Free volumes in bulk nanocrystalline metals studied by the complementary techniques of positron annihilation and dilatometry.

Free-volume type defects, such as vacancies, vacancy-agglomerates, dislocations, and grain boundaries represent a key parameter in the properties of ultrafine-grained and nanocrystalline materials. Such free-volume type defects are introduced in high excess concentration during the processes of structural refinement by severe plastic deformation. The direct method of time-differential dilatometry is applied in the present work to determine the total amount and the kinetics of free volume by measuring the irreversible length change upon annealing of bulk nanocrystalline metals (Fe, Cu, Ni) prepared by high-pressure torsion (HPT). In the case of HPT-deformed Ni and Cu, distinct substages of the length change upon linear heating occur due to the loss of grain boundaries in the wake of crystallite growth. The data on dilatometric length change can be directly related to the fast annealing of free-volume type defects studied by in situ Doppler broadening measurements performed at the high-intensity positron beam of the FRM II (Garching, Munich, Germany).

Introduction

Severe plastic deformation (SPD) of metals by high-pressure torsion (HPT) or equal channel angular processing (ECAP) is currently seen as the most prospective processing route for the synthesis of nanocrystalline bulk metals [1-3]. The attractive mechanical properties such as high strength in combination with good ductility which are associated with the pore-free ultrafine grained structure of SPD-processed metals have been subject of comprehensive research. However, the understanding of the underlying atomic processes is still rudimentary. This is particularly true with respect to atomic-sized free volumes in these structurally complex materials including lattice vacancies and their agglomerates in the crystallites or structural free volumes associated with grain boundaries. Free volume-type defects are supposed to play a major role both for the atomic processes occurring during severe plastic deformation and the improved mechanical properties of SPD-processed nanocrystalline metals.

There are number of indications that severe plastic deformation produces lattice vacancies in high excess concentrations. This is for instance derived from comprehensive characterization of the defect structure of SPD processed pure metals and alloys using X-ray diffraction (XRD), transmission electron microscopy (TEM), electrical resistivity and as well as differential scanning calorimetry (DSC) performed by Zehetbauer and coworkers [4-6]. In the case of pure copper the results of the different analysis methods are only consistent if an excess concentration of point defects, i.e., vacancies, significantly higher than the equilibrium concentration at room temperature, is assumed. These remnant point defects should have been produced during the SPD process. A similar conclusion was derived for a SPD processed Mg(Al) alloy from the observation of an irreversible exothermic reaction in the temperature range between 370 and 450 K where no change of the microstructure according to TEM occurred [7].

Indication for lattice vacancies or interfacial excess free volume is also concluded from enhanced diffusivities in SPD-prepared metals. Sauvage et al. reported the dissolution of Fe clusters in Cu during SPD processing as detected by XRD, TEM, and 3-dimensional atom probe [8,9]. According to the authors the enhanced solubility of up to 20 at.% Fe in Cu at the low SPD processing temperatures can only be accounted for if a high vacancy concentration is assumed which enables long range diffusion for complete intermixing. Another indication for enhanced diffusivity during structural transformation was reported by Mazilkin et al. [10] for SPD-processed supersaturated Al(Zn) and Al(Mg) alloys.

In addition to these indirect indications for enhanced diffusivities during the dynamic deformation conditions, there is a direct evidence for enhanced diffusivities in these metals after SPD-processing from a number of tracer diffusion studies [11-14] (for review see Refs. [15,16]). This enhanced diffusivity indicates a non-equilibrium structure of grain boundaries in SPD-prepared metals. After structural relaxation at slightly elevated temperature the diffusivities decrease towards values typical of conventional grain boundaries [11,15,17]. This situation resembles the well-known structural relaxation in amorphous alloys, where annealing out of excess volumes gives rise to a decrease of the diffusivity (see Ref. [15] and references therein). The reported enhanced diffusivities are strong indications for high concentrations of lattice vacancies and/or excess volumes in non-equilibrated grain boundaries. In view of these results, studies of free volumes in SPD-processed metals by direct specific techniques are highly desirable.

Moreover, the ultrafine grain size of SPD-prepared metals makes this class of material also highly attractive with respect to fundamental issues of excess free volume of structurally relaxed, equilibrium-type grain boundaries. Due to the high number of grain boundaries, their excess free volume may become much better accessible for experimental studies compared to coarse grained metals. The amount of excess volume of the grain boundary is the most fundamental parameter as it is also directly related to the grain boundary energy [18]. It also significantly influences structural phenomena such as grain boundary diffusion and segregation [19] or physical phenomena such as the contribution of the grain boundary to the electrical resistance [18].

The present invited paper gives an overview on our recent studies of free volumes in bulk nanocrystalline metals by the complementary and specific techniques of positron annihilation and dilatometry. Whereas positron annihilation in the meantime has become a standard technique for the study free volumes in nanocrystalline metals, dilatometry has only recently been applied for the time to study the absolute concentration of free volumes in bulk nanocrystalline metals [20]. Time-dependent dilatometry [21,22] supplements the positron annihilation techniques in an ideal manner, since it expands the range of accessible defect concentration and, in particular, enables the study of the kinetics of free volumes and vacancies.

Positron annihilation studies have contributed to the field of nanocrystalline materials since the pioneering era [23] and have been systematically applied to probe specifically the size of structural free volumes in a variety of nanocrystalline metals prepared by different synthesis routes such as cluster-condensation and compaction, ball-milling, or crystallization of amorphous alloys (for review see Ref. [24]). A number of positron annihilation studies of free volumes in SPD-prepared nanostructured metals are available. In addition to the initial measurement of one of the authors in collaboration with Valiev [25], more recent studies by Van Petegem et al. [26], Krause-Rehberg et al. [27], and Cizek et al. [28-30] have to be mentioned. Recently, positron annihilation studies were also applied on SPD-prepared alloys [31,32].

In the present work, positron annihilation on bulk nanocrystalline metals was extended for the first time on fast defect annealing kinetics by making use of the high-intensity positron beam at the positron source NEPOMUC of the Heinz-Meier Leibnitz Neutron Source (FRM II Munich, Garching, Germany) [33]. In order to gain insight into the rather complex free volume defect pattern of this type of materials, positron annihilation was combined with the complementary technique of dilatometry. As model systems for the present studies pure metals (Ni, Cu, and Fe) were used which were already characterized in detail with respect to severe plastic deformation.

Results and discussion

Dilatometry

Time-dependent differential dilatometry was used in the present work to study the absolute concentration of free volumes in bulk nanocrystalline metals prepared by high-pressure torsion. This novel type of measurement became feasible since HPT-samples can now prepared in sufficiently large dimensions [34]. With the apparatus installed at the Erich Schmid Institute of Materials Science in Leoben, Austria, high-purity metal discs with a diameter of 30 mm and a height of 10 mm could be deformed in torsion (five revolutions) applying a pressure of 2.2 GPa. From these deformed discs samples for dilatometry with dimensions of were cut at a distance from the center large enough to avoid structural inhomogeneities.

The principle of differential dilatometry is schematically shown in Fig. 1. The irreversible length change upon the thermally induced release of free volume-type defects is determined by simultaneous dilatometric measurement of the length change of the HPT-deformed sample and an undeformed well-annealed reference sample of the same material. The difference in the length change between the two samples opening up during heating is due to the irreversible shrinkage of the HPT-deformed sample which is superimposed to the linear thermal expansion . The measurements were performed by a high-precision vertical difference dilatometer (Linseis L75VD500LT; for experimental details see Ref. [20]).

Fig. 1

Principle of differential dilatometry (schematically). The difference of the length change between the HPT-deformed sample (shaded) and an undeformed reference sample upon linear heating is due to the irreversible annealing out of deformation-induced free volumes. The irreversible contribution is superimposed to the reversible linear thermal length expansion .

Fig. 2 shows an example of the irreversible relative length changes measured on HPT-deformed Fe (a), Ni (b), and Cu (c) upon linear heating with a rate of 3 K/min. In the case of HPT-deformed Fe, one broad annealing stage above about 400 K occurs (Fig. 2a). Assuming isotropic distribution and annealing of free volumes, a total volume change can be determined from the total irreversible length change measured on three HPT-Fe samples with different heating rates. As discussed in more detail elsewhere [20], this volume change considerably exceeds the volume change as expected from the loss of relaxed grain boundaries and dislocations upon annealing-induced crystallite growth. The high volume change therefore indicates a high amount of excess free volumes either present as vacancy-type defects and vacancy agglomerates within the crystallites or as excess free volume of unrelaxed grain boundaries. A more detailed conclusion in the case of Fe is, however, hampered by the fact that the annealing of the different types of free volumes occurs in one single broad stage.

Fig. 2

Relative length change of HPT-deformed (a) Fe, (b) Ni, and (c) Cu upon linear heating with a rate of 3 K/min.

The situation is much more favorable in the case of HPT-Ni and Cu where distinct substages upon heating can be discerned (Fig. 2b and c). Both HPT-Ni and Cu show a distinct narrow stage centered at ca. 473 K (Ni) or 410 K (Cu). This stage is due to the loss of grain boundaries in the wake of crystallite growth which occurs in this temperature regime according to scanning electron microscopy (for Ni see Fig. 3b and c). It is reasonable to assume that prior to the onset of crystallite growth at the elevated temperatures, any relaxation of grain boundaries already has finished, so that the length change during crystallite growth exclusively characterizes free volumes in relaxed, equilibrium-type grain boundaries. This opens up the possibility to determine the absolute value of the excess free volume of grain boundaries by means of dilatometry (see Ref. [35]).

Fig. 3

Micrographs obtained from scanning electron microscopy (SEM) revealing the microstructure of pure HPT-deformed Ni in different states. Top (a): in the as-prepared state at 293 K. Centre (b): after heating with 3 K/min upto 453 K and quenching. Bottom (c): after 3 K/min heating to 493 K and quenching (cf. Fig. 2b).

From the shift of the distinct stage with heating rate the kinetics of the crystallite growth process can be determined. Applying a Kissinger-type analysis or adapting the Johnson–Mehl–Avrami–Kolmogorov theory to linear heating, an activation energy Q of can be deduced for crystallite growth in HPT-Ni [36]. For HPT-Cu an activation energy Q of is obtained from the Kissinger-type analysis of the shift of the stage with heating rate (Fig. 4). The difference of the activation energies between Ni and Cu scales with the difference of their melting points. This is also reflected by the shift of the stage in Ni towards higher temperatures compared to Cu (Fig. 2b and c). The value of 1.02 eV for Cu is also in good agreement with the activation energy deduced from X-ray diffraction and transmission electron microscopy for HPT-deformed Cu [28].

Fig. 4

Kissinger analysis of the temperatures T of the maximum rate of length change of HPT-deformed Cu upon linear heating with the rates .

Prior to the onset of the distinct annealing substage, the initial crystallite size of HPT-Ni of about 260 nm does not change significantly (compare Fig. 3a and b). Therefore, the relative length change , which occurs up to ca. 470 K prior to the distinct substage, has to be attributed to a reduction of the density of free dislocations, to the annealing out of lattice vacancies, as well as to the structural relaxation of grain boundaries. From electron irradiation experiments on pure Ni it is well established that Ni vacancies become mobile at temperatures around 360 K [37]. The finding that by annealing HPT deformed Ni samples up to 470 K besides vacancies also the number of dislocations is drastically decreased is, e.g., supported by results from transmission electron microscopy and X-ray diffraction of other studies [38,39]. Indication of structural relaxation of grain boundaries in nanocrystalline metals upon annealing at slightly elevated temperature, on the other hand, is also deduced from tracer diffusion studies [15,17].

Positron annihilation

The complex defect structure of nanostructured metals after processing by severe plastic deformation (SPD) can also specifically be analyzed by applying positron–electron annihilation techniques. Atomic defects, such as vacancies, dislocations and grain boundaries, are preferable trapping sites of positrons with specific trapping rates. Analysis of such localized positron–electron annihilation events in combination with the defect kinetics, i.e., variation of their concentration with time and temperature will be reported next. The approach is quite powerful if performed in situ and especially, here, if combined with the complementary technique of dilatometry.

For the specimen state directly after SPD processing, in the as-prepared state, defect concentrations are exceptionally high and all positrons injected into the solid get trapped at defects, i.e., are in a localized state. It is manifested by the results of positron lifetime measurements showing positron lifetimes, e.g., and for Cu and Ni, respectively, which substantially exceed the free positron lifetime and which are typical for vacancy-type defects. In this case of positron saturation trapping analysis of changes in the Doppler broadening of the annihilation line is most suitable compared to positron-lifetime analysis. In the following the so-called S-parameter was used that is an integral line parameter representing the positron annihilation events with valence electrons. Compared to a delocalized annihilation event as, e.g., prevalent under defect-free conditions, the S-parameter is significantly enhanced for solids with high defect concentrations.

For a successful combination of the positron annihilation technique with dilatometry the monitoring of processes which occur in a time domain of minutes requires a high intensity of positrons. In the following, the first fast in situ measurements of defect annealing are presented for SPD processed Fe, Cu and Ni employing the high-intensity positron beam at the Heinz-Meier Leibnitz Neutron Source (FRM II Munich, Garching, Germany) [33]. Details of the Cu and Ni results can be found in Ref. [40]. The data of the S-parameter measurement are shown in Fig. 5 where the S-parameter data (left ordinate) are drawn superimposed to the dilatometry data (right ordinate) for Fe, Cu and Ni. Temperature programs identical to the ones for dilatometry were applied on equivalent specimens. In the case of Fe, an improved heating of the specimen stage was used which allowed for much higher temperatures than for the initial measurements on Cu and Ni [40]. Therefore, in the case of Fe, after the first measurement a second one of the annealed, defect-free specimen could be made and the S-parameter data for Fe is the difference, , with respect to the data from the second run used as reference.

Fig. 5

Comparison of the temperature dependence of the S-parameter as determined from positron annihilation (left ordinate) and the relative length change (dashed line, right ordinate) as determined by dilatometry of HPT deformed (a) Fe, (b) Ni, and (c) Cu. Positron annihilation and dilatometry were measured separately on identically prepared specimens applying the identical temperature program.

The overall similar trend of the annealing behavior of the S-parameter and the length change is striking. This correlation demonstrates that the decrease of free volume as observed by dilatometry is associated with the annealing out of free volume-type microscopic defects. As has already been observed in dilatometry, in the case of Ni, several distinct defect annealing stages are observed. In the case of copper with higher defect mobility, as expected from the data from the literature [41] and its lower melting temperature annealing of defects, such as vacancies is known to occur already at room temperature. Therefore, the whole curve for Cu is shifted towards lower temperatures with respect to Ni and Fe. A qualitatively different behavior compared to the fcc Cu and Ni metals is observed for bcc Fe. In the case of Fe no distinct stages can be discerned and only one broad annealing stage covering the temperature range from about 400 to 800 K is observed indicating simultaneous annealing of different types of defects similar to the results obtained from dilatometry.

The sharp decrease of the S-parameter that is observed at temperatures above 430 K in the case of Cu and above 460 K in the case of Ni corresponds to the grain growth process observed by dilatometry and analysis with scanning electron microscopy (see previous subsection). The obvious temperature delay in the visibility of the onset of the grain growth process by positron annihilation compared to dilatometry is due to the positron diffusion length which is initially much larger than the mean radius, r, of the grains . Only after sufficient grain growth has occurred, the state of positron saturation trapping at grain boundaries is left because positron–electron annihilation from the defect-free grain interior also contributes. This lowers the S-parameter significantly. The behavior can quantitatively be understood by applying a model for the diffusion-limited trapping of positrons at grain boundaries [42].

The variation of the S-parameter prior to the onset of crystallite growth appears to be a bit more subtle [40]. First of all, it has to be emphasized that the S-parameter of the defect-free state in metals slightly increases with temperature. For the case of Fe, a temperature dependence of the S-parameter, , of about was determined from the second measurement run (not shown). A similar behavior can be anticipated for Cu and Ni. Therefore, the observed trend for Cu and Ni of a nearly constant or only slightly lower S-parameter during annealing below about 450 K indicates a change in the defect structure in this temperature range already. Removal of vacancies and dislocations as well as grain boundary relaxation most likely occurs in this first stage at lower temperatures in Ni and Cu. From the net change of the S-parameter in this regime of saturation trapping of positrons it has therefore to be concluded that the concentration of these various types varies differently with annealing.

Conclusion

In the present work, the direct and specific method of high-precision dilatometry has proven as a powerful tool for the study of free volume in bulk nanocrystalline metals. In addition to issues of defect kinetics, in particular the absolute value of free volumes, such as the grain boundary excess volume, can be directly measured which can be hardly be accomplished by other techniques. Dilatometry, on the one hand, supplements positron annihilation in an ideal manner, since it expands the range of accessible defect concentration. On the other hand, it could be demonstrated that the close combination of the two complementary techniques of dilatometry and fast in situ Doppler broadening measurements allow a deeper insight in the complex atomic processes of defect annealing in bulk nanocrystalline materials.