Ab initio molecular dynamics simulation of low energy radiation responses of α-Al2O3.

In this study, an ab initio molecular dynamics method is employed to investigate the response behavior of α-Al2O3 to low energy irradiation. Different from the previous experiments, our calculations reveal that the displacements of oxygen dominate under electron irradiation and the created defects are mainly oxygen vacancy and interstitial. The experimental observation of the absorption peaks appearing at 203, 233 and 256 nm for α-Al2O3 under electron irradiations should be contributed by the oxygen defects and these defects will reduce the transmittance of α-Al2O3, which agrees well with the very recent experiment. This study demonstrates the necessity to reinvestigate the threshold displacement energies of α-Al2O3, and to introduce recombination center for oxygen defects to improve its optical properties and performance under radiation environment.

Introduction

The sapphire phase of alumina (α-Al2O3) is widely used for numerous industrial applications, such as catalyst support, solid state laser and photovoltaic devices[1, 2]. Due to its high radiation resistance and wide band gap, α-Al2O3 is also used as an effective detector of ionizing radiation[2]. Its potential applications also include components of breeder blanket and diagnostic windows, as well as coating in future fusion reactors to avoid the permeation of light gases[3]. In these applications, α-Al2O3 is exposed to different kinds of radiation environment, i.e., neutron, low and swift heavy ions and γ-ray radiation. This leads to the generation, migration and aggregation of defects or defect clusters, which ultimately may deteriorate the mechanical properties of materials and influence their performance. It is of crucial importance to investigate the phase stability of α-Al2O3 under radiation and the underlying mechanism for defect generation to enhance its radiation tolerance and improve its performance.

In the past decades, the radiation damage effects of α-Al2O3 have been extensively studied both experimentally and theoretically[4-16]. The sapphire crystal of Al2O3 was irradiated by the 238U ions at temperatures around 80 K by Canut et al.[5]. The lattice disorder induced by collective electronic excitation was confirmed by the Rutherford backscattering spectrometry in channeling geometry (RBS-C) analysis, and the optical absorption spectroscopy of α-Al2O3 exhibited the characteristic bands associated with oxygen vacancies[5]. Single crystalline α-Al2O3 samples were implanted at room temperature with 160 keV Pt+ ions by Alves et al., who found that 80% of the implanted ions occupied the aluminum lattice site, and the increase in doses made the implanted region highly damaged[6]. Kabir et al. irradiated the α-Al2O3 with 0.7 MeV 129Xe ions with fluences ranging from 5 × 1011 to 2 × 1014 ion/cm2, and characterized the samples with RBS-C measurements[4]. The RBS-C analysis suggested the presence of two incident ion effects on α-Al2O3 samples[4]: the creation of partial disorder that saturated at ~ 40% with a damage cross section of 7 × 10−14 cm−2, followed by a complete disorder starting from the surface and appearing at fluence larger than ~1.2 × 1013 ion/cm2. Microstructural evolution in crystalline α-Al2O3 during Xe+ ion irradiation has been investigated by Okubo et al., who found that the swift heavy ion irradiation caused lattice expansion and the structural modification led to structural amorphization above the energy around 100 MeV[10]. Kulkarni et al. irradiated the sapphire with various thermal neutron fluences in the range of 1014 to 1018 n/cm2, and found that the neutron irradiation introduced considerable oxygen vacancies, as confirmed by the presence of F (203 nm) and F+ (225 and 255 nm) bands in the optical absorption spectra[7]. Izerrouken et al. investigated the formation of color centers in α-Al2O3, and found that the content of single point defect (F+ center) and defect cluster (F2, F2 +, F2 2+) increased linearly with the increasing fast neutron fluences[8]. Similar results were also reported in the case of 90 MeV Xe+ ion irradiation[9], where F+ center concentration monotonously increased with the ion fluence in the range up to 1013 Xe/cm2.

Theoretically, Williford et al. have investigated the displacement energies of α-Al2O3 using classical molecular dynamics (MD) method[13]. On the other hand, several density functional theory (DFT) calculations have been carried out to investigate the defect formation and migration in α-Al2O3 [3, 14, 16]. In spite of these studies, there still lacks of an atomic-level understanding of the mechanisms for defect generation in α-Al2O3, as well as the defect distribution and the interaction between defects. In recent years, the ab initio molecular dynamics (AIMD) method has been widely employed to simulate the low energy recoil events in ceramic materials like pyrochlores, fluorite-structure oxides and carbides, in which a number of new defective states and new mechanisms for defect generation that are different from classical MD have been predicted[17-20]. In this study, the AIMD method is employed to investigate the radiation responses of α-Al2O3 to low energy irradiation. The threshold displacement energies, the pathway for defect generation, the type of created defects, the role of charge transfer during the dynamic process, as well as the impact of created defects on the electronic structure of α-Al2O3, all have been provided. The presented results will be useful for understanding the structure-property relationship of α-Al2O3 and improving its properties and performances for its application as the substrate material for GaN growth for the production of blue light-emitting diode (LED), thin film passivation material for high-efficiency solar cells, luminescence dosimetry, and so on.

Results and Discussion

Ground-state properties of α-Al2O3

The structural and elastic properties of α-Al2O3 are first calculated and compared with experimental and other theoretical data. The optimized lattice constants for α-Al2O3 are listed in Table 1, which agree well with the theoretical[21] and experimental[22] results. The bulk (B), shear (G) and Young’s (E) modulus for α-Al2O3 are determined to be 264.3, 166.3 and 412.4 GPa, respectively. It appears that our results are in good agreement with the experimental results[23] and are comparable with the theoretical values[24] reported by Holm et al. The calculated Poisson’s ratio for α-Al2O3 of 0.24 also agrees well with the experimental[23] and other theoretical results[24].

Table 1

Calculated lattice constant (Å), elastic moduli (GPa) and Poisson’s ratio (σ) for α-Al2O3. B: bulk modulus, G: shear modulus. E: Young's modulus.

	Lattice Constant	B	G	E	σ
Our cal.	(4.81,4.81,13.14)	264.3	166.3	412.4	0.24
Other cal.	(4.80,4.80,13.11)a	246.4c	158.6c	390.0c	0.24c
Exp.	(4.77,4.77,13.01)b	255.0d	165.3d	404.6d	0.23d

aRef. 21.

bRef. 22.

cRef. 24.

dRef. 23.

The threshold displacement energies in α-Al2O3

The threshold displacement energy (Ed), which is defined as the minimum transferred kinetic energy for primary knock-on atom (PKA) to be permanently displaced from its lattice site, is one of the critical physical parameters for estimating damage production rates and predicting the defect profile under electron, neutron and ion irradiation[19, 25] The calculated Eds for O and Al recoils along different directions in α-Al2O3 are summarized in Table 2.

Table 2

Threshold displacement energies (Ed) for O and Al recoils. The minimum values for O and Al PKAs are indicated in bold.

Direction	Ed (eV)
	O recoils	Al recoils
[0001]	32.5	47.5
[1¯21¯0]	40.5	148
[21¯1¯0]	27	105, 51.4a
[112¯0]	25	74.5
[112¯3]	35	107.5
[101¯0]	30, 54.3a	58, 27.7a
[112¯6]	27	114
[011¯2]	51.5	>150
[2¯42¯3]	76	>150
[21¯1¯3]	29	113
[011¯1]	34.5	87.5
[224¯1]	30	85
[022¯1]	27	66.5
[112¯2]	30.5	105.5
[415¯6]	31.5	>150
[448¯3]	39	71

aRef. 13.

For the oxygen recoils, the maximum and minimum Ed values are determined to be 76 and 25 eV for and directions, respectively, as shown in Table 2. The defect configurations for O and O are both oxygen vacancy and oxygen dumbbell pair, whereas the defect generation pathways show different character. In the case of , the oxygen atom moves 3.63 Å away from its lattice site and forms a dumbbell pair with its neighboring oxygen atoms. As for O , the oxygen atom moves 2.20 Å to collide with its neighboring oxygen atom and occupies its lattice site. The struck oxygen atom moves 1.9 Å away from its equilibrium site and forms a dumbbell pair with the neighboring oxygen atoms eventually. On the other hand, the minimum Ed value for Al PKA is 47.5 eV along the [0001] direction, i.e., the Al atom along this direction is the most likely to be displaced. In the cases of , and for Al PKA, the Eds are predicted to be larger than 150 eV, i.e., the PKA is not permanently displaced at energy up to 150 eV. Among the determined threshold displacement energies, the Ed value of 148 eV for Al is the largest. The associated defects and the pathway for defect generation for Al [0001] and Al recoil events are found to be somewhat different. In the case of Al [0001], the Al PKA moves 1.86 Å away from its lattice site to eject its neighboring aluminum atom and occupies its lattice site. Then, the collided aluminum atom moves along the [0001] direction to hit another neighboring Al atom, and forms an interstitial occupying the octahedral site. The third collided aluminum atom also forms an interstitial occupying the octahedral site, which is 2.01 Å away from its original site. As a result, the final defect structure consists of two aluminum Frenkel pairs (FPs). As for Al recoil along the direction of , besides the Al PKA, its neighboring oxygen atom is also involved in the displacement events. Consequently, the damage end state contains one aluminum interstitial occupying the octahedral site, one aluminum vacancy, one oxygen dumbbell and one oxygen vacancy. These results suggest that the displacement events in α-Al2O3 are strongly dependent on the recoil direction and the species of the PKA.

Theoretically, Williford et al. have studied the displacement energies of α-Al2O3 employing the classical molecular dynamics (MD) method[13]. It is found that the Eds of 51.4 eV for Al and 27.7 eV for Al obtained by the MD method are much smaller than our AIMD results. In the previous AIMD simulation of low energy recoil events in SiC and pyrochlores[18–20, 25], it is also found that the threshold displacement energies and the mechanism for defect generation obtained by AIMD method are generally different from the classical MD results. This may be due to the fact that recoil events are dynamic charge transfer processes, while such charge transfer was not considered in classical MD[26]. In this study, the charge transfer for the O and Al PKAs along the direction during the displacement process as a function of time is illustrated in Fig. 1. In Fig. 1a, the variations of charge difference for O at the energies of 27 and 26.5 eV are compared, which shows that charge transfer from and to the recoil atom takes place during the whole dynamics process. Especially, the charge changes at 27 eV are more significant than those at 26.5 eV, corresponding to reaching a stable defective state and returning to its lattice site, respectively. The Fig. 1b shows the variation in charge difference for Al and O recoils along the direction at 27 eV. For Al PKA, the charge changes slightly and no defects are formed, whereas a relatively more significant charge transfer occurs for the O PKA. The charge-density contours projected onto plane during O recoil events at energy of 27 eV are illustrated in Fig. 2. Taking the initial charge-density (as shown in Fig. 2a) as a reference, it is clear that electron cloud deformation and charge redistribution takes place in the whole process. In Fig. 2b, when the O PKA is displaced to the interstitial site, it interacts with its neighboring atoms and the electron clouds around the lattice O start to deform toward the O PKA. With time evolution, there is a more significant electron cloud deformation to overcome the energy barrier for stable defect formation. The charge redistribution eventually leads to the formation of one O-O dumbbell, as shown in Fig. 2d.

Figure 1

Charge difference for (a) O PKA at energies of 26.5 and 27 eV; (b) O and Al PKAs along the direction at the energy of 27 eV.

Figure 2

Charge-density contours projected onto plane during O recoil events at energy of 27 eV.

Under electron irradiation the maximum energy transferred to an atom can be expressed as , where E is the incident energy, m is the electronic mass, M is the atomic mass and c is the velocity of light[25]. Thus, our calculated minimum Ed values of 25 eV for O recoil and 47.5 eV for Al recoil correspond to 152 and 415 keV electron irradiation, respectively. These radiation energies are comparable with the experimental measurements[27, 28], while discrepancies exist in the threshold displacement energies. Arnold and Compton suggested that at 77 K the threshold radiation energy for α-Al2O3 was 430 keV, and the Ed values were 90 ± 5 for O ions and 50 ± 5 eV for Al ions[27]. In their study, the crystal orientation was not considered and the results were strongly dependent on the temperature, i.e., irradiation at 77 K produced many more centers than did a comparable irradiation at 300 K and the ratio of the yields at these two temperatures was at least ten[27]. Das reported that the threshold voltage was orientation dependent, which was 300 keV for [0001] and 240 keV for direction[29]. Consequently, the predicted Ed values were 32 and 24 eV for Al [0001] and Al , respectively, and 53 and 41 eV for O [0001] and O , respectively[29]. In our study, the threshold displacement energies are determined by the creation of point defects such as oxygen or aluminum Frenkel pair. These defects may be too few to be observed experimentally, for which the threshold displacement energies were determined by the first appearance of defect clusters. Pells and Stathopoulos[30] carried out high voltage electron microscope measurement with optical measurement of electron-irradiation induced color centers on α-Al2O3. They demonstrated that the threshold radiation energies were independent of the temperature and they were 400 ± 20 and 175 ± 20 keV for the oxygen and aluminum ions, respectively, and the determined Ed values were 76 ± 3 eV for O and 18 ± 3 eV for Al[30]. In their work, the crystal orientation was also not considered. Considering that impurities or defects may exist in the sapphire sample and the sapphire has a large band gap, the impurities or defects would make charge transfer process more likely and consequently affect the optical absorption. This may partly cause discrepancy between their work and our simulation.

The defect distribution in α-Al2O3 after recoil events

The defects created by the Al and O PKAs after recoil events are summarized in Table 3, and the defect configurations are illustrated in Fig. 3. As shown in the table, the damage end states after oxygen recoil events generally consist of one oxygen vacancy and one oxygen dumbbell pair with its neighboring oxygen atoms (see Fig. 3a), with the exception of O , O and O . Despite the similar defect distribution, the pathways for defect generation behave different character and the displacement for O PKA is generally different from each other. In the cases of O , O and O , the oxygen PKA moves away from their equilibrium sites, and finally occupies the tetrahedral site, as shown in Fig. 3b.

Table 3

The type of created defects and displacement (dPKA) for O and Al recoils.

	O		Al
	Defect type	dPKA(Å)	Defect type	dPKA(Å)
[0001]	O-O + Ovac	3.57	2Alocta + 2Alvac	1.86
[1¯21¯0]	O-O + Ovac	4.51	Alocta + Alvac + Ovac + Otetra	4.89
[21¯1¯0]	O-O + Ovac	2.52	2Alocta + 2Alvac	2.91
[112¯0]	O-O + Ovac	2.20	Alocta + Alvac	5.89
[112¯3]	O-O + Ovac	3.85	2Alocta + 2Alvac + Ovac + O-O	3.63
[101¯0]	Otetra + Ovac	3.84	Alocta + Alvac	2.39
[112¯6]	O-O + Ovac	2.31	Alocta + Alvac	6.43
[011¯2]	Otetra + Ovac	3.26	—	—
[2¯42¯3]	O-O + Ovac	3.63	—	—
[21¯1¯3]	O-O + Ovac	2.47	Alocta + Alvac	6.57
[011¯1]	O-O + Ovac	2.06	Alocta + Alvac	5.43
[224¯1]	O-O + Ovac	5.21	Alocta + Alvac	5.58
[022¯1]	Otetra + Ovac	2.27	Alocta + Alvac	5.99
[112¯2]	O-O + Ovac	3.59	Alocta + Alvac	5.15
[415¯6]	O-O + Ovac	4.31
[448¯3]	O-O + Ovac	3.91	Alocta + Alvac	5.26

Ovac: oxygen vacancy; Otetra: oxygen interstitial occupying the tetrahedral site; O-O: oxygen-oxygen dumbbell pair; Alvac: aluminum vacancy; Alocta: aluminum interstitial occupying the octahedral site.

Figure 3

Illustration of schematic view of (a) Ovac + O-O dumbbell; (b) Ovac + Otetra and (c) Alvac + Alocta. The large blue and small red spheres represent the aluminum and oxygen atoms, respectively. The magenta large and small spheres represent the aluminum vacancy and oxygen vacancy, respectively. The yellow large and small spheres represent the aluminum interstitial and oxygen interstitial, respectively. O-O: oxygen dumbbell pair; Otetra: oxygen interstitial occupying the tetrahedral site; Alocta: aluminum interstitial occupying the octahedral site.

For aluminum recoil events, one aluminum vacancy (Alvac) and one aluminum interstitial occupying the octahedron site (Alocta) are created in most cases, as shown in Fig. 3c. Similar to the cases of oxygen recoil events, the mechanisms for defect creation and the displacement of Al PKA are generally different. In the cases of Al [0001] and Al , besides the Al PKA, another lattice Al is also displaced to the octahedral site and eventually two pairs of aluminum FP are formed. For Al , the formation of Al FP is accompanied by the involvement of lattice oxygen, which moves to the tetrahedral site and leads to the formation of one oxygen Frenkel pair. The most complex defect configuration is found to be the case of Al , for which two Al FPs, one oxygen vacancy and one O-O dumbbell are formed.

In the literature, the damage end states for α-Al2O3 as a result of exposure to radiation have been reported to be aluminum and oxygen vacancy[14, 31–34], interstitial atom[14, 31, 33], or complementary Frenkel pairs in two sublattice[14, 34], agreeing well with our AIMD calculations. Platonenko and Zhukovskii et al. demonstrated that the oxygen interstitial could migrate above certain temperature and form the dumbbell pair (Oreg−Oi) in α-Al2O3 [3, 14], which is also in good agreement with our simulations.

Impact of point defects on the electronic structure of α-Al2O3

Aluminum oxide is one of the earlier materials used in luminescence dosimetry, while the application is limited by its low thermo-luminescence sensitivity. Great efforts have been devoted to study the thermo-luminescence and optical stimulated luminescence sensitivity, the electronic structure as well as the optical absorption of α-Al2O3. In order to explore how the radiation damage influences the band gap and optical absorption, first-principles calculations based on density functional theory are further carried out to study the electronic structures of damaged α-Al2O3. As discussed above, the associated defects are mainly aluminum FP and oxygen FP. The total density of state distribution of damaged α-Al2O3 with oxygen FP and aluminum FP are analyzed and compared with that of pristine state in Fig. 4. The band gap for pristine sapphire phase of alumina is predicted to be 7.7 eV, which is much smaller than the experimental data of 8.7 eV[35]. This underestimation is because of the well-known discontinuity of exchange-correlation energy of the local-density approximation. For the damaged α-Al2O3 with Ovac + O-O dumbbell and Ovac + Otetra, the Fermi level shifts from 7.6 eV to the higher energy value of 9.9 and 9.3 eV, respectively. Besides, defect levels are observed near the valence band maximum (VBM) and in the forbidden band region. Obviously, the presence of point defect influences the electronic structure of α-Al2O3 significantly, indicating that the optical absorption of α-Al2O3 under irradiation will be affected. As for α-Al2O3 with Alvac + Alocta, the defect levels appear around the VBM and conduction band minimum.

Figure 4

Total density of state distribution for (a) α-Al2O3 with oxygen vacancy and oxygen dumbbell pair; (b) α-Al2O3 with oxygen vacancy and oxygen interstitial occupying the tetrahedral site; (c) α-Al2O3 with aluminum vacancy and aluminum interstitial occupying the octahedral site. EF indicates the Fermi level.

To identify the contribution of the defect to optical absorption, we further analyze the electronic structures of defective α-Al2O3 with single O vacancy and interstitial, as illustrated in Fig. 5. Here, the Al oxygen and interstitial are not considered because the Al recoils have generally much larger threshold displacement energies than oxygen atoms and the oxygen defects dominate under electron irradiation. For α-Al2O3 with Ovac, there are two defect levels appearing at 5.35 and 5.65 eV, corresponding to the wavelengths of 232 and 219 nm within the ultraviolet (UV) light region, respectively. In the cases of α-Al2O3 with O-O dumbbell and Otetra, the induced defect levels are located at 4.73 eV (262 nm) and 5.27 eV (235 nm), respectively. Wang et al. investigated the optical properties of α-Al2O3 under 1.2 MeV electron irradiations using the optical absorption spectra, and found that the absorption peaks mainly appeared at the wavelength of 203, 233 and 256 nm[36]. Our calculations show that these peaks should be contributed by the oxygen vacancy and interstitial defects. Obviously, the presence of these defects will reduce the transmittance of α-Al2O3. Ke et al. investigated the change of the surface roughness and transmittance caused by electron and proton irradiation, and found that the transmittance of α-Al2O3 decreased most remarkably in the ultraviolet band under the 100 ~ 150 keV electron irradiation[37]. This is also in good agreement with our simulations. These results suggest that it is necessary to enhance the radiation tolerance of α-Al2O3 or introduce recombination center for oxygen defects to improve its optical properties and performance under radiation environment.

Figure 5

Total density of state distribution for α-Al2O3 with (a) oxygen vacancy; (b) oxygen dumbbell pair; (c) oxygen interstitial occupying the tetrahedral site. EF indicates the Fermi level and is set to be zero.

Conclusions

In summary, low energy recoil events in α-Al2O3 have been investigated by an initio molecular dynamics method. Generally, the threshold displacement energies for oxygen are smaller than those for aluminum, indicating that the displacement of oxygen dominates under electron irradiation and the created defects are mainly oxygen vacancy and interstitials. Moreover, the oxygen interstitial forms the dumbbell defect configuration or occupies the tetrahedral site. For α-Al2O3 with Ovac, there are two defect levels appearing at 232 and 219 nm within the ultraviolet (UV) light region. In the cases of α-Al2O3 with O-O dumbbell and Otetra, the induced defect levels are located at 262 nm and 235 nm, respectively. These defects will influence the optical absorption and reduce the transmittance of α-Al2O3 significantly.

Methods

All calculations are carried out using the Spanish Initiative for Electronic Simulation with Thousands of Atoms (SIESTA) code. The norm-conserving Troullier-Martins pseudopotentials[38] are employed to determine the interaction between ions and electrons, and the exchange-correlation potential is described by the local-density approximation (LDA) in Ceperly-Alder parameterization[39]. The valence electron configurations are 2s22p4 for O, with cutoff radii of 1.46 bohr for both orbitals. For Al the valence electron configurations are 3s23p1, and the cutoff radii are 1.86 and 2.06 bohr for 3 s and 3p orbitals, respectively. The all electron and pseudo valence wave function and the Fourier transfer of ionic pseudo potential for Al and O are presented in Figs 6 and 7, respectively. As shown in Figs 6 and 7, when the cutoff radius is larger than 1.0 bohr, the pseudo valence wave functions for O and Al are in reasonable agreement with the all electron wave functions. A series of test calculations have shown that these relatively hard pseudopotentials can be used to describe the short-range interactions between atoms for recoil energy larger than 100 eV. The valence wave functions are expanded by a basis set of localized atomic orbits, and single-ζbasis sets (SZ) are employed, with a K-point sampling of 1 × 1 × 1 in Brillouin zone and a cutoff energy of 60 Ry. In the displacement events, sixteen directions for α-Al2O3, as illustrated in Fig. 8b and c, are taken into account. To simulate the low energy recoil events, a 3 × 3 × 1 supercell consisting of 270 atoms is used. The simulations are conducted with a NVE ensemble and a variable time step scheme is employed to avoid the instability of the system.

Figure 6

(a,b) All-electron (AE) and pseudo (PS) valence wave functions as a function of radius for aluminum 3 s and 3p orbitals; (c,d) Fourier transfer of the ionic pseudo potential as a function of radius-1 for aluminum 3 s and 3p orbitals.

Figure 7

(a,b) All-electron (AE) and pseudo (PS) valence wave functions as a function of radius for oxygen 2 s and 2p orbitals; (c,d) Fourier transfer of the ionic pseudo potentials as a function of radius−1 for oxygen 2 s and 2p orbitals.

Figure 8

Illustration of schematic view of (a) α-Al2O3 structure; (b,c) incident directions in α-Al2O3.