The grain size determined by transmission electron microscopy (TEM) has similar evolution as for the crystallite size. The minimum grain size in pure Cu processed by ECAP at RT is about 200 nm [7,12]. It is noted that the crystallite size measured by X-ray line profile analysis is usually smaller than the grain size obtained by TEM. This phenomenon can be attributed to the fact that the crystallites are the domains in the microstructure which scatter X-rays coherently. As the coherency of X-rays breaks even if they are scattered from volumes having quite small misorientations (1°–2°), the crystallite size corresponds rather to the subgrain size in the severely deformed microstructures [13]. The reduction in the subgrain and grain sizes with increasing imposed strain is attributed to the increase of dislocation density as the grain refinement during SPD usually starts by the arrangement of dislocations into low-energy configurations such as low-angle grain boundaries (the misorientation is smaller than 3° per definition). The clustering of dislocations minimizes the energy stored in the dislocation structure as the strain field of dislocations is screened by other dislocations. The clustering of dislocations was observed directly in TEM images [14,15] and also detected by X-ray line profile analysis [16]. As an example Fig. 3.2 shows a subgrain with a size of about 250 nm in a 99.99% purity Cu sample processed by 14 cycles of repetitive corrugation and straightening (RCS) [14]. The black arrowhead at the left side of the subgrain in Fig. 3.2a points to a boundary segment whose Fourier-filtered high-resolution transmission electron microscopy (HRTEM) image is presented in Fig. 3.2b. The inset in Fig. 3.2a is an HRTEM image from the subgrain showing that the subgrain boundaries are almost parallel to two sets of {111} planes. The average distance between dislocations in the boundary is about 2 nm as estimated from Fig. 3.2b that yields a local dislocation density of about 3 × 10¹⁷ m⁻² (the average distance between dislocations can be approximated as the inverse square root of dislocation density). This local dislocation density value is about two orders of magnitude higher than the average dislocation density in the whole sample. In addition to dislocations, other lattice defects such as interstitial and vacancy loops are also observed in the boundary (see Fig. 3.2b).

X-ray line profile analysis also enables the investigation of dislocation clustering as this method gives a dimensionless dislocation arrangement parameter, M, that is defined as the product of the outer cutoff radius of dislocations and the square root of the dislocation density. Practically, in this quantity the outer cutoff radius of dislocations is normalized by the average dislocation distance that can be expressed as the inverse of the square root of total dislocation density. The value of M usually decreases with increasing number of ECAP passes [16], which indicates a stronger screening of the strain field of dislocations due to their arrangement into low-energy configurations such as dipolar walls or low-angle grain boundaries.

The lattice misorientation across a grain boundary is accommodated by geometrically necessary dislocations. SPD processing results in nonequilibrium grain boundaries that contain high density of extrinsic dislocations in addition to geometrically necessary dislocations. As an example, Fig. 3.3a shows a boundary in a 99.99% purity Cu sample processed by 14 cycles of RCS [14]. The grain boundary plane is curved and changes from the (5 5 12) plane to the (002) plane. The misorientation between the adjacent grains is about 9° as it is revealed by the corresponding electron diffraction pattern in Fig. 3.3b. HRTEM images from the upper-left and lower-right part of the boundary (see the framed areas in Fig. 3.3a) are shown in Fig. 3.3c and d, respectively. Fig. 3.3d is a structural model of the boundary segment in Fig. 3.3c. From this model, it can be seen that two types of dislocations marked by black and white symbols are needed to accommodate the geometrical misorientation. These six dislocations are referred to as geometrically necessary or intrinsic dislocations. However, there are three other dislocations in Fig. 3.3c which are extrinsic (or nongeometrically necessary) dislocations. Therefore, this segment of grain boundary is in nonequilibrium state. At the same time, the segment in Fig. 3.3e contains only geometrically necessary dislocations therefore that is an equilibrium grain boundary. Large density of extrinsic dislocations in grain boundaries was also observed for hexagonal metals processed by SPD [15].

With increasing strain in SPD processing, the dislocation density in the newly formed subgrain or grain boundaries increases, thereby enhancing the angle of misorientation that can be approximated as the ratio of the magnitude of Burgers vector and the spacing between geometrically necessary dislocations in low-angle grain boundaries. Electron backscatter diffraction experiments revealed that the fraction of high-angle grain boundaries (the misorientation is larger than 15° per definition) monotonously increased with increasing number of ECAP passes even after the achievement of the minimum grain size (about 200 nm for pure Cu) [12]. At very large equivalent strain values (ε ≈ 10–30) of SPD processing, the fraction of high-angle grain boundaries in various metals (e.g., Cu, Al, Ni, steel) increased up to 70%–90% [12,17–19]. According to the model of grain refinement, nonequilibrium grain boundaries evolve from dislocation cell boundaries and/or low-angle grain boundaries by absorbing dislocations gliding in the lattice during SPD processing. The grain boundary misorientation increases with increasing dislocation density in grain boundary, similar to the Read–Shockley model of low-angle grain boundaries. At the same time, contrary to low-angle grain boundaries, dislocations in high-angle grain boundaries are stored in nonperiodic, disordered arrays, and the nonequilibrium nature of the boundary can be characterized by the excess free volume and/or energy. The values of these parameters increase with increasing the density of extrinsic dislocations.

Fig. 3.1 shows that between the 3rd and 10th passes of ECAP, the dislocation density and the crystallite size for Cu remains unchanged within the experimental error. At the same time, during ECAP processing between the 10th and 15th passes the dislocation density decreases and after 25 passes even the crystallite size increases. These changes can be attributed to the structural relaxation of grain/subgrain boundaries. The equilibrium state can be approached by the annihilation of extrinsic dislocations. The decrease of the dislocation density after 15 passes can be explained by this annihilation of extrinsic dislocations. This structural recovery at large strain is accompanied by a decrease in the grain boundary thickness corresponding to an evolution from nonequilibrium boundaries to a more equilibrated structure and by an increase in the misorientation between neighboring grains. This is illustrated in Fig. 3.4 where the TEM images taken on the microstructures processed by the 5th and 25th passes are presented [3,12]. It is noted that the decrease of the dislocation density in SPD processing can be also observed for other materials (e.g., in Al [6] or Ag [10]) if the imposed strain is high enough and the applied hydrostatic component of the stress field does not suppress recovery processes.

The grain refinement in metallic materials processed by SPD at high homologous temperatures (0.3–0.4 × T_m or above where T_m is the absolute melting point) may occur by continuous dynamic recrystallization (CDRX) [20]. In CDRX process, new fine grains with HAGBs nucleate homogeneously during SPD as a consequence of the large stored energy. This primary recrystallization may contribute to grain refinement in Mg and Al even at RT due to their low melting points [21]. A secondary recrystallization process should be avoided to maintain the fine grain structure.

Beside the density and the arrangement of dislocations, X-ray diffraction line profile analysis also enables the determination of the type of the prevailing dislocations in nanomaterials [22]. In the case of cubic crystal systems, the edge/screw character of dislocations can be determined. It was found that for face-centered cubic (fcc) metals having high stacking fault energies (SFEs), e.g., for Al and its alloys, the character of dislocation structure is rather edge type after RT SPD processing [23]. Due to the high SFE, the dissociation of screw dislocations is marginal that gives a relatively easy annihilation by cross-slip compared to climb of edge dislocation segments. With decreasing SFE, the splitting distance between partials in dissociated dislocations increases that retards both cross-slip and climb [24,25]. As cross-slip is more sensitive to the degree of dislocation dissociation than climb [10], the decrease of SFE leads to a gradual enhancement of the screw character of dislocation structure. In the case of body-centered cubic (bcc) metals, e.g., interstitial-free (IF) steel processed by ECAP at RT, the character of dislocations is more screw [11], which can be explained by the reduced mobility of screw dislocations compared to edge dislocations in bcc structures. This difficulty in motion of screw dislocations is due to the fact that the ground state dislocation core is dissociated into a nonplanar configuration [26]. As a consequence, during ECAP processing the edge dislocation segments can annihilate more easily than the screw ones thereby the remaining dislocations have more screw character.

In the case of hexagonal close-packed (hcp) materials, X-ray line profile analysis provides the relative fractions of dislocations having 〈a〉, 〈c〉, and 〈c+a〉 Burgers vectors [27,28]. Generally, SPD processing of hexagonal materials is carried out at high homologous temperatures (at about 0.4 × T_m) due to their rigidity. However, high-pressure torsion (HPT) processing can be carried out on hcp materials even at RT without an early failure of the samples, as the high pressure applied in HPT suppresses crack propagation. There is an abundance of 〈a〉-type dislocations (usually with 60%–70%) in all hexagonal UFG or nanomaterials (e.g., sintered WC [29,30], SPD-processed Ti [15,31], and Mg alloys [32]) that can be explained by their smallest Burgers vector compared to other types of dislocations. The amount of 〈c〉-type dislocations is usually negligible; however, a significant fraction (30%–40%) of 〈c+a〉 dislocations is detected. The relatively high fraction of 〈c+a〉 dislocations in these materials can be attributed to the elevated temperature of SPD processing and/or the high stresses developed at grain boundaries which facilitates the activation of 〈c+a〉 dislocations [33]. At RT, the critical resolved shear stress of pyramidal 〈c+a〉 dislocations is about five times larger than that for basal slip [34], but this value decreases with increasing temperature.

The evaluation of X-ray diffraction profiles also enables the determination of the population of the individual slip systems (e.g., basal, prismatic, or pyramidal systems) in UFG or nanocrystalline hcp materials [28]. As an example, Fig. 3.5 describes the evolution of the dislocation structure as a function of HPT revolutions in the center of an AZ31 alloy (Mg–3% Al–1% Zn) disk [35]. The HPT processing was carried on a well-annealed material at RT under the pressure of 2.5 GPa and the zero turn corresponds to a compression in the HPT device without torsional deformation. The parameters of the dislocation structure saturate even after ¼ HPT turn, and significant changes were not observed with increasing deformation up to 15 revolutions. The maximum dislocation density is about 7 × 10¹⁴ m⁻². The analysis of the population of the different slip systems shows that the majority of dislocations have 〈a〉-type Burgers vector (60%–80%) for the compressed sample (zero turn) and also in the HPT-processed specimens. Fig. 3.5b shows that among 〈a〉-type edge slip systems the fraction of nonbasal dislocations (the sum of the prismatic and pyramidal edge dislocations) decreases from about 55% to 30%, while the population of basal edge dislocations slightly increases from 15% to 20%. A similar evolution of the dislocation fractions occurred in the periphery of the disks. This change in the dislocation population can be explained by the fact that in Mg, which has larger c/a lattice parameter ratio than 1.6, the slip occurs most easily in basal plane at low temperatures [36]. Fig. 3.5c reveals that the relative fraction of screw dislocations increases from ∼10% (only compressed state) to 30%–40% owing to HPT straining. It should be noted that the fraction of screw dislocations saturates already at ¼ turn and significant difference between the values in the center and the periphery was not observed, in accordance with the evolution of other parameters of the dislocation structure. It is noted that the fraction of screw dislocations during ECAP processing was even larger (50%–70%) than in the case of HPT, since the high pressure in the latter procedure hinders the lattice diffusion, thereby impeding the annihilation of edge dislocations [37].

The grain refinement in hcp metals during SPD processing has different features than in fcc materials. For instance, there is an evidence in different Mg alloys (e.g., AZ31 and ZK60) that above a critical initial coarse grain size, the grain refinement starts with the development of an inhomogeneous grain structure [38–40]. The new grains form along the boundaries of the initial coarse grains in a necklace-like arrangement as depicted in Fig. 3.6. As a consequence, if the initial grain size is large enough, the fine grains at the grain boundaries and the internal volumes of the initial coarse grains give a bimodal grain structure in the beginning of SPD processing. With increasing strain, the grain refinement spreads into the initial grain interiors, thereby leading to a more homogeneous fine grain structure. In hcp metals and alloys, dislocation mechanism of grain refinement requires the activation of both nonbasal and basal slips [41]. As dislocations on the basal plane have the smallest 〈a〉-type Burgers vector, their activation is easy by the external stresses. The glide on nonbasal slip systems is more difficult, and the activation of these dislocations is facilitated by the high stresses and/or the elevated temperature. Therefore, the stress concentrations at the boundaries of the initial grains yield the activation of both basal and nonbasal slip processes leading to the formation of fine grains at the preexisting grain boundaries [42]. If the grain size is smaller than a critical value, the formation of fine grains at the initial grain boundaries does not cause a bimodal grain structure. This critical grain size is between 3 and 9 μm for AZ31 alloy processed by ECAP at RT [40]. In this alloy, the bimodal grain size distribution developed during the first pass disappears after six passes. However, the critical grain size depends not only on the selected alloy but also on the SPD conditions. For instance, the critical grain size becomes larger, when the temperature of ECAP increases as the higher temperature facilitates the activity of nonbasal slip systems.

The very high dislocation density after HPT can be attributed to the high pressure (p = 4 GPa) applied during HPT as it hinders annihilation of dislocations by retarding climb and cross-slip in the following ways:

Fig. 3.8a and b compare the maximum dislocation density and the minimum grain size, respectively, achievable by ECAP and HPT at RT for 2N5 purity Al, Al–1% Mg alloy, IF steel, oxygen-free (99.98% purity) Cu, and 4N purity Ag. The data are taken from Refs. [6,10,11,43,53,54]. For Cu and Ag, the maximum dislocation density after HPT is much larger than after ECAP, while for the other three materials the saturation dislocation densities after ECAP and HPT are practically the same. Most probably, in the latter materials the dislocation density was also higher under the large pressure applied during HPT than in ECAP processing; however, when the pressure was released a large fraction of dislocations annihilated due to the accelerated diffusion, as shown in Ref. [44]. In the case of Cu and Ag, the relatively low SFE (compared to other materials in Fig. 3.8) retarded this annihilation process, as discussed in the previous paragraphs, hereby resulting in a higher dislocation density after HPT than that obtained in ECAP processing. The low SFE also hindered the arrangement of excess dislocations into grain boundaries in Cu and Ag during HPT, therefore the minimum grain size values are similar after processing by the two different SPD methods. At the same time, in Al, Al–Mg alloy, and IF steel the increased dislocation density during HPT processing yielded a smaller grain size as a part of excess dislocations were arranged into grain boundaries.

The grain boundary character depends on both the imposed strain and the route of SPD processing. The evolution of a reasonably equiaxed UFG microstructure with large fraction of high-angle grain boundaries is usually most rapid for route B_C among the different routes of ECAP [56,57]; however, the difference in the grain boundary misorientation distribution produced by the various ECAP routes decreases with increasing number of passes [12]. At very high imposed strains (ε ≈ 10–40), the high-angle grain boundary fraction is the largest in the materials processed by ECAP and HPT compared to other SPD methods [12,17].

The saturation dislocation density is determined by the dynamic equilibrium between the formation and annihilation of dislocations. The more difficult the dislocation annihilation during SPD processing, the higher the maximum dislocation density. The annihilation processes are hindered by (1) the low homologous temperature of SPD, (2) the solid solution alloying, (3) the second phase particles, and (4) the high degree of dislocation dissociation due to the low SFE. The homologous temperature of SPD can be kept at low values either by processing at low temperatures (e.g., cryogenic rolling at liquid nitrogen temperature, 77 K [60]) or by applying SPD on metals having high melting points. Fig. 3.10 illustrates that the higher the melting point (T_m) in pure fcc metals having medium or high SFE (Al, Ni, Cu, and Au), the larger the maximum dislocation density achievable by ECAP at RT. As the grain refinement occurs by arranging of dislocations into subgrain and grain boundaries, the higher saturation dislocation density is accompanied by smaller crystallite and grain sizes as shown in Fig. 3.10. The effect of the melting point on the saturation dislocation density can be explained by the thermally activated processes (cross-slip and climb) of dislocation annihilation. For instance, in fcc metals having medium or high SFE, the degree of dislocation dissociation is not very large, therefore cross-slip of screw dislocations occurs more easily than climb of edge segments during SPD processing. As a consequence, the maximum dislocation density at high strains is determined by the diffusion-controlled climb process. The diffusion coefficient is given by

It is noted that climb is usually considered as an important process only at high temperatures due to the slow diffusion at RT. However, UFG materials produced by SPD have a high volume fraction of grain boundaries and a large density of dislocations together with a large concentration of excess vacancies. The activation energy of diffusion along grain boundaries and dislocation cores is about half of that for self-diffusion; therefore the vacancy migration in nanomaterials is faster than in their coarse-grained counterparts by a factor of 10¹⁰ to 10²⁰ [78]. Consequently, diffusion may control the annihilation of dislocations even at RT. The high internal stresses developed in SPD-processed nanomaterials due to the large defect densities also assist climbing considerably.

Fig. 3.10 shows that the saturation dislocation density for pure Ag is much higher than the values for other fcc metals having similar melting points (Au, Cu). The very large dislocation density in Ag can be explained by its extremely low SFE (16 mJ/m² [51]) yielding a high degree of dislocation dissociation that hinders both cross-slip and climb thereby retarding dislocation annihilation. The evolution of the defect structure in low SFE materials will be presented in Chapter 4.

The temperature and strain rate of SPD processing have a significant effect on the defect structure and grain size in nanocrystalline or UFG metals and alloys. For a given strain and processing method, the higher the strain rate and/or lower the temperature of deformation, the larger the dislocation density and smaller the grain size. The combined effects of strain rate (ε˙) and temperature can be expressed by the Zener–Hollomon parameter defined as

Similarly to pure metals, in solid solution alloys the dislocation density, the crystallite, and grain sizes saturate after approximately four to eight passes of ECAP [5–9,81–84]. At the same time, alloying usually leads to an increase of the critical imposed strain that corresponds to saturation. For instance, in 99.99% purity Al and Al–3% Mg alloy processed by ECAP at RT the maximum value of the dislocation density is achieved after the first and fourth passes, respectively. Additionally, the maximum dislocation density increases while the minimum values of the crystallite and grain sizes decrease due to alloying. As an example, Fig. 3.11 shows the saturation values of the dislocation density and the grain size as a function of the Mg concentration in Al processed by ECAP at RT [9]. Both the larger strain needed for saturation and the higher value of the saturation dislocation density in alloys can be explained by the pinning effect of solute atoms on dislocations that hinders their annihilation. As grain refinement in SPD metals occurs usually by the rearrangement of dislocations into subgrain and grain boundaries, the higher dislocation density results in a decrease of grain size for higher Mg concentrations as shown in Fig. 3.11 and demonstrated in the TEM images of Fig. 3.12. In pure Al the saturation grain size is 1200 nm while 3 wt.% Mg alloying leads to a reduction to 300 nm. It is noted that although the minimum grain size in Al–3% Mg alloy is only 4 times smaller than in pure Al, the maximum dislocation density is approximately 13 times higher (see Table 3.1). The dragging effect of solute atoms on dislocations also hinders the evolution of low-angle grain boundaries into high-angle boundaries during SPD. For instance, although in both 99.99% purity Al and Al–1% Mg alloy the fraction of high-angle grain boundaries increases with increasing the number of ECAP passes, its maximum value in Al–1% Mg (∼65%) is lower than that for pure Al (∼75%) [85,86].

It is worthwhile to mention that the minimum grain size achievable by SPD is rather affected by the deformation conditions than the initial grain size before deformation. For instance, if RT HPT processing is performed on electrodeposited nanostructured Ni with the grain size of 30 nm, there is a grain growth to 129 nm [87], which is close to the grain size limit for HPT-treated coarse-grained Ni (140–170 nm [18]). Although the dislocation density increases from 120 × 10¹⁴ to 200 × 10¹⁴ m⁻² during HPT of electrodeposited Ni, this cannot compensate the softening effect of grain growth and the hardness decreases from 7.2 to 6.1 GPa. Similar grain growth was also observed during indentation of nanomaterials, while there is a lack of grain growth during tensile testing. This suggests that only stresses above a critical value induce grain growth in nanocrystalline materials. The large dislocation density in the electrodeposited Ni after HPT may be a consequence of the high impurity content that is usually a characteristic feature of electrodeposited materials.

The concentration of excess vacancies was investigated mainly in Cu and Ni processed by ECAP and HPT [8,48,78–83]. In HPT-deformed 99.95% purity Cu, positron annihilation spectroscopy (PAS) revealed the absence of monovacancies while a large amount of vacancy clusters were identified [88]. Most probably, the monovacancies created during HPT processing either disappear by diffusion to sinks such as grain boundaries or agglomerate into small clusters. The vacancy clusters at the center of the HPT-processed Cu and Ni disks consist of four to five vacancies, while the clusters at the periphery consist of seven to nine vacancies [88]. Neither the increase of number of HPT revolutions nor the raise of pressure from 2 to 4 GPa results in a change of the size of vacancy clusters. The densities of dislocations and vacancies were so high in the HPT-processed Cu samples that every positron is very quickly trapped at dislocations or vacancy clusters (referred to as saturated positron trapping). As a consequence, the concentration of vacancy clusters could be only evaluated from the PAS signal with the help of the dislocation density determined by X-ray line profile analysis. The ratio, I₂/I₁, of the intensities of PAS signals corresponding to positrons trapped in vacancy clusters and at dislocations is directly proportional to the ratio of cluster concentration and dislocation density [88]:

For ECAP-processed Cu, the vacancy concentration was determined by a combination of X-ray line profile analysis and residual electrical resistometry or differential scanning calorimetry (DSC) [8]. The decrease of electrical resistivity during annealing of the ECAP-processed samples is caused by the annihilation of lattice defects such as vacancies (vacancy clusters) and dislocations. The contribution of dislocations to resistivity can be estimated from the dislocation density determined by X-ray line profile analysis and the specific dislocation resistivity of Cu being 0.8 × 10⁻²⁵ Ωm⁻³ [89]. Subtracting this contribution from the total decrease of resistivity, the vacancy concentration can determined as the ratio of the remaining resistivity and the resistivity per unit vacancy concentration (0.62 × 10⁻⁴ Ωcm for Cu [90]). The vacancy concentrations obtained by this way are 1.5 × 10⁻⁴ and 3.5 × 10⁻⁴ after the first and fourth ECAP passes, respectively. These values are smaller than the concentrations determined in HPT-processed Cu samples. This can be explained by the larger imposed strain in HPT compared to ECAP. The vacancy concentration values determined from the released heat measured in DSC agree well with those obtained by resistometry [8]. In the DSC thermograms for ECAP-processed Cu samples, one exothermic peak was observed. The released heat is assumed to be a sum of the contributions of vacancies and dislocations. The stored energy in a unit volume corresponding to dislocations having half edge—half screw character is determined as [8]:

In the case of HPT-processed 99.99% and 99.998% purity Ni, two exothermic peaks were observed on the DSC thermograms [48]. The first peak at lower temperature corresponds to the disappearance of single/double vacancies while the second one at higher temperature is related to the annihilation of vacancy clusters and dislocations. The first DSC peak was not observed for 99.99% Cu processed under the same conditions (see earlier) as most probably all the vacancies are clustered due to the smaller values of SFE and melting point of Cu. In Ni with lower purity than 99.99%, single/double vacancy peak is also not detected as impurities facilitate the formation of vacancy clusters. The single/double vacancy concentration in Ni was determined as the ratio of the heat released in the first peak and the formation energy of a vacancy (0.29 × 10⁻¹⁸ J for Ni [90]). The concentration of single/double vacancies increases with increasing shear strain during HPT, and it saturates at about 1.0 ± 0.1 × 10⁻⁴ after a shear strain of about 20 irrespective of the pressure (2–8 GPa) [48]. The concentration of vacancy clusters also increases with increasing strain and its saturation values are 3.5 ± 1.0 × 10⁻⁴ and 5.1 ± 1.0 × 10⁻⁴ for 2 and 8 GPa, respectively [48]. The cluster size in the HPT-processed Ni samples was not determined. However, if we assume that the clusters consist of four to nine vacancies similarly as in Cu and we take into account the difference between the concentrations of clusters and single/double vacancies, it is evident that more than 90% of vacancies are clustered.

The microstructure and the phase composition of the ECAP-processed Al–Zn–Mg–Zr and Al–Zn–Mg–Cu alloys were compared with samples artificially aged at the same temperature and for the same time (30 min) as applied during ECAP. In the ECAP-processed specimens, stable incoherent MgZn₂ precipitates (η-phase particles) formed while artificial aging yielded only negligible concentration of η precipitates and mainly coherent Guinier-Preston (GP) zones develop [67]. As the precipitation sequence in these alloys is coherent GP zones, semicoherent η′ precipitates and incoherent η-phase particles, the observed difference in the phase compositions of the ECAP-processed and the aged samples indicates the promoting effect of SPD on precipitation. The experimental results show that processing by ECAP at a high temperature influences not only the precipitation kinetics but also there is a significant effect on the shape of the η precipitates. The Al–Zn–Mg–Zr and Al–Zn–Mg–Cu alloys aged for long times contain long rod-like precipitates but these are absent and only essentially spherical particles are present in the specimens processed by ECAP [67]. On the other hand, the precipitation during SPD most probably influences the grain refinement since the pinning effect of the second phase particles on dislocations and grain boundaries yields higher dislocation density and smaller grain size than for the pure counterparts.

In multiphase nanomaterials, the energy of interfaces strongly influences the phase composition [76,93]. This phenomenon is caused by the Gibbs–Thomson effect which reveals that the solubility limit in the matrix phase depends on the size of secondary phase particles (d) and the interface energy (γ) as [94,95]:

The influence of the Gibbs–Thomson effect on the microstructure evolution in multiphase materials was demonstrated in a Cu–Ag alloy [76]. Supersaturated solid solution Cu–3 at.% Ag alloy was SPD-processed by cryorolling at liquid nitrogen temperature (∼77 K). The total thickness reduction during cryorolling was 85% which corresponds to a logarithmic strain of ∼2. The Ag solute content in the cryorolled Cu matrix was about 1 at.% while ∼2 at.% Ag was present as secondary Ag-rich phase. This phase was formed from the supersaturated alloy due to the promoting effect of SPD on precipitation (see above). The grain size of the Cu matrix was 100–200 nm. The average size of secondary Ag particles was ∼20 nm, however, a large number of Ag precipitates with sizes smaller than 8 nm was also detected by TEM. The dislocation density in the cryorolled Cu–3 at.% Ag alloy was very high (∼48 × 10¹⁴ m⁻²) due to the pinning effect of Ag solute atoms on dislocations.

Annealing of the cryorolled UFG Cu–3 at.% Ag alloy at 623 ​K yielded formation of a strongly heterogeneous microstructure, as indicated by the splitting of each Cu diffraction peak into two components [76]. As an example, Fig. 3.17 shows reflection (220) for the sample annealed for 20 min. For comparison, the same reflection for the cryorolled specimen is also presented. The splitting of the peaks is caused by the development of an inhomogeneous solute atom distribution in the Cu matrix during annealing, resulting in a variation of the lattice parameter of the Cu matrix. For the simplicity, each line profile was evaluated by fitting it with the sum of two profile components having different Bragg angles which correspond to two distinct regions of the matrix with different average lattice parameters. The subprofiles appeared at higher and lower diffraction angles correspond to the matrix volumes with low- and high-solute Ag contents, which are referred to as Regions 1 and 2, respectively [76]. From the positions, intensities and shapes of the diffraction subprofiles, the solute Ag content in the Cu matrix, the fractions of Cu and Ag phases, and the dislocation density in the two matrix regions were determined, respectively. According to the results, the development of the heterogeneous microstructure during annealing at 623 ​K is depicted schematically in Fig. 3.18. In the cryorolled sample, the average Ag solute concentration is 1%. However, as it is shown in Fig. 3.16, around Ag particles with semicoherent interfaces and sizes smaller than ∼4 nm, the equilibrium Ag solute concentration in the Cu matrix is higher than 1%. Therefore, these particles tend to dissolve into the matrix during annealing, resulting in an increase of solute Ag content and a corresponding decrease of the volume fraction of Ag particles (see the second picture in Fig. 3.18). The matrix regions around these small Ag particles correspond to Region 2. The particles larger than the critical value (∼4 nm for semicoherent interfaces, see Fig. 3.16) grow since the equilibrium solubility limit around them is smaller than the initial 1%. In these volumes, denoted as Region 1, the solute Ag content decreases while the fraction of Ag phase increases (see the second picture in Fig. 3.18). Thus, it can be concluded that the Gibbs–Thomson effect resulted in the development of a heterogeneous two-phase microstructure in Cu–3 at.% Ag alloy processed by cryorolling and subsequent annealing. It is noted that for coherent interfaces the critical Ag particle size is larger (∼10 nm), as shown by the solid curve in Fig. 3.16.

Fig. 3.19 shows the solute Ag content in Regions 1 and 2, the relative fractions of these two matrix regions and their dislocation densities as a function of annealing time at 623 ​K for cryorolled UFG Cu–3 at.% Ag alloy [76]. In Region 2, the solute Ag content increased from ∼1 at.% to ∼2.6 at.% within 5 min annealing and it decreased slightly to ∼1.9 at.% with increasing annealing time up to 75 min (see Fig. 3.19a). For longer durations of heat treatment the solute Ag concentration in Region 2 was not determined due to the low volume fraction of this region (see below). In Region 1, the solute Ag concentration decreased to ∼0.3 at.% during the first 10 min of annealing and remained unchanged within the experimental error up to 120 min. This value agrees with the equilibrium Ag concentration in Cu at 623 ​K (0.33%) within the experimental error. The increase and the decrease of solute Ag concentration during annealing suggest the dissolution and the precipitation of Ag in Regions 2 and 1, respectively. In the cryorolled state, the relative X-ray intensity of the Ag phase is ∼8% which decreased to ∼5% after 5 min annealing and remained unchanged within the experimental error up to 30 min (Fig. 3.19b). This observation is in accordance with the dissolution of Ag precipitates in Region 2. In this period, the fractions of Regions 1 and 2 are ∼60% and ∼35%, respectively [76]. Between 30 and 120 min the fractions of Regions 1 and 2 increased and decreased, respectively. This indicates that precipitation occurred in Region 2 which reduced the solute Ag concentration to the equilibrium value (∼0.3 at.%). After 120 min annealing, the fraction of Region 2—where the dissolution of Ag had occurred in the beginning of the heat treatment—was practically zero. Concerning the relative intensity of the Ag phase, it increased gradually to ∼13% between 30 and 120 min in accordance with the reduction of the fraction of the matrix volume with high solute Ag content (Region 2).

The variation in the dislocation density in Regions 1 and 2 of the Cu matrix as a function of the annealing time is shown in Fig. 3.19c. In Region 1, the dislocation density decreased to ∼1 × 10¹⁴ m⁻² during the first 30 min of annealing, then it remained unchanged within the experimental error up to 120 min [76]. In Region 2, the dislocation density decreased only to about half of the initial value (∼20 × 10¹⁴ m⁻²) due to the stronger pinning effect of the higher solute Ag concentration. Further annealing up to 75 min resulted in only a slight change in the dislocation density in Region 2. Between 75 and 120 min the dislocation density and the crystallite size in Region 2 were not determined since the fraction of this region was very low (<10%) for long annealing times (see Fig. 3.19b). The twin boundary probability in both regions of the heat-treated Cu matrix was found to be in the range of 0%–0.4% without any clear trend with the variation of annealing time. It is also worth to note that the route and the strain of SPD processing most probably influence the size and interface energy of Ag precipitates, i.e., SPD can be applied for interface engineering. Therefore, the functional properties (strength, ductility, conductivity, etc.) of Cu–Ag alloys can be tuned by an appropriate selection of the SPD-processing conditions, the chemical composition, as well as the time and temperature of annealing.

Finally, it is worth noting that HPT processing at RT yielded an elemental decomposition of supersaturated Al–30 wt.% Zn alloy [68]. Before HPT, the material was solution treated at 673 ​K for 1 h which resulted in a lamellar structure with varying Zn content inside the Al(Zn) grains due to spinodal decomposition. HPT processing destroyed this lamellar structure, leading to precipitation of Zn particles within the Al-rich grains. This elemental decomposition is facilitated by the rapid diffusion along lattice defects. In addition to decomposition, ∼3-nm thick Zn-rich layers were formed at Al–Al grain boundaries [103]. The fast diffusion along these layers caused grain boundary wetting, i.e., it strongly facilitates grain boundary sliding, thereby increasing the ductility of Al–Zn alloys during plastic deformation.