X-ray diffraction data and analysis to support phase identification in FeSe and Fe7Se8 epitaxial thin films

X-ray diffraction (XRD) data and analysis for epitaxial iron selenide thin films grown by pulsed laser deposition (PLD) are presented to support the conclusions in the related research article “Double epitaxy of tetragonal and hexagonal phases in the FeSe system” [1]. The films contain β-FeSe and Fe7Se8 phases in a double epitaxy configuration with the β-FeSe phase (001) oriented on the (001) MgO growth substrate. Fe7Se8 simultaneously takes on two different epitaxial orientations in certain growth conditions, exhibiting both (101)- and (001)- orientations. Each of these orientations are verified with the presented XRD data. Additionally, XRD data used to determine the PLD target composition as well as mosaic structure of the β-FeSe phase are shown.

greatest interest in recent years is tetragonal b-FeSe (space group P4/nmm), due to intense interest in its superconducting properties, and has been successfully isolated in thin films across a broad range of conditions [2]. Several hexagonal iron selenide variants lie in close proximity to b-FeSe in the FeeSe phase diagram. Stoichiometric d-FeSe forms with the NiAs structure (space group P6 3 mc) at high temperatures and Fe 7 Se 8 can form concurrently with b-FeSe in the presence of a slight excess of Se at lower temperatures [3,4]. This property, in combination with proper choice of substrate, can be taken advantage of to grow epitaxial thin films which contain two phases of iron selenide in a configuration known as double epitaxy. Double epitaxy may be useful to modulate the properties of the grown materials by introducing many interfaces at fixed angles with respect to each other as well as to the substrate. Fe 7 Se 8 has a fundamental NiAs-type lattice, identical to d-FeSe, but with ordered Fe vacancies which take on several different arrangements depending on the synthesis technique and annealing times and temperatures [5]. The two Fe vacancy orderings most commonly observed and with relevance to the present work are the 3c and 4c structures of Fe 7 Se 8 . Ordered Fe vacancies in these structures repeat along the c-axis at increments that are three (3c) or four (4c) times the fundamental NiAs-type c lattice constant. The 3c unit cell is defined with lattice constants A ¼ 2a and C ¼ 3c while the 4c unit cell is defined by where a and c are the shared NiAs-type lattice constants [5].
In the related research article [1], epitaxial thin films were grown by pulsed laser deposition (PLD) using a target formed of a mixture of b-FeSe (22%) and 3c-Fe 7 Se 8 (78%) whose X-ray diffraction (XRD) is shown in Fig. 1. All observed diffraction peaks in Fig. 1 index to either b-FeSe or 3c-Fe 7 Se 8 . 3c-Fe 7 Se 8 is easily identified in the PLD target, instead of 4c-Fe 7 Se 8 , by the 3c-(115) peak at 2q ¼ 35.41 . The (115) reflection is due to the iron vacancy ordering so it is not present in the fundamental NiAs structure (d-FeSe) and there are no possible 4c reflections near the same location. During certain growth conditions, the resulting films took on a doubly epitaxial configuration in which both b-FeSe and Fe 7 Se 8 grew epitaxially oriented. b-FeSe was c-axis oriented, with the (001) plane oriented parallel to the substrate surface. Rocking curve analysis (Fig. 2) of the (001) reflection indicates mosaic structure in this phase, with a FWHM ¼ 1.30 that is much larger than the instrumental resolution of 0.08 .

Value of the Data
The data provide insight on how to identify crystal phases in epitaxial thin films that share the same fundamental structure but differ in their the vacancy superstructure or lack thereof. Similar measurements and analysis procedures as shown in this article can be used to aid in the phase identification of other closely related crystal structures in single crystal samples.
The data provides important supplementary information to the related research article.
It cannot be assumed that 3c-Fe 7 Se 8 formed during PLD growth because the specific structure of Fe 7 Se 8 is highly dependent on growth conditions. Because 3c-and 4c-Fe 7 Se 8 share the same fundamental NiAs-type structure, their powder XRD patterns differ only in vacancy superstructure diffraction peaks. Standard q-2q scans do not provide enough information to differentiate between the two structures when they are epitaxially oriented because the orientation makes many reflections geometrically unavailable. Based on the q-2q XRD scans in Fig. 1 of [1], the orientation of the Fe 7 Se 8 Fig. 1. Undoped FeSe target XRD shows a mixture of 22% b-FeSe and 78% 3c-Fe 7 Se 8 . phase was found to take on two different orientations with (101) and (001) planes oriented parallel to the substrate surface, using Miller indices referred to the setting of the fundamental NiAs-type structure of Fe 7 Se 8 . This convention of indexing the Fe 7 Se 8 lattice planes and reflections with respect to its fundamental NiAs-type structure is adopted throughout this paper, unless otherwise noted, and is necessary whenever it is not possible to specify which Fe vacancy superstructure (3c or 4c) is present, which is our case.
In order to verify the (001) orientation of Fe 7 Se 8 , powder diffraction patterns were generated to compare with the q-2q scan of a thin film grown with a substrate temperature of 550 C and laser fluence of 3.4 J/cm 2 , in which the c-axis diffraction peaks were more intense than in any other sample. In Fig. 4, the 2q scans predominantly feature two major reflections, one near 2q ¼ 42.5 and the other near 2q ¼ 55.5 . The peak near 2q ¼ 42.5 is the (102) reflection of Fe 7 Se 8 , which is equivalent to either 3c-(206) or 4c-(408). The angle of this measured plane with respect to the substrate surface is 19.2 which is a good match to the 18.8 interplanar angle between Fe 7 Se 8 (101) and (102), confirming the (101) orientation of Fe 7 Se 8 . The second major peak near 2q ¼ 55.5 is consistent with the b-FeSe This means that the majority, if not all, of the intensity measured near 2q ¼ 55.5 is due to the b-FeSe (103) reflection. Discrepancies between interplanar angles and 2q positions are due to differences in the theoretical lattice constants used for calculations and the lattice constants of the actual thin film.
The choice of u ¼ 2 is a compromise that enables both Fe 7 Se 8 (102) and b-FeSe (103) to be visualized on the same XRD scan. Since mosaicity is confirmed in the films, the peaks observed in the 2q scans are actually observable over a range of u with the true peak intensity existing at some optimized u value for each phase, which is unlikely to be exactly 2 . Therefore, the presented 2q scans should not be used to calculate lattice constants because the peak 2q value may be false. Reciprocal space mapping would enable the identification of the true peak intensity and correct lattice constants could be calculated.
The raw data for all of the XRD scans that were discussed have been uploaded alongside the article to be made available for download.

Experimental design, materials, and methods
Rocking curve and 2q XRD scans were carried out on a Philips X'Pert-MPD with Cu Ka radiation. Incident and diffracted optics, as well as scan parameters were the same in each case. A 1/8 divergence slit and 10 mm mask were used on the incident side and the diffracted x-rays were passed through a parallel plate collimator and detected with a proportional counter. The step size was 0.05 with a time per step of 0.5 s. The incident angle for the 2q scans was fixed at u ¼ 2 and 2q was fixed at 16.064 for the rocking curve scan. PLD target composition was calculated using the Rietveld refinement function in Powder Cell [6].
The powder diffraction patterns for d-FeSe, 3c-, and 4c-Fe 7 Se 8 were generated using the VESTA software [7]. The 4c unit cell was defined in VESTA based on the crystal structure given by Okazaki [5] and the 3c structure was adapted from Parise [8] to have the lattice parameters a ¼ 7.2631 Å and c ¼ 17.550 Å. The 4c structure was made orthorhombic with lattice parameters a ¼ 12.580 Å, cos4 ¼ h 1 h 2 þ k 1 k 2 þ 1 2 ðh 1 k 2 þ h 2 k 1 Þ þ 3