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![Hcp Ti a [1 1 2 ̄ 0] screw dislocation partial DD maps (screw component) for 3 the six IPs of figure 2 calculated within the DFT scheme. The red triangles indicate the positions of the partial dislocations. The blue straight lines indicate the prismatic easy stacking fault.](profile/Joseph-Morillo/publication/262807879/figure/fig3/AS:296433770090496@1447686726139/Hcp-Ti-a-1-1-2-0-screw-dislocation-partial-DD-maps-screw-component-for-3-the-six.png)
Hcp Ti a [1 1 2 ̄ 0] screw dislocation partial DD maps (screw component) for 3 the six IPs of figure 2 calculated within the DFT scheme. The red triangles indicate the positions of the partial dislocations. The blue straight lines indicate the prismatic easy stacking fault.
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![Figure 4. Hcp Ti a [1 1 2 ̄ 0] screw dislocation full DD maps (screw...](profile/Joseph-Morillo/publication/262807879/figure/fig2/AS:296433765896195@1447686725947/Hcp-Ti-a-1-1-2-0-screw-dislocation-full-DD-maps-screw-component-for-the-3-six-IPs_Q320.jpg)
![Figure 5. Hcp Ti a [1 1 2 ̄ 0] screw dislocation partial DD maps...](profile/Joseph-Morillo/publication/262807879/figure/fig3/AS:296433770090496@1447686726139/Hcp-Ti-a-1-1-2-0-screw-dislocation-partial-DD-maps-screw-component-for-3-the-six_Q320.jpg)
An extensive DFT search of (meta)stable structures of the screw dislocation in hcp-Ti is presented. It reveals that the stable core structures are never basal but always prismatic. This prismatic core dissociates into two partial dislocations in the same or neighboring prismatic planes depending on the initial position of the dislocation line, lead...
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... order to evidence a possible dissociation of the dislocations into partials, we report on figure 5 the partial differential maps corresponding to half the Burger's vector partial dislocations. The (a)symmetric character of the spreading can be more easily observed on figure 5 where the two closed triangles identifying the partials are aligned in a prismatic plane for the symmetric spreading and are in two adjacent prismatic planes for the asymmetric ones. The corresponding dissociation lengths are of the order of 7 Å, a value compatible with the one deduced from the prismatic easy stacking fault and the elasticity theory [25] and comparable to those obtained by Ghazisaeidi and Trinkle [21] in their DFT calculation. ...
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Citations
... Human observers of dislocation core structures have tended to sort the structures into a small number of bins. For example in HCP metals most references only discuss basal, prismatic, pyramidal, and something along the lines of asymmetric or mixed morphologies [13,17,28,34,35]. This human classification scheme may in fact be glossing over the significance of core structures that do not fit neatly into one of these bins, and/or the importance of intermediate core structures. ...
The atomic scale computation of dislocation core structures has become an essential tool in the development of models for the plasticity of metals. Competing dislocation core structures are often analyzed at T=0 K (with T the temperature), and the dislocation core structure with the lowest energy is assumed to be the structure dictating the dynamics of the individual dislocation at finite temperatures. It is shown here that, for some hexagonal-close-packed (HCP) metals, this approach may be too simplistic. As a prototypical example, 〈a〉-type screw dislocations within HCP Ti modeled using an empirical interatomic potential are considered. It is shown using molecular dynamics simulations that, at room temperature and above, the core structure of the dislocation is remarkably complex and variable. The implications of this complexity for the dynamics of the dislocations are discussed.
... A basal dissociation of the gliding dislocation will therefore not be required to allow for basal slip. Ab initio calculations have actually not managed to stabilize such a basal configuration of the screw dislocation until now [17], probably because the basal I 2 stacking fault associated with such a dissociation has a too high energy in titanium [18][19][20][21]. Here, we use ab initio calculations to examine more closely the stability of such a basal dissociation of the a screw dislocation in pure Ti, before determining the transition pathway corresponding to basal slip, taking into account all configurations which have been found stable for the a screw dislocation. ...
... Such prepared basal screw dislocations subjected to ab initio ionic relaxation spontaneously reconfigure to the ground state π l or high energy pyramidal π h geometry depending on their initial position (Fig. 1b), with an energy difference ∆E = 11.9 meV/Å between these two states in good agreement with previous ab initio studies [11,25,31]. Our investigation therefore conclude to the instability of basal dissociation in pure Ti, which is in line with the ab initio calculations of Tarrat et al. [17] relying on different boundary conditions. ...
Basal slip of screw dislocations in hexagonal closed-packed titanium is investigated with ab initio calculations.
We show that a basal dissociation is highly unstable and reconfigures to other structures dissociated in a first order pyramidal plane. The obtained mechanism for basal slip corresponds to the migration of the
partial dislocations and of the associated stacking fault ribbon in a direction perpendicular to the dissociation plane. Presented results indicate that both basal and pyramidal slip will operate through the Peierls mechanism of double-kink nucleation and will be equally active at high enough temperature.
... A basal dissociation of the gliding dislocation will therefore not be required to allow for basal slip. Ab initio calculations have actually not managed to stabilize such a basal configuration of the screw dislocation until now [17], probably because the basal I 2 stacking fault associated with such a dissociation has a too high energy in titanium [18][19][20][21]. Here, we use ab initio calculations to examine more closely the stability of such a basal dissociation of the a screw dislocation in pure Ti, before determining the transition pathway corresponding to basal slip, taking into account all configurations which have been found stable for the a screw dislocation. ...
... Such prepared basal screw dislocations subjected to ab initio ionic relaxation spontaneously reconfigure to the ground state π l or high energy pyramidal π h geometry depending on their initial position (Fig. 1b), with an energy difference ∆E = 11.9 meV/Å between these two states in good agreement with previous ab initio studies [11,25,31]. Our investigation therefore conclude to the instability of basal dissociation in pure Ti, which is in line with the ab initio calculations of Tarrat et al. [17] relying on different boundary conditions. ...
Basal slip of a screw dislocations in hexagonal closed-packed titanium is investigated with ab initio calculations. We show that a basal dissociation is highly unstable and reconfigures to other structures dissociated in a first order pyramidal plane. The obtained mechanism for basal slip corresponds to the migration of the partial dislocations and of the associated stacking fault ribbon in a direction perpendicular to the dissocia-tion plane. Presented results indicate that both basal and pyramidal slip will operate through the Peierls mechanism of double-kink nucleation and will be equally active at high enough temperature.
... There are several limitations to this method: a large inner radius is required to fully converge the dislocation core properties; the outer surface of the cluster may become charged when modeling ionic materials; and interactions between a moving dislocation and the surface separating region I from region II render accurate calculation of the Peierls stress s p difficult. Additionally, because the simulation cell includes surfaces, the core energy cannot easily be calculated using DFT, as the energy will include a component due to relaxation of the electron density at the surface (although see Tarrat et al., 2014). However, the absence of dislocation-dislocation interactions in the cluster-based approach, combined with its ease 4 64 of implementation, has made it a valuable tool for simulating dislocations in ionic materials. ...
Water can be incorporated into the lattice of mantle minerals in the form of protons charge-balanced by the creation of cation vacancies. These protonated vacancies, when they interact with dislocations, increase strain rates by enhancing dislocation climb and, potentially, by reducing the Peierls barrier to glide. We use atomic scale simulations to investigate segregation of Mg vacancies to atomic sites within the core regions of dislocations in MgO. Energies are computed for bare and protonated Mg vacancies occupying atomic sites close to 1/2<110> screw dislocations, and 1/2<110>{100} and 1/2<110>{110} edge dislocations. These are compared with energies for equivalent defects in the bulk lattice to determine segregation energies for each defect. Mg vacancies preferentially bind to 1/2<110>{100} edge dislocations, with calculated minimum segregation energies of -3.54 eV for {VMg}′′ and -4.56 eV for {2HMg}X. The magnitudes of the minimum segregation energies calculated for defects binding to 1/2<110>{110} edge or 1/2<110> screw dislocations are considerably lower. Interactions with the dislocation strain field lift the 3-fold energy degeneracy of the {2HMg}X defect in MgO. For edge dislocations, defect configurations in which the O-H bond vector is perpendicular to the glide plane normal are preferred, which may have implications for the ability of protonated vacancies to influence dislocation glide.
... 23 The second harmonic response of metals is known to be closely related to the electronic density of states and degree of delocalization of the electrons involved. [24][25][26] Dislocations in metals such as titanium have been found to alter the electronic density of states, 27,28 and it should therefore be possible to relate dislocation density to the second harmonic response. In this work, we show for a pre-fatigued polycrystalline Titanium specimen that optical second harmonic generation can indeed sense dislocation density with a high spatial resolution of 100 lm. ...
... 4 The Ti DOS has also been found to depend on both the structure and the structural defects in density functional calculations. 27,28 The close-packed hexagonal a phase at ambient temperature and pressure has a relatively low partial DOS from d-electrons at the Fermi level, while the bcc b phase found at higher temperatures and pressures possesses a much higher partial d-DOS. 40 Screw dislocations also introduce characteristic changes in the partial DOS of d-electrons, mostly within the occupied states about 0.5 eV below the Fermi level. ...
The optical second harmonic response of a pre-fatigued titanium specimen to picosecond 800 nm pulses has been investigated. Polarization-dependent measurements show that the zxx component of the nonlinear susceptibility tensor χ⁽²⁾ differs markedly when measured in a region of unfatigued polycrystalline titanium compared to the plastic deformation zone ahead of a crack tip and even changes the sign within the plastic wake. This tensor component is sensitive to bulk currents, and we attribute the observed changes to a changed density of states at the Fermi level, caused by the accumulation of dislocations. Second harmonic polarization analysis could thus be useful in non-invasive fatigue analysis.
... Except when the tensile axis is parallel to the < c > axis, < a > dislocations generally accommodate deformation. The low Peierls barrier in the prismatic planes makes glide of < a > dislocations easy, as confirmed by atomistic and experimental studies on single crystals or polycrystals [24,25]. The present observations are indeed consistent with these studies, especially in Ti0 samples, where many grains are well oriented for prismatic slip. ...
... These observations are correlated to the high SF on the basal plane, rather than to the oxygen content. Previous studies all report that basal slip is difficult at room temperature [26,27] in line with the dissociation instability for < a > dislocations cores in this plane [25]. Despite the low SFs on prismatic and first order pyramidal systems, the stress was high enough to activate it. ...
Plastic deformation micro-mechanisms, dislocation structures and glide kinetics in two titanium batches with moderate and high oxygen contents (450 and 3200 wppm, respectively) are investigated by in situ tensile tests in a transmission electron microscope, at room temperature. In both materials, plastic deformation is accommodated with type screw dislocations gliding mainly in prismatic planes. The movement of screw segments is jerky, oxygen-dependent and strongly controlled by pinning on localized obstacles if the oxygen content is high. Dislocation multiplication is mainly controlled by the opening of loops produced by a double-cross slip mechanism at super-jogs. Evidences of composite glide between prismatic, first order pyramidal and basal planes are pointed out, proving the existence of intensive cross slip.
... For titanium (N ¼ 33), 3 <a> screw 1120, 3 <a> edge on basal planes f0001g1120, 3 <a> edge on prismatic planes f1010g1120, 6 <a> edge on 1st order pyramidal planes f1011g1120, 6 <cþa> screw 1123 and 12 <cþa> edge on 1st order pyramidal planes f1011g1123 are believed to be the slip modes present according toJones and Hutchinson (1981). In this crystal orientation based GND framework, readiness of activation for each individual type of slip due to electronic interaction of atoms will not be concerned (Ghazisaeidi and Trinkle, 2012;Tarrat et al., 2014), since only the residual dislocation networks that has geometric consequence is being measured via an EBSD scan. Nevertheless, the adopted energy minimization scheme should be able to provide a reasonable criterion for resolving the <a> and <cþa> type dislocations (Britton et al., 2010;Dunne et al., 2012). ...
The influence of microstructural anisotropy on shear response of high-purity titanium was studied using the compact forced-simple-shear specimen (CFSS) loaded under quasi-static loading conditions. Post-mortem characterization reveals significant difference in shear response of different directions in the same material due to material crystallographic texture anisotropy. Shear bands are narrower in specimens in which the shear zone is aligned along the direction with a strong {0001} basal texture. Twinning was identified as an active mechanism to accommodate strains in the shear region in both orientations. This study confirms the applicability of the CFSS design for the investigation of differences in the shear response of materials as a function of process-induced crystallographic texture. A detailed, systematic approach to quantifying shear band evolution by evaluating geometrically necessary dislocations (GND) associated with crystallographic anisotropy is presented. The results show that: i) line average GND density profiles, for Ti samples that possess a uniform equiaxed-grain structure, but with strong crystallographic anisotropy, exhibit significant differences in GND density close to the shear band center; ii) GND profiles decrease steadily away from the shear band as the plastic strain diminishes, in agreement with Ashby's theory of work hardening, where the higher GND density in the through-thickness (TT) orientation is a result of restricted type slip in the shear band compared with in-plane (IP) samples; iii) the anisotropy in deformation response is derived from initial crystallographic texture of the materials, where GND density of GNDs are higher adjacent to the shear band in the through-thickness sample oriented away from easy slip, but the density of <c+a> type GNDs are very similar in these two samples; and iv) the increase in grain average GND density was determined to have strong correlation to an increase in the Euler Φ angle of the grain average orientation, indicating an increased misorientation angle evolution.
... Note that dissociation in the basal plane (Eq. (4)) is unstable in both Ti [200] and Zr [84]. ...
Dislocation cores, the regions in the immediate vicinity of dislocation lines, control a number of properties such as dislocation mobility, cross-slip and short-range interactions with other defects. The quantitative modeling of dislocation cores requires an electronic-level description of atomic bonding. Ab initio quantum mechanical calculations of dislocation cores based on the density functional theory have progressed rapidly thanks to the steady increase in computing capacities and the development of dedicated numerical methods and codes. Our aim in this overview paper is, after a description of the methodology regarding in particular the boundary conditions, to review the new and unexpected results obtained on dislocation cores from first principles, including the identification of unforeseen stable and metastable cores and the quantitative evaluation of both interaction energies and energy pathways, in pure metals and alloys of different crystallography (FCC, BCC, HCP) as well as semiconductors. We also identify key challenges to be explored in this rapidly growing field.
... For the α-Ti phase we consider slip on both the basal (0001) and prismatic (1010) planes [62][63][64], whereas for the hydrides only the (111) close-packed planes are assumed to be active [65,66]. To compute the unstable stacking fault energy for those systems we need to identify the appropriate saddle point on the generalised stacking fault energy surface (also known as γ-surface [67]) that corresponds to the threshold energy for dislocation nucleation. ...
... In order to investigate how the hydrogen content affects the ductility of the different phases considered, we evaluated the unstable stacking fault energies and Rice's ductility parameters for the hydrides and compared them with those of the matrix. Experimental observations have indicated that slip in α-Ti preferentially occurs by prismatic slip as opposed to basal slip [86], although recent studies have revealed that the microscopic dislocation mechanisms are more complex [62][63][64]. Nevertheless, the prefered prismatic slip concurs with the results from the DFT modelling for which the unstable stacking fault energy for prismatic slip (0.29 J/m 2 ) is lower than that of basal slip (0.40 J/m 2 ). ...
In this work we have studied transgranular cleavage and the fracture toughness of titanium hydrides by means of quantum mechanical calculations based on density functional theory. The calculations show that the surface energy decreases and the unstable stacking fault energy increases with increasing hydrogen content. This is consistent with experimental findings of brittle behaviour of titanium hydrides at low temperatures. Based on Griffith-Irwin theory we estimate the fracture toughness of the hydrides to be of the order of 1 MPa⋅m^{1/2}, which concurs well with experimental data. To investigate the cleavage energetics, we analyse the decohesion at various crystallographic planes and determine the traction-separation laws based on the Rose's extended universal binding energy relation. The calculations predict that the peak stresses do not depend on the hydrogen content of the phases, but it is rather dependent on the crystallographic cleavage direction. However, it is found that the work of fracture decreases with increasing hydrogen content, which is an indication of hydrogen induced bond weakening in the material.
... Among hcp metals, Ti and Zr, two transition metals from group IV of the periodic table with four valence electrons, deform mainly by glide of 1/3 1210 dislocations in prismatic planes 5 , in agreement with first-principles calculations showing that screw dislocations are stable when dissociated in their prismatic plane in both metals [6][7][8][9] . One can therefore expect that, like in fcc metals, dislocations in Ti and Zr glide in their prismatic habit plane with a negligible lattice friction. ...
... Non-planar sessile cores have been proposed based on hypothetical dislocation dissociations 11,15,16 . More recently, ab initio calculations 8,9 have indicated that several configurations of the screw dislocation exist in Ti, in addition to the well-known configuration with a planar core spread in a prismatic plane, but their relative stability and ease of glide could not be evaluated. Moreover, it remains to be explained why in pure Zr, where metastable cores also exist 17,18 , tensile tests on single crystals have not shown any evidence of lattice friction [19][20][21][22] . ...
... The dislocation is introduced at different positions of the atomic lattice, either as a perfect dislocation or dissociated as two partial dislocations. Atomic relaxations then lead to different configurations of the dislocation core, in agreement with previous ab initio calculations 8,9,17,18 . The dislocation adopts similar configurations in both metals, with the core spread either in a {1011} pyramidal plane (see Figs 4b,c for Ti and 5b,c for Zr) or in a {1010} prismatic plane (see Figs 4d,e for Ti and 5d,e for Zr). ...
The ease of a metal to deform plastically in selected crystallographic planes depends on the core structure of its dislocations. As the latter is controlled by electronic interactions, metals with the same valence electron configuration usually exhibit a similar plastic behaviour. For this reason, titanium and zirconium, two transition metals of technological importance from the same column of the periodic table, have so far been assumed to deform in a similar fashion. However, we show here, using in situ transmission electron microscopy straining experiments, that plasticity proceeds very differently in these two metals, being intermittent in Ti and continuous in Zr. This observation is rationalized using first-principles calculations, which reveal that, in both metals, dislocations may adopt the same set of different cores that are either glissile or sessile. An inversion of stability of these cores between Zr and Ti is shown to be at the origin of the profoundly different plastic behaviours.
