First-principles Calculation For Ionicity Of Spinel Ferrites MFe₂O₄?M=Mn,Fe,Co,Ni?

(A)[B]₂O₄ spinel ferrites have many interesting characteristics,whose crystal structure,magnetic properties,catalytic properties,and semiconductor properties relate to the doping of different elements and the content of doping elements.This unique adjustable property can make them have high research value and broad application prospects.The experimental results of a large number of photoelectron spectroscopy in recent years show that not all oxygen ions in oxides including spinel ferrites have the negative divalent state,that is,they contain a portion of negative monovalent oxygen ions besides negative divalent oxygen ions.This is important for a proper understanding of the nature of such materials.The content ratio of negative divalent oxygen ions can be described by the ionicity f.If the valence states of all oxygen ions are negative divalent state,f=1.0,its value decreases with the increase of the content ratio of negative monovalent oxygen ions.In this paper,the first-principles calculation was used to calculate the valence electron density of states?DOS?of spinel ferrites MFe₂O₄?M=Mn,Fe,Co,Ni?.By the method that the DOS curves were integrated,the average number of 3d electrons of each Fe and M ion was calculated.Then the average valences and ionicity values of the materials were obtained.The calculated ionicity values are very close to the experimental results given by X-ray photoelectron spectroscopy.We used the Vienna Ab-initio Simulation Package?VASP?for first-principles calculation.The Kohn-Sham?KS?equation was used to perform spin-polarized quantum mechanical calculations.The key problem is to solve the KS equation.The Perdew-Burke-Ernzerh?PBE?functional used in the calculation is an improved version of the Generalized Gradient Approximation?GGA?.In order to describe the strong correlation between valence electrons in spinel ferrites,Hubbard U parameters were introduced and the PBE+U method was used to calculate the d orbital electrons.And the method of Projector Augmented-Wave?PAW?was used to describe the electron correlation between the inner electron and its valence electron.The main calculation results of this paper are as follows:?1?The DOS of?A?[B]₂O₄ spinel ferrite Fe₃O₄ was calculated by using the methods of PBE+U and hybrid functional.The ionicity values obtained by the two methods are slightly different.Using the PBE+U method,the numbers of the average 3d electron per Fe ion at the?A?and[B]sites were 5.903 and 5.933,respectively;the average valences were 2.097 and2.067,respectively.Assuming that the other 3d electrons and 4s electrons in Fe atoms are all obtained by oxygen atoms,the average valence of O ions is-1.558[=?2.097+2.067�2?/4],and the ionicity of Fe₃O₄ is f=0.779.Using the hybridization functional method,the average 3d electrons per Fe ion at the?A?and[B]sits were 5.780 and 5.818,respectively;the average valences were 2.220 and 2.182,respectively.Assuming that the other 3d electrons and 4s electrons in Fe atoms are all obtained by oxygen atoms,the average valence of O ions is-1.646[=?2.220+2.182�2?/4],and the ionicity of Fe₃O₄ is f=0.823.?2?The DOS of spinel ferrites MFe₂O₄?M=Mn,Co,Ni?was calculated by using the method of PBE+U.For the different distributions of the M cations at the[B]sites,we found that the systems have lowest energy when the magnetic moments of M cations are parallel with those of Fe cations at the[B]sites.The average numbers of 3d electrons of per Fe and M ion were obtained by integrating the DOS curves of cations.Assuming that other 3d electrons and 4s electrons in the transition metal atoms are obtained by oxygen atoms,the average valence of oxygen is calculated,from which the ionicity values of MnFe₂O₄,CoFe₂O₄ and NiFe₂O₄ are obtained.They are 0.786,0.770 and 0.758,respectively.