Order Pressure Derivatives Research Articles

Study of Nanomaterials Under Second Order Bulk Modulus

In this study, we analyze the variation of pressure under different values of (𝑽𝑽𝟎) for nanomaterials using secondorder pressure derivative of bulk modulus equation of state. Second order pressure derivative of bulk modulus show fine studies of nanomaterials. The Gupta & Gupta EOS is used to calculate the resultant data of ε-Fe (Hexagonal iron), α-Fe2O3 and Ni-filled MWCNT nanomaterials and compared with other equations of state, like Tait EOS, Mie–Gruneisen EOS, Vinet EOS and experimental data available in literature. The resultant data show good agreement with experimental data and other EOSs.

Elastic properties of TiC and TiN crystals in high temperature range

The elastic properties of crystals at high temperature are of significant interest as they affect the mechanical stability and performance of materials at elevated temperatures. In present study a theory for evaluating the temperature variation of second third and fourth order elastic constants for face centred cubic crystal structure solids is used on the basis of Coulomb and Born-Mayer potential using nearest-neighbour distance and hardness parameter. The theory is first applied to get the second order elastic constants (SOECs) and third order elastic contants (TOECs) for TiC and TiN crystals at different temperatures up to 500 K. In addition, the elastic constants thus obtained are used to evaluate the first order pressure derivatives (FOPDs) SOECs and TOECs. The elastic properties of these crystals at high temperature are of significant interest and are related to other important material properties such as thermal expansion, thermal conductivity, phase transformations, creep behaviour, oxidation resistance, and high-temperature strength.The results obtained show that the second order elastic constants and third order elastic constants of TiC are highest, so mechanical properties of TiC will be better than TiN, which makes it stiffer and more resistant to deformation under an applied load. These properties make TiC a popular material for cutting tools, wear-resistant coatings, and other high-performance applications.

Pressure effect on some physical properties of calcium oxide material

The present investigation aims to study the high-pressure dependence up to 65.2GPa of the bulk modulus, Vickers hardness, mass density, Grüneisen parameter, Debye temperature, and average acoustic velocity for calcium oxide (CaO) binary compound. First, we calculated the normal conditions of Vickers hardness, which is equal to 14.8GPa, and then we employed the high-pressure Mukhanov's et al (2009) model to determine the high-pressure effect on the Vickers hardness. Using this model, commonly the hardness increases with increased pressure. Our data show that the bulk modulus, the mass density, the Debye temperature, and the average acoustic wave speed of CaO material increase gradually with increasing pressure, while both the first order pressure derivative of the bulk modulus and the Grüneisen parameter decrease with enhanced pressure up to 65.2GPa. Furthermore, we determined the normal conditions fracture toughness of CaO material; it is around 1.46MPa.m1/2, which is slightly higher than those of Si and GaP semiconducting materials.

Theoretical prediction of Grüneisen Parameter for γ-Fe2O3

The application of nanomaterials in modern technologies requires the study of its Grüneisen parameter. For this purpose, we have theoretically calculated the pressure, bulk modulus, and first order pressure derivative of bulk modulus at different compression ratios (V/V0). Further, we have tried to predict the variation of Grüneisen parameter with respect to compression ratio (V/V0) for ɣ-Fe2O3 nanomaterial. The Grüneisen parameter was calculated using the Borton and Stacey model at compressions up to V/V0 = 0.64. We have used three different equations of state: Birch- Murnaghan EOS, Brennan-Stacey EOS, and Vinet-Rydberg.

Anharmonic Properties of Rocksalt Structure Solids of TOECs

An effort has been made for obtaining the anharmonic properties of rocksalt structure solid starting from primary physical parameters VIZ. nearest neighbour distance and hardness parameter assuming long- and short-range potentials at an elevated temperature.The elastic energy density for a deformed crystal is expanded as power series of strains for obtaining coefficients of quadratic cubic and quartic terms which are known as the second, third and fourth order elastic constant respectively.When the values of the higher order elastic constants are known for a crystal, many of the anharmonic properties of the crystal can be treated within the limit of the continuum approximation in a quantitative manner.The higher order elastic constant are computed at 300K for rocksalt structure solids which are Alkali cyanides, Sodium and Potassium Halides. The first order pressure derivatives of second and third order elastic constants, the second order pressure derivative of second order elastic constant and partial contractions are evaluated at room temperature for these substances. The results thus obtained are compared with experimental and theoretical data and found in well agreement with present values.

Anharmonic Properties of Rocksalt Structure Solids of SOECs

An effort has been made for obtaining the anharmonic properties of rocksalt structure solid starting from primary physical parameters VIZ. nearest neighbour distance and hardness parameter assuming long- and short-range potentials at an elevated temperature. The elastic energy density for a deformed crystal is expanded as power series of strains for obtaining coefficients of quadratic cubic and quartic terms which are known as the second, third and fourth order elastic constant respectively. When the values of the higher order elastic constants are known for a crystal, many of the anharmonic properties of the crystal can be treated within the limit of the continuum approximation in a quantitative manner. The higher order elastic constant are computed at 300K for rocksalt structure solids which are Alkali cyanides, Sodium and Potassium Halides. The first order pressure derivatives of second and third order elastic constants, the second order pressure derivative of second order elastic constant and partial contractions are evaluated at room temperature for these substances. The results thus obtained are compared with experimental and theoretical data and found in well agreement with present values.

Tuning the onset pressure of pressure-induced phase transition in indium phosphide by extrinsic doping

In-situ angle-dispersive X-ray diffraction (ADXRD) and Raman scattering were carried out to delineate the phase transitions under pressure in p-type zinc-doped indium phosphide (InP:Zn) at ambient temperature. The ADXRD measurements with pressure up to 17.3(2) GPa reveal that InP:Zn transforms from zinc-blende (ZB) to rock-salt (RS) structure in a pressure range of 8.1(2) - 8.6(1) GPa. The Raman scattering measurements indicate that the phase transition proceeds continuously over a wide range of pressure and reaches completion at the highest pressure applied (14.5(2) GPa) with significant metallization, as suggested by the disappearance of the transverse optical (TO) and longitudinal optical (LO) modes. In contrast, originally absent at ambient pressure, additional Raman shift of Zn local vibrational modes (LVMs), appeared at 276 cm-1 and 420.7(1) cm-1 within the pressure range of 2.2(1) up to 10.1(2) GPa, which can be attributed to Zn3P2 and VPZnInVP LO modes, respectively. The zero-pressure isothermal bulk moduli and its first order pressure derivatives for the zinc-blende InP:Zn are 79.44(2) GPa and 3.92(1), respectively. A total enthalpy change of about 45.45 KJ•mole-1 was derived for the ZB to RS structure transformation occurring at the pressure of 8.6(1) GPa. The present results suggest that diffusion of Zn in InP:Zn may have been governed by the modified substitution and interstitial (S–I) mechanism. Moreover, comparisons on the pressure-dependent behaviors in InP:Zn, InP:S, and InP:Fe extrinsically doped systems revealed that the exact type of the defects introduced into the lattice upon doping may have played crucial roles in the pressure-induced phase transitions.

Anharmonic Properties of Oxides Having Face Centered Cubic Crystal Structure of Fourth Order

A theory has been evolved for obtaining anharmonic properties of oxides having face centered cubic crystal symmetry using long-range Coulomb and short-range Born-Mayer potentials starting from the nearest-neighbour distance and hardness parameter. The fourth order elastic constants are obtained for oxides of Cd, Co, Fe, Nb, Ni, Te, Ti and Zr at elevated temperature. The room temperature data are utilized for obtaining the first order pressure derivatives of second and third order elastic constants, the second order pressure derivatives of second order elastic constants and partial contractions of these oxides. The results are presented and discussed.

Third Order Pressure Derivative Elastic Properties of Alkali Cyanide

In this paper we have evaluated the pressure derivatives of third order elastic constants in the CsCN material. An extended three body force shell model (ETSM), which incorporates the effects of translational– rotational (TR) coupling, three body interactions (TBI) and anharmonicity, has been applied. The pressure derivatives of TOECs, dc111/dp, dc112/dp, dc166/dp, dc111/dp dc123/dp and dc456/dp show increasing trend with increasing temperature. However their values could not be compared due to lack of experimental data.

Differentiative Study of Anharmonic Properties of Oxides Having Face Centered Cubic Crystal Structure of Third and Fourth Order

A theory has been evolved for obtaining anharmonic properties of oxides having face centered cubic crystal symmetry using long-range Coulomb and short-range Born-Mayer potentials starting from the nearest-neighbour distance and hardness parameter. The second order elastic constants are obtained for oxides of Cd, Co, Fe, Nb, Ni, Te, Ti and Zr at elevated temperature. The room temperature data are utilized for obtaining the first order pressure derivatives of second order elastic constants, the second order pressure derivatives of second order elastic constants and partial contractions of these oxides. The results are presented and discussed.

Melting temperature of metals under pressure

In the present study, a thermodynamic model is formulated to determine the melting temperature of metals with increasing pressure using an equation of state (EoS). The model is applied to determine the melting temperature of Cu, Au, Ag, Zn, Cd, In and Pb at high pressure. The model formulation is based on Goyal and Gupta EoS which follows Stacey's criteria and is valid in high pressure conditions and also it does not involve any adjustable parameter. The volume compression, bulk modulus and its first order pressure derivative is determined using the EoS with an increase in pressure. It is observed that melting temperature show increase with the increase in pressure, however, variation is not linear. The comparison of present computed results of melting temperature under pressure is done with the theoretical and experimental results available and good consistency between the compared results is observed. This study helps in understanding the quantitative effect of pressure on the melting behavior of metals. The melting temperature at high pressures can also be predicted using the present formalism.

FP-LAPW calculations on electronic and thermoelectric properties of Mn2CoCr Heusler compound

Heusler compounds have been remarkable among the materials due to their fascinating properties. These materials are also important in terms of applications in thermoelectric device formation. The Mn2CoCr is one of the Heusler compounds investigated in reference to its band structure and thermo-electric properties by using density functional theory. Mn2CoCr crystallizes in Fm-3m (space group 225) phase and ferromagnetically stable under ambient conditions. We have calculated its bulk modulus, first order pressure derivative of bulk modulus, band structure, density of states, Seebeck coefficient and power factor.

Comparative Study of Anharmonic Properties of Oxides Having Face Centered Cubic Crystal Structure of Second and Third Order

A theory has been evolved for obtaining anharmonic properties of oxides having face centered cubic crystal symmetry using long-range Coulomb and short-range Born-Mayer potentials starting from the nearest-neighbour distance and hardness parameter. The second order elastic constants are obtained for oxides of Cd, Co, Fe, Nb, Ni, Te, Ti and Zr at elevated temperature. The room temperature data are utilized for obtaining the first order pressure derivatives of second order elastic constants, the second order pressure derivatives of second order elastic constants and partial contractions of these oxides. The results are presented and discussed.

Anharmonic Properties of Oxides Having Face Centered Cubic Crystal Structure

A theory has been evolved for obtaining anharmonic properties of oxides having face centered cubic crystal symmetry using long-range Coulomb and short-range Born-Mayer potentials starting from the nearest-neighbour distance and hardness parameter. The second ,third and fourth order elastic constants are obtained for oxides of Cd, Co, Fe, Nb, Ni, Te, Ti and Zr at elevated temperature. The room temperature data are utilized for obtaining the first order pressure derivatives of second and third order elastic constants, the second order pressure derivatives of second order elastic constants and partial contractions of these oxides. The results are presented and discussed.

Anharmonic Properties of Oxides Having Face Centered Cubic Crystal Structure of Third Order

A theory has been evolved for obtaining anharmonic properties of oxides having face centered cubic crystal symmetry using long-range Coulomb and short-range Born-Mayer potentials starting from the nearest-neighbour distance and hardness parameter. The third order elastic constants are obtained for oxides of Cd, Co, Fe, Nb, Ni, Te, Ti and Zr at elevated temperature. The room temperature data are utilized for obtaining the first order pressure derivatives of second and third order elastic constants, the second order pressure derivatives of second order elastic constants and partial contractions of these oxides. The results are presented and discussed.

Applicability of equation of state in extreme compression region and study of diatomic solids under pressure

In the present study, the expression of first pressure derivative of bulk modulus B′ earlier derived by Goyal and Gupta EoS [7] is corrected and the validity of the EoS is then verified in extreme compression region. The expressions of second and third order pressure derivative (B″,B″′)of bulk modulus are obtained. The values of B′, B2B‴ to BB″, Grunesien parameters λ∞, γ∞, q∞ at infinite pressure (P → ∞) are calculated using the identities [11–13] to check the validity of the equation in extreme compression region. The Goyal and Gupta EoS is then used to study the volume compression in diatomic solids, LiH and MgO. The values of pressure, bulk modulus and its first order pressure derivative at different compressions are calculated and compared with the results obtained from Hama–Suito EoS. The results justify the validity of the present EoS in high pressure region and the results for diatomic solids are also found in good consistency with the compared results.

Phase Instability and Thermal Properties of Multilayered Vanadium Diselenide: DAC-Based High Pressure Studies

Two-dimensional layered trichalcogenides are of current research interest because of their robust opto-electronics, and thermal properties. Mechanical and phonon vibrational properties of these materials are of significant importance in the field of stress and thermal management. Here we report the pressure dependence of structural and phonon behaviors of high quality few-layers vanadium diselenide nano-sheets grown by hydrothermal method employing synchrotron x-rays and micro-Raman scattering techniques. The high crystalline nature of the nanosheets was examined using transmission electron microscopy. Synchrotron x-ray studies at high pressure (up to 22 GPa) using a diamond-anvil cell identify a displacive type phase transition to a low symmetry monoclinic phase (C2/m) around 7 GPa corroborated with the P-dependent Raman scattering results. Raman spectroscopic studies at high pressure (up to 34 GPa) identify two prominent Raman bands with symmetry Eg and A1g. Eg band at 207 cm-1 shows normal hardening and A1g band at 236 cm-1 softens. The first order pressure derivatives of these phonons at ambient phase (P-3m1) are found to be -3.547(2) and 0.388(6) cm-1/ GPa, respectively. Using the experimental mode Grüneisen parameter of Eg Raman mode, the in-plane thermal expansion coefficient of the titular compound at the ambient phase is estimated. The observed results are expected to be useful in calibration and performance of next generation nano-electronics and optical devices under extreme stress conditions. These experimental results corroborated with our ab-initio calculations will be presented in the ECS meeting.

Insight into the structural, electronic, elastic and optical properties of the alkali hydride compounds, XH (X = Rb and Cs)

The equilibrium structural parameters, electronic and optical properties of the alkali hydrides RbH and CsH compounds in rock-salt (RS) and cesium chloride (CsCl) structures have been studied using the full-potential linearized augmented plane-wave (FP-LAPW) method. Wu and Cohen generalized gradient approximation (WC-GGA) was used for the exchange-correlation potential to compute the equilibrium structural parameters, such as the lattice constant (a0), the bulk modulus (B) and bulk modulus first order pressure derivative (B'). In addition to the WC-GGA, the modified Becke Johnson (mBJ) scheme has been also used to overcome the underestimation of the band gap energies. RbH and CsH compounds are found to be semiconductors (wide energy-band gap) using the WC-GGA method, while they are insulators using the mBJ-GGA method. Elastic constants, mechanical and thermodynamic properties were obtained by using the IRelast package. RbH and CsH compounds at ambient pressure are mechanically stable in RS and CsCl structures; they satisfy the Born mechanical stability criteria. Elastic constants (Cij), bulk modulus (B), shear modulus (S) and Debye temperatures (θD) of RbH and CsH compounds decrease as the alkali radius increases. The RS structure of these compounds at ambient conditions is mechanically stronger than CsCl structure. RbH and CsH in RS and CsCl structures are suitable as dielectric compounds. The wide direct energy band gap for these compounds make them promising compounds for optoelectronic UV device applications. Both RbH and CsH have a wide absorption region, on the other hand RbH absorption is very huge compared to the CsH absorption, RbH is an excellent absorbent material, maximum absorption regions are located in the middle ultraviolet (MUV) region and far ultraviolet (FUV) region. The absorption coefficient α (w), imaginary part of the dielectric constant ε2(w) and the extinction coefficient k(w) vary in the same way. The present calculated results are in good agreement with the experimental data, indicating the high accuracy of the performed calculations and reliability of the obtained results.

Anharmonic Properties of Oxides Having Face Centered Cubic Crystal Structure of Second Order

A theory has been evolved for obtaining anharmonic properties of oxides having face centered cubic crystal symmetry using long-range Coulomb and short-range Born-Mayer potentials starting from the nearest-neighbour distance and hardness parameter. The second order elastic constants are obtained for oxides of Cd, Co, Fe, Nb, Ni, Te, Ti and Zr at elevated temperature. The room temperature data are utilized for obtaining the first order pressure derivatives of second order elastic constants, the second order pressure derivatives of second order elastic constants and partial contractions of these oxides. The results are presented and discussed.

Higher order derivatives of bulk modulus of materials at infinite pressure

Pressure derivatives of bulk modulus of materials at infinite pressure or extreme compression have been studied using some basic principles of calculus. Expressions for higher order pressure derivatives at infinite pressure are obtained that are found to have the status of identities. A generalized formula is derived for the nth-order pressure derivative of bulk modulus in terms of the third-order Grüneisen parameter at infinite pressure.