A three-phase confocal elliptical cylinder model is proposed to analyze micromechanics of one-dimensional hexagonal piezoelectric quasicrystal （PQC） compos- ites. Exact solutions of the phonon, phason, and electric ...A three-phase confocal elliptical cylinder model is proposed to analyze micromechanics of one-dimensional hexagonal piezoelectric quasicrystal （PQC） compos- ites. Exact solutions of the phonon, phason, and electric fields are obtained by using the conformal mapping combined with the Laurent expansion technique when the model is subject to far-field anti-plane mechanical and in-plane electric loadings. The effective elec- troelastic constants of several different composites made up of PQC, quasicrystal （QC）, and piezoelectric （PE） materials are predicted by the generalized self-consistent method. Numerical examples are conducted to show the effects of the volume fraction and the cross-sectional shape of inclusion （or fiber） on the effective electroelastic constants of these composites. Compared with other micromechanical methods, the generalized self- consistent and Mori-Tanaka methods can predict the effective electroelastic constants of the composites consistently.展开更多
Rate constants for the reactions of NO3 and SO4 radicals with oxalic acid and oxalate anions in aqueous solution have been measured using pulse radiolysis and laser flash photolysis.
Antiferroelectric ferroelectric （AFE-FE） phase transition in ceramic Pbo.97Lao.02（Zro.75Snon36Tion14）O3 （PLZST） was studied by dielectric spectroscopy as functions of frequency （102-105 Hz） and pressure （0-50...Antiferroelectric ferroelectric （AFE-FE） phase transition in ceramic Pbo.97Lao.02（Zro.75Snon36Tion14）O3 （PLZST） was studied by dielectric spectroscopy as functions of frequency （102-105 Hz） and pressure （0-500 MPa） under a DC electric field. The hydrostatic pressure-dependent remnant polarization and dielectric constant were mea- sured. The results show that remnant polarization of the metastable rhombohedral ferroelectric PLZST poled ceramic decreases sharply and depoles completely at phase transition under hydrostatic pressure. The dielectric constant um dergoes an abrupt jump twice during a load and unload cycle under an electric field. The two abrupt jumps correspond to two phase transitions, FE AFE and AFE-FE.展开更多
A laser flash photolysis study of the reactivity of Cl˙with glyoxal, glyoxal mono- and dibisulfite adducts, 1-hydroxy-2, 2-diol-ethanesulfonate and 1, 2-dihydroxy-1, 2-ethanedi sulfonate in the aqueous phase was ca...A laser flash photolysis study of the reactivity of Cl˙with glyoxal, glyoxal mono- and dibisulfite adducts, 1-hydroxy-2, 2-diol-ethanesulfonate and 1, 2-dihydroxy-1, 2-ethanedi sulfonate in the aqueous phase was carried out. The obtained rate constants can be used for atmospheric modeling.展开更多
The equilibrium lattice constants, elastic constants and elastic moduli of wll- and post-spinel Si3Na have been investigated in the pressure ranges of 0-40 GPa and 160-240 GPa, respectively. These two phases are found...The equilibrium lattice constants, elastic constants and elastic moduli of wll- and post-spinel Si3Na have been investigated in the pressure ranges of 0-40 GPa and 160-240 GPa, respectively. These two phases are found to be dynamically stable. The post-spinel phase is one of the strongest materials yet investigated under extreme compressions. Some fundamental properties and phase transition characters are evaluated from the quasi-harmonic approximation. The transition pressures from the γ phase to the post-spinel phase are 152.5 GPa （at 300 K） and 181.8 GPa （at 1500 K）. The phase transition pressures of theβ→wll and γ→postspinel transitions increase with the rise of temperature; hence, at higher temperature it requires higher pressure to synthesize post-spinel Si3Na. The heat capacity, thermal expansion and bulk modulus of the new phases are computed as functions of pressure and temperature. The heat capacity of post-spinel Si3Na is large at high temperature and only weakly pressure dependent.展开更多
A Landau-Ginsburg-Devonshire(LD)-type thermodynamic theory was used to describe the effect of external stress on phase diagrams and dielectric properties of epitaxial ferroelectric thin films grown on orthorhombic sub...A Landau-Ginsburg-Devonshire(LD)-type thermodynamic theory was used to describe the effect of external stress on phase diagrams and dielectric properties of epitaxial ferroelectric thin films grown on orthorhombic substrates which induce nonequally biaxial misfit strains in the films plane. The “misfit strain-external stress” and “external stress-temperature” phase diagrams were constructed for single-domain BaTiO3(BT) and PbTiO3(PT) thin films. It is shown that the external stress may lead to the rotation of the spontaneous polarization and a gradual change of its magnitude, which may result in phase transition. Nonequally biaxial misfit strains dependence of the stability of polarization states may be governed by external stress. At room temperature, stress-induced ferroelectric/paraelectric phase transition which occurs in film on cubic substrate does not take place in the ferroelectric thin film grown on orthorhombic substrate. It is also shown that the nonequally misfit strains in the film plane may lead to the appearance of new phases which do not form in films grown on cubic substrates under external stress. The dependence of the dielectric response on the external stress is also studied. It is shown that the dielectric constants of single-domain PT and BT films are very sensitive to the external stress under the given anisotropic misfit strains-temperature conditions. It presents theoretical evidence that the external stress and anisotropic misfit strains can be employed for improving the thin films physical properties.展开更多
The equations for energy, momentum, frequency, wavelength and also Schr?dinger equation of the electromagnetic wave in the atom are derived using the model of atom by analogy with the transmission line. The action con...The equations for energy, momentum, frequency, wavelength and also Schr?dinger equation of the electromagnetic wave in the atom are derived using the model of atom by analogy with the transmission line. The action constant A0 = (μ0/ε0)1/2s02e2 is a key term in the above mentioned equations. Besides the other well-known quantities, the only one unknown quantity in the last expression is a structural constant s0. Therefore, this article is dedicated to the calculation of the structural constant of the atoms on the basis of the above mentioned model. The structural constant of the atoms s0 = 8.277 56 shows up as a link between macroscopic and atomic world. After calculating this constant we get the theory of atoms based on Maxwell’s and Lorentz equations only. This theory does not require Planck constant h, which once was introduced empirically. Replacement for h is the action constant A0, which is here theoretically derived, while the replacement for fine structure constant α is 1/(2s02). In this way, the structural constant s0 replaces both constants, h and α. This paper also defines the stationary states of atoms and shows that the maximal atomic number is equal to 2s02 = 137.036, i.e., as integer should be Zmax=137. The presented model of the atoms covers three of the four fundamental interactions, namely the electromagnetic, weak and strong interactions.展开更多
Vapor-liquid phase equilibrium data of tertpentanol in carbon dioxide were measured at temperatures of 313.4, 323.4, 333.5 and 343.5 K and in the pressure range of 4.56--11.44 MPa. The phase equilibium apparatus used ...Vapor-liquid phase equilibrium data of tertpentanol in carbon dioxide were measured at temperatures of 313.4, 323.4, 333.5 and 343.5 K and in the pressure range of 4.56--11.44 MPa. The phase equilibium apparatus used in the work was a variable-volume high-pressure cell. The experimental data were reasonably correlated with Peng-Robinson equation of state（PR-EOS） together with van der Waals-2 two-parameter mixing rules. Henry＇s Law constants and partial molar volumes of CO2 at infinite dilution were estimated with Krichevsky-Kasarnovsky equa- tion, and Henry＇s Law constants increase with increasing temperature, however, partial molar volumes of CO2 at infinite dilution are negative whose magnitudes decrease with temperature. Partial molar volumes of CO2 and tertpentanol in liquid phase at equilibrium were calculated.展开更多
We report results on the ab initio study of the mechanical and electronic properties of the iron Pnictide compound CaFe<sub>2</sub>As<sub>2</sub> and its phase transition under pressure using Q...We report results on the ab initio study of the mechanical and electronic properties of the iron Pnictide compound CaFe<sub>2</sub>As<sub>2</sub> and its phase transition under pressure using Quantum Espresso code. We do analysis of the strength of bonds in individual points of this material and proper Cauchy pressure calculation which will give more insight on the elastic responses. Ground state energy was done in the framework of density functional theory (DFT) based on plane wave self-consistent field (PWscf) and ultrasoft pseudo potential (USPP) method as treated in the Perdew-Burke Ernzerhof (PBE) generalized gradient approximation and local density approximations. Elastic constants were computed using thermo_pw and the values were used to calculate mechanical properties and pressure phase changes. From the non-zero positive elastic constants, the Iron Pnictide compound is found to be mechanically stable and its Poisson’s ratio indicates that it is brittle and isotropic. Pressure induced phase transition is here found to happen at an applied external pressure of 0.2 GPa causing the tetragonal phase to change to an orthorhombic phase which agrees well with previous reports.展开更多
We report results on the ab initio study of the mechanical and electronic properties of the iron Pnictide compound CaFe<sub>2</sub>As<sub>2</sub> and its phase transition under pressure using Q...We report results on the ab initio study of the mechanical and electronic properties of the iron Pnictide compound CaFe<sub>2</sub>As<sub>2</sub> and its phase transition under pressure using Quantum Espresso code. We do analysis of the strength of bonds in individual points of this material and proper Cauchy pressure calculation which will give more insight on the elastic responses. Ground state energy was done in the framework of density functional theory (DFT) based on plane wave self-consistent field (PWscf) and ultrasoft pseudo potential (USPP) method as treated in the Perdew-Burke Ernzerhof (PBE) generalized gradient approximation and local density approximations. Elastic constants were computed using thermo_pw and the values were used to calculate mechanical properties and pressure phase changes. From the non-zero positive elastic constants, the Iron Pnictide compound is found to be mechanically stable and its Poisson’s ratio indicates that it is brittle and isotropic. Pressure induced phase transition is here found to happen at an applied external pressure of 0.2 GPa causing the tetragonal phase to change to an orthorhombic phase which agrees well with previous reports.展开更多
Using a field equation with a phase factor, a universal analytic potential-energy function applied to the interactions between diatoms or molecules is derived, and five kinds of potential curves of common shapes are o...Using a field equation with a phase factor, a universal analytic potential-energy function applied to the interactions between diatoms or molecules is derived, and five kinds of potential curves of common shapes are obtained adjusting the phase factors. The linear thermal expansion coefficients and Young's moduli of eleven kinds of face-centered cubic (fcc) metals - Al, Cu, Ag, etc. are calculated using the potential-energy function; the computational results are quite consistent with experimental values. Moreover, an analytic relation between the linear thermal expansion coefficients and Young's moduli of fcc metals is given using the potential-energy function. Finally, the force constants of fifty-five kinds of diatomic moleculars with low excitation state are computed using this theory, and they are quite consistent with RKR (Rydberg-Klein-Rees) experimental values.展开更多
The subsolidus of Nd 2O 3 SrO TiO 2 system were determined at 1200℃. Two ternary compounds, SrO·Nd 2O 3·3TiO 2 and SrO·Nd 2O 3·4TiO 2, were confirmed in the ternary system. The latter e...The subsolidus of Nd 2O 3 SrO TiO 2 system were determined at 1200℃. Two ternary compounds, SrO·Nd 2O 3·3TiO 2 and SrO·Nd 2O 3·4TiO 2, were confirmed in the ternary system. The latter exists over a solid solution area. Discrepancies among the various stoichiometric compounds claimed in literature in the binary system Nd 2O 3 SrO were explained. Only one compound, Sr 3Nd 4O 9, was confirmed at 1200℃. Its structure belongs to orthorhombic with a =1.221 nm, b =1.016 nm, c =0.7138 nm, Z =3 and unit cell volume 0.8852 nm 3. The electrical conductivity and dielectric constants of some phases have been measured. All phases measured are poor semiconductor.展开更多
In the present work, the elastic constants and derived properties of tetragonal Heusler compounds were calculated using the high accuracy of the full-potential linearized augmented plane wave (FPLAPW) method. To find ...In the present work, the elastic constants and derived properties of tetragonal Heusler compounds were calculated using the high accuracy of the full-potential linearized augmented plane wave (FPLAPW) method. To find the criteria required for an accurate calculation, the consequences of increasing the numbers of k-points and plane waves on the convergence of the calculated elastic constants were explored. Once accurate elastic constants were calculated, elastic anisotropies, sound velocities, Debye temperatures, malleability, and other measurable physical properties were determined for the studied systems. The elastic properties suggested metallic bonding with intermediate malleability, between brittle and ductile, for the studied Heusler compounds. To address the effect of off-stoichiometry on the mechanical properties, the virtual crystal approximation (VCA) was used to calculate the elastic constants. The results indicated that an extreme correlation exists between the anisotropy ratio and the stoichiometry of the Heusler compounds, especially in the case of Ni2MnGa. Metastable cubic Ni2MnGa exhibits a very high anisotropy (≈28) and hypothetical cubic Rh2FeSn violates the Born-Huang stability criteria in the L21 structure. The bulk moduli of the investigated tetragonal compounds do not vary much (≈130 ...190 GPa). The averaged values of the other elastic moduli are also rather similar, however, rather large differences are found for the elastic anisotropies of the compounds. These are reflected in very different spatial distributions of Young’s moduli when comparing the different compounds. The slowness surfaces of the compounds also differ considerably even though the average sound velocities are in the same order of magnitude (3.2 ... 3.6 km/s). The results demonstrate the importance of the elastic properties not only for purely tetragonal Heusler compounds but also for phase change materials that exhibit magnetic shape memory or magnetocaloric effects.展开更多
基金Projected supported by the National Natural Science Foundation of China(Nos.11502123 and11262012)the Natural Science Foundation of Inner Mongolia Autonomous Region of China(No.2015JQ01)
文摘A three-phase confocal elliptical cylinder model is proposed to analyze micromechanics of one-dimensional hexagonal piezoelectric quasicrystal （PQC） compos- ites. Exact solutions of the phonon, phason, and electric fields are obtained by using the conformal mapping combined with the Laurent expansion technique when the model is subject to far-field anti-plane mechanical and in-plane electric loadings. The effective elec- troelastic constants of several different composites made up of PQC, quasicrystal （QC）, and piezoelectric （PE） materials are predicted by the generalized self-consistent method. Numerical examples are conducted to show the effects of the volume fraction and the cross-sectional shape of inclusion （or fiber） on the effective electroelastic constants of these composites. Compared with other micromechanical methods, the generalized self- consistent and Mori-Tanaka methods can predict the effective electroelastic constants of the composites consistently.
文摘Rate constants for the reactions of NO3 and SO4 radicals with oxalic acid and oxalate anions in aqueous solution have been measured using pulse radiolysis and laser flash photolysis.
基金Project supported by the National Basic Research Program of China (Grant No.2009CB623306)the International Science & Technology Cooperation Program of China (Grant No.2010DFR50480)the National Natural Science Foundation of China (Grant No.10976022)
文摘Antiferroelectric ferroelectric （AFE-FE） phase transition in ceramic Pbo.97Lao.02（Zro.75Snon36Tion14）O3 （PLZST） was studied by dielectric spectroscopy as functions of frequency （102-105 Hz） and pressure （0-500 MPa） under a DC electric field. The hydrostatic pressure-dependent remnant polarization and dielectric constant were mea- sured. The results show that remnant polarization of the metastable rhombohedral ferroelectric PLZST poled ceramic decreases sharply and depoles completely at phase transition under hydrostatic pressure. The dielectric constant um dergoes an abrupt jump twice during a load and unload cycle under an electric field. The two abrupt jumps correspond to two phase transitions, FE AFE and AFE-FE.
文摘A laser flash photolysis study of the reactivity of Cl˙with glyoxal, glyoxal mono- and dibisulfite adducts, 1-hydroxy-2, 2-diol-ethanesulfonate and 1, 2-dihydroxy-1, 2-ethanedi sulfonate in the aqueous phase was carried out. The obtained rate constants can be used for atmospheric modeling.
基金supported by the National Natural Science Foundation of China(Nos.11005088 and 11105115)the Project of Basic and Advanced Technology of Henan Province of China(No.112300410021)+1 种基金the Key Project of Henan Educational Committee(No.12A140010)the Young Teacher's Program of Xinyang Normal University(No.2011084)
文摘The equilibrium lattice constants, elastic constants and elastic moduli of wll- and post-spinel Si3Na have been investigated in the pressure ranges of 0-40 GPa and 160-240 GPa, respectively. These two phases are found to be dynamically stable. The post-spinel phase is one of the strongest materials yet investigated under extreme compressions. Some fundamental properties and phase transition characters are evaluated from the quasi-harmonic approximation. The transition pressures from the γ phase to the post-spinel phase are 152.5 GPa （at 300 K） and 181.8 GPa （at 1500 K）. The phase transition pressures of theβ→wll and γ→postspinel transitions increase with the rise of temperature; hence, at higher temperature it requires higher pressure to synthesize post-spinel Si3Na. The heat capacity, thermal expansion and bulk modulus of the new phases are computed as functions of pressure and temperature. The heat capacity of post-spinel Si3Na is large at high temperature and only weakly pressure dependent.
基金Project(10472099) supported the National Natural Science Foundation of China Project(05JJ30208) supported by the Natural Science Foundation of Hunan Province+1 种基金 Project(05FJ2005) supported by Key Project of Scientific and Technological Department of Hunan Province Project(GY2006-2) supported by Scientific and Technological Project of Xiangtan City
文摘A Landau-Ginsburg-Devonshire(LD)-type thermodynamic theory was used to describe the effect of external stress on phase diagrams and dielectric properties of epitaxial ferroelectric thin films grown on orthorhombic substrates which induce nonequally biaxial misfit strains in the films plane. The “misfit strain-external stress” and “external stress-temperature” phase diagrams were constructed for single-domain BaTiO3(BT) and PbTiO3(PT) thin films. It is shown that the external stress may lead to the rotation of the spontaneous polarization and a gradual change of its magnitude, which may result in phase transition. Nonequally biaxial misfit strains dependence of the stability of polarization states may be governed by external stress. At room temperature, stress-induced ferroelectric/paraelectric phase transition which occurs in film on cubic substrate does not take place in the ferroelectric thin film grown on orthorhombic substrate. It is also shown that the nonequally misfit strains in the film plane may lead to the appearance of new phases which do not form in films grown on cubic substrates under external stress. The dependence of the dielectric response on the external stress is also studied. It is shown that the dielectric constants of single-domain PT and BT films are very sensitive to the external stress under the given anisotropic misfit strains-temperature conditions. It presents theoretical evidence that the external stress and anisotropic misfit strains can be employed for improving the thin films physical properties.
文摘The equations for energy, momentum, frequency, wavelength and also Schr?dinger equation of the electromagnetic wave in the atom are derived using the model of atom by analogy with the transmission line. The action constant A0 = (μ0/ε0)1/2s02e2 is a key term in the above mentioned equations. Besides the other well-known quantities, the only one unknown quantity in the last expression is a structural constant s0. Therefore, this article is dedicated to the calculation of the structural constant of the atoms on the basis of the above mentioned model. The structural constant of the atoms s0 = 8.277 56 shows up as a link between macroscopic and atomic world. After calculating this constant we get the theory of atoms based on Maxwell’s and Lorentz equations only. This theory does not require Planck constant h, which once was introduced empirically. Replacement for h is the action constant A0, which is here theoretically derived, while the replacement for fine structure constant α is 1/(2s02). In this way, the structural constant s0 replaces both constants, h and α. This paper also defines the stationary states of atoms and shows that the maximal atomic number is equal to 2s02 = 137.036, i.e., as integer should be Zmax=137. The presented model of the atoms covers three of the four fundamental interactions, namely the electromagnetic, weak and strong interactions.
基金Supported by the Youth Key Teacher Foundation of Henan Educational Committee,China(No.2010GGJS-162)
文摘Vapor-liquid phase equilibrium data of tertpentanol in carbon dioxide were measured at temperatures of 313.4, 323.4, 333.5 and 343.5 K and in the pressure range of 4.56--11.44 MPa. The phase equilibium apparatus used in the work was a variable-volume high-pressure cell. The experimental data were reasonably correlated with Peng-Robinson equation of state（PR-EOS） together with van der Waals-2 two-parameter mixing rules. Henry＇s Law constants and partial molar volumes of CO2 at infinite dilution were estimated with Krichevsky-Kasarnovsky equa- tion, and Henry＇s Law constants increase with increasing temperature, however, partial molar volumes of CO2 at infinite dilution are negative whose magnitudes decrease with temperature. Partial molar volumes of CO2 and tertpentanol in liquid phase at equilibrium were calculated.
文摘We report results on the ab initio study of the mechanical and electronic properties of the iron Pnictide compound CaFe<sub>2</sub>As<sub>2</sub> and its phase transition under pressure using Quantum Espresso code. We do analysis of the strength of bonds in individual points of this material and proper Cauchy pressure calculation which will give more insight on the elastic responses. Ground state energy was done in the framework of density functional theory (DFT) based on plane wave self-consistent field (PWscf) and ultrasoft pseudo potential (USPP) method as treated in the Perdew-Burke Ernzerhof (PBE) generalized gradient approximation and local density approximations. Elastic constants were computed using thermo_pw and the values were used to calculate mechanical properties and pressure phase changes. From the non-zero positive elastic constants, the Iron Pnictide compound is found to be mechanically stable and its Poisson’s ratio indicates that it is brittle and isotropic. Pressure induced phase transition is here found to happen at an applied external pressure of 0.2 GPa causing the tetragonal phase to change to an orthorhombic phase which agrees well with previous reports.
文摘We report results on the ab initio study of the mechanical and electronic properties of the iron Pnictide compound CaFe<sub>2</sub>As<sub>2</sub> and its phase transition under pressure using Quantum Espresso code. We do analysis of the strength of bonds in individual points of this material and proper Cauchy pressure calculation which will give more insight on the elastic responses. Ground state energy was done in the framework of density functional theory (DFT) based on plane wave self-consistent field (PWscf) and ultrasoft pseudo potential (USPP) method as treated in the Perdew-Burke Ernzerhof (PBE) generalized gradient approximation and local density approximations. Elastic constants were computed using thermo_pw and the values were used to calculate mechanical properties and pressure phase changes. From the non-zero positive elastic constants, the Iron Pnictide compound is found to be mechanically stable and its Poisson’s ratio indicates that it is brittle and isotropic. Pressure induced phase transition is here found to happen at an applied external pressure of 0.2 GPa causing the tetragonal phase to change to an orthorhombic phase which agrees well with previous reports.
基金This work was supported by the National Natural Science Foundation of China (No. 40274044).
文摘Using a field equation with a phase factor, a universal analytic potential-energy function applied to the interactions between diatoms or molecules is derived, and five kinds of potential curves of common shapes are obtained adjusting the phase factors. The linear thermal expansion coefficients and Young's moduli of eleven kinds of face-centered cubic (fcc) metals - Al, Cu, Ag, etc. are calculated using the potential-energy function; the computational results are quite consistent with experimental values. Moreover, an analytic relation between the linear thermal expansion coefficients and Young's moduli of fcc metals is given using the potential-energy function. Finally, the force constants of fifty-five kinds of diatomic moleculars with low excitation state are computed using this theory, and they are quite consistent with RKR (Rydberg-Klein-Rees) experimental values.
文摘The subsolidus of Nd 2O 3 SrO TiO 2 system were determined at 1200℃. Two ternary compounds, SrO·Nd 2O 3·3TiO 2 and SrO·Nd 2O 3·4TiO 2, were confirmed in the ternary system. The latter exists over a solid solution area. Discrepancies among the various stoichiometric compounds claimed in literature in the binary system Nd 2O 3 SrO were explained. Only one compound, Sr 3Nd 4O 9, was confirmed at 1200℃. Its structure belongs to orthorhombic with a =1.221 nm, b =1.016 nm, c =0.7138 nm, Z =3 and unit cell volume 0.8852 nm 3. The electrical conductivity and dielectric constants of some phases have been measured. All phases measured are poor semiconductor.
文摘In the present work, the elastic constants and derived properties of tetragonal Heusler compounds were calculated using the high accuracy of the full-potential linearized augmented plane wave (FPLAPW) method. To find the criteria required for an accurate calculation, the consequences of increasing the numbers of k-points and plane waves on the convergence of the calculated elastic constants were explored. Once accurate elastic constants were calculated, elastic anisotropies, sound velocities, Debye temperatures, malleability, and other measurable physical properties were determined for the studied systems. The elastic properties suggested metallic bonding with intermediate malleability, between brittle and ductile, for the studied Heusler compounds. To address the effect of off-stoichiometry on the mechanical properties, the virtual crystal approximation (VCA) was used to calculate the elastic constants. The results indicated that an extreme correlation exists between the anisotropy ratio and the stoichiometry of the Heusler compounds, especially in the case of Ni2MnGa. Metastable cubic Ni2MnGa exhibits a very high anisotropy (≈28) and hypothetical cubic Rh2FeSn violates the Born-Huang stability criteria in the L21 structure. The bulk moduli of the investigated tetragonal compounds do not vary much (≈130 ...190 GPa). The averaged values of the other elastic moduli are also rather similar, however, rather large differences are found for the elastic anisotropies of the compounds. These are reflected in very different spatial distributions of Young’s moduli when comparing the different compounds. The slowness surfaces of the compounds also differ considerably even though the average sound velocities are in the same order of magnitude (3.2 ... 3.6 km/s). The results demonstrate the importance of the elastic properties not only for purely tetragonal Heusler compounds but also for phase change materials that exhibit magnetic shape memory or magnetocaloric effects.
