, is orthorhombic (space groupPmmn) witha= 3.27,b= 3.03,c= 4.70 Å. This orthorhombic phase of NiSi may be considered as a ferroelastic distortion of the hypothetical tetragonal (space groupP4/nmm) NiSi structure that was predicted to be the most stable phase (at 0 K) for pressures between 23 and 61 GPa in an earlierab initiostudy by Vočadlo, Wood & Dobson [J. Appl. Cryst.(2012),45, 186–196]. Furtherab initiosimulations have now shown that, with increasing pressure (at 0 K), NiSi is predicted to exist in the following polymorphs: (i) the MnP structure; (ii) the new orthorhombic structure with space groupPmmn; and (iii) the CsCl structure. Experimentally, all of these structures have now been observed and, in addition, a fourth polymorph, an ∊-FeSi-structured phase of NiSi (never the most thermodynamically stable phase in athermalab initiosimulations), may be readily synthesized at high pressure (P) and temperature (T). On the basis of both experiments and computer simulations it is therefore now clear that the phase diagram of NiSi at highPandTis complex. The simulated free-energy differences between different structures are often very small (<10 meV atom−1) and there is also the possibility of two displacive ferroelastic phase transformations, the first between structures withPmmnandP4/nmmsymmetry, and the second fromP4/nmmto a different orthorhombic phase of NiSi with space groupPbma. A complete understanding of the NiSi phase diagram (which may be of relevance to both planetary cores and the use of thin films of NiSi in semiconductor technology) can, therefore, only comevia in situexperiments at simultaneous highPand highT.


2006 ◽  
Vol 19 (1) ◽  
pp. 65-68 ◽  
Author(s):  
Zi-jiang Liu ◽  
Xin-lu Cheng ◽  
Fang-pei Zhang ◽  
Xiang-dong Yang ◽  
Yuan Guo

2000 ◽  
Vol 98 (24) ◽  
pp. 2045-2052
Author(s):  
Keshawa P. Shukla, Walter G. Chapman
Keyword(s):  

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