Cation Site Occupancy Research Articles

Ti- and Ba-rich phlogopitic micas in alkaline basic and upper mantle igneous rocks; stoichiometry, stability, and Fe valence estimation reassessed and rationalised

Ti- and Ba-rich tri-octahedral micas occur in fractionated basic igneous rocks, metasomatized mantle peridotites, metamorphosed pelites/carbonates, and hydrothermally altered mineral deposits. Electron microprobe analyses (EMP), with all iron reported as FeO, were widely used in the 1970/80s to interpret Ti and Ba substitution mechanisms, based on 22 O2– unit cell calculations, implying that cation vacancies occur in octahedral and/or intersheet sites. In 1996 EMP with chemical and physical analyses for ferric and total Fe, H2O, (OH), and element-specific Fe X-ray Absorption Spectroscopy (both K and L-edges) established valence states for Fe and Ti and cation site occupancies, that ∼50 % O replaces (OH) molecules, and that 24 anion cell formulae show the absence of cation vacancies. Cell formula calculation protocol for phlogopitic micas is refined here and results tested against the stoichiometric formula for vacancy-free phlogopite, XIIK2VIMg6IV[Si6Al2]O20(OH)4. Hypothetical sheet silicate compositions, calculated with fixed contents of vacancies linked to particular mixed-valence element substitutions, confirm that reliable unit cell formulae for natural mica solids require that each stoichiometric vacancy must be accounted for. If reliable estimates for ‘excess O’ (denoted WO2−) are assigned to EMP analyses, the proportion of the oxy-mica component in a mica solid solution can be defined. This approach is tested using published analyses for Ti- and Ba-rich biotites from fractionated basic and ultramafic volcanic igneous rocks (oxymica range 2.5–45 %; TiO2 up to 14 %; BaO up to 23 %), upper mantle peridotites (equivalent values 7–18 %; 6 %; 0.7 %), and metasomatised upper mantle (2–37 %; 9 %; 23 %). Enrichments of Ti and Ba in micas are clearly linked to the extra oxygen charge required to neutralise the more highly charged Ba2+ and Ti4+ replacing K+ and Mg2+.Substitution mechanisms involving Ba, Ti, and Fe3+ in ideal phlogopite involve coupled inter-site/inter-valence interactions so both site-ordering and valence-balance between the different cation sites must be accounted for. The cation exchange 2XIIK+ + 4VI(Mg2+ + Fe2+) + 4IVSi4+ ↔ XIIBa2+ + 3VITi4+ + 4(Altotal + Fe3+ + Crtotal)3+ is used here so that valence and site order can be considered together. Compositional variations show well-defined trends towards high-oxymica content and vacancy-free Ti and Ba mica end-members, rather than to oxy-free end-members with essential vacancies. Average compositions for different source rock micas are used to assess compositional trends; molecular WO2− values are refined by relating initial estimates directly to the wt.% TiO2 contents; and refined WO2− and stoichiometrically calculated Fe3+/Fetotal ratios ranging ∼0.1–0.5) are correlated with possible primary magmatic values.

Structure of ZnxFe3−xO4 nanoparticles studied by neutron diffraction and its relation with their response in magnetic hyperthermia experiments

The mixed zinc-ferrite spinel magnetic nanoparticles (MNPs) with the general formula ZnxFe3−xO4 are among the most extensively studied families of Fe oxides due to their interesting and diverse chemical, electronic, and magnetic properties. These systems offer the possibility of surface functionalization and possess high biocompatibility, making them highly attractive for applications in biomedicine, such as magnetic fluid hyperthermia (MFH). The efficiency of the MFH process relies on the magnetic, structural and morphological properties of the MNPs. The substitution with the Zn ion and the cationic distribution, as well as the synthesis process employed, have a direct impact on the final properties of these oxides. Therefore, it is essential to have tools that enable a comprehensive characterization of the system to assess its performance in MFH. In this study, we have synthesized four ZnxFe3−xO4 MNP systems using three different methods: two by thermal decomposition at high temperatures, one by co-precipitation, and another by co-precipitation followed by ball milling. We analyze the effect of these various synthesis processes on the magnetic and crystallographic properties, aiming to correlate them with the response of each system in MFH. Neutron diffraction data are employed to determine the cation site occupation and to investigate the correlation with the synthesis method. MFH measurements were conducted in media of diverse viscosities, revealing different values of specific loss power, thus demonstrating a clear dependence on the synthesis process and Zn content.

Effect of cation site occupancy on the structure and magnetic properties of SrCoxTixFe12–2xO19 thin films

Multiferroic materials have potential applications in multifunctional electronic devices, and M-type hexaferrite with conical spin order is a promising candidate. In this paper, a series of SrCoxTixFe12–2xO19 thin films were prepared by a sol-gel method, and x-dependent structure, cation site occupancy and magnetic properties were investigated to explore the origin of conical spin order in M-type hexaferrite. It was found that the introduction of Co2+ and Ti4+ ions decreases the uniaxial magnetocrystalline anisotropy and breaks the threefold symmetry of the lattice, inducing a conical magnetic structure. Moreover, the appearance temperature of the conical spin order (Tcone) increases first and then decreases with the increase of x, and the largest Tcone of about 324 K is obtained in SrCo1.8Ti1.8Fe8.4O19 thin film. The evolution of magnetization is closely related to the site occupancy of Co2+ and Ti4+ ions, and the net effective substitution ratio of spin-down Fe3+ is positive correlation to the Tcone of SrCoxTixFe12–2xO19 and thus considered to be responsible for the introduction of conical spin order. The results reveal the correlation between the structure, magnetic properties and cation site occupancy, pointing out an effective method to induce conical spin order in M-type hexaferrites.

All-Around Electromagnetic Wave Absorber Based on Ni-Zn Ferrite.

Exploring a convenient, scalable, yet effective broadband electromagnetic wave absorber (EMA) in the gigahertz (GHz) region is of high interest today to quench its expanding demand. Ni-Zn ferrite is considered as a potential EMA; however, their performance study as a scalable effective millimeter-length absorber is still limited. Herein, we investigated EM wave attenuation properties of Ni0.5Zn0.5Fe2O4 (NZF) samples substituting Mn ion in place of Fe3+ as well as Zn2+ within a widely used frequency range of 0.1-9 GHz. Through composition optimization, Ni0.5Zn0.4Mn0.1Fe2O4 (NZM0.1F) EMA demonstrates excellent microwave absorption performance accompanied by simultaneous maximum reflection loss (RL) of -50.2 dB and wide BW of 6.8 GHz (with RL < -10 dB, i.e., attenuation >90%) at an optimum thickness of 6 mm. Moreover, the attenuation constant significantly increases from ∼217 to 301 Np/m with Mn doping. The key contribution arises from magnetic-dielectric properties synergy along with enhanced dielectric and magnetic losses owing to cation chemistry and site occupation in spinel NZF. In addition, porosity is induced in the system by a controlled two-step heat treatment process that promotes total loss with multiple internal reflections of the EM wave. Furthermore, RL is simulated by varying incident EM wave angles for the NZM0.1F sample displaying its angle insensitivity up to 50°. Our results reveal NZM0.1F as a futuristic environment-friendly microwave absorber material that is suitable for practical high-frequency applications.

Optical Information Transmission and Multimode Fluorescence Anticounterfeiting of Ca2-xMgxGe7O16:Mn2.

Multimode emission of Mn2+ for multimode fluorescence anticounterfeiting is achieved by cation site and interstitial occupancy in Ca2-xMgxGe7O16. The rings in Ca2-xMgxGe7O16 have a significant distortion for Mn2+ ions to enter the ring interstitials with a luminescence center at 665 nm, which is supported by XRD refinement results and first-principles calculations. The interstitial Mn2+ ion has good thermal stability with an activation energy of 0.36 eV. Surprisingly, these two luminescence centers, the cation site Mn and the interstitial Mn, have an obvious afterglow, and the disappearing afterglow will reappear by heating or irradiating with the 980 nm laser. The afterglow is significantly enhanced, as MnO2 is used as the manganese source, which is explained in detail by the thermal luminescence spectrum. Finally, Ca2-xMgxGe7O16:Mn2+ fully demonstrates its excellent prospects in fluorescent anticounterfeiting, information encryption, and optical information storage.

Designing Multidimensional and Interconnected Multi-Element Nanostructures by Exsolution-Self-Assembly in a Complex Concentrated Oxide

Complex concentrated oxides (CCOs) are an emerging material class that includes high-entropy oxide (HEOs) and entropy-stabilized oxides (ESOs), whose unprecedented properties stem from disorder-induced distributions in electronic structure and chemistry caused by stabilizing many-cation (typically > 5) solid solutions [1-2]. Integrating these materials into composites with nanoscale tunability will enable tailored (multi)functionality beyond what is possible in a single phase [3]. Here, we demonstrate a novel, highly extensible approach, exsolution self-assembly (ESA), to realize CCO-based nanocomposite thin films with intricate multi-element nanostructures [4]. Using pulsed-laser deposition (PLD), we selectively reduce cations in a 6-cation model perovskite CCO, inducing defect-interaction-driven exsolution and simultaneous self-assembly of metal nanorods and metal-oxide core-shell nanoparticles, depending on film growth conditions. ESA using a CCO precursor enables novel multielement composite morphologies with finely tuned sub-phase chemical composition that are not possible by conventional exsolution or self-assembly independently. By mapping the distribution of distinct sub-phase structure and chemistry with sub-nanoscale electron microscopy and atom probes, we show that Ellingham's model of cation reducibility predicts nanostructure chemical composition while mass transport via extended defects governs local morphology formation. Importantly for various applications, the electronic conductivity of our nanocomposites exceeds 0.1 S/cm at room temperature, with transport correlated to nanostructure formation primarily through B-site cation mixed valency and site occupancy in the CCO matrix.A correlated analysis using aberration-corrected scanning transmission electron microscopy (STEM) imaging, energy dispersive X-ray spectroscopy (EDS), electron energy-loss spectroscopy (EELS), geometric phase analysis (GPA) strain mapping, atom probe tomography (APT) with 3D mass spectrometry, and X-ray photoemission spectroscopy (XPS) was performed to elucidate the fundamental nanostructure formation mechanisms underlying the highly tailorable synthesis approach. We show that the method achieves uniform bulk exsolution with short process time and is manipulated by tuning readily accessible PLD conditions. Detailed characterization resolved the impact of increasing oxygen vacancy concentration and varying cation reducibility on nanostructure self-assembly. For example, metal nanorods grow from the bottom of the thin film to the top surface, with growth restricted by compressive stress exerted by the matrix in the in-plane direction. Metal-oxide core-shell nanoparticles embedded in the matrix form via seed growth effect triggered by metal nanoparticle formation followed by subsequent reduction of additional mobile cations. This work demonstrates a route towards vast morphological tunability and compositional complexity through nanocomposite design of CCO thin films. Given CCOs’ vast combinatorial space, ESA is expected to be highly extensible via application to novel compositions and crystal structures, with the understanding presented here enabling one to take advantage of chemical complexity in a rational way.

Experimental and Theoretical Investigation of Cation Site Occupation and Magnetic Ordering in CoFe2O4

Experimental and Theoretical Investigation of Cation Site Occupation and Magnetic Ordering in CoFe₂O₄

(Mg,Mn,Fe,Co,Ni)O: A rocksalt high-entropy oxide containing divalent Mn and Fe.

High-entropy oxides (HEOs) have aroused growing interest due to fundamental questions relating to their structure formation, phase stability, and the interplay between configurational disorder and physical and chemical properties. Introducing Fe(II) and Mn(II) into a rocksalt HEO is considered challenging, as theoretical analysis suggests that they are unstable in this structure under ambient conditions. Here, we develop a bottom-up method for synthesizing Mn- and Fe-containing rocksalt HEO (FeO-HEO). We present a comprehensive investigation of its crystal structure and the random cation-site occupancy. We show the improved structural robustness of this FeO-HEO and verify the viability of an oxygen sublattice as a buffer layer. Compositional analysis reveals the valence and spin state of the iron species. We further report the antiferromagnetic order of this FeO-HEO below the transition temperature ~218 K and predict the conditions of phase stability of Mn- and Fe-containing HEOs. Our results provide fresh insights into the design and property tailoring of emerging classes of HEOs.

Synthesis, densification, and cation inversion in high entropy (Co,Cu,Mg,Ni,Zn)Al2O4 spinel

ABSTRACT The synthesis, densification behavior, and crystallographic site occupancy were investigated for four different spinel-based ceramics, including a high-entropy spinel (Co0.2Cu0.2Mg0.2Ni0.2 Zn0.2)Al2O4. Each composition was reacted to form a single phase, but analysis of X-ray diffraction patterns revealed differences in cation site occupancy with the high-entropy spinel being nearly fully normal. Densification behavior was investigated and showed that fully dense ceramics could be produced by hot pressing at temperatures as low as 1375°C for all compositions. Vickers’ hardness values were at least 10 GPa for all compositions. The cations present in the high-entropy spinel appear to have a stabilizing effect that led to nearly normal site occupancy compared to full cation inversion behavior of nickel aluminate spinel. This is the first report that compares cation site occupancy of a high-entropy spinel to conventional spinel ceramics.

Nanoscale chemical and structural investigation of solid solution polyelemental transition metal oxide nanoparticles

Although it has been shown that configurational entropy can improve the structural stability in transition metal oxides (TMOs), little is known about the oxidation state of transition metals under random mixing of alloys. Such information is essential in understanding the chemical reactivity and properties of TMOs stabilized by configurational entropy. Herein, utilizing electron energy loss spectroscopy (EELS) technique in an aberration-corrected scanning transmission electron microscope (STEM), we systematically studied the oxidation state of binary (Mn,Fe)3O4, ternary (Mn, Fe, Ni)3O4, and quinary (Mn, Fe, Ni, Cu, Zn)3O4 solid solution polyelemental transition metal oxides (SSP-TMOs) nanoparticles. Our findings show that the random mixing of multiple elements in the form of solid solution phase not only promotes the entropy stabilization but also results in stable oxidation state in transition metals spanning from binary to quinary transition metal oxide nanoparticles.

Stoichiometry driven tuning of physical properties in epitaxial Fe3-xCrxO4 thin films

Tuning magnetic and electronic transport properties in spinel oxides requires a faithful description between chemical composition and cation site-occupation. Here this challenge is addressed using Fe3-xCrxO4 thin films grown by oxygen-assisted molecular-beam epitaxy within a wide range of composition (0.0 ≤ x ≤ 1.2). Spectroscopic measurements (e.g., X-ray magnetic circular dichroism), refined by theoretical simulations (e.g., crystal field multiplet), are performed to establish a quantitative link between chromium content, Fe2+/Fe3+ site-occupation and macroscopic physical properties of the layers. It is found that Fe3-xCrxO4 thin films (i) delay the transition from inverse to normal spinel configuration with increasing chromium content and (ii) promote collinear spin structure, at odds with bulk material. As a result, strong antiferromagnetic interactions are preserved between spins in tetrahedral and octahedral spinel sublattices, so that chromium-rich thin films exhibit Curie temperatures above room temperature and higher magnetization. Electron hopping is also favored by this singular cation distribution and electronic band gap is smaller than expected for these thin films. The cation site-occupation is therefore a key feature to consider for applications of Fe3-xCrxO4 thin films in spintronics and photocatalysis, as it enables manipulation of magnetic properties (Curie temperature and magnetization) and band gap engineering.

Relation between cation distribution and chemical bonds in spinel NiFe2O4

In spinel oxides, the cation distribution plays an important role in determining their technologically important properties. Herein computational predictions based on the first principles calculations are presented to elucidate the relation between cation distribution and chemical bonds in spinel NiFe 2 O 4 . The variation of physical properties (such as system energy, lattice parameter, and atomic magnetic moment) with respect to the cation distribution (i.e., degree of inversion) in spinel NiFe 2 O 4 oxide is discussed. This study further reveals that the energy of spinel NiFe 2 O 4 oxide is linearly proportional to the number of different types of cation-oxygen-cation bonds in the spinel structure. The equilibrium degree of inversion in spinel NiFe 2 O 4 at elevated temperatures and the transformation from an ordered to disordered cation distribution in inverse spinel NiFe 2 O 4 are predicted and found to be driven by competition between bond enthalpy and entropy of cation site occupancy.

Investigation of multiferroic properties of dysprosium substituted bismuth ferrite (Bi1-xDyxFeO3) prepared by auto combustion technique

A simple and inexpensive auto combustion procedure was used to create the Bi1-xDyxFeO3 (x=0.0, 0.015, 0.03, 0.045, 0.060) multiferroics samples. In bismuth ferrite, the average crystallite size increased with growing Dy3+ concentration in BFO, revealing a rhombohedral distorted perovskite structure of space group R3c. During morphological analyses of the produced samples, a spherical structure with little aggregation was found. When Dy3+ is substituted at the B-site, the Raman modes widen and the cation site occupancy changes even more. The frequency-dependent dielectric properties (εr, tanδ), electric conductivity (ac), impedance (Z), and electric modulus (M' and M′′) of the samples were assessed using an impedance analyzer at frequencies between 20 Hz and 20 MHz. All samples had the maximum dielectric constant, which was discovered at a relatively low frequency. The highest value of impedance was found at low frequency and it lowers with increasing frequency as a result of the contributions from the grain and grain boundary. It is discovered that the samples' ac conductivity is frequency-dependent and changes depending on how much Dy3+ is doped into the BFO.

Mechanical Activation and Cation Site Disorder in MgAl2O4.

The synthesis and crystallographic site occupancy were investigated for MgAl2O4 with and without mechanical activation of the precursor powders. Heating to 1200 °C or higher resulted in the formation of a single spinel phase regardless of whether the powders were mechanically activated or not. Neutron diffraction analysis was used to determine cation site occupancy and revealed that mechanical activation resulted in a lower degree of cation site inversion compared to the nonactivated materials, which indicated that the powders were closer to thermodynamic equilibrium. This is the first study to characterize the effects of mechanical activation on crystallographic site occupancy in magnesium aluminate spinel using neutron diffraction.

Structural, Degree of Inversion, and Magneton Number Studies on Fe3+‐Substituted MAl2O4 (M = Ni, Cu, Zn) Spinel Powders: The Evidence for Local Site Exchange of Cation and Magnetization Increment

Nanocrystalline Fe‐substituted metal aluminates, MFe x Al2−x O4 powders (M = Ni2+, Cu2+, and Zn2+) with different Fe3+ ion concentrations (x = 0, 0.5, 1.0, 1.5, and 2), are successfully synthesized by the sol–gel auto combustion method. Characterization of the calcined samples is carried out using X‐ray diffraction (XRD), synchrotron Extended X‐ray Absorption Fine Structure (EXAFS), and vibrating sample magnetometer (VSM) measurements. The XRD results confirm the formation of single‐phase spinel structure with Fd‐3m space group of all samples. The EXAFS spectra illustrate the main translocation trends in the trivalent and divalent ions between the tetrahedral and octahedral sublattices. When XRD Rietveld refinement, Williamson–Hall analysis, and EXAFS curve‐fitting analysis are applied to the data, the precise structural parameters, degree of inversion, and cation site occupancy are obtained. Furthermore, the Fe‐substituted samples show intense increase in the saturation magnetization with the increasing of Fe3+ ion concentrations. This occurrence is due to the rise in the net magnetic moment of the modified aluminates which took place as the distribution of the cations within the structure underwent changes. It is possible to explain the variation observed in the magneton number in the context of Fe3+ content through the application of Néel's collinear spin ordering model.

Specific features of synthesis and luminescence for lithium–aluminum spinels doped with manganese ions

Ceramic samples of lithium aluminates doped with manganese ions have been synthesized by a solid-state reaction method. The ceramics sintered at temperatures of 1000, 1100, 1200 or 1300 °C for 4 h in air are identified as LiAl5O8 compounds belonging to a spinel-like crystal structure with the P4132 space group. Nonetheless, ceramic compositions obtained by annealing at temperatures 1000, 1100 or 1200 °C have larger lattice parameters than that of a LiAl5O8 single crystal and are considered as metastable LiAl5O8 phases having partial disorder for the occupation of two inequivalent octahedral sites by Li+ and Al3+ ions, i.e. possessing Li - Al inversion. Such Mn doped disordered compositions show typical Mn4+ red luminescence with an emission peak at ∼662 nm. The charge compensation of Mn4+ replacing Al3+ ions in octahedral sites is achieved by Li+ ions entering some adjacent Al3+ sites due to inversion. On the other hand, annealing at a higher temperature (1300 °C) or prolonged (170 h) annealing at a lower temperature (1100 °C) leads to complete ordering of Li+ and Al3+ in ratio 1:3 at different octahedral sites in the LiAl5O8 structure in which Mn4+ luminescence is not observed due to the lack of a charge compensation mechanism. Doping Mn ions in such an ordered structure are realized in di- and trivalent states causing green and far-red luminescence, respectively. Additional annealing of the mixtures of the Mn-doped ordered LiAl5O8 composition and Li2CO3 at 1300 °C in air results in the production of phosphors which again show intense Mn4+ red luminescence and have the spinel-like crystal structure with the Fd3‾m space group due to random occupation of cationic sites by Li+ and Al3+ ions.

Cation distribution and site occupancy of nanoscale Cu2+-Er3+ substituted strontium hexaferrites via Raman and Mössbauer spectroscopy

In this research, we report on the cation distribution and site occupancy of Cu2+ and Er3+ ions in the hexagonal lattice of M-type strontium hexagonal ferrites with chemical composition Sr1-xCuxFe12-yEryO19 (x=0.0, 0.1, 0.2, and y=0.0, 0.4, 0.5) fabricated using sol-gel autocombustion technique. Raman analysis of the synthesized samples was conducted based on the group theory analysis of hexagonal ferrites based on the D6h symmetry. The Raman active modes based on the mode assignment and symmetry and were typical of M-type hexaferrite. Mössbauer spectroscopy shows the density of the s electron cloud at the 12k, 4f2, and 4f1 is affected by Cu2+-Er3+ substitution which indicate that all the five sexets originate from Fe3+ ion with high spin and that Er3+ ion (with d10 orbitals) occupies Fe3+ ion position at 12k, 4f2, 2a, and 2b sites in different proportion based on the Ligand theory.

Enhanced multiferroics properties of strontium substituted bismuth ferrite prepared by auto combustion method

A low cost and simple auto combustion method was used to prepare the Bi1-xSrxFeO3 (x=0.0, 0.04, 0.08, 0.12, 0.16) multiferroics samples. X-ray diffraction patterns confirms the integration of BFO pure phase nanoparticles with a perovskite structure of ABO3 type having space group R3c. Spherical structure with little agglomeration was observed during the morphological studies of the prepared samples. Sr2+ substituted at the A-site produces expansion in Raman modes and increased variations in cation site occupancy. Impedance analyzer was used to examine the frequency dependent dielectric parameters (ε´, tanδ), electric conductivity (σac), impedance (Z) and electric modulus (Mʹ and M″) of the samples in frequency between 20 Hz and 20 MHz). Maximum value of dielectric constant was observed at very low frequency for x=0.0 samples and it decreases by increasing concentration. Resonance peak was observed in tangent loss for high content of strontium. Maximum value of Impedance was observed at low frequency and it decreases by increasing frequency which is due to the grain and grain boundary contributions. It is observed that ac conductivity of the samples is found to be frequency dependent and it varies with doping of Sr in BFO. Improved polarization was examined in P-E loop of Sr doped BFO nanoparticles.

Cubic to Tetragonal Phase Transition in CuFe₂O₄2. Experimental Details Nanoparticles

We report the influence of annealing temperature (600 °C-1000 °C) on structure, crystallographic phase transition, morphology, ibrational, and magnetic properties of CuFe₂O₄ nanoparticles synthesized by a facile solgel auto combustion technique. The as-prepared and 600 °C air annealed samples show cubic spinel structure, secondary phases of α-Fe₂O₃, and CuO (minute reflections), resulting in inferior magnetic properties. Further, the 800 °C air annealed sample discloses a structural phase transition from cubic to tetragonal phase and minute α-Fe₂O₃ secondary phase. This sample exhibits the highest coercivity (HSUBC/SUB) 1221.4 Oe and squareness ratio (MSUBR/SUB/MSUB20kOe/SUB) = 0.56. On the other hand, the sample annealed at 1000 °C in air reveals superior magnetic properties (magnetization = 24.5 emu/g & HSUBC/SUB = 484.7 Oe) compared to all other samples. The revolution of magnetic properties with annealing temperature originates from the morphology, cubic to a tetragonal structural phase transition, c/a 1, and cation site occupation induced by Jahn–Teller distortion.

Breakdown of the Small-Polaron Hopping Model in Higher-Order Spinels.

The small-polaron hopping model has been used for six decades to rationalize electronic charge transport in oxides. The model was developed for binary oxides, and, despite its significance, its accuracy has not been rigorously tested for higher-order oxides. Here, the small-polaron transport model is tested by using a spinel system with mixed cation oxidation states (Mnx Fe3- x O4 ). Using molecular-beam epitaxy (MBE), a series of single crystal Mnx Fe3- x O4 thin films with controlled stoichiometry, 0 ≤ x≤ 2.3, and lattice strain are grown, and the cation site-occupation is determined through X-ray emission spectroscopy (XES). Density functional theory + U analysis shows that charge transport occurs only between like-cations (Fe/Fe or Mn/Mn). The site-occupation data and percolation models show that there are limited stoichiometric ranges for transport along Fe and Mn pathways. Furthermore, due to asymmetric hopping barriers and formation energies, the polaron is energetically preferred to the polaron, resulting in an asymmetric contribution of Mn/Mn pathways. All of these findings are not contained in the conventional small-polaron hopping model, highlighting its inadequacy. To correct the model, new parameters in the nearest-neighbor hopping equation are introduced to account for percolation, cross-hopping, and polaron-distribution, and it is found that a near-perfect correlation can be made between experiment and theory for the electronic conductivity.