A variational-perturbation approach is invoked to study the effect of the environment potential a... more A variational-perturbation approach is invoked to study the effect of the environment potential around Fluoride ion on some important electronic properties. The dipole polarisability α, oscillator strength S(-٢) and S (-١) and magnetic susceptibility χ are theoretically estimated for Fluoride ion in different potentials. Also we calculate these electronic properties in many Fluoride structure crystals such as CdF ٢ , CaF ٢ , PbF ٢ , SrF ٢ BaF ٢ , and LiF.
This work applies the shell model to study the behaviour of the internuclear interactions of diat... more This work applies the shell model to study the behaviour of the internuclear interactions of diatomic alkali halide molecules from data given by the dynamical models for alkali halide crystals. Our interest is to test the breathing shell model when core holes have been introduced. This will provide another source of information on the nature of the interaction potential between
We have investigated the effects of the environment potential around Fluoride ion on some importa... more We have investigated the effects of the environment potential around Fluoride ion on some important electronic and magnetic properties such as dipole polarisability, moment of oscillator strengths S(k) and magnetic susceptibility. The theoretical procedure is based on the variational-perturbation theory with two parameter trial functions incorporated in an ionic model. We estimate these properties in four cases for Fluoride ion; free ion, ion under different potentials, ion in the crystals and ion in nanocrystal, CdF 2 , CaF 2 , PbF 2 , SrF 2 and BaF 2. Our results indicate that these properties vary with ion environments and the free state of Fluoride ion has higher values and there is linearity behaviour of these properties with lattice constant. For Fluoride ion in nanocrystal, we have found that there is an extra parameter that can also affect the dipole polarisability, the number of ions in the structure.
We generalize two parameters trial wave function in the KirkwoodPople and Schofield approach to ... more We generalize two parameters trial wave function in the KirkwoodPople and Schofield approach to obtain multipole moments for atoms or ions. Madelung factor is calculated for bulk rocksalt structure nanocrystal. Then we apply our generalized approach to calculate ...
Equilibrium molecular dynamics based Einstein relation with an appropriate definition for integra... more Equilibrium molecular dynamics based Einstein relation with an appropriate definition for integrated heat current (i.e., with modified energy moment) are combined to quantify the thermal conductivity of individual single-walled carbon nanotubes, armchair, zigzag and chiral tubes. The thermal conductivity has been investigated as a function of three parameters, tube radius, length and chirality at and near room temperature with Brenner potential model. Thermal conductivity is found to have unusually high value and varies with radius, length and chirality of tubes. Also the thermal conductivity at temperature range from 50 to 100 K is found to have a maximum value. For 12.1 nm tube length, the thermal conductivity has converging trend which its value dependents on the tube radius and chirality. Tubes with large radius have lower values of thermal conductivity. Furthermore, the results show that armchair tubes have large values of the thermal conductivity comparing with zigzag and chiral tubes. It seems possible to uncover carbon nanotubes thermal properties based on measurements having heat dependence by adding another methods for calculations.
Based on the helical and rotational symmetries and Tersoff-Brenner potential with couple of modif... more Based on the helical and rotational symmetries and Tersoff-Brenner potential with couple of modified parameters, we investigate the variation of bond length/lengths in equilibrium structure due to tube length as well as due to applied hydrostatic pressure for a series of high symmetry armchair (n,n) single-wall nanotubes having different radii. Assuming that two different bond lengths dictate the tube geometry, these are monitored as a function of radius. It turns out that one of these bond lengths is greater than bond length of graphite whereas other one was less than it. These deviations from graphite value appear to be related to the curvature-induced rehybridization of the carbon orbitals. Lengths are found to have very important effect on the values of both bond lengths. The results under hydrostatic pressure indicate many linear behaviors having different slopes in the values of bond lengths with increasing pressure leading to a pressure induced-phase transition. This behaviour is strongly dependent on the tube radius. We also calculate the bulk moduls for this structure which reflects clearly this behavior of armchair nanotubes and thus predicts mechanical resilience of nanotubes.
Based on the helical and rotational symmetries and Tersoff potential, the structural parameters, ... more Based on the helical and rotational symmetries and Tersoff potential, the structural parameters, i.e., bond lengths and bond angles, have been investigated for armchair single-wall carbon nanotubes. The bond lengths and bond angles are determined for several radii tubes of various lengths. Results for armchair tubes show that one bond length is greater than that of the graphite while the other is smaller. Furthermore, the tube length is found to have significant effects on these bond lengths and bond angles. We have also recalculated the variation of these bonds under hydrostatic pressure. With the application of pressure, the bond lengths compress and the larger bond length decreases faster with pressure in comparison to the shorter one. As a consequence, at some critical pressure the bond lengths become equal. An analysis regarding the cross-sectional shape of the nanotubes and its pressure dependence has also been done. At some particular pressure, the first transition from circular to elliptical cross section takes place. For ͑10,10͒ tube the first transition pressure is found to be equal to 2.2 GPa.
We investigate structural parameters, i.e., bond lengths and bond angles of isolated uncapped zig... more We investigate structural parameters, i.e., bond lengths and bond angles of isolated uncapped zigzag single-wall nanotubes in detail. The bond lengths and bond angles are determined for several radii tubes by using a theoretical procedure based on the helical and rotational symmetry for atom coordinates generation, coupled with Tersoff potential for interaction energy calculations. Results show that the structure of zigzag tubes is governed by two bond lengths. One bond length is found to have a value equal to that of graphite, while the other one is larger. Furthermore, the tube length is found to have significant effect only on larger bond length in zigzag tubes. With the application of the pressure, only the larger bond length compresses, the other one remaining practically constant. At some critical pressure, this bond length becomes equal to constant bond length. This behavior of bond lengths is different from those of armchair tubes. An analysis regarding the cross sectional shape has also been done. At some higher pressure, transition from circular to oval cross section takes place. This transition pressure is found to be equal 2.06GPa for (20,0) tube. Some comparison with chiral tubes has also been made and important differences on bond length behavior have been observed.
We investigate the structural parameters, i.e. bond lengths and bond angles of chiral tubes of va... more We investigate the structural parameters, i.e. bond lengths and bond angles of chiral tubes of various chiralities. The procedure used is based on helical and rotational symmetries and Tersoff potential. The results indicate that at ambient condition, there are equal bond lengths and three unequal bond angles in the structure of chiral tubes. The bond length depends much more on the chirality and very slightly on the tube radius. Length of the tubes does not play very significant role on bond length and bond angles. These CC bonds were recalculated under hydrostatic pressure. The bond length compresses with pressure while the bond angles remain practically unchanged. We also carry out analysis regarding the cross sectional shape of chiral tubes and its pressure dependence. It is found that at some pressures, transition from circular to oval cross section takes place. The transition pressure is found to strongly depend on the radius and chirality of tube. At this transition, corresponding to given elliptical cross section, the bond length for all chiral tubes is identical. This behavior of bond length is different from achiral tubes.
We investigate the equilibrium structure of armchair single-wall carbon nanotubes at ambient cond... more We investigate the equilibrium structure of armchair single-wall carbon nanotubes at ambient conditions and under hydrostatic pressure. The structural parameters investigated are the bond lengths and bond angles. The bond lengths are determined for several radii tubes of various lengths. The procedure adopts generation of atomic coordinates based on the helical and rotational symmetries using two different bond lengths and then minimizing the energy to obtain best possible set of these bond lengths using Tersoff potential. Results show that one bond length is greater than that of the graphite while the other is smaller than that in graphite. The tube length is found to have significant effects on these bond lengths. These bonds were recalculated under hydrostatic pressure. The larger bond length decreases faster with pressure in comparison to the shorter one. As a result, at some critical pressure, depending upon the tube radius, these bond lengths match up each other before reversing their behavior above this critical pressure. It seems possible to uncover tube characteristics based on measurements having pressure dependence.
Results of the bond lengths for various chiralities of single-wall carbon carbon nanotubes (SWNTs... more Results of the bond lengths for various chiralities of single-wall carbon carbon nanotubes (SWNTs) (armchair, zigzag and chiral) are obtained. We use modified helical and rotational symmetries to describe the structure of SWNTs and Tersoff potential to minimize the energy of these tubes. It emerges that in general, two bond lengths are required for obtaining minimum energy structure, in contrast to one bond length commonly used. The difference in bond lengths depends on chirality and radius of achiral tubes. Significantly, even a small deviation from zigzag or armchair character leads to interesting behavior of bond lengths. A reduction in diameter is responsible for difference in the bond lengths of achiral nanotubes. We also calculate the bond lengths under hydrostatic pressure. The behavior of bond lengths for armchair singlewall nanotubes when calculated under pressure shows that the larger bond length decreases faster with pressure in comparison to the shorter bond length. At some critical pressure (depending upon the radius of the tube), the two bond lengths become equal to each other, reversing their difference above this critical pressure. We suggest that this behavior can be exploited to experimentally determine the chirality and radius of the carbon nanotubes, for example by observing the presence and disappearance of modes typical of two different bond lengths. This change occurs only within a few GPa of pressure.
A variational-perturbation approach is invoked to study the effect of the environment potential a... more A variational-perturbation approach is invoked to study the effect of the environment potential around Fluoride ion on some important electronic properties. The dipole polarisability α, oscillator strength S(-٢) and S (-١) and magnetic susceptibility χ are theoretically estimated for Fluoride ion in different potentials. Also we calculate these electronic properties in many Fluoride structure crystals such as CdF ٢ , CaF ٢ , PbF ٢ , SrF ٢ BaF ٢ , and LiF.
This work applies the shell model to study the behaviour of the internuclear interactions of diat... more This work applies the shell model to study the behaviour of the internuclear interactions of diatomic alkali halide molecules from data given by the dynamical models for alkali halide crystals. Our interest is to test the breathing shell model when core holes have been introduced. This will provide another source of information on the nature of the interaction potential between
We have investigated the effects of the environment potential around Fluoride ion on some importa... more We have investigated the effects of the environment potential around Fluoride ion on some important electronic and magnetic properties such as dipole polarisability, moment of oscillator strengths S(k) and magnetic susceptibility. The theoretical procedure is based on the variational-perturbation theory with two parameter trial functions incorporated in an ionic model. We estimate these properties in four cases for Fluoride ion; free ion, ion under different potentials, ion in the crystals and ion in nanocrystal, CdF 2 , CaF 2 , PbF 2 , SrF 2 and BaF 2. Our results indicate that these properties vary with ion environments and the free state of Fluoride ion has higher values and there is linearity behaviour of these properties with lattice constant. For Fluoride ion in nanocrystal, we have found that there is an extra parameter that can also affect the dipole polarisability, the number of ions in the structure.
We generalize two parameters trial wave function in the KirkwoodPople and Schofield approach to ... more We generalize two parameters trial wave function in the KirkwoodPople and Schofield approach to obtain multipole moments for atoms or ions. Madelung factor is calculated for bulk rocksalt structure nanocrystal. Then we apply our generalized approach to calculate ...
Equilibrium molecular dynamics based Einstein relation with an appropriate definition for integra... more Equilibrium molecular dynamics based Einstein relation with an appropriate definition for integrated heat current (i.e., with modified energy moment) are combined to quantify the thermal conductivity of individual single-walled carbon nanotubes, armchair, zigzag and chiral tubes. The thermal conductivity has been investigated as a function of three parameters, tube radius, length and chirality at and near room temperature with Brenner potential model. Thermal conductivity is found to have unusually high value and varies with radius, length and chirality of tubes. Also the thermal conductivity at temperature range from 50 to 100 K is found to have a maximum value. For 12.1 nm tube length, the thermal conductivity has converging trend which its value dependents on the tube radius and chirality. Tubes with large radius have lower values of thermal conductivity. Furthermore, the results show that armchair tubes have large values of the thermal conductivity comparing with zigzag and chiral tubes. It seems possible to uncover carbon nanotubes thermal properties based on measurements having heat dependence by adding another methods for calculations.
Based on the helical and rotational symmetries and Tersoff-Brenner potential with couple of modif... more Based on the helical and rotational symmetries and Tersoff-Brenner potential with couple of modified parameters, we investigate the variation of bond length/lengths in equilibrium structure due to tube length as well as due to applied hydrostatic pressure for a series of high symmetry armchair (n,n) single-wall nanotubes having different radii. Assuming that two different bond lengths dictate the tube geometry, these are monitored as a function of radius. It turns out that one of these bond lengths is greater than bond length of graphite whereas other one was less than it. These deviations from graphite value appear to be related to the curvature-induced rehybridization of the carbon orbitals. Lengths are found to have very important effect on the values of both bond lengths. The results under hydrostatic pressure indicate many linear behaviors having different slopes in the values of bond lengths with increasing pressure leading to a pressure induced-phase transition. This behaviour is strongly dependent on the tube radius. We also calculate the bulk moduls for this structure which reflects clearly this behavior of armchair nanotubes and thus predicts mechanical resilience of nanotubes.
Based on the helical and rotational symmetries and Tersoff potential, the structural parameters, ... more Based on the helical and rotational symmetries and Tersoff potential, the structural parameters, i.e., bond lengths and bond angles, have been investigated for armchair single-wall carbon nanotubes. The bond lengths and bond angles are determined for several radii tubes of various lengths. Results for armchair tubes show that one bond length is greater than that of the graphite while the other is smaller. Furthermore, the tube length is found to have significant effects on these bond lengths and bond angles. We have also recalculated the variation of these bonds under hydrostatic pressure. With the application of pressure, the bond lengths compress and the larger bond length decreases faster with pressure in comparison to the shorter one. As a consequence, at some critical pressure the bond lengths become equal. An analysis regarding the cross-sectional shape of the nanotubes and its pressure dependence has also been done. At some particular pressure, the first transition from circular to elliptical cross section takes place. For ͑10,10͒ tube the first transition pressure is found to be equal to 2.2 GPa.
We investigate structural parameters, i.e., bond lengths and bond angles of isolated uncapped zig... more We investigate structural parameters, i.e., bond lengths and bond angles of isolated uncapped zigzag single-wall nanotubes in detail. The bond lengths and bond angles are determined for several radii tubes by using a theoretical procedure based on the helical and rotational symmetry for atom coordinates generation, coupled with Tersoff potential for interaction energy calculations. Results show that the structure of zigzag tubes is governed by two bond lengths. One bond length is found to have a value equal to that of graphite, while the other one is larger. Furthermore, the tube length is found to have significant effect only on larger bond length in zigzag tubes. With the application of the pressure, only the larger bond length compresses, the other one remaining practically constant. At some critical pressure, this bond length becomes equal to constant bond length. This behavior of bond lengths is different from those of armchair tubes. An analysis regarding the cross sectional shape has also been done. At some higher pressure, transition from circular to oval cross section takes place. This transition pressure is found to be equal 2.06GPa for (20,0) tube. Some comparison with chiral tubes has also been made and important differences on bond length behavior have been observed.
We investigate the structural parameters, i.e. bond lengths and bond angles of chiral tubes of va... more We investigate the structural parameters, i.e. bond lengths and bond angles of chiral tubes of various chiralities. The procedure used is based on helical and rotational symmetries and Tersoff potential. The results indicate that at ambient condition, there are equal bond lengths and three unequal bond angles in the structure of chiral tubes. The bond length depends much more on the chirality and very slightly on the tube radius. Length of the tubes does not play very significant role on bond length and bond angles. These CC bonds were recalculated under hydrostatic pressure. The bond length compresses with pressure while the bond angles remain practically unchanged. We also carry out analysis regarding the cross sectional shape of chiral tubes and its pressure dependence. It is found that at some pressures, transition from circular to oval cross section takes place. The transition pressure is found to strongly depend on the radius and chirality of tube. At this transition, corresponding to given elliptical cross section, the bond length for all chiral tubes is identical. This behavior of bond length is different from achiral tubes.
We investigate the equilibrium structure of armchair single-wall carbon nanotubes at ambient cond... more We investigate the equilibrium structure of armchair single-wall carbon nanotubes at ambient conditions and under hydrostatic pressure. The structural parameters investigated are the bond lengths and bond angles. The bond lengths are determined for several radii tubes of various lengths. The procedure adopts generation of atomic coordinates based on the helical and rotational symmetries using two different bond lengths and then minimizing the energy to obtain best possible set of these bond lengths using Tersoff potential. Results show that one bond length is greater than that of the graphite while the other is smaller than that in graphite. The tube length is found to have significant effects on these bond lengths. These bonds were recalculated under hydrostatic pressure. The larger bond length decreases faster with pressure in comparison to the shorter one. As a result, at some critical pressure, depending upon the tube radius, these bond lengths match up each other before reversing their behavior above this critical pressure. It seems possible to uncover tube characteristics based on measurements having pressure dependence.
Results of the bond lengths for various chiralities of single-wall carbon carbon nanotubes (SWNTs... more Results of the bond lengths for various chiralities of single-wall carbon carbon nanotubes (SWNTs) (armchair, zigzag and chiral) are obtained. We use modified helical and rotational symmetries to describe the structure of SWNTs and Tersoff potential to minimize the energy of these tubes. It emerges that in general, two bond lengths are required for obtaining minimum energy structure, in contrast to one bond length commonly used. The difference in bond lengths depends on chirality and radius of achiral tubes. Significantly, even a small deviation from zigzag or armchair character leads to interesting behavior of bond lengths. A reduction in diameter is responsible for difference in the bond lengths of achiral nanotubes. We also calculate the bond lengths under hydrostatic pressure. The behavior of bond lengths for armchair singlewall nanotubes when calculated under pressure shows that the larger bond length decreases faster with pressure in comparison to the shorter bond length. At some critical pressure (depending upon the radius of the tube), the two bond lengths become equal to each other, reversing their difference above this critical pressure. We suggest that this behavior can be exploited to experimentally determine the chirality and radius of the carbon nanotubes, for example by observing the presence and disappearance of modes typical of two different bond lengths. This change occurs only within a few GPa of pressure.
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