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Thermal conductivity of self-ion irradiated nanocrystalline zirconium thin films
Thin Solid Films 638 (2017) 17–21
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Thin Solid Films journal homepage: www.elsevier.com/locate/tsf
Thermal conductivity of self-ion irradiated nanocrystalline zirconium thin films Raghu Pulavarthy a, Baoming Wang a, Khalid Hattar b, M.A. Haque a,⁎ a b
Mechanical and Nuclear Engineering, Penn State University, University Park, PA 16802, United States Sandia National Laboratories, PO Box 5800, Albuquerque, NM 87185, United States
a r t i c l e
i n f o
Article history: Received 21 December 2016 Received in revised form 10 July 2017 Accepted 14 July 2017 Available online 15 July 2017 Keywords: Thermal conductivity Ion irradiation Nanocrystalline metal Transmission electron microscopy (TEM)
a b s t r a c t Thermomechanical stability and high thermal conductivity are important for nuclear cladding material performance and reliability, which degrade over time under irradiation. The literature suggests nanocrystalline materials as radiation tolerant, but little or no evidence is present from thermal transport perspective. In this study, we irradiated 10 nm grain size zirconium thin films with 800 keV Zr+ beam from a 6 MV HVE Tandem accelerator to achieve various doses of 3 × 1010 to 3.26 × 1014 ions/cm2, corresponding to displacement per atom (dpa) of 2.1 × 10−4 to 2.28. Transmission electron microscopy showed significant grain growth, texture evolution and oxidation in addition to the creation of displacement defects due to the irradiation. The specimens were co-fabricated with micro-heaters to establish thermal gradients that were mapped using infrared thermometry. An energy balance approach was used to estimate the thermal conductivity of the specimens, as function of irradiation dosage. Up to 32% reduction of thermal conductivity was measured for the sample exposed to a dose of 2.1 dpa (3 × 1014 ions/cm2). © 2017 Elsevier B.V. All rights reserved.
1. Introduction Radiation in nuclear applications adversely influences the defect density and microstructure of the fuel cladding material. Energetic particles, such as neutrons, with sufficient kinetic energy knocks off atoms from their lattice sites of the cladding materials, creating defects associated with the missing lattice atoms (vacancies) and the dislodged atoms that reside in the lattice interstices. When the atomic displacement exceeds a threshold, this is followed by further displacement in the neighboring atoms in a cascaded manner [1]. The process takes time from femto to picoseconds and results in the partial recombination of the vacancy and interstitial point defects, while the remaining defects may agglomerate to form vacancy clusters and dislocation loops [2] due to their surface energy [3,4]. Depending on the radiation fluence, temperature and other harsh environmental factors, these one-dimensional defects lead to two and three dimensional defects dislocations and voids. The literature is well-established on the mechanical and microstructural aspects. However, thermal transport is also very important the materials are continuously exposed to intense radiation at high temperatures and the heat (with high flux) must be removed to ensure safety and reliability [5]. For example, radiation induced amorphization [2] can reduce thermal conductivity of metals. Similarly, oxidation or hydration
⁎ Corresponding author. E-mail address: [email protected] (M.A. Haque).
http://dx.doi.org/10.1016/j.tsf.2017.07.035 0040-6090/© 2017 Elsevier B.V. All rights reserved.
can severely deteriorate both mechanical and thermal properties [6,7], which has led researchers to innovate on protecting the surfaces from radiation [8]. The motivation for this study comes from the application potentials of nanocrystalline materials, which are hypothesized to exhibit have better resistance to irradiation [9,10]. The hypothesis driving this area of research is that grain boundaries act as sinks for radiation induced defects [11,12]. Since the volume fracture of grain boundary atoms scales in a cubic power or grain size (the fraction can reach ~ 50% for grain size of ~6 nm [13]), the abundance of defect sinks may render nanocrystalline materials more radiation tolerant. However, the existing studies are mostly on mechanical properties and a limited literature is available on the thermal transport aspect in nanostructured nuclear materials [14]. Literature shows that the thermal conductivity of nanocrystalline metal films can be as low as one-third of the bulk value at room temperature and even smaller at lower temperature [15]. This not unexpected because when this grain approaches the electron mean free path (around 10 nm for Zr [16]), metallic thermal conductivity will experience enhanced scattering at the boundaries. First principles calculations show that lack of crystallinity reflected by vacancies and disorder as well as non-planarity/misorientation of grain boundaries contribute significantly to grain boundary reflectivity [17]. In the present study, we investigate thin films, for which surface scattering can play roles typically non-existent in bulk form. However, the literature suggests that the reduction in thermal conductivity is predominantly caused by grainboundary and less by surface scattering [18].
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R. Pulavarthy et al. / Thin Solid Films 638 (2017) 17–21
Accordingly, we propose that the large volume fraction of grain boundaries, compounded by the vacancies, interstitials and voids introduced by radiation, is not only expected to increase the thermal resistance, but also lattice resistance for grain sizes below the phonon mean free path [18]. We study self-ion irradiation in zirconium since the metal and its alloys are used as cladding material for the fuel rods in pressurized water reactors and boiling water reactors. This class of materials has low neutron cross-section [19], high hardness, and high corrosion resistance [20,21]. For metals, any change in thermal conductivity by high temperature irradiation (similar to cladding material environment) is recovered immediately due to annealing [22]. The focus of this study however is on the thermal transport in the nanocrystalline regime. Thermal conductivity measurement on irradiated materials is particularly challenging because the radiation fluence is strong function of the thickness. This means a spatial gradient of damage exists along the path of the neutrons or ions. Conventional thermal conductivity measurement techniques for bulk materials on the other hand assume microstructural homogeneity. Therefore, the underlying heat transfer models need to be adapted to capture these gradient effects accurately. Conventional technique, such as laser flash, 3-ω [23], thermo-reflectance [24], etc. can still be applied if a thin section specimen of uniform irradiation dosage is cut out from the bulk. Another way to avoid this problem is perform the irradiation experiments on thin film specimens, which results in approximately uniform damage throughout the crosssection. 2. Experimental setup and results To study the role of irradiation on thermal transport in nanocrystalline materials, we developed a micro-electro-mechanical (MEMS) setup that integrates thin film specimens with micro-heaters. The design is essentially a version of the technique developed by Shi et al. [25], adopted for freestanding thin films. The essence of the design is to suspend the specimen between micro fabricated heaters. The specimen is then
heated to establish a temperature gradient so that the data can be used in a thermal conductivity model. Shi et al. used electrical resistance based thermometry at the two ends of the specimen, which is modified by using a thermal (infrared) microscope for enhance spatial mapping. Fig. 1 shows the device design where the freestanding thin film specimen is co-fabricated with the micro-heaters. First, the thin film (100 nm-thick zirconium) is deposited by physical vapor deposition (PVD) on silicon-on-insulator (SOI) wafer with 20 μm-thick device layer silicon. Alternatively, a thin section coupon can be nano-manipulated on to this device if the specimen is obtained from bulk material. The deposition is a traditional lift-off process where an inverse pattern of photoresist is created on the SOI substrate using standard photolithography. After the deposition, the unwanted photoresist is removed thereby leaving zirconium specimen in the desired pattern. After a second lithography process, the device layer silicon in the exposed areas is etched by SF6 plasma using a deep reactive ion etch (DRIE) process. The third lithography step is done on the back side of the handle layer silicon and a similar DRIE process removes the exposed silicon. The buried oxide (BOX) layer is etched away in CF4 plasma using standard reactive ion etch (RIE) process, leaving the specimen freestanding. Individual dies containing multiple partially processed samples were ion irradiated with an 800 keV Zr+ beam using the 6 MV HVE Tandem accelerator at Sandia's Ion Beam Lab. Ion irradiation is a popular surrogate for neutron irradiation with advantages of (a) faster experimentation since damage rates (~ 10−2 dpa/s) are higher compared to the typical ~10−7 dpa/s for actual reactors (b) no residual radioactivity hazard and (c) precise control of irradiation conditions [26]. The ion energy was chosen based on a SRIM simulations [27] to have the majority of the ion species past through the Zr film leaving a relatively uniform damage profile, as a function of depth in the Zr. All of the irradiations occurred at nominally room temperature with a rastered ion beam at the maximum dose rate achievable that day. The six doses that were achieved were 3 × 1010 ions/cm2, 3 × 1011 ions/cm2, 3 × 1012 ions/cm2, 3 × 1013 ions/cm2, 3 × 1014 ions/cm2 and 3.26 × 1014 ions/cm2. Damage
Fig. 1. Fabrication scheme of co-fabricating freestanding thin film specimens with MEMS heaters for thermal conductivity measurements.
R. Pulavarthy et al. / Thin Solid Films 638 (2017) 17–21
level in term of displacement per atom can be calculated as [26] dpa ¼
∅ 108 Damage rate N
ð1Þ
where ∅ is the fluence in ions/cm2, the damage rate is in vacancies/ion/ A° obtained with SRIM, and N is the atomic number density in atoms/ cm3. It is predicted using SRIM that this ion irradiation conditions will result in damage levels in the 100 nm thick Zr film of 2.10− 04, 2.10−03, 2.10−02, 2.10−01, 2.10 and 2.28 dpa respectively. After the irradiation, the device layer silicon under the sample specimen is removed by SF6 plasma exposing only the sample length using a physical shadow mask. An Infrared Microscope (QFI Infrascope) is used to map the temperature of device under operation. It has an Indium-Antimonide (InSb) detector, cooled by liquid nitrogen, which detects radiance from the sample and measures temperature. Since the specimen is a transition metal with low emissivity, this technique can potentially over-predict emissivity and under-predict the temperatures. We therefore calibrated the temperature field carefully in the range of 25–100 °C. Fig. 2c highlights various components of the device on an infrared thermal map of the device under operation. An electrical bias is applied between the electrodes resulting a current in the silicon structures, which act as heat source to the sample due to Joule heating. Our design allows us to actuate both the heaters, or a single one so that any temperature boundary conditions can be applied. In this study, we used only one end heating to establish a monotonically decreasing temperature profile. This is shown in Fig. 3a after obtaining the data from a line scan along the length of the specimen. We used a 15 × objective lens, which offers pixel resolution of about 2 μm. The focal plane array type detector measures the radiance from the specimen to calculate the temperature with 0.1 °C resolution, even though for each of the experiments, we established at least 20 °C temperature differential between the hot and cold end to ensure fidelity of the data. Since the specimens are 100 μm long, we can reliably capture the spatial temperature profile with about 50 data points. The experimental data is then fitted to a one dimensional heat transfer model described in detail below with best fit according to the least squares method. The sample specimen is of rectangular geometry and heat transport within the solid occurs by conduction, while it also loses heat to the surrounding atmosphere by convection and radiation. Convection loss was accounted for by using a vacuum environment, while radiation losses were minimized by (i) keeping the hot end temperature lower and (ii) estimating the loss by linearizing the radiation equation to obtain an equivalent heat transfer coefficient. There are two heaters; one on either side of the sample. Both can be activated simultaneously or one can be cut off such that the current entirely passed through a single heater. In either scenario, the temperature at two ends
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of the sample can be maintained at constant values. The temperature profile T(x) in the sample specimen with two ends held at constant temperatures can be expressed as [28]: TðxÞ−T∞ ½TL −T∞ =Tb −T∞ sinhðmLÞ þ sinhðmðL−xÞÞ ¼ Tb −T∞ sinhðmLÞ
ð2Þ
where, T∞ is the ambient temperature, Tb is the temperature at base (x = 0) and TL is the temperature at length L of the sample. The parameter ‘m’ relates to the dimensions of sample geometry such that m pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ hP=ðκAÞ where P, A, κ are the perimeter, cross-sectional area and thermal conductivity of the sample, respectively, while h is the heat transfer coefficient of the energy lost from the sample to surrounding atmosphere. Measurement of h is critical for accuracy in the κ calculation because it is known to be a strong function of the surface area to volume ratio of the specimen [29–31]. This parameter can be obtained by applying energy conservation principle near the heated specimen surface [32], −kair A
∂ T−T sÞ y¼0 ¼ hc AðT s −T ∞ Þ ∂y
ð3Þ
where, y is the axis extending to the medium (y = 0 denotes specimen surface) and Ts is the specimen temperature. This can be re-written as ln
ðT−T ∞ Þ ¼ −sy ðT s −T ∞ Þ
ð4Þ
where, s ¼ khairc , which can was determined from the logarithm plot of the temperature difference ratio against distance y from the specimen surface with temperature Ts as detailed in [33]. The assumption of one-dimensional (in plane) heat conduction in the sample is deemed appropriate since specimen width is N20 times smaller than the length. Fig. 3a shows the model prediction juxtaposed with the experimentally measured temperature gradient along the length of the sample. The fitting parameter of the model is thermal conductivity, which is extracted for all the specimens. Fig. 3b shows the measured values of thermal conductivity for various irradiation dosage. We quantified the uncertainty in the measurement to be b8%, which scales with the errors in measuring various parameters. The total uncertainty is contributed by the effective temperature resolution, convective/radiation heat transfer coefficient and spatial measurements such as specimen length, width and thickness. To conservatively estimate the error in measurement, we took the temperature resolution to be 1 °C. This is ten times higher than the vendor quoted resolution. The specimen dimensions were measured with a SEM will b 0.1 μm resolution. Perhaps the most influential parameter is the specimen thickness, which was measured with an optical profilometer. Even though the sputtered specimen showed
Fig. 2. (a) Damage and Zr-ion distribution profiles in the specimen and the substrate, simulated with the SRIM program, (b) cross-sectional SEM image of the specimen before substrate etching (c) infrared image of the thermal conductivity measuring device.
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R. Pulavarthy et al. / Thin Solid Films 638 (2017) 17–21
Fig. 3. (a) Temperature gradient in the specimen fitted with an energy balance model (b) thermal conductivity of Zr+ ion irradiated specimens as function of radiation dosage.
excellent uniformity, the thickness variation induced error could be as high as 5%. 3. Discussion To compare the thermal transport in the ion-irradiated specimens, we also measured thermal conductivity measurements of un-irradiated (control) specimens using the same calibration and technique. The thermal conductivity of un-irradiated specimens was around 20 W/m-K, which matches very well with the literature values for zirconium [34]. The specimens were observed to be nanocrystalline with grain size approximately 10 nm measured by the intercept technique applied on a transmission electron microscope image. SEM images taken in crosssection and Moiré fringes present in TEM images suggest that the microstructure was not columnar in the 100 nm-thick film further complicating the heat transport path. This again validates the methodology that Fourier's law of heat conduction can be applied to govern the heat transport along the length of sample specimen, which is at least 100 times greater than the grain size. It ensures diffusion is the dominant mode of heat transport in the film. Fig. 3c shows the measured thermal conductivity of zirconium thin film specimens, as function of irradiation dosage. To explain the observed decrease in thermal conductivity as a function of radiation dosage, we note that nanocrystalline metals are different from the bulk counterpart considering the volume fraction of the grain boundaries. In metals, heat is carried by the electrons, which gets scattered in the lattice as well as the grain boundaries and surfaces. Surface scattering is important, but not strong as the other two contributions. In a nanocrystalline metal, as in this study, the grain boundary scattering dominates thermal transport because the electronic mean free path is comparable to the grain size, or in other words, the electrons
scatter more at the boundaries than the grain interior. Since grain boundaries are known to act as sinks for radiation induced defects, the irradiated grain boundaries are more disordered compared to as-prepared specimens. This leads to enhanced electronic scattering, resulting decrease in thermal conductivity as function of radiation dosage. Our results indicating decrease in thermal conductivity from 20 to 13.6 W/mK for irradiation of 3 × 1014 ions/cm2 (2.1 dpa) are consistent with this discussion. While the grain boundaries act as a very effective defect sink, ion irradiation induces defects (vacancy or interstitial) within the lattice as well. However, the effect of ration on lattice defects (and hence thermal conductivity) could be very different from the grain boundaries. According to [12], radiation causes the interstitials to be ‘loaded’ into the grain boundaries. The grain boundaries that emit or ‘unload’ the interstitials to the grain interior, where they can recombine with vacancies. It is shown that the energy barrier of such recombination mechanism is much lower than the conventional vacancy diffusion. The overall result is annealing of the radiation damage in the grain interior. It is also important to note that radiation also causes grain growth [35], a mechanism that can influence the contribution of the grain boundaries on the thermal transport. As shown in Fig. 4, the grains grow from nominally 10 nm to about 40 nm. Electron mean free path in zirconium is about 10 nm [36]. For grain sizes larger than the electron mean free path, thermal conductivity is expected to increase. However, the continued decreasing trend in the thermal conductivity shown in Fig. 3c suggests that the radiation damage accumulated in the grain boundaries overshadow the slight effects of the grain growth. Currently, we are exploring methodologies to model and quantify these two mechanisms to predict the thermal transport in irradiated nanocrystalline metals and alloys, as a function of damage and grain size.
Fig. 4. Bright field transmission electron microscopy of the specimen (a) before and (b) after Zr+ ion irradiation. Insets show electron diffraction patterns.
R. Pulavarthy et al. / Thin Solid Films 638 (2017) 17–21
An alternative explanation of the decreasing trend of the thermal conductivity is the morphological change in the material during irradiation. Fig. 4 insets show the electron diffraction patterns clearly indicating oxidation of zirconium at about 3 × 1014 ions/cm2 (2.1 dpa). The appearance of an additional ring representing the {220} planes in ZrO2 can be explained by the formation of an oxide at the metal surface and the strongly enhanced athermal oxygen diffusivity due to ion irradiation [37]. Thermal conductivity of ZrO2 is phonon dominated and is about 1.7 W/m-K, which is N 10 times smaller than that of zirconium, which could reduce the overall measured value of thermal conductivity. Further work is underway to deconvolute the role of the oxide and internal structure on the observed thermal properties. 4. Conclusion We have measured thermal conductivity of self-ion irradiated zirconium thin films. The nominal film thickness and initial grain size were 100 nm and 10 nm, respectively. An 800 keV Zr+ beam from a 6 MV HVE Tandem accelerator was used to irradiate the specimens from 3 × 1010 to 3.26 × 1014 ions/cm2, corresponding to displacement per atom of 2.1 × 10−4 to 2.28. Transmission electron microscopy showed significant grain growth, texture evolution, and oxidation in addition to the evolution of defects due to the irradiation. Thermal conductivity decreased with increasing radiation dosage. Up to 32% reduction of thermal conductivity was measured for dose of 2.1 dpa (3 × 1014 ions/cm2). This observation was explained by the increased level of defects as well as oxidation of zirconium, both resulting from ion irradiation. Acknowledgement BW and AH acknowledge the support of the U.S. Department of Energy funding (DE-NE0008259). AH also acknowledges support from the National Science Foundation (DMR 1609060) to carry out the MEMS fabrication at the Pennsylvania State University Nanofabrication Facility. The ion irradiation was carried out at the Sandia National Laboratories. The authors would like to thank Daniel Buller for his assistance with the ion irradiation. This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. References [1] M. Griffiths, A review of microstructure evolution in zirconium alloys during irradiation, J. Nucl. Mater. 159 (1988) 190–218. [2] F. Onimus, J.L. Béchade, 4.01 - radiation effects in zirconium alloys A2, in: Rudy J.M. Konings (Ed.), Comprehensive Nuclear Materials, Elsevier, Oxford 2012, pp. 1–31. [3] C. Yan, R. Wang, Y. Wang, X. Wang, G. Bai, Effects of ion irradiation on microstructure and properties of zirconium alloys—a review, Nucl. Eng. Technol. 47 (2015) 323–331. [4] S. Di, Z. Yao, M.R. Daymond, X. Zu, S. Peng, F. Gao, Dislocation-accelerated void formation under irradiation in zirconium, Acta Mater. 82 (2015) 94–99. [5] S.J. Zinkle, J.T. Busby, Structural materials for fission & fusion energy, Mater. Today 12 (2009) 12–19. [6] H.-H. Hsu, M.-F. Chiang, Y.-C. Chen, The influence of hydride on fracture toughness of recrystallized Zircaloy-4 cladding, J. Nucl. Mater. 447 (2014) 56–62. [7] D. Rodgers, M. Griffiths, G. Bickel, A. Buyers, C. Coleman, H. Nordin, S.S. Lawrence, Performance of Pressure Tubes in CANDU Reactors, CNL Nucl. Rev. 5 (2016) 1–15. [8] I. Kratochvílová, R. Škoda, J. Škarohlíd, P. Ashcheulov, A. Jäger, J. Racek, A. Taylor, L. Shao, Nanosized polycrystalline diamond cladding for surface protection of zirconium nuclear fuel tubes, J. Mater. Process. Technol. 214 (2014) 2600–2605.
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Contents lists available at ScienceDirect
Thin Solid Films journal homepage: www.elsevier.com/locate/tsf
Thermal conductivity of self-ion irradiated nanocrystalline zirconium thin films Raghu Pulavarthy a, Baoming Wang a, Khalid Hattar b, M.A. Haque a,⁎ a b
Mechanical and Nuclear Engineering, Penn State University, University Park, PA 16802, United States Sandia National Laboratories, PO Box 5800, Albuquerque, NM 87185, United States
a r t i c l e
i n f o
Article history: Received 21 December 2016 Received in revised form 10 July 2017 Accepted 14 July 2017 Available online 15 July 2017 Keywords: Thermal conductivity Ion irradiation Nanocrystalline metal Transmission electron microscopy (TEM)
a b s t r a c t Thermomechanical stability and high thermal conductivity are important for nuclear cladding material performance and reliability, which degrade over time under irradiation. The literature suggests nanocrystalline materials as radiation tolerant, but little or no evidence is present from thermal transport perspective. In this study, we irradiated 10 nm grain size zirconium thin films with 800 keV Zr+ beam from a 6 MV HVE Tandem accelerator to achieve various doses of 3 × 1010 to 3.26 × 1014 ions/cm2, corresponding to displacement per atom (dpa) of 2.1 × 10−4 to 2.28. Transmission electron microscopy showed significant grain growth, texture evolution and oxidation in addition to the creation of displacement defects due to the irradiation. The specimens were co-fabricated with micro-heaters to establish thermal gradients that were mapped using infrared thermometry. An energy balance approach was used to estimate the thermal conductivity of the specimens, as function of irradiation dosage. Up to 32% reduction of thermal conductivity was measured for the sample exposed to a dose of 2.1 dpa (3 × 1014 ions/cm2). © 2017 Elsevier B.V. All rights reserved.
1. Introduction Radiation in nuclear applications adversely influences the defect density and microstructure of the fuel cladding material. Energetic particles, such as neutrons, with sufficient kinetic energy knocks off atoms from their lattice sites of the cladding materials, creating defects associated with the missing lattice atoms (vacancies) and the dislodged atoms that reside in the lattice interstices. When the atomic displacement exceeds a threshold, this is followed by further displacement in the neighboring atoms in a cascaded manner [1]. The process takes time from femto to picoseconds and results in the partial recombination of the vacancy and interstitial point defects, while the remaining defects may agglomerate to form vacancy clusters and dislocation loops [2] due to their surface energy [3,4]. Depending on the radiation fluence, temperature and other harsh environmental factors, these one-dimensional defects lead to two and three dimensional defects dislocations and voids. The literature is well-established on the mechanical and microstructural aspects. However, thermal transport is also very important the materials are continuously exposed to intense radiation at high temperatures and the heat (with high flux) must be removed to ensure safety and reliability [5]. For example, radiation induced amorphization [2] can reduce thermal conductivity of metals. Similarly, oxidation or hydration
⁎ Corresponding author. E-mail address: [email protected] (M.A. Haque).
http://dx.doi.org/10.1016/j.tsf.2017.07.035 0040-6090/© 2017 Elsevier B.V. All rights reserved.
can severely deteriorate both mechanical and thermal properties [6,7], which has led researchers to innovate on protecting the surfaces from radiation [8]. The motivation for this study comes from the application potentials of nanocrystalline materials, which are hypothesized to exhibit have better resistance to irradiation [9,10]. The hypothesis driving this area of research is that grain boundaries act as sinks for radiation induced defects [11,12]. Since the volume fracture of grain boundary atoms scales in a cubic power or grain size (the fraction can reach ~ 50% for grain size of ~6 nm [13]), the abundance of defect sinks may render nanocrystalline materials more radiation tolerant. However, the existing studies are mostly on mechanical properties and a limited literature is available on the thermal transport aspect in nanostructured nuclear materials [14]. Literature shows that the thermal conductivity of nanocrystalline metal films can be as low as one-third of the bulk value at room temperature and even smaller at lower temperature [15]. This not unexpected because when this grain approaches the electron mean free path (around 10 nm for Zr [16]), metallic thermal conductivity will experience enhanced scattering at the boundaries. First principles calculations show that lack of crystallinity reflected by vacancies and disorder as well as non-planarity/misorientation of grain boundaries contribute significantly to grain boundary reflectivity [17]. In the present study, we investigate thin films, for which surface scattering can play roles typically non-existent in bulk form. However, the literature suggests that the reduction in thermal conductivity is predominantly caused by grainboundary and less by surface scattering [18].
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R. Pulavarthy et al. / Thin Solid Films 638 (2017) 17–21
Accordingly, we propose that the large volume fraction of grain boundaries, compounded by the vacancies, interstitials and voids introduced by radiation, is not only expected to increase the thermal resistance, but also lattice resistance for grain sizes below the phonon mean free path [18]. We study self-ion irradiation in zirconium since the metal and its alloys are used as cladding material for the fuel rods in pressurized water reactors and boiling water reactors. This class of materials has low neutron cross-section [19], high hardness, and high corrosion resistance [20,21]. For metals, any change in thermal conductivity by high temperature irradiation (similar to cladding material environment) is recovered immediately due to annealing [22]. The focus of this study however is on the thermal transport in the nanocrystalline regime. Thermal conductivity measurement on irradiated materials is particularly challenging because the radiation fluence is strong function of the thickness. This means a spatial gradient of damage exists along the path of the neutrons or ions. Conventional thermal conductivity measurement techniques for bulk materials on the other hand assume microstructural homogeneity. Therefore, the underlying heat transfer models need to be adapted to capture these gradient effects accurately. Conventional technique, such as laser flash, 3-ω [23], thermo-reflectance [24], etc. can still be applied if a thin section specimen of uniform irradiation dosage is cut out from the bulk. Another way to avoid this problem is perform the irradiation experiments on thin film specimens, which results in approximately uniform damage throughout the crosssection. 2. Experimental setup and results To study the role of irradiation on thermal transport in nanocrystalline materials, we developed a micro-electro-mechanical (MEMS) setup that integrates thin film specimens with micro-heaters. The design is essentially a version of the technique developed by Shi et al. [25], adopted for freestanding thin films. The essence of the design is to suspend the specimen between micro fabricated heaters. The specimen is then
heated to establish a temperature gradient so that the data can be used in a thermal conductivity model. Shi et al. used electrical resistance based thermometry at the two ends of the specimen, which is modified by using a thermal (infrared) microscope for enhance spatial mapping. Fig. 1 shows the device design where the freestanding thin film specimen is co-fabricated with the micro-heaters. First, the thin film (100 nm-thick zirconium) is deposited by physical vapor deposition (PVD) on silicon-on-insulator (SOI) wafer with 20 μm-thick device layer silicon. Alternatively, a thin section coupon can be nano-manipulated on to this device if the specimen is obtained from bulk material. The deposition is a traditional lift-off process where an inverse pattern of photoresist is created on the SOI substrate using standard photolithography. After the deposition, the unwanted photoresist is removed thereby leaving zirconium specimen in the desired pattern. After a second lithography process, the device layer silicon in the exposed areas is etched by SF6 plasma using a deep reactive ion etch (DRIE) process. The third lithography step is done on the back side of the handle layer silicon and a similar DRIE process removes the exposed silicon. The buried oxide (BOX) layer is etched away in CF4 plasma using standard reactive ion etch (RIE) process, leaving the specimen freestanding. Individual dies containing multiple partially processed samples were ion irradiated with an 800 keV Zr+ beam using the 6 MV HVE Tandem accelerator at Sandia's Ion Beam Lab. Ion irradiation is a popular surrogate for neutron irradiation with advantages of (a) faster experimentation since damage rates (~ 10−2 dpa/s) are higher compared to the typical ~10−7 dpa/s for actual reactors (b) no residual radioactivity hazard and (c) precise control of irradiation conditions [26]. The ion energy was chosen based on a SRIM simulations [27] to have the majority of the ion species past through the Zr film leaving a relatively uniform damage profile, as a function of depth in the Zr. All of the irradiations occurred at nominally room temperature with a rastered ion beam at the maximum dose rate achievable that day. The six doses that were achieved were 3 × 1010 ions/cm2, 3 × 1011 ions/cm2, 3 × 1012 ions/cm2, 3 × 1013 ions/cm2, 3 × 1014 ions/cm2 and 3.26 × 1014 ions/cm2. Damage
Fig. 1. Fabrication scheme of co-fabricating freestanding thin film specimens with MEMS heaters for thermal conductivity measurements.
R. Pulavarthy et al. / Thin Solid Films 638 (2017) 17–21
level in term of displacement per atom can be calculated as [26] dpa ¼
∅ 108 Damage rate N
ð1Þ
where ∅ is the fluence in ions/cm2, the damage rate is in vacancies/ion/ A° obtained with SRIM, and N is the atomic number density in atoms/ cm3. It is predicted using SRIM that this ion irradiation conditions will result in damage levels in the 100 nm thick Zr film of 2.10− 04, 2.10−03, 2.10−02, 2.10−01, 2.10 and 2.28 dpa respectively. After the irradiation, the device layer silicon under the sample specimen is removed by SF6 plasma exposing only the sample length using a physical shadow mask. An Infrared Microscope (QFI Infrascope) is used to map the temperature of device under operation. It has an Indium-Antimonide (InSb) detector, cooled by liquid nitrogen, which detects radiance from the sample and measures temperature. Since the specimen is a transition metal with low emissivity, this technique can potentially over-predict emissivity and under-predict the temperatures. We therefore calibrated the temperature field carefully in the range of 25–100 °C. Fig. 2c highlights various components of the device on an infrared thermal map of the device under operation. An electrical bias is applied between the electrodes resulting a current in the silicon structures, which act as heat source to the sample due to Joule heating. Our design allows us to actuate both the heaters, or a single one so that any temperature boundary conditions can be applied. In this study, we used only one end heating to establish a monotonically decreasing temperature profile. This is shown in Fig. 3a after obtaining the data from a line scan along the length of the specimen. We used a 15 × objective lens, which offers pixel resolution of about 2 μm. The focal plane array type detector measures the radiance from the specimen to calculate the temperature with 0.1 °C resolution, even though for each of the experiments, we established at least 20 °C temperature differential between the hot and cold end to ensure fidelity of the data. Since the specimens are 100 μm long, we can reliably capture the spatial temperature profile with about 50 data points. The experimental data is then fitted to a one dimensional heat transfer model described in detail below with best fit according to the least squares method. The sample specimen is of rectangular geometry and heat transport within the solid occurs by conduction, while it also loses heat to the surrounding atmosphere by convection and radiation. Convection loss was accounted for by using a vacuum environment, while radiation losses were minimized by (i) keeping the hot end temperature lower and (ii) estimating the loss by linearizing the radiation equation to obtain an equivalent heat transfer coefficient. There are two heaters; one on either side of the sample. Both can be activated simultaneously or one can be cut off such that the current entirely passed through a single heater. In either scenario, the temperature at two ends
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of the sample can be maintained at constant values. The temperature profile T(x) in the sample specimen with two ends held at constant temperatures can be expressed as [28]: TðxÞ−T∞ ½TL −T∞ =Tb −T∞ sinhðmLÞ þ sinhðmðL−xÞÞ ¼ Tb −T∞ sinhðmLÞ
ð2Þ
where, T∞ is the ambient temperature, Tb is the temperature at base (x = 0) and TL is the temperature at length L of the sample. The parameter ‘m’ relates to the dimensions of sample geometry such that m pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ hP=ðκAÞ where P, A, κ are the perimeter, cross-sectional area and thermal conductivity of the sample, respectively, while h is the heat transfer coefficient of the energy lost from the sample to surrounding atmosphere. Measurement of h is critical for accuracy in the κ calculation because it is known to be a strong function of the surface area to volume ratio of the specimen [29–31]. This parameter can be obtained by applying energy conservation principle near the heated specimen surface [32], −kair A
∂ T−T sÞ y¼0 ¼ hc AðT s −T ∞ Þ ∂y
ð3Þ
where, y is the axis extending to the medium (y = 0 denotes specimen surface) and Ts is the specimen temperature. This can be re-written as ln
ðT−T ∞ Þ ¼ −sy ðT s −T ∞ Þ
ð4Þ
where, s ¼ khairc , which can was determined from the logarithm plot of the temperature difference ratio against distance y from the specimen surface with temperature Ts as detailed in [33]. The assumption of one-dimensional (in plane) heat conduction in the sample is deemed appropriate since specimen width is N20 times smaller than the length. Fig. 3a shows the model prediction juxtaposed with the experimentally measured temperature gradient along the length of the sample. The fitting parameter of the model is thermal conductivity, which is extracted for all the specimens. Fig. 3b shows the measured values of thermal conductivity for various irradiation dosage. We quantified the uncertainty in the measurement to be b8%, which scales with the errors in measuring various parameters. The total uncertainty is contributed by the effective temperature resolution, convective/radiation heat transfer coefficient and spatial measurements such as specimen length, width and thickness. To conservatively estimate the error in measurement, we took the temperature resolution to be 1 °C. This is ten times higher than the vendor quoted resolution. The specimen dimensions were measured with a SEM will b 0.1 μm resolution. Perhaps the most influential parameter is the specimen thickness, which was measured with an optical profilometer. Even though the sputtered specimen showed
Fig. 2. (a) Damage and Zr-ion distribution profiles in the specimen and the substrate, simulated with the SRIM program, (b) cross-sectional SEM image of the specimen before substrate etching (c) infrared image of the thermal conductivity measuring device.
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R. Pulavarthy et al. / Thin Solid Films 638 (2017) 17–21
Fig. 3. (a) Temperature gradient in the specimen fitted with an energy balance model (b) thermal conductivity of Zr+ ion irradiated specimens as function of radiation dosage.
excellent uniformity, the thickness variation induced error could be as high as 5%. 3. Discussion To compare the thermal transport in the ion-irradiated specimens, we also measured thermal conductivity measurements of un-irradiated (control) specimens using the same calibration and technique. The thermal conductivity of un-irradiated specimens was around 20 W/m-K, which matches very well with the literature values for zirconium [34]. The specimens were observed to be nanocrystalline with grain size approximately 10 nm measured by the intercept technique applied on a transmission electron microscope image. SEM images taken in crosssection and Moiré fringes present in TEM images suggest that the microstructure was not columnar in the 100 nm-thick film further complicating the heat transport path. This again validates the methodology that Fourier's law of heat conduction can be applied to govern the heat transport along the length of sample specimen, which is at least 100 times greater than the grain size. It ensures diffusion is the dominant mode of heat transport in the film. Fig. 3c shows the measured thermal conductivity of zirconium thin film specimens, as function of irradiation dosage. To explain the observed decrease in thermal conductivity as a function of radiation dosage, we note that nanocrystalline metals are different from the bulk counterpart considering the volume fraction of the grain boundaries. In metals, heat is carried by the electrons, which gets scattered in the lattice as well as the grain boundaries and surfaces. Surface scattering is important, but not strong as the other two contributions. In a nanocrystalline metal, as in this study, the grain boundary scattering dominates thermal transport because the electronic mean free path is comparable to the grain size, or in other words, the electrons
scatter more at the boundaries than the grain interior. Since grain boundaries are known to act as sinks for radiation induced defects, the irradiated grain boundaries are more disordered compared to as-prepared specimens. This leads to enhanced electronic scattering, resulting decrease in thermal conductivity as function of radiation dosage. Our results indicating decrease in thermal conductivity from 20 to 13.6 W/mK for irradiation of 3 × 1014 ions/cm2 (2.1 dpa) are consistent with this discussion. While the grain boundaries act as a very effective defect sink, ion irradiation induces defects (vacancy or interstitial) within the lattice as well. However, the effect of ration on lattice defects (and hence thermal conductivity) could be very different from the grain boundaries. According to [12], radiation causes the interstitials to be ‘loaded’ into the grain boundaries. The grain boundaries that emit or ‘unload’ the interstitials to the grain interior, where they can recombine with vacancies. It is shown that the energy barrier of such recombination mechanism is much lower than the conventional vacancy diffusion. The overall result is annealing of the radiation damage in the grain interior. It is also important to note that radiation also causes grain growth [35], a mechanism that can influence the contribution of the grain boundaries on the thermal transport. As shown in Fig. 4, the grains grow from nominally 10 nm to about 40 nm. Electron mean free path in zirconium is about 10 nm [36]. For grain sizes larger than the electron mean free path, thermal conductivity is expected to increase. However, the continued decreasing trend in the thermal conductivity shown in Fig. 3c suggests that the radiation damage accumulated in the grain boundaries overshadow the slight effects of the grain growth. Currently, we are exploring methodologies to model and quantify these two mechanisms to predict the thermal transport in irradiated nanocrystalline metals and alloys, as a function of damage and grain size.
Fig. 4. Bright field transmission electron microscopy of the specimen (a) before and (b) after Zr+ ion irradiation. Insets show electron diffraction patterns.
R. Pulavarthy et al. / Thin Solid Films 638 (2017) 17–21
An alternative explanation of the decreasing trend of the thermal conductivity is the morphological change in the material during irradiation. Fig. 4 insets show the electron diffraction patterns clearly indicating oxidation of zirconium at about 3 × 1014 ions/cm2 (2.1 dpa). The appearance of an additional ring representing the {220} planes in ZrO2 can be explained by the formation of an oxide at the metal surface and the strongly enhanced athermal oxygen diffusivity due to ion irradiation [37]. Thermal conductivity of ZrO2 is phonon dominated and is about 1.7 W/m-K, which is N 10 times smaller than that of zirconium, which could reduce the overall measured value of thermal conductivity. Further work is underway to deconvolute the role of the oxide and internal structure on the observed thermal properties. 4. Conclusion We have measured thermal conductivity of self-ion irradiated zirconium thin films. The nominal film thickness and initial grain size were 100 nm and 10 nm, respectively. An 800 keV Zr+ beam from a 6 MV HVE Tandem accelerator was used to irradiate the specimens from 3 × 1010 to 3.26 × 1014 ions/cm2, corresponding to displacement per atom of 2.1 × 10−4 to 2.28. Transmission electron microscopy showed significant grain growth, texture evolution, and oxidation in addition to the evolution of defects due to the irradiation. Thermal conductivity decreased with increasing radiation dosage. Up to 32% reduction of thermal conductivity was measured for dose of 2.1 dpa (3 × 1014 ions/cm2). This observation was explained by the increased level of defects as well as oxidation of zirconium, both resulting from ion irradiation. Acknowledgement BW and AH acknowledge the support of the U.S. Department of Energy funding (DE-NE0008259). AH also acknowledges support from the National Science Foundation (DMR 1609060) to carry out the MEMS fabrication at the Pennsylvania State University Nanofabrication Facility. The ion irradiation was carried out at the Sandia National Laboratories. The authors would like to thank Daniel Buller for his assistance with the ion irradiation. This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. References [1] M. Griffiths, A review of microstructure evolution in zirconium alloys during irradiation, J. Nucl. Mater. 159 (1988) 190–218. [2] F. Onimus, J.L. Béchade, 4.01 - radiation effects in zirconium alloys A2, in: Rudy J.M. Konings (Ed.), Comprehensive Nuclear Materials, Elsevier, Oxford 2012, pp. 1–31. [3] C. Yan, R. Wang, Y. Wang, X. Wang, G. Bai, Effects of ion irradiation on microstructure and properties of zirconium alloys—a review, Nucl. Eng. Technol. 47 (2015) 323–331. [4] S. Di, Z. Yao, M.R. Daymond, X. Zu, S. Peng, F. Gao, Dislocation-accelerated void formation under irradiation in zirconium, Acta Mater. 82 (2015) 94–99. [5] S.J. Zinkle, J.T. Busby, Structural materials for fission & fusion energy, Mater. Today 12 (2009) 12–19. [6] H.-H. Hsu, M.-F. Chiang, Y.-C. Chen, The influence of hydride on fracture toughness of recrystallized Zircaloy-4 cladding, J. Nucl. Mater. 447 (2014) 56–62. [7] D. Rodgers, M. Griffiths, G. Bickel, A. Buyers, C. Coleman, H. Nordin, S.S. Lawrence, Performance of Pressure Tubes in CANDU Reactors, CNL Nucl. Rev. 5 (2016) 1–15. [8] I. Kratochvílová, R. Škoda, J. Škarohlíd, P. Ashcheulov, A. Jäger, J. Racek, A. Taylor, L. Shao, Nanosized polycrystalline diamond cladding for surface protection of zirconium nuclear fuel tubes, J. Mater. Process. Technol. 214 (2014) 2600–2605.
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