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Radiation Tolerance of Piezoelectric Bulk Single-Crystal Aluminum Nitride David A. Parks and Bernhard R. Tittmann, Life Fellow, IEEE Abstract—For practical use in harsh radiation environments, we pose selection criteria for piezoelectric materials for nondestructive evaluation (NDE) and material characterization. Using these criteria, piezoelectric aluminum nitride is shown to be an excellent candidate. The results of tests on an aluminumnitride-based transducer operating in a nuclear reactor are also presented. We demonstrate the tolerance of single-crystal piezoelectric aluminum nitride after fast and thermal neutron fluences of 1.85 × 1018 neutron/cm2 and 5.8 × 1018 neutron/ cm2, respectively, and a gamma dose of 26.8 MGy. The radiation hardness of AlN is most evident from the unaltered piezoelectric coefficient d33, which measured 5.5 pC/N after a fast and thermal neutron exposure in a nuclear reactor core for over 120 MWh, in agreement with the published literature value. The results offer potential for improving reactor safety and furthering the understanding of radiation effects on materials by enabling structural health monitoring and NDE in spite of the high levels of radiation and high temperatures, which are known to destroy typical commercial ultrasonic transducers.
I. Introduction
C
urrently, ultrasonic nondestructive evaluation (NDE) is employed periodically on passive reactor components, but continuous online monitoring has not been widely implemented. The need for continuous online monitoring is becoming all the more important with the need for reactor license extension, the development of small and medium reactors (SMRs), and next-generation nuclear power plants. Additionally, ultrasound is a highly attractive NDE methodology, given that it allows for inspection in optically opaque materials, such as liquid metal coolants. Further applications may be found in materials research reactors, where ultrasonic NDE can be used for in situ analysis of radiation effects on novel radiation-hard materials currently being developed. The theoretical radiation tolerance prediction method herein consists of a three-pronged approach considering depoling, amorphization, and unstable atomic species. The most basic form of ultrasonic inspection, namely the A-scan, has the potential to yield a wealth of data in a single waveform. These data include: • Time of flight (dimensional changes, elastic moduli, density, temperature);
Manuscript received February 18, 2014; accepted April 2, 2014. D. A. Parks is with the NDE Physics Department, Idaho National Laboratory, Idaho Falls, ID. B. R. Tittmann is with the Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park, PA (email: [email protected]). DOI http://dx.doi.org/10.1109/TUFFC.2014.3020 0885–3010
• Nonlinear parameter β (micro-crack formation and growth, dislocation density); and • Ultrasonic attenuation (average grain size, viscoelastic effects). This list essentially sells itself, although bringing such a method to fruition in a reactor environment has been delayed by the lack of a suitable ultrasonic sensor. Admittedly, development of sensors for specific applications and the corresponding data analysis is anything but trivial; however, the first step would appear to be the selection of a suitable piezoelectric material, which is our objective. In addition to use as a pulsed ultrasonic transducer, hard piezoelectric materials such as AlN and those listed in Table I have great potential for acoustic emission applications. In fact, the receiving sensitivity of AlN is quite high, at roughly 0.07 V·m/N, which is higher than that of PZT ceramics. This high receiving sensitivity and relatively weak generating efficiency is characteristic of all hard piezoelectric materials. In this context, “hard” implies low dielectric permittivity, low piezoelectric strain constant, and low resistivity. II. Candidate Materials The most straightforward down-selection parameter seems to be the transition temperature, which provides an upper limit on the operating range of the piezoelectric material. In fact, a higher Curie temperature has been found to correlate with increased radiation tolerance and the primary effect of radiation damage in piezoelectric materials appears to be depolarization [1]. With this in mind, a table of candidate materials for longitudinal wave generation is provided in Table I; however, this is only the first step. The final column in Table I is of substantial importance because it has been found that crystal structure plays a significant role in the radiation tolerance of ceramics [2]. III. Radiation Effects A. Overview To keep things as simple as possible, and in line with the data available in the literature, consider the case in which the bulk of the crystal is kept below any transition temperature. In this case, four primary forms of damage are anticipated in the piezoelectric material during irradiation:
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TABLE I. Candidate Piezoelectric Materials. Material
Transition temperature (°C)
Transition type
Structure
AlN Bi3TiNbO9 LiNbO3 Sr2Nb2O73 La2Ti2O7 GaPO4 RareEarthCa4(BO3)3 ZnO
2826 909 ~1200 1342 1500 970 >1500 1975
melt Curie Curie Curie Curie α-β melt melt
Wurtzite [3] Perovskite layered [4] Perovskite [5] Perovskite layered [6] Perovskite layered [6] SiO2 homeotype [6] Oxyborate homeotype [6] Wurtzite [4]
• depoling via thermal spike processes; • amorphization/metamictization resulting from displacement spikes or high concentration of point defects; • increase in point defect concentration; and • development of defect aggregates. In this work, two likely damage mechanisms are considered, namely, thermal spikes and displacement spikes. Additionally, transmutation products are considered, because these, in fact, induce both thermal spikes and displacement spikes in some cases. Neither the thermal spike model nor the displacement spike model has previously been applied to piezoelectrics in the literature, but we propose that this is a useful approach. In this work, the thermal spike theory developed in [7] is presented and shown to produce the correct order of magnitude for loss in transduction in PZT. It is noteworthy that the thermal spike model leads one to anticipate an increase of the damage rate with increasing irradiation temperature, which has been observed by Glower [8]. On the other hand, the displacement spike mechanism is less damaging as the temperature is increased. Therefore, it is reasonable to expect that materials with Curie temperatures below that generated in thermal spikes will succumb to depoling in the thermal spike region. Likewise, one may reasonably suspect that materials with Curie temperatures above that generated by thermal spikes will succumb to displacement spike damage. It must be stressed that a material having a Curie temperature above the thermal spike temperature is not necessarily radiation hard, because such a material may have atomic species which are very unstable and thus become self-irradiating. Lithium niobate is an excellent example of such a material because of the 6Li(n,α)3H reaction [9]. This reaction is quite energetic and has a very high thermal neutron cross section, as can be seen in Table II.
This self-irradiating behavior was observed quite early on by geologists and was referred to as metamictization. This is likely why Primak and Anderson [9] chose to describe the state rendered on lithium niobate by thermal neutrons as metamict. Therefore, one may say that materials which contain atomic species with large transmutation cross sections are susceptible to metamictization. The peak temperature of a thermal spike generated by fast neutron scattering of relatively light atoms (~20 u or lighter) is on the order of 900° to 1200°C. Incidentally, many of the transmutation products listed in Table II produce similar thermal spikes. As a result, the materials considered here all have transition temperatures >900°C. Of course, materials with high transition temperatures generally have a low electromechanical coupling when compared with PZT, but are nonetheless very capable of producing useful ultrasonic data. The tolerance of these materials to amorphization is then treated by way of the topological freedom model [2], [10]. Inventory of the potential transmutation reactions is conducted last. It should be noted that isotope tailoring could potentially overcome these transmutation products to some extent. The literature [8], [11]–[13] supports the notion of thermal spike depolarization as opposed to bulk heatinginducing depolarization. In fact, research on all crystals reported in the references [8], [11]–[13] involved keeping the bulk of the piezoelectric material well below any transition temperature during irradiation. On the other hand, work in [14] and [15] demonstrates that the temperature introduced by thermal spikes certainly exceeds the Curie temperature of typical piezoelectric materials, albeit in a microscopic volume. A potential oversight in this type of damage model lies in the fact that the accumulation of isolated point defects or defect aggregates is neglected. However, in a study conducted on PZT, the calculated decrease in the piezoelec-
TABLE II. Mean Free Path for Transmutation Reactions in Relevant Materials. Material LiNbO3 AlN YCa4(BO3)3
(n,α) 0.83 cm >100 cm 0.31 cm
(n,p)
Product energy
NA
α (2.05 MeV) T (2.75 MeV) p (0.58 MeV) C (0.04 MeV) α (1.74 MeV) Li (0.84 MeV)
13.1 cm NA
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ning at the left with isolated point defects and energy loss to electrons and ending on the right with displacement spikes, are illustrated in Fig. 2. Neutron absorption reactions generate significantly less damage, and thus are not given substantial attention in this work. Gamma irradiation is not treated in this work, but has been investigated by Kazys et al. [17]. We simply propose a model for predicting radiation tolerance based on damaged caused by fast neutrons and energetic transmutations. C. Thermal Spikes Fig. 1. Thermal spike caused by an oxygen PKA in PZT.
tric effect resulting from neutron irradiation induced point defects at a modest fluence is only 0.1%, whereas the observed decrease was dramatically higher [16]. On the other hand, hard piezoelectric materials exhibit a relatively low resistivity and dielectric constant, leaving them more susceptible to dielectric losses causing loss of transduction. To the authors’ knowledge, no material has exhibited this as the cause of transduction loss when subjected to neutron irradiations, but the possibility cannot be ruled out. B. Introduction to the Model of Radiation Tolerance The neutrons in the reactor core will interact with the lattice atoms and potentially initiate a variety of processes. The nuclear cross section is an indication of the probability that a given process will occur when a material composed of the selected atoms is exposed to a neutron flux. The microscopic cross section, σ, has units of square centimeters and hence if a material of atomic density N (expressed in number per cubic centimeter) is exposed to a fluence of neutrons φ (in neutrons per square centimeter) one can expect σNφ events to take place per unit volume in the material. All nuclear cross section data in this work were obtained from the evaluated nuclear data files (ENDF). Transmutation reactions and fast neutrons generating primary knock-on atoms (PKAs) cause significant amounts of energy to be transferred to the lattice atoms, causing displacement cascades and, in the case of light energetic nuclei, highly localized electronic excitation along a fairly linear track. These two energy loss regimes, begin-
Fig. 2. Initial damage from an Al PKA in Al illustrating the regimes of energy loss. Results of a TRIM simulation.
Thermal spikes are generated when an energetic charged particle imparts energy to the lattice electrons in a highly localized manner. Specifically, when the energy loss to electrons reaches on the order of 10 keV/nm, thermal spikes dominate and cause localized melting as the primary damage mechanism [14], [15]. However, in a typical light water reactor core environment, it is highly unlikely to find electronic energy losses reaching this level. That is to say, thermal spikes do occur; however, the spike temperature is below the melting temperature but well above the Curie temperature, as shown in Fig. 1. This is where we have made an assumption of the validity of the thermal spike model as applied to a transition other than melting. In a reactor environment, the PKAs and transmutation products generate energy losses of several hundred electronvolts per nanometer, as indicated in Transport and Range of Ions in Matter (TRIM) simulations (srim.org), as shown in Fig. 2. This observation is confirmed in Friedland’s article [18]. The number of PKAs per unit volume per unit fluence is given by the macroscopic cross section
Σ = N ∗ σ, (1)
where N is the atomic density and σ is the scattering cross section. As an example, consider an oxygen PKA in PZT, for which (1) yields 0.095 PKA/cm3 per unit fluence in neutron/cm2, or for the sake of bookkeeping on units, 0.095 PKA·cm−1·neutron−1. Then utilizing (6), the PKA energy is 0.12 MeV. Utilizing this result as the input to a Stopping and Range of Ions in Matter (SRIM) simulation reveals that 500 eV/nm is imparted to the electrons over a range of roughly 200 nm. The PKAs of the heavier atomic species deposit comparable energy per unit track length but travel much shorter distance, thus affecting comparably insignificant volumes. This energy loss to electrons per unit path length can then be used to calculate the thermal spike temperature. The heat generated in a thermal spike has been quantified [14], [15], [19]. Additionally, the Dulong–Petit rule may then be utilized to express the specific heat capacity, as was put forth in [14]. Thus, the spike temperature is given by
∆T (r, t = 0) =
0.4S e −r 2/a o2 , (2) e 3πNKa o2
parks and tittmann: radiation tolerance of piezoelectric bulk single-crystal aluminum nitride
where r is the radial distance from the spike center, N is the atomic density, K is Boltzmann’s constant, Se is the electronic energy deposition per unit length, and ao is the initial spike width, which is taken as 4.5 nm for insulators and increases slightly with decreasing band gap in semiconductors. The heat distribution in the spike generated by an oxygen PKA in PZT is provided in Fig. 1. This temperature profile corresponds to the time at which peak temperature has been reached, and as time goes by the peak temperature will decrease and the width of the spike exceeding the Curie temperature will increase. This spreading of heat in turn means that the radius that exceeds the Curie temperature is given by [14]
S R e2 = a o2 ln e S e < 2.7S et (3) S et
S e R e2 = a o2 S > 2.7S et, (4) 2.7S et e
where Set is the threshold energy for which the spike will exceed the Curie temperature. If one assumes a Curie temperature of 347°C, the threshold is found, from (2), to be 100 eV/nm. Assuming a cylindrical track, the volume which exceeds the Curie temperature of 347°C for an irradiation temperature of 30°C is 2.3 × 10−17 cm3. Further, from (1), there are 0.095 PKAs generated per cubic centimeter per unit fast neutron fluence. As a result, the depoled fraction per unit fast neutron fluence is (2.3 × 10−17 cm3/PKA) × (0.095 PKA·cm−1·neutron−1) = 2.25 × 10−18 cm3/PKA. The fraction becomes unity if scaled by a fluence of 4.4 × 1017 neutron/cm2. This is the correct order of magnitude for depoling of PZT as reported by Glower [8]. Further indication that thermal spikes may be an appropriate damage mechanism is provided by the fact that Glower found that the damage rate doubled when the temperature was increased from room temperature to 100°C. Proceeding with the process we have outlined and noting that (2) gives the temperature increase above ambient, the threshold energy becomes 75 eV/nm, giving a depoled volume increase, and hence depoling rate increase, of a factor of 1.33. Glower found that the damage rate increased by a factor of 2, and hence the thermal spike model predicts the correct order of magnitude for significant depoling and passes the additional consistency check of increased damage rate for increased irradiation temperature. On the other hand, the amorphization resistance, to be discussed in the following section, increases with increasing irradiation temperature. D. Displacement Cascades and Amorphization Resistance In the case of displacement cascades, the focus is on regions along the PKA or transmutation product path wherein the energy is less than 1 keV/nucleon and the mean free path is therefore small compared with the interatomic spacing. In this case, a contiguous volume of material is pushed to the melting point regardless of the
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pressure caused by the surrounding solid [20]. The likelihood that the material will recrystallize in the pre-irradiated state depends on the interatomic bonding and/or the crystal structure. The long-range ionic type bonding will encourage recovery of the pre-irradiated state, whereas short-range covalent bonding allows considerable disordering to occur [21]. Alternatively, the crystal structure may be utilized to predict resistance to amorphization. When utilizing crystal structure to predict amorphization resistance, one assumes that the solid is composed of polytopes that are essentially unbreakable but which may be rotated during the spike process, with the allowed rotations depending on the topology of the polytope [2], [10]. A polytope which results in a low topological freedom will then result in a material which is resistant to amorphization. The polytope ascribed to a given material is undoubtedly a result of the nature of the interatomic bond, and thus both the iconicity and polytope methods of predicting resistance to amorphization are quite similar. However, both methods for predicting resistance to amorphization must be used with considerable care. For example, Trachenko [7], [21] explains that the ionic character of the bond must be determined by way of simulations yielding the electron density, as opposed to empirical rules such as the Pauli scale approach. Similarly, many piezoelectric materials are composed of interlocking polytopes and difficulty is encountered in utilizing the topological freedom approach. Fortunately, these two methods have been proven effective by both Hobbs et al. [2], [10] and Trachenko [7], [21] by way of considerable experimental confirmation. Focusing on the topological method, the perovskite and wurtzite structures, very relevant to this work, are well understood in this regard. The topological freedom, f, has been shown to relate to the amorphization dose, D, as [2], [10]
f = 3 − 2.51D 0.187. (5)
As can be seen in Table I, many high-temperature piezoelectric materials crystalize in the perovskite structure, for which f = −1 and the dose is thus 12 eV/atom. The wurtzite structure yields f = −3, and hence the amorphization dose is 106 eV/atom. The SiO2 homeotypes are among the least resistant to amorphization [21], with an amorphization dose of a fraction of 1 eV/atom. Finally, little is known of the oxyborates’ amorphization resistance; however, the transmutation of boron prevents this material from being a viable candidate. To put this into perspective, one may utilize kinematics and the scattering cross section to relate a fast neutron fluence to the dose. The average energy transferred by an isotropic fast neutron scatter is given by
Et =
2EA , (6) 1 + A2
where E is the fast neutron energy and A is the atomic mass of the lattice atom. The dose per unit fluence is then
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D = E tσφ, (7)
where ϕ is the fast neutron fluence. The fast neutron scattering cross section is generally on the order of 1 b and, taking fast to mean 1 MeV neutrons, the transferred energy is on the order of 10 keV. The ideal material will withstand a fluence of 1021 neutron/cm2, giving a dose on the order of 10 eV/atom; hence, we see that the higher amorphization dose of the wurtzite structure is of paramount importance if the material is to withstand 1021 neutron/ cm2. Of course, the metaminct materials will experience a much higher dose because of self-irradiation. E. Transmutation Reactions and Metamictization 1) Introduction: The transmutation reactions listed in Table II, which occur with thermal neutrons, are quite relevant to this work. Although the cross sections are illustrative, the atomic density of the atom of interest should be considered as well for the sake of completeness. For example the culprit in AlN, 14N, comprises some 99.634% of the naturally occurring nitrogen, whereas 6Li is only 7.5% of the natural abundance. However, regardless of this, the very large cross section (955 b) associated with the 6Li(n,α)3H reaction makes the mean free path significantly smaller than that of 14N(n,p)14C. The mean free path of a thermal neutron within the compound represents the distance the neutron can be expected to traverse in the compound before being absorbed and producing, in this case, a transmutation reaction. 2) Lithium: The reaction of 6Li with thermal neutrons is quite detrimental to lithium niobate and is credited with causing a dramatic decrease in the piezoelectric constant when exposed to 8 × 1019 neutron/cm2 thermal neutrons [9]. The α particles and tritium primarily result in ionization and thermal spikes but lack the mass to generate displacement cascades. However, the energy in the megaelectronvolt energy range results in the particles ionizing along a track of roughly 1 µm length at a rate of 450 eV/ nm, thereby generating a large thermal spike. Additionally, the large cross section for this reaction means that these spikes occur more frequently than those generated by fast neutron scattering in a typical reactor flux. Additionally, all 6Li will be replaced with helium and tritium at the fluence by the time 1021 neutrons/cm2 is reached. 3) Boron: The rare earth oxyborates contain 10B which will be subject to a reaction very similar to that of lithium described previously. In fact, boron absorbs thermal neutrons so well that it is utilized in control rods to absorb the thermal neutrons that would otherwise go on to cause more fission. A notable difference, however, occurs because of the generation of energetic lithium which will indeed cause displacement cascades. Finally, the natural abundance of 10B is 19.9%, all of which will transmute by our target fluence, thereby imparting significant chemical changes in the crystal.
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4) Nitrogen: The similar reaction occurring in aluminum nitride is more than a factor of 100 less likely to occur and substantially less energetic than that of the 6Li(n,α)3H reaction or the 10B(n,α)7Li. The interaction between 14N and thermal neutrons appears to play a very minor role in the damage evolution of AlN in a neutron field [22]. The proton is generated with 580 keV and the carbon 40 keV. The abundance of 14N is 99.634%, and hence there are 4.76 × 1022/cm3 of such species per cubic centimeter, each of which has a thermal cross section of 1.81 b for this reaction. As a result, on average 0.9 protons and carbon atoms are generated per cubic centimeter per thermal neutron. SRIM indicates that the proton will cause at most one displacement because of its low mass, and hence most of the energy will go toward electronic excitation at a rate of 90 eV/nm, which is insufficient for thermal spike phase transitioning. The carbon, on the other hand, causes 140 displacements, roughly 75% of which are N lattice atoms because of the closer match in mass. There is an additional nitrogen vacancy because this atom has transmuted, and at 1021 neutron/cm2, 0.18% of the nitrogen atoms have been replaced by carbon and a proton which is much less significant than the chemical changes imparted by way of boron or lithium transmutation. The 140 displacements generated each time this reaction occurs introduce 0.13 displacements/atom at the target fluence of 1021 neutron/cm2. 5) Conclusion to Predicting Radiation Effects: It is apparent that that AlN and ZnO are most resistant to amorphization among the candidate materials; the reasoning being similar for each of these wurtzite-structured hard piezoelectrics. Aluminum nitride has been discussed more up to this point because of the nitrogen transmutation and the fact that this is the material we have tested. Moreover, their very high transition temperatures render these materials immune to thermal spike damage. It is also clear that the transmutation reaction 14N(n,p)14C is generating a fraction of a displacement per atom at 1021 neutron/cm2 and insignificant doping. IV. Experimental Method A single-crystal AlN element (4.8 mm in diameter and 0.45 mm thick) resonant at 13.4 MHz, was coupled to an aluminum cylinder via mechanical pressure. Aluminum foil was used as an acoustic coupler between the aluminum cylinder and the AlN element, allowing for strong, clear A-scan data to be obtained. The AlN element was loaded, on the side opposite the aluminum cylinder, with a sintered carbon/carbon composite to reduce ringing and improve the signal clarity. The test fixture is illustrated in Fig. 3. The aluminum cylinder acted as the lower electrical contact and the plunger provided the upper electrical contact. The setup was connected to a radiation-hard 50-Ω coaxial
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Fig. 5. Amplitude of the A-scan signal throughout irradiation.
the first day of testing. It is possible that the cable terminal was compromised from the start of the experiment. However, the TRIGA reactor core was moved through the open water pool several times a day to conduct experiments typical of such reactors. This movement may have stressed the cable terminal, causing it to fail. All other data points are unchanged from the measured value. V. Post-Irradiation Testing Fig. 3. Test fixture irradiation of piezoelectric AlN while operating a pulse–echo transducer.
cable. This radiation-hard cable consisted of an aluminum conduit sleeve over fused quartz dielectric tubing with an aluminum inner conductor. The cylinder/piezo setup was placed in the core of the Penn State TRIGA reactor and irradiated to a fast and thermal neutron fluence of 1.85 × 1018 neutron/cm2 and 5.8 × 1018 neutron/cm2, respectively, and a gamma dose of 26.8 MGy. Throughout the irradiation, the A-scan data was recorded with impedance measurements interspersed. The A-scan data, illustrated in Fig. 4, was recorded and analyzed in terms of the echo amplitude, which is presented in Fig. 5. The data shown in Figs. 4 and 5 correspond to times when the temperature was below 40°C to eliminate the confounding effect of thermal expansion in the test fixture. The amplitude over the course of irradiation remains nearly constant and indicates the radiation hardness of the AlN and the test fixture. The first data point was increased by a factor of 1.82 because of a change of cable that was necessitated by a faulty terminal before
Fig. 4. A-scans obtained from AlN in the TRIGA reactor core; Φ is the fast neutron fluence.
Prior high-temperature experiments with AlN [23] may lead one to suspect that crystalline defects can degrade the high-temperature transduction of AlN. Considering that radiation causes displacement damage and transmutation doping, one may wonder how the irradiated AlN would fare at high temperatures. To answer this, the irradiated crystal, having negligible activity after cooling for a few weeks, was tested up to 500°C. The resulting waveforms are provided in Fig. 6. Additionally, d33 was measured before and after irradiation and found to be 5.5 pC/N, which is unchanged from the pristine value. Further, subjecting the irradiated AlN crystal to temperatures of 950°C for 72 h caused no change in the performance of the AlN crystal. VI. Conclusion The thermal spike model indicates that a Curie temperature well in excess of the irradiation temperature is required if a fast neutron fluence of 1021 neutron/cm2 is anticipated. This limits one to materials with somewhat lower coupling coefficients; however, this may change in the future as material science progresses.
Fig. 6. Waveforms from post-irradiation testing of AlN.
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More completely, the radiation tolerance of piezoelectric materials is governed by not only resistance to depoling in thermal spikes, but also resistance to amorphization, and a lack of atomic species having large cross sections for thermal neutron-induced transmutations. According to these criteria, the high transition temperature wurtzite materials AlN and ZnO are most promising. The experimentally observed radiation tolerance of AlN supports the radiation tolerance explanation put forth in this paper. The radiation hardness of AlN is most evident from the unaltered piezoelectric coefficient d33, which measured 5.5 pC/N after a fast and thermal neutron fluence of 1.85 × 1018 neutron/cm2 and 5.8 × 1018 neutron/cm2, respectively, and a gamma dose of 26.8 MGy. In addition to the post irradiation analysis, the AlNbased transducer was successfully operated in a reactor core with no degradation in signal amplitude up to the fluence and dose stated previously. Under our experimental conditions, the Q value increased, particularly when the reactor was on, which is attributed to the test fixture. References [1] “Evaluation of irradiation test results for candidate NERVA piezoelctric accelerometers,” Aerojet Nuclear Systems Co., Azusa, CA, ground test reactor irradiation test no. 22, 1971. [2] L. W. Hobbs, C. E. Jesurum, and B. Berger, “Rigidity constraints in amorphization of singly and multiply-polytopic structures,” in M. F. Thorpe and P. M. Duxbury, Eds., Rigidity Theory and Applications, New York, NY: Kluwer Academic/Plenum, 1999, pp. 191–216. [3] L. Berger, Semiconductor Materials. Boca Raton, FL: CRC Press, 1997. [4] X. Y. Kong, Y. Ding, R. Yeng, and Z. L. Wang, “Single-crystal nanorings formed by epitaxial self-coiling of polar nanobelts,” Science, vol. 303, no. 5662, pp. 1348–1351, 2004. [5] A. Meldrum, L. A. Boatner, W. J. Weber, and R. C. Ewing, “Amorphization and recrystallization of the ABO 3 oxides,” J. Nucl. Mater., vol. 300, no. 2, pp. 242–254, 2002. [6] S. Zhang and F. Yu, “Piezoelectric materials for high temperature sensors,” J. Am. Ceram. Soc., vol. 94, no. 10, pp. 3153–3170, http:// dx.doi.org/10.1111/j.1551-2916.2011.04792.x, 2011. [7] K. Trachenko, “Understanding resistance to amorphization by radiation damage,” J. Phys. Condens. Matter, vol. 16, no. 49, pp. R1491–R1515, http://dx.doi.org/10.1088/0953-8984/16/49/R03, 2004. [8] D. Glower, “Effects of radiation-induced damage centers in lead zirconate titanate ceramics,” J. Am. Ceram. Soc., vol. 48, no. 8, pp. 417–421, 1965. [9] W. Primak and T. Anderson, “Metamimictization of lithium niobate by thermal neutrons,” Nucl. Technol., vol. 23, no. 2, pp. 235–248, 1975. [10] L. W. Hobbs, F. W. Clinard, S. J. Zinkle, and R. C. Ewing, “Radiation effects in ceramics,” J. Nucl. Mater., vol. 216, pp. 291–321, http://dx.doi.org/10.1016/0022-3115(94)90017-5, Oct. 1994. [11] V. M. Baranov and S. P. Martynenko, “Durability of ZTL piezoceramic under the action of reactor irradiation,” translated from At. Energ., vol. 53, no. 5, pp. 803–804, 1982. [12] I. Lefkowitz, “Radiation-induced changes in the ferroelectric properties of some barium titanate-type materials,” J. Phys. Chem. Solids, vol. 10, no. 2–3, pp. 169–173, 1958. [13] Y. P. Meleshko, S. V. Babaev, S. G. Karpechko, V. I. Nalivae, Y. A. Safin, and V. M. Smirnov, “Studying the electrophysical parameters of piezoceramics of various types in an IVV-2M reactor,” translated from At. Energ., vol. 57, no. 2, pp. 544–548, http://dx.doi. org/10.1007/BF01123756, 1984. [14] G. Szenes, “Ion-induced amorphization in ceramic materials,” J. Nucl. Mater., vol. 336, no. 1, pp. 81–89, http://dx.doi.org/10.1016/j. jnucmat.2004.09.004, 2005.
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[15] G. Szenes, “Thermal spike analysis of ion-induced tracks in semiconductors,” Nucl. Instrum. Methods Phys. Res. B, vol. 269, no. 19, pp. 2075–2079, http://dx.doi.org/10.1016/j.nimb.2011.06.014, 2011. [16] C. Miclea, C. Tanasoiu, C. F. Miclea, I. Spanulescu, and M. Cioangher, “Effect of neutron irradiation on some piezoelectric properties of PZT type ceramics,” J. Phys IV France, vol. 128, pp. 115–120, Sep. 2005. [17] R. Kazys, A. Voleisis, R. Sliteris, L. Maze, R. Van Nieuwenhove, P. Kupschus, and H. A. Abderrahim, “High temperature ultrasonic transducers for imaging and measurements in a liquid Pb/Bi eutectic alloy,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 52, no. 4, pp. 525–537, 2005. [18] E. Friedland, “Influence of electronic stopping on amorphization energies,” Surf. Coat. Tech., vol. 201, no. 19–20, pp. 8220–8224, http:// dx.doi.org/10.1016/j.surfcoat.2006.01.095, 2007. [19] G. J. Dienes and G. H. Vineyard, Radiation Effects in Solids. New York, NY: Interscience, 1957. [20] J. A. Brinkman, “On the nature of radiation damage in metals,” J. Appl. Phys., vol. 25, no. 8, pp. 961–970, http://dx.doi. org/10.1063/1.1721810, 1954. [21] K. Trachenko, J. M. Pruneda, E. Artacho, and M. T. Dove, “How the nature of the chemical bond governs resistance to amorphization by radiation damage,” Phys. Rev. B, vol. 71, no. 18, art. no. 184104, http://dx.doi.org/10.1103/PhysRevB.71.184104, 2005. [22] T. Yano, K. Inokuchi, M. Shikama, and J. Ukai, “Neutron irradiation effects on isotope tailored aluminum nitride ceramics by a fast reactor up to 2 × 1026 n/m2,” J. Nucl. Mater., vol. 329–333, pt. B, pp. 1471–1475, 2004. [23] D. A. Parks, B. R. Tittmann, and M. M. Kropf, “Aluminum nitride as a high temperature transducer,” Rev. Prog. Quant. Nondestruct. Eval., vol. 1211, pp. 1029–1034, 2009.
David Parks received his Ph.D. degree from the Pennsylvania State University in 2012. He is currently an acoustic engineer for Navico.
Bernhard R. Tittmann (M’76–F’90) was born in Moshi, Tanganjika Territory, and moved to Vienna, Austria, where he grew up until moving to the United States in 1950. He entered the University of California at Los Angeles as a Howard Hughes Fellow and received his Ph.D. degree in 1965. In 1966, he joined the North American Science Center, where he remained until 1989 as the manager of the Materials Evaluation Group. Since then, he was appointed as the chair of the Schell Professorship of Engineering in the Department of Engineering Science and Mechanics at the Pennsylvania State University, University Park, PA. He established and has been the Director of the Pennsylvania State University Engineering Nano-Characterization Center since its inception in 1994. He is best known for his contributions in physical acoustics to materials characterization, which first led to the study of superconductivity, then rock mechanics, SAW devices, NDE, sensors for process monitoring and control of composites, sensors for health monitoring of pressure vessels, and, more recently, acoustic microscopy of biological cells and tissue. He was Visiting Professor at the University of Paris and the Kepler University in Linz, Austria. Dr. Tittmann is a Fellow of the Acoustical Society of America (ASA) and the American Society of Materials (ASM) International. He is a member of the American Ceramic Society (ACS), the American Physical Society (APS), the American Society of Nondestructive Testing (ASNT), the Materials Research Society (MRS), the American Society of Mechanical Engineers (ASME) International, and the International Society for Optical Engineering (SPIE). He was a Senior Fulbright Scholar, IEEE-UFFC Distinguished Lecturer and winner of the PSU Engineering Society Outstanding Research Award. He strongly promoted the Ultrasonics Symposium to be held overseas and was either Technical Chair or General Co-chair for the IEEE-UFFC Ultrasonics Symposia in Cannes, France; Sendai, Japan and Munich, Germany.
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Radiation Tolerance of Piezoelectric Bulk Single-Crystal Aluminum Nitride David A. Parks and Bernhard R. Tittmann, Life Fellow, IEEE Abstract—For practical use in harsh radiation environments, we pose selection criteria for piezoelectric materials for nondestructive evaluation (NDE) and material characterization. Using these criteria, piezoelectric aluminum nitride is shown to be an excellent candidate. The results of tests on an aluminumnitride-based transducer operating in a nuclear reactor are also presented. We demonstrate the tolerance of single-crystal piezoelectric aluminum nitride after fast and thermal neutron fluences of 1.85 × 1018 neutron/cm2 and 5.8 × 1018 neutron/ cm2, respectively, and a gamma dose of 26.8 MGy. The radiation hardness of AlN is most evident from the unaltered piezoelectric coefficient d33, which measured 5.5 pC/N after a fast and thermal neutron exposure in a nuclear reactor core for over 120 MWh, in agreement with the published literature value. The results offer potential for improving reactor safety and furthering the understanding of radiation effects on materials by enabling structural health monitoring and NDE in spite of the high levels of radiation and high temperatures, which are known to destroy typical commercial ultrasonic transducers.
I. Introduction
C
urrently, ultrasonic nondestructive evaluation (NDE) is employed periodically on passive reactor components, but continuous online monitoring has not been widely implemented. The need for continuous online monitoring is becoming all the more important with the need for reactor license extension, the development of small and medium reactors (SMRs), and next-generation nuclear power plants. Additionally, ultrasound is a highly attractive NDE methodology, given that it allows for inspection in optically opaque materials, such as liquid metal coolants. Further applications may be found in materials research reactors, where ultrasonic NDE can be used for in situ analysis of radiation effects on novel radiation-hard materials currently being developed. The theoretical radiation tolerance prediction method herein consists of a three-pronged approach considering depoling, amorphization, and unstable atomic species. The most basic form of ultrasonic inspection, namely the A-scan, has the potential to yield a wealth of data in a single waveform. These data include: • Time of flight (dimensional changes, elastic moduli, density, temperature);
Manuscript received February 18, 2014; accepted April 2, 2014. D. A. Parks is with the NDE Physics Department, Idaho National Laboratory, Idaho Falls, ID. B. R. Tittmann is with the Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park, PA (email: [email protected]). DOI http://dx.doi.org/10.1109/TUFFC.2014.3020 0885–3010
• Nonlinear parameter β (micro-crack formation and growth, dislocation density); and • Ultrasonic attenuation (average grain size, viscoelastic effects). This list essentially sells itself, although bringing such a method to fruition in a reactor environment has been delayed by the lack of a suitable ultrasonic sensor. Admittedly, development of sensors for specific applications and the corresponding data analysis is anything but trivial; however, the first step would appear to be the selection of a suitable piezoelectric material, which is our objective. In addition to use as a pulsed ultrasonic transducer, hard piezoelectric materials such as AlN and those listed in Table I have great potential for acoustic emission applications. In fact, the receiving sensitivity of AlN is quite high, at roughly 0.07 V·m/N, which is higher than that of PZT ceramics. This high receiving sensitivity and relatively weak generating efficiency is characteristic of all hard piezoelectric materials. In this context, “hard” implies low dielectric permittivity, low piezoelectric strain constant, and low resistivity. II. Candidate Materials The most straightforward down-selection parameter seems to be the transition temperature, which provides an upper limit on the operating range of the piezoelectric material. In fact, a higher Curie temperature has been found to correlate with increased radiation tolerance and the primary effect of radiation damage in piezoelectric materials appears to be depolarization [1]. With this in mind, a table of candidate materials for longitudinal wave generation is provided in Table I; however, this is only the first step. The final column in Table I is of substantial importance because it has been found that crystal structure plays a significant role in the radiation tolerance of ceramics [2]. III. Radiation Effects A. Overview To keep things as simple as possible, and in line with the data available in the literature, consider the case in which the bulk of the crystal is kept below any transition temperature. In this case, four primary forms of damage are anticipated in the piezoelectric material during irradiation:
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TABLE I. Candidate Piezoelectric Materials. Material
Transition temperature (°C)
Transition type
Structure
AlN Bi3TiNbO9 LiNbO3 Sr2Nb2O73 La2Ti2O7 GaPO4 RareEarthCa4(BO3)3 ZnO
2826 909 ~1200 1342 1500 970 >1500 1975
melt Curie Curie Curie Curie α-β melt melt
Wurtzite [3] Perovskite layered [4] Perovskite [5] Perovskite layered [6] Perovskite layered [6] SiO2 homeotype [6] Oxyborate homeotype [6] Wurtzite [4]
• depoling via thermal spike processes; • amorphization/metamictization resulting from displacement spikes or high concentration of point defects; • increase in point defect concentration; and • development of defect aggregates. In this work, two likely damage mechanisms are considered, namely, thermal spikes and displacement spikes. Additionally, transmutation products are considered, because these, in fact, induce both thermal spikes and displacement spikes in some cases. Neither the thermal spike model nor the displacement spike model has previously been applied to piezoelectrics in the literature, but we propose that this is a useful approach. In this work, the thermal spike theory developed in [7] is presented and shown to produce the correct order of magnitude for loss in transduction in PZT. It is noteworthy that the thermal spike model leads one to anticipate an increase of the damage rate with increasing irradiation temperature, which has been observed by Glower [8]. On the other hand, the displacement spike mechanism is less damaging as the temperature is increased. Therefore, it is reasonable to expect that materials with Curie temperatures below that generated in thermal spikes will succumb to depoling in the thermal spike region. Likewise, one may reasonably suspect that materials with Curie temperatures above that generated by thermal spikes will succumb to displacement spike damage. It must be stressed that a material having a Curie temperature above the thermal spike temperature is not necessarily radiation hard, because such a material may have atomic species which are very unstable and thus become self-irradiating. Lithium niobate is an excellent example of such a material because of the 6Li(n,α)3H reaction [9]. This reaction is quite energetic and has a very high thermal neutron cross section, as can be seen in Table II.
This self-irradiating behavior was observed quite early on by geologists and was referred to as metamictization. This is likely why Primak and Anderson [9] chose to describe the state rendered on lithium niobate by thermal neutrons as metamict. Therefore, one may say that materials which contain atomic species with large transmutation cross sections are susceptible to metamictization. The peak temperature of a thermal spike generated by fast neutron scattering of relatively light atoms (~20 u or lighter) is on the order of 900° to 1200°C. Incidentally, many of the transmutation products listed in Table II produce similar thermal spikes. As a result, the materials considered here all have transition temperatures >900°C. Of course, materials with high transition temperatures generally have a low electromechanical coupling when compared with PZT, but are nonetheless very capable of producing useful ultrasonic data. The tolerance of these materials to amorphization is then treated by way of the topological freedom model [2], [10]. Inventory of the potential transmutation reactions is conducted last. It should be noted that isotope tailoring could potentially overcome these transmutation products to some extent. The literature [8], [11]–[13] supports the notion of thermal spike depolarization as opposed to bulk heatinginducing depolarization. In fact, research on all crystals reported in the references [8], [11]–[13] involved keeping the bulk of the piezoelectric material well below any transition temperature during irradiation. On the other hand, work in [14] and [15] demonstrates that the temperature introduced by thermal spikes certainly exceeds the Curie temperature of typical piezoelectric materials, albeit in a microscopic volume. A potential oversight in this type of damage model lies in the fact that the accumulation of isolated point defects or defect aggregates is neglected. However, in a study conducted on PZT, the calculated decrease in the piezoelec-
TABLE II. Mean Free Path for Transmutation Reactions in Relevant Materials. Material LiNbO3 AlN YCa4(BO3)3
(n,α) 0.83 cm >100 cm 0.31 cm
(n,p)
Product energy
NA
α (2.05 MeV) T (2.75 MeV) p (0.58 MeV) C (0.04 MeV) α (1.74 MeV) Li (0.84 MeV)
13.1 cm NA
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ning at the left with isolated point defects and energy loss to electrons and ending on the right with displacement spikes, are illustrated in Fig. 2. Neutron absorption reactions generate significantly less damage, and thus are not given substantial attention in this work. Gamma irradiation is not treated in this work, but has been investigated by Kazys et al. [17]. We simply propose a model for predicting radiation tolerance based on damaged caused by fast neutrons and energetic transmutations. C. Thermal Spikes Fig. 1. Thermal spike caused by an oxygen PKA in PZT.
tric effect resulting from neutron irradiation induced point defects at a modest fluence is only 0.1%, whereas the observed decrease was dramatically higher [16]. On the other hand, hard piezoelectric materials exhibit a relatively low resistivity and dielectric constant, leaving them more susceptible to dielectric losses causing loss of transduction. To the authors’ knowledge, no material has exhibited this as the cause of transduction loss when subjected to neutron irradiations, but the possibility cannot be ruled out. B. Introduction to the Model of Radiation Tolerance The neutrons in the reactor core will interact with the lattice atoms and potentially initiate a variety of processes. The nuclear cross section is an indication of the probability that a given process will occur when a material composed of the selected atoms is exposed to a neutron flux. The microscopic cross section, σ, has units of square centimeters and hence if a material of atomic density N (expressed in number per cubic centimeter) is exposed to a fluence of neutrons φ (in neutrons per square centimeter) one can expect σNφ events to take place per unit volume in the material. All nuclear cross section data in this work were obtained from the evaluated nuclear data files (ENDF). Transmutation reactions and fast neutrons generating primary knock-on atoms (PKAs) cause significant amounts of energy to be transferred to the lattice atoms, causing displacement cascades and, in the case of light energetic nuclei, highly localized electronic excitation along a fairly linear track. These two energy loss regimes, begin-
Fig. 2. Initial damage from an Al PKA in Al illustrating the regimes of energy loss. Results of a TRIM simulation.
Thermal spikes are generated when an energetic charged particle imparts energy to the lattice electrons in a highly localized manner. Specifically, when the energy loss to electrons reaches on the order of 10 keV/nm, thermal spikes dominate and cause localized melting as the primary damage mechanism [14], [15]. However, in a typical light water reactor core environment, it is highly unlikely to find electronic energy losses reaching this level. That is to say, thermal spikes do occur; however, the spike temperature is below the melting temperature but well above the Curie temperature, as shown in Fig. 1. This is where we have made an assumption of the validity of the thermal spike model as applied to a transition other than melting. In a reactor environment, the PKAs and transmutation products generate energy losses of several hundred electronvolts per nanometer, as indicated in Transport and Range of Ions in Matter (TRIM) simulations (srim.org), as shown in Fig. 2. This observation is confirmed in Friedland’s article [18]. The number of PKAs per unit volume per unit fluence is given by the macroscopic cross section
Σ = N ∗ σ, (1)
where N is the atomic density and σ is the scattering cross section. As an example, consider an oxygen PKA in PZT, for which (1) yields 0.095 PKA/cm3 per unit fluence in neutron/cm2, or for the sake of bookkeeping on units, 0.095 PKA·cm−1·neutron−1. Then utilizing (6), the PKA energy is 0.12 MeV. Utilizing this result as the input to a Stopping and Range of Ions in Matter (SRIM) simulation reveals that 500 eV/nm is imparted to the electrons over a range of roughly 200 nm. The PKAs of the heavier atomic species deposit comparable energy per unit track length but travel much shorter distance, thus affecting comparably insignificant volumes. This energy loss to electrons per unit path length can then be used to calculate the thermal spike temperature. The heat generated in a thermal spike has been quantified [14], [15], [19]. Additionally, the Dulong–Petit rule may then be utilized to express the specific heat capacity, as was put forth in [14]. Thus, the spike temperature is given by
∆T (r, t = 0) =
0.4S e −r 2/a o2 , (2) e 3πNKa o2
parks and tittmann: radiation tolerance of piezoelectric bulk single-crystal aluminum nitride
where r is the radial distance from the spike center, N is the atomic density, K is Boltzmann’s constant, Se is the electronic energy deposition per unit length, and ao is the initial spike width, which is taken as 4.5 nm for insulators and increases slightly with decreasing band gap in semiconductors. The heat distribution in the spike generated by an oxygen PKA in PZT is provided in Fig. 1. This temperature profile corresponds to the time at which peak temperature has been reached, and as time goes by the peak temperature will decrease and the width of the spike exceeding the Curie temperature will increase. This spreading of heat in turn means that the radius that exceeds the Curie temperature is given by [14]
S R e2 = a o2 ln e S e < 2.7S et (3) S et
S e R e2 = a o2 S > 2.7S et, (4) 2.7S et e
where Set is the threshold energy for which the spike will exceed the Curie temperature. If one assumes a Curie temperature of 347°C, the threshold is found, from (2), to be 100 eV/nm. Assuming a cylindrical track, the volume which exceeds the Curie temperature of 347°C for an irradiation temperature of 30°C is 2.3 × 10−17 cm3. Further, from (1), there are 0.095 PKAs generated per cubic centimeter per unit fast neutron fluence. As a result, the depoled fraction per unit fast neutron fluence is (2.3 × 10−17 cm3/PKA) × (0.095 PKA·cm−1·neutron−1) = 2.25 × 10−18 cm3/PKA. The fraction becomes unity if scaled by a fluence of 4.4 × 1017 neutron/cm2. This is the correct order of magnitude for depoling of PZT as reported by Glower [8]. Further indication that thermal spikes may be an appropriate damage mechanism is provided by the fact that Glower found that the damage rate doubled when the temperature was increased from room temperature to 100°C. Proceeding with the process we have outlined and noting that (2) gives the temperature increase above ambient, the threshold energy becomes 75 eV/nm, giving a depoled volume increase, and hence depoling rate increase, of a factor of 1.33. Glower found that the damage rate increased by a factor of 2, and hence the thermal spike model predicts the correct order of magnitude for significant depoling and passes the additional consistency check of increased damage rate for increased irradiation temperature. On the other hand, the amorphization resistance, to be discussed in the following section, increases with increasing irradiation temperature. D. Displacement Cascades and Amorphization Resistance In the case of displacement cascades, the focus is on regions along the PKA or transmutation product path wherein the energy is less than 1 keV/nucleon and the mean free path is therefore small compared with the interatomic spacing. In this case, a contiguous volume of material is pushed to the melting point regardless of the
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pressure caused by the surrounding solid [20]. The likelihood that the material will recrystallize in the pre-irradiated state depends on the interatomic bonding and/or the crystal structure. The long-range ionic type bonding will encourage recovery of the pre-irradiated state, whereas short-range covalent bonding allows considerable disordering to occur [21]. Alternatively, the crystal structure may be utilized to predict resistance to amorphization. When utilizing crystal structure to predict amorphization resistance, one assumes that the solid is composed of polytopes that are essentially unbreakable but which may be rotated during the spike process, with the allowed rotations depending on the topology of the polytope [2], [10]. A polytope which results in a low topological freedom will then result in a material which is resistant to amorphization. The polytope ascribed to a given material is undoubtedly a result of the nature of the interatomic bond, and thus both the iconicity and polytope methods of predicting resistance to amorphization are quite similar. However, both methods for predicting resistance to amorphization must be used with considerable care. For example, Trachenko [7], [21] explains that the ionic character of the bond must be determined by way of simulations yielding the electron density, as opposed to empirical rules such as the Pauli scale approach. Similarly, many piezoelectric materials are composed of interlocking polytopes and difficulty is encountered in utilizing the topological freedom approach. Fortunately, these two methods have been proven effective by both Hobbs et al. [2], [10] and Trachenko [7], [21] by way of considerable experimental confirmation. Focusing on the topological method, the perovskite and wurtzite structures, very relevant to this work, are well understood in this regard. The topological freedom, f, has been shown to relate to the amorphization dose, D, as [2], [10]
f = 3 − 2.51D 0.187. (5)
As can be seen in Table I, many high-temperature piezoelectric materials crystalize in the perovskite structure, for which f = −1 and the dose is thus 12 eV/atom. The wurtzite structure yields f = −3, and hence the amorphization dose is 106 eV/atom. The SiO2 homeotypes are among the least resistant to amorphization [21], with an amorphization dose of a fraction of 1 eV/atom. Finally, little is known of the oxyborates’ amorphization resistance; however, the transmutation of boron prevents this material from being a viable candidate. To put this into perspective, one may utilize kinematics and the scattering cross section to relate a fast neutron fluence to the dose. The average energy transferred by an isotropic fast neutron scatter is given by
Et =
2EA , (6) 1 + A2
where E is the fast neutron energy and A is the atomic mass of the lattice atom. The dose per unit fluence is then
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D = E tσφ, (7)
where ϕ is the fast neutron fluence. The fast neutron scattering cross section is generally on the order of 1 b and, taking fast to mean 1 MeV neutrons, the transferred energy is on the order of 10 keV. The ideal material will withstand a fluence of 1021 neutron/cm2, giving a dose on the order of 10 eV/atom; hence, we see that the higher amorphization dose of the wurtzite structure is of paramount importance if the material is to withstand 1021 neutron/ cm2. Of course, the metaminct materials will experience a much higher dose because of self-irradiation. E. Transmutation Reactions and Metamictization 1) Introduction: The transmutation reactions listed in Table II, which occur with thermal neutrons, are quite relevant to this work. Although the cross sections are illustrative, the atomic density of the atom of interest should be considered as well for the sake of completeness. For example the culprit in AlN, 14N, comprises some 99.634% of the naturally occurring nitrogen, whereas 6Li is only 7.5% of the natural abundance. However, regardless of this, the very large cross section (955 b) associated with the 6Li(n,α)3H reaction makes the mean free path significantly smaller than that of 14N(n,p)14C. The mean free path of a thermal neutron within the compound represents the distance the neutron can be expected to traverse in the compound before being absorbed and producing, in this case, a transmutation reaction. 2) Lithium: The reaction of 6Li with thermal neutrons is quite detrimental to lithium niobate and is credited with causing a dramatic decrease in the piezoelectric constant when exposed to 8 × 1019 neutron/cm2 thermal neutrons [9]. The α particles and tritium primarily result in ionization and thermal spikes but lack the mass to generate displacement cascades. However, the energy in the megaelectronvolt energy range results in the particles ionizing along a track of roughly 1 µm length at a rate of 450 eV/ nm, thereby generating a large thermal spike. Additionally, the large cross section for this reaction means that these spikes occur more frequently than those generated by fast neutron scattering in a typical reactor flux. Additionally, all 6Li will be replaced with helium and tritium at the fluence by the time 1021 neutrons/cm2 is reached. 3) Boron: The rare earth oxyborates contain 10B which will be subject to a reaction very similar to that of lithium described previously. In fact, boron absorbs thermal neutrons so well that it is utilized in control rods to absorb the thermal neutrons that would otherwise go on to cause more fission. A notable difference, however, occurs because of the generation of energetic lithium which will indeed cause displacement cascades. Finally, the natural abundance of 10B is 19.9%, all of which will transmute by our target fluence, thereby imparting significant chemical changes in the crystal.
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4) Nitrogen: The similar reaction occurring in aluminum nitride is more than a factor of 100 less likely to occur and substantially less energetic than that of the 6Li(n,α)3H reaction or the 10B(n,α)7Li. The interaction between 14N and thermal neutrons appears to play a very minor role in the damage evolution of AlN in a neutron field [22]. The proton is generated with 580 keV and the carbon 40 keV. The abundance of 14N is 99.634%, and hence there are 4.76 × 1022/cm3 of such species per cubic centimeter, each of which has a thermal cross section of 1.81 b for this reaction. As a result, on average 0.9 protons and carbon atoms are generated per cubic centimeter per thermal neutron. SRIM indicates that the proton will cause at most one displacement because of its low mass, and hence most of the energy will go toward electronic excitation at a rate of 90 eV/nm, which is insufficient for thermal spike phase transitioning. The carbon, on the other hand, causes 140 displacements, roughly 75% of which are N lattice atoms because of the closer match in mass. There is an additional nitrogen vacancy because this atom has transmuted, and at 1021 neutron/cm2, 0.18% of the nitrogen atoms have been replaced by carbon and a proton which is much less significant than the chemical changes imparted by way of boron or lithium transmutation. The 140 displacements generated each time this reaction occurs introduce 0.13 displacements/atom at the target fluence of 1021 neutron/cm2. 5) Conclusion to Predicting Radiation Effects: It is apparent that that AlN and ZnO are most resistant to amorphization among the candidate materials; the reasoning being similar for each of these wurtzite-structured hard piezoelectrics. Aluminum nitride has been discussed more up to this point because of the nitrogen transmutation and the fact that this is the material we have tested. Moreover, their very high transition temperatures render these materials immune to thermal spike damage. It is also clear that the transmutation reaction 14N(n,p)14C is generating a fraction of a displacement per atom at 1021 neutron/cm2 and insignificant doping. IV. Experimental Method A single-crystal AlN element (4.8 mm in diameter and 0.45 mm thick) resonant at 13.4 MHz, was coupled to an aluminum cylinder via mechanical pressure. Aluminum foil was used as an acoustic coupler between the aluminum cylinder and the AlN element, allowing for strong, clear A-scan data to be obtained. The AlN element was loaded, on the side opposite the aluminum cylinder, with a sintered carbon/carbon composite to reduce ringing and improve the signal clarity. The test fixture is illustrated in Fig. 3. The aluminum cylinder acted as the lower electrical contact and the plunger provided the upper electrical contact. The setup was connected to a radiation-hard 50-Ω coaxial
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Fig. 5. Amplitude of the A-scan signal throughout irradiation.
the first day of testing. It is possible that the cable terminal was compromised from the start of the experiment. However, the TRIGA reactor core was moved through the open water pool several times a day to conduct experiments typical of such reactors. This movement may have stressed the cable terminal, causing it to fail. All other data points are unchanged from the measured value. V. Post-Irradiation Testing Fig. 3. Test fixture irradiation of piezoelectric AlN while operating a pulse–echo transducer.
cable. This radiation-hard cable consisted of an aluminum conduit sleeve over fused quartz dielectric tubing with an aluminum inner conductor. The cylinder/piezo setup was placed in the core of the Penn State TRIGA reactor and irradiated to a fast and thermal neutron fluence of 1.85 × 1018 neutron/cm2 and 5.8 × 1018 neutron/cm2, respectively, and a gamma dose of 26.8 MGy. Throughout the irradiation, the A-scan data was recorded with impedance measurements interspersed. The A-scan data, illustrated in Fig. 4, was recorded and analyzed in terms of the echo amplitude, which is presented in Fig. 5. The data shown in Figs. 4 and 5 correspond to times when the temperature was below 40°C to eliminate the confounding effect of thermal expansion in the test fixture. The amplitude over the course of irradiation remains nearly constant and indicates the radiation hardness of the AlN and the test fixture. The first data point was increased by a factor of 1.82 because of a change of cable that was necessitated by a faulty terminal before
Fig. 4. A-scans obtained from AlN in the TRIGA reactor core; Φ is the fast neutron fluence.
Prior high-temperature experiments with AlN [23] may lead one to suspect that crystalline defects can degrade the high-temperature transduction of AlN. Considering that radiation causes displacement damage and transmutation doping, one may wonder how the irradiated AlN would fare at high temperatures. To answer this, the irradiated crystal, having negligible activity after cooling for a few weeks, was tested up to 500°C. The resulting waveforms are provided in Fig. 6. Additionally, d33 was measured before and after irradiation and found to be 5.5 pC/N, which is unchanged from the pristine value. Further, subjecting the irradiated AlN crystal to temperatures of 950°C for 72 h caused no change in the performance of the AlN crystal. VI. Conclusion The thermal spike model indicates that a Curie temperature well in excess of the irradiation temperature is required if a fast neutron fluence of 1021 neutron/cm2 is anticipated. This limits one to materials with somewhat lower coupling coefficients; however, this may change in the future as material science progresses.
Fig. 6. Waveforms from post-irradiation testing of AlN.
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IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,
More completely, the radiation tolerance of piezoelectric materials is governed by not only resistance to depoling in thermal spikes, but also resistance to amorphization, and a lack of atomic species having large cross sections for thermal neutron-induced transmutations. According to these criteria, the high transition temperature wurtzite materials AlN and ZnO are most promising. The experimentally observed radiation tolerance of AlN supports the radiation tolerance explanation put forth in this paper. The radiation hardness of AlN is most evident from the unaltered piezoelectric coefficient d33, which measured 5.5 pC/N after a fast and thermal neutron fluence of 1.85 × 1018 neutron/cm2 and 5.8 × 1018 neutron/cm2, respectively, and a gamma dose of 26.8 MGy. In addition to the post irradiation analysis, the AlNbased transducer was successfully operated in a reactor core with no degradation in signal amplitude up to the fluence and dose stated previously. Under our experimental conditions, the Q value increased, particularly when the reactor was on, which is attributed to the test fixture. References [1] “Evaluation of irradiation test results for candidate NERVA piezoelctric accelerometers,” Aerojet Nuclear Systems Co., Azusa, CA, ground test reactor irradiation test no. 22, 1971. [2] L. W. Hobbs, C. E. Jesurum, and B. Berger, “Rigidity constraints in amorphization of singly and multiply-polytopic structures,” in M. F. Thorpe and P. M. Duxbury, Eds., Rigidity Theory and Applications, New York, NY: Kluwer Academic/Plenum, 1999, pp. 191–216. [3] L. Berger, Semiconductor Materials. Boca Raton, FL: CRC Press, 1997. [4] X. Y. Kong, Y. Ding, R. Yeng, and Z. L. Wang, “Single-crystal nanorings formed by epitaxial self-coiling of polar nanobelts,” Science, vol. 303, no. 5662, pp. 1348–1351, 2004. [5] A. Meldrum, L. A. Boatner, W. J. Weber, and R. C. Ewing, “Amorphization and recrystallization of the ABO 3 oxides,” J. Nucl. Mater., vol. 300, no. 2, pp. 242–254, 2002. [6] S. Zhang and F. Yu, “Piezoelectric materials for high temperature sensors,” J. Am. Ceram. Soc., vol. 94, no. 10, pp. 3153–3170, http:// dx.doi.org/10.1111/j.1551-2916.2011.04792.x, 2011. [7] K. Trachenko, “Understanding resistance to amorphization by radiation damage,” J. Phys. Condens. Matter, vol. 16, no. 49, pp. R1491–R1515, http://dx.doi.org/10.1088/0953-8984/16/49/R03, 2004. [8] D. Glower, “Effects of radiation-induced damage centers in lead zirconate titanate ceramics,” J. Am. Ceram. Soc., vol. 48, no. 8, pp. 417–421, 1965. [9] W. Primak and T. Anderson, “Metamimictization of lithium niobate by thermal neutrons,” Nucl. Technol., vol. 23, no. 2, pp. 235–248, 1975. [10] L. W. Hobbs, F. W. Clinard, S. J. Zinkle, and R. C. Ewing, “Radiation effects in ceramics,” J. Nucl. Mater., vol. 216, pp. 291–321, http://dx.doi.org/10.1016/0022-3115(94)90017-5, Oct. 1994. [11] V. M. Baranov and S. P. Martynenko, “Durability of ZTL piezoceramic under the action of reactor irradiation,” translated from At. Energ., vol. 53, no. 5, pp. 803–804, 1982. [12] I. Lefkowitz, “Radiation-induced changes in the ferroelectric properties of some barium titanate-type materials,” J. Phys. Chem. Solids, vol. 10, no. 2–3, pp. 169–173, 1958. [13] Y. P. Meleshko, S. V. Babaev, S. G. Karpechko, V. I. Nalivae, Y. A. Safin, and V. M. Smirnov, “Studying the electrophysical parameters of piezoceramics of various types in an IVV-2M reactor,” translated from At. Energ., vol. 57, no. 2, pp. 544–548, http://dx.doi. org/10.1007/BF01123756, 1984. [14] G. Szenes, “Ion-induced amorphization in ceramic materials,” J. Nucl. Mater., vol. 336, no. 1, pp. 81–89, http://dx.doi.org/10.1016/j. jnucmat.2004.09.004, 2005.
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David Parks received his Ph.D. degree from the Pennsylvania State University in 2012. He is currently an acoustic engineer for Navico.
Bernhard R. Tittmann (M’76–F’90) was born in Moshi, Tanganjika Territory, and moved to Vienna, Austria, where he grew up until moving to the United States in 1950. He entered the University of California at Los Angeles as a Howard Hughes Fellow and received his Ph.D. degree in 1965. In 1966, he joined the North American Science Center, where he remained until 1989 as the manager of the Materials Evaluation Group. Since then, he was appointed as the chair of the Schell Professorship of Engineering in the Department of Engineering Science and Mechanics at the Pennsylvania State University, University Park, PA. He established and has been the Director of the Pennsylvania State University Engineering Nano-Characterization Center since its inception in 1994. He is best known for his contributions in physical acoustics to materials characterization, which first led to the study of superconductivity, then rock mechanics, SAW devices, NDE, sensors for process monitoring and control of composites, sensors for health monitoring of pressure vessels, and, more recently, acoustic microscopy of biological cells and tissue. He was Visiting Professor at the University of Paris and the Kepler University in Linz, Austria. Dr. Tittmann is a Fellow of the Acoustical Society of America (ASA) and the American Society of Materials (ASM) International. He is a member of the American Ceramic Society (ACS), the American Physical Society (APS), the American Society of Nondestructive Testing (ASNT), the Materials Research Society (MRS), the American Society of Mechanical Engineers (ASME) International, and the International Society for Optical Engineering (SPIE). He was a Senior Fulbright Scholar, IEEE-UFFC Distinguished Lecturer and winner of the PSU Engineering Society Outstanding Research Award. He strongly promoted the Ultrasonics Symposium to be held overseas and was either Technical Chair or General Co-chair for the IEEE-UFFC Ultrasonics Symposia in Cannes, France; Sendai, Japan and Munich, Germany.
