First principles calculation of the elastic constants of intermetallic compounds: metastable Al 3 Li
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I. INTRODUCTION
Al-Li alloys have attracted considerable attention in the past decade because they serve as promising materials for aerospace application due to the combination of light weight and high strength.1 The alloying of Li to Al causes some unusual physical properties of the alloy. For example, while the atomic volume of Li is 20% greater than that of Al, the volumes of Al-Li alloys decrease significantly with increase of Li content leading to substantial deviations from Vegard's Law.2 Furthermore, according to the experimental analysis of Muller et al.,3 when more Li is added the bulk modulus of Al-Li alloys decreases but the elastic or Young's modulus is higher than that of pure Al metal (e.g., Ref. 4), even though pure Li is much softer than Al. According to theoretical studies,5 this might be understood from the formation of anisotropic bonding in Al-Li compounds. It is generally believed that while the Al-Li solid solution contributes largely to the increase of the elastic modulus, the strengthening effect of Al-Li alloys is mainly due to the precipitation of the metastable 8' phase (which is an ordered Al3Li compound crystallizing in the Ll 2 structure). This strengthening effect of the alloys is still, however, not fully understood. According to experimental analyses,6 two major mechanisms should contribute to the strengthen-
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Permanent address: Institute of Physical Chemistry, University of Vienna, Wahringerstrape 42, A-1090 Vienna, Austria.
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J. Mater. Res., Vol. 6, No. 2, Feb 1991 Downloaded: 12 Mar 2015
ing of the alloys: (i) a modulus strengthening which is due to the shear modulus difference between the precipitates and the matrix; and (ii) some kind of order strengthening which is related to the possible creation of antiphase boundaries due to the interaction between dislocations and the precipitated Al3Li. It is obvious from these considerations that a study of the elastic properties of the Al 3 Li-S' phase is important for understanding the elastic and mechanical properties of the Al-Li alloys. However, because Al3Li is a metastable phase precipitating in a solid solution matrix it is difficult to obtain reliable experimental results, especially about its elastic properties. Therefore, a first principles study might serve as a valuable tool to supply the wanted information. Although reliable electronic structure calculations yielding many important ground state properties of solid matter are more or less standard today, calculations of elastic constants from first principles are still rather rare. The reason is that such calculations demand highly precise methods which obviously need considerable computer resources. The fundamental quantity needed is the total energy as a function of the geometrical arrangement of the atoms. Generally, the elastic constants can be obtained from a first principles electronic structure method by calculating the change of the total energy as a function of appropriate lattice distortions.7 Since the elastic constants invo
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