First-principles determination of the Ni-Al phase diagram

Pasturel, A.; Colinet, C.; Paxton, Anthony; Schilfgaarde, Mark van

doi:10.1088/0953-8984/4/4/005

Cited by 78 publications

(53 citation statements)

References 39 publications

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“…To illustrate this, we first examine a short-range cluster expansion in real space: one whose input structures and figures are userselected based on intuition alone. 12 Many CE-based works 12,[33][34][35][36][37][38][39][40] consider only a set of the spatially smallest J f , which are then combined with a similar number of "usual suspect" ordered input configurations. Consider the Connolly-Williams method 12 on the fcc lattice: It employed the five shortest figures, obtained from five structural energies-a fully determined fit.…”

Section: Short-range Real-space Cluster-expansion For Mo-tamentioning

confidence: 99%

Mixed-basis cluster expansion for thermodynamics of bcc alloys

2004

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To predict the ground-state structures and finite-temperature properties of an alloy, the total energies of many different atomic configurations ϵ͕ i ; i =1, . . . ,N͖, with N sites i occupied by atom A ͑ i =−1͒, or B ͑ i = +1͒, must be calculated accurately and rapidly. Direct local-density approximation (LDA) calculations provide the required accuracy, but are not practical because they are limited to small cells and only a few of the 2 N possible configurations. The "mixed-basis cluster expansion" (MBCE) method allows to parametrize LDA configurational energetics E LDA ͓ i ; i =1, . . . ,N͔ by an analytic functional E MBCE ͓ i ; i =1, . . . ,N͔. We extend the method to bcc alloys, describing how to select N ordered structures (for which LDA total energies are calculated explicitly) and N F pair and multibody interactions, which are fit to the N energies to obtain a deterministic MBCE mapping of LDA. We apply the method to bcc Mo-Ta. This system reveals an unexpectedly rich ground-state line, pitting Mo-rich (100) superlattices against Ta-rich complex structures. Predicted finite-T properties such as order-disorder temperatures, solid-solution short-range order and the random alloy enthalpy of mixing are consistent with experiment. PACS number(s): 61.66.Dk, 71.15.Nc I. INTRODUCTION A. The cluster expansion method: Definition and scopeAlloy thermodynamics, including properties at T = 0, require the knowledge of the excess energy ͑1͒of the solid A 1−x B x relative to the total energy of its constituents A and B. For a given underlying lattice, the degrees of freedom form a configurational vector , whose components i = ±1 record whether a lattice site i is occupied by element A ͑ i =−1͒ or B ͑ i = +1͒. Since ⌬H direct ͑͒ is difficult to calculate quantum mechanically for an exhaustive set of structures , it is often described by way of a cluster expansion (CE) Hamiltonian 1-6 ͑2͕͒J͖ are the interaction parameters for each pair or many-body combination of lattice sites i , j , k, etc. The cluster expansion 7-10 attempts to describe the energies of all different configurations with the accuracy of present-day densityfunctional methods. It is based on the fact that Eq.(2) allows to map an arbitrarily complex Hamiltonian with electronic degrees of freedom exactly onto a simple sum over crystallographic degrees of freedom. 8 For practical purposes, Eq.(2) is typically recast in terms of symmetry-inequivalent figures. 11 Also, without a loss of generality one may subtract 9 a configuration-dependent reference energy E ref from ⌬H. We may expand ⌬H LDA = ⌬H LDA − E ref as ⌬H CE , so thatThe interaction parameters ͕J f ͖ now signify all possible inequivalent pairs and many-body (MB) figures f. They are configuration independent, 8 with D f as each figure's symmetry degeneracy per site-any configuration dependence is contained in the lattice-averaged correlation functions ⌸ f ͑͒. Although Eqs.(2) and (3) contain, in principle, many interactions, the energetics of bonding is usually determined by relatively short length sca...

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Section: Short-range Real-space Cluster-expansion For Mo-tamentioning

confidence: 99%

Mixed-basis cluster expansion for thermodynamics of bcc alloys

2004

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“…1,2͒ have given rise to a variety of commercial applications in the aircraft industry, electronics, and catalysis industry. During the last decade, a number of ab initio studies of NiAl have been performed in order to describe the nature of the interatomic bonding, [3][4][5][6] electronic structure, [7][8][9][10][11][12] cohesive properties, 7,[13][14][15][16][17] defect energetics, [18][19][20][21][22] and optical properties [23][24][25][26][27] of this Hume-Rothery electronic compound leading to a scientific basis for the understanding of the complicated phenomena which take place during manufacturing and application of NiAl-containing alloys.…”

Section: Introductionmentioning

confidence: 99%

Constitutional and thermal point defects inB2NiAl

et al. 2000

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The formation energies of point defects and the interaction energies of various defect pairs in NiAl are calculated from first principles within an order N, locally self-consistent Green's-function method in conjunction with multipole electrostatic corrections to the atomic sphere approximation. The theory correctly reproduces the ground state for the off-stoichiometric NiAl alloys. The constitutional defects ͑antisite Ni atoms and Ni vacancies in Ni-rich and Al-rich NiAl, respectively͒ are shown to form ordered structures in the ground state, in which they tend to avoid each other at the shortest distance on their sublattice. The dominant thermal defects in Ni-rich and stoichiometric NiAl are calculated to be triple defects. In Al-rich alloys another type of thermal defect dominates, where two Ni vacancies are replaced by one antisite Al atom. As a result, the vacancy concentration decreases with temperature in this region. The effective defect formation enthalpies for different concentration regions of NiAl are also obtained.

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“…In figure 3, the Ni-AI equilibrium phase diagram [32] shows the different phases that are obtained when Ni and Al are combined in different proportions. This diagram is characterized by a liquid phase, a face-cubic-center (fcc) phase at both the Al and Ni rich ends, a non-congruently melting compound Al3Ni and three intermediate phases with a variable range of solubilities, AI3Ni2, AlNi and AlNi3.…”

Section: Preparation and Characterization Of Raney Nickelmentioning

confidence: 99%