2023 Volume 64 Issue 7 Pages 1401-1409
Publications on obtaining bulk nanostructured materials with special properties by various modes of severe plastic deformation, using nickel as an example, are briefly reviewed. Particular attention is paid to the state of grain boundaries, commonly referred to as nonequilibrium, or deformation-modified boundaries, revealed by electron microscopy, including scanning tunneling, Mossbauer spectroscopy, and diffusion studies. It is shown that contribution of specific state of grain boundaries to additional strengthening is often overestimated. In particular, in Ni processed by high pressure torsion, nonequilibrium grain boundaries are formed, which have increased energy and are ultrafast diffusion paths, but they contribute relatively little to the total strengthening.
One of the most effective ways to produce bulk ultrafine-grained (UFG) materials is severe plastic deformation (SPD), which has been widely developed in recent decades.1) Great interest in SPD is mainly based on the fact that UFG metals and alloys processed by various modes of severe deformation can acquire more attractive properties than in the coarse-grained state.1–4) Higher strength and hardness in UFG materials compared to conventional coarse-grained materials are characteristic of most metals and alloys processed by SPD.5–8) They can also demonstrate increased toughness, wear resistance, higher fatigue strength and superplasticity.9–12)
The most important microstructural components of any polycrystalline materials affecting their bulk properties are grain boundaries (GBs).13) GBs have a particularly strong effect on the properties of UFG materials, in which their volume fraction is very high, and this corresponds, first of all, to UFG materials processed by various SPD modes.2) Since such materials have a very high grain boundary density, they can be considered as materials controlled by internal interfaces. Any SPD mode leads to a significant grain refinement and introduces a great number of crystal structure defects, mainly vacancies and dislocations.14)
In a number of early publications, it was suggested that GBs in UFG materials processed by SPD are in a greatly “nonequilibrium” metastable state, which partially or completely relaxes upon subsequent heat treatment or even under deformation.15,16) In the works by Nazarov, a theoretical model was proposed, according to which modification in the structure and properties of GBs under SPD results from the absorption of lattice dislocations.16–19) According to this model, the “nonequilibrium” GBs formed under the SPD are characterized by an excess free energy, higher fields of long-range elastic stresses and a larger free volume compared to conventional relaxed high-angle grain boundaries.
According to Valiev et al., these “nonequilibrium” GBs should be responsible for the improved mechanical properties of materials processed by SPD, which exceed the properties expected only due to grain refinement.2–5) Moreover, it is the long-range elastic stresses created by nonequilibrium GBs, along with the UFG structure that are responsible for the unique properties of materials processed by SPD. However, it should be noted that direct evidence of this has not yet been obtained.
Since, in principle, any grain boundaries in polycrystals are nonequilibrium defects, the term “nonequilibrium” GBs, which appeared in connection with specific properties of UFG materials processed by SPD, is not entirely correct. Therefore, the term “deformation-modified” GBs is now more often used.20,21) In addition, it should be noted that there is still no unambiguous evidence for the existence of long-range elastic stress fields created by deformation-modified boundaries, and according to recent works, it is more correct to speak about localized residual strain fields located in the near-boundary regions of “nonequilibrium” GBs.22)
There are a number of methods for revealing the specific state of GBs in materials processed by SPD. In the earliest works, the conclusion about nonequilibrium state of boundaries in nanostructured materials was made based on the transmission electron microscopy data, including high-resolution microscopy. For example, in Ref. 23), a noticeable broadening of thick extinction contours in the nanostructured state compared to the conventional polycrystalline state was found, and the authors attributed that to a high level of internal stresses and distortions near the GBs. In Ref. 24), the HREM method revealed significant elastic distortions of the crystal lattice near GBs in nanocrystalline Ni and Ni3Al. The conclusion about the nonequilibrium state of boundaries was also made in Refs. 25)–27) based on the observation of a special diffuse contrast on GBs in various UFG materials. Deformation-induced changes in GBs in UFG materials were also observed in Ref. 28), where “zigzag” stepped configurations of GBs were reported in UFG pure copper and Al–3% Mg alloy processed by high-pressure torsion (HPT).
A more accurate, not only qualitative, but also quantitative assessment of grain boundary features requires special research methods. In particular, the method of emission Mössbauer spectroscopy, the capabilities of which are discussed in detail in Ref. 29), has a high efficiency. It was this method that revealed the specific deformation-modified state of GBs in molybdenum, tungsten and niobium.30–37)
The state of GBs can also be revealed by diffusion methods, since the coefficients of grain-boundary diffusion are very sensitive to the finest parameters of the structure of boundaries. For example, in Ref. 38), the tracer diffusion method established the presence of an additional excess volume in the deformation-modified boundaries of Ti subjected to equal-channel angular pressing (ECAP). In a number of publications, based on diffusion studies, it has been established that under the SPD, due to the high rate of defect formation and the inhomogeneity of their distribution, GBs of different types arise, with different diffusion rates along them.39–46) In this case, a part of high-angle boundaries acquire the deformation-modified state, which is characterized by accelerated atomic transfer and higher elastic stress fields.
Some additional information on the specific state of deformation-modified GBs can be obtained from the joint analysis of the emission Mössbauer spectroscopy and the radiotracer data. Such an approach was developed in Refs. 47), 48) using the specified model of grain boundary diffusion proposed in Refs. 49), 50). This approach was used in Ref. 51) in the study of grain-boundary diffusion in UFG Mo processed by HPT. It is shown that the GBs in this material are paths of ultrafast diffusion, the coefficients of which are several orders of magnitude higher than the values for coarse-grained Mo with GBs of recrystallization origin. This is a direct evidence of the specific nonequilibrium state of GBs in UFG Mo.
When studying the history of science on nanostructured materials processed by various modes of SPD,1) it becomes obvious that nickel is one of the most suitable objects for studying various aspects of this science. Nickel has high ductility, a relatively high melting point and stacking fault energy, which makes it possible to create a fairly uniform fine-grained structure in it under the SPD. It was on nickel that the first pioneering works on obtaining the nanocrystalline structure by HPT were carried out.52–54) These studies were subsequently actively carried out and are being carried on by scientists from different countries, as evidenced by a large number of publications.55–64) It was shown in Ref. 55) that, despite the inhomogeneity of strain distribution over the sample radius inherent in the HPT method, at sufficiently high applied pressures and torsional strain it is possible to obtain homogeneous UFG structure in Ni, with an average grain size of 170 nm, and the microhardness in this case more than doubles. According to Ref. 56), the microhardness of Ni after HPT is almost four times higher than in the initial state and remains at this level upon annealing at 0.2 and 0.3Tm. In Refs. 57), 58), the evolution of the structure of Ni single crystals upon HPT is considered in detail. It is noted that for any initial orientations of single crystals, with an increase in strain the structure is refined and the strength increases up to the saturation stage.
The purity of Ni significantly affects the formation of structure upon HPT. It was shown in Refs. 60), 61) that with a decrease in Ni purity, the structure becomes more dispersed under the HPT, and its thermal stability and microhardness increase. An important role is also played by the temperature at which the HPT is performed.62–64) According to Ref. 62), in high-purity nickel the HPT at cryogenic temperatures results in the formation of micro-twins and micro-bands, which delay the formation of a homogeneous UFG structure. In commercial grade Ni, the HPT in liquid nitrogen makes it possible to obtain the nanocrystalline structure with an average crystallite size of 80 nm, and the microhardness reaches 6200 MPa, which is significantly higher than after the room temperature HPT.63)
Along with HPT, the evolution of Ni structure was also studied under other SPD methods, such as equal-channel angular pressing (ECAP) and dynamic channel-angular pressing (DCAP).65–71) The refinement of the structure and, accordingly, the increase in microhardness under ECAP and DCAP are less significant than under HPT, but the thermal stability of the resulting structure is higher.68–71) It is important to note that, as under HPT, upon ECAP and DCAP the GBs also acquire the specific deformation-modified state, which is characterized by high internal stresses and increased coefficients of grain-boundary diffusion.65,69,71)
From this brief review, it is obvious that a large amount of experimental material has been accumulated on the structure and properties of Ni subjected to various modes of SPD. Nevertheless, some questions remain open, in particular, about the contribution of the state of GBs to strengthening. Therefore, in the experimental part of this work, the effect of HPT on the grain structure of Ni was studied, with special attention being focused on GBs and the possibility of additional strengthening due to their special state.
The studies were carried out on samples of coarse-grained and ultrafine-grained Ni with a nominal purity of 99.98 mass%, the content of the residual impurities in which is given in Table 1.
Samples of coarse-grained Ni were obtained by annealing the initial bars at 1000°C for 2 h. According to optical microscopy and scanning electron microscopy, they had a coarse-grained structure with grain sizes from 70 to 300 µm, with an average size of ∼160 µm and microhardness of ∼980 MPa. Samples of UFG Ni were obtained by HPT, for which rods 10 mm in diameter were cut into disks 0.5 mm thick and deformed in Bridgman anvils at room temperature under a pressure of 4 GPa for 0.5, 1, 3 and 5 revolutions at an angular velocity of 0.3 rpm. The true strain value, e, was calculated as the sum of the true strains by shear and compression:
| \begin{equation} e = \ln \sqrt{1 + \left(\frac{\varphi R}{h_{f}} \right)^{2}} + \ln \frac{h_{0}}{h_{f}}, \end{equation} | (1) |
The structure of the samples after HPT was studied in Technai G-30 Twin transmission electron microscope, with the acceleration voltage of 200 kV, followed by image processing by SIAMS-600 software package. The foils for TEM studies were prepared as follows. The disks of Ni were mechanically thinned, polished in an electrolyte containing orthophosphoric acid H3PO4 (860 g/l) and chromium anhydride CrO3 (100 g/l), washed in distilled water and dried. Histograms of grain size distribution were constructed and statistical processing of the results obtained was carried out. In addition, the grain structure was studied in QUANTA-200 scanning electron microscope with a Pegasus system for structural and texture analysis EBSD to determine the proportion of boundaries with different misorientations, with the acceleration voltage of 30 kV. Microhardness was measured in the NEOPHOT-21 optical complex and calculated as H = 18192 · P/C2, MPa, where P is load in grams, and C is the indentation diagonal in µm. Every value of C was calculated as an average of not less than 9 indentations.
X-ray studies were carried out in Empyrean PANalytical B.V. X-ray diffractometer (PHILIPS) in CuKα radiation. The texture was studied by the method of inverse pole figures, the pole density calculated as:
| \begin{equation} P_{hkl} = \frac{I_{T,\textit{HLK}}/I_{0,\textit{HKL}}}{\displaystyle\sum_{n}(Z_{hkl}I_{T,\textit{HKL}}/I_{0,\textit{HKL}})}\sum_{n}Z_{hkl}, \end{equation} | (2) |
| \begin{equation} \beta = 0.5B(1 - b/B + \sqrt{1 - b/B}). \end{equation} | (3) |
Two diffraction profiles were taken to separate the contributions to the true broadening of the profile from the dispersion of coherent scattering areas (CSA), βM, and microstrains, βN. The broadening of the diffraction profile due to the CSA dispersity and the broadening due to microstrain were approximated by function (1 + γx2)−2. When using such approximation functions, the integral width of the true profile is related to the components as:
| \begin{equation} \beta = \frac{(\beta_{M} + 2\beta_{N})^{2}}{\beta_{M} + 4\beta_{N}}. \end{equation} | (4) |
The CSA size D was calculated as D = 0.94λ/βM · cos Θ, and microstrain ε was determined as ε = 1/4βNtgΘ, where λ is wave length, nm, and Θ is the Wulf-Bragg angle.
The relative grain boundary energy was determined from measurements of the dihedral angle of the etch grooves. The most widely used method for determining the GB energy is the method of measuring the dihedral angle of a thermal etch groove obtained by heating the metal in vacuum or an appropriate atmosphere. In this case, the relative GB energy can be calculated from the formula:
| \begin{equation} \gamma_{\text{rel}} = \frac{\gamma_{\text{gb}}}{\gamma_{\text{s}}} = 2\cos\frac{\psi}{2}, \end{equation} | (5) |
However, it should be noted that at temperatures required for the formation of grooves when using thermal etching, the recovery might proceed, which can significantly change the state of grain boundaries. This is evidenced by the results of self-diffusion studies in ECAP-processed Ni,42) which showed that the state of GBs formed under the SPD changes upon annealing at temperatures above 400 K. At the same time, it is known that the rate of etching of boundaries in the grain–subgrain structure of metals depends on the degree of their nonequilibrium.78) Therefore, a technique for measuring the relative energy of GBs by measuring the dihedral angle in grooves formed under the chemical etching was suggested in Ref. 79). The comparison of relative energies of equilibrium GBs in copper determined by measuring the angles in the grooves of thermal74) and chemical79) etching shows that they are quite close.
In the present study, the relative energy of GBs was estimated on samples with grooves obtained by chemical etching. The samples were prepared as follows. After grinding and polishing to a mirror quality by standard metallographic procedures, the sample was electropolished to form a smoother relief. Then, to reveal the grain boundaries, chemical etching was carried out in an 11% solution of ammonium persulfate (NH4)2S2O8, followed by washing in bidistilled water and ethanol in order to remove electrolyte residues and prevent the possible formation of an oxide film. To prevent the formation of an oxide film on the surface, the sample after washing was placed in a beaker with a porous membrane in a solution of HBF4, which results in the formation of a protective film from HBF4 vapors. This technology of surface protection was used in Ref. 80).
The studies were carried out using an SMM-2000 scanning multi-microscope operating as scanning tunneling microscope (STM). The images were taken at the radius middle of the studied samples. The STM images were processed using the Gwyddion application by constructing lines perpendicular to GBs. As a result, a GB profile was obtained, based on which the dihedral angle at the bottom of the etching groove was calculated. An example of such profile is shown in Fig. 1. The relative energy of GBs was calculated by expression (5).
An example of a GB profile for calculating the dihedral angle.
The X-ray studies by the method of inverse pole figures showed that not very sharp texture is formed in Ni samples under the HPT. Figure 2 shows inverse pole figures in form of standard stereographic triangles for samples deformed by 0.5 and 5 revolutions. It can be seen that already after HPT by 0.5 revolution, a two-component axial texture with ⟨111⟩ and ⟨100⟩ axes is formed in the sample, the contributions of which are approximately the same. The strain increasing only slightly affects the characteristics of texture, and after HPT by 5 revolutions, the contribution of both texture components remains almost at the same level.
Inverse pole figures of Ni samples after HPT by 0.5 (a) and 5 (b) revolutions. The numbers within the stereographic triangles are the pole densities.
Since upon HPT the strain is distributed unevenly over the sample radius, increasing from the center to periphery, the structure is also refined non-uniformly, and hence the microhardness varies depending on the distance from the center. On the other hand, many experimental data indicate that as the degree of HPT deformation increases, this inhomogeneity of the structure and properties (in particular, microhardness) levels out.55,81,82) This is illustrated in Fig. 3(a), which shows the change in microhardness along the radius of samples after HPT with different degrees of deformation. At small deformations (small angles of rotation of the anvils), the difference in microhardness in the center and at the periphery is significant, which indicates a significant inhomogeneity of the structure along the radius of the sample. With an increase in the degree of deformation, the leveling occurs, and at HPT by 5 revolutions, the microhardness over the entire cross section of the samples is almost the same. Figure 3(b) shows the dependence of microhardness (at the radius middles) on the strain (number of revolutions). It can be seen that with an increase in strain, the microhardness increases significantly.
Microhardness of Ni versus strain by HPT: (a) – over the sample radii; (b) – in the radius middle.
It is known that grain refinement under HPT occurs in three stages.83,84) The first stage is the formation of cellular structure, in which the density of dislocations increases with strain increasing, and they concentrate in cell walls. The second stage is the formation of a mixed structure containing smaller cells and subgrains with low-angle boundaries, the misorientation of which increases with an increase of strain. The third stage is characterized by the formation of homogeneous submicro- or nanocrystalline structure with high-angle boundaries between crystallites.
These stages can be traced in Ni sample deformed by HPT by 0.5 rev. The cellular structure with cell sizes of 0.5–0.9 µm, high density of dislocations and their non-uniform distribution is observed in the sample center (Fig. 4(a), (b)). In this case, the electron diffraction patterns show reflections corresponding to one zone axis, for example [001] in Fig. 4(b). At the radius middle, the structure is mixed, subgrains appear along with the cells, and the electron diffraction patterns show Debye rings with groups of closely spaced reflections, which is typical of low-angle boundaries (Fig. 4(c), (d)). The UFG structure with predominantly high-angle boundaries is formed at the periphery, and the reflections form almost continuous Debye rings in the electron diffraction patterns (Fig. 4(e), (f)).
Structure of Ni after HPT by 0.5 rev. in sample center (a), (b), in radius middle (c), (d) and in periphery (e), (f): (a), (c), (e) – bright-field images; (b), (d), (f) – dark-field images in $(\bar{2}00)_{\text{Ni}}$ (b) and (111)Ni (d), (f) reflections indicated with circles in SAED patterns shown as inserts.
With strain increasing to e = 4.1 at the radius middle (HPT by 1 rev.), further fragmentation of the structure occurs, the refinement becomes more pronounced, although heterogeneity along the sample radius remains. At the radius middle, a submicrocrystalline structure is formed, and the electron diffraction patterns show a large number of reflections on Debye rings (Fig. 5(a), (b)). The grain boundaries look like thin and straight lines, which is clearly seen in the micrographs taken at high magnifications (Fig. 5(c)).
Structure of Ni after HPT by ha 1 rev. (in radius middle): (a), (c) – bright-field images; (b) – dark-field image in (111)Ni reflection indicated with circles in SAED pattern shown as insert.
Pronounced modification of the structure is observed after HPT by 3 revs. The structure becomes more uniform along the sample radius, although some inhomogeneity is still retained. The crystallite sizes and grain size scattering decrease. All electron diffraction patterns demonstrate the large number of reflections on Debye rings (Fig. 6(a)–(c)). In this state, high-angle boundaries predominate. Along with thin and straight boundaries, there are noticeably curved and uneven boundaries with steps (Fig. 6(c)), which indirectly indicates a specific nonequilibrium state of GBs. In most of the studied areas, the crystallites have an equiaxed shape. Most grains contain relatively few dislocations.
Structure of Ni after HPT by 3 (a)–(c) and 5 (d)–(f) revs. (in radius middle): (a), (c), (d), (f) – bright-field images; (b), (e) – dark-field images in (111)Ni reflections indicated with circles in SAED patterns shown as inserts.
Of greatest interest is the structure of Ni after HPT by 5 revs, since in this case the saturation stage is reached, at which, with strain increasing further refinement does not occur and microhardness does not increase. This is the most dispersed nanocrystalline structure, uniform along the sample radius (Fig. 6(d)–(f)). Coarser crystallites contain individual dislocations, but the dislocation density is low. The inhomogeneous contrast inside crystallites indicates high level of elastic stresses. All electron diffraction patterns are ring-wise. Most of GBs are uneven and curved, some have steps, which indicates their nonequilibrium state (Fig. 6(f)).
Electron micrographs of Ni structure after HPT were processed by SIAMS-600 image processing program, based on which grain size distribution histograms were constructed (Fig. 7) and the results obtained were statistically processed (Table 2). It is obvious that with strain increasing the grain sizes and grain size scattering decrease, and after HPT by 5 revolutions the almost nanocrystalline structure is formed.
Histograms of grain size distribution in Ni after HPT by 0.5 (a), 1 (b), 3 (c) and 5 revolutions (d).
Similar grain size distributions were obtained from the electron backscattered diffraction (EBSD) analysis. This technique was also used to obtain the GB distributions over misorientation angles (Fig. 8). It can be seen that with strain increasing the proportion of low-angle GBs decreases, while that of high-angle GBs increases.
Histograms of GBs distribution over misorientation angles in Ni after HPT by 0.5 (a), 1 (b), 3 (c) and 5 (d) revolutions.
Based on the X-ray diffraction analysis, parameters of fine structure in Ni after HPT were determined (Table 3). With strain increasing, the microstrains increase from 0.0011 for samples deformed by 0.5 rev. to 0.0017 for samples deformed by 5 revs.
Our previous studies have shown that diffusion coefficients of Co along grain boundaries of UFG Ni processed by HPT are several orders of magnitude higher than the diffusion coefficients along relaxed GBs of coarse-grained Ni.85,86) This allows us to conclude that the grain boundaries in HPT-processed UFG Ni are in the nonequilibrium (deformation-modified) state.
In order to assess quantitatively the degree of deviation of GBs in HPT-processed Ni from the equilibrium state, the relative energy of GBs was studied by the method of etching grooves. Figure 9 shows histograms of the GB distribution over relative energies, and Table 4 shows the average relative energies of GBs (γrel) of a coarse-grained sample and samples processed by HPT.
Histograms of GBs distribution over relative energies in Ni after HPT by 0.5 (a), 1 (b), 3 (c) and 5 (d) revolutions.
As seen in Fig. 9, the relative energies of GBs in HPT-processed Ni are in a fairly wide range, and with strain increasing the fraction of boundaries with high relative energies increases. It is obvious that the average relative GB energy of samples processed by HPT increases with strain increasing, and in the entire strain range studied it is much higher than the relative GB energy of a coarse-grained sample with conventional relaxed high-angle boundaries.
A certain contribution to the increase in the relative energy of grain boundaries could be made by an increase in the fraction of high-angle GBs of higher energy. However, the results obtained in Ref. 77) show that in the annealed materials that do not contain nonequilibrium GBs, the relative energy of GBs does not exceed 0.6. However, in the case under consideration, significant fractions of GBs have relative energies higher than 0.6, especially after higher deformations. This indicates that GBs in SPD-processed Ni are in a nonequilibrium (deformation-modified) state.
As noted in the Introduction, according to some authors, nonequilibrium grain boundaries are responsible for the enhanced properties of materials processed by SPD, which exceed the properties expected only due to grain refinement.2–5) However, no direct evidence of this has yet been obtained. One of the goals of this study was to assess the effect of nonequilibrium GBs on the properties of SPD-processed materials by an example of Ni processed by HPT.
To assess the contribution to strengthening from grain refinement under the SPD, the Hall-Petch dependence of microhardness on the square root of the average crystallite size has been plotted (Fig. 10). It includes, along with the results obtained in this work, the data from other studies. Here we present the results not only for samples in the state after SPD, but also after SPD and subsequent annealing, as well as the results for samples obtained by other methods (electrodeposition, rolling, etc.). It can be seen that for grain sizes up to ∼50 nm, the dependence of microhardness on d−1/2 is close to linear. A similar dependence was obtained in Ref. 69). This shows that for pure nickel, the main strengthening factor is grain refinement.
Microhardness versus grain sizes in Ni processed by various techniques.
According to Ref. 2), nonequilibrium GBs contribute to strengthening through long-range fields of elastic stresses. In the case under consideration, this contribution can be estimated via the values of microstresses. Taking into account the results of X-ray studies, based on which the microstrains were determined, it is possible to estimate the microstresses, multiplying the value of microstrains by the elastic modulus, which is 206.8 GPa for Ni.89) This estimate shows that the value of microstresses in HPT-processed nickel varies from 0.23 GPa for a sample deformed by 0.5 rev. to 0.35 for a sample deformed by 5 revs. Since dislocations make a certain contribution to microstrains, the contribution to strengthening from nonequilibrium grain boundaries will be even smaller.
Thus, the present study shows that under the severe plastic deformation nonequilibrium grain boundaries are formed in Ni, which have an increased energy and are the paths of ultrafast diffusion. However, they make a relatively small contribution to the overall strengthening. The main contribution to strengthening of Ni processed by SPD comes from grain refinement.
By an example of nickel, the possibility of obtaining nanostructured materials with special properties by such methods of severe plastic deformation as high-pressure torsion, equal-channel angular pressing and dynamic channel-angular pressing is discussed.
It is shown that under all these SPD modes, grain boundaries in Ni acquire the specific deformation-modified state, which is characterized by excess free energy, and larger free volume compared to conventional relaxed high-angle grain boundaries.
In nickel processed by HPT, the nonequilibrium state of GBs has been revealed by diffusion studies, electron microscopy and scanning tunneling microscopy. Deformation-modified boundaries have increased energy and significantly higher coefficients of grain boundary diffusion.
The contribution of the nonequilibrium state of GBs to strengthening has been estimated. It is shown that it is relatively small, and the main contribution to the strengthening of Ni subjected to SPD comes from grain refinement.
The authors are thankful to I.V. Blinov and A.Yu. Istomina for their help in tunneling microscopy studies.
The research was carried out within the State Assignment of Russian Federation on themes “Pressure” and “Function” and supported in part by the RFBR (project No. 20-32-90100).
