Mössbauer Analysis of Deformation–Induced Acceleration of Short-Range Concentration Separation in Fe-Cr Alloys—Effect of the Substitution Impurity: Sb and Au

The effect of doping the ferrite alloy Fe-16Cr by the oversized impurities Sb and Au on the mechanism of the short-range ordering induced by “warm” severe plastic deformation was studied using the method of Mössbauer spectroscopy. A comparison between the results obtained and the positron annihilation data on the evolution of the defects of vacancy type stabilized by the impurities Sb and Au was performed. It has been established that the impurities Sb and Au entail a shift of the temperature region of short-range ordering realization in conditions of applying pressure torsion towards greater temperatures by 250 and 100 K, respectively.


Introduction
A saturation of the structure of metallic systems upon their severe (mega) plastic deformation with point defects is a feature typical of dissipation of a great amount of mechanical energy in these systems, a consequence of which are the anomalous phase transitions occurring at relatively moderate temperatures, dynamic recrystallization, non-equilibrium and equilibrium atomic diffusion, as well as nanostructurization [1][2][3][4][5]. In a number of iron-based alloys, there has already been shown the twofold effect of severe plastic deformation on the processes of atomic redistribution: on the one hand, disordering stipulated by movement of dislocations and, on the other hand, ordering taking place due to generating moveable vacancy complexes [3,[6][7][8]. In this case, the result of influence depends on the temperature of the influence and is determined by concurrency of the processes of disordering (preferentially at "cold" deformation, T  Troom) and ordering (at "warm" deformation, T  0.3 Тmelt [1]). The deformation-induced ordering is an accelerated one and comparable with the action-influence of high-energy electrons at relatively moderate temperatures. In particular, in binary bcc Fe-Mn and Fe-Cr and fcc Fe-Ni alloys it was shown using method of Mössbauer spectroscopy that severe plastic deformation via high pressure torsion (HPT) and milling in ball mills at temperatures close to room temperature, each is accompanied with short-range ordering (SRO) comparable (in degree) with the ordering accelerated due to an irradiation by high-energy electrons of fluence F ~5 × 10 22 m −2 within a nearby range of temperatures [3,[6][7][8][9]. Based on the results obtained, a conclusion was drawn on that accelerated ordering is the consequence of (the presence of) moveable vacancy complexes. The SRO (order) formation as the initial stage of phase transitions affects the alloy properties and, in particular, the stability of the structure in conditions of intense irradiation and deformation-related effects. In this regard, studies of short-range ordering in Fe-Cr alloys, as well as of the effect exerted on this ordering by introduced impurities, are important along with the fact that bcc Fe-Cr alloys are the basis of irradiation-resistant stainless steels of the ferrite-martensite class of such materials [10].
It is known that in iron and in Fe-Cr alloys, oversized impurities of substitution, such as Sb and Au, in conditions of irradiation just form vacancy complexes stable at a thermal annealing [11,12]. In the experiments with employment of positron-annihilation spectroscopy (PAS), the stability of vacancy complexes was determined based on the knowledge of the temperature of their dissociation from the curves of the parameter S versus temperature of heating. In the case of the alloys Fe-16Cr doped with Sb and Au, the onset (in case of each impurity) of dissociation of vacancy-impurity complexes formed as a result of irradiation with a fluence of F = 5 × 10 21 m −2 were found to have shifted into the range of higher temperatures by 250 and 100 К, respectively [11]. Since the substitution impurities essentially weaken the mobility of vacancies in irradiated samples, it is of interest to investigate the effect of these impurities on the mechanism and kinetics of the deformation-induced SRO connected with the mobility of vacancy complexes [6].
Thus, the aim of the present work was investigation of the effect of Sb and Au impurities in the alloys Fe-16Cr on the processes of SRO using Mössbauer spectroscopy. The aim also consisted in verification of the mechanism of deformation-induced SRO with using a comparison between the results of Mössbauer investigation and the data of PAS on the mobility of the vacancy complexes accumulated in the course of irradiation by electrons of the binary and doped alloys with impurities of Sb and Au.

Materials and Methods of Investigation
The objects of investigation were Fe-Cr alloys with bcc crystal lattice: the binary alloy Fe-16Cr and one additionally doped with the impurities of antimony: Fe-16Cr-0.3Sb and gold: Fe-16Cr-0.13Au, see Table 1. The concentrations of Sb and Au were controlled by weighting and confirmed by the methods of Rutherford backscattering and X-ray microanalysis. For a more correct comparison of Mössbauer and PAS data, the investigations were performed on the same samples [11]. The procedure of preparation of alloys is described in [13]. After rolling, cutting, and electrical polishing, the samples about 10  10 mm −2 in size (~0.3 mm thick) were annealed under 10 −5 Pa vacuum at 1070 K (in ferritic area) for 4 h followed by air cooling. This state of the materials is further referred to as initial.
Severe plastic deformation was performed by HPT in Bridgman anvils to the degree ε = 5.9 (n = 3 revolutions of anvils) and rate 2.4 × 10 −2 s −1 (0.3 rev/min) at temperatures of from 298 to 673 K, in a way similar to that from [3,[6][7][8]. The degree of true deformation was estimated by the formula [14].
The scheme of experiment is shown in [7]. The required temperature was achieved usually within 10 or 20 min after placing the anvils with a sample into liquid nitrogen or furnace, respectively. Then a sample at the given temperature was loaded to a pressure of 8 GPa and subjected to deformation torsion by rotating the bottom anvil. The time of HPT was 10 min. After the torsion, the sample was returned to room temperature and unloaded. After that, samples had a shape of a disc of 7 mm in diameter and 150 μm in thickness. For Mössbauer measurements, the disc was thinned, first, mechanically with diamond paste and then electrochemically up to 20 μm. For the Mössbauer measurements, there was used either a full surface area of the sample. Apart from the experiment on HPT, the initial samples were annealed at 773 К, for 1 h. Mössbauer -quantum absorption spectra on 57 Fe were obtained at room temperature in the mode of constant acceleration with the 57 Co(Rh) source. As a calibration standard, that one of an iron foil was used. The measurements were carried out on the 20 μm thick foils. A package of special programs [15] was used for the calculation of Mössbauer spectra. The calculation included the restoration of both distribution of the hyperfine magnetic field p(H). Then the distribution p(H) was used for the modeling and approximation of experimental Mossbauer spectra by a sum of several sub-spectra, sextets A(N1,N2), either of which corresponded to the various possible distributions of Cr atoms in the nearest coordination shells (CSs) of 57 Fe atoms referred further to as the atomic configurations (N1,N2). Here N1 and N2 are the numbers of chromium atoms in the first and second CSs, respectively. The integral intensity of each sextet A(N1,N2) is proportional to the probability W(N1,N2), namely, the probability of finding N1 chromium atoms in the first and N2 atoms of chrome in the second CS.
The redistribution of atoms during SRO formation was analyzed by means of Mössbauer spectra in the same way as it was done in [3,6,[16][17][18][19], i.e., considering various possible distributions of Cr atoms in the two nearest coordination shells (CSs) of 57 Fe atoms. The hyperfine parameters (of spectra) X = H (magnetic field) or Is (isomer shift) were additive, i.e., X(N1,N2) = X(0,0) + N1ΔX1 + N2ΔX2, where X(0,0) is the value of the parameters in the absence of impurity of chromium (Cr), ΔX1 and ΔX2 are the changes of X due to one Cr atom in the first and the second CSs. The values of ΔH1 and ΔH2 were 32(± 1) and 20(± 1) kOe, respectively.
When simulating spectra of the alloys with the impurities of Sb and Au, the influence of the latter on the hyperfine parameters were neglected because of the small (just tenths of an atomic percent) concentration of the impurities. The same circumstance concerns the effect of vacancies. In accordance with [20,21], after HPT, their concentration does not exceed the value 4-5 × 10 -4 of relative units. The probabilities W(N1,N2) of observing in the first and second CSs the different number of Cr atoms without formation of the SR or the long-range (LR) order were taken as correspondent to binomial distribution. In the case of the formation of SR order in an Fe100-cCrc alloy, the average concentrations of the Cr component over the first and second (nearest) CSs differ from that characteristic of disordered state and are equal to c1 = c(1 − α1) and c2 = c(1 − α2), respectively, where αi are the Cowley parameters of SRO in the i-th CS [4]. The effective-i.e., averaged over two CSs-chromium concentration c1,2 is determined by relationship [19] 2 1 where Z1 (= 8) and Z2 (= 6) are the coordination numbers. The total contribution of these sextets, i.e., A(N1,N2), was about 95%, see Tables 2-4. Only sextets with partial contribution exceeding 1% were taken into account in spectra approximation, i.e., A(N1,N2)  1%.
Besides, to obtain the qualitative estimation of redistribution, the linear dependence of the average effective field <H> (kOe) on the chromium concentration c (at %) in Fe-Cr alloys [6], namely, was used additionally, where the coefficient of proportionality k = 2.83 kOe × at % −1 . This dependence was obtained based on the calculated values of the average effective field in the (initial) Fe-Cr alloys annealed at 1073 K and found to be close to that in [14][15][16][17] where Z1 (= 8).
Mössbauer data on the deformation-induced ordering of the alloys were compared with the PAS data on the dissociation of vacancy defects during annealing of the samples preliminarily irradiated by electrons [9].

Experimental Results
In Figures 1-3 we present the spectra, distributions p(H), and values <H> for the alloy samples -initial and HPT-deformed at different temperatures. It is seen that the smallest of the values of <H> was obtained after HPT at 298 К and, further, <H> grows steadily when increasing HPT temperature to 673 K, see Figure 4. The growth of <H> was stipulated by increasing contribution to p(H) from Cr-depleted atomic surroundings of iron. These contributions of W(N1,N2) = A(N1,N2) are the probabilities of an occupation of the first two CSs of iron by Cr atoms of number N1,2 = N1 + N2 = 0, 1. The fields of these surroundings are of larger magnitude, see Tables 2-4. Note that, with lowering chromium concentration, an effective field at an iron atom tends to increase; thus, the growth of <H> proceeds at the expense of lowering the number of atomic configurations with N1,2 = N1 + N2  2.  In accordance with the Equations (1) and (2), the growth of <H> testifies to the decrease in c1,2 at raising the temperature of deformation of samples from 298 К. However, in relation towards "initial" samples, the changes in the occupations W(N1,N2) ~A(N1,N2), <H>, and c1,2 with changing HPT temperature are not regular. The behavior of parameters of the deformed samples in relation to the parameters of the initial state of alloys can be conventionally classified into two regions of temperatures. The first region (of cold deformation) represents the temperatures of HPT, at which one can observe the decrease in the contribution from Cr-depleted (i.e., with N1 = 0, 1) atomic configurations, the decrease in <H>, and the growth in the effective concentration c1,2-in relation to corresponding initial samples. For the alloy Fe-16Cr, as well as for the alloys Fe-13.2Cr and Fe-20.6Cr [6], "cold" deformation (298 К) leads to a decrease in <H> and to a growth of c1, as a consequence of destruction of regions of the short-range order of separation origin that were present in the initial state, see Figures 4а, 5а, and Table 2. The second region of temperatures (of "warm" deformation) is characterized by opposite changes, namely, by growth of the contribution from depleted configurations, by growth of <H>, and by a decrease in c1,2 of deformed samples in relation to an initial sample, i.e., by the process of SR ordering of separation origin. For the alloy Fe-16Cr, the region of "warm" deformation, connected with the decrease in c1,2, commences at temperatures above 373 К, Figures 4а and 5а. In the alloy doped with Sb, the HPT temperature region (outside it one can observe SR ordering as a result of concentration separation) is situated above 250 K relative to that of the binary alloy Fe-16Cr, Figures 4b and 5b and Table 3. The HPT of the alloy Fe-16Cr-0.3Sb at 623 К virtually does not change the values <H> and c1,2 of the «initial» sample. The decrease in c1,2 from 14.4 at % (for the initial sample) to 13.7 at % takes place only after HPT at 673 K, closely approaching the value of c1,2 = 13.4 at % obtained in result of annealing at 773 K, for 1 h.
The results of HPT experiments on the alloy Fe-16Cr-0.13Au concerning the dependence of <H> and c1,2 on the temperature of deformation are presented in Figures 4c and 5c. The same as in the case of the alloy with Sb, there is observed a shift of the temperature border of changing the behavior of <H> and c1,2, which characterize the degree of SRO in the samples towards higher temperatures-approximately by 100 K.
The region of the temperature border of the deformation after which one can observe realization of SR ordering in the alloys studied, is characterized by an enhanced rate of alteration of c1,2, see Figures 4а-с. For the alloy Fe-16Cr this region is situated in the vicinity of 330 K, for the alloy Fe-16Cr-0.3Sb this region is situated in the vicinity of 620 К, and for the alloy F-16Cr-0.13Au in the vicinity of 450 K. Above the border mentioned the derivative from c1,2 by the temperature of deformation is lowered.

Discussion
The fact of existence of a temperature border-a change in the behavior of the parameters of spectra and in c1,2, which characterize the process of SR ordering, is a consequence of the concurrence between two processes, namely, disordering action of moving dislocations and ordering in result of generating a large quantity of mobile point defects [2][3][4]8,[20][21][22]. The first process (dislocation disordering) little depends on the temperature of deformation [3,6]. As is seen from Figure 5 and Tables 2-4, "cold" deformation of the binary alloy Fe-16Cr and alloys doped with Sb and Au brings the values of W(N1,2) ~A(N1,2) and c1,2 to their theoretical values Wtheor and c1,2(random) which correspond to a random distribution of chromium in the solid solution. Such an action of HPT testifies to the "disintegration" of the SR order that existed in the initial state of the alloy. The "disintegration" of the SR order was observed on the samples of Fe100−cCrc (c = 12…20.6) alloys preliminarily aged at 773 К, for 50 h [6], as well as on the other alloys [3,7,8]. The second process (i.e., ordering that is stipulated by generation of mobile point defects) is strongly dependent on the temperature, and manifests itself already at the temperatures close to room temperature. This is seen in the steady growth of <H> and decreasing of c1,2 at raising the temperature of deformation from 298 K to 673 K. The process of SR ordering at "warm" deformation is an accelerated one and takes place during the time period of 10 min (3 revs of anvils at a speed of 3 rev/min.) and it-by the degree of SRO-is close to that one accelerated (i) by the irradiation with high-energy electrons in the region of close temperatures of 400-600 K [3,6] or (ii) at thermal annealing performed at 773 K, 1 h, see Figures 4 and 5. The temperature border of the start of the process of SR ordering corresponds to the dominance of the mechanism of the ordering accelerated in relation to the concurrent process of dislocation disordering. The doping with the impurities Sb and Au, preserving a qualitatively general form of the dependence of c1,2 on the HPT temperature, shifts the border between the first and the second regions of temperatures by ~250 K and by ~100 K in the alloys with Sb and with Au, respectively, in relation towards that typical of the binary alloy Fe-16Cr. To elucidate the mechanism of the effect of a substitution impurity on the deformation-induced process of SR ordering, in the present investigation we have made a comparison between our results and PAS data [11] on the evolution of vacancy defects in alloys of similar compositions, see Figure 6. Positrons are a sensitive indication of the start of stabilization of defects of vacancy type [23]. If a positron is trapped on the vacancy-type defects (small 3-D vacancy clusters), the value of S parameter increases [11][12][13]. The dependence of S parameter of the binary and doped alloys irradiated by electrons has a form of the curve with saturation as a result of stabilization of vacancy complexes in the course of increasing the fluence. This shows that the clusters and complexes are dominant sinks for vacancies that are mobile in conditions of irradiation at Troom [24,25]. In Figure 6 [11], there are presented PAS data on the dependence of S parameter when annealing vacancy defects obtained via electrons irradiation of the Fe-Cr binary and doped alloys with Sb and Au. After irradiation with a fluence of 5  10 21 m −2 , in Fe-Cr alloys doped with Sb and Au, the decrease of S parameter commences in the region of annealing temperatures higher by 250 and 100 K than those characteristic of the alloy Fe-16Cr, see Figure 6 [11]. This means that in the alloys doped with Sb and Au the greater part of mobile vacancies that are formed in the course of irradiation just get stabilized, in other words, form immobile vacancy complexes with Sb and Au atoms. The anneals at higher temperatures, namely, of 400, 600, and 700 K, of the alloys Fe-16Cr, Fe-16Cr-0.13Au, and Fe-16Cr-0.3Sb, respectively, lead to the decline of S parameter as a consequence of dissociation of vacancy complexes. Earlier [3,6], on the binary Fe-Cr alloys, the deformation-induced acceleration of short-range (SR) ordering in conditions of raising the HPT temperature was explained as the result of saturation of the structure by the vacancy complexes [20,21], the mobility of which strongly depends on the temperature. As it follows from the comparison between Mössbauer and PAS data, the temperature boundary (TB) between "cold" and "warm" deformation in the vicinity of which the increase in the derivative of c1,2 is observed, this TB coincides with the beginning of an active decrease in the parameter S at annealing of preliminarily irradiated samples. This means that the processes of SR ordering of concentration-separation origin in the HPT experiments coincide with the start of movement of vacancies as a consequence of dissociation of vacancy complexes. The impurities Sb and Au just form with the vacancies right immobile complexes and, thus, stabilize vacancies up to 600 K. At temperatures above 600 K, vacancy complexes dissociate, vacancies acquire mobility and participate in the processes of SR ordering. Thus, the correlation between the temperature boundary (which characterizes an acceleration of SR ordering) and the data [11] on the temperature of the beginning of the dissociation of "vacancy-impurity" complexes, confirms the participation of vacancy complexes in the SRO processes upon deformation. We can conclude that a shift of the beginning of SRO in the direction of increasing temperature in the alloys doped with Sb and Au is due to the (i) strengthening of the bonds between vacancies and impurities and, thus, (ii) increasing of the mobility of the vacancies.
The data obtained in this work, on the temperature boundary of deformation-induced SR ordering, can employ Mössbauer spectroscopy to further investigate (i) the mobility of vacancy complexes and (ii) the bond energy between vacancies and impurities in Fe-Cr alloys.

Conclusions
Via methods of Mössbauer spectroscopy, there has been studied the mechanism of the short-range ordering induced by severe plastic deformation of/in the ferritic binary alloy Fe-16Cr, as well as in the alloys Fe-16Cr-0.3Sb and Fe-16Cr-0.13Au doped with Sb and Au. The conditional presence is established of two temperature regions of changing of the degree of short-range ordering in the course of HPT action, namely, the region of (the) "cold" deformation after which the degree of SR order (SRO) in the initial state of the alloy exhibits a decrease, and the range of (the) "warm" deformation that entails an increase in the degree of the SRO. It is shown that the temperature boundary between regions of the "cold" and the "warm" deformation is dependent on the degree of alloy's doping with the oversized impurities Sb and Au and experiences a shift (of increase) by ~250 (Sb) and ~100 (Au) K in comparison with the case of the binary alloy Fe-16Cr. A comparison between the results of Mössbauer spectroscopy on the degree of (the) SRO and data of positron annihilation on the temperature of dissociation of defects of "vacancy-impurity" type has confirmed the relation between the mechanism of deformation-induced short-range ordering in Fe-Cr alloys and vacancy complexes that form in the course of severe plastic deformation.

Funding:
The research was carried out within the state assignment of Ministry of Science and Higher Education of the Russian Federation (theme "structure" no. AAAA-A18-118020190116-6) supported in part by the Russian Foundation for Basic Research grant (project no. 18-03-00216).