The Mechanisms of Nickel-Iron Spinel Phase Nucleation in Aquous Solutions: Crystal Quasichemical Approach

The phenomenological model of nikel-iron spinel nucleation with spinel structure based on the partial charge theory and analysis of hydrolysis and polycondensation processes at the interaction of Fe-, Feand Nihydroxocomplexes at different pH values of reaction medium was proposed. UV-vis optical spectroscopy was used for verification of the obtained results about the regularities of hydroxocomplexes formation. Crystal quasichemistry approach was applied for nucleation of nikel-iron spinel under the conditions of predomination of different defect types in NixFe3-xO4-δ (δ is oxygen non-stoichiometry) spinel lattice. The analysis of changes in electrical conductivity and lattice parameter of defect nickel-iron spinel as a function of Ni atomic concentration was done for different values of δ parameter.


Introduction
Ultrafine ferrites with spinel structure are attractive materials due to interesting magnetic, electrical, catalityc and elelctrochemical properties. Nickel-iron spinel has attractive wide application field because of its fascinating electromagnetic characteristics which allow using of these materials as magnetic storage systems [1], catalysts [2], photocatalysts [3], materials with negative differential resistance [4], gas sensors [5], in drug delivery [6] as MRT imaging agent [7], electrode materials. The possibility of successful application of ferrite nanopowder is determined by the magnetic and electrical properties that depend on the crystal ordering and average particle size. There are several synthesis approach of ultrafine nickel spinel. Ceramic, sol-gel and self-combustion syntheses [8][9][10] are the most widespead ones. The conrtol and prognosis of crystal structure formation at a stage of oxide phase nucleation is an important task which allows obtaining of ultrafine spinel materials with complex predicted properties.

I. NiFe 2 O 4 spinel nucleation: protolysis and polycondensation
The nucleation of the condensed phases from the solution of metal (M) salts is based on the procesess of hydrolysis and polycondensation of metal hydrocomplexes and is described by the terms of nucleophilic substitution as: -M-OR + XOH→-M-OX + ROH, where R is a radical, X = H for protolysis and X = M for condensation processes. Partial Charge Model (PCM) [11] allows decribing the hydrolization of metal ions and finding out the regularities of olation and oxolation interactions between hydrocomlpexes which determine the nuclaetion of new phases. The theory is based on the Sanderson principle of electronegativity equalization. The hydrolysis of metal ions in an aqueous medium involves the formation of [M(OH 2)N ] z+ complexes, where N is a coordination number (for transition metals the formation of octahedrally coordinated ionic complexes is typical, N = 6), z is an oxidation degree. Iron chloride hydrolysis in acidic medium leads to the formation of chlorine-containing complexes [ Fe (III) 6 ] 2+ mononuclear complexes are predominant [13]. Redistribution of charges between the cation and the ligands occurs with the formation of σbonds of M-OH 2 , which leads to the redistribution of the electron density from the binding 3a l molecular orbital of the coordinated water molecules to the unburned cation orbitals. As a result O-H bond in the coordinated water molecules is weakened and the protolysis occures according to the scheme: The electronegativity ( χ p ) of the obtained hydrocomplex is determined by the type of central cation and the hydrolysis degree ( h ). The theory of partial charge allows calculating the electronegativity of the complex, which allows determining the degree of hydrolysis and defining the most possible nucleation mechanism of the condensed phase [14]. The pH of the reaction medium is one of the key factors to determine the hydrolysis degree. The electronegativity of water molecules at a 25 °C is a function of pH according to the equation: χ w =2.732-0.035⋅pH. The protolysis degree h of [M(OH 2 ) N ] z+ species at a certain pH value can be determined from the condition of equality of the total charge +(z-h) and the sum of charges of all the components of the complex as: The electronegativity values in Allred-Rochow symbols for oxygen, hydrogen, iron and nickel are 3.50, 2.10, 1.72 and 1.80, respectively [11].
The calculated h(pH) dependences for the hydrolysis of Fe 3+ , Fe 2+ and Ni 2+ cations under the condition of octahedrally coordinated hydrocomplexes formation (Fig. 1).
The transmission spectra of 0.0001 M iron nitrate aqueous solution were analyzed depending on the pH value which was determined by ammonia solution adding (Fig. 2, a).
Three type of olation reactions are possible:  An additional asymmetry of the tetramer complex formed by both Fe 3+ and Fe 2+ ions stimulates the olation combining of two dimers [Fe (III) Fe (II) (ОН) 3 (OH 2 ) 7 ] +2 ( Fig. 3, a, b) with the possible olation as a next step (Fig. 3, c).
Spectroscopic studies demonstrate changes in the transmittance of the iron nitrate solution at pH value of about 11.3 that corresponds to the olation-oxolation interactions between [ Fe (III) 2 Fe (II) 2 (ОН) 6 (OH 2 ) 10 ] +4 tetramers (Fig. 3) At the next stage the oxolation processes 10 ] +4 complexes formation (Fig. 3,c) The olation-oxolation reaction and [Fe (III) 2 Fe (II) 2 (ОН) 6 (OH 2 ) 10 ] 4+ complexes formation took place with the nucleation of the oxide phase (Fig. 5   The Mechanisms of Nickel-Iron Spinel Phase Nucleation… of a coagulation. The magnetic ordering has an important role in the processes of clusters organizing at the nucleation stage. Structures of this type were predicted theoretically in [16]. Similar approach was used for the case of the formation and interaction of nickel-based hydrocomplexes. Changes in the transmission spectra of 0.0001 M nickel nitrate aqueous solution at increasing of pH were analyzed (Fig. 6). A redistribution of a transmittance between the spectral regions in the vicinity of 390 nm and 360 nm was found at pH value in a range of 10.75-10.95 (Fig. 6, a). According to PCM the formation of [Ni (II) (OH)(OH 2 ) 5 ] + hydrocomplexes occurs at pH values of about 10.0-10.5 (Fig. 1) At the same time, an increase in the absorption coefficient in the vicinity of 1040 nm was observed, that may be the evidence of the possible formation of low-dimensional polymeric complexes like [Ni 2 (OH) 2 (OH 2 ) 8 ] 0 (Fig. 6, b).
Nickel ferrite nucleation takes place according to a scheme similar to the formation of magnetite with the Ni 2+ -based hydrocomplexes instead Fe 2+ . Spectrophotometric studies of the mixture of 0.0001 M iron and nickel nitrate aqueous solutions (Fe:Ni molar ratio is 2:1) were carried out at different pH values. The transmission spectra at pH > 10.28 were observed (Fig. 7).  10 ] +4 complexes begins with the next olation and oxolation (Fig. 5). These processes leads to complex oxyhydroxydes spieces formation which are the centers of spinel phase nucleation.

II. Crystal-quasichemical analysis of nikel iron spinel nucleation and properties
The precipitation synthesis from mixture of nickel and both (II) and (III) iron aqueous solutions was performed. Ammonium hydroxide solution was used for are double-and triple-charged vacancies, respectively and "/", "•" and "x" symbols denote negative, positive and neutral charges, respectively. According to PCM theory the olation-oxolation processes with participation of Fe 3+ -based hydrocomplexes occur at relatively low рН value of reaction medium. The increasing of pH value leads to Fe 2+ -and Ni 2+ -based complexes formation and the nucleation of nickel-ion spinel. Stoichiometric spinel structure is a result of superposition of these clusters: The concentration of oxygen vacancies for NiFe 2 O 4 nanoparticles obtained in aqueous medium is up to about 0.10 per formula unit [21]. The Fe 2+ content decreases drastically with the increasing of Ni 2+ concentration and at different values of oxygen non-stoichiometry when Fe 3+ content doesn't depend on the presence of Ni 2+ ions (Fig. 8, a,b). At the same time the presence of the oxygen excess leads to non-linear growth of cation vacancies concentration located in octahedral site. The next analysis can be done applying basic crystal quasichemistry approaches at δ > 0 and δ < 0: the dominant mechanism of electrical conductivity of bulk NiFe 2 O 4 [23]. The increasing of the specific electrical conductivity of Ni x Fe 3-x O 4 spinel at the increase in Ni 2+ ions content was observed experimentally in [24].
The changes in Fe 2+ ions content in B-sites of Ni x Fe 3-x O 4-δ spinel at increasing of Ni 2+ concetration corelate with specific electrical conductivity dependency (Fig. 9), but the oxygen non-stoichiometry can cause the additional influence on the electrical characteristics of the material. The analysis of an electron percolation was done in the crystal-quasichemical terms: The crystallochemical approach allows us to establish the relationship between the cations distribution and the geometry of crystal lattice. The semiempirical correlations between the parameters of the nickel ferrite lattice and the crystallographic parameters (the ratio of nickel cations to iron cations, the availability of vacancies in cationic and anionic sublattices, and deviation from oxygen stoichiometry) can be calculated.
Each anion in the crystal spinel lattice is surrounded by one tetrahedrically coordinated and three octahedronically coordinated cations. The displacement of one of the anions determines the change in the coordinates of the other atoms. The change in bondlengths causes the interlattice stresses. The mimimization of a resulting energy of an elastic deformation determines the equilibrium value of the lattice parameter. The correlation between ion radii of the lattice component and interatomic distances is caused by close-packing character of a spinel structure. There is a number of semiempirical models that calculate the lattice parameter as a function of distances between anion and cation, type, coordination number and ions oxidation degree [25]. The development of [26] approach was implemented in our case which is based on usіng the  3  23  2  22  2  21   3  3  23  2  2  22  2  2  21  3  3  13  2  12  2  11   3  3  13  2  2  12  2  2  11  3 [27] (Fig. 10) It can be assumed that the case of negative values of oxygen non-stoichiometry δ with the formation of cation vacancies in the B-sites are the most probable at relatively low (0.0-0.4 at per formula unit) concentration of Ni 2+ ions for Ni x Fe 3-x O 4-δ spinel structure. For the same case the increasing of substitution degree leads to changes in the predominant defect type wtih the anionic non-stoichiometry predomination.