Grain growth in nanocrystalline Fe–Ag thin film

Materials Letters 59 (2005) 1458 – 1462 www.elsevier.com/locate/matlet

Grain growth in nanocrystalline Fe–Ag thin film Feng Liu* Institute for Materialphysik, University of Gottingen, Tammannstr.1, 37077, Germany Received 24 June 2004; received in revised form 2 January 2005; accepted 7 January 2005 Available online 28 January 2005

Abstract Isothermal grain growth kinetics of nanocrystalline Fe–Ag single-phase thin film, prepared by pulsed laser deposition, was investigated by X-ray diffraction (XRD). Using an empirical relation assuming that r b reduces with solute segregation, grain growth stops with saturated grain boundaries, corresponding to a metastable equilibrium system. It was found that higher Ag concentration gives smaller grain size at the metastable equilibrium, but favours phase separation upon annealing. D 2005 Published by Elsevier B.V. Keywords: Nanocrystalline materials; Grain growth; Kinetics; X-ray diffraction (XRD)

1. Introduction Taking advantage of the novel properties of nanocrystalline materials generally necessitates stabilizing the microstructure against grain growth. Two strategies have until now been devised for improving its thermal stability: a kinetic one, in which the grain boundary (GB) mobility is reduced [1–3], or a thermodynamic one, in which the driving force, i.e. GB energy, r b, is suppressed [4–6]. Potentially more effective would be a reduction in r b, which manifests only weak temperature dependence [7]. According to the Gibbs adsorption theorem [8,9], r b reduces with segregation of solute species to the GBs [4,6]. rb ¼ r0  Cb0 tRTlnX0 þ DHseg b

ð1Þ

where r 0 is the GB energy for pure solvent, X 0 the bulk solute concentration, C b0 the solute excess of GB monolayer available for segregation at saturation, and DH seg the enthalpy change of segregation per mole of solute. Whenever r b is positive, grain growth will decrease the free energy of the system. Therefore the only case where grain growth can be suppressed is r b=0 [6]. Experiment has

* Corresponding author. Present address: Max Planck Institute for Metals Research, Heisenbergstrasse 3, D-70569, Stuttgart, Germany. E-mail address: [email protected]. 0167-577X/$ - see front matter D 2005 Published by Elsevier B.V. doi:10.1016/j.matlet.2005.01.003

shown that the effect of solute segregation on r b can be substantial, and theoretical considerations predict that driving r b to zero is possible in alloy system with a high enthalpy of segregation [5,6]. As compared to an unchanged grain size and solute segregation, precipitation of solute or stable phase at GBs and grain growth leads to a more stable equilibrium [6]. So stopping nano-scale grain growth corresponds to the saturated GB with zero GB energy, a metastable nanocrystalline system. The grain diameter, D*, at the metastable equilibrium is given as [6,10], DT ¼

3Cb0 VM   r C DH Xtotal  exp 0 Cb0b0RT seg

ð2Þ

where X total is the summation of the bulk and GB concentration, and V M the molar mass of the alloy. Hence Eq. (2) demonstrates there exists a state for which the polycrystal is stable with respect to variation of GB area, i.e. grain size. Pulsed laser deposition (PLD) was used to grow thin films particularly of Fe–Ag alloys onto substrates cooled to 150 K, leading to the formation of nanocrystalline singlephase bcc films with up to 40 at.% Ag [11]. The most striking feature of PLD in the preparation of alloys is the formation of solid states far away from thermodynamic equilibrium. The high particle energy and the high

F. Liu / Materials Letters 59 (2005) 1458–1462 RT 473K–1h 573K–1h 673K–1h

1459

thermodynamical model to verify that nano-scale grain growth is inhibited by reducing GB energy through solute segregation, and that the grain size can be attributed to the combined effect of solute concentration and GB excess, C b0.

intensity (a.u.)

(a)

2. Experimental procedure

45

50

Fe(Ag) alloys with a thickness of 100–300 nm were laser deposited at room temperature (RT) onto Si substrates in an ultrahigh vacuum system (with a base pressure of about 5109 mbar). At a laser fluency of 8 J/cm2 and with a target-to-substrate distance of 3 cm, thin films with different concentrations were prepared by alternating illumination of Fe and Ag foils with a focused KrF excimer laser beam as described earlier [11]. The overall composition of the films was determined using X-ray fluorescence (XRF). Structural characterization was performed by X-ray diffraction (XRD) with monochromatic Co Ka radiation. Diffraction patterns of selected samples were taken in situ during successive isothermal 1 h anneals at various temperatures in a vacuum better than 106 Torr; the duration of each scan was 10 min. The corresponding XRD-patterns at RT were also taken. From the Bragg angles (2h) of the RT reflections of the phases the lattice parameters, a, of the phases can be determined.

55

2θ (deg) RT 473K–1h 573K–1h 673K–1h RTaging–4 weeks

intensity (a.u.)

(b)

40

45

50

55

2θ (deg) RT 473K–1h 573K–1h 673K–1h

(c)

intensity (a.u.)

3. Results

40

45

50

55

2θ (deg) Fig. 1. XRD patterns after successive 1 h isothermal anneals of Fe98.2Ag1.8 (a), Fe96.8Ag3.2 (b) and Fe95Ag5 (c) alloys at different temperatures.

deposition rate [13] result in the formation of metastable nanocrystalline solid solutions. Here, we conducted isothermal annealing of Fe–Ag thin films (by PLD) at temperatures between 473 K and 673 K. The gain growth behaviour was analysed using the above

Fig. 1 (a–c) displays enlarged parts of XRD-patterns of the as-prepared Fe100x Agx (initial concentration, x=1.8, 3.2, 5.0 at.%) thin films after isothermal 1 h anneals between 473 K and 673 K (for different times). The asprepared state and corresponding XRD-patterns at RT for Fe98.2Ag1.8 and Fe96.8Ag3.2 are shown in Fig. 1 (a and b), respectively. Unfortunately, RT XRD-patterns were not recorded for Fe95Ag5 and in situ XRD patterns were provided instead. Although the resolution of Fig. 1c is not as good as that of Fig. 1 (a and b), the influence on the experimental results is negligible. The grain sizes of the Fe– Ag films were determined with the aid of the Scherrer formula [12] and were gathered in Table 1. The change of the lattice parameter of Fe(Ag) solid solutions upon annealing is shown in Fig. 2a. The lattice parameter can be reasonably expected according to Vegard’s law [11,13,14], thus giving Ag concentration as a function of

Table 1 Evolution of grain size and peak position (2h) of the XRD patterns upon annealing Fe(Ag) supersaturated solid solutions Ag content

RT

473 K

523 K

573 K

623 K

2h/8

D, nm

2h/8

D, nm

2h/8

D, nm

2h/8

D, nm

1.8 at.% 3.2 at.% 5.0 at.%

51.94 51.70 51.45

12.1 11.5 10.4

51.96 51.77 51.50

12.8 12.2 11.7

51.98 51.84 51.59

13.2 12.9 12.2

51.99 51.90 51.72

15.5 14.3 12.8

2h/8 52.02 51.99 51.85

673 K D, nm 16.9 15.2 13.4

2h/8

D, nm

52.09 52.41 51.98(0.5 h) 52.41(1 h)

19.2 17.2 14.7 16.4

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F. Liu / Materials Letters 59 (2005) 1458–1462 0.293

lattice parameter / nm

1.8at% Ag 3.2at% Ag 5at% Ag 5at% Ag, after Ag precipitation

(a)

0.292 0.291 0.29 0.289 0.288 0.287

(pure Fe)

0.286 300

400

500

600

700

temperature / K 0.05

1.8at% Ag 3.2at% Ag 5at% Ag 5at% Ag, after Ag precipitation

Ag – c oncentration

(b) 0.04 0.03 0.02 0.01 0 51

51.5

52

52.5

2θ (deg) Fig. 2. Lattice parameter (a) and bulk Ag concentration (b) as a function of (a) annealing temperature and (b) peak positions according to XRD patterns, respectively.

the 2h value of the peak position according to the XRD patterns, as shown in Fig. 2b. All reflections from as-prepared films and films annealed below 573 K are from the bcc (110) Fe(Ag) supersaturated solid solution (Fig. 1 and Table 1). Upon annealing, the 2h value of the XRD peak corresponding to the bcc (110) Fe(Ag) solid solution increases (Fig. 1), while the lattice parameter decreases (Fig. 2a) due to the decrease of bulk Ag concentration (Fig. 2b). With increasing the initial Ag concentration, the bulk Ag concentration in the bcc (110) solid solution is enhanced, thus increasing the lattice parameter of the as-prepared films and films annealed below 573 K. Accordingly the 2h value of the XRD peak corresponding to the bcc (110) Fe(Ag) solid solution decreases (see Figs. 1 and 2). For the films annealed at 673 K, the XRD patterns differ as a result of different structure evolutions due to different Ag concentrations. Upon annealing of the as-prepared Fe98.2Ag1.8 film for 1 h between RT and 673 K, the only reflection is from the bcc (110) Fe(Ag) solid solution (see Fig. 1a). The grain size was found to increase in the as-prepared state from c12.1 nm to c19.2 nm after a 1 h anneal at 673 K, accompanied by a continuous decrease in the half width and a shift of 2h value from c51.948 to c52.098 from the XRD-patterns (see Table 1). For Fe96.8Ag3.2 film (see Fig. 1b), grain size was found to increase from 11.5 nm in the as-prepared state to 17.2 nm after 1 h anneal at 673 K (Table 1). Below 673 K, the

changes of half width and 2h value of the bcc (110) Fe(Ag) solid solution are analogous to that of Fe98.2Ag1.8 film. After a 1 h anneal at 673 K, two (110) peaks at 2hc50.48 and 2hc52.48 (see Fig. 1b) correspond to a metastable Fe(Ag) solid solution (a=0.2973 nm [15]) and pure Fe (a=0.2866 nm in Fig. 2a), respectively. According to Vegard’s law, the lattice parameter (a=0.2973 nm) corresponds to c9.0 at.% Ag. XRD scanning performed at RT immediately after 673 K annealing (Fig. 1b) indicates that Ag (111) precipitation does not take place after 673 K annealing, and a metastable equilibrium between pure Fe and Fe(Ag, c9 at.%) solid solution develops [15]. Subsequent aging for 4 weeks at RT results in Ag precipitation, as indicated by the presence of the fcc Ag (111) peak and the entire disappearance of the (110) peak at 2hc50.48 in the XRD-pattern (Fig. 1b). For detailed explanation see Ref. [15]. Due to higher Ag concentration, relatively smaller grain sizes and lower 2h values of the bcc Fe(Ag) (110) solid solution (i.e. compared with those films with lower Ag concentration) result upon annealing of Fe95Ag5 film until 30 min anneal at 673 K (see Table 1). After 1 h anneal at 673 K, further grain growth occurs and the lattice parameter of the bcc (110) Fe(Ag) solid solution almost equals to that of Fe96.8Ag3.2 film, a=0.2866, a value corresponding to pure Fe (see Fig. 2a). However, pronounced precipitation (high phase fraction, Fig. 1c) of Ag takes place without formation of the metastable Fe(Ag, c9 at.%) solid solution at 2hc50.48 (small phase fraction, Fig. 1b), inferring that the intensity of the original bcc (110) Fe(Ag) solid solution of Fe96.8Ag3.2 film is higher than that of Fe95Ag5 film.

4. Discussion Concurrent with grain growth, interfacial segregation, i.e. a redistribution of the solute between the bulk and GBs, and the formation of phases with lower Gibbs free energy can take place. Since in GBs more bonds are broken than in the bulk, elements with lower cohesive energy tend to segregate to GBs. Since the cohesive energy of Ag (3.0 eV) is smaller than that of Fe (4.25 eV) [17], Ag atoms are more likely to segregate to GBs than Fe atoms. Upon annealing, diffusion of Ag atoms from the bulk to GBs is favoured, and sufficient segregation (e.g. in case of Fe95Ag5) would result in a microstructure where a bcc Fe grain is surrounded by a layer of almost pure Ag (Fig. 1c). Such a microstructure has been suggested on the basis of Mfssbauer and electron energy loss spectrometry investigations of bcc Fe–Cu alloys (possessing a high positive energy of formation of +14 kJ/ mol), which show a rather thick, Cu-enriched GB layer of c1 nm thickness after isothermal annealing at 530 K [18]. Recognising that grain growth stops with saturated GBs with zero GB energy [6,10], the grain size at the metastable equilibrium is according to Eqs. (1) and (2) determined by three important properties of GBs, namely, GB energy, r b, enthalpy change of GB segregation, DH seg, and GB excess,

F. Liu / Materials Letters 59 (2005) 1458–1462

1.8

1.8at%Ag, measured 1.8at.%Ag, fitted 3.2at.%Ag, measured 3.2at.%Ag, fitted 5at.%Ag, measured 5at.%Ag, fitted

1.6 1.4 1.2 1 300

400

500

600

700

temperature / K Fig. 3. Fits using Eq. (2) to the evolution of the grain size obtained in the single-phase nanocrystalline solid solutions of Fe100x Agx with temperature.

C b0. Fe–Ag system is characterized by a high positive enthalpy of mixing of +28 kJ/mol and almost no solubility in the solid and the liquid state [11], i.e. a high value for DH seg, so Eq. (2) can reasonably reduce to, DT ¼

3Cb0 VM Xtotal

ð3Þ

It can be inferred from Eq. (3) that if C b0 holds constant at GB saturation independent of X total, D* should be inversely proportional to X total, e.g. the initial Ag concentration in the film. As given in Table 1, the grain size of the Fe–Ag films upon annealing does decrease with increasing Ag concentration, however, some simple calculations (not shown here) prove that this decreasing relation does not follow Eq. (3). This indicates that C b0 must change with increasing the initial Ag concentration. Long-term annealing between 473 and 673 K shows that grain sizes almost keep stable after 1 h isothermal anneals. As above-mentioned, grain growth stops with saturated GBs with zero GB energy, independent of the annealing temperature. Fig. 3 shows the fits using Eq. (2) to the grain sizes of the supersaturated Fe(Ag) solid solutions upon annealing the as-prepared Fe100x Agx (x=1.8, 3.2, 5.0 at.%) thin films. The values for fitting parameters were considered to be reasonable for Fe–Ag system [6,16], as gathered in Table 2. As would be expected, C b0 increases with increasing the Ag content. The change of C b0 can be explained by the change of lattice parameter upon annealing. According to Fig. 2a and b, reduction of lattice parameter of Fe(Ag) solid solution means diffusion of Ag from bulk to GBs, i.e., a decrease of bulk Ag concentration. For Fe98.2Ag1.8 film, a right shift of Table 2 Values for r 0, C b0, and DH seg, as well as the errors by fitting Eq. (2) to the experimental data Solute content Fe98.2Ag1.8 Fe96.8Ag3.2 Fe95Ag5

r 0 (J/m2) 0.79 0.79 0.79

DH seg (kJ/mol)

C b0 (mol/m2)

60–100

1.2105 1.9105 3.1105

Error (%) 1.3 1.4 0.8

(110) peak in the as-prepared state from 2hc51.95 to 2hc52.09 after 1 h anneal at 673 K indicates a decrease of the bulk concentration from ~1.8 to ~1.3 at.% (Fig. 2b), and corresponds to the smallest value for C b0 (see Table 2). Due to the formation of the metastable Fe(Ag, c9 at.%) solid solution (Fig. 1b), Fe96.8Ag3.2 film cannot keep as stable as Fe98.2Ag1.8 until 673 K, as indicated by a change of bulk concentration of Ag from ~3 at.% to zero and a higher value of C b0 (see Fig. 2b and Table 2). As shown in Fig. 2b and Table 1, higher Ag concentration (Fe95Ag5) gives smaller grain size at saturation and tends to increase the systemic stability, while a decrease of bulk Ag concentration from ~4.2 to ~1.5 at.% was observed before Ag precipitation. However, instability of a nanocrystalline material with respect to precipitation of a second phase is due to its excess energy, which results from supersaturation in solid solution and is released upon precipitation of intermatallic compound or pure component. Although smaller grain size was obtained in Fe95Ag5 sample at saturation, earlier Ag precipitation occurs upon annealing, corresponding to the highest C b0 (see Table 2). Neglecting the temperature dependence of r b and DH seg a simpler relation was derived by differentiating Eq. (1) with respect to T as [6],
d 1=DT X0 lnX0 ¼  ð4Þ dlnT 3Cb0 VM The right-hand side of Eq. (4) depends also on temperature: changes in D result in changes in X 0, i.e. the configurational interfacial excess entropy. However, the interfacial excess entropy plays a negligible role for the temperature dependence of the metastable grain size [11]. Some simple calculations (not shown here) prove that the agreement with experimental data will not be affected if the configurational (ideal) interfacial excess entropy is taken into account. Therefore, Eq. (4), neglecting the influence of a change of X 0, turns out to be useful for comparison with experimental results. Fig. 4 presents good linear relation according to Eq. (4) for Fe98.2Ag1.8 with a slope of 1108 m1. This is the same 8.5

7.5

1/D / (102/nm)

grain size / 10-8 m

2

1461

6.5

5.5

4.5 6.15

6.25

6.35

6.45

6.55

log(T) Fig. 4. Linear relation according to Eq. (4) for grain size obtained upon annealing Fe98.2Ag1.8.

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F. Liu / Materials Letters 59 (2005) 1458–1462

order of magnitude as obtained from Eq. (4) giving 2.5108 m1 for X 0=1.5 at.% and C b0=1.2105 mol/m2 (Table 2). This further provides evidence that r b reduces to zero when grain growth is suppressed with saturated GBs.

5. Conclusions Investigation of grain growth conducted in pulsed laser deposited Fe–Ag single-phase thin film by XRD leads to the following results: (a) grain growth of Fe–Ag thin film can be described using an empirical relation assuming that grain boundary energy reduces with grain growth. (b) Effect of solute atoms on grain growth is revealed by the exact grain boundary excess at grain boundary saturation. (c) For Fe–Ag system with positive heat of mixing, it is due to higher grain boundary excess arising from higher solute content that gives smaller grain size at saturation, but favours phase separation upon further annealing.

Acknowledgement The authors gratefully acknowledge support from the Alexander von Humboldt Foundation.

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