Glass-Transition-Like Behavior of Grain Boundaries in Nanocrystalline Gold
Terigele Xi, Takahiro Sato
*, Ryoma Suzuki and Hisanori Tanimoto
Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305–8573, Japan
Characteristic property changes were observed for high density and high purity nanocrystalline (n-) Au prepared by the gas deposition method. The increase in internal friction with a modulus defect started at 180 K and became steep above 200 K. An increase in endothermic heat flow began at 170 K. The electrical resistivity showed a deviation from a linear increase with the temperature at 130 K. All the charac-teristic changes were reproduced by the repetition of the thermal cycle below 300 K, but the amounts diminished after the grain growth. These characteristic temperature changes indicate a glass-transition-like behavior of the grain boundaries in n-Au.
[doi:10.2320/matertrans.M2017270]
(Received September 4, 2017; Accepted October 26, 2017; Published November 27, 2017)
Keywords: nanocrystalline metals, grain boundaries, thermal property, electrical resistivity, glass transition
1. Introduction
Nanocrystalline (n-) materials have attracted attention be-cause of their unique structure, in which ultrafine crystallites with a grain size of less than 100 nm are surrounded by dis-ordered grain boundaries. For metallic materials with ultraf-ine polycrystallultraf-ine states, the most promultraf-inent and techno-logically important feature is the increase in strength with decreasing grain size (Hall-Petch effect). A strength and hardness much higher than those of the conventional poly-crystalline (p-) counterparts were reported for n-metals1–3).
However, the increase in strength of n-metals showed satura-tion and decreased with the further decrease in grain size to less than 20 nm (inverse Hall-Petch effect)4,5). The inverse
Hall-Petch effect was attributed to sliding or shear deforma-tion at the grain boundaries6,7). The increased volume
frac-tion of the grain boundaries also affected other physical properties of n-metals; for example, higher electrical resis-tivity than that of p-metals was reported8,9). These
observa-tions suggest that the behavior of the grain boundaries play an important role on the characteristic properties of
n-metals.
For p-metals, the positions of atoms at the grain boundar-ies are not random like they are in amorphous solids; further, periodic arrangements of structural units with atoms were observed for the grain boundaries of p-metals via scanning transmission electron microscopy10,11). From the molecular
dynamics simulation, on the other hand, dynamic behavior similar to that of glass-forming liquids was suggested for the grain boundaries of p-materials at high temperatures12).
Furthermore, first-order transition of order-disorder in the grain boundaries below the melting point13) and reversible
structural transformation in Cu ∑5(310) grain boundaries14)
have also been observed. Moreover, the liquid-like state of grain boundaries was identified using molecular dynamics simulations of n-Si and n-metals15–17). For colloidal crystals
with a diameter of 600 nm, the glass transition of grain boundaries was recently suggested from confocal optical mi-croscope observations18). However, no experimental results
have been reported to support the amorphous state or
glass-like characteristics of the grain boundaries in metals. For n-Au in the as-prepared state, we reported that the in-ternal friction showed an anomalous large increase above 200 K (Q−1
>200K, see Fig. 2)19). It was found that Q−>1200K was
repeatedly observed for cooling and warming below 350 K but the amount decreased with grain growth after heating above 350 K. These observations suggested that some anelastic process of grain boundaries was thermally acti-vated above 200 K in n-Au20). The internal friction due to
grain boundaries was observed in p-Au also but at much higher temperatures above 400 K at a similar measurement frequency21). In our previous thermal analysis, an
endother-mic tendency of n-Au compared with p-Au was observed above 200 K22). The endothermic tendency disappeared
af-ter grain growth by annealing above 350 K. Further, the strongly preferred orientation of the crystallites in n-Au turned to random orientations but no grain growth was ob-served after plastic creep deformation at room tempera-ture23). On the other hand, it was suggested that the plastic
creep deformation of n-Au at liquid nitrogen temperature was governed by dislocation motions or twin formation22).
These results indicate that the grain boundaries of n-Au be-come anelastic or viscoelastic above 200 K, like metallic glasses above the glass transition temperature; the viscoelas-ticity of the grain boundaries aids plastic deformation by grain sliding with the rotation of the crystallites. The visco-elastic state appears to be quasi-stable because no grain growth occurs during the plastic deformation.
If Q−1
>200K reflects a state change of the grain boundaries
from ideal elastic to anelastic or viscoelastic, corresponding variations are expected for other physical properties. In the present study, possible changes in thermal properties and electrical resistivity of n-Au were carefully measured at low temperatures, and the results were compared with those of anelasticity in order to survey the amorphous behavior of the grain boundaries.
2. Experimental
Nanocrystalline Au specimens were prepared by the gas deposition (GD) method19). In this method, ultrafine Au
par-ticles formed by the gas condensation process were directly deposited on a cooled glass substrate by using a He gas jet
* Present address: Body Assembly Facilities Design Section, Nissan Motor
Co., Ltd., Zama 252–8502, Japan
flow. The purity of He was maintained above 99.9999% by a purification system in order to obtain contamination-free and fully dense specimens. Ribbon-like specimens with a length, width, and thickness of 23 mm, 1 mm, and 0.05 mm, re-spectively, were deposited on the glass substrate. The sub-strate was cooled by a cold finger connected to a liquid ni-trogen reservoir. The deposition rate (deposited thickness per unit area and unit time) was controlled by the crucible temperature for the nanoparticle preparation by the gas con-densation method. The crucible temperature was measured by using a pyrometer and the substrate temperature was measured by using a thermocouple. The deposition rate, cru-cible temperature, and substrate temperature are listed in Table 1. The deposited ribbons were carefully removed from the substrate. After the preparation, all n-Au specimens were stored in a refrigerator at 260 K.
The density of the specimens was evaluated using the Archimedes method with high-purity ethanol. The lattice pa-rameter and mean grain size were determined by X-ray dif-fraction measurements with Cu-Kα radiation (X Pert PRO, PANalytical, 45 kV and 40 mA). Nelson-Riley analysis24)
was applied for diffraction peaks to evaluate the lattice pa-rameter. The mean grain size and microstrain were evaluated from the broadening of diffraction peaks by using Halder-Wagner plots25). The internal friction and resonant frequency
were measured by using the electrostatically excited flexural resonant vibration of a reed specimen (resonant fre-quency 650 Hz)19).
Differential scanning calorimetry (DSC) was conducted on an X-DSC7000 (Seiko Instruments Inc.) for a specimen of 5 mg at a heating rate of 20 K/min in the temperature range between 140 and 300 K. The electrical resistivity was measured by the four-probe method in the temperature range between 80 and 300 K.
3. Results
3.1 Textures of n-Au
The mean grain size, microstrain, lattice parameter, and density of n-Au prepared and used in the present study are listed in Table 1. In the as-prepared state, the mean grain size of n-Au used ranged from 28 to 40 nm and the density was more than 98% of that of p-Au. The lattice parameters
of specimens B and C in the as-prepared state were identical to those of p-Au (a0 = 4.07865 nm) within the present
exper-imental error. However, the lattice parameters of specimen A were smaller than those of p-Au and the normalized change (Δa/a0 = (a − a0)/a0, a0 is the lattice parameter of p-Au) of
specimen A was Δa/a0 = −0.13%. For comparison, Δa/a0 =
−0.006% was reported for IGCC n-Pd26) with the grain size
of 40 nm. A maximum lattice contraction of Δa/a0 =
−0.01% was also reported for BM n-Ni, n-Cu27), and n-W28).
Our previous study suggested that the lattice parameters of
n-Au were smaller than those of p-Au by 0.05% and the vacancy concentration was 0.1% in the as-prepared state29).
Figure 1 shows the XRD patterns of specimens A, B and C. All specimens show a strong (111) preferred orientation in which the (111) planes of most crystallites are parallel to the specimen surface in the as-prepared state. The (111) pre-ferred orientation of specimen A was changed to the (100) preferred one by the grain growth after heat treatment to 660 K. Grain growth and weakening in the (111) preferred
[image:2.595.321.529.319.731.2]Fig. 1 X-ray diffraction patterns of n-Au used for (a) internal friction (specimen A), (b) differential scanning calorimetry (specimen B), and (c) electrical resistivity (specimen C) measurements. In (a) and (b), the patterns after warm-up to elevated temperatures and aging at 260 K for 18 months are also shown.
Table 1 Experimental conditions (deposition rate, crucible temperature, and substrate temperature) for the preparation by the gas deposition method and characteristics of n-Au (lattice parameter, mean grain size, microstrain, and relative density to the p-Au value (19.3 g/cm3)) in the as-prepared state.
Specimen A B C
Depo. rate [nm/s] 202 161 112
Crucible temp. [K] 1882 1807 1726
Substrate temp. [K] 255 256 256
Lattice parameter
[Å] 4.0732 ± 0.0008 4.0783 ± 0.0008 4.0794 ± 0.0008 Mean grain size
[nm] 28 ± 2 31 ± 1 40 ± 2
[image:2.595.46.289.664.787.2]orientation were observed for specimen B after aging at 260 K for 18 months or after heat treatment to 723 K. There were several reports that the grain growth was enhanced in
n-metals. Grain growth of n-Cu was reported during the in-dentation test at 83 K30). The grain growth of n-Ni during
deformation was reported even at an applied stress as low as 20% of its yield stress31). Without the applied stress, the
grain size of n-Pd increased from 10 to 45 nm when kept at room temperature for 20 h32,33). For GD n-Au, no obvious
grain growth was observed after plastic deformation at room temperature23) or storage at room temperature for several
days.
3.2 Anelasticity measurements
Figure 2 shows the temperature changes in the resonant frequency (f) and internal friction (Q−1) of n-Au (specimen
A). As reported by our previous study19), a rapid increase in
Q−1 was observed above 200 K (Q−1
>200K) in the as-prepared
state. In Fig. 2(a), careful observation indicates that the in-crease in Q−1 started below 200 K. Corresponding to
Q−1
>200K, the resonant frequency showed a rapider decrease as
the temperature increases above 200 K. The same tempera-ture dependences in f and Q−1 were observed for the
repeti-tion of the measurements from 30 to 300 K. Since Q−1
>200K
became small with the grain growth induced by annealing above 350 K, Q−1
>200K was attributed to an anelastic process
activated in the grain boundaries above 200 K29,34). It is
noted that Q−1
>200K was commonly reported for other FCC
n-metals such as n-Cu34), n-Al35), and n-Ag36). The sliding
motions of grain boundaries in p-metals were intensively in-vestigated by anelasticity measurements37). The atomistic
process of grain boundary anelasticity was investigated from
the experiments using bi-crystals and molecular dynamics simulations38,39). Migration of the grain boundaries
perpen-dicular to the boundary plane was attributed to the origin of grain boundary anelasticity at lower temperature, and the sliding motion along the boundary plane was to the origin of anelasticity at higher temperature.
In the resonant vibration measurement, the increase in f reflects the increase in the dynamic modulus. The dynamic modulus of anelastic materials normally shows an increase with the decrease of the anelastic strain. In Fig. 1, Q−1 was
decreased but f showed a decrease by the grain growth after warm-up. As shown in Fig. 1(a), the (111) preferred orienta-tion in the as-prepared state was changed to the (100) pre-ferred one by the grain growth after thermal treatment to 660 K. The value of dynamic Young s modulus of Au much depends on the crystallographic directions, and those along the <111>, <110>, and <100> directions are 116, 81.3, and 41.3 GPa at 300 K, respectively40). The decrease in f by the
grain growth in Fig. 2(a) mainly reflects the texture change by the grain growth as the mean dynamic modulus along the specimen length direction became lower.
For plastically deformed FCC p-metals, a relaxation peak with the modulus defect was observed (Bordoni peak) and explained by the kink-pair formation process of disloca-tions41). The Bordoni peak of p-Au was observed at 110 K
under the measurement frequency at 650 Hz. The disloca-tion activity in n-metals is still an open quesdisloca-tion and the mechanism for the Q−1 peak at 100 K displayed in Fig. 1 is
outside the scope of the present study.
3.3 Thermal properties
As mentioned in section 3.2, the observation of Q−1
>200K
in-dicates that certain atomic motions are thermally activated in the grain boundaries above 200 K. Our previous and pre-liminary thermal measurements suggested that the heat ca-pacity increased above 200 K22). Figure 3(a) shows the
re-sults of differential scanning calorimetry (DSC) measurements during heating from 140 to 300 K, where the heat flow curves of n-Au (specimen B) in the as-prepared state and n-Au after heating to 723 K are depicted. The heat flow of n-Au in the as-prepared state became endothermic above 170 K compared with that of n-Au after heating to 723 K. It is noted that the heat flow curve was reproduced within the variation shown in Fig. 3(a) for the repetition of the thermal measurements from 140 to 300 K. The deviation in the endothermic heat flow of n-Au after heating to 723 K is plotted in Fig. 3(b). An endothermic tendency above 170 K was clearly seen for n-Au in the as-prepared state. It is known that thermally stable amorphous alloys known as metallic glasses, showed a step-like increase in heat capacity42) and a rapid increase in anelasticity43) at the
glass transition temperature during heating. In Fig. 3, the re-sult of specimen B stored at 260 K for 18 months is also shown. The endothermic tendency was similar to that in the as-prepared state, but the onset temperature shifted slightly to a higher temperature. The grain growth from 31 to 67 nm was found by the aging at 260 K. At the same time, the in-ternal friction shows a slight decrease (see Fig. 5(a)); how-ever, Q−1
>200K remained similar to that observed in the
as-pre-pared state. These observations suggest that the amount of
[image:3.595.66.271.476.734.2]grain boundaries decreased but the nature of the grain boundaries was not greatly modified by the aging at 260 K.
3.4 Electrical resistivity
The temperature change in electrical resistivity of n-Au (specimens B and C) in the as-prepared state is depicted in Fig. 4. The same temperature dependence is observed for the repetition of the cool-down and warm-up procedure below room temperature. The electrical resistivity of n-Au in the as-prepared state is higher than that of p-Au for the tempera-ture range investigated. In the range between 90 and 300 K, the electrical resistivity of p-Au increases linearly with the temperature. Above 130 K, the electrical resistivity of both specimens B and C show a slight downward deviation from a linear increase with increasing temperature. The deviations in the resistivity from the linear extrapolation for the ob-served data below 120 K (dashed lines in Fig. 4(a)) are shown in Fig. 4(b). The magnitude of the deviation is not the same but the behavior is quite similar for both the speci-mens. The temperature dependence of the resistivity of GD
n-Au was reported by Ederth et al. and a discontinuous change in electrical resistivity below 10 K was discussed44).
A similar deviation from the linear temperature increase above 150 K was observed for Ederth data by carefully monitoring the temperature dependence.
The electrical resistivity of specimen C was higher than that of specimen B. The mean grain size of specimen C was somewhat larger than that of specimen B. In Table 1, the deposition rate of specimen C is about 30% smaller than that
of specimen B. We reported that the texture and property of
n-Au prepared at the higher deposition rate were different from those at the lower rate23,29). The resistivity of specimen
C higher than that of specimen B indicates the difference in the grain boundary state between them; however, the details of the relationship between the grain boundary state and re-sistivity are still unclarified at present.
4. Discussion
Characteristic changes in anelastic, thermal, and electrical properties were found above 130 K as shown in Figs. 2, 3, and 4, respectively. These characteristic changes were simi-larly observed for the repetition of the cool-down and warm-up procedure below room temperature. However, the proportion of the characteristic changes decreased with the grain growth. These results are summarized in Fig. 5. The DSC measurements clearly indicated that the endothermic tendency or the increase in specific heat began at 170 K in the as-prepared state. The careful observation of the internal friction spectrum also revealed that the increase started above 180 K.
As already mentioned, the metallic glasses showed a step-like increase in the specific heat42) and a rapid increase in
anelasticity43) at the glass transition temperature, where
amorphous materials transform from an elastic solid to a su-percooled viscoelastic liquid state. It was reported that the electrical resistivity of the metallic glasses decreased upon heating (negative Temperature Coefficient of Resistivity (TCR)) and the TCR became more negative at glass transi-tion temperature42,45). The negative TCR below the glass
Fig. 3 (a) Heat flow curves measured for n-Au (specimen B) in the as-pre-pare state (solid line), stored at 260 K for 18 months (dotted and dashed line), after heating to 723 K (p-Au, dashed line) measured by differential scanning calorimetry. The smaller bar indicates the maximum variation in the heat flow curve, where the measurement during heating from 140 to 300 K was repeated. (b) Subtracted endothermic heat flow curves for
n-Au in the as-prepare state and aged at 260 K, where the heat flow of
n-Au after heating to 723 K was used as a reference.
[image:4.595.64.274.63.332.2] [image:4.595.321.529.71.328.2]transition was qualitatively explained by the variation in the structure factor of Ziman s model for pure liquid metals, and the configurational changes as well as the phonon properties for the more negative values around the glass transition.
As shown in Fig. 5(a)–(c), an increase in the anelasticity, endothermic tendency, and deviational decrease in the elec-trical resistivity can be observed, but the onset temperatures were somewhat different between the specimens or proper-ties. Furthermore, the temperature changes in the anelastic-ity and endothermic tendency were rather gradual compared with the step-like changes of metallic glasses at the glass transition. The XRD patterns displayed in Fig. 1 indicate that the grain size and degree of the (111) preferred orienta-tion are not identical among specimens A, B and C. The strong (111) preferred orientation suggests that the charac-teristics of the grain boundaries along or perpendicular to the thickness were different. It is known that the characteris-tics of the grain boundaries depend on the geometrical con-ditions14,46). It is surmised that the distribution of the grain
boundary states leads to the broad temperature range where the characteristic changes were observed. The lower onset temperature of electrical resistivity compared with those of the anelasticity and endothermic tendency may reflect that the negative TCR of metallic glasses is observed even below the glass transition temperature.
The temperature range observed is much lower in n-Au than in the amorphous alloys; however, the transitional
[image:5.595.67.269.66.331.2]changes in anelasticity, thermal properties, and resistivity in Fig. 5 are qualitatively similar to the glass transition of the metallic glasses. It is noted that n-Au showed a creep defor-mation above 200 K under the applied stress of 80 MPa but no plastic deformation at 80 K under a few 100 MPa of stress22). This plastic deformation behavior is in good
agree-ment with the assumption that the grain boundaries of n-Au are ideal elastic solids below 130 K and the anelastic or viscoelastic nature becomes thermally activated above 130 K22). It was reported that reversible first-order
structural transformation in ∑5 grain boundaries of FCC metals was caused by temperature from molecular dynamics simulation13). The characteristic changes in anelastic,
ther-mal, and electrical properties in Fig. 5 indicate that the tran-sition in grain boundaries of n-Au is second-order like. We surmise that these characteristic changes reflect the glass-transition-like behavior of the grain boundaries in
n-Au; in other words, the grain boundaries are in an amor-phous state and different from those of p-metals.
5. Conclusion
For n-Au prepared by the gas deposition (GD) method, characteristic temperature changes were observed in the low-temperature anelastic, thermal, and electrical resistivity measurements below room temperature. In the anelastic measurement, the internal friction started to increase above 180 K and a rapid increase linearly with temperature was observed above 200 K (Q−1
>200K). Differential scanning
calorimetry revealed that the heat flow of n-Au showed an endothermic tendency above 170 K or a gradual increase in heat capacity. The increases in internal friction and endo-thermic tendency disappeared with the progression of the grain growth after annealing. The electrical resistivity of
n-Au between 90 and 300 K was much higher than that of
p-Au and showed a monotonous increase with temperature. However, the temperature coefficient of the resistivity of
n-Au showed a deviation from a linear change and a slight upward convex curve above 130 K. These characteristic temperature changes were similarly observed for the repeti-tion of the cool-down and warm-up procedure below room temperature. It was reported that metallic glasses showed a step-like increase in the specific heat, a rapid increase in anelasticity, and a decrease in electrical resistivity at the glass transition temperature. The characteristic temperature changes of n-Au mentioned above are qualitatively similar to those of metallic glasses at the glass transition tempera-ture. It indicates that the glass-transition-like change is ther-mally activated in the grain boundaries of n-Au.
Acknowledgments
The present study was financially supported by the JSPS KAKENHI Grant 25390027 from the Japan Society for the Promotion of Science (JSPS). The differential scanning cal-orimetry was carried out at the Chemical Analysis Division and the OPEN FACILITY, Research Facility Center for Science and Technology, University of Tsukuba. The authors thank Prof. Hiroshi Mizubayashi (University of Tsukuba) for valuable discussions.
REFERENCES
1) M.A. Meyers, A. Mishra and D.J. Benson: Prog. Mater. Sci. 51 (2006) 427–556.
2) G.W. Nieman, J.R. Weertman and R.W. Siegel: Scr. Metall. 23 (1989) 2013–2018.
3) J.R. Weertman: Mater. Sci. Eng. A 166 (1993) 161–167.
4) R.A. Masumura, P.M. Hazzledine and C.S. Pande: Acta Mater. 46 (1998) 4527–4534.
5) H. Tanimoto, N. Yagi, T. Yamada, H. Mizubayashi, Characterization and Mechanical Properties of High-Density Nanocrystalline Copper, Proc. of Int. Conf. on Advanced Technology in Experimental Mechanics 2003 (ATEM 03), Nagoya Congress Center, Nagoya, Japan, 10–12 Sept., 2003, ed. by Y. Akiniwa et al., OS06W0399(6 pages).
6) S. Takeuchi: Scr. Mater. 44 (2001) 1483–1487.
7) G.J. Tucker and D.L. McDowell: Int. J. Plast. 27 (2011) 841–857. 8) H. Zeng, Y. Wu, J. Zhang, C. Kuang, M. Yue and S. Zhou: Prog. Nat.
Sci. 23 (2013) 18–22.
9) L.H. Qian, Q.H. Lu, W.J. Kong and K. Lu: Scr. Mater. 50 (2004) 1407–1411.
10) K. Inoue, M. Saito, C. Chen, M. Kotani and Y. Ikuhara: Microscopy (Oxf.) 65 (2016) 479–487.
11) K. Inoue, B. Feng, N. Shibata, M. Kotani and Y. Ikuhara: J. Mater. Sci. 52 (2017) 4278–4287.
12) H. Zhang, D.J. Srolovitz, J.F. Douglas and J.A. Warren: Proc. Natl. Acad. Sci. USA 106 (2009) 7735–7740.
13) M. Tang, W.C. Carter and R.M. Cannon: J. Mater. Sci. 41 (2006) 7691–7695.
14) T. Frolov, D.L. Olmsted, M. Asta and Y. Mishin: Nat. Commun. 4 (2013) 1899.
15) P. Keblinski, S.R. Phillpot, D. Wolf and H. Gleiter: Phys. Rev. Lett. 77 (1996) 2965.
16) P. Keblinski, S.R. Phillpot, D. Wolf and H. Gleiter: Acta Mater. 45 (1997) 987–998.
17) D. Wolf: Curr. Opin. Solid State Mater. Sci. 5 (2001) 435–443. 18) K.H. Nagamanasa, S. Gokhale, R. Ganapathy and A.K. Sood: Proc.
Natl. Acad. Sci. USA 108 (2011) 11323–11326.
19) S. Sakai, H. Tanimoto and H. Mizubayashi: Acta Mater. 47 (1998) 211–217.
20) H. Tanimoto, K. Mutou, Y. Hosonuma, K. Yamamoto and H. Mizubayashi: Mater. Sci. Eng. A 521–522 (2009) 295–298.
21) S. Okuda, F. Tang, H. Tanimoto and Y. Iwamoto: J. Alloys Comp. 211–212 (1994) 494–497.
22) H. Tanimoto: Solid State Phenom. 184 (2012) 42–51.
23) N. Yagi, A. Rikukawa, H. Mizubayashi and H. Tanimoto: Phys. Rev. B
74 (2006) 144105.
24) H.P. Klug and L.E. Alexander: X-ray diffraction procedures, second ed.,(Wiley, New York, 1974)pp. 661–665.
25) N.C. Halder and C.N.J. Wagner: Acta Crystallogr. 20 (1966) 312–313. 26) R. Birringer, M. Hoffmann and P. Zimmer: Phys. Rev. Lett. 88 (2002)
206104.
27) G.K. Rane, U. Welzel, S.R. Meka and E.J. Mittemeijer: Acta Mater. 61 (2013) 4524–4533.
28) A.K. Srivastav, N. Chawake and B.S. Murty: Scr. Mater. 98 (2015) 20–23.
29) H. Tanimoto, S. Sakai, E. Kita and H. Mizubayashi: Mater. Trans. 44 (2003) 94–103.
30) K. Zhang, J.R. Weertman and J.A. Eastman: Appl. Phys. Lett. 87 (2005) 061921.
31) B. Wang, M.T. Alam and M.A. Haque: Scr. Mater. 71 (2014) 1–4. 32) M. Grewer, J. Markmann, R. Karos, W. Arnold and R. Birringer: Acta
Mater. 59 (2011) 1523–1529.
33) M. Ames, J. Markmann, R. Karos, A. Michels, A. Tschöpe and R. Birringer: Acta Mater. 56 (2008) 4255–4266.
34) N. Yagi, A. Ueki, H. Mizubayashi and H. Tanimoto: J. Metastable Nanocryst. Mater. 24–25 (2005) 503–506.
35) Y. Kabe, H. Tanimoto and H. Mizubayashi: Mater. Trans. 45 (2004) 119–124.
36) H. Mizubayashi, J. Matsuno and H. Tanimoto: Scr. Mater. 41 (1999) 443–448.
37) A. S. Nowick and Berry, B. S., Anelastic Relaxation in Crystalline
Solid, Academic Press, New York, (1972), p. 436.
38) A.K. Maier, D. Mari, I. Tkalcec and R. Schaller: Arch. Metall. Mater. 60 (2015) 377–380.
39) A.-K. Maier, D. Mari, I. Tkalcec and R. Schaller: Acta Mater. 74 (2014) 132–140.
40) Landolt-Börnstein, Numerical Data and Functional Relationships in
Science and Technology, New Series, Group III: Crystal and Solid State Physics, ed. by K.-H. Hellwege and A. M. Hellwege (Springer-Verlag, 1979) Vol. 11, p. 9.
41) G. Fantozzi, C. Esnouf, W. Benoit and I.G. Ritchie: Prog. Mater. Sci. 27 (1982) 311–451.
42) O. Haruyama, H. Kimura, N. Nishiyama and A. Inoue: Mater. Sci. Eng. A 304–306 (2001) 740–742.
43) L.-F. Wang, Q.-D. Zhang, Z.-Y. Huang, X. Cui and F.-Q. Zu: J. Non-Cryst. Solids 406 (2014) 127–132.
44) J. Ederth, L.B. Kish, E. Olsson and C.G. Granqvist: J. Appl. Phys. 88 (2000) 6578–6582.
45) D.P. Aji and G.P. Johari: J. Chem. Phys. 141 (2014) 224508.
