Isotropic compression

Q. Johnson, A. Mitchell, and L. Evans, X-Ray Diffraction Evidence for Crystallographic Order and Isotropic Compression During the Shock-Wave Process, Nature 231, 310-311 (1971). 

The shock-compression pulse carries a solid into a state of homogeneous, isotropic compression whose properties can be described in terms of perfect-crystal lattices in thermodynamic equilibrium. Influences of anisotropic stress on solid materials behaviors can be treated as a perturbation to the isotropic equilibrium state. ... 

Perhaps the most dramatic exception to the perfectly elastic, perfectly plastic materials response is encountered in several brittle, refractory materials that show behaviors indicative of an isotropic compression state above their Hugoniot elastic limits. Upon yielding, these materials exhibit a loss of shear strength. Such behavior was first observed from piezoelectric response measurements of quartz by Neilson and Benedick [62N01]. The electrical response observations were later confirmed in mechanical response measurements of Waekerle [62W01] and Fowles [61F01]. 

Re-entrant foam provides a counter-intuitive demonstration of processing (5). Polyurethane can be isotropically compressed in a mold and heated to about 170 °C. The microstructure of the resulting solid yields a material that bulges in cross section when stretched More information on polymers will be available from John Droske s complementary NSF-funded project (described in the preceding section). 

Goldman, S. and Joslin, C. 1992. Spectroscopic properties of an isotropically compressed hydrogen atom. J. Phys. Chem. 96 6021-27. 

Figure 1,12 Potential well for Ni2Si04 olivine. Abscissa values are fractional values of isotropic compression and/or expansion.

Note Also referred to as volume compression, isotropic compression and bulk compressive strain. 

The predicted course of reaction between a heteronuclear pair of atoms is shown in Figure 7.2. Promotion is once more modeled with isotropic compression of both types of atom. The more electropositive atom (at the lower quantum potential) reaches its valence state first and valence density starts to migrate from the parent core and transfers to an atom of the second kind, still below its valence state. The partially charged atom is more readily compressible to its promotion state, as shown by the dotted line. When this modified atom of the second kind reaches its valence state two-way delocalization occurs and an electron-pair bond is established as before. It is notable how the effective activation barrier is lowered with respect to both homonuclear (2Vq)i barriers to reaction. The effective reaction profile is the sum of the two promotion curves of atoms 1 and 2, with charge transfer. 

S. Goldman and C. Joslin, Spectroscopic Properties of an Isotropically Compressed Hydrogen Atom, J. Phys. Chem., 1992 (96) 6021-6027. 

Pressures from 1 bar to 1 kbar can be attained by using a hand-operated hydraulic piston, similar to what is used in an automobile repair shop. Above 1 kbar, pressure intensifiers can boost these pressures tenfold, reaching about 10 kbar. Both hydraulic pistons and pressure intensifiers require a hydraulic fluid (heavy oil at room temperature, n-pentane down to 77 K or so) which can be compressed isotropically for some pressures, talcum powder can act as an almost isotropic pressure-transmitting medium. If higher pressures are needed, the demand for isotropic compression must be abandoned, and anisotropies creep in. 

The physical interpretation of the periodic relationship suggested by numerical pattern generation relies on the known effect of isotropic compression on the electronic structure of atoms [24]. Compression causes all energy levels to rise and removes the degeneracy of sub-levels. The effect becomes more pronounced with increasing quantum number l. Relative energies for hydro-... 

An example of an electron in a phase-locked cavity has been encountered in the study of compressed atoms [76, 24]. Isotropic compression of an atom, simulated by imposing a finite boundary condition on the electronic wave function, i.e. linv xpe = 0, r0 < oo, raises electronic energy levels, until an electron is decoupled from the core at a characteristic atomic ionization radius. This electron then exists in a field-free cavity with a spherical Bessel wave function. In the ground state... 

Chemical reaction occurs between reactants in their valence state, which is different from the ground state. It requires excitation by the environment, to the point where a valence electron is decoupled from the atomic or molecular core and set free to establish new liaisons, particularly with other itinerant electrons, likewise decoupled from their cores [114]. The energy required to promote atoms into their valence state has been studied before [24] in terms of the simplest conceivable model of environmental pressure, namely uniform isotropic compression. This was simulated by an atomic Hartree-Fock procedure, subject to the boundary condition that confines all electron density to within an impenetrable sphere of adjustable finite radius. 

Another direct consequence of the non-autonomous character of interfaces is that they can be created or annihilated by deforming the adjoining bulk phases. The three-dimensional analogue of this phenomenon does not exist isotropic compression or expansion of a bulk material can only be Ccuried out in such a way that the amounts of matter remciln constant. One cannot compress a three-dimensional phase to a zero volume. Bulk liquids have a finite compressibUify. 

Assuming that, as a consequence of a 2D isotropic compression of the overlayer, the corresponding increase of the specific surface energy is given by the elastic strain energy according to eq, (3,23), one gets ... 

In order to explain the moird structure, one can consider the following two cases (i) isotropic compression or (ii) anisotropic compression of the Pb overlayer. 

The results obtained from the pressure dependence of the lattice parameters agree with those obtained from thermal studies (see Table 1). A significant anisotropy is deduced for the linear compressibility coeficients of [Fe(phen)2(NCS)2] whereas [Fe(btz)2(NCS)2] exhibits an almost isotropic compressibility. The anisotropy of [Fe(phen)2(NCS)2] is slightly reduced at high pressure, however, a remains the stiffest direction while c is the more compressible one. 

They studied the lifetimes of the 2s, 2p, 3s, 3p and 3d states. For the 2p, 3s, 3p and 3d states an isotropic compression reduces their lifetimes as compared to those of the free atom. One very important result refers to the 2s state lifetime for the free atom, the transition 2s -> Is is forbidden, which in the dipole approximation implies that the associated lifetime is infinite. By contrast, under compression, the 2p state energy lies lower than the 2s, whereas the Is state remains below the 2p state, therefore, the transitions 2s -> 2p and 2p -> Is are allowed. Under these conditions, the 2s state thus possesses a finite lifetime, which in fact becomes very sensitive in terms of the box size for (4 < ro < 8) au, Goldman and Joslin obtained a lifetime in the range (7.5 x 10-10, 4.4 x 10-7) s. 

The modulus is the most important small-strain mechanical property. It is the key indicator of the "stiffness" or "rigidity" of specimens made from a material. It quantifies the resistance of specimens to mechanical deformation, in the limit of infinitesimally small deformation. There are three major types of moduli. The bulk modulus B is the resistance of a specimen to isotropic compression (pressure). The Young s modulus E is its resistance to uniaxial tension (being stretched). The shear modulus G is its resistance to simple shear deformation (being twisted). 

The preliminary analysis of diffraction data for the pure azide at 9.8 GPa without heating indicates it remains a possible monoclinic structure with space group Ca/m- The cell parameters are determined to be a=5.635(8) A, b=3.419 (6) A and c=4.936(8) A, P=99.5(l) and V=93.8 A. Compared with the monoclinic structure at ambient pressure and low temperature, for which the cell parameters are a=6.1654 A, b=3.6350 A and c=5.2634 A, P= 107.543°, the high-pressure phase seems to remain monoclinic structure but with isotropic compression of three axes with compression ratio of 91%, 94% and 94% respectively. This indieates that high-pressure phase at 9.8 GPa has the same or a similar structure as ambient low temperature phase, although the unit cell may be a further distorted monoclinic structure characterized by a different P angle. 

Ma et al. [147,162,163] argued that pressure-induced covalency effects can be understood in terms of the radial expansion of the valence electron wavefunc-tions as the nearest neighbor bond length decreases with pressure. They considered an isotropic compression model based on the scaHng of the Slater integrals... 

One of the most frequently observed phenomena in epitaxial growth is the formation of strain relief patterns. These are caused by the mismatch of the unit cell size of the substrate and the deposited film. In many cases the strain or stress, which is imposed on the thin film by fhe subsfrafe lattice is relieved by reconstruction of the film. This reconsfrucfion can but must not necessarily lead to a nanopatterned film. An inferesfing example is the growth of Ag on Pt(l 11) (see Fig. 10) [41]. It has been shown for this particular system that the first Ag layer grows pseudomorphically exhibiting an isotropic compressive strain of 4.3% whereas in higher layers this strain is relieved by the formation of a dislocation network [42-47]. In order to improve the long-... 

Sitharam, T. G., Vinod, J. S. (2009). Critical state behaviour of Granular materials from isotropic compression and rebound paths DEM simulations. Granular Matter, 77(1), 33-42. doi 10.1007/sl0035-008-0113-3... 

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