Petr Řehák

Dynamic stability of fcc crystals under isotropic loading from first principles

Lattice dynamics and stability of four fcc crystals (Al, Ir, Pt and Au) under isotropic (hydrostatic) tensile loading are studied from first principles using the linear response method and the harmonic approximation. The results reveal that, contrary to former expectations, strengths of all the studied crystals are limited by instabilities related to soft phonons with finite or vanishing wavevectors. The critical strains associated with such instabilities are remarkably lower than those related to the volumetric instability. On the other hand, the corresponding reduction of the tensile strength is by 20% at the most. An analysis of elastic stability conditions is also performed and the results obtained by means of both approaches are compared.

Stability and strength of covalent crystals under uniaxial and triaxial loading from first principles

The response of three covalent crystals with a diamond lattice (C, Si and Ge) to uniaxial and a special triaxial (generally nonhydrostatic) loading is calculated from first principles. The lattice deformations are described in terms of variations of bond lengths and angles. The triaxial stress state is simulated as a superposition of axial tension or compression and transverse (both tensile and compressive) biaxial stresses. The biaxial stresses are considered to be adjustable parameters and the theoretical strengths in tension and compression along <100>, <110>, <111> crystallographic directions are calculated as their functions. The obtained results revealed that the compressive strengths are, consistently to fcc metals, almost linear functions of the transverse stresses. Tensile transverse stresses lower the compressive strength and vice versa. The tensile strengths, however, are not monotonic functions of the transverse biaxial stresses since they mostly exhibit maxima for certain values of the transverse stresses (e.g., tensile for <100> and <110> loading of Si and Ge or compressive for <100> loading of C).

Grain boundary segregation of elements of groups 14 and 15 and its consequences for intergranular cohesion of ferritic iron

The experimentally determined data—enthalpy and entropy—of the grain boundary segregation of substitutional solutes of 14th and 15th groups of the periodic table, i.e., silicon, phosphorus, tin, and antimony, in α-iron are compared. The consequences of the grain boundary segregation of these elements for the intergranular strengthening or embrittlement are also shown. It is documented that all these solutes except silicon segregate at the grain boundaries interstitially at enhanced temperatures although substitutional segregation is preferred at zero K. Despite some variations, the values of the strengthening/embrittling Gibbs energy of all solutes are nearly linearly dependent on the differences in the sublimation energies of the host and solute.

Mechanical stability of Ni and Ir under hydrostatic and uniaxial loading

Two fcc crystals, Ni and Ir, are subjected to simulated isotropic and uniaxial tension along the direction. Their structural stability is assessed by analyzing phonon spectra that are calculated from first principles for different values of strain. A relevant analysis of elastic stability conditions is also performed. Predicted elastic instabilities correspond well to those associated with soft phonons with vanishing wavevectors. Although most of previous studies predicted that first instabilities in crystals correspond to macroscopic (elastic) instabilities, we found soft phonons of finite wavevectors at lower strains (and stresses) during both considered loadings in the crystal of Ir. Predicted instabilities were confirmed by our models of microscopic deformation.

The [100] Compressive Strength of Perfect Cubic Crystals under Superimposed Biaxial Stresses

Stress-strain responses of five fcc crystals subjected to triaxial loading are investigated by means of pseudopotential density functional method. Particularly, the influence of superimposed transverse biaxial stresses on the maximum uniaxial stresses is evaluated for both tensile and compressive regions. The obtained results revealed that the compressive strengths (maximum compressive stresses) of all studied metals are more sensitive to the superimposed stresses than their tensile strengths. The compressive strengths were found to be increasing linear functions of the compressive transverse stresses.

The origin of lattice instability in bcc tungsten under triaxial loading

Abstract Stability of ideal bcc tungsten crystal under triaxial tensile loading was explored from first principles using an analysis of both elastic and dynamic stability. The triaxial stress state was considered as a superposition of axial and biaxial transverse stresses. The region of attainable stresses which was delimited using the computed tensile stress maxima was marginally reduced by occurrence of soft phonons in the crystal lattice. While, under purely hydrostatic tension, the crystal was predicted stable up to 48 GPa, greater magnitude of a differential stress reduced the value of a mean (hydrostatic) stress associated with first phonon instabilities to about 35 GPa. This value is rather close to that recently determined in experiment. Computed phonon spectra were successfully verified with the help of atomistic models of microscopic lattice deformation.

Prediction of the Critical Energy Release Rate of Nanostructured Solids Using the Laplacian Version of the Strain Gradient Elasticity Theory

The aim of the paper is quantify the material length scale parameter of the simplified form of the strain gradient elasticity theory (SGET) using first principles density-functional theory (DFT). The single material length scale parameter l is extracted from phonon-dispersions generated by DFT calculations and, for comparison, by adjusting the analytical SGET solution for the displacement field near the screw dislocation with the DFT calculations of this field. The obtained results are further used in the SGET modeling of cracked nanopanel formed by the single tungsten crystal where due to size effects and nonlocal material point interactions the classical fracture mechanics breaks down.

Dynamic Stability of Ni FCC Crystal under Isotropic Tension

Lattice dynamics and stability of fcc crystal of Ni under isotropic (hydrostatic) tensile loading are studied from first principles using supercell method and a harmonic approximation. According to the results, strength of the crystal is determined by occurrence of an instability related to soft phonons with finite wave vector. On the other hand, the critical strains and stresses associated with such instabilities are only slightly lower than those related to the volumetric instability.