- Email: [email protected]
Radiation induced disordering in Cu3Au
Journal Pre-proof Radiation induced disordering in Cu3Au N.V. Proskurnina, V.I. Bobrovskii, B.N. Goshchitskii, A.Yu Volkov, V.I. Voronin PII:
S0969-806X(19)31196-X
DOI:
https://doi.org/10.1016/j.radphyschem.2019.108654
Reference:
RPC 108654
To appear in:
Radiation Physics and Chemistry
Received Date: 11 September 2019 Revised Date:
25 November 2019
Accepted Date: 15 December 2019
Please cite this article as: Proskurnina, N.V., Bobrovskii, V.I., Goshchitskii, B.N., Volkov, A.Y., Voronin, V.I., Radiation induced disordering in Cu3Au, Radiation Physics and Chemistry (2020), doi: https:// doi.org/10.1016/j.radphyschem.2019.108654. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
CRediT author statement
N.V. Proskurnina: Resourses, Visualization, Writing - Review & Editing; V.I. Bobrovskii: Methodology, Writing - Original Draft; B.N. Goshchitskii: Conceptualization; A.Yu. Volkov: Resourses, Methodology; V.I. Voronin: Investigation, Formal analysis.
Radiation induced disordering in Cu3Au N.V. Proskurnina*, V.I. Bobrovskii, B.N. Goshchitskii, A.Yu. Volkov, V.I. Voronin M.N. Miheev Institute of Metal Physics of Ural Branch of Russian Academy of Sciences, 620108 Ekaterinburg, S.Kovalevskaya Str., Bld.18, Russia * Corresponding author: E-mail address: [email protected] (N.V. Proskurnina), tel.: +7 343-378-38-75 Abstract In the work, a specially prepared powder of the model ordered Cu3Au alloy was used to investigate peculiarities of internal processes that take place in the ordered precipitates similarly to those occurring in austenitic reactor steel under irradiation with fast neutrons. It is shown that, unlike the thermal or deformation disordering, in the case of such impact, the dependence of the lattice parameter on the degree of long-range order presents a kink that testifies to the development under irradiation of competitive processes in the defect structure of the studied material.
Keywords: reactor steels, radiation damages, anti-site defects, radiation induced processes, long range order parameter, X-ray diffraction.
1. Introduction Despite a long-term history and substantial bulk of data gained on the influence of radiation on the reactor steels, the mechanism and peculiarities of many structural changes that takes place under irradiation, especially, with varying temperature and dose, have not been fully ascertained so far. It is well known that under irradiation, along with changes in characteristics of the matrix structure, there can occur variations in composition of initial solid solution, radiation-induced atomic segregation, and formation and modification of the secondary-phase precipitates. In the case of ordered precipitates, there can be observed two processes: (1) disordering of ordered phase and (2) dissolution of precipitates via atomic mixing. However, commonly, models of evolution of such heterostructures take into account only composition, particle size, and the number of the phases precipitated. Yet, it is quite predictable that the internal radiation-induced modification of precipitates has to affect their structure and physical properties rather than solely mechanical properties of the system, which is evident. Investigation of these points in detail is hindered by a small volume of these phases. Several aspects of the behavior of precipitates and their impact on the material properties are given in [1-4]. In [1], it was shown that irradiation of the model alloy Fe62Ni35Ti3 triggers two processes: formation of radiation defects and precipitation of γ΄ phase Ni3Ti. Both the amount and size of precipitates grow with the fluence of fast neutrons thus affecting 1
the material properties. However, in this investigation, similarly to virtually all works of the kind, the state of lattice of the precipitates proper was not studied intently. In our study, we performed X-ray structure investigation of the influence of irradiation with fast neutrons in a wide range of fluences on the model ordered binary compound Cu3Au. The object chosen is structurally isomorphous to the γ΄-Ni3Ti phase and its properties in the state after irradiation with high-energy particles and fast neutrons have already been studied, yet in few details. Thus, [5-10] it is shown that electrical resistivity changes under the action of radiation mainly due to the lattice disordering. However, the data on the degree of order, which can be determined directly from the diffraction experiments on the irradiated Cu3Au samples, are lacking. Only in [11], via comparison of film X-ray diffraction patterns of the initial and irradiated Cu3Au samples was the effect of the alloy disordering under fast-neutron irradiation registered, no estimates of the degree of long-range order (LRO) being presented. Note also that when studying the effects of disordering in the compound Ni3Al, which is isostructural to Cu3Au, the main attention was paid to the LRO-parameter, i.e., anti-site defects [12-14]. The intemetallic Ni3Al differs from the compound Cu3Au in high resistance to disordering and efficient mechanism of reordering. Along with the disordering proper, we were interested in the behavior of other lattice characteristics of Cu3Au, specifically, under cascade-forming neutron irradiation. It should be noted that to obtain a sample of the Cu3Au alloy in the initial state with the maximal degree of ordering is rather a complicated problem. 2. Samples and Research Methods 2.1 Samples preparation The alloy investigated in this study contains 25 at% Au (50.85 wt%) leading to Cu3Au. The task of the first step of the sample fabrication was to gain elemental distribution as homogeneously as possible. The alloy was melted from copper 99.98% in purity and gold, 99.99%, in a vacuum of no less than 10-2 Pa by the method of double remelting with pouring in a graphite crucible. The main impurity in gold was platinum (<0.01%). The ingot 5mm in diameter was homogenized at a temperature of 750ºС for 3 h, cooled inside the furnace to 450°С, and quenched into water. X-ray analysis showed that the crystal structure of the material corresponded to the cubic phase Cu3Au, but the atomic distribution over the lattice sites was not ordered in full measure. At the second step, the samples were subjected to long-term annealing aiming at the formation of a highly ordered state. The heat treatment consisted in annealing of the samples at 450°С for 1h and subsequent stepped cooling by the following scheme: cooling to 350°С, holding for 24h, cooling to 300°С, and again holding for 24 h. Such stepped annealing with 24-h holdings was carried out to a temperature of 100°С and then, the sample was cooled inside the furnace to room temperature. The powder for investigation was manufactured from the bulk using a steel file with 2
shallow cutting teeth. The particle size was controlled by optical microscopy and did not exceed 0.5 mm. Moreover, the experimental X-ray pattern of the as prepared material accorded well with the calculated one, thus indicating the absence of effects caused by coarser grains. This powder was pressed into tablets 5mm in diameter and 3mm in height and subjected to additional annealing for ordering at the temperature 300°С with the subsequent cooling with a rate of 50°С per 24h. 2.2 Methods of measurements Crystal structure of the samples was studied by X-ray diffraction at a diffractometer UM-1М with a copper anode (CuKα, PG-monochromator) in the Bragg-Brentano geometry. Experimental X-ray patterns were taken in the angular range 20 – 145 degree with a step of 0.02. The samples were rotated in the vertical plane. Analysis of the experimental spectra was performed by the method of full-profile Rietveld analysis with the use of program package FullProf [15]. The profiles of reflections were fitted with the pseudo-Voigt function. The anisotropy of broadening of diffraction peaks was treated through the analytical procedures of the program Fullprof [15] using the reference function of the instrumental resolution, which was obtained in measuring specially designed reference powder samples of Na2Al2Ca3F12 and CeO2. Irradiation of the synthesized sample Cu3Au was performed in the vertical in-core wet channel of a 15 MW research reactor IVV-2M (Zarechny-city near Ekaterinburg, Russia. The unit is under operation of the Institute of Nuclear Materials. Also, the Neutron Material Science Complex of the Institute of Metal Physics is located on its premises). The density of the flow of fast neutrons with the energy En ≥ 0.1 MeV was equal to ∼2.23×1014 cm−2s-1. The temperature of irradiation corresponded to the temperature of reactor tank and equals about 353 K. The sample had been sequentially irradiated for three years with the fast-neutron fluence of (3, 10, 15, 22, 42) ×1018 n/cm2. After each act of irradiation and the necessary decay time, the sample was investigated by X-ray diffraction method.
3. Results Figure 1 presents X-ray diffraction pattern taken from the powder tablet Cu3Au prepared by heat treatments to subsequent neutron irradiation. The set of reflections corresponds to the ordered cubic phase Cu3Au (L12-type structure). The FullProf analysis showed that the form and width of the lines correspond to those of the reference, which means that internal stresses in the sample bulk are absent and the coherent scattering domain size exceeds 1000Å. Moreover, the probability of occupation of gold atomic positions by copper atoms, x, which is an indicator of deviation of the atomic distribution over the lattice from ideal, made up less than 4%. 3
In the ideal case, large gold atoms occupy corner sites of an ordinary crystal lattice, whereas copper atoms, face centers. With fully statistical atomic distribution over lattice sites, we evidently have the set of structural reflections in the diffraction pattern that corresponds to the face-centered lattice. A preferential occupation of certain positions by atoms of one sort gives rise to additional superstructure reflections. In such situation, the structural factors for the fundamental structure and additional superstructure reflections are written as follows: =<
> +3 <
=< respectively, where <
> −<
> and <
>; >;
(1) (2)
> are the average (with allowance for the occupancies)
amplitudes of X-ray scattering at gold and copper positions. It is important noting that if the stoichiometry of compound is preserved and its structure rearrangement is reduced to exchanging place by different atoms (so-called anti-site defects), the values of the structural factors
and, correspondingly, intensity of the fundamental structure
reflections must be constant. These rearrangements affect the value of
and intensity of
superstructure reflections. For quantitative estimation of the degree of ordering, a long-range order parameter (LROparameter) of Bragg-Williams is used, which for our compound Cu3Au can be written as follows: = where
( )
=1−
is the concentration of Au and
( )
,
( ) ( )
(3)
are the occupancy probabilities of Au position by
atoms of Au and Cu correspondingly. The degree of long-range order in the initial tablet made up 0.95. The X-ray diffraction patterns of the irradiated materials are shown in Figure 2. It is seen from Fig. 2 that with growing fluence, the intensity of structure reflections changes insignificantly, whereas that of superstructure reflections virtually vanishes at the maximal fluence of 42×1018 n/cm2. This result agrees with the conception on the disordering of the given alloy by the mechanism of formation of anti-site defects, i.e., through the exchanging places of different atoms, which is described by the LRO-parameter (3). In Fig. 3, the change in the LRO-parameter under irradiation, which was determined from the diffraction patterns given in Fig. 2 with the use of FullProf analysis and formula (3), is shown. One more impact of irradiation with growing fluence on the crystal lattice of the compound manifests itself in the displacement of reflections toward lower angles, which testifies to an increase in the lattice parameter. (Fig. 4). Also, as the analysis shows, changes in the intensity of fundamental structure reflections with fluence, which are more distinctly seen in large scattering angles, can be described via increasing the Debye-Waller factor (Fig. 5). At last, the full-profile analysis showed that under irradiation, not 4
only intensities and angular positions of the reflections change but their form and width as well. For example, reflection (420) is given in Fig. 6 for the initial (nonirradiated) sample and that irradiated with the fast-neutron fluence of 42×1018 n/cm2. As is seen, the irradiation results in both the broadening of the reflection and change in its form, which, judging by wings, becomes closer to Lorentzian. Such changes in the reflection form, according to the theory of X-ray and thermal neutron scattering [16], arise due to internal microstresses caused by the defects “of the second class”, according to the Krivoglaz classification (namely, dislocations, clusters of point defects, etc.). Based on this supposition and using the capacity of the FullProf program [15], we determined the dependence of microstrains in the Cu3Au lattice on the fluence of fast neutrons (Fig. 7). The internal microstresses are connected with them through the elastic modulus. 4. Discussion The above results indicate that the irradiation of the highly ordered compound Cu3Au with increasing fluence results in its radiation-induced disordering, the main mechanism of which is the formation of anti-site defects; at the maximal fluence 42×1018 n/cm2 the long-range order parameter falls to 0.1. At the same time, the lattice parameter and Debye-Waller factor grow and the form and width of reflections change. The latter points to the appearance in the crystal lattice of microstresses. In general, such a behavior is typical of materials undergone the action of fast neutrons or highenergy particles. Also, it is known that the destruction of long order in intermetallic compounds is as a rule accompanied by an increase in the lattice parameter. This phenomenon, which was discussed in, say, [17], apparently is conditioned mostly by the dependence of energy of ordering on the level of interatomic interactions rather than only on the geometrical mismatch of the atomic size in the compounds. This conclusion is supported by the results of investigation of correlation of the lattice parameter with changes in the long-range order in Ni3Al (which possesses the same crystal lattice as Cu3Au) [18]. It was shown that for Ni3Al, the lattice parameter changes linearly with S in all the range 0≤S≤1, which agrees with changes in the length of “unlike” interatomic bonds. To compare the results, we constructed the dependence of the lattice parameter of the alloy Cu3Au on the degree of long-range order for our irradiated samples, as well as for the samples of Cu3Au and Ni3Al described in [17, 19] where disordering was produced by heat treatments (Fig. 8). The dependence of ∆ / on LRO-parameter S in Fig. 8 demonstrates a more complicated course. At low fluences (to 10×1018 n/cm2), the lattice parameter grows with S much faster than upon thermal disordering. It is known that irradiation of metals and alloys results in the formation of primary defects, which are interstitial atoms and vacancies (Frenkel defects). It is considered that in metals in the 5
state of thermal equilibrium, interstitial atoms go toward the crystal boundaries, thus creating new unit cells, vacancies being retained inside the bulk (Schottky defects). However, it should be taken into account that under cascade-generating irradiation with fast neutrons, in the material there are formed point defects in much higher concentrations than upon thermal actions. After withdrawing from the irradiation channel, the material retains residual defect structure, being in a thermodynamically nonequilibrium state [120-23]. The highly ordered alloy Cu3Au is peculiar in that the formation of vacancies and interstitials proceeds at the background of disordering of the initial crystal lattice upon which there are created anti-site defects, i.e., atoms of Cu and Au exchange places. In this case, the total change of ∆ / is the sum of contributions made by anti-site defects proper and interstitials and vacancies. !" "
# = $
!" "
#
%&
!"
+
"
#
(4)
However, as the conditions of formation of interstitials and vacancies obviously depend on the distribution of atoms of Cu and Au over lattice sites, the first term in the right part of (4) also depends on LRO degree. In Fig. 8, the lower line describes the behavior of a system with anti-site defects and vacancies in concentrations that are preserved after quenching from the temperature at which the thermal disordering of the lattice was carried out. Apparently, the main contribution to it is made by anti-site defects. When interpreting the behavior of the upper line, it should be taken into consideration that it refers to a post-radiation thermodynamically nonequilibrium structure in which not only single vacancies and interstitials were formed by radiation but, in the process of their evolution, their clusters and dislocations as well [24]. Such coarse formations can create microstresses in the crystal lattice, and, what is more, serve as sinks for point defects, thus affecting the concentration of the latter in the system. It is seen from Fig. 8, that at comparatively low irradiation doses, one can see in the vicinity of ≈ 1 a quick accumulation of defects with increasing dose, which provides their high postirradiation concentrations in comparison with the lower curve. The positive sign of the ∆ / value evidences the preservation of rather a high concentration of the interstitials (most probably in the form of dumbbells typical of the fcc-lattices [24]), which are responsible for the considerable positive lattice relaxation. The course of the upper line in Fig. 8 evidences that after reaching a certain value of S (and corresponding fluence of fast neutrons), competitive processes start developing in the system, which 6
efficiently compensate for the influence of vacancies and interstitials. As a result, the further course of the upper line is controlled by anti-site defects solely. Increasing the Debye-Waller factor upon irradiation is another manifestation of the behavior of defects (Fig.5). Its value is controlled by the mean-square amplitudes of atomic displacements from the equilibrium positions, which are contributed to by both thermal atomic oscillations and uncorrelated statistical displacements which arise due to microstresses created by defects. At the initial stage of irradiation, when the concentration of defects (anti-site, vacancies, and interstitials) is small and their distribution over the bulk is homogeneous, the value of the Debye-Waller factor virtually does not change, which is the consequence of thermal oscillations. However, with growing fluence, coarse clusters of interstitial atoms and vacancies, as well as dislocations, start forming and generate lattice microsresses [16], thus giving rise to the Debye-Waller factor at fluences higher than 10×1018 n/cm2 (Fig.6). Such microstresses lead to the lattice microstrains, which manifests itself in the reflection broadening in the X-ray patterns (Figs. 6, 7). It is worth paying attention to the changes in the intensity of structure and superstructure reflections depending on fluence. To discard the influence of effects described by Fig. 5, corrections that exclude the influence of the Debye-Waller factor are applied to the intensities of superstructure reflection (110) and structure reflections (111) and (420), shown in Fig. 9. It is seen that the intensity of superstructure reflection (110), which depends on the degree of long-range order, virtually vanishes, testifying to the atomic disordering, as shown above. At the same time, the intensities of structure reflections, independent of the degree of long-range order, remain constant up to the fluence 10×1018 n/cm2 and then start decreasing, though much slower than that of the superstructure one. Such a decrease can be explained by the absence of contributions to reflections from part of material. The plausible cause for this is the formation at this stage of the abovementioned atomic clusters with another structural type than Cu3Au. 5. Conclusions The experimental data obtained testify to the development of competitive processes in the defect structure of the material under study upon its irradiation with fast neutrons. For the first time, direct structure investigations by the method of X-ay diffraction are employed to trace the changes in the degree of long-range order, characterized by LRO-parameter, upon irradiation of the ordered compound Cu3Au with fast neutrons. It is shown that unlike the thermal or deformation disordering, in the dependence of the lattice parameter on the fluence there is a kink related to the radiation defects. At high fluences, along with the anti-site disordering, there arise defect clusters that give rise to the emergence of internal microstresses. Thus, radiation defects result in a more significant growth of the lattice parameter than solely anti-site disordering does. Using these data, we can 7
better understand the processes that take place in reactor materials, including evolution of defect structure. Acknowledgments The research was carried out at IMP Neutron Material Science Complex within the state assignment of Minobrnauki of Russia (theme “Flux”, No АААА-А18-118020190112-8), supported in part by RFBR (project No. 18-02-00270). References [1] V.I. Voronin, I.F. Berger, B.N. Goshchitskii, Structural changes in a model alloy after irradiation of Fe62Ni35Ti3 with fast neutrons and isochronous temperature annealing, Phys. Met. Metallogr., 113 (9) (2012) 878-882. https://doi.org/10.1134/S0031918X12090141 [2] V.V. Chuyev, V.F. Rosljakov, V.V. Maltsev, Features of Constructional Materials' Behavior within Fast High-Power Reactor's Spectrum of Neutrons, Izvestiya Vysshikh Uchebnykh Zavedeniy: Yadernaya energetika, 1 (2005) 113-126. ISSN 0204-3327 [3] P.L. Mosbrucker, D.W. Brown, O. Anderoglu, L. Balogh, S.A. Maloy, T.A. Sisneros, A.C. Dippel, Neutron and X-ray diffraction analysis of the effect of irradiation dose and temperature on microstructure of irradiated HT-9 steel, J. Nucl. Mater. 443 (2013) 522-530. https://doi.org/10.1016/j.jnucmat.2013.07.065 [4] L. Balogh, D.W. Brown, P. Mosbrucker, F. Long, M.R. Daymond, Dislocation structure evolution induced by irradiation and plastic deformation in the Zr–2.5 Nb nuclear structural material determined by neutron diffraction line profile analysis, Acta Mater. 60 (15) (2012) 55675577. https://doi.org/10.1016/j.actamat.2012.06.062 [5] J. S. Huang, M. W. Guinan, F. A. Hahn, Irradiation disordering and ordering of Cu3Au by fusion neutrons, J. Nucl. Mater, 141-143 (1986) 888-892. https://doi.org/10.1016/00223115(86)90112-1 [6] H. L. Click, F. C. Brooks, W. F. Witzig, and W. E. Johnson, The resistivity of Cu3Au during neutron irradiation, Phys. Rev. 87 (6) (1952) 1074. https://doi.org/10.1103/PhysRev.87.1074 [7] S. Siegel, Effect of neutron bombardment on order in the alloy Cu3Au, Phys. Rev. 75 (12) (1949) 1823-1824. https://doi.org/10.1103/PhysRev.75.1823 [8] A Dunlop, D Lesueur, N Lorenzelli, A Audouard, C Dimitrov, J M Ramillon and L Thome, Search for damage and/or disordering effects due to intense electronic excitation in crystalline metallic alloys irradiated by high-energy heavy ions, J. Phys.: Condens. Matter. 2 (7) (1990) 17331741. [9] L. C. Wei, E. Lang, C. P. Flynn, and R. S. Averback, Freely migrating defects in ion-irradiated Cu3Au, Appl. Phys. Lett. 75 (1999) 805. https://doi.org/10.1063/1.124519
8
[10] L. Wei, Y. S. Lee, R. S. Averback, and C. P. Flynn, Antistructure and Point Defect Response in the Recovery of Ion-Irradiated Cu3Au, Phys. Rev. Lett. 84 (26) (2000) 6046-6049. https://doi.org/10.1103/PhysRevLett.84.6046 [11] L.G. Cook and R.L. Cushing, The effects of neutron irradiation in the NRX reactor on the order-disorder alloy Cu3Au, Acta metallurgica. 1 (1953) 539-548. https://doi.org/10.1016/00016160(53)90084-4. [12] H.C.Liu, T.E.Mitchell, Irradiation induced order-disorder in Ni3Al and NiAl, Acta Metall. 31 (6) (1983) 863-872. https://doi.org/10.1016/0001-6160(83)90114-1. [13] S. Muller, C. Abromeit, S. Matsumura, N. Wanderka, H. Wollenberger. Disordering kinetics of Ni3Al under ion irradiation, J. Nucl. Mater. 271-272 (1999) 241-245. https://doi.org/10.1016/S0022-3115(98)00711-9. [14] C. Abromeit, S. Miiller and N. Wanderka, Stability of γ΄ phase in the stoichiometric Ni3Al alloy under ion irradiation, Scr. Metall. et Mater. 32 (10) (1995) 1519-1523. [15] J. Rodriguez-Carvajal, Recent advances in magnetic structure determination by neutron powder diffraction, Physica B. 192 (1993) 55-69. https://doi.org/10.1016/0921-4526(93)90108-I [16] M.A. Krivoglaz, X-ray and neutron diffraction in nonideal crystals, Springer Verlag Publ, Berlin, Heidelberg, 1996, pp. 466. [17] R. W. Cahn, Lattice parameter changes on disordering intermetallics, Intermetallics, 7 (1999) 1089-1094. https://doi.org/10.1016/S0966-9795(99)00035-7 [18] S. Gialanella, R.W. Cahn, J. MalageladaJ, S. Suriñach, M.D. Baró, A.R. Yavari, in: H. Chen and V.K. Vasudevan (Eds), Kinetics of ordering transformations in metals, Warrendale, PA: TMS, 1992, pp. 161. [19] M.L. Bhatia, R.W. Cahn, Lattice parameter and volume changes on disordering, Intermetallics. 13 (2005) 474–483. https://doi.org/10.1016/S0966-9795(99)00035-7 [20] V.I. Voronin, I.F. Berger, N.V. Proskurnina, B.N. Goschitskii, Defects in a lattice of pure nickel subjected to fast-neutron irradiation followed by annealings: Neutron-diffraction examination, Phys. Met. Metallogr. 117 (4) (2016) 348-354. https://doi.org/10.1134/S0031918X16040141 [21] D.I. Gray, W.V. Cummings, An X-Ray diffraction study of irradiated molybdenum, Acta Metallurgica. 8 (1960) 446-452. https://doi.org/10.1016/0001-6160(60)90031-6 [22] Sh.Sh. Ibragimov and A.G. Karmilov, Investigation of neutron radiation effects on iron properties, Fiz. Metal. i Metalloved. 16 (1963) 40-43. [23] B.C. Larson, High-precision measurements of lattice parameter changes in neutron-irradiated copper, J. App. Phys. 45 (2) (1974) 514-518. https://doi.org/10.1063/1.1663274 [24] G.S. Was, Fundamentals of Radiation Materials Science: Metals and Alloys, second ed., Springer, New York, 2017. 9
Figure caption Fig.1. Experimental (red circles) and calculated (blue envelope) X-ray pattern of annealed powder tablet Cu3Au. Lower green line is the difference between experiment and calculation, bars show positions of reflections. Fig.2. Full X-ray patterns for the sample Cu3Au in the nonirradiated state (a) and after irradiation with fast neutrons of fluence 6×1018 n/cm2 (b), 15×1018 n/cm2 (c), and 42×1018 n/cm2 (d). Fig. 3. Dependence of the LRO parameter S in Cu3Au on fluence of fast neutrons. Fig. 4. Dependence of the lattice parameter of Cu3Au on fluence of fast neutrons. Fig. 5. Dependence of Debay-Waller factor on fast-neutron fluence for Cu3Au. Fig. 6. Reflection (420) of the initial sample (lower line) and irradiated with fast-neutron fluence 42×1018 n/cm2 (upper line) For better visualization, intensities and angular positions are superimposed. Fig. 7. Change of ∆d/d with fast-neutron fluence. Fig. 8. Relative change in the lattice parameter of Cu3Au versus LRO-parameter S upon irradiation with fast neutrons (upper line) and upon thermal disordering in Cu3Au and Ni3Al [17, 19] (lower line). Fig. 9. Corrected dependences of structure (111) and (420) superstructure (110) reflections on fluence of fast-neutrons.
10
• • • •
Effects of fast-neutron irradiation on model alloy Cu3Au are studied. Unusual dependence of the lattice parameter on long-range order parameter is found. This behavior greatly differs from that upon thermal disordering. Results evidence development of competitive processes in evolution of defect system.
Declaration of interests
× The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
S0969-806X(19)31196-X
DOI:
https://doi.org/10.1016/j.radphyschem.2019.108654
Reference:
RPC 108654
To appear in:
Radiation Physics and Chemistry
Received Date: 11 September 2019 Revised Date:
25 November 2019
Accepted Date: 15 December 2019
Please cite this article as: Proskurnina, N.V., Bobrovskii, V.I., Goshchitskii, B.N., Volkov, A.Y., Voronin, V.I., Radiation induced disordering in Cu3Au, Radiation Physics and Chemistry (2020), doi: https:// doi.org/10.1016/j.radphyschem.2019.108654. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
CRediT author statement
N.V. Proskurnina: Resourses, Visualization, Writing - Review & Editing; V.I. Bobrovskii: Methodology, Writing - Original Draft; B.N. Goshchitskii: Conceptualization; A.Yu. Volkov: Resourses, Methodology; V.I. Voronin: Investigation, Formal analysis.
Radiation induced disordering in Cu3Au N.V. Proskurnina*, V.I. Bobrovskii, B.N. Goshchitskii, A.Yu. Volkov, V.I. Voronin M.N. Miheev Institute of Metal Physics of Ural Branch of Russian Academy of Sciences, 620108 Ekaterinburg, S.Kovalevskaya Str., Bld.18, Russia * Corresponding author: E-mail address: [email protected] (N.V. Proskurnina), tel.: +7 343-378-38-75 Abstract In the work, a specially prepared powder of the model ordered Cu3Au alloy was used to investigate peculiarities of internal processes that take place in the ordered precipitates similarly to those occurring in austenitic reactor steel under irradiation with fast neutrons. It is shown that, unlike the thermal or deformation disordering, in the case of such impact, the dependence of the lattice parameter on the degree of long-range order presents a kink that testifies to the development under irradiation of competitive processes in the defect structure of the studied material.
Keywords: reactor steels, radiation damages, anti-site defects, radiation induced processes, long range order parameter, X-ray diffraction.
1. Introduction Despite a long-term history and substantial bulk of data gained on the influence of radiation on the reactor steels, the mechanism and peculiarities of many structural changes that takes place under irradiation, especially, with varying temperature and dose, have not been fully ascertained so far. It is well known that under irradiation, along with changes in characteristics of the matrix structure, there can occur variations in composition of initial solid solution, radiation-induced atomic segregation, and formation and modification of the secondary-phase precipitates. In the case of ordered precipitates, there can be observed two processes: (1) disordering of ordered phase and (2) dissolution of precipitates via atomic mixing. However, commonly, models of evolution of such heterostructures take into account only composition, particle size, and the number of the phases precipitated. Yet, it is quite predictable that the internal radiation-induced modification of precipitates has to affect their structure and physical properties rather than solely mechanical properties of the system, which is evident. Investigation of these points in detail is hindered by a small volume of these phases. Several aspects of the behavior of precipitates and their impact on the material properties are given in [1-4]. In [1], it was shown that irradiation of the model alloy Fe62Ni35Ti3 triggers two processes: formation of radiation defects and precipitation of γ΄ phase Ni3Ti. Both the amount and size of precipitates grow with the fluence of fast neutrons thus affecting 1
the material properties. However, in this investigation, similarly to virtually all works of the kind, the state of lattice of the precipitates proper was not studied intently. In our study, we performed X-ray structure investigation of the influence of irradiation with fast neutrons in a wide range of fluences on the model ordered binary compound Cu3Au. The object chosen is structurally isomorphous to the γ΄-Ni3Ti phase and its properties in the state after irradiation with high-energy particles and fast neutrons have already been studied, yet in few details. Thus, [5-10] it is shown that electrical resistivity changes under the action of radiation mainly due to the lattice disordering. However, the data on the degree of order, which can be determined directly from the diffraction experiments on the irradiated Cu3Au samples, are lacking. Only in [11], via comparison of film X-ray diffraction patterns of the initial and irradiated Cu3Au samples was the effect of the alloy disordering under fast-neutron irradiation registered, no estimates of the degree of long-range order (LRO) being presented. Note also that when studying the effects of disordering in the compound Ni3Al, which is isostructural to Cu3Au, the main attention was paid to the LRO-parameter, i.e., anti-site defects [12-14]. The intemetallic Ni3Al differs from the compound Cu3Au in high resistance to disordering and efficient mechanism of reordering. Along with the disordering proper, we were interested in the behavior of other lattice characteristics of Cu3Au, specifically, under cascade-forming neutron irradiation. It should be noted that to obtain a sample of the Cu3Au alloy in the initial state with the maximal degree of ordering is rather a complicated problem. 2. Samples and Research Methods 2.1 Samples preparation The alloy investigated in this study contains 25 at% Au (50.85 wt%) leading to Cu3Au. The task of the first step of the sample fabrication was to gain elemental distribution as homogeneously as possible. The alloy was melted from copper 99.98% in purity and gold, 99.99%, in a vacuum of no less than 10-2 Pa by the method of double remelting with pouring in a graphite crucible. The main impurity in gold was platinum (<0.01%). The ingot 5mm in diameter was homogenized at a temperature of 750ºС for 3 h, cooled inside the furnace to 450°С, and quenched into water. X-ray analysis showed that the crystal structure of the material corresponded to the cubic phase Cu3Au, but the atomic distribution over the lattice sites was not ordered in full measure. At the second step, the samples were subjected to long-term annealing aiming at the formation of a highly ordered state. The heat treatment consisted in annealing of the samples at 450°С for 1h and subsequent stepped cooling by the following scheme: cooling to 350°С, holding for 24h, cooling to 300°С, and again holding for 24 h. Such stepped annealing with 24-h holdings was carried out to a temperature of 100°С and then, the sample was cooled inside the furnace to room temperature. The powder for investigation was manufactured from the bulk using a steel file with 2
shallow cutting teeth. The particle size was controlled by optical microscopy and did not exceed 0.5 mm. Moreover, the experimental X-ray pattern of the as prepared material accorded well with the calculated one, thus indicating the absence of effects caused by coarser grains. This powder was pressed into tablets 5mm in diameter and 3mm in height and subjected to additional annealing for ordering at the temperature 300°С with the subsequent cooling with a rate of 50°С per 24h. 2.2 Methods of measurements Crystal structure of the samples was studied by X-ray diffraction at a diffractometer UM-1М with a copper anode (CuKα, PG-monochromator) in the Bragg-Brentano geometry. Experimental X-ray patterns were taken in the angular range 20 – 145 degree with a step of 0.02. The samples were rotated in the vertical plane. Analysis of the experimental spectra was performed by the method of full-profile Rietveld analysis with the use of program package FullProf [15]. The profiles of reflections were fitted with the pseudo-Voigt function. The anisotropy of broadening of diffraction peaks was treated through the analytical procedures of the program Fullprof [15] using the reference function of the instrumental resolution, which was obtained in measuring specially designed reference powder samples of Na2Al2Ca3F12 and CeO2. Irradiation of the synthesized sample Cu3Au was performed in the vertical in-core wet channel of a 15 MW research reactor IVV-2M (Zarechny-city near Ekaterinburg, Russia. The unit is under operation of the Institute of Nuclear Materials. Also, the Neutron Material Science Complex of the Institute of Metal Physics is located on its premises). The density of the flow of fast neutrons with the energy En ≥ 0.1 MeV was equal to ∼2.23×1014 cm−2s-1. The temperature of irradiation corresponded to the temperature of reactor tank and equals about 353 K. The sample had been sequentially irradiated for three years with the fast-neutron fluence of (3, 10, 15, 22, 42) ×1018 n/cm2. After each act of irradiation and the necessary decay time, the sample was investigated by X-ray diffraction method.
3. Results Figure 1 presents X-ray diffraction pattern taken from the powder tablet Cu3Au prepared by heat treatments to subsequent neutron irradiation. The set of reflections corresponds to the ordered cubic phase Cu3Au (L12-type structure). The FullProf analysis showed that the form and width of the lines correspond to those of the reference, which means that internal stresses in the sample bulk are absent and the coherent scattering domain size exceeds 1000Å. Moreover, the probability of occupation of gold atomic positions by copper atoms, x, which is an indicator of deviation of the atomic distribution over the lattice from ideal, made up less than 4%. 3
In the ideal case, large gold atoms occupy corner sites of an ordinary crystal lattice, whereas copper atoms, face centers. With fully statistical atomic distribution over lattice sites, we evidently have the set of structural reflections in the diffraction pattern that corresponds to the face-centered lattice. A preferential occupation of certain positions by atoms of one sort gives rise to additional superstructure reflections. In such situation, the structural factors for the fundamental structure and additional superstructure reflections are written as follows: =<
> +3 <
=< respectively, where <
> −<
> and <
>; >;
(1) (2)
> are the average (with allowance for the occupancies)
amplitudes of X-ray scattering at gold and copper positions. It is important noting that if the stoichiometry of compound is preserved and its structure rearrangement is reduced to exchanging place by different atoms (so-called anti-site defects), the values of the structural factors
and, correspondingly, intensity of the fundamental structure
reflections must be constant. These rearrangements affect the value of
and intensity of
superstructure reflections. For quantitative estimation of the degree of ordering, a long-range order parameter (LROparameter) of Bragg-Williams is used, which for our compound Cu3Au can be written as follows: = where
( )
=1−
is the concentration of Au and
( )
,
( ) ( )
(3)
are the occupancy probabilities of Au position by
atoms of Au and Cu correspondingly. The degree of long-range order in the initial tablet made up 0.95. The X-ray diffraction patterns of the irradiated materials are shown in Figure 2. It is seen from Fig. 2 that with growing fluence, the intensity of structure reflections changes insignificantly, whereas that of superstructure reflections virtually vanishes at the maximal fluence of 42×1018 n/cm2. This result agrees with the conception on the disordering of the given alloy by the mechanism of formation of anti-site defects, i.e., through the exchanging places of different atoms, which is described by the LRO-parameter (3). In Fig. 3, the change in the LRO-parameter under irradiation, which was determined from the diffraction patterns given in Fig. 2 with the use of FullProf analysis and formula (3), is shown. One more impact of irradiation with growing fluence on the crystal lattice of the compound manifests itself in the displacement of reflections toward lower angles, which testifies to an increase in the lattice parameter. (Fig. 4). Also, as the analysis shows, changes in the intensity of fundamental structure reflections with fluence, which are more distinctly seen in large scattering angles, can be described via increasing the Debye-Waller factor (Fig. 5). At last, the full-profile analysis showed that under irradiation, not 4
only intensities and angular positions of the reflections change but their form and width as well. For example, reflection (420) is given in Fig. 6 for the initial (nonirradiated) sample and that irradiated with the fast-neutron fluence of 42×1018 n/cm2. As is seen, the irradiation results in both the broadening of the reflection and change in its form, which, judging by wings, becomes closer to Lorentzian. Such changes in the reflection form, according to the theory of X-ray and thermal neutron scattering [16], arise due to internal microstresses caused by the defects “of the second class”, according to the Krivoglaz classification (namely, dislocations, clusters of point defects, etc.). Based on this supposition and using the capacity of the FullProf program [15], we determined the dependence of microstrains in the Cu3Au lattice on the fluence of fast neutrons (Fig. 7). The internal microstresses are connected with them through the elastic modulus. 4. Discussion The above results indicate that the irradiation of the highly ordered compound Cu3Au with increasing fluence results in its radiation-induced disordering, the main mechanism of which is the formation of anti-site defects; at the maximal fluence 42×1018 n/cm2 the long-range order parameter falls to 0.1. At the same time, the lattice parameter and Debye-Waller factor grow and the form and width of reflections change. The latter points to the appearance in the crystal lattice of microstresses. In general, such a behavior is typical of materials undergone the action of fast neutrons or highenergy particles. Also, it is known that the destruction of long order in intermetallic compounds is as a rule accompanied by an increase in the lattice parameter. This phenomenon, which was discussed in, say, [17], apparently is conditioned mostly by the dependence of energy of ordering on the level of interatomic interactions rather than only on the geometrical mismatch of the atomic size in the compounds. This conclusion is supported by the results of investigation of correlation of the lattice parameter with changes in the long-range order in Ni3Al (which possesses the same crystal lattice as Cu3Au) [18]. It was shown that for Ni3Al, the lattice parameter changes linearly with S in all the range 0≤S≤1, which agrees with changes in the length of “unlike” interatomic bonds. To compare the results, we constructed the dependence of the lattice parameter of the alloy Cu3Au on the degree of long-range order for our irradiated samples, as well as for the samples of Cu3Au and Ni3Al described in [17, 19] where disordering was produced by heat treatments (Fig. 8). The dependence of ∆ / on LRO-parameter S in Fig. 8 demonstrates a more complicated course. At low fluences (to 10×1018 n/cm2), the lattice parameter grows with S much faster than upon thermal disordering. It is known that irradiation of metals and alloys results in the formation of primary defects, which are interstitial atoms and vacancies (Frenkel defects). It is considered that in metals in the 5
state of thermal equilibrium, interstitial atoms go toward the crystal boundaries, thus creating new unit cells, vacancies being retained inside the bulk (Schottky defects). However, it should be taken into account that under cascade-generating irradiation with fast neutrons, in the material there are formed point defects in much higher concentrations than upon thermal actions. After withdrawing from the irradiation channel, the material retains residual defect structure, being in a thermodynamically nonequilibrium state [120-23]. The highly ordered alloy Cu3Au is peculiar in that the formation of vacancies and interstitials proceeds at the background of disordering of the initial crystal lattice upon which there are created anti-site defects, i.e., atoms of Cu and Au exchange places. In this case, the total change of ∆ / is the sum of contributions made by anti-site defects proper and interstitials and vacancies. !" "
# = $
!" "
#
%&
!"
+
"
#
(4)
However, as the conditions of formation of interstitials and vacancies obviously depend on the distribution of atoms of Cu and Au over lattice sites, the first term in the right part of (4) also depends on LRO degree. In Fig. 8, the lower line describes the behavior of a system with anti-site defects and vacancies in concentrations that are preserved after quenching from the temperature at which the thermal disordering of the lattice was carried out. Apparently, the main contribution to it is made by anti-site defects. When interpreting the behavior of the upper line, it should be taken into consideration that it refers to a post-radiation thermodynamically nonequilibrium structure in which not only single vacancies and interstitials were formed by radiation but, in the process of their evolution, their clusters and dislocations as well [24]. Such coarse formations can create microstresses in the crystal lattice, and, what is more, serve as sinks for point defects, thus affecting the concentration of the latter in the system. It is seen from Fig. 8, that at comparatively low irradiation doses, one can see in the vicinity of ≈ 1 a quick accumulation of defects with increasing dose, which provides their high postirradiation concentrations in comparison with the lower curve. The positive sign of the ∆ / value evidences the preservation of rather a high concentration of the interstitials (most probably in the form of dumbbells typical of the fcc-lattices [24]), which are responsible for the considerable positive lattice relaxation. The course of the upper line in Fig. 8 evidences that after reaching a certain value of S (and corresponding fluence of fast neutrons), competitive processes start developing in the system, which 6
efficiently compensate for the influence of vacancies and interstitials. As a result, the further course of the upper line is controlled by anti-site defects solely. Increasing the Debye-Waller factor upon irradiation is another manifestation of the behavior of defects (Fig.5). Its value is controlled by the mean-square amplitudes of atomic displacements from the equilibrium positions, which are contributed to by both thermal atomic oscillations and uncorrelated statistical displacements which arise due to microstresses created by defects. At the initial stage of irradiation, when the concentration of defects (anti-site, vacancies, and interstitials) is small and their distribution over the bulk is homogeneous, the value of the Debye-Waller factor virtually does not change, which is the consequence of thermal oscillations. However, with growing fluence, coarse clusters of interstitial atoms and vacancies, as well as dislocations, start forming and generate lattice microsresses [16], thus giving rise to the Debye-Waller factor at fluences higher than 10×1018 n/cm2 (Fig.6). Such microstresses lead to the lattice microstrains, which manifests itself in the reflection broadening in the X-ray patterns (Figs. 6, 7). It is worth paying attention to the changes in the intensity of structure and superstructure reflections depending on fluence. To discard the influence of effects described by Fig. 5, corrections that exclude the influence of the Debye-Waller factor are applied to the intensities of superstructure reflection (110) and structure reflections (111) and (420), shown in Fig. 9. It is seen that the intensity of superstructure reflection (110), which depends on the degree of long-range order, virtually vanishes, testifying to the atomic disordering, as shown above. At the same time, the intensities of structure reflections, independent of the degree of long-range order, remain constant up to the fluence 10×1018 n/cm2 and then start decreasing, though much slower than that of the superstructure one. Such a decrease can be explained by the absence of contributions to reflections from part of material. The plausible cause for this is the formation at this stage of the abovementioned atomic clusters with another structural type than Cu3Au. 5. Conclusions The experimental data obtained testify to the development of competitive processes in the defect structure of the material under study upon its irradiation with fast neutrons. For the first time, direct structure investigations by the method of X-ay diffraction are employed to trace the changes in the degree of long-range order, characterized by LRO-parameter, upon irradiation of the ordered compound Cu3Au with fast neutrons. It is shown that unlike the thermal or deformation disordering, in the dependence of the lattice parameter on the fluence there is a kink related to the radiation defects. At high fluences, along with the anti-site disordering, there arise defect clusters that give rise to the emergence of internal microstresses. Thus, radiation defects result in a more significant growth of the lattice parameter than solely anti-site disordering does. Using these data, we can 7
better understand the processes that take place in reactor materials, including evolution of defect structure. Acknowledgments The research was carried out at IMP Neutron Material Science Complex within the state assignment of Minobrnauki of Russia (theme “Flux”, No АААА-А18-118020190112-8), supported in part by RFBR (project No. 18-02-00270). References [1] V.I. Voronin, I.F. Berger, B.N. Goshchitskii, Structural changes in a model alloy after irradiation of Fe62Ni35Ti3 with fast neutrons and isochronous temperature annealing, Phys. Met. Metallogr., 113 (9) (2012) 878-882. https://doi.org/10.1134/S0031918X12090141 [2] V.V. Chuyev, V.F. Rosljakov, V.V. Maltsev, Features of Constructional Materials' Behavior within Fast High-Power Reactor's Spectrum of Neutrons, Izvestiya Vysshikh Uchebnykh Zavedeniy: Yadernaya energetika, 1 (2005) 113-126. ISSN 0204-3327 [3] P.L. Mosbrucker, D.W. Brown, O. Anderoglu, L. Balogh, S.A. Maloy, T.A. Sisneros, A.C. Dippel, Neutron and X-ray diffraction analysis of the effect of irradiation dose and temperature on microstructure of irradiated HT-9 steel, J. Nucl. Mater. 443 (2013) 522-530. https://doi.org/10.1016/j.jnucmat.2013.07.065 [4] L. Balogh, D.W. Brown, P. Mosbrucker, F. Long, M.R. Daymond, Dislocation structure evolution induced by irradiation and plastic deformation in the Zr–2.5 Nb nuclear structural material determined by neutron diffraction line profile analysis, Acta Mater. 60 (15) (2012) 55675577. https://doi.org/10.1016/j.actamat.2012.06.062 [5] J. S. Huang, M. W. Guinan, F. A. Hahn, Irradiation disordering and ordering of Cu3Au by fusion neutrons, J. Nucl. Mater, 141-143 (1986) 888-892. https://doi.org/10.1016/00223115(86)90112-1 [6] H. L. Click, F. C. Brooks, W. F. Witzig, and W. E. Johnson, The resistivity of Cu3Au during neutron irradiation, Phys. Rev. 87 (6) (1952) 1074. https://doi.org/10.1103/PhysRev.87.1074 [7] S. Siegel, Effect of neutron bombardment on order in the alloy Cu3Au, Phys. Rev. 75 (12) (1949) 1823-1824. https://doi.org/10.1103/PhysRev.75.1823 [8] A Dunlop, D Lesueur, N Lorenzelli, A Audouard, C Dimitrov, J M Ramillon and L Thome, Search for damage and/or disordering effects due to intense electronic excitation in crystalline metallic alloys irradiated by high-energy heavy ions, J. Phys.: Condens. Matter. 2 (7) (1990) 17331741. [9] L. C. Wei, E. Lang, C. P. Flynn, and R. S. Averback, Freely migrating defects in ion-irradiated Cu3Au, Appl. Phys. Lett. 75 (1999) 805. https://doi.org/10.1063/1.124519
8
[10] L. Wei, Y. S. Lee, R. S. Averback, and C. P. Flynn, Antistructure and Point Defect Response in the Recovery of Ion-Irradiated Cu3Au, Phys. Rev. Lett. 84 (26) (2000) 6046-6049. https://doi.org/10.1103/PhysRevLett.84.6046 [11] L.G. Cook and R.L. Cushing, The effects of neutron irradiation in the NRX reactor on the order-disorder alloy Cu3Au, Acta metallurgica. 1 (1953) 539-548. https://doi.org/10.1016/00016160(53)90084-4. [12] H.C.Liu, T.E.Mitchell, Irradiation induced order-disorder in Ni3Al and NiAl, Acta Metall. 31 (6) (1983) 863-872. https://doi.org/10.1016/0001-6160(83)90114-1. [13] S. Muller, C. Abromeit, S. Matsumura, N. Wanderka, H. Wollenberger. Disordering kinetics of Ni3Al under ion irradiation, J. Nucl. Mater. 271-272 (1999) 241-245. https://doi.org/10.1016/S0022-3115(98)00711-9. [14] C. Abromeit, S. Miiller and N. Wanderka, Stability of γ΄ phase in the stoichiometric Ni3Al alloy under ion irradiation, Scr. Metall. et Mater. 32 (10) (1995) 1519-1523. [15] J. Rodriguez-Carvajal, Recent advances in magnetic structure determination by neutron powder diffraction, Physica B. 192 (1993) 55-69. https://doi.org/10.1016/0921-4526(93)90108-I [16] M.A. Krivoglaz, X-ray and neutron diffraction in nonideal crystals, Springer Verlag Publ, Berlin, Heidelberg, 1996, pp. 466. [17] R. W. Cahn, Lattice parameter changes on disordering intermetallics, Intermetallics, 7 (1999) 1089-1094. https://doi.org/10.1016/S0966-9795(99)00035-7 [18] S. Gialanella, R.W. Cahn, J. MalageladaJ, S. Suriñach, M.D. Baró, A.R. Yavari, in: H. Chen and V.K. Vasudevan (Eds), Kinetics of ordering transformations in metals, Warrendale, PA: TMS, 1992, pp. 161. [19] M.L. Bhatia, R.W. Cahn, Lattice parameter and volume changes on disordering, Intermetallics. 13 (2005) 474–483. https://doi.org/10.1016/S0966-9795(99)00035-7 [20] V.I. Voronin, I.F. Berger, N.V. Proskurnina, B.N. Goschitskii, Defects in a lattice of pure nickel subjected to fast-neutron irradiation followed by annealings: Neutron-diffraction examination, Phys. Met. Metallogr. 117 (4) (2016) 348-354. https://doi.org/10.1134/S0031918X16040141 [21] D.I. Gray, W.V. Cummings, An X-Ray diffraction study of irradiated molybdenum, Acta Metallurgica. 8 (1960) 446-452. https://doi.org/10.1016/0001-6160(60)90031-6 [22] Sh.Sh. Ibragimov and A.G. Karmilov, Investigation of neutron radiation effects on iron properties, Fiz. Metal. i Metalloved. 16 (1963) 40-43. [23] B.C. Larson, High-precision measurements of lattice parameter changes in neutron-irradiated copper, J. App. Phys. 45 (2) (1974) 514-518. https://doi.org/10.1063/1.1663274 [24] G.S. Was, Fundamentals of Radiation Materials Science: Metals and Alloys, second ed., Springer, New York, 2017. 9
Figure caption Fig.1. Experimental (red circles) and calculated (blue envelope) X-ray pattern of annealed powder tablet Cu3Au. Lower green line is the difference between experiment and calculation, bars show positions of reflections. Fig.2. Full X-ray patterns for the sample Cu3Au in the nonirradiated state (a) and after irradiation with fast neutrons of fluence 6×1018 n/cm2 (b), 15×1018 n/cm2 (c), and 42×1018 n/cm2 (d). Fig. 3. Dependence of the LRO parameter S in Cu3Au on fluence of fast neutrons. Fig. 4. Dependence of the lattice parameter of Cu3Au on fluence of fast neutrons. Fig. 5. Dependence of Debay-Waller factor on fast-neutron fluence for Cu3Au. Fig. 6. Reflection (420) of the initial sample (lower line) and irradiated with fast-neutron fluence 42×1018 n/cm2 (upper line) For better visualization, intensities and angular positions are superimposed. Fig. 7. Change of ∆d/d with fast-neutron fluence. Fig. 8. Relative change in the lattice parameter of Cu3Au versus LRO-parameter S upon irradiation with fast neutrons (upper line) and upon thermal disordering in Cu3Au and Ni3Al [17, 19] (lower line). Fig. 9. Corrected dependences of structure (111) and (420) superstructure (110) reflections on fluence of fast-neutrons.
10
• • • •
Effects of fast-neutron irradiation on model alloy Cu3Au are studied. Unusual dependence of the lattice parameter on long-range order parameter is found. This behavior greatly differs from that upon thermal disordering. Results evidence development of competitive processes in evolution of defect system.
Declaration of interests
× The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: