Chemical bond in Fe_xTiSe₂ intercalation compounds: dramatic influence of Fe concentration

Abstract

The introduction of 3d transition metals into the van der Waals gaps of titanium dichalcogenides with layered structures gives rise to an interesting family of intercalation compounds, the physical properties of which differ substantially from those of the host compound due to “host–guest” and “guest–guest” interactions, resulting in ordering of the intercalated metal. Fe_xTiSe₂ is one of the most intriguing of such intercalation compounds due to its special electronic and magnetic properties. In this paper, the influence of the iron concentration on the crystal structure, electronic structure and chemical bond in the Fe_xTiSe₂ intercalation compounds is studied across a wide composition range (0 ≤ x ≤ 0.50) within the homogeneous region of the system. Photoelectron, resonance photoelectron and X-ray absorption spectroscopy methods were combined with thermodynamic electromotive force (EMF) measurements for the Li|Li⁺|Fe_xTiSe₂ cell in order to monitor the Fermi energy concentration dependence. The electronic structure changed substantially as the Fe content increased. A proposed model of the Fe_xTiSe₂ electronic structure transformation implies that iron atoms form Ti–Fe–Ti bonds at x < 0.40, but that Fe–Fe bonds prevail at x ≥ 0.40 when nanoscale iron chains appear in the van der Waals gap.

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1. Introduction

Transition metal dichalcogenides with layered structures have been the subject of numerous investigations for decades due to their scientific interest and potential for technological utilisation.^1–4 This interest is related to their extraordinary ability to intercalate a wide range of atomic and molecular species with significant modifications of their electronic structure and minimal changes in their crystal structure.^1–5 By intercalation of various guest species into the van der Waals gaps, these materials exhibit a variety of novel and exotic properties, such as changes in the stability of the charge-density-wave (CDW) state,^6–8 thermoelectricity,^9,10 superconductivity^11–13 and magnetism.^14–16 Therefore, these materials find many promising technological applications in battery systems,^17,18 solar cells,^19,20 cooling detectors and other electronic devices.^9,21

Titanium dichalcogenides (TiX₂, X = S, Se and Te) are isomorphous members of a group of compounds that crystallise in a characteristic 1T-CdI₂ layered structure (P3̄m1 space group). Their structure consists of stacked composite layers with each layer consisting of two sheets of hexagonally close-packed chalcogen atoms that sandwich a sheet of metal atoms.^1–5,22 Because the primary valence is saturated within the sandwich X–Ti–X structure, the adjacent layers are only held together by relatively weak forces due to overlap of the chalcogen Xp_z orbitals of atoms from neighbouring layers (typically for historical reasons, they are referred to as van der Waals forces).^23,24

TiSe₂ is of a particular interest among the layered transition metal dichalcogenides. The electronic phase transition found in this material is usually interpreted as a transition to the excitonic insulator state predicted by Keldysh and Kopaev.²⁵ At the same time, a number of studies have revealed that a relatively weak external pressure²⁶ and copper intercalation⁸ suppresses the insulating state and leads to the formation of a superconducting state. This suggests the possibility of the excitonic superconductivity scenario suggested by Ginzburg.²⁷ If it were possible to distort the excitonic insulator state in such a way as to convert it into a superconducting state, this would constitute a fundamental breakthrough in physics.

One of the problems related to this phenomenon is if the low-temperature phase TiSe₂ really is the excitonic insulator. On the one hand, the precision spectral experiments support this possibility;²⁸ on the other hand, the strange effect represented by the reappearance of the CDW state in the heavy intercalated materials is against this possibility.^6,29 Indeed, the intercalation associated with electron doping should lead to a destabilisation of excitons and destruction of the excitonic insulator state. This is shown in many theoretical and experimental studies (see e.g. ref. 7, 30 and 31). However, it remains fundamentally unclear how to associate such behaviour with the appearance of CDW at high intercalant concentrations. The only way to clarify this phenomenon seems to be to compare the electronic structure of TiSe₂ with varying degrees of intercalation.

It is worth noting that this experiment is not one that admits an easy solution. Single crystals of these materials can be easily cleaved along a plane of the interlayer gap (van der Waals gap) thus forming an atomic surface plane in the case of non-intercalated material and forming a surface coated with a monolayer of intercalated metal in the case of intercalated compound. The intercalant concentration on the surface is lower than its bulk concentration since a proportion of the intercalant atoms is always removed together with a part of the crystal under the cleavage procedure. Therefore, the surface is actually a monolayer of another material covering the basal plane of the crystal. This opens up the opportunity of constructing two-dimensional quantum wells by simple cleavage of the crystal; however, this direct construction requires knowledge of the electronic structure of both the surface monolayer and the bulk material. The high surface sensitivity provided by spectroscopic methods allows information to be derived primarily concerning the surface state of the material. Nevertheless, such experimental data are usually extended to the bulk material, which differs from the surface in terms of its chemical composition and crystal structure. At the same time, phases with intercalant ordering within the interlayer gap can be observed depending on the bulk intercalant concentration. This should lead to the reconstruction of the Brillouin zone and change the geometry of the Fermi surface. However, the problem remains that conventional methods of investigating electronic structure based on photoelectron spectroscopy are not capable of detecting these changes. Thus, no currently known ARPES studies (e.g. ref. 32 and 33 for the M_xTiS₂ materials, or ref. 34 and 35 for M_xTiTe₂) show differences in the electronic structure of the intercalation compounds, with or without ordering: experimental spectral data on the electronic structure of the transition metal dichalcogenides intercalation compounds relate only to the surface layer upon which the intercalated metal is disordered.

The physical properties of the M_xTiX₂ (M = 3d transition metal, x ≤ 1) intercalation compounds differ from those of the host TiX₂ matrix due to “host–guest” interactions^1,36 and “guest–guest” interactions.³⁷ For example, various magnetic states were observed in 3d transition metal intercalates with M = V, Cr, Mn, Fe, Co and Ni.^36,38 The intercalated M atoms partially occupy octahedral interstices between the layers. At a high concentration of intercalated guest atoms (x ≥ 0.25), M_xTiX₂ exhibits various types of M and vacancy ordering as well as superstructure formation.^5,39,40 The intercalation of 3d transition metal atoms leads to the hybridisation of their 3d states with the band states of the TiX₂ matrix.^36,38,41 The degree of participation of the 3d states in the formation of new molecular orbitals depends on both M and TiX₂ type. In the M_xTiX₂ intercalation compounds, the formation of these hybridised states is accompanied by a distortion of the crystal lattice and a change in the electrical conductivity and effective magnetic moment.^36,42

Fe_xTiSe₂ is one of the most intriguing intercalation compounds due to its electronic and magnetic properties. Both polycrystalline samples and single crystals have been used to study the crystal structure as well as transport and magnetic properties of iron-intercalated titanium diselenide.^39,43–49 The crystal structure and phase composition of Fe_xTiSe₂ has been investigated over a wide concentration range (i.e., 0 ≤ x ≤ 0.66).^43–45 The iron solubility limit strongly depends on the annealing temperature and is equal to x = 0.66 at 900 °C.⁴³ Metallic iron or iron compounds can appear as a separate phase in the Fe_xTiSe₂ samples above the limiting Fe concentration. The magnetic properties of this compound are highly dependent on the Fe concentration.^{39,44,46–49} Only a few studies have been devoted to investigating the electric properties and electronic structure of these materials.^6,7,46,48 Electron localisation in the form of CDW occurs at an iron concentration up to x = 0.07, which corresponds to the percolation threshold for a triangle lattice; and Fe_xTiSe₂ becomes a metal as the iron concentration increases.⁴⁶ A resistivity anomaly corresponding to a CDW state was observed for iron-intercalated titanium diselenide with x = 0.5.^6,48 Only one study⁷ has focused on studying the CDW state in TiSe₂, Fe_0.05TiSe₂ and Fe_0.14TiSe₂. The electronic structures of the other Fe_xTiSe₂ intercalates (including the 0.25 < x < 0.5 concentration range with magnetic ordering in the Fe sublattice) remains unexplored. One more insufficiently investigated question involves the chemical bond in Fe_xTiSe₂, and this problem is closely related to the electronic structure of this intercalation compound. It is important to note that the effect of the Fe concentration on the chemical bond in the Fe_xTiSe₂ intercalation compound has not been previously addressed in the literature.

The goal of the current study was to investigate the influence of iron concentration on the crystal and electronic structure, as well as chemical bonds, in the Fe_xTiSe₂ intercalation compound over a wide range of concentrations (0 ≤ x ≤ 0.50), and to compare this data with the CDW stability regions. Photoelectron, resonance photoelectron and X-ray absorption spectroscopy were combined with thermodynamic electromotive force (EMF) studies to monitor the Fermi energy concentration dependence. For the first time, it was possible to determine changes in Ti 3d- and Fe 2p- states (which accompany an ordering of intercalated iron in the interlayer space) using resonant photoelectron spectroscopy. These changes were due to the difference in the coordination of titanium with iron arising from iron ordering. The difference in Fe 2p spectra was associated with the state of the iron atom, i.e., whether it was isolated or involved in a chain.

2. Experimental

2.1. Synthesis of intercalation compounds

Polycrystalline TiSe₂, which was used as a starting material, was prepared from the following elements: titanium (after iodine purification, 99.96%) and selenium (OSCh19-5, 99.999%) (St. Petersburg Krasnij Khymik Plant). The appropriate amounts of titanium and a small excess of chalcogen (∼3 wt%) were sintered at a temperature of 800 °C for 10–12 days in sealed quartz ampoules evacuated to 10⁻⁵ torr. Then, the ampoules were cooled and opened. The samples were ground into powder, pressed, placed into quartz ampoules along with the same excess of selenium (for homogenising and saturation by chalcogen), evacuated to 10⁻⁵ torr and annealed again for 10–12 days at 700 °C (TiSe₂). After cooling, the ampoules were opened and the samples were ground into a powder. The homogeneity and phase uniformity of the TiSe₂ product were determined using X-ray analysis (ICDD-ICPDS card no. 30-1383). The obtained TiSe₂ powder and carbonyl iron (St. Petersburg Krasnij Khymik Plant) that was reduced in a hydrogen stream were used as starting materials for the synthesis of the Fe_xTiSe₂ polycrystalline samples (i.e., x = 0.05 to 0.50). The precise stoichiometric amounts of the starting materials were placed in a quartz ampoule that was evacuated to 10⁻⁵ torr. The reaction mixture was annealed at a temperature of 800 °C for 10–12 days. After cooling, the ampoule was opened and the sample was ground into a powder.

2.2. X-ray diffraction

The structure and phase purity of the powder Fe_xTiSe₂ samples were determined using X-ray powder diffraction (XRD) on a Shimadzu XRD 7000 Maxima diffractometer (Cu Kα₁ radiation, graphite monochromator, 2θ = 5–90°). Full profile analysis was performed using the General Structure Analysis System (GSAS) software package.⁵⁰

2.3. Single crystal preparation

Single crystals of Fe_xTiSe₂ in the shape of thin plates with dimensions of approximately 2 × 2 × 0.05 mm³ were grown from the polycrystalline products using a gas transport technique with iodine as the carrier gas. The chemical composition of the single crystal samples was determined by energy dispersive X-ray analysis on a JEOL-733 spectrometer.

2.4. X-ray spectroscopy

The X-ray absorption spectra (XAS) as well as the photoelectron spectra in non-resonant (XPS) and resonant (ResPES) modes were obtained on the CiPo beamline⁵¹ at the ELETTRA synchrotron facility (Trieste, Italy). All of the samples were cleaved in situ in a vacuum chamber at a pressure of at least 1 × 10⁻⁹ torr. The purity of the surface was confirmed by the absence of oxygen and carbon peaks in the survey spectra. The angle between the incident radiation and normal to the basal plane ([001] direction) was 60°. The direction of the analyser axis coincided with that of the c-axis of the sample. Both the c-axis of the sample and the polarisation plane of the incident X-ray radiation lay in the horizontal plane. The total resolution was approximately 0.2 eV. The valence band (VB) spectra were calibrated using the Au VB spectrum on the Fermi edge. Ti and Fe L_2.3 XAS were performed in total yield mode and calibrated using the corresponding absorption spectra of the pure metals. The core level spectra were calibrated using the Au 4f_7/2 signal from a clean gold foil (E_B (4f_7/2) = 84.0 eV).

2.5. EMF measurements

The EMF measurements were performed at 25 °C in hermetically sealed two-probe test cells (Li|Li⁺|Fe_xTiS₂) with 1 M LiClO₄ in propylene carbonate as the lithium-conducting electrolyte. The Fe_xTiS₂ electrodes were prepared by pressing the powdered samples into a Ni grid (current collector). The area of the cathode/electrolyte interface used in the cells was approximately 0.5 cm². The anode consisted of a freshly scraped 1 cm diameter lithium disk that was 1 mm thick, which was pressed into a Ni grid. All of the sample preparation procedures, as well as assembling of the test cells, were carried out in a dry argon atmosphere glove box UNILAB MBRAUN. A V7-34A voltmeter and P-8S Elins potentiostat with a large internal resistance were used for the EMF measurements.

3. Results and discussion

3.1. Crystal structure

The iron solubility and crystal structure of polycrystalline Fe_xTiSe₂ were studied for the first time by Arnaud et al.⁴³ in a concentration range of x = 0–0.66. Metallic iron or iron compounds appeared as a separate phase in the Fe_xTiSe₂ samples above the limiting Fe concentration, which was strongly dependent on the annealing temperature. These inclusions are not always possible to observe by X-ray diffraction. However, these inclusions can provide an additive contribution to the X-ray spectra of the Fe_xTiSe₂ samples, which may result in distorted information regarding the chemical bond in the compound. Therefore, only samples with x from 0.05 to 0.50 in the homogeneous region of the system were investigated in the current study.

Arnaud et al.⁴³ reported that iron atoms occupy the octahedral positions in the van der Waals gaps (Fig. 1(A)). A detailed neutron diffraction study of the Fe_xTiSe₂ compound with x = 0.25 and 0.5 was performed by Calvarin et al.³⁹ The iron atoms occupy octahedral sites. At x = 0.25 and x = 0.5, the monoclinic structure and ordering of the iron atoms were established as shown in Fig. 1(C). However, in our previous study,⁴⁵ the crystal structure of the Fe_xTiSe₂ polycrystalline samples with x = 0.05–0.33 were treated as hexagonal in the P3̄m1 space group because the intensity of the additional lines caused by monoclinic distortion did not exceed 0.5% compared to the intensity of the main phase line. Therefore, in this study, we used the results from the crystal structure refinement presented in ref. 45 for Fe_xTiSe₂ with x < 0.40. At x = 0.40, the structure crystallised into the I2/m space group, which was in good agreement with previously reported results.³⁹ It is important to note that the crystal structure and morphology of Fe_0.4TiSe₂ remain layered. Some of the octahedral sites in the interlayer space of Fe_0.4TiSe₂ were occupied by iron atoms. The results of the crystal structure refinement for Fe_0.4TiSe₂ are listed in Table 1. The experimental and calculated X-ray diffraction patterns of Fe_0.4TiSe₂ as well as the difference curves are shown in Fig. 2 as an example.

Fig. 1 (A) The crystal structure of Fe_xTiSe₂. (B and C) The projection of the crystal structure on the intercalant plane at different types of iron ordering. Dark circles represent iron atoms while light coloured circles represent empty octahedral positions in the van der Waals gap. Small circles show selenium atoms in the underlying plane. In (B) iron atoms are disordered (x < 0.25); in (C) the separated structural fragments are formed like atomic chains. In the case where x = 0.25, chains 2 and 4 are empty; in the case where x = 0.5, chains 2 and 4 are filled with iron atoms.

Table 1 Unit cell dimensions and atomic parameters for Fe_0.4TiSe₂ (space group I2/m, a = 6.2298 Å; b = 3.5845 Å; c = 11.9408 Å; β = 89.7924°)^a

Element	x	y	z	D	Multiplicity	α	Agreement factors
a x, y, z are atomic coordinates; D is the occupation number; α is the concentration of atoms per formula unit of the compound; RF^2, wRp, Rp and χ^2 are commonly used agreement factors for refinement.^44
Fe	0	0	0	0.8	×2	0.4	RF^2 = 5.14%
Ti	0.00165	0	0.24891	1	×4	1	wRp = 13.12%
Se	0.1708	1/2	0.87623	1	×4	1	Rp = 9.33%
Se	0.33833	0	0.11967	1	×4	1	χ^2 = 4.989

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Fig. 2 The experimental (+) and calculated (−) X-ray diffraction patterns of Fe_0.4TiSe₂. The difference curve between calculated and observed profiles is shown at the bottom; the diffraction line with the maximum difference between the experimental and theoretical spectra is shown in the inset.

The concentration dependences of the c lattice parameter for the Fe_xTiSe₂ samples are shown in Fig. 3 along with the literature data. As shown in Fig. 3, the c values as well as the character of the dependence obtained in this study are in agreement with the previously reported results,^43,52 which indicates good reproducibility of the results.

Fig. 3 The concentration dependence of the c lattice parameter for the Fe_xTiSe₂ samples.

3.2. EMF measurements

EMF measurements are an excellent tool in solid-state physics.^53,54 For alkaline metal-intercalated transition metal compounds with a general formula of A_xM_aX_b (A = alkaline metal, M = transition metal, X = O, S, Se), the changes in the EMF (E) of the A|A⁺|A_xM_aX_b electrochemical cell with x at a fixed temperature and pressure provide thermodynamic information on the changes in the phase composition induced by the intercalation process.^2,53–55 The value of E(x) measures the change in the molar Gibbs free energy of intercalation ΔḠ(x) in the reversible reaction

xA + M_aX_b = A_xM_aX_b (1)

The continuous decrease in E with increasing x is characteristic of a single-phase system and indicates solid-solution behaviour. Co-existing phase regions (first-order phase transformation) appear as plateaus in the EMF as a function of x plots because the chemical potential of A in the co-existing phases is the same. Second-order phase transitions that do not involve two-phase regions can also be detected because they lead to changes in the slope of the voltage curve.^2,53–60 Recently, EMF measurements for the Li|Li⁺|Li_xTiS₂ electrochemical cells over a wide range of x values were successfully employed to investigate the phase equilibria in the Li–TiS₂ system.⁶¹ In addition to characterisation of the phase relationship, investigation of the A_xM_aX_b potential by measuring the EMF of the A|A⁺|A_xM_aX_b cells permits direct observation of the Fermi level changes due to metal intercalation. In a first approximation, the cell voltage is equal to the difference in the Fermi levels between the two electrode materials (i.e., A metal and A_xM_aX_b intercalation compound).^62,63 If the negative electrode exhibits a constant voltage (as A metal), the variation of the cell voltage with x directly reflects all of the changes that occur within the positive electrode. Therefore, measurement of this voltage and the number of electrons transferred, which indicates the material composition, is a very sensitive probe for the material.^20,53,56,64

However, these EMF measurements are not easily performed for transition metal-intercalated compounds, especially Fe_xTiSe₂, due to a problem with the selection of a suitable Fe conducting electrolyte. In addition, the coefficient of Fe diffusion in Fe_xTiSe₂ is very low even at enhanced temperatures. Therefore, in this case, a modified electrochemical cell (i.e., Li|Li⁺|Fe_xTiSe₂) can be used, and the negative electrode (lithium metal), which exhibits a constant voltage, also serves as the reference electrode. For the series of Li|Li⁺|Fe_xTiSe₂ cells with varied x, the EMF values measure the changes in the molar Gibbs free energy of lithium intercalation in the reversible reaction

yLi + Fe_xTiS₂ = Li_yFe_xTiS₂ (2)

as a function of the Fe concentration (i.e., as ΔḠ(x,y), where y → 0). The obtained EMF dependence on x does not directly characterise the phase relationships in the Fe–TiSe₂ system, but it is very sensitive to changes in the electronic structure and composition. Therefore, the shape of the EMF as a function of x curve can be used to identify the x values at which these changes occur.

For the reaction (2) of lithium dissolution in the Fe_xTiSe₂ host, the Gibbs free energy can be expressed as:

ΔG(x,y) = eE = −(μLiLi − μFeLixTiSe2) (3)

where e is the electron charge and μLiLi and μFeLixTiSe2 are the Li chemical potentials in the lithium metal anode and the FexTiSe2 cathode, respectively. Because this reaction is a redox reaction, the chemical potential of the Li atoms can be expressed as a sum as follows:

μ_Li = μ_e + μ_i, (4)

where μ_Li is the chemical potential of the lithium atom in any of the considered environments, and μ_e and μ_i are the electronic and ionic contributions to the chemical potential of the lithium atom, respectively. Therefore, eqn (3) can be rewritten as:where the subscript notes the subsystem and the superscript notes the corresponding environment. Therefore, a decrease in the E values may be caused by a reduction in the chemical potentials of the electronic or ionic subsystems.

To estimate the contribution of the lithium ion chemical potential, the lattice gas model was used. According to ref. 65 and 66, and taking into account the isobaric characteristic of the process, the ionic contribution to the chemical potential can be written as:

μ_i = H_i − TS_i, (6)

where H_i and S_i are the specific enthalpy and entropy, respectively, of the lithium ion dissolution. The entropy change of the system caused by the introduction (or extraction) of one lithium ion can be written as:

S_i = S^vibr_i + S^conf_i, (7)

where S^vibr_i and S^conf_i are the changes in the vibration and configuration contributions, respectively. Because the described thermodynamic studies were performed at a temperature that was substantially higher than the Debye temperature, which is at least 250 K for Fe_xTiSe₂,⁶⁷ the Einstein model for the heat capacity, where atoms vibrate identically and independently, can be used to determine the vibration contribution. Therefore, the vibration entropy can be written as:⁶⁸where ν is the vibrational frequency of the atoms. First, the number of vibrational modes will change upon introduction of lithium. However, due to the low lithium concentration, these modes have the same frequency. Therefore, the specific entropy will not change. Secondly, the change in composition may lead to a change in frequency due to changes in the binding forces quasi-elastic constant. However, this effect can also be neglected because the lithium concentration in the studied sample is lower than the concentration of the uncontrolled impurities.

The configuration contribution to the entropy can be expressed as:

where M_m is the number of sites available for filling in the m sublattice and m_m is the number of impurity atoms distributed over the m sublattice. In the m_m → 0 limit S^conf_i → 0, this contribution can also be neglected.

In a “lattice gas” approximation, the specific enthalpy (H_i) of the ion can be expressed as:

where H₀ is “the defect formation enthalpy” due to ion–lattice interactions and describes the interaction in the intercalated ion sublattice.⁶⁹ The last term takes into account the elastic distortions arising from the introduction of the ion into the lattice, as proposed in ref. 70. In the limit y → 0, all of the terms except H₀ also tend to be 0 regardless of the type of lattice that the selected ion is introduced into. The H₀ value is determined by the position of the lithium atom in the lattice. In the low concentration limit, lithium is able to occupy only octahedral positions.^2,56 Therefore, H₀ is the same for all of the materials under investigation, and the chemical potential of the lithium ion in Fe_xTiSe₂ remains constant and independent of the iron concentration. The value of the electronic contribution to the EMF of the cell is determined by the Fermi energy and tends to be the value of the intercalation compound Fermi energy in the limit y → 0.

Therefore, the EMF of the cell described by eqn (5) is determined only by the electronic contribution to the difference between the chemical potential of lithium atoms in metallic lithium and Fe_xTiSe₂, which is equal to the Fermi level difference in these materials.

It is important to note that the EMF of the cell defined by eqn (3) is not equivalent to the EMF measured relative to the intercalated metal. Indeed, the “plateau” on the atom chemical potential concentration dependence (I) uniquely identifies the first-order phase transition; but the “plateau” on the electron chemical potential concentration dependence (II) is associated with a high density of states or its concentration dependence within the single-phase region. Therefore, “plateau” I will always be accompanied by “plateau” II; but “plateau” II will not necessarily be accompanied by “plateau” I.

For the Li|Li⁺|Fe_xTiSe₂ cells, the E dependence on x is shown in Fig. 4. As expected, the iron intercalation into TiSe₂ causes a monotonic decrease in the EMF values with x due to electron transfer from Fe to the TiSe₂ lattice, but only in a 0 ≤ x ≤ 0.20 concentration range. Because the portion of the EMF curve within this interval can be approximated as a straight line, the free energy changes will be the same over the whole range where this approximation is valid. However, a linear decrease in the c lattice parameter was observed in the same concentration range (see Fig. 3), which indicates a decrease in the distance between the layers in the TiSe₂ lattice. Therefore, an increase in the Fe concentration reduces the size of the available positions for lithium atom intercalation. As shown in ref. 4, the change in the lattice parameters due to alkali metal intercalation, including lithium intercalation, is inversely proportional to the initial width of the interlayer space and directly proportional to the ionic radius of the intercalated atom. Therefore, the same alkali metal intercalation into the material with a smaller interlayer gap width leads to an increase in the energy cost of the lattice expansion, which is in agreement with eqn (10). A linear decrease in the EMF values with the Fe concentration can be uniquely associated with compression of the Fe_xTiSe₂ lattice, which leads to an increase in the host lattice deformation energy and an increase in the ionic contribution to the free energy of the dissolution reaction.

Fig. 4 The EMF dependence on x for the Li|Li⁺|Fe_xTiSe₂ cells at 25 °C and atmospheric pressure.

As shown in Fig. 4, above x = 0.20, a break in the EMF concentration dependence was observed. Moreover, E becomes constant and nearly equal to 2.3 V, which is only slightly lower than the typical value for pristine TiSe₂, starting at x = 0.30. This behaviour is indicative of substantial changes in the Fe_xTiSe₂ electronic structure. Because the c parameter is also nearly independent of the iron content within the same concentration range (see Fig. 3), the influence of the ionic contribution must be negligible. In addition, the change in the EMF value between x = 0.20 and x = 0.30, which was nearly 1 V, is extraordinarily high for the elastic contribution, which is typically estimated to be 0.01–0.1 V.⁷¹ Therefore, the observed significant change in the EMF values was associated with the dependence of the Fermi energy on the iron content.

The unusual behaviour of the Fermi energy as a function of the iron concentration in Fe_xTiSe₂ indicates a possible difference in the nature of the chemical bond at x ≤ 0.20 and x ≥ 0.30. Spectral methods are the most suitable for confirming this conclusion and determining the nature of the chemical bond in Fe_xTiSe₂.

3.3. XPS core levels

Core level XPS provides insight into the charge state of the atoms as well as the changes in the charge state as a function of the iron concentration in Fe_xTiSe₂. In addition, XPS can be used as an additional homogeneity test for the studied samples. The core level spectra of iron and titanium for the Fe_xTiSe₂ compounds are shown in Fig. 5.

Fig. 5 The Ti 2p (left panel) and Fe 2p (right panel) spectra for Fe_xTiSe₂ with 0 < x ≤ 0.40. The dashed line gives the decomposition into component lines.

The Ti 2p_3/2,1/2 spectra broadened as the iron content increased (Fig. 3, left panel). The Ti 2p_3/2 line broadened with x within the 0 < x < 0.20 range (Table 2), which may be due to the presence of two non-equivalent titanium atoms (with and without an iron atom in the nearest neighbourhood). An increase in the iron content resulted in an increase in the concentration of Ti atoms coordinated by Fe. A similar result has been previously described in ref. 72 for Mn-intercalated TiSe₂. It is important to note that the broadening of the Ti 2p line for Fe_xTiSe₂ is much smaller than that observed for Mn_xTiSe₂. The bandwidth remains nearly unchanged at 0.20 ≤ x ≤ 0.38 and decreased at x = 0.40 up to values smaller than x = 0.10 (Table 2). This behaviour does not correspond to the above assumption regarding the increase in the number of titanium atoms with iron atoms in the nearest neighbourhood.

Table 2 Full width at half maximum (FWHM) for the Ti 2p_3/2 spectra

x in FexTiSe2	FWHM, eV
0	1.60
0.10	1.90
0.20	2.55
0.33	2.40
0.38	2.50
0.40	1.85

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The Fe 2p spectra were indicative of two types of chemical bonds formed by iron atoms (Fig. 5, right panel). As the iron concentration increased to x = 0.33, low energy B-band with a binding energy (E_B) of 707.8 eV appeared, and the intensity of the A-band (E_B = 708.9 eV) decreased. The contributions of these bands were nearly equal for Fe_0.33TiSe₂, and the B-band contribution dominated in the Fe 2p_3/2 spectrum of Fe_0.4TiSe₂. The energy position of the Fe 2p maximum for Fe_0.4TiSe₂ (B-band) was close to the Fe 2p_3/2 binding energy for metallic iron (E_B = 707 eV (ref. 73)), which indicates the presence of two non-equivalent sites occupied by iron atoms. These sites differ in the composition of the second coordination sphere. The A-band is associated with the covalent bond between the Fe atoms and the nearest neighbour, and the B-band corresponds to the metallic Fe–Fe bond.

One important feature should be discussed. The ordering of iron atoms, which is characteristic of a monoclinic structure, results in the formation of a sequence of octahedral site chains in the van der Waals gap. The chains occupied by iron atoms and the vacant chains alternate. Evidently, deviation from the ideal composition from x = 0.50 to a lower iron content means that some of the iron atoms are involved in a chain while other atoms are not included. These two types of iron atoms most likely produce two contributions to the Fe 2p spectra described above. It is important to note that the photoelectron escape depth is limited to approximately 10 to 12 atomic layers. The contribution from more deep-lying layers decreases exponentially, which leads to the outer iron layer (is located on the cleaved surface of the crystal) providing the main contribution to the Fe X-ray photoelectron spectrum. As reported in ref. 74, the intercalant concentration in this layer is lower than that in the bulk crystal. This concentration should be taken into account for comparing the structural and electrochemical data with the results of XPS. Therefore, the surface concentration of the iron atoms in the Fe_xTiSe₂ sample with x = 0.40 must be slightly less, and not all of the iron atoms are involved in a chain despite the fact that strict monoclinic ordering with iron chains is observed in this sample based on the structural data (see Section A). For Fe_xTiSe₂ with x = 0.10, the iron chains are absent, and therefore, the contribution of only one type of iron atom is observed in its spectrum (peak A in Fig. 5). At x = 0.33, both iron chains and iron atoms outside of the chains were observed. As a result, the two contributions described above were observed in its spectrum (peaks A and B in Fig. 5). These two contributions are also present in the spectrum of the sample with x = 0.40, and the intensity of the B-peak becomes higher than that of the A-peak, which is due to the influence of the crystal surface.

3.4. XAS

The titanium absorption spectra provide information regarding the ratio of the ionic and covalent contributions to the chemical bond of the selected atom.⁷⁵ Because these characteristics are related to the local environment of the atom, they should be sensitive to structural transitions associated with the iron distribution.

The Ti L_2.3 absorption spectra are shown in Fig. 6. The intensity ratio of the A and B lines changed as the iron concentration increased to x = 0.38. Simultaneously, a common shift in the absorption spectrum to low energy occurred. As previously reported in ref. 75, these changes may be due to an increase in the covalent component of the chemical bond of titanium with the nearest neighbour. However, when the composition was Fe_0.4TiSe₂, the titanium absorption spectrum changed substantially and became nearly identical to the pristine TiSe₂ spectrum. This observation indicates a strong reduction in the covalent component of the Ti chemical bonds according to ref. 75.

Fig. 6 Ti L_2.3 XAS for Fe_xTiSe₂ with 0 < x ≤ 0.40.

The Fe L_2.3 absorption spectra are shown in Fig. 7. The shape and energy position of these spectra are similar to those in the metallic iron absorption spectrum.⁷⁶ No changes in the shape and energy position were observed as a function of the Fe concentration. The analysis of the absorption spectra indicates that the iron atoms are divalent.

Fig. 7 Ti L_2.3 XAS for Fe_xTiSe₂ with 0 < x ≤ 0.40.

3.5. Valence band spectra

The photoemission spectra of the valence band provide insight into the state of the valence electrons that are responsible for the chemical bonds in the material. The use of excitation radiation with a resonant energy close to the 2p–3d transition energy allows for determination of the partial atomic contributions in the density of states in the valence band. The changes in the nature of the chemical bonds can be observed using this experiment.

The valence band spectra, which were obtained at an excitation energy of 700 eV (far from resonances), are shown in Fig. 8. The valence band changed as the iron concentration increased. The A, B and C line energy positions do not change. However, slight broadening of all of the lines occurred, which results in the common broadening of the main line. This result is due to enhancement of the contribution from the iron states to the valence band as the iron concentration increases. These iron states occupy a range from 0 to 6 eV.⁷⁷ An additional line (D) appears in the Fe_0.33TiSe₂ and Fe_0.38TiSe₂ spectra. A further increase in the Fe concentration to x = 0.40 results in the disappearance of the D-line, which may be due to a decrease in the appropriate electronic states or an increase in the D-line binding energy, resulting in its smearing.

Fig. 8 The valence band spectra for Fe_xTiSe₂ with 0 < x ≤ 0.40.

Therefore, the results of the valence band spectral analysis are in good agreement with those of the core level and absorption spectra analyses, and confirm the dramatic changes in the electronic structure of the Fe_0.4TiSe₂ compound.

3.6. ResPES

Resonant photoelectron spectroscopy provides element-specific information on the energy localisation of the electronic states. The photoemission of d electrons from 3d metals and their compounds is strongly enhanced when the incident photon energy is slightly larger than the binding energy of the selected core level upon excitation of the np electrons (n = 2; 3) to an unfilled 3d state, resulting in a resonant electron emission.^78–81 This effect is interpreted as resulting from a coherent process in which a np electron in the initial state is excited to an empty 3d level to form an intermediate bound state (np, 3d). Due to the auto-ionisation process, the intermediate bound state can transform into a final state identical to that resulting from direct photoemission. Resonance of the 3d electrons occurs upon interference of the direct channel of photoemission (np⁶3dⁿ + hν − np⁶3dⁿ⁻¹ef) with the successive decay of the Coster–Kronig type excited state (np⁶3dⁿ⁺¹ + hν − np⁵3dⁿ⁺¹ − np⁶3dⁿ⁻¹ef). The resonant peaks in the VB spectrum are superimposed by the intense peaks of the Auger L_2.3M_4.5M_4.5 line. The most striking contrast in the change in the valence band corresponds to the resonant excitation energy. In most cases, this energy value is equal to the binding energy of the core level of the electrons that are involved in the resonance.⁸² To obtain spectra of the valence bands with maximum resonance excitation, the corresponding absorption spectrum was obtained, and then, the valence band spectra were obtained in an energy range involving the main absorption peak. The energy of the resonance maximum corresponds to crossover emergence (i.e., the transition from the RRAS (resonant Raman–Auger spectra) to the normal Auger spectra).⁸²

As the iron concentration increased to x = 0.40, the contribution from the Fe 3d states to the valence band dominates over the electronic states of the other atoms, as shown in the Fe 2p–3d resonance spectra (Fig. 9, left panel). The Fe 3d states occupy a wide energy range in the valence band. No additional spectral distribution features were observed at x < 0.40.

Fig. 9 The on-maximum valence band spectra in the Fe 2p–3d (left panel) and the Ti 2p–3d resonant excitation modes (right panel) for Fe_xTiSe₂ with 0 < x ≤ 0.40.

Next, the behaviour of the D-line will be discussed. In the off-resonance spectra, this line is observed for Fe_0.33TiSe₂ and Fe_0.38TiSe₂. However, in the on-resonance spectra, this line was smeared by the iron states. For the Fe_0.4TiSe₂ compound, the D-line behaviour is the opposite. This line was observed in the on-resonance spectra, but not in the off-resonance spectra. This result may be due to the contribution from the iron states to the D-line not dominating at an iron concentration up to x = 0.40. A further increase in the iron concentration leads to the domination of Fe states in the D-line.

The VB spectra at the Ti 2p–3d maximum of the resonance excitation are shown in Fig. 9 (right panel). The D-line was observed just below the Fermi level. The D-line intensity increased up to an iron concentration of x = 0.38, which indicates charge transfer to the titanium atoms of the host lattice.⁸³ It is important to note that the binding energy of the D-line decreased with an increase in the iron concentration to x = 0.38. At x = 0.40, the binding energy increased substantially, and the intensity of the D-band decreased, which indicates a significant reduction in the charge transfer from the intercalated iron to the TiSe₂ host lattice.

3.7. Model of Fe_xTiSe₂ electronic structure transformation

The Se–Ti–Se sandwich width and Se–Fe–Se interlayer space width as a function of the iron concentration (x) are shown in Fig. 10. The decrease in the c values was caused by Se–Ti–Se sandwich contraction, which corresponds to the formation of covalent bonds between iron and titanium atoms. At 0.33 ≤ x ≤ 0.40, the Se–Ti–Se sandwich width increased with the c lattice parameter, which corresponds to breaking of the covalent chemical bonds in c direction.

Fig. 10 The Se–Ti–Se sandwich width and Se–Fe–Se interlayer space width as a function of iron concentration x (concentration dependence of c lattice parameter is also shown for clarity).

Three iron concentration regions corresponding to different types of iron chemical bonding environments were observed: 0 < x ≤ 0.25, 0.25 < x ≤ 0.38, and x ≥ 0.4.

The linear dependence of the c₀ lattice parameter on the iron content at x < 0.25 (see Fig. 3) indicates that the introduction of each subsequent iron atom produces the same deformation of the lattice. The broadening of the Ti 2p spectra may be related to the presence of irregularities in the form of titanium atoms, which are coordinated or not coordinated with iron atoms. The Ti absorption spectra exhibit a monotonic increase in the covalency of the Ti chemical bond with the environment as a result of the formation of covalent bonds with the intercalated iron. The dependence of the chemical potential of the electrons on the iron content is monotonic as well (Fig. 4). Such behaviour may result from the accumulation of non-interacting Ti–Fe–Ti centres. This assumption helped to explain the thermodynamics,⁵² concentration dependence of the Pauli contribution to the magnetic susceptibility⁴⁴ and effective iron magnetic moment.⁴² This is in good agreement with the increase in spectral intensity at the Fermi level in Ti 2p–3d RXPS with increasing iron concentration, indicating an increase in the contribution of Ti 3d-states in the near-Fermi region. The presence of the Ti–Fe–Ti centres appears in the formation of the nondispersive band just below the Fermi level.⁷ These centres absorb electrons introduced during iron intercalation without increased filling of the conduction band formed mainly by Ti 3d-states, thus keeping the binding energy of Ti 2p-state as in pristine TiSe₂. Therefore, in this concentration region, a charge transfer from the iron atoms to the TiSe₂ host lattice occurred.

According to ref. 39, the structural ordering of iron atoms occurs at x = 0.25 and x = 0.5. Our results allow the conclusion to be drawn that, in the concentration region 0.25 < x ≤ 0.38, this ordering is related to the change in the chemical bonds: the c₀ lattice parameter starts to be practically independent on x and the Ti 2p spectra broadening is completed. This means that all of the intercalated iron atoms are attached to chains, which reduces the Fe 2p binding energy. The coexistence of “A and “B” peaks (Fig. 5) in this concentration region can be related to the transition of iron atoms from the disordered state (peak “A”) to a chain state (peak “B”). At the boundary of this region, a sharp increase in the chemical potential of the electrons occurs. This may be due solely to the increase in filling of the conduction band formed by Ti 3d-states and is in perfect agreement with the gradual decrease of Ti 2p binding energy, further increase in the intensity and binding energy of the peak at the Fermi level in the Ti 2p–3d RXPS and appearance of the D-band in the VB spectra (Fig. 8). The contribution of the iron states in the near-Fermi region remains negligible since it follows from the Fe 2p–3d RXPS. Therefore, iron atoms in chains differ from isolated atoms and should form a separated band. At the same time, titanium continues hybridisation of its 3d-states with the states of iron inside the chains, as also occurs for the isolated iron atoms.

The most homogeneous state is achieved at x > 0.4; this follows from the minimum width of the Ti 2p XPS. The transition of the iron atoms to the same state is apparently associated with the formation of chains (see Fig. 1(B) and (C)). The covalency of the titanium chemical bond with the environment sharply reduces following from the Ti XAS. Nevertheless, the charge state of the iron atoms did not change based on the Fe L_2.3 XAS. However, the nature of the chemical bond of iron with the nearest neighbour changed. According to the Fe 2p spectra (Fig. 7), the covalent component of the chemical bond decreased, and the chemical state of the iron atoms became more metallic. The charge transfer from the iron atoms to the host lattice was interrupted due to the formation of structural fragments based on the Ti 2p–3d resonance spectrum and Ti L_2.3 XAS. Moreover, an additional line was observed near the Fermi level in the Fe 2p–3d resonance spectra. This line was absent at x < 0.40 and is responsible for the interatomic Fe–Fe interaction in the structural fragments. At the same time, a sharp decrease in the charge transfer between the intercalated iron atoms and the TiSe₂ host lattice is observed.

The filling of the Ti 3d conduction band decreases as a consequence of the disappearance of the D-band in the VB spectrum (Fig. 8) and increase in Ti 2p states binding energy. Iron atoms are organised in chains. The state of iron in the chain does not change in comparison with the state obtaining in the concentration region where iron chains and isolated iron atoms coexist. The appearance of the D-band in the Fe 2p–3d RXPS (Fig. 9) is a result of an increase in the width of the band of iron states in chains and attaining the top edge of this near-Fermi region band. The electrons that filled the conduction band at x < 0.4 participate in the filling of this band. The exhaustion of the conduction band explains the effect of the reappearance of the resistive anomaly, which is typical for the transition to the CDW state observed in ref. 6 as a result of the recovery of the electron–hole balance required for the stability of CDW.⁸⁴ It is likely that this mechanism is universal for all of the observed cases of CDW state recovery in the intercalation compounds with a high concentration of intercalated metal.^6,29,85

It may be validly asked why the ordering of iron atoms, which is observed starting at x = 0.25,³⁹ only leads to the effects observed on the spectra at x = 0.4. The answer to this question may be related to the surface sensitivity of the spectral methods. Indeed, if the spectral methods permit only the surface with 4–5 monatomic layers to be studied, then ordering of iron atoms in the layer that is nearest to the surface and undistorted by the cleavage procedure has a negligible influence on the electronic structure. The surface should contain an iron layer that is distorted due to the removal of a portion of iron atoms under the cleavage procedure. So far as we know, the crystal structure of this layer remains to be studied. It is unclear how iron atoms are removed and whether this is process is random or ordered. It is thought that, due to the symmetry of the removed and remaining fragments, the surface concentration of the intercalant should be equal to approximately half of its volume concentration. Then, in the concentration range 0.25 < x ≤ 0.38, we should obtain the surface composition 0.125 < x_surf ≤ 0.19 and no traces of the chain formation should be observed. In fact, this is contradicted by the obtained results: within the range of 0.25 < x ≤ 0.38, a coexistence of iron chains and isolated iron atoms was observed. Probably, not all of the iron chains at the cleavage procedure remain long enough to form valuable structural fragments. The composition with x = 0.40 corresponds to the surface concentration x_surf = 0.20, which is close to the composition required for the complete ordering. This indicates that the cleavage procedure may keep undistorted structural fragments as separate “islands” on the crystal surface.

4. Conclusions

In this study, it was found that, due to the formation of chains, a change in the nearest environment of intercalated iron atoms significantly changes the chemical bond of iron, making it closer to the metallic state. This advances knowledge about the feature of the chemical bonding of intercalated metal atoms in the van der Waals gap, which can interact not only with the host lattice but also with each other. The observed concentration dependence of the Fe_xTiSe₂ electronic structure can be explained as a result of the transition from a disordered state at low iron concentrations to an ordered state at high iron concentrations. On the surface, this transition appears experimentally as diffuse because an additional disorder is introduced under the cleavage procedure. Because spectral methods only allow information to be obtained about the surface, the experiment was completed with the thermodynamic EMF data, which provide information about the bulk properties of the intercalation compounds. This allows the analysis of the interatomic interactions of the intercalant atoms to be performed in the Fe_xTiSe₂ compounds more carefully. Our results support the proposition that the surface layer of iron may contain fragments of undistorted bulk structure. These fragments on the cleaved crystal surface allow spectral information concerning the electronic structure of the bulk intercalation compound to be obtained.

At the formation of iron chains, the Fe 3d electron charge sharing in the van der Waals gap is due to covalent chemical bond formation in the intercalated iron sublattice and “switching” of iron electron orbitals from Ti–Fe–Ti to Fe–Fe chemical bond along the iron chains. This result leads to the recovery of the electron–hole balance in TiSe₂ and re-emergence of the CDW state at a high iron content, which was observed in ref. 6.

We suppose that this CDW recovery mechanism is universal for all of the M_xTiSe₂ materials in which an increase in intercalant concentration leads to the formation of chemical bonds in the intercalant sublattice.

Acknowledgements

The research was carried out within the state assignment of FASO of Russia (theme “Electron” No. 01201463326 and theme "Spin" No. 01201463330) and the Ministry of Education and Science of Russia, supported in part by RFBR (project No. 14-03-00274). This work has been (partly) done using facilities of the Shared Service Centre “Ural-M”, Institute of Metallurgy of the Ural Branch of the Russian Academy of Sciences.

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