On the electronic contribution to the elastic constants in strained quantum wire superlattices of non-parabolic semiconductors with graded structures: Theory and suggestion for experimental determination

Summary  We study the electronic contribution to the second- and third-order elastic constants in strained quantum wire superlattices of non-parabolic semiconductors with graded structures and compare the same with the constituent materials, by formulating the appropriate dispersion laws. It is found, taking InSb/GaSb quantum wire superlattice as an example, that the said contributions increase with decreasing thickness and with increasing electron concentration in oscillatory manners together with the fact that the influence of the finite interface width enhances their numerical values. An experimental method is suggested for determining the electronic contribution to the elastic constants in materials having arbitrary dispersion laws. In addition, the well-known results for constituent semiconductors in the absence of stress have also been obtained as special cases of our generalized formulations.     

Third-order elastic constants of ZnS and ZnSe

The complete set of non-vanishing third-order elastic constants of the semiconductors ZnS and ZnSe is obtained theoretically. The strain energy density is estimated using finite strain elasticity theory by considering the interactions up to two nearest neighbours of each atom in the unit cell of these compounds. This energy density is compared with the strain dependent lattice energy density from the continuum model approximation. The second-order parameter of the potential function φ is obtained from the measured principal axis C_ij. The third-order potential parameter is estimated by assuming a Lennard-Jones type of interatomic potential. The interlattice displacements as well as the second-order elastic constants are evaluated along with the six third-order elastic constants of ZnS and ZnSe. Using these second- and third-order elastic constants of ZnS, the pressure derivatives of second-order elastic constants are evaluated. The second- and third-order elastic constants of ZnSe are compared with the available experimental values. The third-order elastic constants show anisotropy in different directions.     

Third-order elastic constants and pressure derivatives of the second-order elastic constants of β-tin

The second- and third-order elastic constants and pressure derivatives of second-order elastic constants of tetragonal β-tin have been obtained using the deformation theory. The strain energy density derived using the deformation theory is compared with the strain dependent lattice energy obtained from the elastic continuum model approximation to get the expressions for the second- and third-order elastic constants. Higher order elastic constants are a measure of the anharmonicity of a crystal lattice. The 12 non-vanishing third-order elastic constants and the six pressure derivatives of the second-order elastic constants in tetragonal β-tin are obtained in the present work and are compared with the available experimental values. The second-order elastic constant C₃₃ obtained in the present study is in reasonable agreement with the experimental values. The third-order elastic constants are generally one order of magnitude greater than the second-order elastic constants as expected of a crystalline solid. The third-order elastic constant C₃₃₃ is higher in magnitude than all other values. This shows a greater anharmonicity of β-tin along the c-axis direction of the crystal.     

Third-order elastic constants of the alloy Fe72Pt28

The complete sets of second- and third-order elastic constants of the cubic Fe₇₂Pt₂₈ have been obtained using the strain energy density derived from interactions up to three nearest neighbours of each atom in the unit cell. The finite strain elasticity theory has been used to get the strain energy density of Fe₇₂Pt₂₈. The strain energy density is compared with the strain-dependent lattice energy density obtained from the continuum model approximation and the expressions for the second- and third-order elastic constants of Fe₇₂Pt₂₈ are given. The second-order potential parameter is deduced from the measured second-order elastic constants of Fe₇₂Pt₂₈ and the third-order potential parameter is estimated from the Lennard-Jones inter-atomic potential for Fe₇₂Pt₂₈. The inter-lattice displacements; the three independent second-order elastic constants and the six independent third-order elastic constants of Fe₇₂Pt₂₈ are also determined. The second-order elastic constants are compared with the experimental elastic constants of Fe₇₂Pt₂₈. We also study the effect of pressure on the second-order elastic constants of Fe₇₂Pt₂₈.     

Elastic constants of solids at high pressures

The isothermal and adiabatic nth-order (n ?? 2) elastic constants of a loaded crystal are defined. These constants fully determine the behavior of solids at an arbitrary load and are controlled by both an interatomic interaction and an applied load. Expressions that relate these constants (of the second, third, and fourth order) to Brugger elastic constants of the corresponding order, which are only determined by an inter-atomic interaction, are found for cubic symmetry crystals under hydrostatic pressure. These expressions are used to calculate the equation of state and the second- and third-order elastic constants of bcc tantalum at T = 0 K over a wide pressure range (0?C600 GPa) using an electron density functional method. The results of calculating the equation of state and the second-order elastic constants agree with available experimental data and the calculation results obtained in other works.     

Second- and third-order dispersion in PW prism-sequence with arbitrary apex-angle

Numerical results for the second- and third-order dispersion in PW prism-sequence (double prism-pair) with arbitrary apex-angle by ray-tracing method are presented. The influence of the prism separation distance and apex-angle on second- and third-order dispersion is discussed. In certain conditions, the PW prism-sequence with small apex-angle (20°) is a better choice to reduce third-order dispersion than single prism-pair without requiring excessive length. As a less dispersion material, quartz is suitable to be used with the smallest possible value of third-order dispersion. This result could be the basis of dispersion compensation and pulse compression.     

Anharmonic properties of rocksalt structure solids

An effort has been made for obtaining the anharmonic properties of rocksalt structure solids starting from primary physical parameters viz. nearest-neighbor distance and hardness parameter assuming long- and short-range potentials at elevated temperatures. The elastic energy density for a deformed crystal can be 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 constants, 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. In this study, higher-order elastic constants are computed up to their melting temperature 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 derivatives of second-order elastic constants and partial contractions are also evaluated at different temperatures for these substances. The results thus obtained are compared with experimental data and found in well agreement with present values.     

Anharmonic properties of TmTe

Data on elastic constants and associated properties at high temperature for TmTe crystal are presented and discussed starting from primary physical parameters viz. nearest neighbour distance and hardness parameter assuming long- and short-range potentials. 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. In this study, higher order elastic constants and related properties are computed upto 1000 K for TmTe. 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 are also evaluated at different temperatures. The results thus obtained are compared with other available data and found in well agreement with present values.     

The carrier contribution to the elastic constants in III-V, ternary and quaternary materials in the presence of light waves: Simplified theory, relative comparison and a suggestion for experimental determination

In this paper, we have studied the electronic contribution to the elastic constants for III-V, ternary and quaternary materials in the presence of light waves on the basis of newly formulated electron statistics. It has been found taking n-InAs, n-InSb, n-Hg_1−xCd_xTe and n-In_1−xGa_xAs_yP_1−y lattice matched to InP, as examples that the elastic constants increase with increasing electron concentration, intensity and wavelength in various manners. The strong dependence of the elastic constants on both the light intensity and wavelength reflects the direct signature of the light waves which is in contrast as compared with the corresponding bulk specimens in the absence of photo-excitation. The well-known results for degenerate wide gap materials in the absence of light waves have been obtained as a special case under certain limiting conditions and this compatibility is the indirect test of our generalized formalism. In this context, we have suggested the experimental method of determining the carrier contribution to the elastic constants for materials having arbitrary carrier energy spectra and our results find six important applications in the regime of photon-assisted transport in modern optoelectronic devices.     

Elastic phase transitions in metals at high pressures

The elastic phase transitions of cubic metals at high pressures are investigated within the framework of Landau theory. It is shown that at pressures comparable with the magnitude of the bulk modulus the phase transition is connected with the loss of stability relative to uniform deformation of the crystalline lattice. Discontinuity of the order parameter at the transition point and its equilibrium value are expressed through the second-?to fourth-order elastic constants. The second-,third-?and fourth-order elastic constants and phonon dispersion curves of vanadium under hydrostatic pressure are obtained by first-principles calculations. Structural transformation in vanadium under pressure is studied using the obtained results. It is shown that the experimentally observed at P?≈?69?GPa phase transition in vanadium is the first-order phase transition close to a second-order phase transition.     

Adiabatic bond charge model for the phonons in A3B5 semiconductors

The adiabatic bond-charge model is extended to describe phonon dispersion curves and elastic properties in A³B⁵ semiconductors. Asymmetry of the bond-charge position and of the force constants involving them is found to be the main consequence of ionicity. A six-parameter model provides a good fit to the experimental data for GaAs, GaSb and InSb. A small seventh parameter describing weak second-neighbor interactions is needed in GaP. Trends in the force-constant parameters are discussed.     

Numerical Study on the Performance in High-bit-rate Optical Communication Systems

By numerical simulations, we show that picosecond Gaussian optical pulses with a precise optimal frequency chirping can transmit stably in full-dispersion compensation optical fiber links, with not only second- but also third-order dispersion compensation, using dispersion shift fibers with opposite dispersion sign. The optimal pre-chirp is determined principally by the second-order dispersion scheme and scarcely affected by third-order dispersion scheme. It demonstrates that, to a high bit rate transmission system, the pre-chirping technology and higher-order dispersion compensation are two very efficient measures in improving performance of system.     

Microscopic theory of second-order and third-order elastic constants for an NaCl crystal

Relations between the second-order and third-order symmetry-independent elastic constants and the energy of interatomic interactions dependent on the mutual arrangement of pairs and triplets of atoms are obtained for crystals belonging to the crystal class O _h. The derived relations and experimental data on the elastic constants are used to calculate four third-order elastic constants and the temperature dependence of the elastic anisotropy factor a(T) for an NaCl crystal. The calculated dependence a(T) is in qualitative agreement with the experimental dependence a _exp(T).     

Mutual compensation of higher-order dispersion in chirped pulse amplification system with regenerative amplifier

In this paper, based on ray tracing, the approach of mutual compensation that introduced properly the negative third-order dispersion to balance the higher-order dispersion in the chirped pulse amplification (CPA) system with regenerative amplifier is presented. A shorter pulse with near-transform-limitation can be generated by this method than by the conventional approach that zeros the second- and the third-order dispersion successively in the CPA system.     

The stability and the nonlinear elasticity of 2D hexagonal structures of Si and Ge from first-principles calculations

By using the first-principles calculations based on the density-functional theory (DFT), we study the stability and the nonlinear elasticity of two-dimensional (2D) hexagonal structures of Si and Ge. The reproduced structure optimization and phonon-dispersion curves demonstrate that Si and Ge can form stable 2D hexagonal lattices with low-buckled structures, and provide a good agreement with the previous DFT calculations. The second- and third-order elastic constants are calculated by using the method of homogeneous deformation. The present results of the linear elastic moduli agree well with the previous results. In comparison with the linear approach, the nonlinear effects really matter while strain is larger than approximately 3.5%. The force-displacement behaviors and the breaking strength of 2D hexagonal Si and Ge are discussed using the nonlinear stress-strain relationship. By using the available results of graphene, we reasonably demonstrate that the radius of the atom increases and breaking strength of this element decreases for 2D hexagonal structures of group IV-elements.     

Condensed state physics elastic constants of alkali metal alloys

The second-and third-order Brøgger elastic constants of the disordered Cs-K, Cs-Rb, and Rb-K alloys with different concentrations of the second component are calculated for the pseudopotential model with the use of the Krasko-Gurskii model potential. Results of calculations are in good qualitative agreement with the available experimental data on the elastic constants of alloys.     

Monochromator Wavelength Calibration Standards Extending into the Near-Infrared Using Second- and Third-Order Emission Lines from Mercury Vapor Lamps

The emission spectra of four mercury vapor lamps are used to obtain wavelength calibration curves for the double-grating emission monochromator of a spectrofluorimeter. The use of second- and third-order diffraction lines and emission lines from the argon carrier gas provides a rich spectrum, which extends well into the near-infrared spectral region and produces an improved calibration curve. More than 60 emission lines are listed between 250 and 900 nm, which is sufficient to produce an extremely accurate monochromator calibration. Additional second- and third-order lines can be used to even longer wavelengths (>1200 nm). The effectiveness of three scattering surfaces is compared.     

Harmonic mode locking with reduced carrier-envelope phase noise in ytterbium-doped fiber laser

We experimentally explored the influence of passive harmonic mode locking on the temporal and spectral features of a ytterbium-doped fiber laser. Similar dependences of free-running linewidth of the laser carrier-envelope offset frequency (f₀) on the intracavity net dispersion were observed for the fundamental-, second-, and third-order mode-locking states. Due to the reduction of nonlinear effects and supermode phase locking that balanced the third-order dispersion in the fiber cavity, the third-order harmonic mode-locking exhibited the narrowest free-running f₀linewidth of ～120 kHz in the near-zero net dispersion regime.     

Ultrasonic wave propagation in rare-earth monochalcogenides

The ultrasonic attenuation in thulium monochalcogenides TmX (X=S, Se and Te) has been studied theoretically with a modified Mason’s approach in the temperature and range 100 K to 300 K along 〈100〉, 〈110〉 〈111〉 crystallographic directions. The thulium monochalcogenides have attracted a lot of interest due to their complex physical and chemical characteristics. TmS, TmSe and TmTe are trivalent metal, mixed valence state, and divalent semiconductor, respectively. Coulomb and Born-Mayer potential is applied to evaluate the second- and third-order elastic constants. These elastic constants are used to compute ultrasonic parameters such as ultrasonic velocities, thermal relaxation time, and acoustic coupling constants that, in turn, are used to evaluate ultrasonic attenuation. A comparison of calculated ultrasonic parameters with available theoretical/experimental physical parameters gives information about classification of these materials.      

Transmission Bragg-grating grisms for pulse compression

We design a grism compressor based on transmission gratings and high refractive index prisms to compensate for both the second- and third-order dispersions of SF57 glass at 800?nm. The use of transmission gratings eases the geometrical constraints, allows a final recombination of the spectral components out of the bulk of the prisms and suggests a potential application of these grims to high-energy pulse compression. The dispersion law of this grism compressor is measured in double-pass configuration and negative third-order dispersion is achieved. We demonstrate efficient operation with an overall throughput >60% over a 100?nm bandwidth.