Bulk modulus performance

The detailed first principles study of the three stable polymorphs has been performed recently using the LCAO technique The main drawback of that work is that no cell optimization was performed for anatase or brookite. The energy-volume curves that were used to calculate the bulk modulus, B, and its pressure derivative, B, have been produced by varying the volume with the c/a ratio and fractional atomic coor nates being fixed at experimental values which makes results unreliable. 

Timgsten has been of keen theoretical interest for electron band-structure calculations [1.14-1.25], not only because of its important technical use but also because it exhibits many interesting properties. Density functional theory [1.11], based on the at initio (nonempirical) principle, was used to determine the electronic part of the total energy of the metal and its cohesive energy on a strict quantitative level. It provides information on structural and elastic properties of the metal, such as the lattice parameter, the equilibrium volume, the bulk modulus, and the elastic constants. Investigations have been performed for both the stable (bcc) as well as hypothetical lattice configurations (fee, hep, tetragonal distortion). 

Equations 11.8 and 11.9 are isomorphous to equations 9.9 and 9.10 which define the storage and loss components of the complex dielectric constant . Similar equations are also used to define the complex bulk modulus B, the complex shear modulus G, and the complex Poisson s ratio v, in terms of their elastic and viscous components. The physical mechanism giving rise to the viscous portion of the mechanical properties is often called "damping" or "internal friction". It has important implications for the performance of materials [8-15],... 

The mechanical properties of a gel are influenced by the degree of swelling. The volume phase transition and therefore the switching between two temperatures (above and below the temperature for volume phase transition) can be performed as a process under isobar or under isochoric conditions. For PNIPAAm, the bulk modulus shows a strong increase at 33 °C during heating. The abmpt change in the... 

Calculation is one of the simplest ways to determine the bulk modulus, as experiments are difficult to perform. At the heart of the calculation is an analytical expression for the potential energy of a crystal in terms of interatomic distances and bond angles. The Born-Meyer function. Equation (2.9), is a simple example of such a function. The potential energy is calculated as a function of interatomic distance, bond angles and other parameters included in the potential energy equation. The interatomic... 

This simplified equilibration process holds strictly for a cubic crystal in a general non-cubic case, the volume, static pressure and bulk modulus have to be replaced by the strain components (related to unit-cell parameters), stress components and elastic constants, respectively. The computer program PARAPOCS[17] performs the lattice-dynamical, thermodynamical and quasi-harmonic calculations in the general tensorial formalism, and has been used to obtain all results reported below for calcite and aragonite. 

We have performed these calculations for Ni3Al-based alloyed phases of different composition. Our goal was to find parameters of unit cell, bulk modulus, and the elastic constants. 

Consolidation tests are commonly performed to (1) evaluate the compressibOity of soil samples for the calculation of foundation settlement (2) investigate the stress history of the soils at the boring locations to calculate settlement as weU as to select stress paths to perform most advanced strength tests (3) evaluate elastic properties from measured bulk modulus values and (4) evaluate the time rate of settlement. Consohdation test procedures also can be modified to evaluate if foundation soils are susceptible to coUapse or expansion, and to measure expansion pressures under various levels of confinement. Consohdation tests include incremental consohdation tests (which are performed at a number of discrete loads) and constant rate of strain (CRS) tests where load levels are constantly increased or decreased. CRS tests can generally be performed relatively quickly and provide a continuous stress-strain curve, but require more sophisticated equipment. 

In order to investigate the deformation properties and mechanical memory, it is of interest to study the behavior of polymer fine particles while in an applied external force. One of the experimentally obtained values of those properties is known as Young s modulus, which is a ftmdamental measure of the stiffness of a material. Numerous calculations have been performed for the mechanical property of bulk-like crystalline PE polymer using force field [187-190] semi-empirical [236], ab initio calculation [237,238],and ab initio MD methods [239,240]., We have calculated the compressive (bulk) modulus for the amorphous PE particles using MD with an external force as shown in Fig. 19. At the start, a plate treated as a continuous wall is set at 10 A from the closest atom of the particle in... 

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