ISSN 1063-7834, Physics of the Solid State, 2006, Vol. 48, No. 8, pp. 1425–1432. © Pleiades Publishing, Inc., 2006. Original Russian Text © V.N. Chuvil’deev, A.V. Nokhrin, E. S. Smirnova, Yu.G. Lopatin, I.M. Makarov, V.I. Kopylov, M.M. Myshlyaev, 2006, published in Fizika Tverdogo Tela, 2006, Vol. 48, No. 8, pp. 1345–1351.
METALS AND SUPERCONDUCTORS
Effect of Small Chromium Additions on the Temperature of the Onset of Recrystallization in Microcrystalline Copper Produced by Equal-Channel Angular Pressing V. N. Chuvil’deeva, A. V. Nokhrina, E. S. Smirnovaa, Yu. G. Lopatinb, I. M. Makarovb, V. I. Kopylovc, and M. M. Myshlyaevd, e a Research
Physicotechnical Institute, Lobachevskiœ Nizhni Novgorod State University, pr. Gagarina 23, korp. 3, Nizhni Novgorod, 603950 Russia e-mail:
[email protected] b Blagonravov Institute of Engineering Science, Nizhni Novgorod Branch, Russian Academy of Sciences, ul. Belinskogo 85, Nizhni Novgorod, 603024 Russia c Physicotechnical Institute, Belarussian Academy of Sciences, ul. Tskhodinskaya 4, Minsk, 220141 Belarus d Institute of Solid State Physics, Russian Academy of Sciences, Chernogolovka, Moscow oblast, 142432 Russia e Baœkov Institute of Metallurgy and Materials Science, Russian Academy of Sciences, Leninskiœ pr. 49, Moscow, 117991 Russia Received September 5, 2005; in final form, September 21, 2005
Abstract—The effect of small chromium additions on the temperature of the onset of recrystallization in microcrystalline copper produced by equal-channel angular pressing was studied. The introduction of 0.3–0.5 wt % chromium is shown to decrease this temperature by 40–60°C. The effect of chromium on the diffusion properties of grain boundaries and the temperature of the onset of recrystallization in microcrystalline copper is calculated in terms of the theory of nonequilibrium grain boundaries. The calculation results are compared with experimental data. PACS numbers: 61.43.Gt, 66.30.Jt DOI: 10.1134/S1063783406080014
1. INTRODUCTION It is known that microcrystalline (MC) metals formed via equal-channel angular pressing (ECAP) [1] have low thermal stability: the temperature of the onset of recrystallization (TOR) in them is (0.2–0.3)Tm (where Tm is the melting temperature), which is (0.1– 0.2)Tm lower than that in ordinary metals [2–7]. In particular, after 4 to 12 ECAP cycles, the TOR of commercial-purity MC copper is ~150–200°C [2, 4, 5]. A low TOR substantially restricts possible practical use of MC metals; therefore, it is a challenge to stabilize their structure [8–11]. One approach to solving the problem of increasing the stability of a grain structure in metals is through optimum alloying of a solid solution. The alloy compositions and the concentrations of alloying elements that can stabilize a structure are chosen using classical methods and the approaches described, e.g., in [8, 11, 12]. In addition, new models considering the effect of small additions of alloying elements on the diffusion properties of grain boundaries [13] and the TOR [14, 15] can also be applied.
The purpose of this work is to experimentally check the concepts developed in [13–15] and to use them to solve the problem of stabilization of the structures of MC copper and chromium bronzes. 2. EXPERIMENTAL We studied commercial-purity M1 copper and commercial BrKhr alloys subjected to multiple ECAP [1]; the compositions of the alloys were Cu–0.3 wt % Cr, Cu–0.4 wt % Cr, and Cu–0.5 wt % Cr. The total number of ECAP cycles N was ten for the Cu–Cr alloys and N = 4, 8, 12, and 16 for copper. ECAP was performed in a tool with an angle of intersection of the working and outlet channels of π/2. We used the severest ECAP conditions: a blank was rotated in each cycle by an angle of π/2 about its longitudinal axis. These conditions provide the most intense refinement of a grain structure. The strain rate was 0.4 mm/s. Before ECAP, all bronzes were solid-solution treated: they were held at 1040°C for 40 min and then water-cooled. The copper was preliminarily annealed at T = 600°C for 2 h.
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1.4
5
10 min 4
60 min
30 min 0.6
500
10 min 30 min 60 min 180 min
3
2 0.2
0
ρ, µΩ m
Hµ, MPa
1000
d, µm
1.0
100
200
0 300
1
0
100
300
500
T, °C
T, °C Fig. 1. Dependences of the microhardness and average grain size in the microcrystalline M1 copper (N = 12) on the temperature of annealing for 10, 30, and 60 min.
Fig. 2. Dependence of the electrical resistivity of the microcrystalline Cu–0.4 wt % Cr alloy (N = 10) on the temperature of isothermal annealing for 10, 30, 60, and 180 min.
The thermal stability and properties of the alloys were analyzed when samples were annealed in a furnace in air. The temperature was maintained accurate to ±2°C. After annealing, all samples were water-cooled to room temperature. All tests were carried out at room temperature. Structural studies were performed on JEM 2000EX and JEM 200CX transmission electron microscopes at accelerating voltages of 200 and 120 kV, respectively. Micrographs were taken from an area of ~10 µm2. Foils for electron-microscopic examination were prepared using a standard procedure [16]. For optical and atomic force microscopy examination, sample surfaces were prepared using the technique described in [16]. For the examination, a Neofot-32 optical microscope and a universal air Accurex-2100 atomic force microscope operating in the contact mode were used. We measured the hardness on a PMT-3 device at a load of 50 g and the electrical resistivity ρ by the standard four-point probe method [17].
temperature for the microcrystalline M1 copper (N = 12). The microhardness of the MC metal changes during annealing in three stages. As the annealing temperature increases to T1, Hµ remains constant within the limits of experimental error. At the second annealing stage (T1 < T < T2), Hµ decreases rapidly; as the annealing temperature increases further (T > T2), Hµ changes only weakly. An analysis of the data in Fig. 1 indicates that the temperature of the onset of softening coincides with the TOR in the MC copper within the limits of experimental error. Therefore, we can use microhardness data to estimate the TOR.
3. EXPERIMENTAL RESULTS 3.1. Microcrystalline M1 Copper In our series of studies [2, 4, 5] dealing with MC copper subjected to ECAP, we showed that severe plastic deformation leads to the formation of an MC structure with a grain size of 0.20–0.25 µm. Our investigation of the thermal stability of the grain structure demonstrated that the TOR of copper depends nonmonotonically on the number of ECAP cycles: as N increases from 4 to 12, the TOR increases from 110 to 180–200°C; as N increases further to 16, the TOR decreases to 150°C [4]. As an example, Fig. 1 shows the dependences of the microhardness and average grain size on the annealing
3.2. Microcrystalline Chromium Bronzes Study of the structure of the MC chromium bronzes subjected to ECAP demonstrates that severe plastic deformation produces a rather homogeneous structure with a grain size of 0.18–0.25 µm. Figure 2 shows the dependences of the electrical resistivity of the microcrystalline BrKhr-0.4 alloy on the temperature of isothermal annealing for 10, 30, 60, and 180 min. Figure 3a shows the dependences of the microhardness on the temperature of annealing for 10, 30, 60, and 180 min for the MC alloy with 0.4 wt % chromium. Figure 3b shows the dependences of the microhardness on the temperature of annealing for 1 h for the microcrystalline M1 copper (N = 12) and the MC alloys with 0.3 and 0.4 wt % chromium. The generalization of the results indicates that the dependence of the microhardness on the annealing temperature has four stages. Annealing at T < T1 ≈ 140–220°C changes the microhardness only insignificantly. Heating of the MC alloy to T1 is accompanied by a small decrease in the microhardness (~10–15% of the initial value). An increase in PHYSICS OF THE SOLID STATE
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(a) (a)
Hµ, MPa
1200
900
0.5 µm
10 min 30 min 60 min 180 min
600
0
(b)
200
400
600
T, °C 1500 (b)
Hµ, MPa
1200 1 µm 900
600
0
Fig. 4. TEM images of the microcrystalline BrKhr-0.4 (Cu– 0.4 wt % Cr) chromium bronze subjected to ECAP followed by annealing (a) at 350°C for 1 h and (b) at 350°C for 10 h.
Cu–0.4 wt % Cr Cu–0.3 wt % Cr Cu M1 200 T, °C
400
Fig. 3. (a) Dependence of the microhardness of the microcrystalline Cu–0.4 wt % Cr alloy (N = 10) on the temperature of annealing for 10, 30, 60, and 180 min and (b) dependences of the microhardness of the microcrystalline M1 copper (N = 12) and the MC chromium bronzes Cu–0.3 wt % Cr alloy (N = 10) and Cu–0.4 wt % Cr alloy (N = 10) on the temperature of annealing for 1 h.
the annealing temperature to T2 (T1 < T < T2) leads to an increase in the microhardness to values characteristic of the MC alloy subjected to ECAP. A further increase in the temperature of isothermal annealing to T2 ≈ 360– 440°C results in rapid softening of the metal to values characteristic of a standard coarse-grained state [18]. The grain growth in the microcrystalline BrKhr alloys containing 0.3–0.5 wt % Cr is anomalous (Fig. 4) and is similar to the grain growth detected in microcrystalline M1 copper in [4, 5]. As is seen from these results, annealing of the microcrystalline BrKhr alloys at temperatures above T1 is accompanied by the appearance of coarse (~1–2 µm) recrystallized grains against the background of a relatively stable MC matrix, whose average grain size is ~0.2–0.3 µm. PHYSICS OF THE SOLID STATE
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By generalizing the results of microstructural studies and microhardness measurements, we can conclude that recrystallization processes resulting in a decrease in the microhardness begin in the MC bronzes at a temperature T1 ~ 180–220°C (Fig. 3). However, the process of decomposition of a solid solution and precipitation of chromium particles, which begins under these conditions [18] and manifests itself in a decrease in the electrical resistivity (in an increase in ∆ρ (Fig. 2), increases the microhardness. It should be noted that, in the temperature range 250–350°C, the microhardness coincides with that of the MC alloys subjected to ECAP within the limits of experimental error. A further increase in the annealing temperature above T2 ≈ 350– 400°C leads to rapid softening of the metal. It is interesting that an increase in the chromium concentration in a solid solution decreases the TOR (T1) by 40–60°C and increases the T2 at which rapid softening occurs (in the temperature range 350–400°C). The values of T1 at various times of isothermal holding for the MC alloys with 0.3 and 0.4 wt % Cr are given in Table 1. The dependences of the temperatures T1 and T2 on the chromium concentration are shown in Fig. 5. Figure 6 illustrates the dependences of the temperature T1 on the time of isothermal annealing. It is seen that an increase in the time of isothermal holding from
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Table 1. Experimental and calculated temperatures of the onset of recrystallization in microcrystalline M1 copper and MC chromium bronzes Experiment Material
Annealing time, min
MC M1 (N = 12)
10 30 60 10 30 60 180 10 30 60 180
MC Cu–0.3 wt % Cr (N = 10)
MC Cu–0.4 wt % Cr (N = 10)
T r /Tm
T r /Tm
220 200 180 200 180 160 160 180 160 140 140
0.364 0.349 0.334 0.364 0.349 0.319 0.319 0.334 0.319 0.305 0.305
0.363 0.345 0.335 0.350 0.332 0.320 0.307 0.335 0.317 0.307 0.290
T1, °C
200
10 min 30 min 60 min 180 min
(b)
400 T2, °C
with 0.4 wt % Cr on the temperature of isothermal annealing for 1 h. The temperature of the onset of softening in the MC alloy (T ~ T2) is seen to correspond to the temperature of the beginning of a change in the resistivity.
In [14], we proposed a model for the TOR in pure metals. According to this model, a necessary condition for the boundary of a recrystallization center to move is a decrease in the density of dislocations distributed in this boundary to a certain threshold value, at which the migration mobility of dislocations becomes comparable to the mobility of this boundary. The dislocation density in grain boundaries decreases due to the diffusion-controlled processes of removal and redistribution of localized and delocalized dislocations in a grain boundary, and this decrease depends on the diffusion coefficient in a nonequilibrium grain boundary.
150
50 500
exp
4. MODEL FOR THE EFFECT OF IMPURITY ATOMS ON THE TEMPERATURE OF THE ONSET OF RECRYSTALLIZATION IN MICROCRYSTALLINE METALS
(a)
100
th
Tr , °C
10 to 180 min decreases the TOR of the MC alloy with 0.3 wt % Cr from 220 to 160°C and the TOR of the MC alloy with 0.4 wt % Cr from 180 to 140°C. Figure 7 shows the dependences of the resistivity ∆ρ = ρin – ρ(t) and the microhardness of the MC alloy 250
Theory
At a given time of isothermal holding t*, the TOR Tr in pure metals is given by the expression [14]
300
Σ
Q b /kT m – χ 1 ∆α ( w ) T -, -----r- = -----------------------------------------------Σ Tm ln z – χ 2 ∆α ( w )
10 min 30 min 60 min 180 min
200
0.6
A α α* χ 1 = ------2- ⎛ A 1 + ------2 -------⎞ , ⎝ 2 α*⎠ α
Fig. 5. Dependences of the temperatures (a) T1 and (b) T2 on the chromium concentration in MC copper at various annealing temperatures.
B α α* χ 2 = ------2- ⎛ B 1 + -----2 -------⎞ , ⎝ 2 α*⎠ α
100
0
0.2
0.4 Cr, wt %
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EFFECT OF SMALL CHROMIUM ADDITIONS ON THE TEMPERATURE
δD b0⎞ ⎛ t* GΩ - --------------------------⎞ ⎛ ---------⎞ , z = ⎛ ----------⎝ A'd 3 ⎠ ⎝ ln ( ω 0 /ω* )⎠ ⎝ kT ⎠ 0 3
2
0
2
T1/Tm
0
Cu Cu–0.3 wt % Cr Cu–0.4 wt % Cr
0.40
A 1 = 2π ( λρb + γ S/ L b – γ 0 b /2 )/kT m ,
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2
A 2 = 4πγ S/ L b /kT m , 2
B 2 = 4πS S/ L b /k.
The designations and characteristic values of the most important quantities in Eq. (1) are given in Table 2. According to [14], the quantity ∆α(wΣ) in Eq. (1) is the free volume introduced by dislocations into a grain boundary. The quantity ∆α(wΣ) is proportional to the total density of misfit dislocations ρb and the density wt of the glide components of the Burgers vector of delocalized dislocations [14]. The dislocation density in grain boundaries depends on both the diffusion characteristics of these boundaries and the annealing time and temperature. The kinetics of the defect density in pure metals as a function of these factors is described in detail in [14]. Impurity atoms segregating at grain boundaries are known to change the diffusion properties of the boundaries [13]. For example, in a substitutional solid solution, an impurity whose atomic volume exceeds that of the matrix decreases the free volume of the boundary (∆α < 0) and, accordingly, decreases the diffusion coefficient Db in nonequilibrium grain boundaries. However, an impurity whose atomic volume is smaller than that of the host atoms increases the free volume of the boundary (∆α > 0) and, accordingly, increases Db [13]. An impurity-induced change in the diffusion properties of grain boundaries containing impurities changes the kinetics of all grain-boundary processes. In particular, the rate of escape of defects from grain boundaries changes. To a first approximation, these changes can be taken into account by replacing the standard grain-boundary diffusion coefficient Db with Db(Cb), where Cb is the impurity concentration at a grain boundary. According to [13], the grain-boundary diffusion coefficient at a low impurity concentration at a grain boundary can be determined from the formula D b ( C b ) = D b exp ( ∆α ( C b )/α b ),
(2)
0.25 0
50
100 t, min
150
Fig. 6. Dependence of T1 on the annealing time for MC copper and BrKhr-0.3 and BrKhr-0.4 alloys.
1500
3
1200
2 T1
900
600
1
0
200
0 600
400 T, °C
Fig. 7. Dependences of the microhardness and resistivity of the microcrystalline Cu–0.4 wt % Cr alloy (N = 10) on the temperature of annealing for 1 h.
impurity atom [13]. The quantity ∆V is determined by the difference in the atomic volumes of the impurity (V2) and grain-boundary host atoms (V1). For substitutional impurity atoms, we have [13] 3
∆V = ( V 2 – V )/V 1 = 1 – ( r 2 /r 1 ) , 3
–1
α b = ( χ 1 /kT ) – χ 2 .
(3)
The change in the relative free volume of the boundary ∆α(Cb) is connected with the concentration of impurity atoms Cb by the relation [13] ∆α ( C b ) = ( ∆V /V m )C b ,
(4)
where Vm is the volume jump upon melting [19] and ∆V is the change in the free volume of the boundary per PHYSICS OF THE SOLID STATE
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(5)
and for interstitial atoms we have ∆V = V 2 /V 1 = ( r 2 /r 1 ) .
where αb is
200
∆ρ, µΩ cm
2
Hµ, MPa
3
B 1 = 2π ( λρb /T m + S S/ L b )/k,
(6)
As was shown in [13], the concentration of impurity atoms in grain boundaries Cb can be expressed through the bulk concentration C using a distribution coefficient K [20]: C b = αC/K.
(7)
In Eq. (1) for the TOR in pure metals, we replace ∆α(wΣ) by ∆αc which is the sum of the change in the free volume caused by dislocations and of the change
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Table 2. Parameters used to calculate the temperature of the onset of recrystallization Parameter
Designation
Value
Recrystallization temperature of pure copper Energy of self-diffusion activation in equilibrium grain boundaries Preexponential factor for a grain-boundary diffusion coefficient, 1014 m3/s Initial grain size, µm Burgers vector, 10–10 m Boundary width Atomic volume, 10–23 cm3 Melting temperature, K Shear modulus Copper atomic (ionic) radius, nm Ratio of the initial and threshold strengths of junction disclinations Annealing time, s Relative free volume of a grain boundary Critical free volume of a grain boundary Excess free volume of a grain boundary in pure copper Volumetric expansion upon melting Specific heat of melting Density
Tr /Tm Qb /kTm δDb0 d0 b δ Ω Tm GΩ/kT r1 ω0/ω* t α α* ∆α(w) Vm λ ρ
0.334 9 [22] 5.0 [22] 0.2 2.56 [22] 2b [19] 1.18 [22] 1356 [22] 50 [19] 0.128, 0.098+, 0.082+* 10 [14] 3600 0.35 0.5 [19] 2.3 × 10–2 0.043
Enthalpy of liquid–crystal interface
γ S/ L
0
γ S/ L b2 = 0.9kTm
Entropy of liquid–crystal interface Free energy of the S phase of the boundary Numerical parameter Distribution coefficient of chromium in copper Chromium atomic (ionic) radius, nm
SS/L γ0 A1 K r2
SS/Lb2 = 0.767k γ0b2 1.95kTm 10 0.4 0.127, 0.0832+, 0.0643+*
λρb3 = 1.64kTm 0
* Values used for the calculation.
due to impurity atoms ∆α(wΣ(Cb)). As a result, we obtain an expression for the TOR for an impurity-containing metal that is analogous to Eq. (1). In Eq. (1), the quantities χ1, χ2, and z should be replaced by the parameters
c χ1
,
c χ2
, and zc for the impurity-containing metal. c χ1
c χ2
zc
The values of , , and are calculated using formulas (1) with the thermodynamic parameters of a pure metal replaced by the corresponding parameters for the impurity-containing metal. Thus, the TOR for an alloy containing impurity atoms that increase the free volume of the boundary can be written as [15] (1)
Tr (C) -----------------Tm
(8) Q b /kT m – χ 1 [∆α(C b) + ∆α(w ) exp {– ∆α(C b)/α b}] -. = ------------------------------------------------------------------------------------------------------------------------Σ ln z – χ 2 [ ∆α(C b) + ∆α(w ) exp { – ∆α(C b)/α b } ] Σ
The TOR for an alloy containing impurity atoms that decrease the free volume of the boundary is given by [15] (2)
Tr (C) -----------------Tm Σ
Q b /kT m – χ 1 [ ∆α(w ) {– ∆α(C b)/α b} – ∆α(C b) ] = ----------------------------------------------------------------------------------------------------------------. Σ ln z – χ 2 [ ∆α(w ) exp { ∆α(C b)/α b } – ∆α(C b) ]
(9)
5. COMPARISON WITH EXPERIMENT The coefficient of chromium distribution in copper is known to be ~0.4 [20], which means that chromium tends to segregate at grain boundaries [13]. It is also known that the atomic size of chromium is smaller than that of copper (Table 2) [21]. Thus, the introduction of chromium into copper should increase the free volume of grain boundaries and decrease Tr(C) according to Eq. (8). This conclusion is in qualitative agreement PHYSICS OF THE SOLID STATE
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Table 3. Experimental and calculated values of the recrystallization temperature in Cu–Cr alloys with various chromium concentrations Alloy parameters
Tr /Tm
C, wt %
Cb, wt %
∆α(C)
∆αΣ(C)
αb ( T r )
–1
theory
experiment
0.3 0.4
0.26 0.35
3 × 10–2 4.05 × 10–2
3.2 × 10–2 4.07 × 10–2
85.1 117
0.32 0.307
0.319 0.305
with the experimentally observed decrease in the TOR with increasing chromium content. Let us quantitatively compare the experimental and calculated values of the recrystallization temperature in the Cu–Cr system. Equation (8), which is used to calculate the TOR, seems to contain many poorly defined parameters, and it seems easy to fit the calculated values of Tr to the experimental values. However, the choice of the parameters only seems to be arbitrary. We will dwell on this issue in more detail. The numerical values required to calculate the parameters are given in Table 2. All the parameters form four groups. The first group consists of the well-known thermodynamic, elastic, and diffusion constants of pure copper (see, e.g., [21, 22]). The second group contains the parameters related to the thermodynamic and diffusion properties of grain boundaries in copper, which were calculated in [19]. The third group consists of the parameters that are set in a recrystallization model for pure metals and are checked for pure copper at t = 3600 s in [14]: ω0 /ω* ≈ 10 and d0 = 0.2 µm. Thus, the relatively free parameters to be determined in this work are the excess free volume in grain boundaries in pure copper ∆α(w) and the value of ∆α(Cb), which depends on the ratio between the ionic radii of chromium and copper. The value of ∆α(w) can be readily calculated using Eq. (1) for the TOR Tr/Tm of pure copper: Q b – ( T r /T m ) ln z* -. ∆α ( w ) = -----------------------------------------χ 1 – ( T r /T m )χ 2
(10)
Substituting the parameters given in Table 2 and Tr/Tm = 0.334, which is characteristic of copper [11, 14], into Eq. (10), we obtain ∆α(w) = 2.3 × 10–2. Thus, the ionic radius ratio of chromium to copper r2 /r1 remains the only fitting parameter of the model. The chromium ionic radius r2 in copper and the copper ionic radius r1 in the presence of chromium atoms have not been rigorously determined. Indeed, the ionic radius of an impurity in solids depends on many factors, such as the ionic radius of the matrix, the ion charge, etc. [23]. Therefore, the ionic radii can vary over fairly wide limits. Of the several tabulated values given in [21], we chose r1 = 0.08 nm and r2 = 0.064 nm. By substituting these values into the expression for the recrystallization temperature and using the parameters PHYSICS OF THE SOLID STATE
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given in Table 2, we can determine Tr(C) at any low chromium concentration, in particular, at C = 0.3 and 0.4 wt % (Table 3). Using Eq. (8), we can calculate Tr at various times of annealing of pure copper and Cu–Cr alloys (Table 1). The good agreement between the calculated and experimental values of Tr (Table 1) achieved with only one fitting parameter proves the validity of our model. ACKNOWLEDGMENTS This work was supported by the International Scientific Technical Center (ISTC) (project no. 2809), the Civilian Research and Development Foundation (project no. Y2-E-01-03), the Russian Foundation for Basic Research (project nos. 03-02-16923, 04-0216129, 04-02-17627, 04-02-97261, 04-02-97255), the Ministry of Education of the Russian Federation (project nos. E02-4.0-131, A03-3.17-214, 4087), the Russian Academy of Sciences (program “Fundamental Problems of the Physics and Chemistry of Nanosystems and Nanomaterials”), the Scientific and Educational Center for the Physics of Solid-State Nanostructures at the Lobachevskiœ Nizhni Novgorod University, and the program for Basic Research in Higher Education (BRHE). REFERENCES 1. V. M. Segal, V. I. Reznikov, V. I. Kopylov, D. A. Pavlik, and V. F. Malyshev, Processes of Plastic Structuring in Metals (Nauka i Tekhnika, Minsk, 1994) [in Russian]. 2. A. V. Nokhrin, E. S. Smirnova, V. N. Chuvil’deev, and V. I. Kopylov, Metally, No. 3, 27 (2003). 3. T. I. Chashchukhina, M. V. Degtyarev, L. M. Voronova, L. S. Davydova, and V. P. Pilyugin, Fiz. Met. Metalloved. 91 (5), 75 (2001) [Phys. Met. Metallogr. 91 (5), 500 (2001)]. 4. V. N. Chuvil’deev, V. I. Kopylov, A. V. Nokhrin, I. M. Makarov, L. M. Malashenko, and V. A. Kukareko, Materialovedenie, No. 4, 9 (2003). 5. A. V. Nokhrin, E. S. Smirnova, V. N. Chuvil’deev, I. M. Makarov, Yu. G. Lopatin, and V. I. Kopylov, Metally, No. 5, 63 (2003). 6. V. M. Degtyarev, L. M. Voronova, V. V. Gubernatorov, and T. I. Chashchukhina, Dokl. Akad. Nauk 386 (2), 180 (2002) [Dokl. Phys. 47, 647 (2002)]. 7. V. N. Chuvil’deev, V. I. Kopylov, and W. Zeiger, Ann. Chim. Sci. Mater. 27 (3), 55 (2002).
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17. O. A. Shmatko and Yu. V. Usov, Structure and Properties of Metals and Alloys. Electrical and Magnetic Properties of Metals and Alloys: Handbook (Naukova Dumka, Kiev, 1987) [in Russian]. 18. V. M. Rozenberg and V. T. Dzutsev, Phase Diagrams of Isothermal Decomposition in Copper-Based Alloys: Handbook (Metallurgiya, Moscow, 1989) [in Moscow]. 19. V. N. Chuvil’deev, Fiz. Met. Metalloved. 81 (4), 53 (1996) [Phys. Met. Metallogr. 81 (4), 387 (1996)]. 20. K. Hein and E. Buhrig, Kristallisation aus Schmelzen (VEB Deutscher Verlag für Grundstoffindustrie, Leipzig, 1983; Metallurgiya, Moscow, 1989). 21. Handbook on Physical Quantities, Ed. by I. S. Grigor’ev and E. Z. Meœlikhov (Énergoatomizdat, Moscow, 1991; CRC, Boca Raton, FL, 1997). 22. H. J. Frost and M. F. Ashby, Deformation Mechanism Maps (Pergamon, Oxford, 1982; Metallurgiya, Chelyabinsk, 1989). 23. V. K. Grigorovich, The Metallic Bond and the Structure of Metals (Nauka, Moscow, 1988; Nova Science, New York, 1989).
Translated by K. Shakhlevich
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