DFT predicting structural stability of Li-doped Al-Li solid solution using first principles

By using the first-principles method based on density functional theory (DFT), the CASTEP module in Materials studio was used to calculate the substitution positions of Li atom doped with Al lattice, and different substitution configurations, total energy, average atom formation energy, and charge density distributions were calculated. By calculating the total energy and the average forming energy of atoms, it is concluded that when the Li atom is doped with an Al lattice to form a replacement solid solution, it is the easiest to replace the Al atom on the surface, and the resulting replacement solid solution has the smallest binding energy and the most stable structure. By calculating the density of electron states and analyzing the Fermi energy surface, it is found that the Al-Li solid solution substituting Al atoms at the zero Fermi surface has the smallest electron state density and the most stable structure.


Introduction
Elemental aluminum (Al) has been the first choice of metal fuel, due to its low melting point, high combustion heat, high density and economic applicability.However, in the actual combustion process, because the aluminum atoms are easy to agglomerate and the oxide film exists on the surface, the ignition temperature is high and the ignition is difficult [1,2] .In order to solve the problems existing in the combustion process of aluminum, the use of aluminum base alloy fuel is an effective way.Currently, commonly used doping elements include lithium (Li), magnesium (Mg), titanium (Ti), and nickel (Ni).Among the commonly used elements, Li element has attracted more attention because its calorific value exceeds Al, its melting point is lower than Al, and it can promote the combustion of Al through the "micro-explosion" effect in the combustion process [3][4][5] .The first principle based on density functional theory can accurately predict the electronic structure and thermodynamic information of alloys without the limitation of experimental conditions and can reflect the intrinsic physical properties of materials more accurately than experimental studies.It was found in the study that the influence of doped metals or small atoms such as C and N on the stability of metal elements of different structures could be obtained through first-principle calculation [6][7] , and the occupying tendency of different atoms in the matrix could be explored more accurately, and the influence of doped atoms on the stability of the matrix and the mechanism of action could be further explored.
Therefore, this work takes Al as the research object, uses the first-principles calculation method to calculate the substitution position of the doped element Li, and further verifies the structure and energy state density.

Calculation model and method
All calculations in this study are made using the Castep module in Materials studio.generalized gradient approximation (GGA) based on PBE(Perdew-Burke-Ernzerh) functional method is used to deal with exchange-correlation energy.The truncation energy of the plane-wave unit is 360ev, and the K-point is set to 2×2×2 when relaxing the supercell and doping structure.The convergence criteria of the relaxation process are: the maximum force of the atom is 0.05 eV/A, the energy change is less than 2×10-5 eV/atom, the maximum position is 0.002 eV/A, and the maximum stress is 0.1GPa.After complete relaxation, the lattice parameters of Al atomic monocytes are a=b=c=4.038,and that of Li atomic monocytes are a=b=c=6.244,similar to the experimental values.In order to restore the real situation of the experiment to the greatest extent, a 2×2×2 Al supercell was constructed in this calculation, and then the Al supercell structure was optimized.At the same time, Li atoms were selected to replace Al atoms at different positions, the most stable Al-Li structure was calculated, and the replacement mechanism was discussed.
The atomic radius of Li is 1.57A, and the atomic radius of Al is 1.43A.According to the rules of solid solution formation, when the difference in atomic radius is less than 15%, only a replacement solid solution can be formed between the two atoms, but no interstitial solid solution can be formed.Li atoms cannot enter the gaps in the Al lattice to form a solid solution.Because the Al lattice has a face-centered cubic (FCC) structure, there are only two ways to replace atoms at the corners of the lattice or at the face-centered.Since the Al lattice is designed as a supercell with a total of 32 atoms in it, three substitution modes are constructed in this experimental model, as shown in Figure .

Energy stability
The reparability and room temperature stability of crystalline materials is the key to the development of materials.Theoretically, the stability of materials can be characterized by the average atomic formation energy.The average atomic formation energy can be expressed as [8] ： In the formula, Et represents the total energy of the crystal cell, and E xi represents the single atom energy of different elements after complete relaxation in the case of a single substance.Through calculation, the single atom energy of Al is -110.6439eV,and the single atom energy of Li is -199.4692eV.N represents the total number of atoms in the cell.The calculation results of the total energy and average atomic formation energy of each system are shown in Table 1.It can be seen from the table that the total energy and the average atomic formation energy of each system are negative, which indicates that each system can exist stably.By comparing the calculation results, it can be seen that the Li atom replaces the Al atom on the surface, and the average atom formation energy of the system is the lowest, so Al-2 is presumed to be the most stable structure at room temperature.

Charge density
The results of Xu et al [9] .show that for a stable multiparticle system, the smaller the density of the electron states at the Fermi level, the more stable the structure of the multiparticle system.Therefore, the total state densities of the three doped structures were calculated, as shown in Figure .3(a) in which Fermi levels were marked by dashed lines.It can be seen from the figure that the electron state density of the three different configurations at the Fermi level is AL-2>AL-1=AL-3 in order of magnitude.The lower the electron state density at the Fermi level, the higher the energy stability of the system.From the perspective of electronic structure, the Al-2 configuration is the most stable, that is, Li atom is the easiest to replace the Al atom on the surface.This is consistent with the calculated result of the average formation energy of atoms.

Conclusions
(1) By calculating the total energy and the average formation energy of atoms, it is concluded that when Li atom is doped with Al lattice to form a replacement solid solution, the Al atom on the surface is most easily replaced, and the resulting replacement solid solution has the smallest binding energy and the most stable structure.
(2) By calculating the density of electronic states and analyzing the Fermi energy surface, it is found that the Al-Li solid solution replacing the face-centered Al atom has the smallest electron state density and the most stable structure at the Fermi surface of 0.
Fully relaxed Al and Li atomic monocytes are shown in Figure.1.

Figure. 1
Figure. 1 (a) Al atomic monocytes (b) Li atomic monocytes 2, which are respectively represented by AL-1, AL-2, and AL-3 on the edge, surface, and corner of the substituted Al atom (the green atom represents Li atom).

Figure. 3
Figure.3 (a) Total state density of AL-1, AL-2, and AL-3.(b) Total state density diagram of singleatom Al and Li, and total state density diagram of doped AL-2 In order to further analyze the change of electron state density of Al after Li doping, AL-2, which has the best stability, is further analyzed.Figure.3(b) depicts the total state density diagram of single-atom Al and Li, as well as the doped total state density diagram.

Table 1
Total energy and formation energy of Li-doped Al lattice system