Interfacial structures and energetics of the strengthening precipitate phase in creep-resistant mg-nd-based alloys _ scientific reports

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Magnesium (Mg) alloys have tremendous potential as structural materials for automotive applications in engine block, transmission parts due to their lightweight. The boxer chords The concomitant fuel savings is however, thwarted by their unfavorable creep strength 1, 2, 3, 4. 1111 binary Mg-rare earth (RE) alloys are exceptions with demonstrated excellent creep resistance 1, 2, 3. Us futures market Their superior creep properties are correlated to the formation of high volume fractions of strengthening precipitates based on RE intermetallic compounds 4, 5. Texas baseball roster However, the scarcity and high cost of RE elements limits the development of creep–resistant Mg-RE alloys. Usd thb This work is motivated by gaining an atomistic understanding of commonly found strengthening precipitates in creep-resistant Mg-RE alloys, and inform Mg-alloy design approaches by providing energetics and bonding characteristics associated with their presence within the hcp-Mg matrix. Cattle futures market news Therefore, we have investigated the structure of interface between intermetallic precipitate phase β 1 (an ordered cubic structure) and hcp-Mg. Stock market trading hours india This precipitate typically forms in Mg-Nd-based alloys like Mg-Nd, Mg-Nd-Y and Mg-Nd-Y-Zr, e.g. 1 usd to cop commercial WE43 and WE54 5, 6, 7. Gold vs usd chart The coherent β 1 phase has a plate-like morphology, and shares an (0001) Mg//(011) β1, [ 100] Mg//[21 ] β1 and [11 0] Mg//[1 1] β1 orientation relationship (OR) with hcp-Mg 5, 6, 7, 8, 9, 10, 11, 12. Exchange rate us to aud TEM results also indicate that plate-like β 1 precipitates always forms with a high aspect ratio, and its broad-face {21 } β1 parallel to { 100} Mg 4, 5, 6, 7, 8, 9, 10, 11. Definition of binary Furthermore, β 1 nucleating within the Mg-matrix is associated with the orthorhombic β′ precipitate phase 5, 7, or as self-accommodating β 1 triads 5, 11, and heterogeneously along dislocation lines via accommodation of β 1 stress-free transformation strains associated with β 1 formation 7, 8, 9, 13, 14. Market value of futures Heterogeneous formation is particularly useful in restraining high-temperature creep deformation, because its dynamic nucleation arrests dislocation movement and enhances the creep-resistance of Mg-RE alloys 4, 9, 10, 11.

The formation tendencies of β 1 precipitates have been characterized experimentally 5, 6, 7, 8, 9, 10, 11, and its evolution within Mg matrix and on dislocations studied via phase-field models 12, 13, 14. Binary search c program Despite extensive studies on β 1 phase, basic thermodynamic quantities like β 1/Mg interfacial energies are yet to be determined unequivocally.


Dollar euro exchange rate history Quantitative understanding of β 1/Mg interfaces is crucial for three reasons. Gbp to usd graph First, atomic resolution transmission electron microscopy (TEM) studies have shown that the{112} β1/{ 100} Mg interfaces form both longer and shorter edges of β 1 plates 11. 1 usd to bdt This is surprising. Today’s stock market futures One would have expected at least an additional {111} β1/{11 0} Mg interface, because both {112} β1 and {111} β1 planes take part in forming the hcp-Mg/β 1 orientation relationship. Is the futures market open Second, a well-developed β 1 plate shares a substantial interfacial-area with the parent Mg-matrix. Usd to brl Thus the interfacial energy, in conjunction with transformation strain energy, will likely determine the plate-like morphology 12, 13, 14, 15. Learn binary code Therefore, determination of hcp-Mg/β 1 interfacial energies will provide valuable inputs to refine phase field models 12, 13, 14, 15. Dollar exchange rate calculator Third, this study allows us to rationalize whether these coherent interfaces have lower excess energies 16.

Density functional theory (DFT)-based first principles calculations have been used in the past to determine interfacial energies of coherent precipitates in Mg-RE alloys 14, 15, 17. Funny quotes with pictures for facebook So far, DFT studies on Mg-Nd have largely examined the stability of the β″ (ordered hcp structure 5) and the β′ precipitate phases 15, 17; both precipitate phases form at early stages prior to β 1 precipitation. Us stock market futures index For example, Issa et al. Live pound to euro exchange rate reported that β″ have positive and negative interfacial energies, when it joins with basal {0001} Mg and prismatic { 100} Mg planes respectively 15, 17. Binary conversion Based on these interfacial energy calculations they proposed that β″ is unstable in Mg-Nd 17, which was later corroborated with TEM observations 18. Stock market futures prices The good agreement with experiments validates the available RE pseudopotentials with frozen-core f-electrons, and permits us to study other systems. Cnn money futures market However, the methodology used for determining negative interfacial energies needs further investigation because one intuitively associates an interface with positive excess energy. Flower quotes shakespeare Therefore, the rationale for predicted negative interfacial energy was also investigated from the perspective of β 1/Mg interfaces, especially since β 1 is a key-strengthening phase in many commercial alloys 17.

Previous DFT studies on Mg-Nd have not investigated β 1 formation, its interfacial structure, and the associated bonding environment 14, 15, 17. The box nyc Furthermore, they did not examine thermodynamic quantities like surface excess energies – a difficult quantity to measure experimentally in the larger system limit 14, 15, 17. Php to usd conversion Thus, guided by TEM studies 5, 6, 7, 8, 9, 10, 11, we have investigated the energetics and structure of two types of β 1/Mg interfaces, namely {112} β1/{ 100} Mg and {111} β1/{11 0} Mg, via DFT calculations.

The geometry used for calculating β 1/Mg interfacial energies (γ β1/Mg) is schematically shown in Fig. Usd to myr 3a as vacuum-space/bulk-β 1/bulk-Mg/vacuum-space. 40 euro shoe size to us Here the interacting β 1/Mg surfaces are {111} β1(Iv/Cv)/{11 0} Mg and {112} β1/{01 0} Mg (see Supplementary Figure 2). Binary to text converter This methodology was previously used by Liu et al. Pound to usd to examine the interface between an ordered intermetallic compound and the disordered matrix 25. Binary bingo This approach further avoids the development of excess artificial interfacial strains by having vacuum on both sides of the unconstrained interfacial supercell. Current exchange rate usd to aud Thus, one need not include additional coherency strain energy terms (e.g. Futures markets cnn ref. Usd jpy exchange rate history 17) to evaluate the interfacial energies. Binary math Furthermore, since β 1 and Mg are exposed to the vacuum on either ends ( Fig. Cad usd graph 3a), we are required to determine the “free” surface of the participating {111} β1, {11 0} Mg, {112} β1 and { 100} Mg planes. Brl usd exchange rate The free surface energy, γ S-p, for a phase “p” was calculated using the expression , where E p(N) is the calculated ground state energy for a “N” atomic layer supercell slab of phase “p”, E Bulk-P is the bulk energy of phase “p”, and A is the surface area 25, 26, 27. Funny jokes for adults dirty The calculations involved a maximum of 24 (~35 Å) and 60 (~50 Å) layers for Mg and β 1 respectively, and a minimum of ~12 Å of vacuum space. Binary list E Bulk-P was determined from the slope of E p(N) vs N plot. Us stock market futures bloomberg For pure metals, E Bulk-P corresponds to their cohesive energy 27, and our calculations yielded 1.53 eV/atom for Mg – in excellent agreement with literature 26, 27, 28. Fraction to decimal conversion chart Figure 3b shows that plot of γ S-p vs. Usd to jpy N for different β 1 and Mg planes, and the results indicated that the γ S-p values, for {111} β1(Iv/Cv), {11 0} Mg, {112} β1 and { 100} Mg planes rapidly converge within the chosen range of N.

In Fig. 10101 binary 4a and c the atom colors are assigned by CNA environment type 18, 20 and the bonds depict in-plane – i.e. Gold chart 2016 (0001) Mg//(011) β1 – coordination around an atomic site: (i) red denotes hcp-Mg with 6 in-plane coordination, (ii) blue denotes bcc-ordered β 1 with 4 in-plane coordination, and (iii) green depicts sites which were not identified as either hcp-Mg or β 1. Usd to yen conversion Thus, the green-colored bonds/atoms near the interfacial regions – indicated with shaded boxes across Fig. Stock market futures definition 4a–d – can be interpreted as distortion of the lattice sites, from bulk hcp-Mg and β 1 structures.

A comparison of the interfacial regions, and their corresponding bonding environment reveal that the distorted lattice sites (shown by green colored bonds) are invariably located around regions with significant depletion of electron charge density distributions (marked by red arrows in Fig. Binary pdf 4b and d). Commodity definitions In other words, interfacial lattice distortions correlate well with lower electron density or weak bonding 29. Fx rate cad usd Furthermore, the electron density distributions near the interfacial regions of {111} β1(Iv)/{11 0} Mg was discernibly lower (compare Fig. Euro to aud chart 4b and c with legend at the bottom), and spread over a wider region than {112} β1/{ 100} Mg. Us to rmb exchange rate Correspondingly, lattice significantly distorted near the {111} β1(Iv)/{11 0} Mg interface. Rmb conversion to usd Therefore, considering the larger differences in the energies of {112} β1/{ 100} Mg (98 mJ/m 2) and {111} β1(Iv)/{11 0} Mg (282 mJ/m 2) interfaces, it is evident that smaller population of distorted lattice sites and narrow spatial extent near the interface correlate with lower interfacial energy. Dollar rupee exchange rate today This is further confirmed for {111} β1(Cv)/{11 0} Mg system (762 mJ/m 2) in Fig. Yen to usd 4e, which displayed a wider spatial extent of distorted interfacial lattice sites (overlapping both hcp-Mg and β 1 structures) than the other two interfaces.

One of our motivations was to rationalize the existence of only {112} β1/{ 100} Mg interfaces seen in Mg-Nd alloys, which was contrary to the exceptions based on β 1/Mg OR 11. Us stock market today The DFT calculations revealed that, unlike {112} β1/{ 100} Mg, formation of {111} β1/{11 0} Mg requires the presence of vacancy-like excess volume near the interfaces, which causes interfacial distortions, higher lattice strains and presumably strain energy within the mating phases. Funny quotes about love and life Such pronounced distortion/strain increases the interatomic spacings near the interface, reduces charge density between the atoms, and creates weaker interfacial bonding in {111} β1/{11 0} Mg. Exchange rate pound to us dollar The relatively poor bonding increases the excess energy of {111} β1/{11 0} Mg incomparison to the {112} β1/{ 100} Mg interface, and makes the latter an energetically preferable interface.”

Despite the fact that excess volume results in an energetically unstable {111} β1/{11 0} Mg interface. Ft future of marketing summit 2016 However, the presence of such excess volume near the interfaces may explain the growth of plate-like β 1 within Mg-matrix and along dislocation lines 5, 6, 7, 8, 9, 10, 11. Usd to inr conversion rate Nie and Muddle have proposed that shear transformation strains are associated with β 1 formation, because of which excess vacancy concentration is created at the short ends oriented along 〈11 0〉 Mg. Convert nzd to usd It is likely β 1 growth can occur via vacancy migration to the interfaces. Usd to pound conversion However, to maintain elongated plate-like morphology during the growth process, β 1 needs a stable interface in its long edge. Python tutorial download Our DFT results suggest that a low lattice strain and interfacial energy of {112} β1/{100} Mg interfaces allows β 1 precipitates to acquire a plate-like morphology with a high aspect ratio and possess a broad {112} β1-face parallel to {1 00} Mg as seen in experiments 4, 5, 6, 7, 8, 9, 10, 11, 12. Silver chart price In the case of dislocation assisted β 1 form as linear chains along 〈11 0〉 Mg 10, 13, 30, which are also observed in our creep-tested microstructures 10. Australian dollar trend 2016 We postulate that such linear growth of β 1 along dislocation lines occur via transfer of vacancies to metastable interfaces like {111} β1(Iv)/{11 0} Mg ( Fig. Stock market futures bloomberg 2b), which tends to have lower interfacial energy than vacancy formation away form the β 1/Mg interface (i.e. Malaysian ringgit to usd history {111} β1(Cv)/{11 0} Mg in Figs 2c and 3d). Convert aed to usd Since dislocations can rapidly supply vacancies via dislocation pipe diffusion, the diffusion assisted movement of {111} β1(Iv)/{11 0} Mg type interfaces rapidly consumes a large portion of the host dislocation line, and orients β 1 along 〈11 0〉 Mg. Aud to usd graph Finally, since {111} β1(Iv)/{11 0} Mg interfaces are energetically unfavorable, interfacial atomic rearrangements, e.g. World stock market futures bloomberg via shear process 5, 6, produces {112} β1/{ 100} Mg interfaces in the final microstructure.

From the perspective of alloy design approaches; the contribution of this report is two fold. Binary code to english We demonstrate that in order to develop alloys with advantages associated with “β 1-like” precipitation one needs to (i) retain a well bonded coherent interface at the precipitate broad faces, e.g. Euro football scores {112} β1/{ 100} Mg, while simultaneously (ii) form mobile yet unstable interfaces on the short edges to allow precipitate growth along dislocation lines. Stock market futures 2014 However, finding non-RE substitutions, which fits these two criteria, is our next challenge, and is currently being tackled by coupling evolutionary algorithms with first principle calculations.

Formation of nanoscale β 1-Mg 3Nd precipitates in hcp-Mg matrix is known to enhance the creep resistance of Mg-alloys because of their tendency to form on dislocation lines and sluggish coarsening kinetics when they form in the hcp alloy matrix. Financial futures market Using first principles calculations, we have compared the excess energy and the structure of {112} β1/{ 100} Mg and {111} β1/{11 0} Mg interfaces. Call option definition Our calculations revealed that the formation of {112} β1/{ 100} Mg interfaces, compared to {111} β1/{11 0} Mg interface, is associated with significant reduction in both the interfacial energy and lattice strains in the adjacent β 1 and Mg matrix. Ice futures europe trading hours The favorable formation energetics of the {112} β1/{ 100} Mg interface, in conjunction with small lattice strains, influences β 1 acquiring a plate-like morphology with its broad-face {112} β1 parallel to { 100} Mg. Call and put options explained Electronic structure of these interfaces revealed that a lower interfacial energy also correlates with a smaller population of distorted lattice sites near the interfacial regions. Dollar pound exchange rate graph Additionally, our DFT investigation informs that creep-resistant Mg alloys will benefit from “β 1-like” precipitation because of two key features (i) retain a well bonded coherent interface at the precipitate broad faces, e.g. Exchange rate usd chf {112} β1/{ 100} Mg, and (ii) destabilize other interfaces (corresponding to precipitate-Mg OR) to promote growth along a desired direction, e.g 〈11 0〉 Mg.

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