Crystal structure and stability of complex precipitate phases in Al–Cu–Mg–(Si) and Al–Zn–Mg alloys
Introduction
Heat treatment of aluminum alloys is often employed in practice in order to strengthen the alloy via precipitation hardening. Precipitation microstructures improve the yield strength of the alloy because the precipitates act to impede dislocation motion through the material. The magnitude of the strengthening effect is, naturally, dependent on the microstructural morphology of the precipitates, which in turn is governed by the interfacial and strain energies of the precipitate/matrix system. These interfacial and strain energies are sensitive to the nature of the atomic-scale crystal structure of the precipitate phase, the matrix phase, and the interface between the two. Hence, a large amount of effort has gone into understanding the crystal structure of precipitate phases in aluminum-based alloys [1], [2].
However, despite decades of study, there are several commonly-occurring precipitate phases in multicomponent (ternary, quaternary, and higher order) aluminum alloys whose crystal structures are still the subject of significant controversy. In some cases, even the stoichiometry of the precipitate phase is not established. Notable among these controversial cases are:
- 1.
the S (and/or S′) phase occurring in Al–Cu–Mg alloys;
- 2.
the η′ phase which occurs in Al–Zn–Mg alloys (with relatively low levels of Mg); and
- 3.
the “ubiquitous” Q phase which occurs in a wide variety of quaternary Al–Cu–Mg–Si alloys.
In many of these alloys, the nature and structure of the Guinier–Preston (GP) zones formed in the early stages of aging are also a matter of debate.
The study of these multicomponent precipitate phases goes back more than 50 years, using techniques such as X-ray diffraction (XRD), electron microscopy, electron diffraction, and more recently, high-resolution electron microscopy (HREM), and both one- and three-dimensional atom probe techniques. The determination of precipitate crystal structure by diffraction experiments can be complicated by several factors: weak diffraction spots above the Al background scattering; significant overlap between precipitate and Al peaks; and low contrast between neighboring elements, such as Mg, Al, and Si. Despite the long history of this subject, the field is still quite active, as evidenced by many recent papers (within the past 5 years) addressing the crystal structures and precipitation sequences in these systems: S/S′ [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13] η′, [14], [15], [16], [17], [18], [19], [20] and Q [21], [22], [23], [24], [25]. The crystal structure of these three precipitate phases is the subject of the current paper. We also investigate GP zone orderings in Al–Cu–Mg and Al–Zn–Mg.
We show here how an existing technique may be brought to bear in a new way on problems of precipitate structure determination: first-principles total energy calculations based on density functional theory. While the XRD and HREM experimental efforts yield structural and chemical information, first-principles atomistic calculations give structural, chemical, and energetic information. Energetic information is not typically utilized in attempting to ascertain crystal structures, but it is reasonable to assume that the energies of precipitate phases are bounded above and below by the parent phase from which they transform, and the product phase into which they transform, respectively. These bounds place restrictions on the allowed energies of precipitate phases, and as we show here, they may be used to exclude many proposed structural models as “energetically unreasonable”.
State-of-the-art first-principles calculations are particularly useful for obtaining the energetics of these precipitate phases for several reasons: The accuracy of relative energetics (e.g., the energy differences between two solid phases, as in a formation or mixing enthalpy) is quite high. As we show here, a comparison between first-principles and experimentally assessed CALPHAD (CALculation of PHAse Diagrams) data for Al-rich intermetallics yields a typical accuracy to within 2 kJ/mol for formation enthalpies. Also, first-principles methods are generally applicable to any elements in the periodic table and are not constrained by equilibrium thermodynamics. That is, these methods should be just as accurate for the energies of metastable states as they are for stable states. They are unbiased towards any particular structural model, making them a useful predictive tool for critically assessing various proposed precipitate structures.
In this paper, we apply arguments based on T=0K energetics to the crystal structures of precipitates. However, precipitation is inherently a finite-temperature, kinetic process. So, the zero-temperature energetics do not yield a complete picture of the precipitation process, and hence one might wonder about the applicability of such an approach. As we show here, the energetic separation between various models of precipitate structures is very large (>10 kJ/mol), making several proposed crystal structure models unreasonably high in energy (e.g., higher in energy than either the solid solution phase or the GP zones phases from which the precipitates nucleate). Temperature-dependent effects (e.g., configurational and vibrational entropy) certainly will quantitatively effect the phase stability of these precipitates; however, entropic contributions are not likely to be large enough to qualitatively reverse these types of large energetic differences1.
Section snippets
First-principles method
The first-principles calculations described utilize the plane wave pseudopotential method, as implemented in the highly efficient Vienna ab initio simulation package (VASP) [27], [28], [29], [30], using ultrasoft pseudopotentials [31], [32]. In the vast majority of calculations reported here, the local density approximation (LDA) was employed, with the exchange-correlation functional of Ceperley and Alder [33], [34]. For a few calculations involving magnetic 3d elements Cr, Mn, Fe, Co, and Ni,
Structure and formation enthalpies of Al–Cu–Mg phases: S/S′ phases, GPB zones, and solid solution
The precipitation sequence formed upon heat treating Al–Cu–Mg has been studied for decades [3], [5], [6], [7], [8], [9], [10], [11], [12], [13], [44], [45], [46], [47], [48], [49]. Al–Cu–Mg alloys have historically formed the basis of many alloys used in aerospace and other applications, and have been suggested as an alternative to 6xxx series alloys for use in automotive body panels (see, e.g., Refs. [6], [7]) In alloys close to the pseudo-binary Al–Al2CuMg compositions, the sequence is [44]:
Al–Mg–Zn: η, η′ phases, GP zones, and solid solution
Additions of Mg and Zn to Al form the basis of many 7xxx series high-strength, heat treatable alloys. Consequently, the precipitation sequence in Al–Zn–Mg alloys has been the subject of much interest [1], [2], [20], [16], [15], [17], [18], [19], [53]. For relatively high Zn:Mg ratios, this sequence (see the recent review in Ref. [20]) is:
Upon aging, the solid solution gives way to (two types of) GP zones, then to a semicoherent metastable phase η′, and finally to
Al–Cu–Mg–Si: Q phase
The quaternary “Q phase” is found in a wide variety of Al–Cu–Mg–Si alloys, for example, 6xxx series Al–Mg–Si alloys with Cu additions [24], or Al–Si–Cu casting alloys containing Mg, such as Al 319 [60]. Despite its common presence in these alloys, relatively little is known about the Q phase compared to other commonly-occurring precipitates. Even the stoichiometric composition of Q varies from one study to another, reported as Al4Cu2Mg8Si7 [61], Al5Cu2Mg8Si6 [62] and Al4Cu1Mg5Si4 [2]. Another
Summary
We have demonstrated the utility of first-principles calculations in elucidating the crystal structures and phase stability of several complex, multicomponent precipitate phases in Al alloys: S (Al–Cu–Mg); η′ (Al–Zn–Mg); and Q (Al–Cu–Mg–Si). A critical assessment of the accuracy of first-principles formation enthalpies in a wide variety of ordered Al-rich intermetallics shows that the calculated energetics are in excellent quantitative agreement (to within 2 kJ/mol) with experimentally assessed
Acknowledgements
The author gratefully acknowledges many useful discussions with Drs J. Allison, W. Donlon and R. Jahn.
References (64)
- et al.
Acta Mater.
(2000) - et al.
Acta Mater.
(1999) - et al.
Acta Mater.
(1998) - et al.
Appl. Surf. Sci.
(1996) - et al.
Scripta Mater.
(1997) - et al.
Scripta Mater.
(1998) - et al.
Scripta Mater.
(1998) - et al.
Acta Mater.
(1999) - et al.
Acta Mater.
(1999) - et al.
Scripta Mater.
(1999)
Mater. Sci. Engng
Acta Mater.
Comput. Mat. Sci.
Thermochim. Acta
Scripta Met.
Acta Met.
Aluminum: Properties and Physical Metallurgy
Aluminum Alloys—Structure and Properties
J. Mater. Res.
Mater. Trans. JIM
Phys. Rev. B
Phil. Mag. Lett.
Mater. Trans. JIM
Z. Metallkd.
Mater. Sci. Forum
J. Mater. Sci.
Metal. Mater. Trans.
Phil. Mag. Lett.
Phys. Rev. Lett.
Phys. Rev. B
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