Peierls deformation

For the deformation of NiAl in a soft orientation our calculations give by far the lowest Peierls barriers for the (100) 011 glide system. This glide system is also found in many experimental observations and generally accepted as the primary slip system in NiAl [18], Compared to previous atomistic modelling [6], we obtain Peierls stresses which are markedly lower. The calculated Peierls stresses (see table 1) are in the range of 40-150 MPa which is clearly at the lower end of the experimental low temperature deformation data [18]. This may either be attributed to an insufficiency of the interaction model used here or one may speculate that the low temperature deformation of NiAl is not limited by the Peierls stresses but by the interaction of the dislocations with other obstacles (possibly point defects and impurities). 

The (110) dislocations are from our calculations not expected to contribute significantly to the plastic deformation in hard oriented NiAl because of the very high Peierls stresses. Experimentally, these dislocations do not appear unless the temperature is raised to about 600 K [18]. At this temperature the experimental data strongly suggest a transition from (111) to (110) slip. 

Excellent agreement between experiment and onr calculations is obtained when considering the low temperature deformation in the hard orientation. Not only are the Peierls stresses almost exactly as large as the experimental critical resolved shear stresses at low temperatures, but the limiting role of the screw character can also be explained. Furthermore the transition from (111) to (110) slip at higher temperatures can be understood when combining the present results with a simple line tension model. 

A second major difficulty with the Peierls model is that it is elastic and therefore conservative (of energy). However, dislocation motion is nonconservative. As dislocations move they dissipate energy. It has been known for centuries that plastic deformation dissipates plastic work, and more recently observations of individual dislocations has shown that they move in a viscous (dissipative) fashion. 

The phase transition consists of a cooperative mechanism with charge-ordering, anion order-disorder, Peierls-like lattice distortion, which induces a doubled lattice periodicity giving rise to 2 p nesting, and molecular deformation (Fig. 11c). The high temperature metallic phase is composed of flat EDO molecules with +0.5 charge, while the low temperature insulating phase is composed of both flat monocations... 

The details of what actually happens are presented elsewhere.16 The situation is intricate the observed structure is only one of several likely ways for the parent structure to stabilize—there are others. Diagram 95 shows some possibilities suggested by Hulliger et al.72 CeAsS chooses 95c.75 Nor is the range of geometric possibilities of the MAB phases exhausted by these. Other deformations are possible many of them can be rationalized in terms of second order Peierls distortions in the solid.16... 

There is one aspect of the outcome of a Peierls distortion—the creation of a gap at the Fermi level—that might be taken from the last case as being typical, but which is not necessarily so. In one dimension one can always find a Peierls distortion to create a gap. In three dimensions, atoms are much more tightly linked together. In some cases a stabilizing deformation... 

Extensive studies have revealed the mechanism for these novel properties. It is the interplay among many mechanisms the Peierls instability characteristic of one-dimensional system, the Mott transition in Coulomb interacting system, the mixed valence of Cu, the Jahn-Teller effect of Cu ions, and the Curie-Weiss paramagnetism of the 1/2-spin of Cu. The key role in showing the variety of properties was played by the structural deformation which causes a shift in the energy level of d-electrons of Cu. 

The mechanical strength of hard materials is critical for load-bearing, structural applications. These brittle materials only deform plastically at high temperatures, or under severe hydrostatic constraint, since the Peierls stress for dislocation movement is high. Failure is usually by unstable crack propagation under a tensile stress that exceeds the tensile strength of the material. In terms of fracture mechanics, brittle failure occurs when the Mode I stress intensity factor Kj reaches the fracture toughness of the material, Kic (see below). 

In the case of borides, the production of pure dense materials is more difficult because TiB2 does not deform plastically even at very high temperatures due to its intrinsically high concentration of Peierls barriers to dislocation movement. Recent investigations on borides have been totally devoted to the synthesis of composites either metal-ceramic or ceramic-ceramic. Woodger et al. [94,95]... 

On the other hand materials deform plastically only when subjected to shear stress. According to Frenkel analysis, strength (yield stress) of an ideal crystalline solid is proportional to its elastic shear modulus [28,29]. The strength of a real crystal is controlled by lattice defects, such as dislocations or point defects, and is significantly smaller then that of an ideal crystal. Nevertheless, the shear stress needed for dislocation motion (Peierls stress) or multiplication (Frank-Read source) and thus for plastic deformation is also proportional to the elastic shear modulus of a deformed material. Recently Teter argued that in many hardness tests one measures plastic deformation which is closely linked to deformation of a shear character [17]. He compared Vickers hardness data to the bulk and shear... 

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