Solid State Phenomena Vol. 184 (2012) pp 271-276 Trans Tech Publications. Switzerland Doi:10.4028/www.scientific.net/SSP.184.271
High Temperature Internal Friction in Fine Grain and Nano- Crystalline Zirconia P. Simas1,a, M. Castillo-Rodríguez1,b, M. L. Nó2,a, S. De-Bernardi3,a, D. Gomez3,b, A. Domínguez-Rodríguez3,c, J. San Juan1,c. 1
Dpto Física de la Materia Condensada, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Aptdo 644, 48080 Bilbao (Spain) 2
3
Dpto Física aplicada II, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Aptdo 644, 48080 Bilbao (Spain)
Dpto Física de la Materia Condensada, Facultad de Física, Universidad de Sevilla, Aptdo 1065, 41080 Sevilla (Spain) 1,b
[email protected] (corresponding author) and 1,
[email protected]
Keywords: Mechanical spectroscopy, advanced ceramics, internal friction, nano-materials.
Abstract. Engineering ceramics are being developed to improve their high-temperature mechanical properties and in particular creep resistance. Recently the production of fine grain ceramics undergoes another step-forward with the development of new technologies to produce nanocrystalline materials. The question is whether the properties depending on the grain size can be extrapolated at nano-scale or, on the contrary, new microscopic mechanisms could appear to be dominant at this nanometer grain size. In the present work we study, by mechanical spectroscopy, the high temperature behavior up to 1350ºC of a fine grain Zirconia and a nano-crystalline Zirconia sintered in a conventional way. A new forced torsion pendulum, recently built, has been used for the mechanical spectroscopy measurements. The high temperature background (HTB) of internal friction has been measured as a function of temperature for different frequencies in both materials. The analysis of the HTB shows that the fine grain Zirconia exhibits a single process of defects mobility, with an apparent activation enthalpy similar to the one measured by creep. On the contrary, the HTB of the nano-crystalline sample becomes more complex, showing a much higher energy loss, which will be discussed at the light of the internal friction spectra analysis. Introduction Yttria-tetragonal ZrO2 polycrystals (YTZP) is one of the most promising materials for mechanical applications due to its excellent strength and fracture toughness. Many studies on the high temperature plastic deformation of this material have been performed with different yttria contents [1-5]. In particular, fine-grained tetragonal zirconia exhibits superplastic flow as was shown by Wakai et al [6]. Grain boundary sliding has been considered to be the principal microscopic mechanism during high temperature deformation of this material. It is widely admitted that superplasticity could be obtained at lower temperatures or at high strain rates by decreasing the grain size. Several measurements have been performed in this material obtaining a value of the apparent activation enthalpy between 5 and 7 eV, depending on the applied stress and temperature [7]. Mechanical spectroscopy is a powerful technique that can give useful information about the deformation mechanism. Moreover, it is a not destructive techniqueas the sample is submitted to a low level stress oscillation in the elastic range, allowing the micro-structural units (dislocations, point defects,…) to move between near equilibrium positions. However there is a phase lag between the applied stress and the deformation, since the motion of the defects does not take place immediately, but is delayed because of the time required to -thermally activated jumps. This phase lag which is called internal friction (IF), can provide helpful information like the activation enthalpy associated with the motion of the defects [8], and then give an idea about the operating deformation
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mechanism that takes place in this material. In this work we present the study, performed by means of mechanical spectroscopy, on two sets of YTZP specimens with micro and nano metric grain size. It is expected that the mechanical behavior be different and the present analysis could help about how this material deforms. The good agreement between the results obtained by creep experiments and by mechanical spectroscopy shows that this last technique should be a good candidate to test materials before creep experiments. Experimental procedure The equipment used in this work has been developed few years ago [9]. It has a vacuum system that reaches 10-4 Pa, an anti-vibratory system to provide stability to the pendulum, a temperature control system with a stability of ± 0.1 K. A permanent magnet is excited by two Helmholtz coils driven by a KEPCO power supply, which amplifies the sinusoidal signal from a Solartron frequency analyzer. The response signal due to the torsion angle is detected by the displacement of the laser beam spot on a photocell. This response is filtered, magnified and sent to the frequency analyzer which measures the phase lag between the excitation and the response signal. The oscillating strain is measured through an Agilent 34970A voltmeter. Two sets of specimens have been studied by mechanical spectroscopy, both of them sintered in a conventional way using a temperature rate of 600 C/h. One set of samples was sintered at 1250 ºC during 2 hours displaying an average grain planar diameter of about 50 nm and then henceforth they are called nano-YTZP specimens. The other set was sintered at 1450 ºC during 4 hours and consequently an average grain size in the micro-scale range was obtained (∼ 0,6 µm), so this set is called micro-YTZP (Fig. 1). a)
b)
Fig. 1. Micrographs of the two sets of YTZP samples. The average grain planar diameter is 0,6 µm in a) and 50 nm in b). For mechanical spectroscopy analysis we assume that the high temperature background HTB can be described from Maxwell model where the internal friction Q-1 can be written as [10,11]: Q-1= 1/(ωτ)n (1) being ω the oscillating stress frequency, τ the relaxation time and n a parameter that corresponds to the distribution of the relaxation times. Taking logarithm we obtain: Ln Q-1= -nLnω –Ln τn (2) Since viscoelastic behavior is determined by thermally activated processes an Arrhenius equation is expected for the relaxation time τ: τ*=τn= τ0n exp (n Hact/kBT) (3) -1 τ* being an apparent relaxation time. So plotting Ln Q versus Lnω we obtain the parameter n and also τ* for each temperature. And plotting τ* versus 1/T allows one to determine the apparent
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activation enthalpy associated to the microscopic mechanism responsible of the relaxation process, for instance grain boundary sliding. Results and discussion Fig. 2 shows the internal friction versus temperature at an oscillating frequency of 1 Hz, performed in a micro-YTZP specimen. All the measurements have been realized with an initial oscillating amplitude at RT of ε=10-5 at a heating rate of 1.5 K/min. The dynamic modulus variation is also plotted, and its smooth behavior indicates that nothing strange took place during the test, like a specimen failure. The internal friction experiences an exponential increase around 1300 K, which is relatively monotonous in the whole high temperature background region. That indicates the uniqueness of the nature of the micro-structural units stimulated during the experiments. 0.06 14
Var.Mod 0.04
1 Hz
12
10 0.03 8
0.02
6
0.01
0 800
Var.Mod
Internal Friction
0.05
4 900 1000 1100 1200 1300 1400 1500 1600
T emperature [K]
Fig. 2. Internal friction versus temperature with the application for the oscillating stress of 1 Hz, in the micro YTZP specimen. From 1300 K this value increases monotonously.
Internal Friction
0.2
0.15
3 Hz 1 Hz 0.3 Hz 0.1 Hz 0.03 Hz 0.01 Hz
0.1
0.05
0 800
900 1000 1100 1200 1300 1400 1500 1600
Temperature [K]
Fig. 3. Internal friction vs. temperature for different frequencies. For a given temperature, the internal friction decreases with the frequency.
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In Fig. 3 we show the internal friction versus temperature for different oscillating stress frequencies. It is clear that the internal friction value increases by decreasing the frequency, and in all cases we observe an exponential increase in the high temperature background region. That indicates that in the range of temperatures and frequencies studied here the micro-structural units stimulated have the same nature. So only one process is being thermally activated, although it could be the result of the coupling of several individual mechanisms related to the grain boundary sliding. From the experimental results shown in figure 3, we have selected different temperatures and for each one we have measured the internal friction as a function of frequency. Then we have plotted fondo alta temperatura Al O 2 3 the internal friction logarithm versus the logarithm of the frequency, as it shown in Fig. 4, following the method developed by Weller [11] and recently applied to intermetallics [12,13]. -1.5 1575 [K] 1550 [K] 1525 [K] 1500 [K] 1475 [K] 1450 [K] 1425 [K]
-2
ln Q
-1
-2.5 -3 -3.5 -4
y = -2.4666 - 0.29864x R= 0.99939 y = -2.6748 - 0.29827x R= 0.99926 y = -2.9009 - 0.30776x R= 0.99861 y = -3.1197 - 0.31487x R= 0.99673 y = -3.3464 - 0.30112x R= 0.99208 y = -3.6155 - 0.308x R= 0.99475 y = -3.8854 - 0.30151x R= 0.99215
-4.5 -5
-3
-2
-1
0
1
2
3
ln ω
Fig. 4. Plot of LnQ-1 vs. Lnω for various temperatures. A value of about n=0,3 is obtained for the distribution of the relaxation time. A linear dependence of LnQ-1 on Lnω is clearly demonstrated. From the slopes of the linear regressions at each temperature it is possible to obtain the distribution factor of the relaxation time n=0.3 , and from the intercept with the Ln Q-1 axis the apparent relaxation time τ* for each temperature. Assuming an Arrhenius dependence of τ* on temperature (Eq. 3) we can obtain the activation enthalpy of the mechanism involved in the HTB. Fig. 5 shows the plot of Ln τ* vs. 1/T whose fit provides an activation enthalpy of Hact=6,3 ± 0,2 eV and a relaxation time τ0≅ 4,3 18-18 s. This activation enthalpy value is in good agreement with the one obtained by other authors from creep experiments, since they reported a value for the activation enthalpy between 5 and 7 eV depending on creep conditions [7]. For one hand, this agreement is surprising if we take into account the large difference between creep and mechanical spectroscopy experiments due to the much lower stresses involved in the latter. But, on the other hand it constitutes a proof that mechanical spectroscopy is a helpful non-destructive technique that can provide useful information like activation enthalpy of thermally activated deformation mechanism, and therefore its use as a complementary technique for creep experiments is obviously of huge worth.
275 3.5
Ln τ
∗
3
Hact=6,3 ± 0,2 eV τ0≅ 4,3 10-18 s
2.5
2
1.5 0.00062
0.00064
0.00066
0.00068
0.0007
0.00072
1/Temperature [K]
Fig. 5. Ln τ* versus 1/T plot. Following Eq. 3 an activation energy Hact=6,3 ± 0,2 eV and a relaxation time τ0≅ 4,3 10-18 s have been obtained. Owed to the good results obtained in the study of the micro-YTZP, it would be interesting to perform the same study to the nano-YTZP in order to see if the properties depending on the grain size can be extrapolated at nano-scale; i. e., how depend the deformation and accommodation mechanisms on the scale in which they operate. Although this study is now in progress, we may advance some interesting previous results. 0.25
Internal Friction
0.2
nano-YTZP micro-YTZP
1 Hz
0.15
0.1
0.05
0 800
900
1000 1100 1200 1300 1400 1500 1600
Temperature [K] Fig. 6. Comparative plot between the internal friction of the micro and nano YTZP performed at 1 Hz. A much higher value for the nano-specimen is observed.
Fig. 6 shows the internal friction versus temperature measured in both sets of samples, micro and nano YTZP at an oscillating frequency of 1 Hz. Clearly it is observed that the nano-YTZP specimen experiences a drastically much higher increase of the internal friction, also starting at lower temperatures than the micro-YTZP. An explanation for this higher internal friction value for nanoYTZP is obtained by taking into account that in both sets grain boundary sliding is the deformation
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mechanism. It is clear that the effective grain boundary area is much larger for nano-YTZP than for micro-YTZP. This effective area is susceptible to glide by the application of the oscillating stress and consequently absorbs energy. So that leads to the higher increase of the internal friction observed in nano-YTZP. A similar analysis applied to the micro-specimen should be performed to the nano-specimen in order to get the activation energy and the relaxation time to study if the grain boundary sliding is somehow perturbed going down from micro to nano-scale. Conclusions A detailed analysis has been carried out in YTZP specimens by means of mechanical spectroscopy. The results obtained in micro YTZP show that only one thermally activated process takes place for the temperatures and frequencies studied here. The activation enthalpy is in good agreement with values reported in literature obtained by creep experiments. This is an evidence that mechanical spectroscopy is a useful complementary technique to creep tests, with the advantage of being a nondestructive technique. Nano-YTZP specimen exhibits a higher increase of the internal friction HTB compared to micro-YTZP, due to a higher effective grain boundary area associated to the former. More work should be carried out to nano-YTZP in order to study how grain boundary sliding operates at nano-scale. Acknowledgments This work was supported by the Spanish MICINN project CONSOLIDER-INGENIO 2010 CSD2009-00013, by the Consolidated Research Group IT-10-310 from the Education Department and the project ETORTEK ACTIMAT-10 from the Industry Department of the Basque Government. M. C-R thanks the Government Basque for the post-doctoral contract in the frame of the IT-10-310. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
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