Acta Polytechnica https://doi.org/10.14311/AP.2024.64.0103 Acta Polytechnica 64(2):103–117, 2024 © 2024 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague PRECIPITATION OF OXIDE DISPERSION STRENGTH STEELS AFTER LONG-TERM ANNEALING AT TEMPERATURE OF 475 °C Dávid Košovskýa,∗, Marcel Miglierinia,b, Tomáš Kmječc,d, Július Dekana, Marek Bujdoše a Slovak University of Technology in Bratislava, Faculty of Electrical Engineering and Information Technology, Institute of Nuclear and Physical Engineering, Ilkovičova 3, 841 04 Bratislava, Slovakia b Czech Technical University in Prague, Faculty of Nuclear Science and Physical Engineering, Department of Nuclear Reactors, V Holešovičkách 2, 180 00 Praha, Czech Republic c Charles University, Faculty of Mathematics and Physics, V Holešovičkách 2, 180 00 Praha, Czech Republic d Czech Academy of Sciences, Institute of Physics, Na Slovance 2, 182 00 Praha, Czech Republic e Comenius University, Faculty of Natural Sciences, Ilkovičova 6, 842 15 Bratislava, Slovakia ∗ corresponding author: david.kosovsky@stuba.sk Abstract. Oxide dispersion strengthened steels are key alloys used in nuclear installations. Steels with chromium content of up to 10 wt % are suitable due to their advantageous properties and these alloys are used for the construction of technological devices in the primary circuit of nuclear power plants. From other studies, it can be concluded that chromium has anti-corrosive properties due to the formation of a passivation layer, which results in reduced activation of the material by thermal neutrons. Macroscopic properties are determined by their microstructure, and therefore, the description of the microstructure is important. Transmission Mössbauer spectroscopy and atom probe tomography were used to characterise the material. This provides information about the physical and/or chemical environment of the resonant atoms can be obtained. Obtained spectral parameters reach saturation values from which the solubility limit of chromium in iron can be determined. In Cr-rich phase, the solubility limit can be estimated from the value of spectral parameters of the single-line in the spectrum annealed for the longest time. The suggested procedures are subsequently applied to the case studies of stainless steels suitable for the construction of various components of the III+/IVth generation of nuclear reactors (including fast and fusion reactors). Keywords: High-chromium steel, hyperfine interactions, Mössbauer spectrometry, atom probe tomography, stainless steel, ferritic-martensitic steel. 1. Introduction Technological progress in the nuclear industry is largely determined by the development of construc- tion materials. Different types of alloys are suitable for advanced applications, and therefore, it is nec- essary to analyse them using different experimental nuclear-physical techniques [1–9]. Undoubtedly, the most important alloys used in the primary circuit are anti-corrosion steels, where, in addition to carbon, other elements, such as chromium, manganese, nickel, and titanium, are added to improve their physical, chemical, and mechanical properties [10–21]. Development of ferritic-martensitic oxide dispersion strengthened (ODS) steels was paralleled by material research for fast reactors with the reduced swelling under higher neutron fluxes. The main advantage of ODS steels is their low neutron activation even at high neutron fluxes (up to 1014 m−2s−1) [22, 23]. Along with the appearance of fusion reactor material pro- grammes, ODS steels also became attractive for the use as base materials in the design of nuclear fusion fa- cilities. A block and sub-block martensite microstruc- ture is responsible for the high strength and toughness of ODS steels as well as increased resistance to vol- umetric swelling under neutron irradiation [24, 25]. The closest application of the ODS steels in nuclear fusion environment is the structural material for the test blanket module for the tritium breeding in fusion reactors. However, the sharp increase in the ductile- to-brittle transition temperature of the steels is one of the undesirable characteristics of their use in a fu- sion environment. When the irradiation temperature is below 350 °C, the formation of dislocation loops, precipitates of α’-phase, and solute-rich clusters leads to dislocation pinning, thus, suppressing the plastic deformation, which is determined by particle distri- bution in a material [26, 27]. ODS steels consist of iron-base matrix with oxide particles dispersed in it. They have high heat resistance, strength, and ductility. Alloys of nickel, chromium, and manganese are the most common ones, but this class of materials also includes iron-aluminium alloys [28–30]. Oxide dispersion strengthening is based on inco- herency of the oxide particles within the lattice of the material. Coherent particles have a continuous lattice plane from the matrix to the particle, whereas incoher- 103 https://doi.org/10.14311/AP.2024.64.0103 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en Dávid Košovský, Marcel Miglierini, Tomáš Kmječ et al. Acta Polytechnica ent particles do not have this continuity, and therefore, both lattice planes terminate at the interface. This mismatch in interfaces results in a high interfacial en- ergy which inhibits dislocation [31, 32]. On the other hand, the oxide particles are stable in the matrix, which prevents creep. Particle stability implies little dimensional change, embrittlement, effects on proper- ties, stable particle spacing, and general resistance to modifications at high temperatures [33, 34]. Precipitation of α’ (Cr-rich) phase causes significant embrittlement of the alloy, which leads to changes in other mechanical properties with the highest embrit- tlement rate at 475 °C. The local chromium content in α’-phase is higher than 80 at %, which causes local embrittlement of the steel. Conversely, the σ-phase is prone to precipitation if the annealing temperature is between 490 °C and 830 °C and the chromium concen- tration is between 15 at % and 85 at %. The phase de- composition of the α’ precipitations at a temperature of 475 °C results in the formation of α (Fe-rich) and α’ (Cr-rich) phases. The applicability of Mössbauer spectrometry is suitable for the characterisation of phases in high-chromium steels, due to different mag- netic properties at a room temperature (RT). Specifi- cally, α (Fe-rich) phase has ferromagnetic properties at RT and α’ (Cr-rich) phase exhibits paramagnetic properties [35–42]. For the analysis of the microstructure of metallic materials, there are many nuclear-physical techniques that provide information not only from the surface of the material, but also from the material’s bulk. Steels containing carbon and further additive elements, such as Cr, Mn, Ni, and Ti, belong, without doubt, among the most important alloys used as construction ma- terials of the primary circuit of nuclear power plants. Transmission Mössbauer spectroscopy (TMS) is one of the most sensitive methods, because it is characterised by unprecedented energetic resolution of the order of neV. Using the measured spectra, we can determine the valence state of the atoms, electrical field gradient, hyperfine magnetic field at the location of the resonat- ing nuclei created by their electron shells, and electron fields of the nearby ions. From the areas of the individ- ual spectral magnetic and paramagnetic components, we can describe the arrangement of cations in the material structure, and from the relative intensities of sextet lines, the orientation of the local magnetic moments [35, 36]. In this work, we studied the microstructure of ODS steel PM80KhV2, which excels in mechanical resis- tance, corrosion resistance, and high hardness due to the presence of chromium carbides and Y2O3 clusters. PM80KhV2 steel with nominal chromium concentra- tion of 20 wt % is suitable for applications where the chemical resistance of the surface is crucial. High chromium content increases toughness, hardness, and tensile strength. Chromium oxides are segregated in surface, thereby contributing to the formation of passivation layers. Sulphur contributes to the machin- ability of the material, but in higher concentrations it is considered as an impurity and can contribute to unwanted pitting corrosion. Most materials from the category of very hard steels have significantly reduced toughness. Steel PM80KhV2 is an exception and has a toughness comparable to ordinary steels even at 61 hrc (according to the Rockwell hardness test). The conventional hardening temperature is 990–1120 °C for 20 minutes. Subsequently, the steel material is tempered, where the selected temperature is directly proportional to the resulting hardness, for example, a tempering temperature of 150 °C results in hardness of 61 hrc, while a tempering temperature of 660 °C results only in 54 hrc. It is a common practise to combine Mössbauer spec- troscopy investigations with other experimental meth- ods to acquire more complex information about the studied materials. In our research, we have used X-Ray Fluorescence (XRF) and Atom Probe Tomog- raphy (APT). The XRF is based on primary exci- tation of atoms in the sample by high-energy X-ray radiation and subsequent de-excitation of atoms via characteristic radiation. The APT was used for three- dimensional description of Cr-rich precipitates. Atom probe tomography is a nanoscale analysis technique that provides three-dimensional spatial imaging with high sensitivity. The technique relies on ionisation and subsequent field evaporation of individual atoms or atomic clusters from a studied sample (around 0.1–0.35 nm resolution in depth and 0.35–0.52 nm lat- erally) [43–45]. In this work, we discuss the possibility of using theoretical procedures applicable to Mössbauer data, which have so far only been used in the evaluation of model binary Fe-Cr alloys. The aim of this article is to demonstrate the use of different evaluation approaches to derive Mössbauer spectral parameters from real ma- terials with special emphasis on high-chromium ODS steels PM80KhV2, which have a significant applica- tion potential in nuclear industry. Using a theoretical fitting model, it is possible to directly quantify the probabilities of the occurrence of individual elements in the immediate vicinity of the resonant 57Fe nuclei using several magnetic components. Values of spec- tral parameters saturate, and therefore, the Avrami’s precipitation mechanism can be used to describe mi- crostructural changes during thermal annealing at a temperature of 475 °C. 2. Materials and methods The samples of ODS steels studied in this work are referred to as high-chromium steels because the con- centration of chromium is higher than 10 wt %. Metal- lic materials in powder form enriched with yttrium oxide particles (Y2O3) with a purity between 99 % and 99.5 % were used as precursors for the produc- tion of PM80KhV2 steel samples. The particles were consolidated by hot isostatic pressing (HIP). Subse- quently, the ferritic structure recrystallised at the 104 vol. 64 no. 2/2024 Precipitation of Oxide Dispersion Strength Steels After . . . value of 0.9 of the melting temperature. After solidi- fication at a rate of Ṫ = 10.4 °C s−1, the steel plates were cold rolled, then heat-treated at a temperature of 1137 °C for 80 minutes, followed by rapid cooling to 717 °C. The resulting steel samples were formed into 3 (±0.2) mm thick plates. To simulate the effect of thermal embrittlement at a temperature of 475 °C, the PM80KhV2 samples were annealed in a high-temperature furnace in medium vacuum (0.54 Pa) for 1012 hours. For the transmission Mössbauer spectroscopy measurements, the material was removed from different areas of the plate samples using a titanium drill covered with a diamond coating at low speeds so as not to chemically or thermally degrade the powdered samples. The samples were drilled to a deep depth, so the powdered material is mainly from the bulk and not just from the surface. Qualitative XRF analysis was carried out using the Amptek Experimenter’s XRF Kit, which con- tains an X-ray tube (Mini-X) and a high-resolution X-ray detector with signal processing electronics (X- 123). The X-ray Wolfram tube was operated at 40 kV with the current of 15 µA. As a detector, a Si-PIN diode was used (size 6 mm2, silicon thickness 500 µm, 12.5 µm thick beryllium window, energy resolution 145 eV FWHM @ 5.9 keV). They were performed with the sample surface positioned at 45° with respect to the X-ray beam direction and 45° to the detector (in one layer). Data analysis was performed using ADMCA software. Exact chemical composition was checked by Flame Atomic Absorption Spectroscopy (F-AAS) using spec- trometer Perkin Elmer 1100. Finally, the chemical composition was determined using Optical Emission Spectroscopy (OES) High- End spark spectrometer SPECTROLAB S, which has a high sensitivity even for light elements in steels. The measurement took place in an argon atmosphere with the help of UV-C radiation (120–240 nm) using a CMOS + T semiconductor detector. The ultra- stable spark (with a frequency of 1000 Hz) is provided by means of a plasma generator. Before measurement, the calibration was performed using low-alloy steel 100Cr6. The TMS measurements were performed at RT using a conventional Wissel TMS spectrometer work- ing in constant acceleration mode and equipped with a 57Co/Rh radiation source. The calibration of the ve- locity scale was performed by an α-Fe foil; the isomer shift values are given relative to the centre of its TMS spectrum recorded at RT. The spectra were analysed using the least squares method assuming Lorentzian line shapes and deconvolution using the Confit pro- gram [46]. In the evaluation process, spectral parame- ters of the individual sextets comprising their relative area (Arel), line width (Γ), average hyperfine mag- netic field (⟨Bhf ⟩), average isomer shift (⟨IS⟩), and χ2- parameter were refined during the fit. Quadrupole shifts were not considered. In order to decrease the overall number of the refined parameters, relative line intensities of 1:A21:1/3 of the corresponding line pairs in the sextets were assumed. The parameter A21 was fitted only for one, the so-called determining sextet, which has the highest probability. Line intensities of the remaining sextets were coupled to those of the determining one and fixed during the evaluation. APT analyses were performed using the EIKOS- UV atom probe microscope which provides three- dimensional tomography with nanoscale character- isation of microstructures and high spatial resolu- tion single atom detection with high efficiency. IVAS (CAMECA) software was used for data reconstruction. The APT technique is particularly suitable if the im- purity concentration is well above the miscibility limit (gap) and provides information of the time evolution of the phase composition (and decomposition), size, and morphology of the analysed precipitates. The Energy Compressed Tomographic Atom Probe (ECTAP) mode was used for the measurements of all samples and the experimental instrument was equipped with an aDLD detector. The presence of the Energy Compressed Lens (ECL) provides high qual- ity resolution of the mass spectrum and the aDLD detector minimises losses due to the element or event overlap during the multi-event detection. The ex- perimental conditions were set in such a way that it was possible to determine the phase distribution in the sample as accurately as possible and to minimise the preferential evaporation of chromium. In ECTAP measurements, it is actually necessary to isolate the precipitates in the material, for which a data filter is used, since the nominal chromium concentration in the matrix is between 5 and 60 at %. Therefore, a threshold of 60 at % was chosen to prevent the con- tribution of chromium atoms from the homogeneous matrix. This value is subsequently calculated around each atom in a spherical volume with a radius of 0.5 nm. The determined composition and morphology is therefore determined with an accuracy of ±1 at % and ±1 nm. 3. Results and discussion 3.1. Chemical analysis The qualitative analysis of ODS steel samples was performed by XRF. The measured spectrum of PM80KhV2 steel compared with spectrum of binary Fe100−xCrx (x = 22.1 at %) alloy is shown in Figure 1. The spectrum clearly shows that the studied steel contains mostly iron and chromium, and the represen- tation of other elements is negligible. The determined chemical composition of PM80KhV2 steel samples measured using F-AAS and OES is shown in Table 1. 3.2. Transmission Mössbauer spectroscopy In order to evaluate the TMS spectra of ODS PM80KhV2 steel samples, a model based on Gaussian 105 Dávid Košovský, Marcel Miglierini, Tomáš Kmječ et al. Acta Polytechnica Figure 1. XRF spectrum of the PM80KhV2 steel compared with that of binary Fe100−xCrx (x = 22.1 at %). Technique/element Concentration [wt %] Fe C Cr Mn P Si S V Mo Ni Nominal 79.50 0.20 20.10 0.59 <0.01 0.40 <0.01 0.04 - 0.10 F-AAS 78.90 - 19.50 - - - - - - 0.10 OES 79.40 0.22 20.50 0.56 <0.01 0.32 <0.01 0.04 0.04 0.13 Table 1. Chemical composition of samples of steel PM80KhV2 determined by F-AAS and OES. distribution function was used. This model is suitable for alloys where the concentration of alloying elements is more than 15 at % [42, 47]. Because the analysed samples predominantly con- sist of chromium and iron, we have applied a distri- bution function model for binary alloys to describe the dominant (>98 %) part of the crystallographic components. Its broad spectral lines (sextets) were refined by convolutions of a narrow Lorentzian sextet with a Gaussian distribution [41]. Gaussian distribution model (GDM) consists of three distributed sextets with the intensity ratio of the first to the third lines (A31) fixed at 0.333 and the Lorentzian sextet linewidth fixed at 0.25 mm s−1. We assume a bcc character of the binary alloy model; therefore, the quadrupole shifts are set to zero. The minor paramagnetic feature in the middle of the spec- tra was described by a single Lorentzian line whose linewidth, isomer shift, and relative area were refined. The first and the second distributed sextets cor- respond to iron atoms located in the first nearest neighbour (1NN), and in the second nearest neigh- bour (2NN), respectively. The third sextet (with the smallest relative area) represents a contribution of the atoms outside the 1NN and the 2NN of the resonant nuclei. In the centre of the spectrum, a paramagnetic component was indicated, a singlet associated with Cr-rich precipitates [48–59]. The measured spectra of the non-annealed sample and the sample annealed for 1012 hours fitted with the GDM model are shown in Figure 2. The individual magnetic components exhibit hyper- fine magnetic fields of approximately 29.2 T, 25.1 T, and 19.5 T (Figure 3). The average hyperfine magnetic field derived from the three distributed sextets mod- erately increases with annealing time and saturates at about 26.8(5) T as shown in Figure 4. Variations in the average hyperfine magnetic field can be related to re-arrangement of non-ferrous nuclides in the vicin- ity of the resonant atoms. Tiny modifications of the isomer shift with the annealing time are within the error range. Thus, possible changes in the chemical composition of the steel as a result of annealing can be ruled out. Rather, a re-arrangement of the constituent elements can be considered. The values of the hyperfine magnetic fields saturate with annealing time, from which the formation of the chromium rich α’ phase can be deduced. Variations in the average hyperfine magnetic field can be related to changes in the presence-arrangement of non-ferrous nuclides in the vicinity of the resonant atoms, reflect- ing the local arrangement of the alloy change during annealing. It has been demonstrated in article by Du- biel et al. [42] for binary alloy that the kinetics of the annealing induced processes could be well described in terms of the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation. The JMAK model is used to de- scribe the crystallisation kinetics in different materials including ODS steels. It assumes that the crystalli- sation is isothermal (nucleation and growth occur at constant temperature). Additional conditions are that the sample is infinitely large, and nucleation is ran- dom throughout the sample volume, grain growth is isotropic until the crystals collide, and the activation 106 vol. 64 no. 2/2024 Precipitation of Oxide Dispersion Strength Steels After . . . (a). As-received (non-annealed) state. (b). After 1012 hours of annealing at 475 °C. Figure 2. Fitted transmission Mössbauer spectra of PM80KhV2 ODS steel measured at RT in as-received (non- annealed) state, and after 1012 hours of annealing at 475 °C. Figure 3. Comparison between the magnetic hyperfine field distribution P(B)-curves derived from the TMS spectra annealed for different annealing times between 0 and 1012 hours. 107 Dávid Košovský, Marcel Miglierini, Tomáš Kmječ et al. Acta Polytechnica Figure 4. Dependence of the average magnetic hyperfine field on the annealing time for the PM80KhV2 steel sample annealed at a temperature of 475 °C measured by TMS at RT. Figure 5. Dependence of the average hyperfine magnetic field, as a function of chromium concentration in Fe-Cr binary alloys. energy for crystallisation and other model parame- ters are independent of time and temperature. Under these circumstances, the crystallisation process can be described with the JMAK equation [60–62]: ⟨Bhf (t)⟩ = ⟨B0⟩ + α[1 − e(1−(kt)n)], (1) where ⟨B0⟩ is the average magnetic hyperfine field for the non-annealed steel sample, k is the rate constant, n is the Avrami exponent, α is a free parameter. The kinetic parameter gives information on the de- composition mechanism and the rate constant can be used for determining the activation energy via the Arrhenius law. The obtained value of the Avrami ex- ponent, n, is equal to 0.52(9), indicating thereby that the process responsible for the phase decomposition in the material could be a diffusion-controlled thickening of plates. The entire recrystallisation process took place in two phases, where the second part of the pro- cess at higher annealing times is associated with the formation of σ-phase. The process of formation of the σ-phase is slow, and therefore, longer annealing times of up to 8000 hours would be necessary for a clearer identification. The maximum value of Bhft can be used to estimate the solubility limit of chromium in steels at 475 °C. Annealing of steel, however, takes place partially in a linear heating mode. Efficient methods have been proposed for the calculation of kinetic parameters for a non-isothermal measurement. Kissinger’s method was used to determine the activation energies of the first and the second stages of crystallisation [59]. On the basis of previous studies [47–49], it can be con- cluded that the dependence of the magnetic hyperfine field as a function of the impurity atom has a linear character: x [at % Cr] = ⟨Bhf (t)⟩ − ⟨B0⟩ β , (2) where β coefficient describes the decrease of the hy- perfine magnetic field with increasing chromium con- centration in 1NN-2NN (Figure 5). Based on the results from the articles by Košovský et al. [47] and 108 vol. 64 no. 2/2024 Precipitation of Oxide Dispersion Strength Steels After . . . Figure 6. Dependence of Θ-angle (and A21) as a function of annealing time. Red solid lines represent the best-fit of the experimental data fitted using Avrami mechanism (Equation (4)). Dubiel et al. [48, 49, 54], the chromium concentration was calculated, which reaches between 22.4(4) and 24.7(4) at % Cr and is similar to the value determined by the chemical analysis. The TMS technique provides information about the magnetic arrangement of nanostructures (grains) or of the overall magnetic texture. Specifically, the angle between the local magnetisation vector and the normal vector to the sample surface (the direction of gamma rays). The Θ-angle can be determined from the value of A21 (Equation (3)), which was the fitted parameter: Θ [°] = arccos (( 2 3A21−1 − 1 2 ) 1 2 ) . (3) The value of A21 varies according to the annealing time, while the saturation course is also assumed (Equation (4)). The dependence of Θ(t)-angle on the annealing time can be seen in Figure 6. It can be noticed that Θ(t)-angle increases with annealing time, i.e. the magnetisation vector rotates towards the sample’s surface, however, as evidenced by the inset, the rate of the increase is not constant but tends to saturate within the first ∼1000 hours of annealing. This effect seems to be related to the decomposition and creation of Fe-rich and Cr-rich phase (first stage of the transformation). It is assumed that for longer annealing times, Θ(t)-angle (and A21) continues to increase and saturation of Θ(t)-angle (according to Equation (4)) is obviously related to the growth of grains in the direction parallel to the sample’s surface: ⟨Θ(t)⟩ = ⟨Θ0⟩ + χ[1 − e(1−(kt)n)], (4) where ⟨Θ0⟩ is the angle between the local magnetisation vector and the normal vector to the sample surface for non-annealed PM80KhV2 steel sample (⟨Θ0⟩ = 45.30°), k is the rate constant (k = 0.15(2) h−1), n is the Avrami kinetic exponent (n = 0.14(3)), χ is a free parameter (χ = 21.9(8)). For longer annealing times (over 5000 hours), a de- crease in Θ(t)-angle is assumed, which is associated with σ-phase creation. The single-line component in the central part of the TMS spectra (Figure 2) may correspond to the structure, where chromium probably segregates to form the paramagnetic Cr-rich phase or locally non- magnetic cementite. Based on the isomer shift of paramagnetic component for the longest annealing time (1012 hours), the solubility limit in α’ phase can be estimated (Figure 7). Using the article by Du- biel et al. [54, 62], the calculated solubility limit is 87.1(3) at % at a temperature of 475 °C. The spectral area of this paramagnetic component increases with the annealing time (Figure 8). This modelled spectral component is in agreement with theoretical calculations where a non-zero probability of the majority presence of chromium atoms around the resonance atom exists, where prevalent number of chromium atoms are supressing the magnetic ordering of resonant nuclei in this chromium rich α’ phase, while non-magnetic cementite (Fe3C) can contribute to this phase as well, if present. The above interpretation of the paramagnetic com- ponent cannot be made with complete certainty due to the low concentration of iron nuclei present in this Cr-rich phase, resulting in a low manifestation of this phase in the TMS spectra. Rising relative area of this paramagnetic component during the prolonged annealing time has a similar course as in the study by Degmová et al. [40], where the authors assigned this 109 Dávid Košovský, Marcel Miglierini, Tomáš Kmječ et al. Acta Polytechnica Figure 7. Dependence of isomer shift of single-line component as a function of chromium concentration. Figure 8. Dependence of the relative area of paramagnetic component versus annealing time for the PM80KhV2 ODS steel sample annealed at a temperature of 475 °C, measured by TMS. paramagnetic phase to the chromium-rich α’ phase as well. 3.3. Atom probe tomography From the results of Mössbauer spectrometry mea- surements, it is possible to declare a homogeneous bcc distribution in the materials, and thus one can consider a random distribution of atoms in the sam- ple. One randomly selected Cr-rich nanoprecipitate obtained from a PM80KhV2 steel sample annealed for 1012 hours is shown in Figure 9. The measured chromium concentration in the sample was 21.9 at %. The measurement uncertainty can be determined ac- cording to the relationship: σ [%] = x(100 − x)√ ν , (5) where x is the atomic concentration of chromium, ν is the number of collected atoms. Based on the measurements of the unannealed sample, it is possible to say that the distribution of chromium in the sample corresponds to a value of 0.98(1) % with respect to the distribution determined based on the theoretical binomial distribution model (BDM). No precipitates were observed in the sample where the chromium concentration exceeded the threshold level. These statements are also confirmed by Figure 10, which compares the dependence of the probability of the occurrence of a chromium atom in 1-2NN as a function of the atomic concentration of chromium in the sample, which always represents 100 randomly selected atoms. The theoretical probability was calcu- lated according to the equation: P (m, n) = M !N ! ⟨m⟩!⟨n⟩!(M − ⟨m⟩)!(N − ⟨n⟩)! × x(m+n)(1 − x)((M+N)−m+n), (6) where m is the number of chromium atoms in 1NN, n is the number of chromium atoms in 2NN, M is the maximum number of atoms in 1NN (in our case M = 8), N is the maximum number of atoms in 2NN (N = 6). 110 vol. 64 no. 2/2024 Precipitation of Oxide Dispersion Strength Steels After . . . (a). TEM image of APT sample of PM80KhV2 ODS steel annealed at 475 °C for 1012 hours. (b). APT representation of Cr-rich (α’) phase capped in the iron (α) matrix. Figure 9. TEM image of APT sample of PM80KhV2 ODS steel annealed at 475 °C for 1012 hours and APT representation of Cr-rich (α’) phase capped in the iron (α) matrix. Figure 10. Chromium concentration frequency distribution versus concentration of chromium atoms in 1NN-2NN assuming random distribution of atoms. The experimental values are obtained with sampling boxes of 500 atoms. 111 Dávid Košovský, Marcel Miglierini, Tomáš Kmječ et al. Acta Polytechnica Figure 11. Distribution of chromium-enriched precipitates in PM80KhV2 ODS steel after annealing at 475 °C for 5, 55, 150, and 1012 hours. In all images, the data were treated: only Cr-rich region where the local chromium concentration is as high as 60 at % are displayed. Based on the probability calculations according to Equation (6), it appears that only iron atoms occur in the 1NN-2NN vicinity of the iron probe atom. The probability that there is no chromium atom or one chromium atom in 1NN-2NN reaches the value of 96.9(7) % and therefore it can be approximated that there is a maximum of one impurity atom in each 1NN-2NN structure. On the other hand, the proba- bility that there are 2 or more chromium atoms in the 1NN-2NN neighbourhood reaches 3.0(3) %, and therefore, these configurations can be neglected. The experimental values of the probabilities were calcu- lated with a step of 0.5 at %. Figure 11 shows the 3D distributions of precipitates consisting of the Cr-rich phase for different anneal- ing times, where the local chromium concentration exceeds 60 at % Cr. There is a segregation of α and α’ phases, which is clearly visible from Figure 11. The number of precipitates in the sample is very low (due to the relatively low atomic concentration of chromium), and therefore, precipitates from different parts of the sample volume are shown. The character- istic diameter of the precipitates was calculated based on the averaging of at least 50–260 nanostructures. It can be seen from Figure 11 that the nanostruc- tures have an elliptical character, due to the partial evaporation of the phases in the radial direction. Ap- proximation of near elliptical nanoprecipitates using calculated spherical structures actually introduces an error of less than 0.4 %, which is less than the resolv- ing power of the APT technique. The radius of each nanostructure is derived from the number of detected atoms in the precipitate and is given as follows: ρ = ( 3νa3 8πQ ) 1 2 , (7) where ν is the number of atoms detected by APTin the nanoprecipitate, Q is the atom probe detector efficiency (Q = 0.5), a is the lattice parameter. From Figure 11, it can be concluded that in the case of high-chromium steels, the formation of precipitates takes place in different local materials and with increas- ing time, they are connected through the so-called neck. The initial nuclei of the precipitates are oriented randomly, and it is not possible to establish a pref- erential direction of their growth. As the annealing time increases (over 55 hours), the nanoprecipitates increase, and this statement about the formation of precipitates is also confirmed by the values of the Avrami kinetic parameter from the JMAK mechanism. The mechanism of precipitation formation is consis- tent with other types of steel and with theoretical binary alloys. The concentration of chromium in the 112 vol. 64 no. 2/2024 Precipitation of Oxide Dispersion Strength Steels After . . . Figure 12. Temporal evolution of the chromium concentration of the α’ phase in PM80KhV2 at 475 °C. Dashed line represents solubility limit of chromium in α’ precipitates determined by TMS. Figure 13. Annealing time dependence of the average precipitate radius in PM80KhV2 high-chromium ODS steel. α’ precipitates increases with time (Figure 12), with a maximum value that is assumed to saturate to that determined by TMS. However, this statement cannot be said with certainty, since due to the low concentra- tion, much longer annealing times would be required. These conclusions are in agreement with the work by Dubiel et al., who annealed the samples for more than 4 years. The dependence of the characteristic diam- eter of Cr-rich precipitates (calculated using Equa- tion (7)) as a function of annealing time is shown in Figure 13. Figure 14 shows the chromium dependence of randomly selected 20 precipitates as a function of precipitate radius during 5, 150 and 1012 hours of annealing at 475 °C. It can be concluded that for the given average size of the α’ precipitates, a correla- tion with the concentration of chromium atoms in the precipitates cannot be clearly determined. The size and enrichment of the precipitates with chromium is clearly dependent only on the annealing time. 4. Conclusion We demonstrated the applicability of statistical (Gaus- sian) distribution model used for high-chromium steels and also high-chromium binary Fe-Cr alloys. The Gaussian distribution model of magnetic components is presented, where the residual paramagnetic phase is modelled by one singlet that corresponds to the param- agnetic structure rich in chromium at RT. The sample was subjected to prolonged annealing at a tempera- ture of 475 °C from 5 up to 1012 hours and subsequent structural changes were observed by TMS and APT techniques. The applied fitting model for the TMS 113 Dávid Košovský, Marcel Miglierini, Tomáš Kmječ et al. Acta Polytechnica Figure 14. Chromium concentration in α’ precipitates as a function of their radii for 5, 150, and 1012 hours of ageing in a PM80KhV2 steel at 475 °C. spectra evaluation using the distribution has proven to be suitable tool for the interpretation of the struc- tural changes occurring in the materials as a result of its long-term annealing at a constant temperature of 475 °C. With increasing annealing time, the mag- netic hyperfine field values of the sextets saturate at 26.8(5) T, from which the solubility limit of chromium in the Fe-rich phase can be estimated. The solubility limit was determined to be 23.5(9) ± 0.5(0) at % Cr. Within the experimental error, the calculated value is identical to the value obtained from the chemical analyses. In the middle of the spectra, a single-line component is observed, which can be interpreted as a chromium rich (α’) phase or as another non-magnetic phase (like nanosized, superparamagnetic, cementite). It represents a minor fraction of iron nuclei in the spec- tral areas in all analysed spectra and can be associated with the onset of Cr-rich clusters formation. Based on the isomer shift of the singlet, the solubility limit in α’ (Cr-rich) phase was estimated at 87.1(3) at %. Us- ing the APT technique, it was possible to describe the 3D structure of α’ precipitates after individual anneal- ing steps. This method made it possible to describe, in detail, the time development of the formation of the Cr-rich phase, whereby it was possible to observe the saturation trend. Based on the development of the size of the precipitates and the relative representation of chromium in the precipitates, a clear correlation between these two quantities cannot be established. Using APT, it is possible to monitor and also pre- dict microstructural changes that have a fundamental impact on changes in macroscopic properties. Acknowledgements This work was supported by the Scientific Grant Agency of the Ministry of Education, Science, Research and Sport of the Slovak Republic [grant numbers VEGA 1/0010/24 and VEGA 1/0395/20], and by the European Regional Develop- ment Fund-Project “Centre for Advanced Applied Sciences” [grant number CZ.02.1.01/0.0/0.0/16_019/0000778]. This article was written thanks to the generous support under the Operational Program Integrated Infrastructure for the project: “Research of physical, technical and material aspects of high-temperature reactors with the potential of hydrogen production”, Project no. 313011BUH7, co- financed by the European Regional Development Fund. References [1] J.-O. Nilsson. Super duplex stainless steels. Materials Science and Technology 8(8):685–700, 1992. https://doi.org/10.1179/mst.1992.8.8.685 [2] D. Košovský, J. Dekan, K. Sedlačková, M. Miglierini. Microstructure of high-chromium ferritic-martensitic steels for next-generation reactors. 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