Effect of Annealing on Microstructure , Grain Growth and Hardness of Nanocrystalline Cu-Zr Alloy Prepared by Cryogenic Ball Milling

Nanocrystalline Cu-0.75 at.%Zr alloy was synthesized by high energy ball milling under cryogenic temperature. To investigate the influence of 0.75 at.%Zr addition on thermal stabilization of nanocrystalline state of Copper, milled powder was annealed up to T/Tm = 0.79 for 1h in an inert atmosphere. The microstructural changes of both milled and annealed powders were characterized by X-ray diffraction (XRD) and transmission electron microscopy (TEM). Mechanical properties were determined in terms of hardness. It was found that addition of 0.75 at.%Zr can stabilize grain size at higher temperature, i.e., ~ 32 nm at 800oC (T/Tm = 0.79). The hardness of Cu-0.75 at.%Zr at 800oC was found to decrease by only ~ 13% as opposed to a 65% decrease in pure copper from cryomilled condition. The thermal stability of Cu-0.75 at.%Zr system at high temperatures was attributed to the kinetic stabilization, i.e., grain boundary pinning by intermetallic phases. Thermal stability contributions were assessed by thermodynamic models elicits added Zr is not sufficient for stabilization, rather kinetic stabilization (by intermetallic pinning of grain boundary) became active at higher annealing temperature.


Introduction
Superior combination of mechanochemical properties than conventional one draws attention towards practical implementations of nanocrystalline (grain size<100 nm) materials.However, increased grain boundary energy contribution imposes inherited instability in these nanocrystallinematerials.Curvature dependent driving force for grain coarsening can be obtained in terms of pressure (P) acting on grain boundary (Humphreys & Hatherly, 2012), given as Where A is a constant (value close to 1), is intrinsic grain boundary energy and is the radius of curvature of grains (in order of a few nm).Hence, very high driving force invariably makes difficult retention of nanocrystallinestate especially at higher temperature where grain boundary mobility proliferates.This in turn limits its processing techniques, consolidation and operating temperature.ACombination of FCC crystal structure and high stacking fault (78 mJm 2 ) (Rohatgi, Vecchio, & Gray, 2001) energy makes copper an ideal material to be usedfor investigations.Coarsening of nanocrystalline pure Cu has beenreported even at room temperature (Rohatgi, Vecchio, & Gray, 2001).Established mechanisms of thermal stabilization of nanocrystalline materials include both kinetic and thermodynamic factors.In kinetic or Zener mechanism thermal migration of grain boundaries have been found to be mitigated by particle pinning and/or solute drag, reported in systems like Fe-Cr-Zr (Saber, Kotan, Koch, & Scattergood, 2012), Cu-Y (Mula et al., 2015), Cu-Al-Y (Roy et al., 2014) etc. Particle pinning pressure ( ) on grain boundary is estimated as (Hillert, 1965) thermodynamic mechanism preferential solute segregation on grain boundariesreduces the grain boundary energy of the solvent.Grain boundary energy change ( ) is given by theGibbs interface equation as:

= −
(3) Where is excess solute atoms(mole/area) on grain boundaries and, is the chemical potential of solutes (energy/mole).Decrease in the grain boundary energy can be estimated as: ) Where is intrinsic grain boundary energy, ∆ and ∆ are enthalpy and entropy of segregation.Normally entropy of segregation is taken equal to zero (∆ = 0) (Darling et al., 2014) i.e. if [∆ − ∆ ]<0, thengrain boundary solute segregation becomes effective in thermal stabilization.A higher elastic misfit (∆ > 0) favors grain boundary solute segregation, reported for Pd-Zr (Krill III, Ehrhardt, & Birringer, 2005), Fe-Cr-Hf (Li et al., 2014), Fe-Zr (Darling et al., 2008) systems.A hybrid strengthening mechanism was reported for Cu-Ta system (Darling et al., 2013).Darling et al. (2008) reported that addition of 1at.%Zr in Fe retains 50nm grain size up to T/T m =0.92 (T m is the melting temperature).They attributed the superior thermal stability to reduction in grain boundary energy by Zr segregation.When Zr in added to Cu, the change in elastic enthalpy ( ∆) is ~ 90.8 kj/mol (Roy et al., 2014), which is comparable with the enthalpy change when Zris added in Fe, i.e.∆ = 92 / .(Darling et al., 2008).Moreover, solubility of Zrin Cu (0.12 at.% at 972°C) (Arias & Abriata, 1990) is comparable with the solubility of Zr in Fe (0.5 at.% at 1300°C) (Darling et al., 2008).Previously, Atwater, Scattergood, and Koch (2013) established that addition of 1at.%Zr in Cu retains grain size of 29.5 nm up to 900°C (T/T m =0.87) and proposed a combined strengthening mechanism for the stability of grains at high temperature.Roy et al. (2013) added a lower Zr content of 0.5 at.% and showed that it can stabilize grain size of 35.2 nm up to 800°C.It has been shown that addition of higher Zr content in Cu causes formation of amorphous state (Xu et al., 2004).Cu is extensively used for making conductors materials.In order to design a conductor which can retain high strength at higher operation temperature we need to retain nanocrystalline microstructure.Previously, with 1 at.%Zraddition in Cu numerous intermetallic phases were formed at high temperature (say 900°C) (Atwater, Scattergood, & Koch, 2013).Hence, stabilization potential of Zr by thermodynamically controlled mode was not realized.Furthermore, a detailed thermodynamic calculation for lower (<1 at.%) concentration of Zrin Cu is not yet explored.In present work, Cu-0.75 at.%Zralloy has been prepared by the mechanical alloying route and effect of this small concentration of Zr on the thermal stabilization of the microstructure has been assessed.

Materials and Methods
Copper (Cu)and Zirconium (Zr) powders (99.9%,Alfa Aesar) were mixed in appropriate proportion (0.75at%Zr) and put intoa stainless steel vial (440 stainless steel vial-Spex Sample Prep) for mechanical alloying.The vial was then sealed in an argon atmosphere followed by mechanical milling in Spex 8000 mixer/mill for 8 hrs at cryogenic temperature (-196 ºC).Milling media was specially designed stainless steel balls (440C SS balls) with the ball to powder weight ratio of 10:1.Milled powder was then transferred into sealed vacuum tube for subsequent annealing operation for studying property alteration of powder blend.Isochronal annealing ofthe milled powder was performed for 1hr at a temperature range of 200 to 800°C (i.e. up to T/T m =0.79).To compare with pure copper, same process was performed with Cu powders.

Phase and Microstructure Characterization
Phase identification of both milled and annealed powder samples were performed by X-ray diffraction (XRD) analysis (PANalytical 3 kW X'pert Powder XRD -Multifunctional).XRD patterns were obtained using CuKάincident radiation with scan angle (2θ) range from 30° to 100° and with a scanning rate and step size of 0.02°/min and 0.017°, respectively.The crystallite size was determined by X-rayline broadening using the Scherrer equation (Cullity, 2001) Where, D is the crystallite size, λ is the wavelength of the incident X-ray radiation (0.1541nm), k is the Scherrerconstant (= 0.94), β is the peak width at half maximum intensity (or full width half maximum, FWHM), and θ is the peak maximum position.The broadening of adiffraction peak is attributed to the synergistic contribution of both instrumental and sample condition.The instrumental broadening is corrected by subtracting the integral breadth of standard sampleusing following equation, β = [ ( β 2 ) measured -(β 2 ) standard ] ½ (6) Microstructural characterization of the milled and annealed powders was also carried out by using transmission electron microscopy (JEOL JEM 2000FX) with beam energy of 200 keV.The milled and annealed powders were compacted at 2.6GPa pressure to form disk shaped compact for TEM investigation.The compacts were then mechanically polished to a thickness of ~100 mm followed by electropolishing (30 vol% nitric acid in methanol at -20° C).

Mechanical Properties Evolution
To evaluate the mechanical properties, milled and annealed powders were mounted on a glass slide and polished for surface finishing.Vickers microhardness measurements were performed by a minimum of 10 indents for each annealed conditions using SIMANDZU Semi-Automatic Micro Vickers hardness tester.The microhardness test was carried out using 25g load with a dwell time of 15sec for each indentation.

Phase and Microstructural Analysis
The XRD patterns ofmilled and annealed powders (200°C, 400°C, 600°C and 800°C) are shown in Figure 1a.The absence of Zrpeaks in Figure 1a may be attributed to the complete dissolution of Zrin Cu matrix due to mechanical milling and/or the small amount of Zr (only 0.7 at.%).It is evident that increase in annealing temperature leads to increase in intensity and decrease in width of XRD peaks.This indicates that the lattice parameter of Cu decreased with increase in annealing temperature and this might be attributed to the solute (Zr) leaving the solid solution.For detailed investigation, lattice parameter (a Cu ) was calculated as a function of annealing temperatures from XRD.In order to get precise values of a Cu for a particular condition, calculated values from four major peaks were plotted against sin ⁄ to = 0 (Cullity, 2001).Figure 1b shows variation in lattice parameters of milled and annealed powders (as a function of annealing temperature) against the lattice parameter of pure Cu at room temperature (a Cu =0.36144 nm).Calculated lattice parameters showa rapid decrease from 0.36223nm (milled powders) to 0.36179 nm (T/T m = 0.35 or 200°C annealed) followed by a slow decrease to 0.36171nm (at 400°C or T/T m = 0.49), and then remain almost constant till 800°C.Following Darling et al. (2008), relative fraction of solute (Zr)in a solid solutioncan be assessed from changes in lattice parameters with respect to pure Cu as(1-f), where = =0.66 i.e. 0.34 of total added Zr remains in parent Cu lattice after annealing at 800°C for 1h.2c and 2d, respectively.Apart from the FCC Cu rings, additional rings are also visible in the SAED pattern of annealed alloy.This ringscorrespond to Cu 5 Zr and the same phase has been observed in the previous studies (Atwater, Scattergood, & Koch, 2013;Roy et al., 2013).This intermetallic phase (Cu 5 Zr) is shown by arrows in the dark field TEM image (Figure 2c).During annealing, the Zr solute atoms come out of the solid solution and precipitates as Cu 5 Zr.Due to limited potential of XRD technique, although no detectable peaks of second phase were present in XRD patterns (Figure 1a), TEM images confirms the presence of intermetallic phases at high temperature.Furthermore, the continuous rings of Cu in the SAED pattern, confirm stability of nanocrystalline state even after annealing at high (0.79T m ) temperature.

Thermal Stability of Nanocrystalline Structure and Hardness
Figure 3a shows grain sizes obtained byScherrer equation with respect to normalized isochronal (1h) annealing temperature for pure Cu and Cu 99.25 Zr 0.75 .It can be seen that the both pure Cu and Cu 99.25 Zr 0.75 were nanocrystalline and had approximately same gran size after milling.However, there is a drastic increase in grain size in case of pure Cu compared to Cu 99.25 Zr 0.75 when annealed at 800°C.A small increase in grain size of Cu 99.25 Zr 0.75 compared to pure Cu after annealing indicated that addition of a slight amount of Zr inhibits the grain growth, and therefore, can maintain nanocrystalline nature of the alloy.The stability of nanocrystalline nature of Cu 99.25 Zr 0.75 even at hightemperature can be attributed to the formation of Cu 5 Zr intermetallic phase at grain boundaries, which reduces the movement of grain boundaries and thereby inhibits grain growth.
Figure 3b shows room temperature Vickers microhardnessvalues vs. isochronal annealing temperature of pure Cu and the Cu-Zr alloy.The hardness values of initially milled powders of both pure Cu and Cu 99.25 Zr 0.75 are approximately same (pure Cu~ 2.88GPa and Cu 99.25 Zr 0.75 ~2.93 GPa).This indicates that the solid solution strengthening effect of Zr in Cu is very little due to the small content of Zr (only 0.75 at.%).The hardness values of pure Cu decrease with increase in annealing temperature (~1 GPa) at 800°C (~ 65% decrease in hardness compared to milled condition).In contrast, it is interesting to note that the hardness values of Cu 99.25 Zr 0.75 remain almost constant till annealing temperature of 600°C, however, there is a slight decreases in the hardness value when annealed at 800°C compared to milled condition (~13% decrease).Moreover, the harness of Cu 99.25 Zr 0.75 always remains higher than pure Cu at all annealing temperature.This relative decrease in hardness values can be correlated to the relative increase in grain size (Figure 3a) as well as effect of dispersion strengthening by the presence of Cu 5 Zr intermetallic phases.The dramatic decrease in hardness of pure Cu is related to the excessive grain coarsening with increase in annealing temperature, as shown in Figure 3a.The static hardness values of Cu 99.25 Zr 0.75 till 800°C can be attributed to grain boundary pinning by intermetallic particles, which nullifies the effect of slight increase in grain size.Although, the grain size measurements were performed using XRD data rather than the actual microstructure, grain size calculations from X-ray peak broadening has been found to be accurate even below 40 nm (Roy et al., 2014).Here is the grain boundary solute content (in mole), is the solute concentration within the grain and σ is the molar grain boundary area.Complete thermodynamic stabilization by grain boundary segregation as discussed in Darling et al. (2013) is obtained when normalized grain boundary energy ( ⁄ ) equals with zero and the corresponding is minimum solute content for stabilization.The free surface segregation energyin terms of chemical and elastic effects is given by the classical Wynblatt and Ku bilayer grain boundary model (WK model) (Wynblatt & Ku, 1977;Wynblatt & Chatain, 2006) Where, ∆ = − 24 ( − ) 3 + 4 Where, A and B are the solute and solvent atoms respectively, and are the surface free energies, α is the ratio of interface and bulk bond strengths, (α = 5/6) (Darling, VanLeeuwen, Koch, & Scattergood, 2010), σ is the molar area for solvent, is the enthalpy of mixing of equimolar liquid A and B, Z c (=12) is the coordination number (Z c = + 2 ), (= 6) is the number of in plane bonds and (= 3) is half of the number of out plane bonds, and are the mole fractions of solute on grain boundaries and in the bulk respectively and is the elastic enthalpy.Values required for numerical estimation of grain boundary energy change due to dopant addition are given in table 1.Using the values given in the table 1 and bilayer grain boundary model (i.e.WK model), the variation of grain boundary energy with solute concentration is plotted in Figure 4.It is evident from Figure 4 that the required solute content for zero grain boundary energy is very small.i.e. 0.14 mole Zr.
Since Vickers hardness is related to the yield strength of material by H/σ=3, an analogous Hall-Petch equation for hardness can be formulated as, = + / (Nagumo, & Umemoto, 1997).If change in hardness after annealing is completely grain size dependent then the ratio of ⁄ , ( and arehardness values after and before annealing, respectively) should be equal to ⁄ , , where and are grain sizes in as milled and annealed condition respectively.At T/T m =0.79, the values of ⁄ and ⁄ ,, are 0.87 and 0.73 respectively.This indicates that another strengthening mechanism is also contributing apart from Hall-Petch strengthening.The volume fraction (f) of second phase particles (Cu 5 Zr) can be calculated from grain size (R= 31.6 nm) and particle size (r P = 3.7nm) both obtained from TEM images of 800°C annealed sample as (Doherty, 2012) The calculated volume fraction of second phase particles is ~2.34%.Inter particle spacing (λ)can be calculated from the following equation (Redsten, Klier, Brown, & Dunand, 1995) Considering that the total hardness (H) is a combination of effects from grain boundary strengthening (Hall-Petch, ) and particle strengthening (Orowan, ), the total hardness can be expressed as Atwater, Scattergood, and Koch (2013) Where G is the shear modulus of Cu (42 GPa), b is the Burger's vector (0.25 nm), is the dislocation core radius ( =b) (Atwater, Scattergood, & Koch, 2013), d is the grain size, is the frictional stress (25.5 MPa), k is the Hall-Petch slope (0.11MN/m 3/2 ).From the aforementioned values , and H values can be calculated as0.69 GPa, 1.93 GPa and 2.62 GPa respectively.The theoretical value of 2.61 GPa is very close to the experimentally obtained hardness value (2.61 GPa) obtained at 800°C forCu 99.25 Zr 0.75 alloy.Thisindicates that the hardness of Cu 99.25 Zr 0.75 can be attributed to both grain boundary strengthening (~26%) and particle strengthening (~74%).The contribution from solid solution can be neglected as the initial hardness of the pure Cu and Cu 99.25 Zr 0.75 alloy is approximately same.Based on above discussion it is evident that at higher annealing temperature kinetic pinning by intermetallic is governing strengthening mechanism.This can be verified by comparing experimentally observed grain size with the theoretically estimated one.According to Zener pinning modellimiting grain size can be calculated as (Manohar, Ferry, & Chandra, 1998)

Conclusions
Present findings prescribe a possible route for preparing and retaining high strength of Cu at higher operating temperature.Addition of 0.75 at.%Zr results in stability of nanocrysalline state of copper at higher temperature (up to 800 o C).A decrease of only 13% (or 16%) was observed in the case of Cu-0.75 at.%Zr when annealed at 800 o C compared to cryomilled condition.Employing the modified Wynblatt-Ku, and grain size dependent monolayer model suggests added Zr can stabilize nanocrystalline Cu in thermodynamic controlled mode.However, formation of intermetallic phases excludes possibility of thermodynamically controlled stabilization.TEM investigation of annealed sample shows formation of numerous of Cu 5 Zr intermetallic phase.Good agreement between experimentally obtained grain size and hardness value with the Zener predicted limiting grain size and theoretically predicted hardness values, considering the influence of intermetallic phases, suggests that the high temperature thermal stabilization of Cu-0.75 at.%Zr is dictated mainly by Zener pinning mechanism.

Figure 1
Figure 1(a) XRD patterns of Cu 99.25 Zr 0.75 milled for 8hrs and annealed at various temperatures, (b) variation in lattice parameters with annealing temperatures