A. M. Balagurov, I. A. Bobrikov, R. N. Vasin, T. N. Vershinina, B. Erzhanov, N. Yu. Samoylova, S. V. Sumnikov - Joint Institute for Nuclear Research, Dubna
I. S. Golovin, V. V. Palacheva - National University of Science and Technology MISiS, Moscow

Due to its specific peculiarities, neutron diffraction is an exceptionally powerful technique for studying transient processes in condensed matter. Task oriented regular experiments to observe the restructuring of matter at the atomic level right in the course of this process (in the literature they are called RT (real time) - experiments) using neutron scattering started in the mid-1980s after the development of high-aperture neutron diffractometers. In general, it means both neutron diffraction and small-angle, diffuse neutron scattering, although in most of the experiments, only diffraction spectra that are the most intense components of the scattering process are registered.

The characteristic time scale available for studying irreversible processes, such as solid-state chemical reactions, is determined by the condition t_s << t (t  is the characteristic time of the process, t_s is the measurement time of one spectrum with a level of statistics sufficient for the goals of the experiment). t_s depends on the neutron flux from the source and on the parameters of the diffractometer and for the most powerful neutron diffractometers in stationary reactors it is, as a rule, several minutes. Back in the 1980s, a series of RT experiments with a time resolution in the range of 2 seconds to 5 minutes were implemented at the IBR-2 reactor with a peak pulsed flux [1]. 

In 2016, at FLNP JINR, in cooperation with MISiS staff members (Moscow), investigations of various transient processes in iron-based metal alloys with unusual physical properties started. Such as for instance, the phase composition of Fe-27Ga alloy is known for its record-breaking magnetostriction as compared to other iron-based binary alloys (about 400 ppm) and consequently, unusually high internal friction. In Fe-xGa, Fe-xAl and other alloys, a whole series of structural phase transitions of both the 1st and 2nd order occur on heating, followed by a complex rearrangement of the microstructure. The temperature dependences of the characteristics of these and many other types of transients are efficiently determined in in situ neutron diffraction RT experiments. For instance, data can be obtained on the peculiarities of the kinetics of changes in the volume fraction and unit cell parameters of the current structural phases, the factors filling crystallographic positions, microstresses in crystallites and the characteristic dimensions of coherent scattering regions (CSRs). The main advantages of neutron diffraction in the case of alloys are the possibility of observing volumetric effects and thus eliminating the impact of surface and local inhomogeneities inherent in their coarse-grained structure.       

All the results discussed below have been obtained using High Resolution Fourier Diffractometer (HRFD) at IBR-2. The peculiarities of HRFD are the high resolution d_hkl (Δd/d ≈ 0.0015) and the possibility of comparing it with the accumulation of diffraction data obtained with an average resolution (Δd/d ≈ 0.015), but with a high luminosity. Accordingly, high-quality structural data can be obtained with HRFD, fine details concerning crystal lattice distortions can be identified, diffraction peaks of weak intensity can be measured and real-time variations in structure and microstructure can be tracked during temperature scanning.

At the initial stage of applying this technique to study iron-based alloys, data on the compositions of Fe-xGa and Fe-xAl with an alloying element content x ≈ 27 were obtained, at which one of the magnetostriction maxima in Fe-Ga is observed. One of the most significant results of these experiments has been the formulation of a model for the microstructure of alloys that are developed as coherent clusters of a structurally ordered phase, dispersedly embedded in a disordered or less ordered matrix. This model, being an alternative to the classical model of antiphase domains, has obtained strong evidence due to the experimental capabilities available at HRFD. A series of articles on Fe-Ga and Fe-Al alloys published in the period 2016-2018 was awarded the 1st JINR Prize for 2018.

In subsequent years, the effects of temperature cycling in Fe-Mn-Si alloys [2] and spinodal decomposition of Mn-Cu-Cr alloys [3] have been studied in RT experiments. Comprehensive data on bulk effects occurring during martensitic transformation in Ti-Ni-Hf alloys with the shape memory property have been obtained [4, 5, 6]. The kinetics of nucleation during the first-order phase transition D0₃ ® L1₂ in Fe-Ga alloys has been studied and the complex nature of this transition, passing through the development of disordered phases according to the scheme D0₃ ® A2 ® A1 ® L1₂ [7] has been established. When studying the structure and phase transitions in the composition of Fe-45.5Ga, the identity of the structures indicated in different publications as Fe₇Ga₆, Fe₁₃Ga₁₃ and β-Fe₆Ga₅ has been shown and it has been concluded that the correct composition of this phase is Fe₁₃Ga₁₃ [8]. Below are the most significant results obtained in RT experiments in the last two years.

Fe-38.4Ga alloy. The evolution of the phase composition of the Fe-38.4 at% Ga cast alloy has been studied in neutron diffraction experiments implemented with high resolution and in the mode of constant temperature scanning when heated to 850°C and subsequently cooled to room temperature. It is shown that in the as-cast state the alloy consists of ~70% Fe₁₃Ga₉ intermetallic compound and ~30% disordered A2 solid solution based on VCCL (or its partially ordered variant B2). During the first heating, it was found that the Fe₁₃Ga₉ phase is stable up to T ≈ 570°C, then it passes into the α-Fe₆Ga₅ and L1₂ phases. At the same temperature, the disorder–order transition A2 → B2 starts and ends at Т ≈ 720°С. The Fe₁₃Ga₉ phase is not reduced upon subsequent cooling, nor during repeated heating and cooling cycles (Fig. 1). Among other things, the structural parameters of the phases precipitated as a result of thermal treatment have been refined. Investigations have also shown thereof diffusion-controlled processes are significantly complicated in Fe-Ga alloys, the temperatures of phase transitions depend on the prehistory of the alloy. The results mentioned above are presented in paper [9].

Fig. 1. 2D visualization of the evolution of the phase composition of the Fe-38.4Ga sample in the cast state, obtained using neutron diffraction during slow heating to 900°C, annealing at this temperature for 20 min and subsequent real time cooling

Coherent ordering in clusters. The evolution of structural phases and microstructure morphology of several Fe-xAl and Fe-xGa compositions have been investigated using high-resolution Δd/d neutron diffraction and constant scanning over a wide temperature range. It has been discovered that the ordered structure formation with a change in the content of Al or Ga, either during the phase transition with a change in temperature results in a decrease in the unit cell parameter with a “jump” of the order of Δa/a ~ 0.001. In the intervals 23 at.% < x < 33 at.% for Fe-xAl and 19at.% < x < 24 at.% for Fe-xGa, a specific type of microstructure is developed in the alloys. These are bulk clusters (L ~ 200 – 1000 Å) of the ordered phase, dispersedly embedded in a disordered or less ordered matrix. An independent determination of the parameters of the unit cells of the matrix and clusters has shown coherence of their crystal lattices manifesting itself in the coincidence or proximity of the parameters with an accuracy of Δa/a ≤ 0.0001. This type of phase separation (matrix + clusters) has a quite different nature than incoherent phase separation in outer or thin layers, in which the lattice parameters differ at the level of Δa/a ~ 0.001. More details on the results of the investigation can be found in the published paper [10].

σ-phase in Fe-46Cr. The σ-phase developed on the surface and in the sample volume of the Fe-46Cr alloy has been investigated using X-ray diffraction (PANalytical Empyrean diffractometer) and neutron diffraction (HRFD diffractometer). The measurements have been carried out in real-time mode during the rapid heating of the sample to the target temperature and subsequent holding at this temperature. The kinetics of the σ-phase formation is described within the framework of the Avrami model. According to neutron measurements, at 650°C for 5 hours, the A2 phase completely transforms into σ-phase, while the Avrami parameter n is not constant during the entire transition that indicates changes in the increase mechanism of this phase during its formation. At a temperature of 700ºС, ~0.64 of the A2 phase transforms to σ-phase during 10 hours of exposure, at a constant value of n ≈ 2 (Fig. 2). In contrast to the neutron diffraction results, the X-ray data show a partial and slower transformation of the A2 phase into σ phase. The results obtained suggest that a chromium deficiency is gradually produced in the near-surface layers of the sample under vacuum conditions, resulting in changes in the phase structure with subsequent destabilization of σ-phase and its reverse transformation into a cubic phase. More details on the results of the investigation can be found in the published paper [11].

Fig. 2. 2D evolution of neutron diffraction patterns during fast heating and isothermal holding at 655ºС (a) 700ºC (b) of the Fe–46Cr alloy

Heterogeneity of Fe-27Ga alloy. The joint use of X-ray and neutron diffraction techniques to study the structure of Fe-27Ga alloy has revealed an inhomogeneity in the distribution of the phase composition over the volume of the material. The results of the neutron diffraction experiment have confirmed that the bulk structure of the sample is a completely ordered D0₃ phase. The use of X-ray diffraction with a long time exposure has allowed to precisely study the surface layer, with a thickness of ~4-16 µm. The results obtained have confirmed the occurrence of the ordered D0₃ phase and also revealed the formation of additional phases with a less ordered structure of B2 and A2 (Fig. 3). It has been discovered that the ratio and volume contribution of the identified phases depend on the duration of the contact of the alloy with the air atmosphere. Additional phases occur in small amounts, only in the surface layer that has been confirmed using different wavelengths of the typical X-ray radiation. The observed distortion of peaks caused by the occurrence of the B2 and A2 phases is sometimes wrongly interpreted like the occurrence of the m-D0₃ phase, considered by some authors to be responsible for giant magnetostriction. A thorough analysis has disproved the occurrence of m-D0₃ phase in significant amounts, thereby establishing that magnetostriction is caused by other reasons. More details on the results of the investigation can be found in the published paper [12].

Fig. 3. Dependence of the phase composition on the penetration depth, determined from the analysis of the profiles of various diffraction peaks measured using Cu-Kα radiation

Structure of Fe-Ga-Al ternary alloys. Using neutron diffraction, structural investigations of the series of Fe_100-(x+y)Ga_xAl_y compositions have been carried out in the range 17 ≤ (x + y) ≤ 39 at.%. The goal of the investigation has been to elucidate the evolution of the structural phases and the microstructural state of these compositions with a change in the content of alloying elements. Information about phase transitions and the microstructural state of Fe-Ga-Al alloys is necessary to predict their behavior under changing external conditions. It follows from the data obtained in this paper that up to (x + y) ≤ 31 only А2, D0₃ and B2 phases are observed in Fe–Ga–Al ternary alloys, including those upon heating to ~900°С and subsequent cooling (Fig. 4). Only when the composition is heated with (x + y) = 30.7 in the temperature range (450–700)°C, does the phase A1 occur in a small amount. No signs of monoclinic phases have been detected. The expansion of the range of formation of cubic phases formed on the basis of a bcc cell in ternary alloys as compared to Fe_100-xGa_x indicates the role of Al in the stabilization of these structures. In terms of their structural properties, Fe_100-(x+y)Ga_xAl_y ternary alloys up to (x + y) ≈ 39 repeat Fe_100-yAl_y alloys in the same range of Al content. More details on the results of the investigation can be found in the published paper [13].

Publications:

1. Балагуров А.М., Миронова Г.М. Нейтронографические исследования в реальном масштабе времени. Кристаллография, 36, 314-325 (1991).
2. Sun L., Cheng W.C., Balagurov A.M., et al., Effect of thermal cycling on microstructure and damping capacity of Fe-26Mn-4Si alloy. Materials Characterization, 159 110001 (2020). Doi:10.1016/j.matchar.2019.110001
3. Sun L.Y., Vasin R.N., Islamov A.Kh., et al., Spinodal decomposition in ternary Mn-Cu-Cr alloy and its influence on martensitic transition temperatures. Journal of Alloys and Compounds, 884 161082 (2021). Doi:10.1016/j.jallcom.2021.161082
4. Shuitcev, R.N. Vasin, X.M. Fan, А.M. Balagurov, et al., Volume effect upon martensitic transformation in Ti_29.7Ni_50.3Hf₂₀ high temperature shape memory alloy. Scripta Materialia, 178, 67-70 (2020). Doi:10.1016/j.scriptamat.2019.11.004
5. Shuitcev, R.N. Vasin, А.M. Balagurov, et al., Thermal expansion of martensite in Ti_29.7Ni_50.3Hf₂₀ shape memory alloy. Intermetallics, 125, 106889 (2020). Doi:10.1016/j.intermet.2020.106889
6. Shuitcev, R.N. Vasin, А.M. Balagurov, et al., Study of martensitic transformation in TiNiHfZr high temperature shape memory alloy using in situ neutron diffraction. Journal of Alloys and Compounds, 899, 163322 (2022). Doi:10.1016/j.jallcom.2021.163322
7. M. Balagurov, N.Yu. Samoylova, I.A. Bobrikov, et al., The first- and second-order isothermal phase transitions in Fe₃Ga-type compounds. Acta Crystallographica B75 (6), 1024-1033 (2019). Doi:10.1107/S2052520619013106
8. N. Vershinina, I.A. Bobrikov, S.V. Sumnikov, et al., Crystal structure and phase composition evolution during heat treatment of Fe-45Ga alloy. Intermetallics 131, 107110 (2021). Doi:10.1016/j.intermet.2021.107110
9. T.N. Vershinina, I.A. Bobrikov, S.V. Sumnikov, et al., Structure evolution of as-cast metastable Fe-38Ga alloy towards equilibrium. Journal of Alloys and Compounds, 889, 161782 (2021). Doi:10.1016/j.jallcom.2021.161782
10. A.M. Balagurov, I.A. Bobrikov, S.V. Sumnikov, et al., Coherent cluster ordering in Fe-xAl and Fe-xGa alloys. Journal of Alloys and Compounds, 895, 162540 (2021). Doi:10.1016/j.jallcom.2021.162540      
11. N.Yu. Samoylova, I.A. Bobrikov, E.A. Korneeva, et al., Kinetics of the isothermal A2 to sigma phase transformation in Fe-Cr alloy. Journal of Alloys and Compounds, 913, 165282 (2022). Doi:10.1016/j.jallcom.2022.165282
12. S.V. Sumnikov, I.A. Bobrikov, I.S. Golovin, et al., Bulk vs. surface structural phases in Fe-27Ga alloy. Journal of Alloys and Compounds, 928, 167116 (2022). Doi:10.1016/j.jallcom.2022.167116
13. А.М. Балагуров, И.А. Бобриков, С.В. Сумников, et al., Структуры и фазовые переходы в Fe-Ga-Al сплавах, ФТТ 64 (12), 1873-1881 (2022).