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This book covers the Resistivity Recovery (RR) technique, underlying its physical principles, performance and problematic. A concise review on the state of the art is provided, showing the advances in radiation modelling, linking both experimental and theoretical fields. The reader will find a data compilation and comparison of up-to-date results obtained from the European Fusion Development Agreement model alloys.



Chapter 1. Thermonuclear Fusion

The motivation of this work arises from the need of developing new technologies in order to build the future nuclear fusion reactors . Section 1.1 is devoted to provide an overview of fusion energy, showing the interest of its development and the key problems that need to be overcome for this purpose. Section 1.2 introduces specifically the problematic of radiation damage in the constituent materials of fusion reactors. Next, Sect. 1.3 explains the strong commitment of fusion research community in the development of modelling and experimental validation approach, as a useful tool for radiation resistant materials development in the medium term. Finally, Sect. 1.4 introduces the specific interest and problematic of structural materials which can be modelled to a first approximation as binary FeCrx alloys and which are the object of study of this work.
Begoña Gómez-Ferrer

Chapter 2. Resistivity and Experimental Techniques

As stated by Dulca in his doctoral thesis [1], understanding the electrical resistivity of concentrated metallic alloys is a discouraging task, because of the large number of contributions that may be involved. The electrical resistivity is a physical property that depends on the density of states at the Fermi level. Its value is composed of many contributions such as phonon interaction, concentrations of defects, atomic arrangements, or magnetic interactions . Understanding how such contributions influence the resistivity is the key to be able to design and perform experiments based on resistivity techniques. The presence of solutes is going to change the resistivity values of pure metals by means of the so-called short-range order (SRO) effects and also by its magnetic contribution to the magnetic spin populations of conducting electrons (explained by the two-current model). In this book, the research is focused on the Fe–Cr concentrated model alloys; thus, it is important to be able to evaluate how addition of Cr to Fe and the presence of defects is going to influence the residual resistivity values of the materials under study, in order to interpret the RR results and also to make appropriate comparisons with the more extensively studied pure and impure Fe. Sections 2.1 and 2.2 are devoted to this purpose. Some of the concepts described in Sect. 2.1 will be especially helpful for understanding the literature on modeling, RR, and quenching experiments. Additionally, in Sect. 2.3, it is clearly explained the origin of evolution of defects as the sample temperature is increased and the processes that such simple defects can undergo as the annealing goes. The fundamentals of the RR experiments are described in Sect. 2.4. And finally, based on the predicted SRO residual resistivity changes in the presence of migrating defects, there is a detailed explanation on the new RR method that has been developed and tested along the development of this work in Sect. 2.5. The new method proposed allows making RR experiments erasing the SRO contribution.
Begoña Gómez-Ferrer

Chapter 3. Experimental on Resistivity

The present chapter encloses the primary objective of this research work, at which most of the invested time and efforts have been devoted; this is the design and development of an experimental system to perform in situ RR experiments at the end of one of the beam lines of a Tandetron ion-irradiation facility. Such task requires the acquisition, design and assembling of every component of the setup and the acquisition system, testing of sensors and probes (sensibility and performance), developing of data acquisition program, and optimizing the measurement methodology as well as the data warehousing and treatment. Additionally, a specific method for the specimen preparation and assembly in the developed setup had to be invented. The experimental technique has turned out to be very exigent from a technical point of view as it will be explained along the chapter. As explained in Chap. 2, a classical RR experiment consists of monitoring the residual resistivity of a metallic sample after irradiation at low temperature. It is measured at cryogenic temperature, typically 4.2−30 K, in order to eliminate the electron–phonon contribution to the resistivity and get a resistivity value dependent on point defects and “ordering” of the sample lattice. The low-temperature irradiation is going to create defects in the sample lattice which would increase its residual resistivity. This phenomenon is called RIR and has been described above. A step-like thermal annealing subsequent to irradiation will typically lead to a recovery of non-irradiated residual resistivity values providing the RR curves. The derivative of such curve provides indirect information on the migration processes that created defects perform. Hence, information related to damage creation, recombination, and clustering of defects , both vacancies and interstitials, can be obtained by performing this type of experiments. This section provides a detailed explanation of the experimental techniques and methods used for the resistivity measurements, as the choice of the appropriate probe configuration and measurement methodology is non-straightforward in the case of metallic samples with very low values of electrical resistance. The four-point probe technique in the particular configuration of van der Pauw (VdP) [1] has been chosen to prepare the sample (Sect. 3.1), and the delta method has been used for clean measurement of low voltages by removing the thermoelectric voltage contributions (Sect. 3.2). Beyond these basic concepts, the Sect. 3.3 outlines the requirements and difficulties for undertaking the RR measurements on samples irradiated at cryogenic temperature. The details concerning the sample preparation method, designed in order to fulfill the experimental requirements, is given in Sect. 3.4. An explanation of experimental details and highlight of the technological difficulties needed to be overcome in such experiments are also presented as this discussion is interesting in order to understand the reliability and comparability among results from different authors. In particular, in Sect. 3.5, the design of the sample holder which assembles all the systems for resistivity measurements, heating and temperature monitoring is carefully described as it is a fundamental piece to guarantee the success of the RR measurements. Finally, in Sect. 3.6, an effort has been made to provide good explanation of the measurement details and procedure and to treat the whole uncertainties of a resistivity measurement in a clear and sincere way because in literature this issue is normally omitted. For readers interested in developing their own RR experimental setup, I also recommend, as complementary sources of information, to read the reference literature from former works [28].
Begoña Gómez-Ferrer

Chapter 4. State of the Art

As a starting point in this chapter, there is the fact that the picture which is being established to explain the defect kinetics in Fe–Cr concentrated alloys is based on the model accepted for pure Fe, where agreement has been found between RR and PA validation experiments [1, 2] and combination of ab initio and kMC simulation codes [3]. Although this is a starting point, differences clearly appear when Cr is introduced in the iron lattice. Complementary studies, both experimental [4] and theoretical [5], have been made evaluating the initial distribution of the damage in pure Fe defect kinetics, revealing new stages. Concurrently the theoretical and experimental study on the effects on adding Cr impurities to pure Fe have helped to reveal new migration energy values, and interaction processes between defects [68]. It has also been revealed that the presence of other impurities produce strong modifications of the RR curves by interaction of impurities with defects [911]. All these studies have contributed to build the Fe–Cr picture. In addition, few isolated experimental works have been performed on concentrated Fe–Cr alloys [1215]. Scale limitations of computational codes make not possible up to date to simulate high damaged concentrated alloys. Nevertheless good approaches are being achieved [16]. It is important to notice that, in general, published RR results usually appear represented at different scales and the experimental conditions are different as well. Thus direct visual comparisons between authors are barely impossible. A great work on digitalization and choice of most comparable RR results published along the past 30 years of previously published results has been made in this chapter. The scales have been normalized to the one presented in our results, and purest materials with similar RIRs have been selected for different irradiation probes. A critical review of the state of the art is made here, a work which it is worth mentioning, has not been done before. The structure of this chapter is as follows: The first part (Sect. 4.1) is a revision of results for pure iron, followed by a critical discussion of the existing interpretations/models (Sect. 4.2), next the equivalent information but for Fe–Cr alloys (Sect. 4.3) and finally the contribution of computational simulations is explained (Sect. 4.4).
Begoña Gómez-Ferrer

Chapter 5. RR in Fe and FeCr Alloys

The objective of the present work was to provide complete and high-temperature resolution RR curves on samples with Cr contents of 5, 10, and 15 %, respectively, with a well-controlled composition and microstructure and improvement with respect to the data provided by Benkaddour et al. [1]. In this case, the irradiations have been performed with protons instead that with electrons, and thus, the type of created damage must be evaluated. Also as a consequence of the considerations which have been made in Chap. 2 concerning the SRO and its effects enhanced by defect migration, an improved methodology to measure RR—which has been described in Sect. 2.​5—has been performed on Fe–Cr alloys in order to check the importance of such effects on the RR experiments. As a consequence from the connection between the interpretations of the results in each section with the next one, here both the results and the discussion are presented in one common chapter. This chapter is divided into five main sections. Sect. 5.1 of this chapter is devoted to the characterization of the residual resistivity of studied Fe–Cr alloys and the evaluation of the effects of Cr addition to pure Fe in terms of residual resistivity . Next, the damage produced by electrons, neutrons , and protons is discussed in Sect. 5.2. Also, a detailed study made based on modeling tools of our 5 MeV proton irradiations is presented. The third part, Sect. 5.3, provides a description of specimen characteristics and irradiation runs, the experimental measurements of resistivity values of studied specimens along low-T Irr. This section includes the analysis of effects of irradiation as a function of CCr. Sect. 5.4 includes RR curve and RR spectrum from a proton-irradiated pure Fe specimen. Their analysis is very useful given that it allows comparisons with many experimental results found in the literature and that has been described and critically reviewed in Sect. 4.​2 and help to identify the temperature intervals at which the processes should be occurring in proton-irradiated samples. Finally, the fifth part, 5.5, is the most important, where RR results of concentrated Fe–Cr alloys will be provided and discussed. An initial analysis on the results obtained under the classical RR method put in evidence the important SRO effects. Then, RR results obtained with the proposed improved RR method, its discussion, and some complementary Mössbauer measurements are given.
Begoña Gómez-Ferrer

Chapter 6. Outlook

Begoña Gómez-Ferrer


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