First-principles Investigations Of Mg-Er Alloys

As the lightest engineering metallic material with a good combination of mechanical properties,castability, machinability, thermal conductivity, damping capacity, electromagnetic shielding ability,easy to recycle, etc., magnesium alloys have been widely used in the automobile, aerospace andcommunications industry. Rare earth elements are an important kind of alloying elements to improvethe mechanical properties of magnesium alloys. Among them, the magnesium alloy containing Er is akind of new materials with great development potential. Solution strengthening and second-phasestrengthening are two key strengthening mechanisms of rare earth-magnesium alloys. In order tounderstand more about the strengthening micro-mechanism of magnesium alloys on the atomic level,the first-principle pseudopotential plane wave (PPW) method based on the density functional theory isused to research the internal relations between the stability and crystal structure of the Mg-Erintermetallic compounds, analyze the relationship between the mechanical properties and electronicstructure of Mg35X(X=Al、Er) solid solution, and determine the optimal doped amount of Er in themagnesium alloys with the best mechanical properties, which could hopefully provide the theoreticalbasis for designing even more excellent magnesium alloy materials.Based on the optimized crystal model of MgEr, Mg2Er and Mg24Er5intermetallic compounds in thebinary Mg-Er alloys, the internal relations of the stability and crystal structure of the Mg-Erintermetallic compounds were analyzed by calculating the formation heat, binding energy andelectronic structure. The results show that in Mg-Er alloys, the heats of formation and binding energyof the three intermetallic compounds are all negative, and the alloying ability and structural stabilityof Mg-Er compounds are in decline with the decreasing content of Er. As the Er content decreases, theaverage quantities of bonding electron of each atom at low-energy region of Fermi level drops, whichresults in weakened interaction among valence electrons and reduced stability. There are a largenumber of charges around Mg and Er, suggesting the characteristics of typical metal bond. MeanwhileMg and Er share some charges to form covalent bond, but the distortion of the charge at the junctionis little. Therefore the valence bond of Mg-Er intermetallic compound has a characteristic of theduality wherein the metal bond predominates. With the decreasing of Er content, the amount of chargetransfer between Mg and Er atoms reduces gradually, which leads to the decrement of the proportionof covalent bond and the structural stability.The calculation of the supercell models of pure Mg and Mg35X(X=Er、Al) solid solution shows that the binding energy of Mg35Al and Mg35Er is negative, and the value of Mg35Er is lower than Mg35Erwhich means Mg35Er has the higher stability. When Al and Er elements are added into pure Mg, thebulk modulus(B), Young’s modulus(E) and shear modulus(G) are all improved, and the effect of Er ismuch greater than Al. The toughness of the three structures of Mg, Mg35Er and Mg35Al is compared inthe following sequence: Mg﹥Mg35Er﹥Mg35Al, and the elastic anisotropy of them is compared in thefollowing sequence: Mg﹤Mg35Er﹤Mg35Al. The average quantities of bonding electron of each atomin Mg35Er at low-energy region of Fermi level are much more than that of Mg35Al, and the density ofstate of Mg35Er at the Fermi level is higher than that of Mg35Al, so that Mg35Er has the better ductilityand the capability of resisting. Compared with Al atom, Er atoms share more charges with Mg atoms,which shows a strong covalent bond. Meanwhile, the uniform distribution of charges around Er atomdemonstrates the low directionality.The method of virtual crystal approximation was deployed to control the content of Er in solidsolution and calculate the mechanical properties of Mg-xEr(x=1~6at.%) solid solution. The resultsindicate that the bulk modulus(B) raises with the increasing content of Er, which peaks at4at.%Erand remains at almost same level afterwards. Young’s modulus(E) and shear modulus(G) drop withthe increment of Er content, while they increase slightly when Er content reaches6at.%. The sixMg-xEr(x=1~6at.%) solid solutions are all ductile materials. With the rising of Er doped amount inthe range of1~5at.%, the ductility of solid solution improves significantly, but deteriorates to someextent when Er content arrives at6at.%. As the amount of Er increases, the density of state(DOS)moves to low-energy region as a whole, and the average quantities of bonding electron at low-energyregion of Fermi level grows and the bottom band widens simultaneously, resulting in greater bondingcapacity. Affected by electrons in the4f orbital, a clear pseudogap turns up in the total density ofstates(TDOS) figure when Er content is between1~2at.%. The Fermi level is at the high-energyregion of pseudogap where the electronic transition is hard to achieve. When Er content is higher than2at.%, pseudogap turns blur and nonmetallicity is weakened. And the density of state at the Fermilevel is high, which means these solid solutions have a good activity.