Structural properties and relative stability of (meta)stable ordered, partially ordered, and disordered Al-Li alloy phases (original) (raw)
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Emergent reduction of electronic state dimensionality in dense ordered Li-Be alloys
Nature, 2008
High pressure is known to influence electronic structure and crystal packing, and can in some cases even induce compound formation between elements that do not bond under ambient conditions 1-3. Here we present a computational study showing that high pressure fundamentally alters the reactivity of the light elements lithium (Li) and beryllium (Be), which are the first of the metals in the condensed state and immiscible under normal conditions 4,5. We identify four stoichiometric Li x Be 12x compounds that are stable over a range of pressures, and find that the electronic density of states of one of them displays a remarkable steplike feature near the bottom of the valence band and then remains almost constant with increasing energy. These characteristics are typical of a quasi-two-dimensional electronic structure, the emergence of which in a three-dimensional environment is rather unexpected. We attribute this observation to large size differences between the ionic cores of Li and Be: as the density increases, the Li cores start to overlap and thereby expel valence electrons into quasi-two-dimensional layers characterized by delocalized free-particle-like states in the vicinity of Be ions. Our extensive structural search exploring possible Be-Li compound formation under pressure uses two conceptually different approaches. In the first, we propose possible structures on the basis of established chemical/physical heuristics of alloy stability at 1 atmosphere (atm) and/or high pressure. Phenomenological 1-atm binary intermetallic structure maps 6 proved useful in this endeavour. In the second approach, initial structures are formed from randomly generated unit cells and atom positions, and subsequently optimized using density-functional theory (DFT) 7 , with the random search targeting unit cells with 15 or fewer atoms. This combined staticlattice structure search explores the stoichiometries most common in binary intermetallic compounds, including LiBe, LiBe 2 , Li 2 Be, LiBe 3 , Li 3 B, Li 2 Be 3 , Li 3 Be 2 , LiBe 4 and Li 4 Be. The enthalpy of formation of Li x Be 12x is defined as h f (Li x Be 12x) ; h(Li x Be 12x) 2 xh(Li) 2 (1 2 x)h(Be), where all enthalpies h are given per atom, at the same pressure, and for temperature T R 0. Thermodynamically, an alloy phase is stable against decomposition to elements if its h f is negative. The enthalpies of elements are those of the most stable known structure of elemental Be and Li at a given pressure. Elemental Be adopts the hexagonal close-packed (h.c.p.) structure 8 at low temperature in the pressure range considered, 0-200 gigapascals (GPa), whereas Li in this pressure range undergoes a series of phase transitions: b.c.c. R f.c.c. R cI16 (refs 9, 10; b.c.c., body-centred cubic; f.c.c., face-centred cubic). It is important to recognize that in these light-element phases (elements and alloys), ion dynamics can significantly change the total energies 11. On the other hand, DFT static-lattice energies in general reproduce experimental phase stabilities well even for lightelement high-pressure phases 10 , in part owing to the cancellation of
APL Materials, 2013
The solubility and stability of three possible ordered Al 3 Li structures in Al-Li alloys are studied using first-principles calculations: δ -Al 3 Li(L1 2 ), δ-Al 3 Li(DO 22 ), and β-Al 3 Li(DO 3 ). We find that δ -Al 3 Li(L1 2 ) is the most stable phase and β-Al 3 Li(DO 3 ) is energetically unfavorable. The vibrational formation entropy makes a significant contribution to the solubility for all three ordered Al 3 Li structures and yields a 1.6-fold increase in the calculated solubility of δ -Al 3 Li(L1 2 ), a 1.8-fold increase for δ-Al 3 Li(DO 22 ), and a 2.5-fold increase for β-Al 3 Li(DO 3 ). The solubility of δ -Al 3 Li(L1 2 ) is greater than those of δ-Al 3 Li(DO 22 ) and β-Al 3 Li(DO 3 ), and the δ -Al 3 Li(L1 2 ) solvus curve is in good agreement with the experimental one. © 2013 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.
Ab Initio Calculations of Ordered Intermetallic Phase Equilibria
MRS Proceedings, 1988
ABSTRACTGeneral procedures for computing alloy phase equilibria from ab initio electronic structure calculations are reviewed and applied to the Al-Li phase diagram. Free energies were calculated by the cluster variationm.method (CVM) in the tetrahedron approximation for the fcc and bcc lattices and ordered superstructures. Input was provided by first principles FLAPW calculations. The computed phase diagram for both stable and metastable structures agrees remarkably well with the experimental one.
Coarse-grained density functional theory of order-disorder phase transitions in metallic alloys
Physical Review B, 2009
The technological performances of metallic compounds are largely influenced by atomic ordering. Although there is a general consensus that successful theories of metallic systems should account for the quantum nature of the electronic glue, existing non-perturbative high-temperature treatments are based on effective classical atomic Hamiltonians. We propose a solution for the above paradox and offer a fully quantum mechanical, though approximate, theory that on equal footing deals with both electrons and ions. By taking advantage of a coarse grained formulation of the density functional theory [Bruno et al., Phys. Rev. B 77, 155108 (2008)] we develop a MonteCarlo technique, based on an ab initio Hamiltonian, that allows for the efficient evaluation of finite temperature statistical averages. Calculations of the relevant thermodynamic quantities and of the electronic structures for CuZn and Ni3V support that our theory provides an appropriate description of orderdisorder phase transitions.
Solid State Communications, 1983
A DFT method with the B3LYP functional and the 6-311++G(d,p) diffuse basis set is used to predict geometries, relative stabilities, electronic structures, and the bonding of closo-and nido-Ga m B n-m H 2 n − , Ge m B n-m H 2 m n − , and As m B n-m H 2 2 m n − (n = 10, 12 and m = 1, 2) Clusters are obtained by replacing BH with isolobal GaH, GeH + , and AsH 2+ fragments, keeping the same skeleton electron pairs (SEP). Based on the polyhedral skeletal electron pairs theory (PSEPT), closo and nido structures are predicted and can be of significant interest for experimentalists working in the field of heteroboranes. Different cluster stabilities are studied according to Gimarc′s and Williams′ rules, where our calculations show that the monosubstituted clusters deviate from these rules, giving rise to open structures. As 2 B 8 H 2 n + as 10-vertex structures lead to nido-type clusters, however, Ge m B n-m H 2 m n − (n = 10, 12 and m = 1, 2) give rise to closo isomers with close energies. All optimized structures exhibit large HOMO-LUMO gaps suggesting a good kinetic stability, thus predicting their isolation and characterization.
ChemPhysChem, 2005
A most challenging and important goal of materials science is to achieve an ab initio atomistic description of solids and their surfaces that can predict phenomena and properties occurring on macroscopic length and long timescales. Such methods should quantitatively describe measurable properties without relying on experimental parameters, which implies that they have to start ab initio, that is, from the self-consistent evaluation of the electronic structure. Recently, theoretical ab initio methods for achieving a unification of length-and timescales are being actively tested and developed for a variety of systems (see, e.g., ref. ). Herein, we apply and extend such methods to study the ordering of two-dimensional (2D) Al x Na 1Àx surface alloys. Our approach is quite general and offers a systematic and efficient procedure for reliably investigating (or "screening") the configurational space of materials surfaces as a function of temperature (T) and number of adatoms (or stoichiometry, x).
Physical Review B, 2007
The phase stability of B2 Ti 3 Al 2 X ͑X =Nb or V͒ and slightly rearranged atomic structures is examined by first-principles calculations. The ground-state energy calculations show instability in some of the Ti 3 Al 2 X configurations against the structure type of atomic displacement. We use electronic density of states and Mulliken population analysis to understand the hybridization between the atoms and the electronic origin of the stability or instability of each system. In order to estimate the strength of each bond, the heats of formation for several compounds are calculated. We find that the strength of the transition metal-Al bond increases from V to Nb to Ti, with Ti-V and Ti-Nb being weakly unstable. By examining several atomic configurations, it is shown that the stability of each structure is directly related to the number of Ti-Al bonds in each configuration. It is confirmed that the formation of the phase in Ti 3 Al 2 X is a combined displacive-replacive transformation. The crystal structure parameters, such as lattice constants and bulk modulus, are calculated and compared with available experimental data.
First Principles Theory of Disordered Alloys and Alloy Phase Stability
NATO ASI Series, 1994
Carlomethods or the CVM. The difficulty with such an approacnistnatcomplex electronically mediatedinteractions aremapped ontoaneffective classical Hamiltonian. Unfortunately, thereisno apriori guarantee thatsucha procedure iseither uniqueor " rapidly convergent. In addition, since theparameters areextracted from calculations on smallunitcell systems, thereispossible thattheinteractions contain contributions (e.g. fromtheMadelnng energy) thatwill excessively favor suchstructures withrespect tothe disordered phase. Inthese lecture noteswe shall reviewtheLDA-KKR-CPA method fortreating the electronic structure and energetics ofrandom alloys and theMF-CF and GPM theories ofordering and phasestability thathavebeenbuilt on theLDA-KKR-CPA description ofthedisordered phase.Thus,we takethepoint ofviewthatmuch can be learned about metallic alloys by first studying theelectronic structure and energetics ofideal random solid solutions, which,forentropic reasons, arethenatural hightemperature solid state phasesand thento investigate their instabilities to theeither phaseseparation or to theformation ofspecific orderedphases. We shall stress thata direct connection can oftenbe made betweenspecific features intheelectronic structure associated withthe random solid solution and thedriving mechanismsbehindspecific ordering phenomena. Consequently, our understanding ofphasestability willbe underpinned by the same electronic structure thatisresponsible fordetermining theresidual resistivity and other properties ofthedisordered phaseand thatcan be experimentally verified usingoptical spectroscopies, positron annihilation and otherprobes. These lecture notesare structured as follows. In section 2 we layout the basic LDA-KKR-CPA theory oftheelectronic structure and energetics ofrandom alloys and some examplesof itsapplications to theelectronic structure and energie_ ofrandom alloys arepresented. In section 3 we reviewtheprogress thathas beenmade overthe last few yearsin understanding the mechanismsbehindspecific ordering phenomena observed inbinarysolid solutions basedon theMF-CF and GPM theories ofordering and phasestability. We will giveexamplesofa variety ofordering mechanisms:Fermi surface nesting, band filling, off diagonal randomness, charge transfer, size difference or local strain fluctuations, and magnetic effects. Ineachcasewe will trytomake thelink betweenthespecific ordering phenomenon and the underlying electronic structure of thedisordered phase.Insection 4 we will review theresults ofsome recent calculations on theelectronic structure of_-phaseNicAl1_c alloys usinga version oftheLDA-KKR-CPA codes that has been generalized to systems having complex lattices. In section 5 " we provide a few concluding remarks. 2 Theory of Random Substitutional Alloys 2.1 LDA-KKR-CPA The LDA-KKR-CPA method for calculating the energy and other properties of random solid solution alloys rests on three theoretical developments: the local density approximation to density functional theory, multiple scattering theory for solving the effective single particle SchrSdinger equation that is at the heart of the LDA-DFT self-consistent field equations, and the coherent potential approximation for treating the effects of disorder on the electronic structure i.e. for accomplishing the task of configuradonal averaging inherent in the calculation of observables. 2.1.1 Local Density Approximation and Random Alloys Density functional theory (DFT) is, in principle, an exact method for calculating the energetics of an electron system in the field of the atomic nuclei [4],[5], [21],[22],[6]. The. central result of DFT is that the total ground state energy, ELo], of a system of electrons in the presence of the external field provided by the nuclei is a unique functional ELo] = TIp] + U[p] + E,c[p] of the electron density, p(r-'),where Tip], U[p] and E,c[p] are the kinetic, potential and exchange correlation energies respectively. Furthermore, E[p] takes on its minimum value for the correct ground state p(r-').This minimum principle taken together with the constraint foo dar p(r) = N, the total number of electrons in the system leads to a set of self-consistent field equations whose solution yield the ground state charge density and hence the ground state energy. These basic equations of DFT are made into a practical computational method by making the local density approximation (LDA) in which the unknown, but exact, exchange correlation functional for the inhomogeneous interacting electron gas appropriate to the solid is approximated, at each point in space, r, by the exchange correlation functional, E_A[p], appropriate to an interacting but homogeneous electron gas having the density found at that point. Given the specification of a solid in terms of a set of atomic positions, {R/}, and corresponding nuclear charges, {Zi}, of the atoms occupying these sites, the practical applications the LDA involves the solution of a set of Hartree like, Kohn-Sham selfconsistent field equations that take the form [-V 2-I-v,s! (F;p(e; {P_}; {Zi}))] tb, Cr-') = _&,C r-') (1) J where the crystal potential ve!t(F; p(F; { R/); { Zi })) takes the form @ _2Z _ dFp(_') , [_-R'i[ + 2 IF-JI + v.=(r;'°p(r-')) (2) and where p(F; {R_}; {Zi})is given in terms of the eigen-solutions of eq. 1 as I¢,.(r-')12f(e.-p) (3)
The solid-phase portion of the Al-Li phase diagram has been computed from first principles both at zero pressure and at a hydrostatic compression of 5.4 GPa. Computation of the pressure dependence of the Al-Li phase equilibria answers two questions: ͑1͒ how important is the effect of the atomic size difference, and ͑2͒ is the stability of the Al 3 Li precipitates influenced by high hydrostatic stress. The zero-pressure first-principles phase diagram exhibits excellent qualitative agreement with experimental data. The presence or absence of solid solutions ͑SS͒, of stable and metastable intermetallic phases, and their degree of order are computed correctly. Compression is predicted to affect the phase equilibria in Al-Li as follows: ͑1͒ the solubility of Li in fcc Al-rich SS is decreased, ͑2͒ the solubility of Al in Li is increased. However, the low melting point of Li limits the range of SS, and ͑3͒ the metastable Al 3 Li Al-rich fcc SS phase equilibrium is unaffected and the stability of the precipitates is unchanged, ͑4͒ the ordering tendencies at Li-rich compositions are slightly enhanced. Although high pressure eliminates the difference in atomic volume of the pure constituents, it has almost no effect on the solid-solid phase equilibria in this alloy system. A simple method for verifying the accuracy of the cluster expansion for the configurational internal energy is presented and applied. Moreover, it has been shown that with a convenient choice of the occupation numbers, one can define correlation functions which greatly facilitate the determination of new ground state structures.
Research Gateway, 2023
In the present article, the electronic, magnetic, and thermodynamic behavior of Alloy Al (75%)-Li (25%) has been investigated using the FP-LAPW method and the quasi-harmonic Debye model. The structural elements of Alloy Al-Li belong to space group 221_Pm-3m, and the lattice parameter slide is different from Al unit cells. The electronic behavior of the alloy Al-Li Alloy is shown as metallic. The volume vs. pressure curve shows a normal solid behavior of metal and a hard density of material. The value of specific heat increases rapidly with temperature.