Measurements of the temperature dependence of electrical resistance (R) and neutron powder diffraction (NPD) of a Cr84.7Re15.3 alloy is reported. The magnetism originates from the formation of a spin-density-wave (SDW) as a result of nesting between the electron and hole sheets at the Fermi surface (FS). NPD revealed the magnetic character of the SDW to be commensurate (C) with the lattice with a Néel temperature (TN) of 560 ± 5K that correlates to TN = 585 ± 5K determined from the saddle point in the R(T) results. A power law fit of the neutron data gave β = 0.36(1), indicating that the AF ordering follows the 3D Heisenberg model. An additional antiferromagnetic magnetic contribution, associated with Cr2O3, was observed to co-exist in the alloy. Quantification analyses revealed that the Cr2O3 content was less than 2 wt.%. A β value of 0.30(1) was determined for the magnetic phase transition of Cr2O3 in correspondence with the 3D Ising model.
I. INTRODUCTION
Neutron diffraction (ND) measurement is a powerful technique to determine the magnetic nature of elements and alloys.1 This technique has played a pivotal role in developing an understanding of the spin-density-wave (SDW) antiferromagnetic (AF) nature of Cr1 and its alloys.2 The magnetic ordering originates from the formation of a spin-density-wave (SDW) through the nesting of the electron and hole sheets at the Fermi surface (FS).2 The electron sheet of pure Cr is smaller in size than the hole sheet which leads to a SDW that is incommensurate (I) with the lattice. Doping with an electron donor element, such as Re, that has a higher electron to atom ratio (e/a) increases the size of the electron sheet and leads to perfect nesting and commensurate (C) SDW.2
Neutron powder diffraction (NPD) investigations of a Cr86Ru14 alloy revealed CSDW ordering3 in confirmation of the argument that an electron donor leads to a CSDW. In the (Cr100−xAlx)95Mo5 alloy system, temperature dependent NPD measurements revealed that alloys with x < 1.4 order in the ISDW phase, whilst alloys with x > 4.4 show CSDW order.4 In the case of the Cr84.7Re15.3 alloy of this study, the temperature (T) dependence of its electrical resistance (R) indicated a Néel temperature (TN) above 500 K. Moreover, TN determined from the R(T) using two different approaches gave a large difference. This transition temperature could not be verified using other physical property measurement platforms used due to an upper temperature limit of 400 K. It is also essential to determine the magnetic nature of this alloy to give better insight into the effects of doping on the magnetic character of this base alloy. As NPD reveals the magnetic character directly in relation to the reciprocal lattice, it has been pertinent in identifying the SDW character of polycrystalline alloys of Cr,3,4 and is subsequently applied with this study as well to determine the magnetic ordering and TN in the Cr84.7Re15.3 alloy.
II. EXPERIMENTAL TECHNIQUES
Polycrystalline Cr84.7Re15.3 alloy was prepared as a button by repeated arc-melting of Cr and Re, each of mass fractional purity 99.99% in a purified argon atmosphere. The alloy button was annealed at 1050 K in a sealed quartz ampoule under slight argon pressure for seven days followed by quenching into iced water. Powder X-ray diffraction (XRD) analysis, using Cu K-α radiation confirmed the expected body centred cubic (bcc) crystal structure of the alloy. Electron microprobe analyses confirmed the homogeneity and elemental composition of Cr and Re in the sample. The back scattered electron image though showed dark spots indicative of the presence of oxide inclusions. Electrical resistance (R) was measured using a conventional four-point probe method5 in the temperature range 2 K ≤ T < 700 K.
Since some Cr alloys are known to form large grains,2 the annealed alloy buttons were crushed and ground using a mortar and pestle to minimise the grain sizes and render better uniform intensity distributions over the Debye–Scherrer cones for the NPD measurements.6 NPD measurements were performed on the Wombat powder diffractometer7 at the Australian Nuclear Science and Technology Organisation (ANSTO) using a wavelength of λ = 2.41 Å with the primary beam filtered with a pyrolytic graphite filter to reduce higher order wavelength contamination.8
III. RESULTS AND DISCUSSION
Figure 1 shows the XRD pattern taken at 300 K together with a Rietveld analysis fit, using GSAS II.9 The peak positions are well matched to the Joint Committee of Powder Diffraction Standard Database (JCPDD)10 code (04-008-5187) for bcc Cr, confirming it as the dominant phase. The relevant refinement parameters are a = 2.921 Å and χ2 = 4.2.
Figure 2 shows the temperature (T) dependence of the electrical resistance (R). The anomalous sudden increase in R(T) upon cooling through TN is qualitatively attributed to Coulomb interactions between the electrons and holes at the FS from the nesting process that leads to the formation of the SDW.2 This leads to annihilation of parts of the FS and a reduction in the charge carriers available for conduction. The temperature corresponding to the saddle point or minimum in the temperature dependence is normally taken as TN.2 In cases where the anomaly in the R(T) curve is weak the temperature corresponding to the minimum in the dR/dT(T) curve (inflection point) is used to identify TN2 as shown in the inset to Figure 2. For the Cr84.7Re15.3 alloy, TN values respectively from the saddle and inflection points are 585 ± 5 K and 509 ± 4 K.
NPD patterns were collected as function of temperature upon heating from low temperatures in 20 K intervals to 600 K. Figure 3 shows representative diffraction patterns at selective temperatures focused on the region of the (100) reflection of Cr that is observed at 2θ ≈ 49°. The magnitude of the wave vector along the (100) cube axis is given by Q = 2π/a, where a is the lattice parameter.2
The absence of (1 ± δ, 0, 0) satellite reflections reveals that the bcc phase has CSDW ordering, with δ = 0, confirming the existing magnetic phase diagram of Cr100−uReu alloys.2 Inset of Figure 3 shows the NPD pattern at 20 K, i.e., representative of the antiferromagnetic (AF) ordered region. Note that the intensity of the (100) magnetic peak is less than 15% of the intensity of for example the (110) nuclear peak. This is indicative of the weak magnetic moment in these alloys.
With the ND investigations thus focused on weak peaks, this subsequently revealed the unexpected presence of Cr2O3 as a minor phase corresponding to the observed (012) peak at 2θ ≈ 38° as shown in Figure 3. This confirms the dark spots on the back scattered electron image result discussed earlier. It is known that Cr has a high affinity for oxygen11,12 and the presence of oxides have been reported in arc melted Cr84Re16 alloy.13 Cr2O3 has AF ordering with TN ≈ 308 K14 with the magnetism manifesting at the (012) peak position. Tracking the temperature dependence of the intensity of the (012) nuclear reflection, its intensity decreases abruptly at 590 K compared to the other peaks of this phase. The remnant weak intensity is the nuclear contribution.14
All the peaks in the NPD patterns have been accounted for in the Rietveld refinements using Topas;15 bcc Cr and rhombohedral Cr2O3. The refined lattice parameters show a marginal increase for both Cr (a = 2.915 Å to a = 2.924 Å) and Cr2O3 (a = 4.944 Å; c = 13.579 Å to a = 4.964 Å; c = 13.591 Å) phases, indicating the extent of thermal expansion from 20 K to 590 K.16 Quantification analyses at 20 K and 590 K revealed that the Cr2O3 content was approximately 1.2 wt.%, explaining why it was not detected in the XRD results. The difference curves between the measured and modelled patterns for the two phases primarily indicate the magnetic contributions since this was not included in the Rietveld analyses.
Plots of the integrated intensities of the (100) magnetic peak of Cr and the (012) Cr2O3 overlapped peaks (magnetic and nuclear) taken for the heating measurements are shown in Figure 4. The inset in Figure 4(a) shows a peak fit used to determine the integrated intensity of the (100) peak. Sharp decreases in integrated intensities of the (100) peak of the Cr phase, as well as the (012) peak of the Cr2O3 phase are observed with increased temperature as their respective TN values are approached, beyond which the decrease in intensities level off in the paramagnetic (P) regions. This is due to the weakening of the magnetic interactions and subsequent ordering of the magnetic moments.17 The dashed lines in Figure 4(a) and (b) are linear least-square fits through the intensities of the paramagnetic states extrapolated to lower temperatures.
The solid lines in Figure 4(a) and (b) are power law fits of the form yielding β values of 0.36(1) for the (100) peak and 0.30(1) for the (012) peak, which correspond to that expected from the 3D Heisenberg model and 3D Ising model respectively.18 A better understanding of the critical exponents as well as the magnetic interactions in this alloy can be obtained from isothermal magnetisation measurements.19 TN is identified as the temperature that corresponds to the position at which the solid line in the AF region intersects the dashed line representing the paramagnetic intensity and has values (560 ± 5) K and (312 ± 2) K for the (100) and (012) peaks, respectively. The TN value for the (100) peak obtained using NPD correlates better to the temperature corresponding to the saddle point in the R(T) curve than the temperature of the inflection point. The CSDW state has three polarization states with the fundamental magnetisation wave vector Q along a cube axis and the spin polarisation pointing along one of the other two axes.20 As the sample is subjected to a temperature change, there is a change in the fractional volume occupied by a domain of a given type which in turn will affect the nett contribution to the (100) intensity21 which decreases as the paramagnetic phase is approached.
IV. CONCLUSION
NPD measurements were performed to investigate the magnetic phase in the Cr84.7Re15.3 alloy. The TN values obtained from the saddle point in the temperature dependence of electrical resistance and NPD measurements showed fairly good agreement. This confirms that the temperature corresponding to the saddle point in the R(T) curve is a more accurate value of TN than that obtained from the inflection point in the R(T) curve for the Cr84.7Re15.3 alloy. NPD patterns of the Cr84.7Re15.3 alloy showed a single magnetic peak at the Cr (100) position with no symmetric satellites indicating that this alloy exists in the CSDW phase. The presence of Cr2O3 as a minority phase contributing 1.2 wt.% in the Cr84.7Re15.3 alloy was also detected which gave rise to the prominent peak at 2θ ≈ 38°. Power law fits of the form to the integrated intensity data generated a β value of 0.36(1) indicating that the AF ordering in this sample follows the 3D Heisenberg model. β value of 0.30(1) was obtained for the (012) oxide peak which corresponds to the 3D Ising model. Critical exponents that can be determined from isothermal magnetisation measurements are necessary to further understand the nature of the magnetic interactions in these alloys. This will form part of the future work.
ACKNOWLEDGMENTS
Financial aid from the SANRF (Grant No. 93551, 120856, 126978, 115346, 118016 and 80626), UJ URC and UJ FRC are acknowledged. The use of the neutron powder diffraction instrument Wombat, under proposal P3582 is also acknowledged. The use of Spectrum Analytical Facility within the Faculty of Science at UJ is acknowledged.
DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.