1、Contents lists available at ScienceDirectPhysica B: Condensed Matterjournal homepage: calculations of structure and electronic properties ofaluminum doped by Ge, Sn and PbHongwei Shoua,b, Mingjun Penga,b, Yonghua Duana,b, Lishi Maa,b, Ping Lia,baFaculty of Material Science and Engineering, Kunming U
2、niversity of Science and Technology, Kunming 650093, ChinabKey Lab of Advanced Materials of Yunnan Province, Kunming University of Science and Technology, Kunming 650093, ChinaARTICLE INFOKeywords:DopedFirst-principles calculationElectronic structureAluminumABSTRACTBased on the rst-principles calcul
3、ation of plane wave ultra-soft pseudo-potential technology, the geometricalproperties, impurity formation energy and electronic structures of Al doped by Ge, Sn and Pb were investigated.The structures and energies of three doped systems indicate that the formation of Ge doped Aluminum isminimum and
4、the structure is the most stable. The impurity formation of Ge is2.4070eV and the system willrelease maximum heat, while doping with Pb will absorb heat. Whats more, compared with pure aluminum, thecharge distributions of central aluminum, which directly surround the impurities, are transformed from
5、 squareto triangle. And this phenomenon leads that there is no covalent bond between central aluminum along the110 direction. The charge density dierences illustrate the interaction between Al and M (M=Ge, Sn and Pb)is covalent bonding. The amount of accumulated electrons shows that the system of Al
6、eGe possesses thestrongest covalent bonding, followed by AleSn and nal by AlePb. So the stability of Al-M (M=Ge, Sn and Pb)is AleGe AleSn AlePb. Additionally, according to Mulliken population analysis, it has been found thatdue to the incorporation of impurities elements, there are stronger repulsiv
7、e eects between AlIand the bondsbetween AlIand AlIIis the most covalent.1. IntroductionIn recent years, aluminum alloy conductor cables have graduallybegun to replace copper core cables in medium and low voltage dis-tribution networks. However, aluminum and copper cant be directlywelded, which can e
8、asily form the galvanic cell and lead to electro-chemical corrosion 1. Previous studies have found that using alu-minum tin composite as intermediate transition bond is a good solution.Zhao R et al. have found that when aluminum and tin were composited,tin atom will enter the octahedral gap of the a
9、luminum atomic cell byusing XRD analysis technology 2. And it will form a unique structurethat has both face centered cubic structure and body centered cubicstructure. It is a process called doping that a small amount of impurityelements or compounds are added into a kind of material matrix totransf
10、orm its crystal structure, optical, thermodynamic, electronic,mechanical and magnetic properties. Doping is a quite eective andimportant method to obtain new materials. Nowadays, the rst-prin-ciples calculations are widely used to investigate a lot of the inuenceof elements doping in the materials.
11、Wen et al. have found Nd dopingZnO crystal presents the occupied states near Fermi level, which isconspicuous to strengthen the photoelectric characteristics of materials3. Whats more, the research of Cd, Mg, Eu and Ce doping ZnO alsolays a good theoretical foundation for the application of ZnO in t
12、hevisible light region 48. In addition, Pluengphon P et al. conrmedthat when InP alloyed with Zn, Sn, Si and S, the order of absorptioncoecient is Sn Si S Zn and it will reduce at high pressure9. Mg substitution not only adjust the structural stability of LiBH4bydecreasing the bonding interaction be
13、tween Li and BH, but alsotransform the properties from nonmetallic character (Mg-free system)to semiconducting even metallic character (Mg-doped systems) by de-creasing the band gap 10. And when Re substitutes Co7W6, Re willsubstitute the Co cites which can obviously improve the bondingstrength and
14、the stability of system 11. Whats more, doping can leadto a higher reliability for the chemical compound 12,13. If the Crconcentration is 6.25at.% when Cr doped in LiZnP alloy, LiZnP wouldbe magnetic 14. Besides, it has been found with the increase of Nidoping concentration, the magnetic properties
15、of BiFeO3can rise ob-viously and it is in agreement with the experiments 15,16.As the most abundant metal element in the earth, aluminum and itsalloys show the low density, excellent electrical conductivity and goodductility. For pure aluminum, structural relaxations, which is vertical tothe applied
16、 shear signicantly, can decrease the ideal shear strength,https:/doi.org/10.1016/j.physb.2018.07.033Received 12 June 2018; Received in revised form 19 July 2018; Accepted 30 July 2018Corresponding author. Faculty of Material Science and Engineering, Kunming University of Science and Technology, Kunm
17、ing 650093, China.E-mail address: (M. Peng).Physica B: Condensed Matter 547 (2018) 611Available online 01 August 20180921-4526/ 2018 Elsevier B.V. All rights reserved.Tresulting in strengths of 89% of the shear modulus 17. At the strainof 16%, the theoretical tensile strength of the Al grain boundar
18、y iscounted to be 9.5GPa 18. When the strain is less than 19%, the strainrate of the interface is equal to the interior 19. Besides, the torsionalgrain boundary of aluminum has better tensile toughness than the tiltedgrain boundary 20. About the formation of the intrinsic point defects,AlVis the mos
19、t easy to appear, followed by AlOand AlT21. Whatsmore, the calculations of helium doped Al indicated that helium willoccupy the octahedral interstice in aluminum due to low impurityformation energy 22,23. In addition, there were many investigationsabout impurity doped in grain boundary of aluminum 2
20、429. Cer-tainly, most works focused on aluminum alloys and its compounds. Asfor aluminum alloys, it has been conrmed that there is an intenseSieAl bond in AleMg2Si alloys 30. In AleTi alloys, AleTi also has acovalent-like bonding 31. According to calculations of DFT in ternaryAleCueLi alloys, a new
21、stable structure Al6Cu4Li3is found 32. Aboutthe research of aluminum compound, Li et al. found the direct band gapof WZ-AlN is 6.12eV 33,34. Moreover, the four AlN phases have asmaller plasma frequency than WZ-AlN 35. The nanoribbon of zigzagAlNs band gap is 2.78eV 36.As for the doping of pure alumi
22、num, there are little literature up tonow. Only the helium doped Al has been investigated. Liu X K et al.conrmed that there is ionic interaction between helium and aluminumand the helium atom loses a small amount of electrons 22. The heliumbubble diusion coecient in aluminum containing a kind of met
23、alimpurity is much bigger than pure aluminum 37. Furthermore, theincrease of carbon and iron concentration will restrain the growth andthe migration of helium bubbles 38,39. But lead precipitates are ableto accelerate helium bubble growth 40. Besides, there are some re-searches about Al2X which poss
24、ess outstanding thermodynamic stabi-lity and magnetic properties 41. In the Al2X (X=Mg, Ca, Sr and Ba),Al2Ca has the strongest bond and the most stable crystal structure 42.Whats more, the acoustic phonon in Al2Ca mainly come from Ca 43,which is similar to Al2X (X=Sc, Y) 44. The above investigations
25、mainly pay attention to the optical, thermodynamic, magnetic andelectronic properties of the aluminum alloys and its compounds.The research about aluminum doped with metal impurity is little.However, Zhao R et al. found that the unit cell of the aluminum tinlayered composite material has both face-c
26、entered cubic structure andbody-centered cubic structure by XRD diraction 2. Due to Ge, Sn andPb in the same family, we infer Ge and Pb in the same place of the unitcell of aluminum. Consequently, based on the rst-principles calcula-tion of plane wave ultra-soft pseudo-potential technology which dep
27、endon the density function theory, we investigate the crystal structure,impurity formation energy and electronic properties of Al-M (M=Ge,Sn and Sn). We also compare the results in detail to nd the dierenceamong each other.2. Computational detailsIn this work, we employed the Cambridge sequential to
28、tal energypackage (CASTEP) 45, which is based on density function theory, tocalculate crystal structures, the impurity formation energy and elec-tronic properties of the doped Al systems. The interaction between ionand electrons was described by the plane wave ultra-soft pseudo-po-tential and the ca
29、lculations were adjusted by the Perdew Burke Eruzerhform of the generalized gradient approximation 46,47.Aluminum with space group of fm3m is a face centered cubicstructure, as displayed in Fig. 1 (a). It is generally acknowledged thatthere are two kinds of doped sites in the aluminum cell: tetrahed
30、ral siteand octahedral site. However, theoretically, the atomic radius of ger-manium, tin and lead is much bigger than the tetrahedral interstice inaluminum. So if we add them in the tetrahedral, the lattice of aluminumwould have a large distortion and a big impurity formation energy. Andthe structu
31、re is unstable. Consequently, we put them in the octahedralinterstice, as shown in Fig. 1 (b), to calculate crystal structure, impurityformation energy and electronic properties of Al-M (M=Ge, Sn andPb).First of all, we set up a 333 supercell of aluminum and thenadd germanium, tin and lead in the ce
32、ntre of supercell, respectively, asshown in Fig. 1 (c). As one of the most eective methods in guring outthe optimization problems, the Broyden-Fletcher-Goldfarb-Shanno(BFGS) algorithm was used to optimize the crystal structure 48. Thevalence electron congurations of the atoms was set as Al 3s23p1,Ge
33、4s24p2,Sn5s25p2,Pb5d106s26p2and the remaining electrons weredetermined as core electrons. The plane wave basis cuto energy wasset as 450eV. The total energy of the atom converges was determined tobe 2.0105eV. The displacement vector of atom, maximum atomicforce and maximum stress were conducted with
34、in 2104nm,5106eV/atom and 0.1GPa, respectively. The k-point for Brillouinzone based on Monkhorst-Pack scheme 49 was all set as 444.3. Results and discussion3.1. Crystal structuresTo distinguish the dierence in the crystal structures of Al-M(M=Ge, Sn and Pb) system, the doped surpercells were optimiz
35、ed andthe optimized results were listed in Table 1. From Table 1, it can beobserved that all the crystal structures, no matter doped with any ele-ments, have changed compared with the lattice parameters of purealuminum, indicating that Al doped by Ge, Sn and Pb shows latticedistortion. The change in
36、 volume (3.10%) of AlePb is bigger thanothers. From periodic table of elements, it is well known that the atomicradius of lead is biggest among the doping elements. Moreover, thealuminum doped with germanium system has minimal distortion,which indicates that the AleGe system will be more stable than
37、 theother two doped systems.3.2. Impurity formation energyIn the practical application, the impurity formation energy is a verysignicant concept. The energy required to mix a kind of material intoanother substance is called as the impurity formation energy, which candescribe the degree of diculty an
38、d the inuence of growth environ-ment to form impurities. Besides, it also can represent the degree of thestability of products 50,51. Generally, the following formula can beapplied to calculate the formation energy of impurities:=E EEE(M) (Al M) (Al) (M)for tot tot totHere, M is Ge, Sn or Pb. Eforis
39、 the nal impurity formation energy;Etot(Al-M) represents the total energy of aluminum doped with ger-manium, tin or lead; Etot(Al) is the total energy of undistorted cell ofaluminum. Etot(M) represents the energy of isolated Ge, Sn or Pb, re-spectively. Therefore, it is easy to calculate the nal imp
40、urity formationenergy and investigate the degree of the stability of systems. The cal-culation results are listed in Table 2.As is known, a negative Efor(M) represents exothermic and the po-sitive one represents endothermic. From the results in Table 2, thepositive results of impurity formation ener
41、gy of AleGe and AleSn showthat the systems would release heat to keep stability when Ge or Sn aredoped into pure Al. Whereas the system of AlePb would absorb heat.The value of Efor(Ge) is the minimum, corresponding to the releasingmaximum heat. According to the view of thermodynamic point, thesystem
42、 of AleGe is the most stable and AlePb which absorbs heat isunstable. The order of stability is AleGe AleSn AlePb. Conse-quently, doping germanium into aluminum is more likely than the othertwo doped systems due to more stable structure. The conclusions fromTable 2 are consistent with the peroration
43、s from Table 1. Furthermore,after investigating the binary alloy phase diagrams of AleGe, AleSnand AlePb, it has been found that Al and Ge take possession of max-imum solid solubility 52. Therefore, the conclusion that germanium isH. Shou et al. Physica B: Condensed Matter 547 (2018) 6117easiest to
44、be doped into aluminum is consistent with the experiments.3.3. Electronic structureIn solid physics, the density of states can describe the energy dis-tribution at each energy level which is able to be occupied by electrons53. The height of DOS shows the amount of states at correspondingenergy level
45、. The DOS which can investigate the width of direct bandgap, bonding electrons and hybrid strength is a signicant method toanalyze the change of electronic structure. To research the eect of Ge,Sn or Pb on Al, the total density of states (TDOS) and the partial densityof states (PDOS) were calculated
46、 and the calculations were listed inFig. 2. The vertical dotted lines on zero energy in Fig. 2 represent theFermi level (EF). To distinguish the inuence more obviously, TDOS andPDOS of central octahedron was investigated, as displayed in Fig. 1 (b).It includes six aluminum atoms and an M (M=Ge, Sn a
47、nd Pb) atom.As shown in Fig. 2, it is explicit that there are some densities ofstates which are greater than zero at the Fermi level. Consequently, alldoping systems exhibit metallic characters. The TDOS at the Fermi levelwhich is called N (EF)ofAleGe, AleSn and AlePb are 2.845 electrons/eV, 2.878 e
48、lectrons/eV and 2.905 electrons/eV, respectively. As is well-known, a lower N (EF) expresses the system is more stable 54. As aresult, AleGe takes possession of the most stable structure, which isidentical to the analysis of crystal structures and the impurity formationenergy. As displayed in Fig. 2
49、, the curves of TDOS for Al-M (M=Ge, Snand Pb) is manly derived from Al-p states, followed by Al-s states andM-p (M=Ge, Sn and Pb) states. The TDOS of Al-M (M=Ge, Sn and Pb)are similar at the energy ranging from9eV to 15eV, which indicatesthat all of these Al-M systems possess similar bonds. At the lower energyregion from 12eV to 9eV, Al-M (M=Ge, Sn and Pb) has anabnormal embossing compared with the TDOS of pure Al. CombiningPDOS of Al and M (M=Ge, Sn and Pb), the peak of TDOS from12eVto 9eV is mainly contributed by Al-s and M-s (M=Ge, Sn and Pb),indicating that doping M (M=Ge, Sn and Pb) in
