Ultra-fast diffusion channels in pure Ni severely deformed by equal-channel angular pressing

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Acta Materialia 59 (2011) 1974–1985 www.elsevier.com/locate/actamat

Ultra-fast diffusion channels in pure Ni severely deformed by equal-channel angular pressing Sergiy V. Divinski a,⇑, Gerrit Reglitz a, Harald Ro¨sner a, Yuri Estrin b,c, Gerhard Wilde a b

a Institute of Materials Physics, Westfa¨lische-Wilhelms University of Mu¨nster, Wilhelm-Klemm-Str. 10, 48149 Mu¨nster, Germany ARC Centre of Excellence for Design in Light Metals, Department of Materials Engineering, Monash University, Clayton, Australia c CSIRO Division of Process Science and Engineering, Clayton South, Australia

Received 27 September 2010; received in revised form 23 November 2010; accepted 26 November 2010 Available online 10 January 2011

Abstract Grain boundary self-diffusion in Ni severely deformed by equal-channel angular pressing has been investigated. The radiotracer technique was applied by using the 63Ni isotope and high-precision mechanical grinding. Ultra-fast diffusion rates, which exceed those along general high-angle grain boundaries in annealed coarse-grained Ni by orders of magnitude, were observed. Such high diffusivities were attributed to a non-equilibrium state of grain boundaries produced by severe plastic deformation. A significant downward deviation from an Arrhenius plot for ultra-fast diffusivity for temperatures above 400 K was found. This was interpreted in terms of a partial relaxation of the non-equilibrium grain boundary structure. Additionally, the formation of ultra-fast diffusion channels, presumably in the form of percolating porosity as a result of stepwise annealing of the material, was observed. This phenomenon is discussed in terms of the free volume redistribution in grain boundaries. It is proposed to quantify the excess energy of interfaces in terms of the observed enhancement of diffusivity. This approach allows the excess energy of non-equilibrium grain boundaries to be determined from diffusion measurements. Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Nickel; Severe plastic deformation (SPD); Grain boundary diffusion; Non-equilibrium defects

1. Introduction Many attractive properties of ultra-fine-grained (UFG) materials prepared by different methods of severe plastic deformation (SPD) [1–3] have been claimed to be the result of a special state of the interfaces [2,4]. The term “nonequilibrium” grain boundaries (GBs) was introduced in order to differentiate between interfaces in annealed polycrystals (which are in a metastable equilibrium) and those in severely deformed polycrystals [5,6]. The degree of “non-equilibrium” was proposed to be quantified in terms of the density of specific arrays of so-called extrinsic GB ⇑ Corresponding author.

E-mail addresses: [email protected] (S.V. Divinski), gerrit.reglitz @uni-muenster.de (G. Reglitz), [email protected] (H. Ro¨sner), [email protected] (Y. Estrin), [email protected] (G. Wilde).

dislocations (EGBDs) [7]. Such non-equilibrium GBs are assumed to contain a higher excess volume and presumably possess a larger excess free energy and exhibit enhanced diffusivities [7,8]. Diffusion measurements conducted systematically on UFG pure Cu and Cu-based alloys prepared by equalchannel angular pressing (ECAP) revealed the existence of ultra-fast diffusion paths [9–11]. However, the measured ultra-fast diffusivities were significantly influenced by the presence of microcracks and porosity-related channels that had formed during severe straining of pure Cu and Cu-rich alloys [12,13]. Even percolating porosity was found to form in UFG Cu–1 wt.% Pb alloy [10]. This porosity represents the fastest path for atomic transport in those materials and interferes with a reliable determination of the diffusion properties of non-equilibrium GBs. Our goal was to investigate the kinetic properties of GBs in severely deformed materials without interference of the

1359-6454/$36.00 Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2010.11.063

S.V. Divinski et al. / Acta Materialia 59 (2011) 1974–1985

1975

Table 1 Impurity concentrations (wt ppm) in the investigated Ni material. Al

Co

Cr

Cu

Fe

Mn

Mg

P

Si

S

Ti

Zn

70

100

15

380

350

1100

20

30

170

–

30

4

deformation-induced porosity. Nickel is a good candidate for such a study owing to its higher melting point, larger stacking fault energy, and a greater work-hardening rate in comparison to Cu. As a result, room temperature deformation of Ni will proceed at a lower homologous temperature T/Tm, where Tm is the melting temperature. This should have an inhibiting effect on dynamic recovery processes. Diffusion in ECAP-processed Ni has been studied by Kolobov et al. using natural Cu as a tracer and applying depth profiling by secondary ion mass spectroscopy (SIMS) [14]. In that investigation, diffusion anneals were performed at temperatures which involved a significant grain growth during diffusion annealing of initially UFG Ni. A correct description of diffusion in a metastable microstructure (undergoing recrystallization and/or grain growth) is challenging, but not impossible, as was demonstrated recently [15–17]. However, rigorous diffusion studies on materials with a stable microstructure are preferred. To our knowledge, the kinetic properties of non-equilibrium GBs produced by SPD have never previously been examined. In the present paper, the radiotracer technique using the isotope 63Ni was applied in order to investigate GB selfdiffusion in SPD-processed pure Ni. For the measurements, a temperature interval was chosen in which no grain growth or recrystallization of UFG Ni occurred. 2. Experimental details 2.1. Sample preparation Coarse-grained Ni with a nominal purity of 99.6% was used. The results of the chemical analysis are shown in Table 1. UFG Ni was produced by ECAP using the so-called Route BC4 [18]. The details of the deformation procedure are given elsewhere [10]. Four ECAP passes were

performed on a Ni rod 10 mm in diameter at room temperature with a deformation rate of 5 mm s1. No back-pressure was applied. The microstructure was examined by transmission electron microscopy (TEM) using a Zeiss Libra 200FE fieldemission microscope. In Fig. 1a an example micrograph (bright-field) of the as-prepared UFG microstructure is shown. The produced microstructure is typical for ECAP or high-pressure torsion (HPT) deformation of Ni material of this purity level [19–22]. The dark contrast inside the grains indicates a significant concentration of deformation-induced dislocations. The average grain size, d, was estimated to be about 300 nm. The UFG microstructure remains practically unchanged after annealing at T = 700 K for 17 h (Fig. 1b). This observation agrees well with recent findings of Hansen and co-workers [22] who showed that the UFG microstructure of ECAP-deformed Ni of a similar 99.5 wt.% purity was stable against recrystallization/grain growth up to 623 K. Therefore, all diffusion measurements performed in the present study at T < 500 K are deemed to have been carried out on UFG Ni with a stable microstructure, which is important for the subsequent analysis of the diffusion profiles. After the deformation, samples (10 mm in diameter and 2 mm thick) were cut by spark erosion for the diffusion measurements. Prior to the measurements, the samples were stored in a refrigerator (18 °C) to minimize roomtemperature relaxation effects. For the radiotracer experiments, the samples were ground and polished by standard metallographic methods to a mirror finish. 2.2. Radiotracer measurements The radiotracer 63Ni (half-life 100 a) was purchased from Du Pont NEN in the form of a chloride solution. The original solution was diluted with double-distilled water to obtain the specific activity of about 1 kBq ll1;

Fig. 1. Typical microstructure of ECAP-processed Ni in as-prepared state (a) and after annealing at 700 K for 17 h (b).

S.V. Divinski et al. / Acta Materialia 59 (2011) 1974–1985

about 20 ll of this tracer solution was then dropped on the polished surface of the sample and allowed to dry. The samples were wrapped in Ni foil, sealed in silica tubes in a purified (5N) Ar atmosphere and subjected to the specified diffusion anneals. The temperatures were measured and controlled with a Ni–NiCr thermocouple with an accuracy of about ±1 K. After the diffusion anneals a surface layer (at least 1 mm thick) of a sample was removed to eliminate possible effects of surface and/or radial diffusion. The penetration profiles were determined by parallel mechanical sectioning using a precision parallel grinder and a microbalance. The mass difference before and after the grinding was used to calculate the thickness of the different sections. The radioactivity of each section was determined by measuring the intensity of the radioactive decay of 63Ni in a liquid-scintillation counter (TRI CARB 2500 TR). The time was chosen so that the statistical error of the counting rate was less than 2%. The penetration profiles represent the relative specific activity (the count rate per section mass) plotted against the depth and allow the determination of the GB diffusivity. The temperatures for diffusion annealing were chosen to be sufficiently low so that bulk diffusion could be completely neglected. The estimated uncertainty in the deduced diffusivity values did not exceed 20%. 2.3. Calorimetric measurements Calorimetric measurements were performed by differential scanning calorimetry (Diamond DSC, PerkinElmer, USA) under an Ar atmosphere. A set of DSC scans was recorded in the temperature interval from 323 to 723 K for different heating rates ranging from 5 to 80 K min1. The sample weights were in the range of 130–160 mg. For each sample, three identical DSC runs were carried out. The second run was used as a baseline, which was then subtracted from the first run to obtain only the irreversible part of the heat flow signal. It was found that, within experimental error, the second and third scans yield nearly identical data plots. This fact suggests that the differential heat flux corresponds to irreversible processes which are completed during the first run. 3. Results and discussion 3.1. Diffusion in as-prepared UFG Ni The diffusion experiments were performed in a temperature interval from 331 to 500 K by strictly keeping the conditions of the Harisson C-type [23] kinetic regime. In the present case of self-diffusion, the GB diffusion parameter, a, is defined as: d a  pffiffiffiffiffiffiffi ; 2 Dv t

ð1Þ

and a  1 corresponds to the C regime kinetics [24]. Here Dv is the bulk diffusion coefficient, d the diffusional grain

Table 2 Experimental parameters of 63Ni radiotracer GB diffusion experiments in UFG Ni. a is calculated according to Eq. (1) and s is the relaxation time of an array of extrinsic GB dislocations after Nazarov [33] (Eq. (4)). T (K)

Dgb (m2/s)

t (s)

19

7

1.82  10 2.16  106 2.16  106 2.59  105 2.59  105 2.59  105

331 350 373 400 440 500

3.13  10 8.88  1019 3.77  1018 2.21  1017 5.03  1017 1.74  1016

s (s)

a 5.2  9.6  5.1  7.1  1.6  1.7 

10

2.15  1010 9.30  108 9.21  107 4.46  106 1.51  104 2.62  103

10 109 108 107 106 104

boundary width and t the annealing time. For estimations, the bulk self-diffusion coefficient of Ni, Dv, was taken from the work of Maier et al. [25]. The relevant parameters of the diffusion annealing experiments are listed in Table 2. The relation a  1 is valid for all experiments made. As a result, the tracer penetration is governed solely by short-circuit diffusion paths. Accordingly, the Gaussian-type solution of the relevant diffusion problem may be expected to be valid. The corresponding depth profiles, i.e. the relative layer activity, c, vs. the depth squared, x2, are shown in Fig. 2. Reliable measurements of small amounts of tracer atoms distributed over short-circuit diffusion paths impose severe limitations on the sectioning procedure. A typical profile includes several high-activity near-surface points related to the remnant radioactivity at the outer surface followed by a sudden drop in the radioactivity over several (usually three or four) orders of magnitude. Only then x (μm) 0

5

10

15 500 K 440 K 400 K 373 K

relative specific activity (arb. units)

1976

350 K 331 K

0

5

10

15

20

x2 (10-11 m2) Fig. 2. Penetration profiles of GB self-diffusion in ECAP-processed Ni. x is the penetration depth. The lines represent linear fits according to Eq. (2).

S.V. Divinski et al. / Acta Materialia 59 (2011) 1974–1985

T (K) -15

10

500

400

300

-16

Dgb (m2s -1)

10

-17

10

1977

GB diffusion in coarse grained Ni; (ii) a noticeable deviation from the otherwise linear Arrhenius-type temperature dependence is observed at the two highest temperatures (450 and 500 K). In the temperature interval from 330 to 400 K, where the short-circuit diffusion in ECAP-processed Ni can be described by the Arrhenius law, the following relation holds:   8 Dgb ¼ 1:2þ4:8 1:0  10   ð67  5Þ kJ=mol  exp  ð3Þ m2 =s; RT where R and T are the gas constant and the absolute temperature, respectively. 3.2. Diffusion properties of non-equilibrium GBs

-18

10

-19

10

2.0

3.0

2.5

T

-1

-3

-1

(10 K )

Fig. 3. The temperature dependence of measured diffusion coefficients of 63 Ni in ECAP-processed Ni (symbols) in comparison with Ni self-diffusion along high-angle GBs in annealed coarse-grained Ni [26] (the dasheddotted line).

can the points of interest be reliably measured (Fig. 2). Even a slight carry-over of radioactive material into deeper layers (due to grinding-in effects) would result in artifacts. In order to be able to process profiles over five to six orders of magnitude in the tracer concentration, we carefully etched the outer surface before sectioning, thus removing the disturbing remnant radioactivity and completely suppressing any grinding-in effects. (The removed radioactivity was added to that for the first section.) Similar experiments on undeformed Ni resulted in very short profiles comprising several sections at depths below 3 lm. Therefore, one has to omit the first several points of the penetration profiles from the subsequent consideration. The irregularities in the near-surface part of the profiles, which are related to the method of sectioning used, do not affect the deduced diffusivities. In the corresponding coordinates, the deeper sections of the concentration profiles can be fitted by linear dependences and the relevant slopes were used to derive the grain boundary diffusivity, Dgb, from:  1 1 @ ln c  ; ð2Þ Dgb ¼ 4t @x2 In Fig. 3 the results of the diffusion experiments are plotted as a function of the inverse temperature, T1, and compared to the Ni GB self-diffusion rate in annealed coarsegrained Ni [26] with a grain size larger than 100 lm. Two remarkable results can be highlighted: (i) shortcircuit diffusion in UFG Ni is significantly faster than

Short-circuit diffusion in ECAP-processed Ni proceeds faster than along general high-angle GBs in coarse-grained Ni [26] by orders of magnitude1 (Fig. 3). This diffusion enhancement can hardly be attributed to a hypothetical impurity effect given the relatively low purity of the Ni material applied. To our knowledge [27], any strongly segregating impurity in face-centered cubic (fcc) metals decreases the GB diffusion rate and increases the activation enthalpy of diffusion. This would be the opposite trend to that observed experimentally. The extremely fast tracer penetration in severely deformed pure Ni is consistent with our previous results on ultra-fast transport in SPD-processed pure Cu [11,28,15] and Cu-based alloys [10,9,29]. A difference from the case of ECAP-deformed pure Cu [12] is that percolating porosity, which would lead to a deep penetration of the liquid tracer solution in the specimen even at room temperature [10], was not found in ECAP-processed Ni in the as-prepared state. This reflects the distinctly different material properties of pure Ni and Cu. The higher value of the work-hardening rate seems to play an essential role here. As recent experiments have shown [30], applying a sufficient back-pressure (a description of the technique may be found, for example, in Ref. [31]) during ECAP of pure Cu suppresses the formation of percolating porosity. During ECAP deformation, pure Ni is likely to develop a certain level of effective backpressure due to large work-hardening, which prevents the development of cracks. Internal interfaces represent the ultra-fast paths contributing to Ni transport. As mentioned in the Introduction, a specific configuration of GBs was proposed to explain such behavior in a SPD-processed material [32]. The concept of non-equilibrium arrays of extrinsic GB dislocations has been introduced [5–7] to describe the different levels of deviation from equilibrium. According to the generally accepted view on deformation-driven grain refinement, dislocation activities under SPD contribute to grain 1 Note that the general high-angle GBs present typically the fastest pathways for atomic transport in annealed polycrystals.

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S.V. Divinski et al. / Acta Materialia 59 (2011) 1974–1985

refinement and the continuous transformation of dislocation walls to small-angle GBs and finally to high-angle GBs [7]. Plastic deformation localizes at GBs, introducing “extrinsic GB dislocations” to high-angle GBs. These extrinsic dislocations are not geometrically necessary in that they do not contribute to the misorientation between the adjacent grains. Although the concept of “extrinsic GB dislocations” encounters obvious difficulties in an atomistic description of the respective DSC lattice, we will check whether this model has merit as a practicable way of describing the properties of grain boundaries in SPD materials. For that, we shall estimate GB properties on this basis and compare them with the data derived from diffusion measurements. Since the “extrinsic GB dislocations” are non-equilibrium defects, they will relax by dislocation climb and partially annihilate at elevated temperatures. The relaxation time s of an array of random extrinsic GB dislocations can be estimated as [33]: s¼

kTd 3 ; AdDrel gb GX

ð4Þ

where d is the average grain size, k is the Boltzmann constant, G the shear modulus, X the atomic volume and Drel gb the self-diffusion coefficient for relaxed grain boundaries. The parameter A is a geometrical factor. The first models of spreading of single GB dislocations suggested that A  1 [34,35,5]. More extensive calculations by Nazarov et al. [32,33] for severely deformed materials, which presumably contain a high density of extrinsic GB dislocations, yielded values of A between 100 and 500, depending on the specific disclination model of UFG materials used [32]. In the following, a value of A = 200 will be assumed as a reasonable compromise for the present order-of-magnitude estimations. The grain boundary self-diffusion coefficient in (relaxed) general high-angle GBs of Ni is taken from our previous work [26],   128 kJ=mol 5 rel Dgb ¼ 1:76  10 exp  ð5Þ m2 =s: RT Furthermore, from our previous radiotracer diffusion measurements on coarse-grained Ni we have determined the diffusional GB width, d = 0.5 nm [26]. Note that this value is typically observed for pure fcc metals [27]. Using the material parameters of Ni (G = 76 GPa and X  ˚ 3), we have estimated the relaxation time of the 10.9 A non-equilibrium state of the grain boundaries. Table 2 lists the values of the calculated relaxation time, s. Table 2 indicates that at lower temperatures, T 6 400 K, the relaxation time of an array of the extrinsic GB dislocations is significantly larger than the annealing times used in the experiments, s  t. At T  400 K these parameters have a similar order of magnitude, while s  t holds for higher temperatures. Astonishingly, the measured diffusivities start to deviate from the otherwise linear Arrhenius

temperature dependence almost exactly at this temperature of 400 K (Fig. 3). One may conclude that the present experimental data support the validity of this model approach developed by a number of researchers (e.g. [7,33,36]). A note is due here. If the concept of extrinsic GB dislocations was applied to SPD-processed pure Cu, Eq. (4) would predict a corresponding relaxation time of the order of several hours at room temperature, and thus the contribution of non-equilibrium GBs would hardly be measurable in the as-prepared state. This conclusion is consistent with enhanced relaxation processes observed in UFG Cu at room temperature [37,38]. Using the model of Nazarov et al. [7,32], several further estimates can be made. As mentioned in the Introduction, the extrinsic GB dislocations raise the excess GB energy, cgb. After Nazarov and co-workers [7,32], this increase in energy, Dcgb, is proportional to the density of the extrinsic GB dislocations, q0: Dcgb ¼

Gb2 q0 d ln : 4pð1  mÞ b

ð6Þ

Here b is the magnitude of the Burgers vector of GB dislocations (taken here as half of the lattice constant) and m is the Poisson ratio. By using Eq. (6), the value of q0 can now be estimated if the increase of the excess GB energy, Dcgb, can independently be determined. Based on the present diffusion data, the corresponding excess energies can be estimated within the semi-phenomenological approach of Borisov et al. [39]. Gupta [40] has proposed a useful relation, which allows the determination of the excess GB energy cgb in terms of the increase in the mobility of matrix atoms in GBs with respect to that of bulk atoms. Expressed through the ratio of the respective diffusivities, this relation translates to:   kT Dgb cgb ¼ 2 ln : ð7Þ 2a0 Dv In this equation a0 is the lattice parameter. Here Dgb and Dv represent the self-diffusivities in GBs and the bulk, respectively. The main assumptions and limitations of the model were analyzed in Ref. [40,26]. We propose to use the expression given by Eq. (7) as a generalized definition of the grain boundary energy, regardless of whether or not the grain boundary is in a (metastable) equilibrium. This definition is only valid if the relaxation time for a given grain boundary state is much longer than the diffusion measurement time at the respective temperature. Time independence of the diffusion coefficient provides an Table 3 The excess GB energy in annealed (relaxed, “rel”) polycrystalline Ni [26], crel gb , and in ECAP-processed (non-equilibrium, “ne”) Ni, cne gb , at room temperature. T (K)

2 crel gb (J/m )

2 cne gb (J/m )

300

0.98

1.27

S.V. Divinski et al. / Acta Materialia 59 (2011) 1974–1985

(a)

1979

(b) 0.08 0.06

Shear strain

0.04 0.02 0.00 -0.02 -0.04 -0.06 -0.08 0

2

4 6 Position (nm)

8

Fig. 4. (a) Strain mapping showing the shear strain component xy. “Hot spots” refer to dislocation cores. For more details see Ref. [30]. (b) Strain profile across the GB as indicated by the box in (a). The “zipper-like” structure is revealed as a regular variation of the shear strain with an average shear strain of 4%.

experimental proof that this condition was fulfilled in our experiment. The above definition of the excess GB energy is applied here for ECAP-processed Ni. Table 3 represents the results of the calculation of cgb for relaxed high-angle GBs in coarse-grained Ni [26], crel gb , and for the interfaces providing ultra-fast diffusion paths at T < 400 K in UFG Ni, cne gb . The energies are referred to room temperature. It is seen that the “non-equilibrium” GBs exhibit excess interface energies that are about 30% higher than the corresponding values for GBs in relaxed coarse-grained Ni, 2 rel Dcgb ¼ cne gb  cgb ¼ 0:29 J m . Assuming that this surplus of the excess energy is related to the existence of extrinsic GB dislocations, their density, q0, is estimated at about 5  107 m1, cf. Eq. (6). Alongside the excess GB energy, the extrinsic GB dislocations give rise to a strain, , and an extra excess free volume, DV/V [7]: rffiffiffiffiffiffiffiffiffiffiffiffiffiffi q0 d  ¼ 0:23b ln ð8Þ b d and f¼

DV 2:12b2 q0 d  C ln V b d

ð9Þ

(here the dimensionless parameter C equals 0.2 for edge dislocations in Ni [7,41]). Substituting the numbers, reasonable estimates for both quantities are obtained, i.e.   2  103 and f = 4  105. Note that this is a lower bound estimate of the root mean square of strains in UFG Ni. After Nazarov [32], contributions of junction dislinations and gliding extrinsic GB dislocations have to be added to that of the random extrinsic GB dislocations considered above. Such an analysis is beyond the scope of the present paper. Estimates in Ref. [42], however, indicate that the random extrinsic GB dislocations provide the largest contribution to the excess interface energy. Below, we will compare these predictions of the phenomenological model due to Nazarov [32,33] for ECAP Ni with independent experimental measurements.

3.3. Strains in SPD materials The so-called geometric phase analysis (GPA) is a new powerful method which allows strain mapping using the data of high-resolution TEM [43]. This approach was previously applied to UFG Cu [44] and nanocrystalline Pd [45]. The main difficulty is to find a grain boundary with adjacent grains belonging to a zone axis so that atomic coordinates can be resolved (researcher’s luck is required). Our attempts with ECAP Ni have so far been unsuccessful. We have been more successful in applying the GPA method to a ultrafine-grained (average grain size of about 150 nm) Pd90Ag10 alloy severely deformed by repeated cold rolling [30], and it appears appropriate to mention the results here. Presumably “non-equilibrium” GBs exhibited a “zipper-like” structure (see Fig. 4a) and an enlarged GB width of about 1.6 nm (Fig. 4b) with an average strain of about 4% calculated for the selected area in Fig. 4a. The above value of the GB width determined for the severely deformed Pd90Ag10 alloy is 2–3 times larger than the structural GB width [45].2 The GPA method revealed individual dislocation cores in the grain interior. However, GB defects, which may be considered as (still hypothetical) individual extrinsic GB dislocations, could not be identified in Pd90Ag10 [30]. The strain level in nanocrystalline Pd90Ag10 (4%) is larger than that in ECAP Ni (0.2%), which may be related to the smaller grain size and the higher total strain impacted on the former by cold rolling. The present analysis of the strain level in ECAP Ni seems to yield reasonable estimates. It is instructive to compare the above estimates of dislocation densities calculated from the present diffusion data

2 Strictly speaking, it was the width of interphase boundary that was measured in Ref. [45] for the Al–Pb system. One may expect, however, that the width of a relaxed interphase boundary is somewhat larger than that of an intergranular boundary.

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S.V. Divinski et al. / Acta Materialia 59 (2011) 1974–1985

by Nazarov’s approach with direct experimental measurements. It is important to note that Nazarov’s model treats extrinsic GB dislocations, while X-ray diffraction (XRD) or TEM measurements provide densities of bulk dislocations, i.e. densities of forest dislocations, dislocations in cell walls, etc. It is therefore not easy to compare those quantities directly. The determined linear density of EGBDs, q0 = 5  107 m1, corresponds to an average distance of 20 nm between these defects. According to the GPA analysis, grain boundaries in SPD-processed Pd–Ag alloy are rather wide, having a thickness of about 1.4–2 nm (Fig. 4b). Combining these numbers, the corresponding dislocation density (in terms of dislocation line length per unit volume) would be about 1016 m2 in the GB area. Note that, based on XRD measurements, values as high as 1015–1016 m2 were reported for the lattice dislocation density in nanostructured Ni, processed by HPT [46,47]. The sample-average dislocation density can be estimated pffiffiffiffiffi as 3 q0 =d (the numerical factor depends on the assumption about the grain shape, but the order of magnitude of the estimate is not sensitive to that assumption). From such a simplified analysis, a value of about 5  1014 m2 follows for the average dislocation density. Bulk densities of dislocations of about 1014–1015 m2 were typically reported for ECAP-processed Ni [48]. Therefore, the present estimates are not unreasonable. However, we have to emphasize that the extrinsic GB dislocations are still notional objects and we cannot associate them with specific features in, for example, high-resolution (HR) TEM images. Dislocation cores are clearly visible in the near vicinity of GBs in filtered images after GPA analysis of an SPD-processed PdAg alloy (Fig. 4a)—they are represented by the “hot spots” where elastic theory breaks down—but the average distance between these dislocations is about 1–2 nm. The corresponding linear density of the defects corresponds to 5 10 8–109 m1, which is at least one order of magnitude larger than the values which follow from our analysis. The

3.4. Annealing behavior of defects in ECAP-deformed Ni The recovery of defects in ECAP-processed Ni was examined by DSC measurements. A typical heat flux curve is plotted in Fig. 5a as a function of temperature for the heating rate of 20 K min1. The heat flux can reasonably be deconvoluted into three contributions. The DSC experiments were performed with different heating rates b to investigate the temperature dependence of the signals and to evaluate the activation enthalpies for the three processes. The result of the Kissinger analysis [50] of the low-temperature peak, i.e. the plot of lnðbT 2p Þ vs. T 1 p , is presented in Fig. 5b. Here Tp is the absolute temperature of the respective maximum in the heat flux vs. temperature diagram and b is the heating rate. The activation enthalpy is determined in this way from the slope of the diagrams in Fig. 5b. According to Zehetbauer and co-workers [51], the low-temperature peak (around 450 K) results from the annihilation of deformation-induced vacancies in severely deformed Ni. As follows from Fig. 5b, the activation

(b)

1

-8

0 -9 2

ln (β /Tp )

-1 -2 -3

-10

exo

Normalized Heat Flux (mW/g)

(a)

higher dislocation density on the Pd–Ag alloy processed by repeated cold rolling as compared to ECAP-deformed Ni can be explained by the significantly larger total strain in the former. Eq. (8) yields the value of 0.2%, which fits well the literature values of the root mean square strain measured, for example, for electrolytically deposited Ni (about 0.4% [49]) or ECAP Ni (from 0.5% to 1% [42]). In the SPD-processed Pd–Ag alloy, the average strain is about 4% in the close vicinity of the GB (the area between the vertical dashed lines in Fig. 4b) and about 0.2% for the total area within the dashed box in Fig. 4a. Although the agreement is not fully satisfactory, it is still quite encouraging, as the GPA analysis yields a local value for a small region inspected by HRTEM, whereas XRD provides averaging over much larger areas.

-4 -11

-5 400

450

500

T (K)

550

600

21.5

22

22.5

T

-1

23

23.5

(10-4 K-1)

Fig. 5. A DSC run with a heating rate of 20 K min1 of ECAP Ni sample (a). Three contributions to the total heat flux can be distinguished (dashed lines). The Kissinger analysis [50] of the low-temperature peak is presented in (b).

S.V. Divinski et al. / Acta Materialia 59 (2011) 1974–1985

enthalpy of vacancy annealing is about 96 ± 20 kJ mol1. This value represents the migration enthalpy of deformation-induced vacancies and within the experimental uncertainties is quite close to the independently measured activation enthalpy of Ni self-diffusion in “non-equilibrium” GBs (Eq. (3)). This agreement supports the present interpretation of the first annealing peak on DSC diagrams in terms of annealing of GB vacancy-like defects, and implies that the vacancy supersaturation induced by ECAP processing is retained in the material, especially at interfaces. A few further arguments support this conclusion. The vacancy migration energy in the crystall bulk is about 1.04 eV [52] to 1.18 eV [53] for Ni and the value of 0.7 eV can be accepted for that along high-angle GBs according to Eq. (3). Simple estimates show that a Ni vacancy moves less than several tens of nanometers in the bulk and by several micrometers along GBs during a typical DSC run. In view of the high dislocation density, the bulk vacancies are effectively trapped by those sinks and only a fraction of them contribute to free volume redistribution at GBs. By combining Eqs. (3) and (5) the formation energy of vacancies in Ni high-angle GBs can be estimated as 0.6 eV. Note that the vacancy formation energy in the crystal lattice of pure Ni is in the range of 1.60 eV [54] to 1.79 eV [55], and thus the effective vacancy formation energy in high-angle GBs of Ni amounts to about 30% of those values. The total energy release for the vacancy-related peak during a DSC run was determined to be 5 ± 2 mJ g1. Accordingly, the concentration of removed vacancy-like GB defects can be estimated as 6  106. Taking into account that the vacancy formation volume in the crystal lattice of Ni is about 0.8 X [55] and assuming a similar value for vacancies in GBs, the related free volume, fv, which gets healed in the UFG Ni during continuous heating to 723 K, has a value of about fv = 5  106. The absence of grain growth in the UFG material in the present conditions supports the validity of the estimates. The removed free volume related to the GB vacancies amounts to about 10% of the total free volume f predicted by the extrinsic GB dislocation model (Eq. (9)). This discrepancy casts certain doubts on the validity of Nazarov’s model. This is a delicate situation. The model of extrinsic GB dislocations [7,33] does provide a phenomenological description of the non-equilibrium state of GBs in SPDprocessed metals, giving reasonable estimates for the introduced strains and the relaxation time. The relaxation behavior, however, is not properly represented by this approach. The present results strongly suggest the existence of a specific relaxation mode transforming the deformation-induced non-equilibrium boundaries into a different non-equilibrium state. The latter still exhibits enhanced diffusivity with respect to a fully relaxed high-angle GB (Fig. 3). Note that the excess free volume related to vacancy-like defects, estimated both according to the DSC results (fv) or Nazarov’s model [33] (f), is significantly smaller than the free volume introduced by high-angle GBs in the UFG

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matrix, fgb. The latter can be estimated as fgb  (3d/d)  k, where 3d/d represents the volume fraction of GBs in the material and k is the volume expansion coefficient of the GB [57]. Using the value of k = 0.1 [57], the above relation gives fgb = 5  104. This value is significantly larger than f and fv. This observation leads us to conclude that in terms of the total excess free volume, the non-equilibrium state of interfaces is characterized by a surplus of about 10%. The other two peaks in Fig. 5a are probably related to annealing of vacancy agglomerates and dislocations as found by Zehetbauer and co-workers for UFG Ni (99.998 wt.% purity) processed by HPT [51,46]. Whereas these two peaks could not be separated in [51], they are clearly discernible in the present analysis. However, the detailed discussion of the nature and properties of these peaks is beyond the scope of the present study. 3.5. GB structures in ECAP Ni As stated above, the EGBD model of the non-equilibrium state of interfaces in SPD-processed materials [7,33] seems to provide reasonable estimates for ECAP-deformed Ni at T < 400 K. However, there are serious drawbacks in this model too. According to Nazarov and co-workers [7,33], after relaxation of EGBDs, the “non-equilibrium” structure transforms to a (metastable) equilibrium. Since the general high-angle GBs in relaxed polycrystalline metals represent the fastest diffusion paths, at T > 440 K the diffusion coefficients should decrease to the dashed-dotted line in Fig. 3. Instead, the GB diffusivities in UFG Ni exceed those in a relaxed coarse-grained polycrystal by one to two orders of magnitude, Fig. 3. In Fig. 6, TEM images (bright-field) of typical GBs (presumably high-angle GBs) are shown for three different states: as-prepared (a), after annealing at T = 400 K for 17 h (b) and after annealing at T = 700 K for 3 days (c). A detailed analysis of the GB structures requires atomistic resolution and it will be published elsewhere. Here we will highlight the main qualitative findings. A majority of general GBs in UFG Ni after ECAP deformation exhibit a “zipper-like” structure and a wavy character, indicating a high density of incorporated defects and residual stress– strain fields (Fig. 6a). This observation is in agreement with the study of Zhilyaev et al. [58] on UFG Ni produced by ECAP or HPT, and that of Horita et al. [20] on an Al alloy as well as with our investigation of GBs in SPD-processed Pd90Ag10 alloy (Fig. 4a). An annealing treatment at T = 400 K results in a partial recovery of such defects, although many GBs still show the “zipper” contrast (Fig. 6b). Such features are almost completely absent after annealing at T = 700 K (Fig. 6c). The GBs are straight at small scales. The dark contrast in the grain interior indicates that the residual stresses are not completely removed even after this annealing treatment. The diffusion data suggest a “non-equilibrium” state of GBs in UFG Ni observed after severe deformation. This

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Fig. 6. Typical GB structures in UFG Ni in the as-prepared state (a) and after annealing treatments at 400 K for 3 days (b) and at 700 K for 17 h (c).

state is relaxed at T > 400 K. The majority of GBs after annealing at T P 500 K appear well relaxed, as shown in Fig. 6. However, the ultra-fast diffusivities were still found at these temperatures (Fig. 3). We conclude that the GBs preserve their “non-equilibrium” character even after these annealing treatments. However, the origin and nature of the fast diffusion along these boundaries are fundamentally different from those in the as-prepared state, which calls for a detailed examination. A remark is due here. We emphasize that we are not claiming any direct relationship between any particular GB (observed by TEM, Fig. 6) and the determined GB diffusivities (Fig. 3). The TEM study is a local technique, whereas an integral information is delivered by a diffusion experiment. Only a qualitative correlation between the diffusion data and typical GB structures is highlighted here. 3.6. Relaxation of the “non-equilibrium” state of GBs in ECAP Ni In order to gain further insight into the relaxation behavior of the “non-equilibrium” grain boundaries, the diffusion experiments were repeated after an additional pre-annealing treatment of the samples. The parameters of the heat treatment (T pa1 and tpa1 ) and the results of the diffusion experiments are listed in Table 4. It should be emphasized that the same samples were repeatedly used for these diffusion experiments. The diffusion coefficients determined are shown in Fig. 7 (squares). The preliminary heat treatment (T pa1 , tpa1 ) results in a sigð1Þ nificant decrease in the GB diffusivity, Dgb . This finding seems to be consistent with an expected trend, i.e. a further relaxation of the “non-equilibrium” state of GBs. A relaxation of the SPD-induced non-equilibrium state of GBs in ECAP Ni at T = 423 K after preliminary annealing of the material at T = 523 K has been reported by Kolobov et al. [56]. A significant decrease in the GB diffusivity, by four orders of magnitude, has been observed. However, in the present case the GB diffusivities do not decrease to the level which would be expected for annealed coarse-grained Ni. This circumstance suggested such experiments should be repeated, though with pre-annealing at even higher temperatures. The parameters of the second heat treatment of the samples (T pa2 and tpa2 ) and the results

Table 4 Experimental parameters of 63Ni radiotracer GB diffusion experiments in UFG Ni. The diffusion annealing treatments were performed at three different temperatures T and for a constant time t = 259,200 s. The samples were preliminarily annealed at T pa1 for a time tpa1 and the ð1Þ corresponding diffusion coefficients, Dgb , were measured. Then the same specimens were heat treated at T pa2 and the GB diffusion experiments at corresponding temperatures (T) were repeated. The times of the preliminary heat treatments (without application of the tracer) were set equal, tpa1 ¼ tpa2 ¼ 61; 200 s. ð1Þ

ð2Þ

T (K)

T pa1 (K)

Dgb (m2/s)

T pa2 (K)

Dgb (m2/s)

400 440 500

500 500 612

6.55  1018 3.21  1017 3.06  1017

602 600 883

4.33  1017 9.33  1017 2.10  1016

ð2Þ

of the repeated diffusion experiments, Dgb , are summarized in Table 4 and in Fig. 7 (triangles). Fig. 7 shows a surprising result—the measured GB diffusivities do not decrease after the second annealing treatment, but rather increase significantly, exhibiting even higher transport rates than in the as-prepared state: ð2Þ ð1Þ Dgb > Dgb > Dgb . The enhancement of interface diffusion due to relaxation of the highly defective, “non-equilibrium” state of GBs requires an explanation. Hypothetically, the results might be explained by residual impurities which affect the interface diffusivity. As we mentioned previously, the residual impurities generally reduce the GB diffusivity in fcc metals. Simple estimates of the total volume fraction of interfaces in an UFG material suggest that the GBs in the as-deformed UFG state are more pure than in the coarse-grained state due to the smaller grain size. Grain boundary motion that may be induced by the preliminary heat treatment would result in the segregation of residual impurities due to the impurity drag effects. Therefore, the redistribution of residual impurities cannot explain the observed response of GB diffusion coefficients on the annealing treatment. It is the evolution of residual free volume and vacancylike defects which can enhance diffusion by formation of a more open structure of interfaces. The DSC analysis suggests that an appreciable amount of excess free volume is available in SPD-processed Ni. Even an interconnected porosity, as was observed in the ECAP-induced state of pure Cu and Cu-rich alloys, may be expected to form in ECAP Ni due to the heat treatment of the severely

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T (K) 10

500

400

300

-16

2 -1

Dgb (m s )

10

-15

10

-17

10

10

-18

-19

2.0

3.0

2.5 -1

-3

-1

T (10 K ) Fig. 7. Influence of a subsequent heat treatment of the samples on the GB diffusivity: direct measurements at the temperature T (circles); subsequent annealing at T pa1 and measurements at T (squares); followed by further annealing at T pa2 and measurements at T (triangles). The annealing temperatures are listed in Table 4. The dashed-dotted line represents the GB self-diffusion in annealed coarse-grained Ni [26].

deformed Ni. To check this possibility, radiotracer experiments were performed using the 110mAg tracer. With respect to the 63Ni tracer, which emits exclusively b-quanta, the 110mAg isotope also emits c-quanta, which can be detected with a high precision by c-spectroscopy methods. The following key experiments were performed: an ECAP-processed Ni sample was ground and polished as described above. Then, approximately 20 kBq of the liquid 110m Ag tracer was placed on the surface of the sample and allowed to dry. The sectioning was started without any diffusion annealing. When the sectioning was stopped (i.e. when radioactivity in a section could no longer be detected), the sample was annealed successively in the same way as described before for the experiments with the 63Ni tracer. After each heat-treatment step, the measurement with the 110mAg tracer was repeated. The resulting penetration profiles are plotted in Fig. 8. We emphasize that roomtemperature penetration of the liquid tracer solution was recorded, which was influenced by the pre-annealing history. The concentration profiles measured for penetration of the liquid tracer solution in the as-prepared state, after annealing at 500 K for 72 h (simulated diffusion annealing), and after additional annealing treatments at 600 K for 17 h and again at 500 K for 72 h (i.e. the second diffusion annealing) represent relatively short “grinding-in” profiles. They are caused by grinding-in small amounts of the radio-

Fig. 8. Concentration profiles recorded for the room-temperature penetration of liquid 110mAg tracer solution in the same Ni samples after the following sequence of heat treatments simulating the previous diffusion measurements: the as-prepared state (triangles); annealing at T = 500 K (circles); additional annealing at 600 and 500 K (squares); and finally extra annealing at 700 and 500 K (stars). The annealing times are shown in Table 4. For details see the text. The insert represents near-surface parts of the profiles. The background value for the chose counting conditions is about 5  104 Bq mg1.

isotope from the previous sections. However, the annealing step at 700 K for 17 h followed by 500 K for 72 h results in a penetration depth of over 150 lm, which is much too large to be interpreted as a grinding-in effect. Such penetration of the liquid tracer solution after application at room temperature was observed in ECAP Cu and Cu–1 wt.% Pb alloy [10,12,13]. In our previous studies we have unambiguously shown that this penetration is a “fingerprint” of percolating porosity in the material. The volume fraction of the porosity has been measured for ECAP Cu–1 wt.% Pb alloy to be about 1 ppm [10] and an order of magnitude smaller value is expected in the present case, as suggested by the corresponding values of the specific radioactivity. The formation of percolating porosity highlights the contribution of vacancy-like defects to the evolution of the “non-equilibrium” state of interfaces. The results suggest that at the present low-temperature annealing conditions, the free volume cannot migrate via grain interiors and simply gets redistributed along GBs and triple junctions. Since grains in the UFG material are subjected to additional constraints related to the residual stresses,

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the agglomerated free volume will not disappear by rigid translations of grains. It is probably the relaxation of residual stresses which initiates crack formation. Formation of cracks along triple junctions in Ni tricrystals containing a disclination defect was observed by molecular dynamics simulation [60,59]. Since disclinations are considered to represent typical defects in severely deformed metals [36], this scenario may be relevant to the formation of percolating porosity observed in the present study. It is interesting to note that the direct annealing at T > 700 K of UFG Ni, without the intermediate annealing steps described above, does not result in the formation of ultra-fast diffusion channels (presumably percolating porosity), most probably due to enhanced bulk diffusion of point defects at this temperature. A detailed model of porosity formation under the conditions described has yet to be developed.

and co-workers [32,33], which describes the “non-equilibrium” state of GBs in terms of the concept of arrays of extrinsic GB dislocations, although their occurrence has not yet been substantiated by a direct experiment. However, based on the observed relaxation behavior of the “non-equilibrium” state, serious objections against this model can be raised. The formation of ultra-fast diffusion paths as a result of relaxation of deformation-induced “non-equilibrium” GBs is observed instead. The present study highlights the importance of the excess free volume redistribution in the evolution of GB structures. A definition of the energy of non-equilibrium grain boundaries in terms of their diffusivities provides a way for quantifying the “non-equilibrium” state of interfaces in SPD-processed materials without atomistic description of the introduced defects. Acknowledgments

4. Summary and conclusions In the present paper, self-diffusion in UFG Ni (99.6 wt.% purity) prepared by ECAP was studied experimentally. The radiotracer method using the 63Ni radioisotope was applied. Ultra-fast diffusion rates were observed, especially at lower temperatures, T < 400 K. The observed ultra-fast penetration rates were attributed to a highly defective, “non-equilibrium” state of the interfaces in Ni after severe plastic deformation. The effective activation enthalpy of GB diffusion in UFG Ni at T < 400 K was found to be about 67 kJ mol1, which is almost a factor of two smaller than that for Ni diffusion along general high-angle GBs in the coarse-grained state. The high diffusion rates are believed to be related to higher excess free energies of high-angle GBs in severely deformed Ni, which are 30% larger than in the annealed coarse-grained material. A slightly higher value, about 96 ± 20 kJ mol1, was found for the activation enthalpy for recovery of vacancies by DSC, suggesting that GB self-diffusion in as-prepared UFG Ni is governed by deformation-induced vacancies or vacancy-like defects. A significant downward deviation from the expected linear Arrhenius plot for the self-diffusion rate was observed at T > 400 K. This effect is related to relaxation of the “non-equilibrium” state in UFG Ni which was carefully studied. A particular, multi-step annealing treatment of ECAP-processed Ni triggered the redistribution and annihilation of the extra free volume in the “non-equilibrium” GBs produced by the SPD process along interfaces, thus reducing the effective activation enthalpy of self-diffusion. The exceptionally high diffusivity observed in those specific experiments was associated with the formation of percolating porosity as a result of the heat treatment used. This feature can be explained by crack initiation along selected triple junctions under residual stresses, which contributes to the extra free volume. The results for as-prepared UFG Ni were found to be in a seemingly good agreement with the approach of Nazarov

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