Sample compositions, heat treatments and results of powder-XRD and EDX/WDX are summarized in Table 3. Table 4 contains the results of DTA measurements. A partial Bi-Rh phase diagram for compositions up to 70 at.% Rh based on data obtained in this study and data from Ref 9 and 26, is presented in Fig. 1. Figure 2 and 3 show detail sections for the composition ranges 33.3-52 at.% Rh (if BiRh0.81 is absent) and 19-33.3 at.% Rh (if metastable BiRh3 is present). The Bi-rich part between 0 and 20 at.% Rh was entirely taken from Okamoto. Figure 4(a), (b), (c), and (d) show SEM backscattered images for selected samples.
The liquidus curve in Fig. 1 is based on DTA results of the quenched samples. Its shape, together with the corresponding invariant effects, indicates that the phases BiRh and β-Bi2Rh are formed by peritectic reactions, i.e., liquid with about 47 at.% Rh reacts at 979 ± 2 °C with Rh to form BiRh, and liquid with about 29 at.% Rh reacts at 785 ± 2 °C with BiRh to form β-Bi2Rh. These values are in good agreement with results of Ross and Hume-Rothery (46.0 at.% Rh at 977 °C for BiRh and 29.5 at.% Rh at 780 °C for Bi2Rh), based on results from cooling curves.
The shape of the liquidus curve at higher temperatures above the peritectic decomposition of BiRh could not be determined, because no signals were found except in the sample Bi53Rh47 (1016 °C). This indicates a very steep ascent to the melting point of Rh.
Composition Range 20-33.3 at.% Rh
The obtained results differ somewhat from the phase diagram assessed by Okamoto. In particular, no hint was found for the existence of the Bi3Rh phase in the XRD or EDX measurements of annealed samples. All samples in the investigated composition range showed exclusively Bi4Rh and α- or β-Bi2Rh, independently of their annealing temperatures (Table 3).
DTA analyses of these samples show on first heating an extrapolated onset of the endothermic effect at 460 ± 3 °C which represents the peritectic reaction (L + β-Bi2Rh \(\rightleftharpoons\) Bi4Rh) temperature (Table 4). This value is slightly lower than the one reported by Weitzer et al. (466 °C) but in perfect agreement with the 460 °C assessed by Predel. Two thermal effects with average temperatures of 328 ± 5 and 448 ± 2 °C were observed only in the corresponding second heating runs.
It was concluded that these correspond to the eutectoid and peritectoid reaction temperatures of (metastable) Bi3Rh, described by Weitzer et al. into α-Bi2Rh and Bi4Rh at 336 °C (Bi3Rh \(\rightleftharpoons\) Bi4Rh + α-Bi2Rh) and 433 °C (Bi4Rh + β-Bi2Rh \(\rightleftharpoons\) Bi3Rh). XRD measurements of samples after the DTA analyses did not show the Bi3Rh phase.
Combining the results of all analyses (Tables 3 and 4) suggests that Bi3Rh is actually a metastable phase which does not form in annealed samples, fully consistent with observations by Ross and Hume-Rothery who were likewise not able to detect the Bi3Rh phase. It is probably also in line with the report by Weitzer et al. who considered Bi3Rh to be a stable compound but found that it could only be obtained by annealing a mixture of Bi2Rh with a metastable phase, i.e., Bi14Rh3.
The Phase Bi2Rh
WDX/EDX measurements of all samples containing β-Bi2Rh show an average composition of 34.9 ± 0.5 at.% Rh independent of the annealing temperature. This value differs somewhat from the stoichiometric composition of 33.3 at.% Rh. It is thought that this discrepancy is due to problems with the WDX/EDX measurements: the characteristic XRD radiation spectra of Bi and Rh, especially the Bi M line at 2.419 keV and the Rh L
α1 line at 2.697 keV, are rather close, which makes it difficult to separate them in the measurement (see section 3.2). DTA results of samples containing the Bi2Rh phase show an invariant reaction at 785 ± 2 °C which presents the peritectic reaction (L + BiRh \(\rightleftharpoons\) β-Bi2Rh). This temperature is in better agreement with the results by Ross and Hume-Rothery (780 °C) and Kjekshus and Rakke (778 ± 4 °C) than with those reported by Ref 16, 18, and 22 where it is somewhat lower.
Weitzer et al. indicated the transition of α- into β-Bi2Rh at 370 °C which could not be verified here, neither by DTA nor by powder XRD measurements of annealed samples. The data obtained in this study indicate a much more complex transition, its temperature being different below and above 33.3 at.% Rh, respectively, and also depending on the presence or absence of metastable Bi3Rh or stable BiRh0.81 phase.
XRD analysis of a sample with the stoichiometric composition Bi66.7Rh33.3, annealed for 46 days at 400 °C, shows only α-Bi2Rh (Fig. 5, bottom). A sample with 35 at.% Rh, quenched from 730 °C, showed originally β-Bi2Rh and BiRh (Fig. 6, bottom); this sample was then subjected to high temperature XRD. On heating, the phase α-Bi2Rh appears at 250 °C and disappears between 400 and 450 °C indicating a transition α-Bi2Rh \(\rightleftharpoons\) β-Bi2Rh below 450 °C on the Rh-rich side. Unfortunately, Bi2Rh starts to decompose above 500 °C due to the evaporation of Bi in the evacuated high-temperature x-ray chamber and disappears completely around 550 °C, leaving only the BiRh phase.
The obtained XRD results are in good agreement with DTA data, which show in all samples with Rh contents ≥ 35 at.%, independently of the annealing parameters, an invariant effect at 448 ± 2 °C (Table 4) if the new phase BiRh0.81 is not present. Quenching experiments indicate that this transition temperature is approximately 440 ± 5 °C if the BiRh0.81 phase is present (Table 3).
The α \(\rightleftharpoons\) β transition temperature in the composition range below 33.3 at.% Rh is 426 ± 3 or 433 ± 3 °C, depending on the absence or presence of the metastable Bi3Rh phase. XRD investigations of samples with 23 (Fig. 5, top) and 28.4 at.% Rh, annealed at 430 °C, (Table 3) reveal the β modification of Bi2Rh, the sample with 28 at.% Rh, annealed at 400 °C, showed the α modification. These XRD results are in good agreement with DTA data, which show for all samples, independent of the annealing temperature, thermal arrests between 423 and 427 °C (Table 4). They also agree with values of Kuz´min and Zhuravlev (420 °C, DTA), Ross and Hume-Rothery[9,23] (430, 425 °C, high temperature XRD), Kjekshus and Rakke (425 ± 3 °C, DTA and quenching experiments) and Fjellvag and Furuseth (427 ± 10 °C, high temperature XRD).
It is concluded that this difference in the α \(\rightleftharpoons\) β transition temperature for compositions below and above 33.3 at.% Rh is caused by a eutectoid on the Bi-rich side (β-Bi2Rh \(\rightleftharpoons\) Bi4Rh + α-Bi2Rh) and a peritectoid on the Rh-rich side (α-Bi2Rh \(\rightleftharpoons\) β-Bi2Rh + BiRh/BiRh0.81) as indicated in the inset in Fig. 1.
If the metastable Bi3Rh phase is present, DTA measurements of samples between 28 and 31 at.% Rh show, independent of the annealing parameters, an invariant effect at 433 ± 3 °C for the α \(\rightleftharpoons\) β transition (Table 4). But once again it must be pointed out that metastable Bi3Rh only occurs in second heating loops. A graphical presentation of the reported values is given in Fig. 1 to 3. The average transition temperature of 433 ± 3 °C (< 33.3 at.% Rh) corresponds to the value of 433 °C, which Weitzer et al. reported for the peritectoid decomposition of the Bi3Rh phase.
The Phase BiRh
The obtained homogeneity range of the phase BiRh differs from data reported in the literature[9,17] as well as does the temperature of the peritectic.[16,20,26]
In particular, DTA results of samples between 47 and 60 at.% Rh show an invariant reaction at 979 ± 2 °C which is the peritectic decomposition temperature of BiRh. This value conforms to the 977 °C reported by Ross and Hume-Rothery but is 20 °C lower than assessed by Okamoto. Results on the homogeneity range of BiRh are somewhat contradictory: WDX/EDX results of samples in the adjacent two-phase fields, annealed at 750 °C seem to indicate a rather narrow stability range for BiRh between about 49.8 and 50.9 at.% Rh. These values are in contrast to powder XRD investigations of samples between 47 and 52.5 at.% Rh which show only BiRh and no second phase. As described in section 4.3, the characteristic XRD radiation spectra of Bi and Rh are rather close, which makes it difficult to separate them in the measurement. Therefore, the EDX/WDX values may show unusually high errors and the homogeneity range of BiRh, as it is shown in Fig. 1, is deduced from the lattice parameter measurements (Table 3 and Fig. 7).
The present results are in significant contrast to the values reported in the literature, particularly in Ref 16, 17, 24, and 26. Of these, Glagoleva and Zhdanov annealed their samples at 800 °C but let them slowly cool down to room temperature instead of quenching; thus, their lattice parameters correspond obviously to some lower temperature. The results can be best compared to data by Ross and Hume-Rothery who determined the homogeneity range of BiRh at 780 °C as 48.0-50.6 at.% Rh; this is in reasonable agreement with the present phase boundary on the Bi-rich side at 750 °C, i.e., 46.9 at.% Rh, deduced from lattice parameter investigations. Extrapolating the lattice parameter a of a sample with 46.5 at.% Rh (annealed at different temperatures) to the plotted regression line (Fig. 7) indicates a pronounced retrograde solubility of BiRh, resulting in a phase boundary of about 48 at.% Rh at 900 and about 50.5 at.% Rh at 565 °C. On the Rh-rich side, the lattice parameter measurements give a phase boundary of 53.5 at.% Rh at 750 °C which points to a much wider homogeneity range of BiMn than reported in Ref 9
The Phase BiRh0.81
SEM–EDX investigations of a sample with 50 at.% Rh, annealed for 21 days at 438 °C, showed, besides the known phases BiRh and Bi2Rh, also a phase with a composition of Bi55Rh45 (54.9 at.% Bi and 45.1 at.% Rh). High temperature XRD measurements of the same sample (Table 5 and Fig. 8) showed that the reflexes of this phase disappear between 475 and 500 °C.
Indexing of the unknown diffraction lines and subsequent refinement of the powder XRD pattern of a sample with the composition Bi55Rh45, annealed for 27 days at 440 °C (Table 3), indicates that the new phase is orthorhombic (Pnma) with the lattice parameters a = 6.1753(9) Å, b = 3.7817(1) Å, c = 6.5506(1) Å. Refinement was successful using the structural model for the MnP-type structure, which is closely related to the NiAs type of BiRh. The refined occupancy factor for Rh is 0.81(3), in excellent agreement with the phase composition of Bi55.3Rh44.7 determined by SEM–EDX. Therefore, this new phase was designated BiRh0.81. The refined atomic coordinates and structural parameters are given in Table 6 and Fig. 9 displays a 2θ segment of the powder XRD pattern between 26° and 80°. Detailed structural information was deposited with Fachinformationszentrum Karlsruhe
Footnote 1 and can be obtained on quoting the depository number CSD 433459.
DTA measurements did not show any detectable signal between 475 and 500 °C; thus, it is currently not possible to give a more exact value of the temperature of the peritectoid reaction (β-Bi2Rh + BiRh \(\rightleftharpoons\) BiRh0.81) which is shown tentatively at 480 °C (Fig. 1). The reason for this might be a very small enthalpy effect due to the similar crystal structures of BiRh0.81 and BiRh in combination with a very slow kinetics (see below). A consequence of the presence of the BiRh0.81 phase is that the α \(\rightleftharpoons\) β transition temperature shifts on the Rh-rich side from 448 ± 2 °C to a somewhat lower temperature. Annealing experiments with samples containing 45 at.% Rh (see Table 3) show that it must be around 440 ± 5 °C. Unfortunately, it is not possible to provide a more precise value of the transition temperature, as no DTA signal could be found in this temperature range.
The detection of BiRh, β-Bi2Rh and of traces of α-Bi2Rh in powder XRD and EDX measurements (Fig. 4d and Table 3) showed, that the annealing conditions (440 °C, 27 days) were not sufficient to produce BiRh0.81 as a single phase. Together with the fact that more than 2 weeks were necessary to form this compound, it indicates a very slow diffusion and/or formation kinetics. As noted above, the MnP-type (BiRh0.81) and NiAs-type (BiRh) structures are closely related and a transformation between them could even be of second order (see, e.g. Kjekshus and Pearson or Franzen et al.). In the current case, however, the orthorhombic lattice parameters deviate considerably from those derived from the hexagonal parameters by cell transformation, pointing rather to a first-order transformation. This considerable distortion is probably due to the reduced occupation at the Rh site in BiRh0.81.
Lattice Parameters of the Phases BiRh and BiRh0.81
The unit cell parameters a, c, the ratio c/a and the cell volume V of the BiRh phase, measured on powders quenched from 750 °C, are shown in Fig. 7. The lattice parameter a increases whereas the lattice parameter c decreases with increasing Rh content between 46.9 and 53.0 at.% Rh. The c/a ratio decreases in the same direction and lies between 1.391(5) and 1.383(3) which is in the typical range of NiAs phases (but far away from the ratio c/a = 1.633, typical for hexagonally close packing). From 42.5 to 46.9 at.% Rh and from 53.5 to 60 at.% Rh the unit cell parameters are constant within the error margins. From the lattice parameter a of a sample with 46.5 at.% Rh, annealed at 565 and 900 °C, phase boundary values of 50.5 and 48.6 at.% Rh were derived for BiRh at these temperatures, as indicated by dotted lines in Fig. 7. The corresponding data points are marked by diamonds in Fig. 1.
High temperature powder XRD measurements of a sample with 50 at.% Rh, quenched from 438 °C (Table 5 and Fig. 8), yield slightly different lattice parameter values compared to data by Glagoleva and Zhdanov who analyzed a sample quenched from 780 °C. As shown in Fig. 8, the BiRh phase starts to decompose above 475 °C and disappears completely above 650 °C. This is caused by evaporation of Bi from the BiRh phase into the dynamic vacuum of the high-temperature XRD chamber and leads to the appearance of Rh reflexes only. Rh reflexes in the pattern at ambient conditions are due to small amounts of non-reacted Rh. As a consequence of the loss of the BiRh phase it was not possible to reproduce the significant increase of the lattice parameter c at 800 °C described by Ross and Hume-Rothery.
With increasing temperature, the lattice parameters a and c and the volume of the unit cell V increase (Table 5 and Fig. 10) for the BiRh phase. In contrast to lattice parameter c, which increases in the error margin linearly from 5.667(1) Å at room temperature to 5.726(2) Å at 650 °C, lattice parameter a shows a steep increase between 475 and 550 °C [4.110(3)-4.120(2) Å]. This step is probably related to the continuing decomposition of BiRh in the dynamic vacuum which becomes significant at this temperature. The loss of Bi shifts the composition of BiRh to the Rh rich side connected with an increase of lattice parameter a.
Similar to BiRh, the lattice parameters a, b, and c of the BiRh0.81 phase (Table 5, Fig. 11) increase linearly with increasing temperature, too. Surprisingly, the c/b ratio does not change and remains more or less constant within the error margin at 1.732 Å, which is not the case in most other MnP-type structure compounds (see, e.g., Selte and Kjekshus).