Introduction

Vanadium oxides are a versatile family of materials, with 4 possible oxidation states of vanadium, 2+ to 5+1. This leads to 4 single valence phases and a large number of mixed valence phases, each with distinct properties. For example, many vanadium oxides possess an semiconductor-to-metal transition (SMT). Each specific compound has a different magnitude of resistivity change and temperature of the SMT. \(\hbox {V}_{2}\hbox {O}_{3}\) has a transition temperature of \({168}\,\hbox {K}\) and a resistivity change of \(10^7\)2 corresponding to the largest resistivity change of the VO\(_x\) compounds, while \(\hbox {VO}_{2}\) has a transition temperature \({340}\,\hbox {K}\) and a resistivity change of \(10^5\)3. The precise control of vanadium oxide phase and oxidation state is required to engineer a material with desired physical properties.

Current applications of vanadium oxides are industrial catalysts4 and battery technologies5,6 utilising \(\hbox {V}_{2}\hbox {O}_{5}\) and advanced electronics7,8 and sustainable window coatings utilising \(\hbox {VO}_{2}\)9,10. Mixed valence phases have been explored, for example \(\hbox {V}_{6}\hbox {O}_{13}\) in battery technologies11. However, their properties are not comprehensively understood, partly due to the challenge of synthesising mixed valence phases as a single crystalline product.

The initial and majority of reflectance anisotropy spectroscopy (RAS) studies have been conducted on semiconducting surfaces12,13,14; the technique has been utilised to investigate semiconductor surface reconstructions and to monitor the growth of epitaxially grown semiconductor surfaces. Furthermore, the structure of metal absorbates on metal and semiconductor surfaces or the absorbent induced reconstruction of the substrate has received considerable attention12,15,16,17,18,19. RAS represents a technique which can characterise surface and electronic structure, identify specific surface terminations and monitor changes in surface structure in real-time. Despite this, RAS studies of metal oxides have received little attention; wide-bandgap ZnO20, superconducting cuprates21 and more recently Fe\(_3\)O\(_4\)(110)22,23 and SrTiO\(_4\)(110)24 have been studied. The majority of these works deal with optical anisotropy originating from an anisotropic surface, due to a surface reconstruction or absorbents, on top of an isotropic bulk. RAS can probe bulk anisotropy and the vanadium oxide family is an ideal candidate for RAS measurements, with many of the crystal phases having well documented bulk structural and optical anisotropies.

Orthorhombic \(\hbox {V}_{2}\hbox {O}_{5}\) is the vanadium oxide with the highest oxidation state and is depicted in Figure 1. It is a semiconducting material (bandgap = 2.3 eV25,26) and is used extensively in industry as an oxygen catalyst4 and gas sensor27. The thermal reduction of single crystalline \(\hbox {V}_{2}\hbox {O}_{5}\) at around 800 K in high vacuum28 and oxygen29 environments result in conversion to \(\hbox {V}_{6}\hbox {O}_{13}\). In the case of the reduction of thin films Ramana et al., converted amorphous \(\hbox {V}_{2}\hbox {O}_{5}\) to V\(_2\)O\(_3\) at 860 K30, while Monfort et al. converted polycrystalline \(\hbox {V}_{2}\hbox {O}_{5}\) to \(\hbox {V}_{4}\hbox {O}_{9}\) at 673 K and to \(\hbox {VO}_{2}\)(B) at 773 K31. The reducing conditions and the nature of the \(\hbox {V}_{2}\hbox {O}_{5}\) determines the reduction, which can be due to crystallinity, defects or both. The reduction dynamics and phase evolution as a function of reducing conditions are not well established.

To realise the applications of vanadium oxides, growth and preparation conditions need to be precisely controlled to meet requirements in material characteristics governed by structure and stoichiometry. In-situ non-destructive characterisation methods can provide increased control and accuracy, observing structural changes as they are induced, without exposing the sample to atmosphere. Understanding the reduction dynamics and phase evolution is vital for a fundamental physical understanding and also for the application of the vanadium oxides phases. The co-existence of several VO\(_x\) phases including mixed valance phases whose physical properties are unknown, hinders the interpretation of experiments. Identifying the reduction process and dynamics can assist greatly in the interpretation of mixed phase systems.

In this work we examine the optical anisotropy of both pristine (010) orientated \(\hbox {V}_{2}\hbox {O}_{5}\) single crystals and crystals annealed in vacuum at various temperatures, which results in lower oxide phases in the surface region. Axially resolved ellipsometry measurements are performed and the RAS spectra is calculated from the optical constants. Vacuum annealing the \(\hbox {V}_{2}\hbox {O}_{5}\)(010) crystals at different temperatures results in different phases in the surface region and this is reflected by the drastically modified RAS spectra. A prominent feature in the infrared (IR) is assigned to \(\hbox {V}_{6}\hbox {O}_{13}\)(001) and the influence of \(\hbox {VO}_{2}\) on this IR feature is revealed.

Fig. 1
figure 1

(a) Crystal structure of orthorhombic \(\hbox {V}_{2}\hbox {O}_{5}\) and (b) the (010) plane. The three oxygen atoms are distinguished. In the (010) there are V–O\(_2\) and V–O\(_3\) bonds, the distance of which are illustrated.

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Results

RAS is a non-destructive optical probe in which linearly polarised light is at normal incidence to a sample’s surface. The difference in reflectance (\(\Delta r\)) along two orthogonal axes of a surface plane (x, y)32 is measured. The RAS unit (\(\Delta r/r\)) used is normalised to the mean reflectance (r):

$$\begin{aligned} \frac{\Delta r}{r} = 2 \frac{(r_x - r_y)}{(r_x + r_y)} \end{aligned}$$
(1)

where reflectances r are complex Fresnel reflection amplitudes. This measurement reveals in-plane anisotropies of the sample being analysed, and generally speaking, this is due to the anisotropic electron states or bond structures of plane normal to the light propagation direction in the region of the Fermi level32. Due to the measurement relying on the difference between reflections on orthogonal axes, only optically anisotropic planes give a non-zero RAS signal. In a simple two-layer model33 (atmosphere and bulk crystal) the RAS response is related to the differences in the dielectric function as follows:

$$\begin{aligned} \frac{\Delta r}{r} = \frac{1}{\sqrt{\epsilon }} \frac{\Delta \epsilon }{\epsilon - 1} \end{aligned}$$
(2)

where \(\epsilon\) = \(\frac{1}{2}\)(\(\epsilon _x\) + \(\epsilon _y\)) and \(\Delta\) \(\epsilon\) = \(\epsilon _x\)–\(\epsilon _y\). \(\epsilon _x\) and \(\epsilon _y\) are complex quantities.

\(\hbox {V}_{2}\hbox {O}_{5}\) single crystals have been grown by the floating zone technique. The growth process was carried out in oxygen flow at a crystallisation rate \({8}\,\hbox {mmh}^{-1}\). \(\hbox {V}_{2}\hbox {O}_{5}\) readily cleaves along the (010) due to weak bonding in that plane34 resulting in a reflective surface.

Characterisation of \(\hbox {V}_{2}\hbox {O}_{5}\)(010) single crystal

The sample surface is prepared by cleaving the single crystal in atmosphere. The \(\theta\)-2\(\theta\) scan in figure 2(a) reveals <010> reflexes. No reflexes due to different \(\hbox {V}_{2}\hbox {O}_{5}\) orientation or vanadium oxide phases are observed. The RSM of the \(\hbox {V}_{2}\hbox {O}_{5}\)(010) peak [Figure 2(b)] is characteristic of a single crystal. The distribution in \(\omega\) indicates there is a small angular distribution of crystallites about the surface normal. This is best visualised by the two peaks. The sharpness in \(2\theta\) indicates the crystallites are large with a consistent lattice parameter. The lattice constant (4.354Å) closely matches that of single crystalline \(\hbox {V}_{2}\hbox {O}_{5}\)35. The (110) lattice plane is found using an asymmetric azimuthal \(\phi\)-scan [figure 2(c)]. It reveals a two-fold symmetry confirming the single crystallinity of orthorhombic \(\hbox {V}_{2}\hbox {O}_{5}\).

Fig. 2
figure 2

Structural and chemical characterisation of the \(\hbox {V}_{2}\hbox {O}_{5}\) single crystal. (a) XRD scan with <010> \(\hbox {V}_{2}\hbox {O}_{5}\) reflexes. (b) RSM of the peak at \(2\theta\) = 20.3 degrees indicates a small angular distribution of crystal planes about the surface normal, characteristic of a single crystal. (c) Asymmetric azimuthal scan of the [110] reflex shows two fold symmetry characteristic of a single crystal in this orthorhombic system. (d) XPS scan of the O 1s and V 2p region (\({535}-{510}\,\hbox {eV}\)) shows the O 1s and V 2p\(^{3/2}\) peaks. These have a spacing (\(\Delta\)) of \({12.7}\,\hbox {eV}\), characteristic of V\(^{5+}\)36.

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XPS depicted in Fig. 2d confirms the single V\(^{5+}\) valence state of the crystal. The valence state of vanadium in vanadium oxides dictates the energy difference (\(\Delta\)) between the O 1s and the V 2p\(^{3/2}\) peaks36. The cleaved crystal exhibits a \(\Delta\) of \({12.7}\,\hbox {eV}\), comparable to \(\hbox {V}_{2}\hbox {O}_{5}\) (\({12.8}\,\hbox {eV}\)). For comparison, \(\Delta\) for \(\hbox {VO}_{2}\), V\(_2\)O\(_3\) and VO are around 14.0, 14.5 and 18.0 eV, respectively36.

RAS of the \(\hbox {V}_{2}\hbox {O}_{5}\)(010) plane

Fig. 3
figure 3

(a) Axially resolved complex dielectric function and refractive index of the (010) plane measured via ellipsometry. (b) The measured dielectric function is used to calculate a RAS spectrum, and this is compared against a direct RAS measurement of the (010) plane, showing good agreement in spectral shape.

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The real part of the RAS response of the \(\hbox {V}_{2}\hbox {O}_{5}\)(010) is shown in figure 3(b). The crystal is rotated in order to maximise the RAS signal, which coincide to the x and y axis in equation 1, corresponding to the [100] and [001] lattice directions, respectively. It is noted that rotating the sample only influences the magnitude of the RAS signal, an expected response from a single crystal. The real part of the RAS has sharp positive peaks at \({2.9}\,\hbox {eV}\), \({3.5}\,\hbox {eV}\) and \({4.4}\,\hbox {eV}\), and negative peaks at \({3.2}\,\hbox {eV}\) and \({4.0}\,\hbox {eV}\). Positive denotes a higher reflectivity for light polarized along the [100] axis (\(r_x\)). In the infrared (IR) region the RAS spectrum is positive and almost constant.

The real and imaginary parts of both the dielectric function and the refractive index along the [100] and [001] axes, extracted using ellipsometry measurements, are presented in Fig. 3a. Clear differences in these spectra show the optical anisotropy of the plane. The presented dielectric function is in agreement with the literature25,37,38.With the dielectric function and Equation 2 we calculate the real part of the RAS response (Fig. 3b). Comparison of the direct RAS measurement and calculated spectrum show good agreement. The reduced amplitude and broadening of the measured RAS is likely caused by the larger spot size and lower spectral resolution compared to the ellipsometry.

In the region from 1.3–3 eV the optical constants are well described by a Lorentzian oscillator model, which considers the induced oscillation of bound charge due to an oscillating electric field in the presence of damping39,40. The optical transitions are dominated by filled O 2p orbitals to empty V 3d states41,42,43. Theoretical calculations of the band structure provide insight into the anisotropy41,42,43. The bottom of the conduction band consists of two bands which are separated from several higher conduction bands by a gap in the vicinity of 0.5 eV25,41,42,43. This accounts for the peak in the optical constants in the vicinity of 3 eV beyond the indirect bandgap of 2.3 eV. The valance band maxima show considerable anisotropy. Along the [100] direction the valance band is localised while along the [001] direction exhibits a greater degree of delocalisation25,41,42,43. The localisation in the [100] accounts for the strong peak in \(\epsilon _2\) along this axis (Fig. 3a). While the more delocalised nature of the [001] direction results in a broader \(\epsilon _2\). In agreement with these calculations, Parker et al. report a sharp optical transition at \({2.8}\,\hbox {eV}\) in the [100] direction and a broader optical transition at \({3.2}\,\hbox {eV}\) in the [001] direction25. The anisotropic absorption lines is linked to the oxygen structure in the [010] plane41,42,43, which is depicted in Fig. 1. The V-O bonds vary from 1.60–2.02 Å25,35,41. The spatial carrier densities and the correlated optical transitions strongly depend on the V-O distance, as has been revealed by density functional theory calculations41. Bonds along the [100] axis are V–O(2) coordinated bonds, possessing a length of 1.78 Å, and longer V–O(3) bonds, with length 2.02 Å. Along the [001] axis, there are only V–O(3) bonds with length 1.88 Å.

Annealed \(\hbox {V}_{2}\hbox {O}_{5}\) crystals

Fig. 4
figure 4

RAS and XRD of \(\hbox {V}_{2}\hbox {O}_{5}\) crystals annealed at 600, 700, 800 and 900 K in (a–d). (a) 600 K; Significant changes in the RAS induced by the initial 20 minute anneal. Minima-maxima structure (2.7–3.1 eV) in 4 and 6 h spectra. Optical anisotropy is reduced with additional annealing. XRD is characterised by \(\hbox {V}_{2}\hbox {O}_{5}\)<010> and \(\hbox {V}_{4}\hbox {O}_{9}\)<001>. (b) 700 K; Initial 20 min anneal induces a sharp negative structure at 2.8 eV. Cumulative anneals of 1, 2 and 3 h characterised by minima-maxima structure (2.3–2.9 eV). Additional annealing reduce the optical anisotropy. XRD characterised by strong \(\hbox {V}_{2}\hbox {O}_{5}\)<010> and \(\hbox {V}_{4}\hbox {O}_{9}\)<001> and comparatively weak \(\hbox {V}_{6}\hbox {O}_{13}\)<001>. (c) 800 K; Strong IR structure in all spectra. XRD dominated by \(\hbox {V}_{2}\hbox {O}_{5}\)<010> and \(\hbox {V}_{6}\hbox {O}_{13}\)<001>. \(\hbox {V}_{4}\hbox {O}_{9}\)<001> only observed for the initial 20 minute anneal. (d) 900 K; Considerable positive IR structure and negative structure around 2.5 eV. Spectra is \(\hbox {V}_{2}\hbox {O}_{5}\)<010>-like after 2 and 3 h of cumulative annealing. XRD dominated by \(\hbox {V}_{2}\hbox {O}_{5}\)<010> and \(\hbox {V}_{6}\hbox {O}_{13}\)<001>.

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The four \(\hbox {V}_{2}\hbox {O}_{5}\) crystals were annealed at difference temperatures in a pressure of 5 \(\times\) 10\(^{-5}\) mbar. The evolution of the RAS is summarised in this section. The stated anneal time is the cumulative time of annealing at that temperature. Prior to discussing the results, the reduction pathways of \(\hbox {V}_{2}\hbox {O}_{5}\) are discussed, which motivates our interpretation of the data. The Wadsley phases of the vanadium-oxygen system (V\(_n\)O\(_{2n+1}\)) range from \(\hbox {V}_{2}\hbox {O}_{5}\) (n = 2) to \(\hbox {VO}_{2}\)(B) (n = \(\infty\)). Other Wadsley phases, relevant to our discussion, are \(\hbox {V}_{6}\hbox {O}_{13}\) and \(\hbox {V}_{4}\hbox {O}_{9}\). \(\hbox {V}_{2}\hbox {O}_{5}\) is orthorhombic and consists of a V\(_2\)O\(_3\)-O\(_2\) stacking sequence along its [010] direction. Orthorhombic \(\hbox {V}_{4}\hbox {O}_{9}\) consists of a V\(_2\)O\(_3\)-O\(_2\)-V\(_2\)O\(_3\)-O stacking sequence along its [001] direction44 and is based on a super-lattice of oxygen vacancies within \(\hbox {V}_{2}\hbox {O}_{5}\) residing in the oxygen layers45. Reports of \(\hbox {V}_{4}\hbox {O}_{9}\) are scarce; it is synthesised via the reduction of \(\hbox {V}_{2}\hbox {O}_{5}\)31,44,45,46 with \(\hbox {V}_{4}\hbox {O}_{9}\)[001] aligned with \(\hbox {V}_{2}\hbox {O}_{5}\)[010]31,44,45. Along its [001] direction \(\hbox {V}_{6}\hbox {O}_{13}\) consists of a V\(_2\)O\(_3\)-O\(_2\)-V\(_2\)O\(_3\)-V\(_2\)O\(_3\)-O\(_2\) stacking sequence. \(\hbox {V}_{6}\hbox {O}_{13}\) can be formed from \(\hbox {V}_{2}\hbox {O}_{5}\) via the removal of every third O\(_2\) plane. This reduction and a shear operation produces monoclinic \(\hbox {V}_{6}\hbox {O}_{13}\) from orthorhombic \(\hbox {V}_{2}\hbox {O}_{5}\) with \(\hbox {V}_{6}\hbox {O}_{13}\)[001] aligned with \(\hbox {V}_{2}\hbox {O}_{5}\)[010]28. Similarly to \(\hbox {V}_{2}\hbox {O}_{5}\) and \(\hbox {V}_{6}\hbox {O}_{13}\), \(\hbox {VO}_{2}\)(B) consists of V\(_2\)O\(_3\) and O\(_2\) planes. The stacking sequence is V\(_2\)O\(_3\)-V\(_2\)O\(_3\)-O\(_2\). This corresponds to removing every second O\(_2\) plane of \(\hbox {V}_{2}\hbox {O}_{5}\). This combined with a shear operation can produce monoclinic \(\hbox {VO}_{2}\)(B). This results in \(\hbox {VO}_{2}\)(B)[001] aligned with \(\hbox {V}_{2}\hbox {O}_{5}\)[010]. It is clear that \(\hbox {V}_{4}\hbox {O}_{9}\) (V\(_2\)O\(_3\)-O-V\(_2\)O\(_3\)-O\(_2\)) can act as a seed for the formation of \(\hbox {VO}_{2}\)(B) (V\(_2\)O\(_3\)-V\(_2\)O\(_3\)-O\(_2\)), in agreement with the literature31. Based on these discussed reduction mechanisms, in the following analysis of the XRD spectra \(\hbox {V}_{2}\hbox {O}_{5}\)<010>, \(\hbox {V}_{4}\hbox {O}_{9}\)<001>, \(\hbox {V}_{6}\hbox {O}_{13}\)<001> and \(\hbox {VO}_{2}\)(B)<001> reflexes are considered. The only exception is \(\hbox {V}_{6}\hbox {O}_{13}\)<010>, which has been observed by Transmission Electron Microscopy (TEM)47.

Starting with the crystal annealed at \({600}\,\hbox {K}\), the RAS signal (Fig. 4a) of the \({20}\,{\hbox {min}}\) anneal (black) produces noticeable changes to the pristine (Fig. 3b) spectra with peaks now at negative RAS units at energies greater than 3 eV. However, there is resemblence to the pristine spectra from the IR to around 3.2 eV. Further annealing reduces the optical anisotropy. The spectra after 4 (blue) and 6 hours (green) are qualitatively the same characterised by a minimum-maximum at \({2.7}-{3.1}\,\hbox {eV}\) and a small positive peak at \({3.5}\,\hbox {eV}\). At all stages of the annealing, XRD reveals \(\hbox {V}_{4}\hbox {O}_{9}\)<001> and \(\hbox {V}_{2}\hbox {O}_{5}\)<010> reflexes.

At \({700}\,\hbox {K}\), the initial \({20}\,{\hbox {min}}\) anneal (black) produces a RAS signal that exhibits a minimum-maximum at \({2.7}-{3.1}\,\hbox {eV}\) and a small positive peak at \({3.5}\,\hbox {eV}\) [Figure 4(b)]. The XRD of the \({20}\,{\hbox {min}}\) \({700}\,\hbox {K}\) anneal shows a strong \(\hbox {V}_{4}\hbox {O}_{9}\) peak, with small peaks assigned to \(\hbox {V}_{6}\hbox {O}_{13}\)(001). Additional annealing results in \(\hbox {V}_{6}\hbox {O}_{13}\)(001) increasing in intensity in the XRD. \(\hbox {VO}_{2}\)(B)<001> is assigned tentatively. At the same time the RAS spectra changes, with the minima-maxima shifting the lower energy and the minima becoming broader and lower in magnitude. After 4 h (purple) the optical anisotropy is reduced.

At \({800}\,\hbox {K}\) the initial \({20}\,{\hbox {min}}\) anneal produces a RAS signal (black) that is characterised by a strong IR response and a broad minimum at 2.3 eV (Fig. 4). Turning to the XRD the \({20}\,{\hbox {min}}\) anneal results in only \(\hbox {V}_{6}\hbox {O}_{13}\) peaks indicating the IR response is due to this phase. We note this is the first XRD is characterised entirely by \(\hbox {V}_{6}\hbox {O}_{13}\) and the first observation of the IR structure in the RAS. Further annealing shifts the broad RAS minima from 2.5 to \({2}\,\hbox {eV}\) progressively and to lower magnitude. At the same time the positive IR response is enhanced. The XRD is characterised by \(\hbox {V}_{6}\hbox {O}_{13}\) and \(\hbox {V}_{2}\hbox {O}_{5}\) at further annealing steps. \(\hbox {VO}_{2}\) is present in the crystal after 2 h of annealing and longer. The presence is \(\hbox {VO}_{2}\) is determined by resistance-temperature measurements presented in the Supplemental Information. At around 343 K the resistance of \(\hbox {VO}_{2}\) change by several orders of magnitude. \(\hbox {VO}_{2}\) is not observed in crystal annealed at the other temperatures. The influence of \(\hbox {VO}_{2}\) is discussed below.

At \({900}\,\hbox {K}\) the initial \({20}\,{\hbox {min}}\) anneal (red) produces a strong RAS response in the IR with a positive broad feature but also broad negative structures at higher energies with the most prominent being at \({2.5}\,\hbox {eV}\) (Fig. 4d). A further anneal (1 h) enhances both the positive structure in the IR and the negative structure at \({2.5}\,\hbox {eV}\). The IR structure is shifted to higher energy. Further annealing (blue) modifies the IR structure but at higher energies the spectra is very similar to the \(\hbox {V}_{2}\hbox {O}_{5}\)(010) spectra. A further hour anneal (green) reverts the spectra back to the original \(\hbox {V}_{2}\hbox {O}_{5}\) with very little deviation. The XRD at this temperature is straight forward being dominated by \(\hbox {V}_{6}\hbox {O}_{13}\)(001) (Fig. 4). Clearly the RAS is sensitive to more than XRD as the spectra changes with each annealing step. The spectra becoming \(\hbox {V}_{2}\hbox {O}_{5}\)(010)-like—even when \(\hbox {V}_{6}\hbox {O}_{13}\)(001) is present in the surface region—indicates that the \(\hbox {V}_{6}\hbox {O}_{13}\) is no longer contributing to the RAS signal. This is suggested to be due to a reduction in symmetry; if the (001)-orientated \(\hbox {V}_{6}\hbox {O}_{13}\) is polycrystalline in-plane, it will not produce a net RAS response. Evidently the surface region is less ordered. The \(\hbox {V}_{2}\hbox {O}_{5}\) signal is from the underlying non-reduced bulk.

Fig. 5
figure 5

(a) Comparison between RAS spectra of crystal annealed at different temperatures. A minima-maxima structure at 2.8–3.1eV is observed for the crystal annealed for a considerable duration (4 and 6 h depicted) at 600 K and for the crystal annealed for a short duration (20 minutes) at a higher temperature of 700 K. (b) Corresponding XRD characterised by \(\hbox {V}_{2}\hbox {O}_{5}\)<010> and \(\hbox {V}_{4}\hbox {O}_{9}\)<001>.

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In Fig. 5 we compare spectra of crystals annealed at different temperatures. The initial \({20}\,{\hbox {min}}\) anneal at \({700}\,\hbox {K}\) is qualitatively similar to \({600}\,\hbox {K}\) after 4 and 6 h (Fig. 5a). Each spectra contains a minimum-maximum at \({2.4}-{2.6}\,\hbox {eV}\) and a small positive peak at \({3.5}\,\hbox {eV}\). The XRD of each of these crystals is characterised entirely by \(\hbox {V}_{4}\hbox {O}_{9}\)<001> and \(\hbox {V}_{2}\hbox {O}_{5}\)<010> (Fig. 5b). Therefore, we attribute the minima-maxima feature from \({2.5}-{3.5}\,\hbox {eV}\) to \(\hbox {V}_{4}\hbox {O}_{9}\). Note, the a-axis of \(\hbox {V}_{4}\hbox {O}_{9}\) and \(\hbox {V}_{2}\hbox {O}_{5}\) are aligned48. Similar to \(\hbox {V}_{2}\hbox {O}_{5}\), let’s consider V-O distance in the \(\hbox {V}_{4}\hbox {O}_{9}\)(001) plane. If one assumes the electronic structure of \(\hbox {V}_{4}\hbox {O}_{9}\) is similar to \(\hbox {V}_{2}\hbox {O}_{5}\), the optical transitions are dominated by oxygen (valence band) to vanadium (conduction band) and the energy of the optical transitions is inversely proportional to the V-O distance. The smallest V-O distance of 1.68 Å is along \(\hbox {V}_{4}\hbox {O}_{9}\)[010] (y-axis in Eq. 1), while along \(\hbox {V}_{4}\hbox {O}_{9}\)[100] (x-axis in Eq. 1) the V–O distance is 1.78 Å. This is opposite to \(\hbox {V}_{2}\hbox {O}_{5}\) where the shortest V-O bond is in the x-axis. Within this simple framework of V-O bond distance for \(\hbox {V}_{4}\hbox {O}_{9}\)(001) we can hypothesise a negative RAS peak at lower energies followed by a positive peak, as is observed. An understanding of the electronic and optical properties of \(\hbox {V}_{4}\hbox {O}_{9}\) is required to comprehensively discuss the contributions from this phase, which has received very little attention.

\(\hbox {V}_{6}\hbox {O}_{13}\) IR structure

Fig. 6
figure 6

(a) The calculated (001) RAS spectrum of \(\hbox {V}_{6}\hbox {O}_{13}\) compared to the measured RAS spectrum of two single crystal samples annealed at different times and temperatures. This positive feature between \({1}-{2}\,\hbox {eV}\) is identified as a \(\hbox {V}_{6}\hbox {O}_{13}\) feature. (b) XRD pattern of the two annealed samples showing \(\hbox {V}_{6}\hbox {O}_{13}\)(001) reflections.

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As was discussed above, with increasing temperature (or duration of the anneal in the case of 700 K) a large IR feature develops. This directly coincides with the emergence of \(\hbox {V}_{6}\hbox {O}_{13}\)(001) peaks in the XRD. A RAS feature from \(\hbox {V}_{6}\hbox {O}_{13}\)(001) at low energy is unsurprising as the (001) plane is anisotropic and \(\hbox {V}_{6}\hbox {O}_{13}\) is metallic. In this section on the basis of \(\hbox {V}_{6}\hbox {O}_{13}\) ellipsometry measurements from the literature we confirm that this IR structure is due to anisotropic \(\hbox {V}_{6}\hbox {O}_{13}\)(001).

It is well established that the epitaxial reduction of \(\hbox {V}_{2}\hbox {O}_{5}\)(010) gives rise to the formation of \(\hbox {V}_{6}\hbox {O}_{13}\)(001) with their [100] axes aligned28,47. In Figure 6 we depict two RAS spectra which exhibit a strong IR RAS response. The corresponding XRD reveals these two samples are dominated by \(\hbox {V}_{6}\hbox {O}_{13}\)(001) and \(\hbox {V}_{2}\hbox {O}_{5}\)(010). Van Hove et al. measured the \({45}^{\circ }\) incidence reflection and absorption spectrum of \(\hbox {V}_{6}\hbox {O}_{13}\) along the [100] and [010] directions in the range \({0.2}-{3.2}\,\hbox {eV}\)49. These values are converted to a complex dielectric function and using Equation 2 a RAS spectrum for the \(\hbox {V}_{6}\hbox {O}_{13}\)(001) plane is generated (Fig. 6a). This spectrum has a maximum at \({1.2}\,\hbox {eV}\) and a minimum at \({2}\,\hbox {eV}\), matching the features seen in the presented experimental spectra. \(\hbox {V}_{2}\hbox {O}_{5}\)(010) exhibits a constant RAS in this region, and therefore will only offset this feature. Based on these findings we conclude this IR feature seen in our samples is due to \(\hbox {V}_{6}\hbox {O}_{13}\)(001).

Van Hove et al. attribute the absorption features below \({2.2}\,\hbox {eV}\) to inter-band transitions in the partially filled V3d band49. Anisotropies in charge state and geometry are present, but it is difficult to specifically attribute increased reflectivity in the [100] direction compared to [010] due to V-V structures. DFT electron-structure calculations50 suggest that \(t_{2g}\) transitions will dominate the IR, V 3\(d_{xz}\) \(t_{2g}\) shows strong anisotropy with the [100] direction exhibiting flat bands around the Fermi level and \(\sim\) \({1}\,\hbox {eV}\) above. [010] on the other hand shows significant dispersion. The presented positive RAS feature corresponds to a high reflectivity along the \(\hbox {V}_{6}\hbox {O}_{13}\)[100] direction in comparison to \(\hbox {V}_{6}\hbox {O}_{13}\)[010].

RAS measurements across the \(\hbox {VO}_{2}\) MIT

\(\hbox {VO}_{2}\) undergoes a SMT at \({340}\,\hbox {K}\)3. Below the transition temperature, the structure is monoclinic and semiconducting, while above it becomes rutile (orthorhombic) and metallic. Moving through the transition from the rutile phase, vanadium ions form dimer pairs along the rutile [001] lattice direction creating the monoclinic structure. The shift of ions causes crystal field splitting of the V-O orbitals resulting in a bandgap opening51.

\(\hbox {VO}_{2}\) has been reported to form with a polycrystalline structure through reduction52, so we do not expect an epitaxial relationship between \(\hbox {VO}_{2}\) and \(\hbox {V}_{2}\hbox {O}_{5}\). Furthermore, members of the Wadsley (V\(_n\)O\(_{2n+1}\)) series cannot be related to Magneli (V\(_n\)O\(_{2n-1}\)) phases by a common substructure. This is emphasised by the complex transformation of \(\hbox {VO}_{2}\)(B) (Wadsley) to \(\hbox {VO}_{2}\) (Magneli); it involves an initial disordering step followed by a reordering into \(\hbox {VO}_{2}\)53. In our recent work47, an \(\hbox {V}_{2}\hbox {O}_{5}\) crystal annealed at 800 K in high vacuum was examined by reciprocal space mapping. \(\hbox {VO}_{2}\) was observed in the reduced crystal and was polycrystalline within the probed angular window. Therefore, \(\hbox {VO}_{2}\) will not generate a RAS signal. A clear recorded change in optical properties of \(\hbox {VO}_{2}\) over the transition is an increase in absorption in the \({0}-{1}\,\hbox {eV}\) region54,55. Therefore, the SMT transition can modify the RAS spectra by modifying the total reflectance.

Fig. 7
figure 7

(a) Sheet resistance vs temperature and (b) change in the \(\hbox {V}_{6}\hbox {O}_{13}\) RAS feature as the temperature moves through the \(\hbox {VO}_{2}\) MIT temperature (\({340}\,\hbox {K}\)). The inset graph shows the measured RAS signal at \({0.8}\,\hbox {eV}\) through heating and cooling cycles. The shape of this graph is characteristic of the \(\hbox {VO}_{2}\) MIT transition.

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In order to establish \(\hbox {VO}_{2}\)’s influence on the RAS spectra we have examined a reduced crystal below and above the \(\hbox {VO}_{2}\) SMT temperature. This crystal have been annealed for 6 h at 800 K and XRD and resistance measurements indicate it contains \(\hbox {VO}_{2}\).

Figure 7, shows the previously established \(\hbox {V}_{6}\hbox {O}_{13}\) feature with a maximum at \({1.2}\,\hbox {eV}\) as the sample is heated through \({340}\,\hbox {K}\). The cooling cycle is not not depicted here for the sake of clarity. The RAS signal decreases in the range \({0.8}-{1.5}\,\hbox {eV}\) as the temperature increases, while no change is seen in the \({1.5}-{2}\,\hbox {eV}\) region. The decrease in signal is attributed to the increased absorption, and hence reflectivity, of the metallic \(\hbox {VO}_{2}\) phase in the IR54,55. Figure 7 (inset) plots the RAS signal at \({0.8}\,\hbox {eV}\) as a function of temperature for both heating and cooling. The resulting hysteric plot is characteristic of the \(\hbox {VO}_{2}\) first order transition. The increased reflectivity of \(\hbox {VO}_{2}\) across the transition temperature results in a decreasing RAS as has been observed in temperature dependant Fe\(_3\)O\(_4\) measurements22.

Conclusions

The optical anisotropy of pristine single crystalline and vacuum annealed \(\hbox {V}_{2}\hbox {O}_{5}\) has been examined ex-situ by reflectance anisotropy spectroscopy (RAS) in the range of 0.8–5 eV. The RAS spectra of the (010) plane of \(\hbox {V}_{2}\hbox {O}_{5}\) exhibits a constant signal in the IR range and significant structure beyond 2.5 eV. Axially resolved ellipsometry measurements facilitate the calculation of the RAS spectra, which is in good agreement.

The vacuum annealing of the single crystal \(\hbox {V}_{2}\hbox {O}_{5}\)(010) results in significant changes in the RAS spectra. The changes are characterised by the introduction of additional lower oxide phases, as confirmed by XRD measurements performed after each anneal. The RAS spectra are dependant on the annealing temperature due to the reduction of \(\hbox {V}_{2}\hbox {O}_{5}\) being strongly dependant on the temperature of vacuum annealing. However, RAS is far more sensitive to these structural and chemical changes than XRD, with significant optical modification observed while the diffraction pattern is unchanged.

Spectral signatures of \(\hbox {V}_{4}\hbox {O}_{9}\), \(\hbox {V}_{6}\hbox {O}_{13}\) and \(\hbox {VO}_{2}\) are identified. The IR signal of \(\hbox {V}_{6}\hbox {O}_{13}\) is calculated via the optical constants from the literature and shows good agreement with our RAS measurements. While \(\hbox {VO}_{2}\) does not possess an optically anisotropic response, it’s reflectance in the IR increases as it is heated through the SMT and becomes metallic at around 340 K. This changes the IR RAS magnitude, which is normalised by the total reflectance. The \(\hbox {V}_{4}\hbox {O}_{9}\) response is assigned based on the comparison to XRD measurements. There are no reports of the optical constants of this phase.

RAS can be employed in-situ as a non-destructive probe to identify changes in the stoichiometry and crystal structure in real-time. This ex-situ study demonstrates the sensitivity of RAS to these changes and identifies spectral signatures of multiple phases in this system.

Methods

RAS spectra were recorded at near-normal incidence with an in-house built reflectance anisotropy spectrometer which follows the Aspnes design56. Light from a Xe lamp passes through a Rochon \(\hbox {Mg}_{2}\hbox {F}\) polariser and is reflected from the sample. The beam passes through a photoelastic modulator (PEM), an analyzing polariser, and a monochromator before finally reaching a diode detector system. All measurements were performed from 0.8 to \({5.5}\,\hbox {eV}\); the broad spectral range has been realized using a monochromator and two individual photo diodes (InGaAs, Si). The real component of the complex RAS is presented.

\(\hbox {V}_{2}\hbox {O}_{5}\) single crystals have been grown by the floating zone technique. The growth process was carried out in oxygen flow at a crystallisation rate \({8}\,\hbox {mmh}^{-1}\). \(\hbox {V}_{2}\hbox {O}_{5}\) readily cleaves along the (010) due to weak bonding in that plane34 resulting in a reflective surface.

XRD characterisation utilized a Bruker D8 Discover, with a monochromatic copper K\(\alpha\)1 source and a position-sensitive detector (LynxEye), also used for reciprocal space maps (RSM). Spectroscopic ellispometry of a pristine \(\hbox {V}_{2}\hbox {O}_{5}\) crystal was performed using the variable angle spectroscopic ellispometry (VASE) method on a Sopra GESP 5 spectroscopic ellipsometer, which uses a rotating polariser configuration. RT measurements were performed using a linear four-point probe on a heated stage. Temperatures were restricted to room temperature and above. XPS measurements of the pristine crystal were performed using an Omicron Multi-Probe XPS system using monochromated Al K\(\alpha\) X-rays (XM 1000, \({1486.7}\,\hbox {eV}\)) with an instrumental resolution of 0.6 eV. Spectra have been analysed and fitted with CasaXPS. Temperature dependent RAS measurements were performed using a PID controlled heater for above room temperature measurements.