3.1. Crystals observed in this experiment

The diffraction patterns obtained for the sputtered Ag_3.4In_3.7Sb_76.4Te_16.5 amorphous film are shown in Fig. 1. The amorphous phase transformed into an A7-type crystalline single phase, as seen in this graph, at around 416 K. The results of a search match and Rietveld analyses revealed the diffraction patterns taken from 435 to 545 K to be almost identical to that of an As, Sb or Bi crystal with an A7-type structure (Clark, 1955), as has been previously elucidated (Matsunaga et al., 2001). The (conventional three-dimensional) Rietveld analysis results at 545 K are shown in Table 1(a). This crystal belongs to the space group ; the four constituent elements, Ag, In, Sb and Te, randomly occupy the 6c site (Matsunaga, Akola et al., 2011). The changes in the diffraction lines with increasing temperature show that the single-phase A7-type structure is maintained up to around 545 K. However, the peaks for CuFeS₂-type AgInTe₂ (Wyckoff, 1986) appear at around 590 K, along with those of the A7-type structure. This decomposition can be written as

These two phases formed by heating coexisted up to the high temperatures at which their Bragg peaks almost disappeared as a result of dissolving. As seen in this equation, the second decomposition product can virtually be regarded as an Sb-Te binary compound. Even at high temperatures close to the melting temperature, AgInTe₂ tightly held the CuFeS₂-type structure irrespective of temperature. However, our present analysis revealed that the structure of the second fragment, the Sb-Te compound, gradually changed with increasing temperature until obtaining its final stable atomic configuration. These structures can be closely approximated by the A7-type structure but are not real A7-type ones.

3.2. Homologous structures

We examined many types of chalcogenide materials to clarify the high-speed phase-change mechanism and develop new materials for future ultra-high-density phase-change recording devices. This revealed that, after sufficient heat treatments, almost all these materials finally fell into their stable crystals with so-called homologous structures. It has been found that in thermal equilibrium, the typical phase-change materials, the GeTe-Sb₂Te₃ pseudobinary system, the Sb-Te or Bi-Te binary system, form various intermetallic compounds represented by the chemical formulae (GeTe)_n(Sb₂Te₃)_m, (Sb₂)_n(Sb₂Te₃)_m or (Bi₂)_n(Bi₂Te₃)_m (n, m: integer). All these compounds have trigonal structures with 2n + 5m cubic close-packed periodicity (almost) without exception. [More specifically, the residual of (2n + 5m)/3 = 0 and 0 leads to the formation of crystals having structures with primitive (P) and rhombohedral (R) unit cells; they form structures with N = (2n + 5m) and N = 3*(2n + 5m) layers, respectively.] Table 2 shows the case of the GeTe-Sb₂Te₃ compounds; all of the existing intermetallic compounds in these systems follow this rule (Matsunaga & Yamada, 2004a; Matsunaga, Yamada & Kubota, 2004; Matsunaga et al., 2007a,b, 2010; Matsunaga, Kojima et al., 2008). This could also be confirmed from the relevant tables in other papers (Karpinsky et al., 1998; Kuznetsova et al., 2000; Shelimova et al., 2000, 2004; Shelimova, Karpinskii et al., 2001; Shelimova, Konstantinov et al., 2001; Poudeu & Kanatzidis, 2005). These structures are similar to each other and systematically characterized by the stacking of the (GeTe)_n and (Sb₂Te₃)_m, (Sb₂)_n and (Sb₂Te₃)_m, or (Bi₂)_n and (Bi₂Te₃)_m blocks along the axes, with very long cell dimensions in the conventional three-dimensional structure description (Karpinsky et al., 1998; Shelimova et al., 2000; Shelimova, Karpinskii et al., 2001; Poudeu & Kanatzidis, 2005; Matsunaga & Yamada, 2004a, Matsunaga, Yamada & Kubota, 2004; Matsunaga et al., 2007a,b, 2010; Matsunaga, Kojima et al., 2008; Matsunaga, Morita et al., 2008). More generally and more precisely it has been assumed that these structures should be described as commensurately or incommensurately modulated four-dimensional structures characterized by modulation vectors (Lind & Lidin, 2003), where values are real numbers equal to or around 3(n + 3m)/(2n + 5m) [see equation (3); is the fundamental reciprocal vector formed by three-layer cubic stacking]. For instance, it has been clarified that, in the thermal equilibrium, Sb₈Te₃ (n = 3 and m = 1) has a homologous structure characterized by a modulation vector (Kifune et al., 2005, 2011). Thus, we applied this more universal four-dimensional superspace method for analysis of the Sb-Te compound formed by thermal decomposition [see equation (1)].

3.3. Structures of Ag_3.4In_3.7Sb_76.4Te_16.5 and Sb₈₉Te₁₁ compounds

As the initial structure models for the four-dimensional Rietveld refinements we adopted the layer stacking structures defined by the respective values. In other words, in the Sb-Te compounds examined in this study, the modulation functions for Sb and Te atoms were respectively distributed around t = 0 and t = 1/2 (t: internal parameter along the x₄ axis, the fourth crystal axis in four-dimensional space; Lind & Lidin, 2003). This corresponds to a structure in which Sb and Te are placed at 0, 0, 0 and their atomic species are distinguished using crenel functions (for Sb₈₉Te₁₁, width: 0.89 + center: 0 for Sb and width: 0.11 + center: 0.5 for Te). As there is a difference of only one between the atomic numbers of Sb⁵¹ and Te⁵², it is very difficult for us to distinguish the kinds of atoms in their unit cells. We use the assumption that all of the Sb-Te crystals examined in this study have perfectly ordered atomic arrangements like those of other (binary) systems. The intensities of the satellites for Sb-Te compounds are rather weak in general. Those of Sb₈₉Te₁₁ are no exception; almost all of the satellites observed were reproduced by adopting the maximum satellite index of 2 for the Rietveld analyses. The atomic displacements were represented using harmonic functions.

The four-dimensional Rietveld analyses performed with the diffraction patterns in Fig. 1, as mentioned above, provided the structural dependence on the temperature for Ag_3.4In_3.7Sb_76.4Te_16.5 (at low temperatures) and its thermally decomposed materials (at high temperatures). The results of the Rietveld analyses at 545 K for Ag_3.4In_3.7Sb_76.4Te_16.5, whose crystal still maintains an A7-type structure, are shown in Table 1(b) and Fig. 2 (cf. Table 1a, from the three-dimensional Rietveld analysis). In the four-dimensional analysis for this crystal, displacement for only a single atom in a three-dimensional asymmetric unit has to be described by selecting the appropriate one from among several kinds of modulation functions; in this case, the use of a sawtooth function (Dusek et al., 2010) was revealed to give better results than a harmonic function, as seen in Fourier maps based on F_o (Fig. 3). We can see from Fig. 4, maintained a constant value of 1.5 up to a temperature of around 590 K, at which AgInTe₂ came out. However, above this temperature, grew larger with increasing temperature and reached a value of around 1.55 at high temperatures near the melting point of Sb_76.4Te_9.7 (= Sb_88.7Te_11.3 when expressed as a percentage), which was found at around 870 K according to our present high-temperature measurement. The value was maintained at around 1.55 even when the powder specimen was cooled back to room temperature. The results of the Rietveld analysis at room temperature are shown in Table 3(a) and Fig. 5. The refined modulation functions of Sb and Te and the corresponding de Wolff section of the observed Fourier map are shown in Fig. 6(a), together with a Fourier map based on F_o. The difference Fourier maps obtained from the determined structure models exhibited few significant residual peaks, which showed the need for further structural modification or improvement. This was similar to those obtained at the high temperatures of 774 and 820 K. The values of around 1.55 found in these stagnated structures correspond well with the value of 1.5565 expected from the composition of Sb_88.7Te_11.3. Here we can simply derive in terms of x as

when the chemical formula for the binary system is written as Sb_xTe_1 - x or Bi_xTe_1 - x (Lind & Lidin, 2003). It can be considered that after Sb_76.4Te_9.7 was segregated from AgInTe₂, it revealed its original crystalline nature to change the layer period () from 1.5 (n = 1, m = 0; A7-type six-layer structure) to 1.55 (another long-period layer structure), and it also clarified that, surprisingly enough, even an Sb-Te compound with as much as 89% Sb can exist as a single homologous structure in its binary system. We can obtain

by comparing Sb_xTe_1 - x with (Sb₂)_n(Sb₂Te₃)_m. The crystal structure ( 1.55) at high temperatures at which the growth became stagnant can be approximated reasonably well by a commensurately modulated 29-layer structure with n = 12 and m = 1 ( = 45/29; this three-dimensional structure model is shown in Fig. 7a). We also carried out a Rietveld analysis assuming that this Sb-Te crystal had a commensurately modulated structure with this rational number of . As shown in Table 3(d), this analysis gave almost the same good results as in the incommensurate case (however, for this material it could not be concluded that it had transformed to a commensurate three-dimensional structure, in contrast to Sb₈₇Te₁₃, which will be discussed later). The Fourier map obtained from this four-dimensional analysis performed in the commensurate case is almost identical with all those in Fig. 6, as expected. In addition to the dependence on temperature of this Sb-Te material, the Sb₈Te₃ sputtered amorphous film showed a small value just after the transformation to the crystalline phase. However, became larger with increasing temperature to finally obtain its original long-period layer structure. We found that, in addition to the Sb₈Te₃ film, some other Sb-Te films at various compositions show very similar behavior (we will show the results for these materials elsewhere in the near future). These results strongly suggest that not a few (at least) Sb-Te compounds, just after their crystal formations, transiently assume small values (it is highly probable that these values all start at 3/2), and when adequately treated with heat, they become larger to attain their respective, intrinsic homologous structures, depending on their binary compositions.

The atomic displacements (modulation functions) have already been shown in a stagnant structure of Sb₈₉Te₁₁ (see Fig. 6). However, just after the phase decomposition, the atomic displacements varied appreciably, as seen in Fig. 8. This figure shows, however, that such a varied atomic arrangement becomes more moderate with increasing temperature, and comes closer to those observed in the stagnated structures. In response to this structural change, although the interatomic distances in Sb₈₉Te₁₁ just after the phase decomposition are rather dispersed, especially for Te-Sb pairs, they converge with the structural inactivation, as seen in Fig. 9. As mentioned above, before the phase decomposition, Sb and Te atoms (and the dopants) were randomly distributed in the A7-type structure. Therefore, it is expected that just after the decomposition, the crystal still has a strongly disordered atomic arrangement. However, during the structural change with increasing temperature, it gradually attains the perfectly ordered structure shown above (Kifune et al., 2011).

As mentioned above, we used harmonic functions to describe the atomic displacements. However, to examine them more precisely, the JANA2006 program provides several other functions in addition to the harmonic one. We performed further analyses by using some of these functions. However, these analyses gave us almost the same results as shown in Fig. 6 and Tables 3(b) and (c).

3.4. Suitability of Sb-Te-based compounds for high-speed phase-change recording devices

As has so far been shown, an Sb-Te compound containing Ag and In maintains a six-layer structure ( = 3/2) up to a high temperature, at which phase separation occurs. On the other hand, Sb-Te films without such dopants show values larger than 3/2 immediately after the crystallization. This strongly suggests that the Ag and In dopants play roles in maintaining the simple structure of the Sb-Te matrix. It also inversely implies that every Sb-Te binary-compound film will experience a six-layer structure in a very short time right after the crystal formation because six layers is the simplest and shortest layer structure out of all of the possible homologous structures from Sb ( = 3/2) to Sb₂Te₃ ( = 9/5). Many studies (for instance, Matsunaga, Akola et al., 2011) have shown that phase-change chalcogenide amorphous materials have spatially isotropic atomic arrangements; it is highly likely that they crystallize once into simple and spatially isotropic structures, like a cubic crystal, because a six-layer (A7-type) structure can be well approximated by simple cubic lattices (Matsunaga & Yamada, 2004b).

The atomic configuration in the amorphous phase of this material, which has already been revealed (Matsunaga, Akola et al., 2011), is highly disordered, similar to that of a liquid, and spatially has a completely isotropic symmetry. However, it has also been revealed that it has 3 + 3 coordination structures even in such a disordered atomic arrangement, as well as that of the crystalline phase: that is, both phases have very similar coordination structures, i.e. locally very similar atomic arrangements (it is well known that an A7-type crystal has a 3 + 3 coordination structure; Clark, 1955; Hoffmann, 1988). This is one of the major reasons that this material achieves a sufficiently high phase-change speed by locally minimal bond interchanges. As for the dopants, it has been presumed that either or both Ag and In atoms probably raise the crystallization temperature of the amorphous phase to obtain a sufficient endurance for long-term data preservation. In addition, as mentioned above, they make the atomic arrangement of the crystal simple and spatially isotropic, holding the material in a single phase. It is expected that these are indispensable features for high-speed rewritable data storage media. In the near future, however, the individual roles played by Ag and In in the phase change of this material should be clarified.

3.5. Three- or six-layer structure approximation for Sb-Te compounds

In our previous work (Matsunaga et al., 2001) Sb-Te compounds with small amounts of Ag or In were concluded to hold an A7-type structure up to the melting point. However, we must say that these compounds do not have an exact A7-type structure but a long-period modulated structure defined by the binary composition in thermal equilibrium. The A7-type (six-layer) structure is also one of the modulated structures (corresponding to the shortest period one). All the above-mentioned modulated structures can be approximated by a (cubic stacked) three-layer structure, which provides the fundamental lines in the diffraction patterns. If atoms at the 6c site are located at z = 1/4 in the A7-type structure, it corresponds to the three-layer structure. In the previous temperature measurement, one end of the capillary holding the powder specimen was open to the air, which yielded not a little Sb oxide (Fig. 10). This oxide formed a line of unnecessary Bragg peaks, which hindered us from determining the (weak) satellite peaks identifying the layer period of the structure. Further, at that time, such modulated structures were not familiarly associated with the Sb-Te binary system. All these factors made it difficult for us to discern that these Sb-Te-based alloys can take modulated structures. Thus, in previous work the A7-type structure was exclusively applied in the structural analyses, irrespective of the measurement temperature, which provided apparently sufficient results. In addition, in this work the same structural analysis was carried out to confirm the reproducibility of the previous work; we analyzed the structures by applying this simple 6R structure to them. The results are shown in Table 4. As shown in this table, the R factors were sufficiently low and the positional parameter z gradually increased with temperature (which meant that the structure model for the Rietveld analysis gradually became closer to the three-layer structure), which accurately reproduced the previous results. However, the agreement between the profiles of the observed and calculated intensities became worse as the temperature rose, especially for the (weak) satellite reflections. On the other hand, those obtained through the four-dimensional analyses showed good agreement with each other, even at high temperatures near the melting point, as seen in Fig. 10. This strongly indicates that at high temperatures beyond the phase separation (or in the thermal equilibrium), this Sb-Te compound is not an A7-type structure ( = 3/2) itself but one of the homologous structures defined by > 3/2.

The present examination clarified that this Sb-Te compound has a long-period modulated structure like that of the aforementioned Sb₈₉Te₁₁. The modulation period kept a constant value of almost 1.5 up to a temperature of around 600 K, at which the oxidation of Sb started. However, above this temperature, just as in the Sb₈₉Te₁₁ case, grew larger with increasing temperature and reached a value of around 1.56 at high temperatures near the melting point (in contrast, in the previous experiment, Bragg peaks corresponding to AgInTe₂ were hardly observed for some reason). This value indicated that the composition of the compound should be ca Sb₈₇Te₁₃ [see equation (2)]. Here, we ignore the locations of Ag and In because they are minor elements. We carried out four-dimensional structural analyses for the two cases where this Sb-Te crystal took an incommensurately or commensurately modulated structure. As shown in Table 5 these analyses gave almost the same good results, when = 36/23 (n = 9, m = 1; Sb_87.0Te_13.0) was applied in the commensurate case (this three-dimensional structure model is shown in Fig. 7b). However, the results of the commensurate case could be considered somewhat better than those of the incommensurate case (cf. Table 5a with Table 5b1), in contrast to the examination of Sb₈₉Te₁₁. In addition, we can find a clear t₀ dependence of the R values in the results of the Rietveld analyses performed in the commensurate case (cf. Table 5b1 with Table 5b2). This strongly suggests that this Sb₈₇Te₁₃ compound eventually obtained a (probably stable) commensurate structure through rearrangement of the atoms from the A7-type atomic configuration after sufficient heat treatment for this material, as observed in the case of Sb₈Te₃ (Kifune et al., 2011). Generally, the determination between the commensurate and incommensurate case seems to be beyond the information contained in our powder data. However, we believe that it is very likely that many of these compounds ultimately obtain commensurate structures after sufficient heat treatment. We intend to conduct further experiments and analyses for these materials to reveal their structural features more precisely.