Single crystal growth from separated educts and its application to lithium transition-metal oxides

Thorough mixing of the starting materials is the first step of a crystal growth procedure. This holds true for almost any standard technique, whereas the intentional separation of educts is considered to be restricted to a very limited number of cases. Here we show that single crystals of α-Li2IrO3 can be grown from separated educts in an open crucible in air. Elemental lithium and iridium are oxidized and transported over a distance of typically one centimeter. In contrast to classical vapor transport, the process is essentially isothermal and a temperature gradient of minor importance. Single crystals grow from an exposed condensation point placed in between the educts. The method has also been applied to the growth of Li2RuO3, Li2PtO3 and β-Li2IrO3. A successful use of this simple and low cost technique for various other materials is anticipated.

, in order to investigate the effect of the small temperature gradient observed in b), the whole setup is placed on a platform to equalize the distance of the crucible to the upper and lower heating plate of the furnace. As expected for a symmetric arrangement ∆T ≈ 0 K. The growth is not affected and it is still possible to grow α-Li 2 IrO 3 single crystals in this configuration. This shows the minor importance of a temperature gradient in this method. The crystal structure of α-Li 2 IrO 3 is shown in Suppl. Fig. 4 and consists of an alternate stacking of honeycombs of edge-sharing IrO 6 octahedra with Li in the center, and hexagonal Li layers. Adjacent layers are stacked with an in-plane offset, leading to a monoclinic C2/m space group 1 . Diffraction data were collected on 'Sample 1' (samples are described in the main text, alongside representative data, shown in Fig 4.a-b). The diffraction pattern could be fully indexed with a monoclinic unit cell with lattice parameters (Supplementary Table 2) consistent with earlier reports 1 , with the empirical selection rules for the observed Bragg peaks h + k = even, as expected for a C-centered cell in the ab plane. Importantly, this sample showed no observable diffuse scattering, which would constitute qualitative evidence for stacking faults, nor was there evidence for twinning (discussed below). This allowed for a single phase structural model to be considered without introduction of twin models or site-mixing approximations for disorder. We performed a full structural refinement of the crystal structure parameters against all integrated X-ray diffraction intensities. The refinement gave a good agreement between model and data as shown in Suppl. Fig. 5, with reliability factors R(F 2 ) = 9.83%, wR(F 2 ) = 14.6%, R(F) = 5.82% and χ 2 = 3.82. The refined room temperature crystallographic parameters and quantitative details of the data collection are given in Supplementary Table 2, and the corresponding structure is drawn in Suppl. Fig. 4. In addition, we tested whether or not the crystal structure had lower symmetry than C2/m by describing it within the corresponding P1 primitive unit cell. This unit cell preserves all translational symmetry of the lattice, but only contains inversion symmetry. In this case, no improvement in the fit was achieved, and the same result was found within error as for the higher-symmetry, nominal C2/m cell in Supplementary Table 2. Further tests to explore Ir disorder through site-mixing with the Li ions also showed no improvement in the refinement, leading us to the conclusion that Sample 1 has a fully ordered, layered iridium honeycomb lattice in all three dimensions. We note that a key difference between the solution presented herein and that published by O'Malley et al. is the z-coordinate of O2. In our solution, the oxygen ions lie more closely within a common ab-plane, as observed in Na 2 IrO 3 2 .

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Supplementary Stacking Faults in α-Li 2 IrO 3 As discussed in detail in the case of the iso-structural Na 2 IrO 3 2 , as a result of the near hexagonal symmetry of the honeycomb layers there is only a rather small energy cost associated with a honeycomb layer being displaced in-plane by ±b/3. The presence of such occasional in-plane displacements in the layer stacking sequence is manifested in the X-ray diffraction pattern by diffuse rods of scattering along the l direction with the selection rule k = 3n + 1 or 3n + 2 (n integer) and h + k = even (due to the C-centering).
The diffraction patterns of two samples affected by stacking faults to different extents are compared in Fig. 4b−c in the main text and in the intensity profile in Fig. 4g in the main text. It is clear that while sample 1 shows very strong peaks at integer l with negligible diffuse signal in-between the sharp peaks, by contrast for sample 2 the Bragg peaks are very weak relative to the strong diffuse scattering, which extends across a wide range of l values.
Twinning in α-Li 2 IrO 3 There is a high incidence of twinning in α-Li 2 IrO 3 crystals. Most common are twins with the ab planes rotated relative to one another by 120 • around the normal direction, c * . The occurrence of such twins can be understood as follows. In the nominal structure subsequent honeycomb layers are vertically stacked with an in-plane offset along the −a direction, see Supplementary Figure 4a. Since the honeycomb layers have a near three-fold rotational symmetry around the vertical axis, there would be only a small energy cost if the in-plane offset direction were to rotate in the ab plane by ±120 • , and, if subsequent layers were then to stack according to this new offset direction, a new grain would form, rotated around the c * direction of the primary grain. We label such a twin C ± , where the superscript indicates the sign of the ±120 • rotation.
Another common twin (designated as type A) corresponds to a rotation by 180 • around the (101) direction, which swaps the a and c axes. This might occur because the a and c lattice parameters are very similar in magnitude. A third type of twin found corresponds to a rotation by ±90 • around the (101) axis, designated as B ± . We note that for a = c an A-type rotation is equivalent to two consecutive B-type rotations followed by a 180 • rotation around (010), i.e. A = 2 y (B ± ) 2 . For the given crystal structure the two-fold rotation around b leaves the atomic arrangement invariant as it is a symmetry operation of the C2/m space group. The above twinning types are summarized in Supplementary Table 3, where the last column gives the transformation matrix between the reciprocal space coordinates (h , k , l ) of the rotated twin and the corresponding coordinates of the primary (un-rotated) twin, defined as For simplicity the transformation matrix is given in the case when the structure has a hexagonal metric, where a : b : c = 1 : √ 3 : 1 and cos β = −1/3 (the latter equation corresponds to eclipsed stacking at the third layer). Those conditions are satisfied in the actual crystal structure to better than 1.4%.

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Supplementary  (101), brings the ±b * axis along (101) 4d in the main text shows the diffraction pattern for a multi-twinned crystal. Using the transformation matrices for the various types of twins we identify the peaks near fractional positions (0, 2, n + 1/3) (n integer) as being the nominal (11n) reflections of a C + twin, whereas peaks near (0, 2, n − 1/3) are the nominal (11n) reflections of a C − twin. Similarly, the peaks near (0, k, ±1), k = odd are identified as being the nominal (±1, −k, 0) reflections of an A twin. All peaks seen in the diffraction pattern can then be accounted for by an appropriate weighting of a primary grain with A, C + and C − twins, compare Fig. 4d and h) in the main text. The presence of B ± twins is most easily revealed by the diffraction pattern in the (h0l) plane (not shown) via peaks at (2n/3, 0, 2n/3) (n integer), which correspond to nominal (0, ∓2n, 0) reflections of the rotated grain. The B + or B − twins can subsequently be distinguished for example by the diffraction pattern in the (hkh) plane (not shown) where the nominal (001) reflection of the twins will appear at (−1/2, ±3/2, 1/2), respectively. We note that all the above types of twins could also occur in combination, i.e. an A type twin of the primary grain may have its own C ± twins and so on.