Shear Constants Research Articles

Shear viscosity and dielectric constant of liquid methanol

Molecular dynamics simulations for liquid methanol are used to estimate the dielectric constant and shear viscosity. A rigid, fixed-charge three-site model is used. Three similar models that have been proposed provide estimates for these liquid methanol properties that are within ±30% of the experimental values. This is probably adequate for simulations where methanol is a solvent and induced polarization beyond a mean-field level is not a factor.

Shear elasticity and the orientational glass state of (NaCl)1–x (NaCN) x mixed crystals

The real and imaginary part of the low-frequency shear constant of (NaCl)1–x (NaCN) x single crystals, x = 0·67, 0·62, 0·51, has been measured as function of temperature. The elastic behavior is discussed in terms of ferroelastic phase transitions and of the formation of the orientational glass state. Differences to other series of cyanide mixed crystals are pointed out.

Elastic constants of α-GeO2

The elastic constants of α-GeO2, the quartzlike polymorph of germanium dioxide, have been determined using Brillouin scattering. The data were obtained using a high quality single crystal of α-GeO2. When compared with existing data on α-SiO2, our results show that the shear constants are considerably softened in GeO2. This could be an indication that the observed pressure induced phase change is related to a shear instability.

Bond order potentials of aluminum

The fitting procedure of bond order potentials for Al is presented. The shear constants are well reproduced by fitting the exponent of hopping integrals. The models fitted only to the shear constants show a good estimation of three unrelaxed principal surface energies, but a poor estimation of the monovacancy formation energy. At the lower moment order, further fitting to the cohesive energy gives a more accurate description for the defect energies.

Simultaneous manifestations of the 2D van Hove singularity and the Fermi surface nesting in the acoustic soft phonon mode of alloys

The experimentally observed composition and uniaxial-stress dependences of the soft phonon mode in alloy have been interpreted using numerical calculations of the electronic band structure, elastic shear constant , generalized susceptibility and different sections of Fermi surface as a basis. It is shown that the main features of these dependences are attributable to two different band structure peculiarities, namely, to Fermi surface nesting and 2D van Hove singularity in the density of states. Whereas the nesting vector fixes the position of a dip (Kohn anomaly) in the phonon branch, the separation between the Fermi level and the energy of the 2D van Hove singularity governs the softening (hardening) of this branch as a whole.

Multiaxial linear viscoelastic behavior of a soda–lime–silica glass based on a generalized Maxwell model

The multiaxial linear viscoelastic behavior of a soda–lime–silica glass has been investigated in the transition range using shear and uniaxial creep-recovery experiments. The shear and uniaxial viscoelastic constants and retardation functions have been precisely measured. The no-stress and the no-temperature dependence of the viscoelastic constants show, respectively, linear viscoelastic and simple thermorheological behaviors of the glass. The deviatoric part of the viscoelastic behavior is first investigated from the shear experimental data. A generalized Maxwell model with one set of parameters is shown to correctly simulate the shear creep-recovery experiments. Using the deviatoric part of the model, the spheric part of the viscoelastic behavior is deduced from the uniaxial experimental data. In particular, we show experimental measurements of the bulk equilibrium modulus and the temperature dependence of the hydrostatic pressure viscoelastic behavior for a soda–lime–silica glass. A second set of parameters of the generalized Maxwell model is determined for the hydrostatic pressure viscoelastic behavior.

Viscoelastic behavior of a soda-lime-silica glass: inadequacy of the KWW function

The viscoelastic behavior of a soda-lime-silica glass has been experimentally investigated in the glass transition range using shear and uniaxial creep-recovery experiments. No departure of linearity and thermorheological simplicity is found in the investigated stress and temperature ranges, respectively. The shear and uniaxial viscoelastic constants and retardation functions have been precisely measured from the recovery part. An attempt to model the shear and uniaxial viscoelastic behaviors with KWW functions is made and it is shown that this model cannot be a good representation of the linear viscoelastic behavior of the investigated glass.

Determination of the in-plane elastic tensor of crystalline decanol monolayers on water by x-ray diffraction

We show how high-resolution x-ray studies associated with surface tension measurements allow a determination of the elastic constants of crystalline 1-decanol monolayers at the water-air interface. The shape and position of the power-law diffraction peak yield, respectively, the shear and compression elastic constants. At low temperature, rotation scans of the liquid surface around a vertical axis exhibit six sharp peaks, proving the existence of the long-range order of bond orientations, as expected for a hexagonal two-dimensional (2D) crystal. We find a shear elastic constant of (210\ifmmode\pm\else\textpm\fi{}30) mN/m and a compression modulus of (2500\ifmmode\pm\else\textpm\fi{}500) mN/m. These values are compatible with the existence of a 2D solid, according to the Nelson-Halperin melting theory. Between \ensuremath{\sim}12 \ifmmode^\circ\else\textdegree\fi{}C and melting (${\mathrm{T}}_{\mathrm{m}}$=14.3 \ifmmode^\circ\else\textdegree\fi{}C), the drastic broadening of the diffraction line can be interpreted either as the occurrence of a hexatic phase or as a strong decrease of the shear modulus, as expected in the framework of the weak crystallization theory.

Calculation of the elastic properties of CuCl

The elastic constants of CuCl with zinc-blende structure are calculated by means of two processes. By using, first, a classical bond-orbital model based on the tight-binding method, and secondly, an approach which combines the latter model with an adjusted empirical pseudopotential method. The bond length d, bond polarity α p, bulk modulus B, elastic shear constants (C 11-C 12) 2 , bond-stretching force constant α, bond-bending force constant β, internal displacement parameter ξ, effective atomic charge Z ∗ , transfer parameter β ∗ , transverse charge e T ∗ , and piezoelectric charge e p ∗ are calculated with both methods. The results are compared, with previous theoretical estimates and experiments.

Martensitic phase transformation and lattice dynamics of fcc cobalt.

The phonon dispersion of the high-temperature fcc phase of pure cobalt has been measured by inelastic neutron scattering at 833 K. Transverse phonon branches were measured above and below the Martensitic hcp-fcc transformation in order to learn about an influence of lattice dynamics, if any. No new anomalies could be observed, except those confirming an anomalous decrease of the ${c}_{44}$ (hcp) shear constant when approaching the transformation from below and those confirming a transverse $T{[00\ensuremath{\xi}]}_{\mathrm{hcp}}$ and $T{[\ensuremath{\xi}\ensuremath{\xi}\ensuremath{\xi}]}_{\mathrm{fcc}}$ branch of relative low energy. The small shear constant and results from an analysis of elastic diffuse and Bragg data can be understood in the framework of a dislocation-driven transformation mechanism proposed by Seeger.

The metallic bond: Elastic properties

Establishing relationships between electronic structure and the properties of metals and alloys has relied heavily on assigning various attributes to the metallic bond. Principal among these is that of a directional bond. Bond directionality has been evoked as an explanation for the magnitudes of elastic shear constants, elastic anisotropy, the susceptibility to brittle failure, and preferred allotropic and alloy structure. Though bond directionality is frequently used as an explanation of metallic and alloy properties, it has never been rigorously defined. In this paper, a definition of bond directionality is provided which allows for its quantification. Using this definition, it is shown that the relative magnitudes of the single crystal shear elastic constants for f.c.c. metals can be correlated with bond directionality. The only information which is required to provide a measure of bond directionality is the total charge density corresponding to the given metal or alloy. This information can now be easily determined through the use of modern electronic structure techniques.

Magnetic effects on structural, elastic and surface properties of the 3d ferromagnets

Assuming saturated ferromagnetism, the anomalous crystal structures of the magnetic 3d transition Fe, Co and Ni can be explained from simple band filling arguments. The exceptional elastic properties of Fe and Co are well described by full potential linear muffin-tin orbital (FP-LMTO) electronic structure calculations using the local density approximation for the electron density functional. Analysis shows that the behaviour of the tetragonal shear constant C′ can be understood from the contribution of the partially filled spin down band, whereas the electrons in the almost filled spin up band only play a minor role. This strong reduction in the number of electrons which contribute to the elastic properties explains the anomalous behaviour. The surface magnetism of the 3d metals was studied by means of a Green's function technique within the tight-binding linear muffin-tin orbital (TB-LMTO) method. It was found that the anomalous surface energies of the 3d transition metals can be explained in terms of itinerant surface magnetism. For some of the magnetic metals an unusual property is found, namely that the lowest surface energy is not connected to the most densely packed surface.

Influence of Grouser Size on Soil Shear Constants in Shear Ring Test

Influence of Grouser Size on Soil Shear Constants in Shear Ring Test

Calculation of the elastic properties of semiconductors

For 30 diamond- and zincblende-structure semiconductors, the bond length d, bond polarity alpha p, bulk modulus B, elastic shear constants (c11-c12)/2 and c44, bond-stretching force constant alpha , bond-bending force constant beta , internal displacement parameter zeta , effective atomic charge Z*, transfer parameter beta *, transverse charge eT*, and piezoelectric charge ep* are calculated from bond orbital calculations based on the tight-binding method. The results are compared with previous theoretical calculations and experiments.

Crystal structure and elastic-constant anomalies in the magnetic 3d transition metals.

Assuming a saturated ferromagnet, the anomalous crystal structures of the magnetic 3d transition elements Fe, Co, and Ni are explained from simple band-filling arguments. The full-potential linear muffin-tin orbital (FP-LMTO) method is used to calculate the elastic constants (${\mathit{C}}_{11}$, ${\mathit{C}}_{12}$, and ${\mathit{C}}_{44}$) for the magnetic and cubic 3d transition metals Cr, Fe, and Ni. For Co calculations of the elastic constants have been performed in the fcc crystal structure (\ensuremath{\beta}-Co). Good agreement with the experimental data is found even for Fe and Co which have anomalous elastic constants. The behavior of the elastic shear constant C' can be understood from the filling of the spin-down 3d band for the ferromagnetic elements. It is shown that C' correlates with the relative crystal stabilities of the bcc and fcc structures for these elements as has earlier been found for the paramagnetic 4d and 5d metals and alloys.

Shear constants using angularly dependent bond order potentials

Abstract Analytic expressions for the shear constants of sp-valent zincblende and f.c.c. structure types are obtained using a first-nearest-neighbour bond order potential. Novel expressions for the tetragonal and trigonal zincblende shear constant C' and C 44 are derived. ImportantlyC' is found to vary as the cube of the bond order. The angular character of the bond order potential is shown to remove the anisotropy constraint of C 44/C' = 2 for f.c.c. lattices within a nearest-neighbour model.

Poisson ratios and upper bounds of intrinsic birefringence from brillouin scattering of oriented polymers

AbstractTo overcome the difficulties in measuring high‐frequency shear constants of polymeric materials by ultrasonic or Brillouin scattering technques, we extrapolate results from oriented materials to zero birefringence. Shear constants C44 in the high‐frequency limit (GHz) are determined for polyethylene, poly(ethylene terephthalate), poly(vinyl chloride), poly(methyl methacrylate), and polycarbonate using Brillouin scattering. Accurate values of Poisson's ratio are derived. The extrapolation to full orientation using an amended Moseley relation gives upper bounds for the “intrinsic birefringence.” Changes in the character of the orientation process are easily detected by monitoring the mode numbers, which are defined by analogy to Poisson's ratio. Extrapolation of these ratios to their upper bound 0.5 gives an independent check of the maximum intrinsic birefringence. © 1993 John Wiley & Sons, Inc.

Elastic constants of cubic f-electron elements: Theory.

We report first-principles calculations of the elastic constants of cubic f-electron elements: fcc La (stable at elevated temperatures), \ensuremath{\alpha}-Ce, Th, bcc U (stable at elevated temperatures), bcc Np (stable at elevated temperatures), bcc Pu, and fcc Pu (both these phases of Pu are also stable at elevated temperatures). The zero-temperature calculations employed the linear muffin-tin orbitals method. The computed elastic constants of fcc La and Th are found to be in rather good agreement with experiment. The tetragonal shear constant of the cubic phases of U, Np, and Pu is negative, showing that at zero temperature the bcc or fcc structure is unstable for these systems. The stabilization of cubic structures in these materials must therefore have a significant temperature-dependent contribution, and the elasticity of these materials must also depend heavily on this temperature-dependent contribution. The calculated data of \ensuremath{\alpha}-Ce is a prediction, since no experimental data are available, and may therefore serve as encouragement for experimental work.

Piezoelectric, dielectric, and elastic properties of poly(vinylidene fluoride/trifluoroethylene)

The symmetry-predicted nonzero components of the piezoelectric coefficient, dielectric constant, and elastic compliance matrices have been determined on poly(vinylidene fluoride/trifluoroethylene)(75/25) copolymer at room temperature and a frequency of 500 Hz. The temperature dependence of each of the complex piezoelectric coefficients and complex dielectric constants has been measured in the temperature range of −100 to 65 °C. The frequency dependence of these coefficients has also been measured at room temperature. It is found that the relaxation observed in the tensile piezoelectric coefficients of this material is different from that of the dielectric constants, whereas the relaxation of the piezoelectric shear constants shows behavior similar to that of the dielectric constants.

Theory of elastic constants of cubic transition metals and alloys.

We have from first principles calculated the elastic constants (${\mathit{C}}_{11}$, ${\mathit{C}}_{12}$, and ${\mathit{C}}_{44}$) of all nonmagnetic cubic d transition metals, and obtained good agreement with experimental data. We show that the trend exhibited by the tetragonal shear constant in the transition metals can be simply understood. In particular, we show that .ul4 the trend of the tetragonal shear constant, C', of cubic transition metals and alloys is determined by the energy difference between the fcc and bcc structures of a given system, which in turn is determined by band filling. This finding is in turn due to the result that these systems have a Bains path with similar shape, and our ``canonical'' Bains path illustrates this behavior. The trend of C' is further studied by including selected alloys (thereby obtaining a finer tuning of band-filling effects). The scaling of C' with the bcc-fcc energy difference is found to hold also for the studied alloys (roughly), and the calculated C' is found to agree well with available experimental data.