PCCP View Article Online
Published on 09 February 2016. Downloaded by University of Pennsylvania Libraries on 21/02/2016 14:42:32.
PAPER
Cite this: DOI: 10.1039/c5cp07626a
View Journal
An insight to the role of Cr in the process of intrinsic point defects in a-Al2O3 Xin Xiang, Guikai Zhang, Feilong Yang, Xuexing Peng, Tao Tang, Yan Shi and Xiaolin Wang* Cr is a commonly existing impurity in a-Al2O3, and thus the role of Cr in the process of intrinsic point defects in a-Al2O3 has been studied based on first-principle calculations. The results show that Cr has
Received 10th December 2015, Accepted 9th February 2016
significant influence on the formation, charge state, relative stability and equilibrium configuration of isolated
DOI: 10.1039/c5cp07626a
O-condition, the possible defect types, the dominant defects and the defect formation energies will be
www.rsc.org/pccp
Frenkel defects and antisite pairs, giving a different insight to the defect process in a-Al2O3.
intrinsic point defects in a-Al2O3, resulting in the variation of defect process. Specifically, depending on the altered in a-Al2O3 after Cr doping. Generally speaking, Cr is favorable for the formation of Schottky defects,
1. Introduction It is known that corundum structured a-Al2O3 is the most thermodynamically stable phase among the eight isomerides of alumina, and thus it finds widespread applications in optical devices, electronic substrates, catalyst supports, thermal and tritium permeation barrier coatings, etc.1–6 However, these applications may encounter some difficulties, since the properties of a-Al2O3 depend on its defect chemistry, which has been widely studied in the last three decades.5–10 Therefore, it is essential to understand the basic defect chemistry of a-Al2O3 both for scientific and technologic interests. Recently, based on first-principles plane-wave pseudopotential calculations, we studied the six types of isolated intrinsic point defects in pure a-Al2O3, and then proposed a new perspective for the process of intrinsic point defects in a-Al2O3.11 As a matter of fact, experimentally, it is practically an unachievable task to prepare a perfect pure a-Al2O3 specimen, and trace impurity even at a magnitude of ppm will manipulate the defect chemistry, especially the defect concentration in a-Al2O3.8 The variation of charge state, existing form and atomic transport etc. of intrinsic point defects with impurities in a-Al2O3, however, have seldom been investigated by previous studies. These must, however, be clearly understood, since they are undoubtedly a vital fundamental scientific issue in the practical applications of a-Al2O3 based materials and devices. Natural corundum-structured a-Al2O3 can contain up to 1.81 wt% Cr2O3 beside Fe2O3 and other impurities.12 On the other hand, Cr can be observed experimentally in Al2O3 coatings as thermal or tritium permeation barriers because of the thermal Institute of Materials, China Academy of Engineering Physics, Mianyang, 621908, China. E-mail: [email protected]; Fax: +86 81636 25900; Tel: +86 81636 26483
This journal is © the Owner Societies 2016
diffusion of Cr from steel substrates during the coating preparation.13–15 It thus can be said that Cr is a commonly existing impurity element in Al2O3, which may exert some impact on the properties of Al2O3. Take corundum for example, it will turn from colorless or transparent to red after a certain amount of Cr is introduced. Doping with Cr was also shown to alter the structural, electronic and reactive properties of the a-Al2O3 (0001) surface.12 Therefore, it is anticipated that the defect chemistry of a-Al2O3 will be affected by Cr impurity, no matter whether it is naturally existing or unintentionally doped. For this reason, to focus mainly on the process of intrinsic point defects, the firstprinciples method is used to investigate the influence of Cr addition on the defect chemistry of a-Al2O3 in the present work. The results are anticipated to be meaningful not only to understand the interaction of external impurities with intrinsic defects in a-Al2O3, but also to parameterize multi-scale models of the defect kinetics for oxide ceramics under growth and working environments.
2. Computational method and model All the present first-principle calculations were performed with the DMol316 package in the Materials Studio of Accelrys Inc. For the exchange–correlation potential, the generalized gradient approximation (GGA) given by Perdew and Wang (PW91)17 was used. As for the core treatment, the frameworks of all electron18 and double numerical plus polarization (DNP)19 were employed. The Brillouin-zone was integrated by a 2 2 1 k-point mesh created by the Monkhorst–Pack20 scheme. A thermal orbital occupation of 0.008 Ha incorporated with a global cutoff of 4.3 Å were used for all calculations without considering the spin polarization. The convergence criteria of the energy, force, displacement and self-consistent field (SCF) used in the present
Phys. Chem. Chem. Phys.
View Article Online
Published on 09 February 2016. Downloaded by University of Pennsylvania Libraries on 21/02/2016 14:42:32.
Paper
work were the same as those in our previous work,11 giving an energy convergence within 2 meV per atom. In order to study the Cr effect on the process of intrinsic point defects in a-Al2O3, a 36-layer (2 2 2) a-Al2O3 supercell was firstly built in this work. After full geometry optimization, a Cr atom was introduced to create a Cr interstitial or substituent nearby the geometry center of the supercell. By comparing the total energies of Cr-containing a-Al2O3 supercells after geometry optimization, the preference for Cr occupation, i.e. substitution (CrAl, CrO), and interstitial (Cri) could be determined. Thereafter, the crystal lattice of the most stable optimized Cr-containing supercell was constrained, and all atoms except for those in both the upper and bottom ten layers were relaxed during defect calculations. Then, an isolated intrinsic point defect of vacancy (VAl, VO), interstitial (Ali, Oi) and antisite atom (AlO, OAl) was generated within different atomic distances (1 NN–8 NN, NN stands for the nearest neighbor) from the Cr atom by removing, introducing and substituting a corresponding atom in the a-Al2O3 supercell, respectively. After geometry optimization, the defective supercell with minimum total energy was selected to determine the most stable site for each defect species in Cr-doped a-Al2O3. Taking the interstitial Al atom as an example, as shown in Fig. 1(a), within different atomic distance from the CrAl substituent, an Al atom was placed in the center of an octahedral interstitial site in the supercell, and the relative total energies of these supercells are shown in Fig. 1(b). It can be seen that the most stable site for Ali locates in the 1 NN interstitial site from the CrAl atom. With the same method, the most stable sites for Oi can also be determined, i.e. in the 1 NN interstitial site from the CrAl substituent. The formation energies of isolated intrinsic point defects in Cr-containing a-Al2O3, obtained from the total energy differences between the supercells with and without defects, were firstly calculated to determine the Cr occupation, thermodynamical stable charge state of each defect, and the relative stability of all defect types within the Fermi level. Specifically, the formation
PCCP
energy was calculated by the following equation based on the standard formalism proposed by Zhang et al.:21 X f tot tot ECr;def ðXÞ ¼ ECr;def ECr þ Dni mi þ qEF (1) i
Etot Cr,def
Etot Cr
and are the total energies of the Cr-containing where supercell with and without defects, respectively. The changed atom number Dni of atom species i (Al or O) in the supercell, the atomic chemical potential mi of element i, the charge state q of defect X, and the Fermi level EF in eqn (1) have the same meanings as those described in our previous work,11 and were also treated in the same way in this work.
3. Results and discussion 3.1
Cr occupation in a-Al2O3
Fig. 2 shows the formation energies of Cr-related defects in various charge states in a-Al2O3 as a function of the Fermi level EF under the two extreme conditions of O-rich (oxidation limit) and O-deficient (reduction limit). In this Figure, only results of the most stable charge states of individual defects are exhibited. It is clearly shown that, compared with Cri and CrO, CrAl has the lowest formation energy over the entire Fermi level under O-rich conditions, that is, CrAl is the most stable species among the Cr-related defects in this situation, as shown in Fig. 2(a). On the other hand, as illustrated in Fig. 2(b), under O-deficient conditions, CrAl is more stable than Cri and CrO within a much wider range of Fermi level (EF 4 2.01 eV). Obviously, Cr prefers to occupy the lattice site of the Al atom to form a CrAl substituent under both the O-rich and O-deficient conditions, consistent with previous theoretical12,22 and experimental results.22 The Cr occupation in a-Al2O3 can be related to the isostructure of the two oxides of a-Al2O3 and Cr2O3, since the +3 charged Cr ion has an identical charge and a similar ionic radius to Al3+ (0.755 and 0.675 Å, respectively), resulting in similar crystal lattices of the two metal oxides (4.931 and 4.760 Å accordingly), which is also beneficial for Cr substitution in a-Al2O3.12
Fig. 1 (a) Side view of the Cr-containing (2 2 2) a-Al2O3 supercell (only the relaxed layers are shown). The grey ball depicts a Cr atom, and red and purple ones denote oxygen and aluminum atoms, respectively. The letters I1–I8 indicate possible interstitial sites of Al or O atoms within different atomic distances from the doped Cr atom; (b) relative total energies of the supercells containing a CrAl substituent and an Ali atom within different atomic distances from the CrAl atom.
Phys. Chem. Chem. Phys.
This journal is © the Owner Societies 2016
View Article Online
Published on 09 February 2016. Downloaded by University of Pennsylvania Libraries on 21/02/2016 14:42:32.
PCCP
Paper
Fig. 2 Formation energies of Cr-related defects in various charge states in a-Al2O3 as a function of the Fermi level EF under (a) O-rich and (b) O-deficient conditions.
For the CrAl substituent, the most stable charge state depends on the EF position, either under O-rich or O-deficient conditions, as shown in Fig. 2. When EF locates near the top of valence band, the stable charge state is CrAl3+, and then will change to CrAl2+ and CrAl1+ at higher EF level. The neutral state i.e. Cr0Al will remain at EF Z 2.4 eV. Obviously, over the entire EF range, the neutral state will dominate. By contrast, the formation energies of CrAl in each charge state under the conditions O-deficiency are much larger than those under O-rich conditions, up to about 2.5 eV, indicating that CrAl forms more easily under O-rich conditions. In any case, Cr0Al dominates the substituent, that is, the +3 charged Cr ion substitutes for Al3+ in a-Al2O3. Therefore, only the neutral charge state was considered as the CrAl substituent in the following calculations both under the O-rich and O-deficient conditions. 3.2
Cr effect on isolated intrinsic point defects in a-Al2O3
Fig. 3 plots the formation energy variation of six types of isolated intrinsic point defects in various charge states with the Fermi level EF in Cr-doped a-Al2O3 under O-rich and O-deficient conditions. In this Figure, only the most stable charge states for each defect within the whole Fermi level range are exhibited. It can be
seen that the charge states and their variation tendencies of each defect species in Cr-doped a-Al2O3 are dependent on the EF position, consistent with the most recent theoretical predictions in pure a-Al2O3.5,11,23 However, within the EF range, 2 and 3 charged states are not stable states for OAl in Cr-doped a-Al2O3 under both O-rich and O-deficient conditions, while they will be readily present in pure a-Al2O3.11 Moreover, after Cr doping, the relative stability of intrinsic point defects in a-Al2O3 under O-rich conditions is VAl 4 OAl 4 Oi 4 VO 4 Ali 4 AlO over a fairly wide EF range (Fig. 3(a)), similar to that in pure a-Al2O3.11 The main difference emerges for the more stable EF range of VAl and OAl. In pure a-Al2O3, VAl has a wider (41.6 eV) stable EF range than in Cr-doped a-Al2O3. On the other hand, the relative defect stability in a-Al2O3 will be significantly affected by Cr. As shown in Fig. 3(b), near the bottom of the conduction band, the relative stability in Cr-doped a-Al2O3 is OAl 4 VAl 4 Oi 4 VO 4 AlO 4 Ali, while in pure a-Al2O3 it is VAl 4 OAl 4 Oi 4 VO 4 Ali 4 AlO;11 and at the position of gap center, the relative stability in Cr-doped a-Al2O3 is VO 4 VAl 4 Ali 4 AlO 4 Oi 4 OAl, yet it will change to VAl 4 VO 4 Oi 4 Ali 4 OAl 4 AlO in pure a-Al2O3.11 Therefore, the doped Cr has exerted an influence on the defect chemistry in a-Al2O3.
Fig. 3 Formation energies of isolated intrinsic point defects in various charge states in Cr-doped a-Al2O3 as a function of the Fermi level EF under (a) O-rich and (b) O-deficient conditions.
This journal is © the Owner Societies 2016
Phys. Chem. Chem. Phys.
View Article Online
Published on 09 February 2016. Downloaded by University of Pennsylvania Libraries on 21/02/2016 14:42:32.
Paper
PCCP
Fig. 4 Comparison of formation energies of isolated intrinsic point defects in a-Al2O3 before and after Cr doping under (a) O-rich and (b) O-deficient conditions.
Interestingly, the formation energies of each defect species in a-Al2O3 will be significantly affected by Cr, as shown in Fig. 4. Under the O-rich conditions, over the entire Fermi level, the formation energies of VO, Ali, Oi, AlO and OAl in a-Al2O3 will be reduced by Cr to different extents (Fig. 4(a)), indicating that Cr is favorable for the formation of these defects; while for the defect of VAl, Cr is also beneficial at a small EF range (0–3.89 eV), but unfavorable for defect formation at a larger EF range (43.89 eV). On the other hand, a similar phenomenon will be present under O-deficient conditions, yet Cr will have a negative effect on the formation of VAl over a wider EF range (42.56 eV), as shown in Fig. 4(b). Therefore, depending on the O environment, Cr has great influence on the formation, charge state and relative stability of isolated intrinsic point defects in a-Al2O3. However, under convenient circumstances the constraint of electroneutrality must be satisfied in these materials. For Cr-doped a-Al2O3, the +3 charged Cr ion substitutes for Al3+, leading to no extra charge, neutralizing the charged isolated intrinsic point defects formed in the material. Consequently, the intrinsic point defects in Cr-doped a-Al2O3 cannot be isolated, but exist in charge-neutral combinations, resulting in the formation of Schottky defects, Frenkel defects or antisite pairs; that is, the so-called defect process in materials. Since Cr has great influence on the isolated intrinsic point defects in a-Al2O3, it is anticipated that Cr will definitely exert some effect on the defect process in this material. 3.3
Cr effect on Schottky defect in a-Al2O3
The Schottky defect in a-Al2O3 consists of several VAl and VO, under the constraints of charge neutrality and stoichiometry. Seen from Fig. 3, after Cr doping, the main stable defect form for VAl is VAl3, accompanied with a much smaller proportion of VAl2, VAl1 and V0Al; while for VO, the main defect form is V0O, with a small percentage of 2 and 1 charged states. Therefore, the Schottky defect in Cr-doped a-Al2O3 can be expressed as {mVOp+:nVAlq} (mp = nq, p = 0–2, q = 0–3). According to our previous work, vacancies to form Schottky defects in a-Al2O3 should be sufficiently separated and have no interactions.11 Consequently, following the method proposed by Çakır et al.,24
Phys. Chem. Chem. Phys.
the positively charged part of a Schottky defect will have an identical formation energy to the negatively charged one, i.e. EF(mVOp+) = EF(nVAlq), and thus the average formation energy of the Schottky defect could be determined from 2EF(mVOp+)/(m + n). In earlier studies,25,26 the Schottky defect in a-Al2O3 was directly considered as a quintet i.e. {2VAl3 + 3VO2+}, since Al2O3 is constituted of Al3+ and O2 ions. However, this case will be totally different. Fig. 5(a) plots the formation energies of mVO and nVAl at each charge state in Cr-doped a-Al2O3 as a function of the Fermi level under O-rich conditions. When the formation energy variation line of a negatively charged nVAl intersects with a positively charged mVO line, a possible Schottky defect will form. It thus can be seen that there are three types of possible Schottky defect formed in Cr-doped a-Al2O3 under O-rich conditions, i.e. {VO2+:2VAl1}, {VO2+:VAl2}, {3VO2+:2VAl3}, and the average formation energies are 1.62, 2.71 and 3.92 eV, respectively. Obviously, the most stable Schottky defect is {VO2+:2VAl1} for its smallest average formation energy, and such a small formation energy enables defect formation at room or higher temperatures. The situation is a little different from that in pure a-Al2O3.11 By contrast with pure a-Al2O3, one less type of possible Schottky defect i.e. {VO1+:VAl1} will form in Cr-doped a-Al2O3. As for the same types of Schottky defects, the formation energies will be decreased after Cr doping. Especially for the most stable Schottky defect {VO2+:2VAl1}, the formation energy decrease is up to about 1.6 eV. Therefore, Cr is favorable for the formation of Schottky defects in a-Al2O3 under O-rich conditions. Moreover, the formation energy differences of these three types of Schottky defects in Cr-doped a-Al2O3 are much larger (41.0 eV) than those in pure a-Al2O3 (o1.0 eV), indicating that {VO2+:2VAl1} will dominate among the Schottky defects in a-Al2O3, yet {VO2+:VAl2} and {3VO2+:2VAl3} will only share much smaller proportions after Cr doping, while not a single Schottky defect could be absolutely dominant in pure a-Al2O3.11 In a word, Cr has great influence on the Schottky defects in a-Al2O3 under O-rich conditions. Similarly, as shown in Fig. 6(b), under O-deficient conditions, there are six types of possible Schottky defects in Cr-doped a-Al2O3, i.e. {3VO1+:VAl3}, {2VO1+:VAl2}, {3VO2+:2VAl3}, {VO2+:VAl2},
This journal is © the Owner Societies 2016
View Article Online
Published on 09 February 2016. Downloaded by University of Pennsylvania Libraries on 21/02/2016 14:42:32.
PCCP
Paper
Fig. 5 (a) Formation energies of VAl and VO in various charge states, some of which are multiplied by a factor, and (b) possible Schottky defect configurations formed in Cr-doped a-Al2O3 under O-rich conditions.
Fig. 6 (a) Formation energies of VAl and VO in various charge states, some of which are multiplied by a factor, and (b) possible Schottky defect configurations formed in Cr-doped a-Al2O3 under O-deficient conditions.
{VO1+:VAl1} and {VO2+:2VAl1}, which is consistent with the case in pure a-Al2O3.11 The corresponding average formation energies are 2.59, 2.82, 3.92, 5.19, 3.99 and 4.05 eV. Obviously, the most stable Schottky defect is {3VO1+:VAl3}, for which such a small formation energy allows defect formation under convenient circumstances, also consistent with that in pure a-Al2O3.11 Moreover, the formation energies of Schottky defects except {VO2+:VAl2} will decrease to different extents after Cr doping, suggesting that Cr is generally beneficial for the formation of Schottky defects in a-Al2O3 under O-deficient conditions. Considering the small formation energy differences (o1.0 eV) between the first two types of defects, and much larger differences (41.0 eV) between these two and other four types of defects, it is clear that {3VO1+:VAl3} and {2VO1+:VAl2} will be dominant in Cr-doped a-Al2O3 under the conditions of O-deficiency; while in pure a-Al2O3, one more type of Schottky defect i.e. {3VO2+:2VAl3} will also be dominant.11 Therefore, the Schottky defects in a-Al2O3 under O-deficient conditions will be readily affected by Cr. By contrast, there are three more types of Schottky defects formed in Cr-doped a-Al2O3 under O-deficient conditions than that under O-rich conditions. For the same three defect types
This journal is © the Owner Societies 2016
({VO2+:2VAl1}, {VO2+:VAl2} and {3VO2+:2VAl3}), the formation energy of the first one under O-deficient conditions is B2.4 eV higher than that under O-rich conditions, about 0.6 eV smaller than that in pure a-Al2O3.11 As for the second one, ({VO2+:VAl2}), the formation energy difference under both conditions is twice as large as that in pure a-Al2O3.11 The last one, ({3VO2+:2VAl3}), shares an identical formation energy under both conditions, yet is about 0.3 eV smaller than that in pure a-Al2O3.11 Obviously, Cr has significant influence on Schottky defects in a-Al2O3, and the influence extent depends on the O environment. 3.4
Cr effect on Frenkel defects in a-Al2O3
The Frenkel defect in a-Al2O3 incorporates an interstitial atom and a corresponding identically charged vacancy. As shown in Fig. 3, after Cr doping, four types (3, 2, 1 and 0) of charge states exist for VAl, and three types (0, +1, +2) for VO. Therefore, the cation Frenkel defect can be expressed as {Aliq+:VAlq} (q = 0–3), while the anion one can be described as {Oip:VOp+} ( p = 0–2). When a Frenkel defect forms, the defect constituent of the interstitial and vacancy will have an equal formation energy, which could also be determined as the average formation energy of the Frenkel defect.
Phys. Chem. Chem. Phys.
View Article Online
Published on 09 February 2016. Downloaded by University of Pennsylvania Libraries on 21/02/2016 14:42:32.
Paper
PCCP
Fig. 7 Possible cation (a and b) and anion (c and d) Frenkel defects formed in Cr-doped a-Al2O3 under O-rich (a and c) and O-deficient (b and d) conditions.
Generally, the two types of Frenkel defects in a-Al2O3 are considered to be {Ali3+:VAl3} and {Oi2:VO2+},23,25,26 inconsistent with our previous work.11 Following the statements in Section 3.2, the case must have some difference in Cr-doped a-Al2O3. Fig. 7 plots the formation energies of interstitials and vacancies in each charge state in Cr-doped a-Al2O3 as a function of the Fermi level under O-rich and O-deficient conditions. When the formation energy variation line of a negatively charged interstitial (vacancy) intersects with a positively charged vacancy (interstitial) line, a possible Frenkel defect will form. It thus can be seen that there are two types of possible cation Frenkel defects formed in Cr-doped a-Al2O3 under O-rich conditions (Fig. 7(a)), i.e. {Ali2+:VAl2} and {Ali3+:VAl3}, and the average formation energies are 4.47 and 4.78 eV, respectively, for which the defect formation can be realized at temperatures a little higher than convenient circumstances. Considering the small formation energy difference (0.31 eV), the main Frenkel defect {Ali2+:VAl2} will not dominate, and {Ali3+:VAl3} will also share a big proportion in Cr-doped a-Al2O3. However, only one type of Frenkel defect i.e. {Ali3+:VAl3} with a little higher formation energy forms in pure a-Al2O3 under O-rich conditions,11 indicating that Cr is beneficial for the formation of Frenkel defects in a-Al2O3. On the other hand, three types of possible cation Frenkel defects will form in Cr-doped a-Al2O3 under O-deficient conditions (Fig. 7(b)), i.e. {Ali1+:VAl1}, {Ali2+:VAl2} and {Ali3+:VAl3}, which is consistent with that in pure a-Al2O3.11 Nevertheless, the corresponding
Phys. Chem. Chem. Phys.
formation energies (5.93, 4.47 and 4.78 eV, respectively) are smaller than that in pure a-Al2O3,11 which could be attributed to the doped Cr. Moreover, the defect {Ali1+:VAl1} has a much higher formation energy (41.0 eV) than {Ali2+:VAl2} and {Ali3+:VAl3}, suggesting that the latter will dominate in Cr-doped a-Al2O3, while only {Ali3+:VAl3} will dominate in pure a-Al2O3.11 Obviously, the cation Frenkel defect in a-Al2O3 will be greatly affected by Cr under both O-rich and O-deficient conditions. As for the anion Frenkel defect, there are two possible defect types i.e. {Oi1+:VO1} and {Oi2+:VO2} formed in Cr-doped a-Al2O3 under both O-rich and O-deficient conditions, and the corresponding average formation energies are 5.24 and 5.57 eV in each condition, suggesting that the anion Frenkel defects in Cr-doped a-Al2O3 are independent of the oxygen environment, consistent with the case in pure a-Al2O3.11 Moreover, such formation energies can enable defect formation at temperatures a little higher than a convenient environment. Obviously, the most stable anion Frenkel defect is {Oi1+:VO1} for its lower formation energy; yet a big proportion of {Oi2+:VO2} will also be present in Cr-doped a-Al2O3 because of the rather small formation energy difference (0.33 eV) of the two types of Frenkel defects, which is similar to the case for pure a-Al2O3.11 By contrast, however, the formation energies of {Oi1+:VO1} and {Oi2+:VO2} in a-Al2O3 will be, respectively, reduced by 0.61 and 0.84 eV after Cr-doping, indicating that Cr is favorable for the formation of anion Frenkel defects in a-Al2O3. Therefore, the doped Cr will have some impact on the anion Frenkel defects in a-Al2O3.
This journal is © the Owner Societies 2016
View Article Online
Published on 09 February 2016. Downloaded by University of Pennsylvania Libraries on 21/02/2016 14:42:32.
PCCP
Paper
Fig. 8 (a) Formation energies of antisite atoms in various charge states, and (b) possible antisite defect combinations formed in Cr-doped a-Al2O3 under the O-rich conditions.
3.5
Cr effect on antisite pairs in a-Al2O3
The antisite pair in a-Al2O3 combines two antisite atoms i.e. OAl and AlO, which can be expressed as {AlOq+:OAlq} (q = 0–5). When an antisite pair forms, the two antisite atoms will have identical formation energies. Fig. 8 plots the formation energies of OAl and AlO in all charge states in Cr-doped a-Al2O3 as a function of the Fermi level under O-rich conditions. When the formation energy variation line of a negatively charged OAl defect intersects with a positively charged AlO line, a possible antisite pair will form. It thus can be seen that there are three types of possible antisite pairs formed in Cr-doped a-Al2O3 under O-rich conditions (Fig. 8(b)), i.e. {AlO3+:OAl3}, {AlO4+:OAl4} and {AlO5+:OAl5}, and the average formation energies are 9.53, 9.35 and 11.82 eV, respectively. Obviously, the most stable antisite pair is {AlO4+:OAl4} for its lowest formation energy. This situation is different from what in pure a-Al2O3, in which the most stable antisite pair is {AlO3+:OAl3}.11 By contrast, the formation energies of each antisite pair in Cr-doped a-Al2O3 are a little lower than those in pure a-Al2O3,11 indicating that Cr is somewhat favorable for the formation of antisite pairs in a-Al2O3, although such large formation energies mean that they are still very unlikely to form in Cr-doped a-Al2O3 at conventional conditions as in pure a-Al2O3.
Therefore, Cr has some influence on the antisite pairs in a-Al2O3 under O-rich conditions. On the other hand, there are five possible antisite pairs formed in Cr-doped a-Al2O3 under O-deficient conditions i.e. {AlO1+:OAl1}, {AlO2+:OAl2}, {AlO3+:OAl3}, {AlO4+:OAl4} and {AlO5+:OAl5} (Fig. 9), and the formation energies are 8.81, 8.57, 9.53, 9.35 and 11.81 eV, respectively. Thus the most stable antisite pair is {AlO2+:OAl2}, also different from the case in pure a-Al2O3.11 Moreover, the formation energies of each antisite pair in Cr-doped a-Al2O3 are correspondingly smaller than that in pure a-Al2O3, indicating that Cr is favorable for the formation of antisite pairs in a-Al2O3. Obviously, Cr will exert some influence on the antisite pairs in a-Al2O3 under O-deficient conditions.
4. Conclusions The effect of Cr on the process of intrinsic point defects in a-Al2O3 has been studied based on first-principle calculations. The results obtained can be summarized as follows: (1) Cr prefers to occupy the lattice site of the Al atom to form a CrAl substituent in a-Al2O3.
Fig. 9 (a) Formation energies of antisite atoms in various charge states, and (b) possible antisite defect combinations formed in Cr-doped a-Al2O3 under O-deficient conditions.
This journal is © the Owner Societies 2016
Phys. Chem. Chem. Phys.
View Article Online
Published on 09 February 2016. Downloaded by University of Pennsylvania Libraries on 21/02/2016 14:42:32.
Paper
(2) Depending on the O-conditions, Cr has great influence on the formation, charge state and relative stability of isolated intrinsic point defects in a-Al2O3, and thus will exert some effect on the defect process in this material. (3) The possible Schottky defect types and their relative proportions under both O-rich and O-deficient conditions will be changed by Cr, and Cr is favorable for the formation of Schottky defects in a-Al2O3. (4) The main cation Frenkel defect in a-Al2O3 will be changed from {Ali3+:VAl3} to {Ali2+:VAl2} after Cr doping, yet the anion Frenkel defect will remains as {Oi1+:VO1}, and both the formation energies will be reduced. (5) Cr has a positive effect on the formation of antisite pairs, though this will alter the main possible defect types in a-Al2O3. (6) Based on the above results, Cr has a significant influence on the process of intrinsic point defects in a-Al2O3, and the extent of the influence depends on the O-conditions. Generally speaking, Cr is favorable for the formation of Schottky defects, Frenkel defects and antisite pairs in a-Al2O3.
Acknowledgements This work is supported by the National Magnetic Confinement Fusion Science Program (No. 2013GB110006B) and the National Natural Science Foundation of China (No. 21471137 and 11275175).
Notes and references 1 R. H. Doremus, Alumina, in Ceramic and Glass Materials: Structure, Properties and Processing, ed. J. F. Shackelford and R. H. Doremus, Springer, 2008, pp. 1–26. 2 H. Heuer, D. B. Hovis, J. L. Smialek and B. Gleeson, J. Am. Ceram. Soc., 2011, 94, s146. 3 K. Shirvani, S. Mastali, A. Rashidghamat and H. Abdollahpour, Corros. Sci., 2013, 75, 142. 4 J. K. Bristow, D. Tiana, S. C. Parker and A. Walsh, J. Mater. Chem. A, 2014, 2, 6198. 5 G. K. Zhang, Y. J. Lu and X. L. Wang, Phys. Chem. Chem. Phys., 2014, 16, 17523.
Phys. Chem. Chem. Phys.
PCCP
6 J. Cai, Y. Li, J. M. Wu and G. P. Ling, Oxid. Met., 2014, 81, 253. ¨ger, Solid State Ionics, 1984, 12, 189. 7 F. A. Kro ¨f and R. W. Grimes, Acta Mater., 1998, 8 K. P. D. Lagerlo 46, 5689. 9 K. P. Muthe, K. Sudarshan, P. K. Pujari, M. S. Kulkarni, N. S. Rawat, B. C. Bhatt and S. K. Gupta, J. Phys. D: Appl. Phys., 2009, 42, 105405. 10 S. Ikeda and T. Uchino, J. Phys. Chem. C, 2014, 118, 4346. 11 X. Xiang, G. K. Zhang, X. L. Wang, T. Tang and Y. Shi, Phys. Chem. Chem. Phys., 2015, 17, 29134. 12 J. Baltrusaitis, C. Hatch and R. Orlando, J. Phys. Chem. C, 2012, 116, 18847. 13 L. Xing, Y. Zheng, L. Cui, M. Sun, M. Shao and G. Lu, High Temp. Mater. Processes, 2011, 30, 99. 14 H. G. Yang, Q. Zhan and W. W. Zhao, J. Nucl. Mater., 2011, 417, 1237. 15 Q. Zhan, H. G. Yang, W. W. Zhao, X. M. Yuan and Y. Hu, J. Nucl. Mater., 2013, 442, S603. 16 B. Delley, J. Chem. Phys., 2000, 113, 7756–7764. 17 J. A. White and D. Mbird, Phys. Rev. B: Condens. Matter, 1994, 50, 4954–4957. 18 B. Delley, J. Chem. Phys., 1990, 92, 508–517. 19 J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865–3868. 20 H. J. Monkhorst and J. D. Pack, Phys. Rev. B: Solid State, 1976, 13, 5188. 21 S. B. Zhang and J. E. Northrup, Phys. Rev. Lett., 1991, 67, 2339. 22 E. Gaudry, D. Cabaret, P. Sainctavit, C. Brouder, F. Mauri, J. Goulon and A. Rogalev, J. Phys.: Condens. Matter, 2005, 17, 5467. 23 N. D. M. Hine, K. Frensch, W. M. C. Foulkes and M. W. Finnis, Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 79, 024112. 24 D. Çakır, G. A. de Wijs and G. Brocks, J. Phys. Chem. C, 2011, 115, 24429. 25 N. D. M. Hine, K. Frensch, M. W. Finnis, W. M. C. Foulkes and A. H. Heuer, Int. Conf. on QMC, April 6, 2009, Apuan. 26 K. Matsunaga, T. Tanaka, T. Yamamoto and Y. Ikuhara, Phys. Rev. B: Condens. Matter, 2003, 68, 085110.
This journal is © the Owner Societies 2016
Published on 09 February 2016. Downloaded by University of Pennsylvania Libraries on 21/02/2016 14:42:32.
PAPER
Cite this: DOI: 10.1039/c5cp07626a
View Journal
An insight to the role of Cr in the process of intrinsic point defects in a-Al2O3 Xin Xiang, Guikai Zhang, Feilong Yang, Xuexing Peng, Tao Tang, Yan Shi and Xiaolin Wang* Cr is a commonly existing impurity in a-Al2O3, and thus the role of Cr in the process of intrinsic point defects in a-Al2O3 has been studied based on first-principle calculations. The results show that Cr has
Received 10th December 2015, Accepted 9th February 2016
significant influence on the formation, charge state, relative stability and equilibrium configuration of isolated
DOI: 10.1039/c5cp07626a
O-condition, the possible defect types, the dominant defects and the defect formation energies will be
www.rsc.org/pccp
Frenkel defects and antisite pairs, giving a different insight to the defect process in a-Al2O3.
intrinsic point defects in a-Al2O3, resulting in the variation of defect process. Specifically, depending on the altered in a-Al2O3 after Cr doping. Generally speaking, Cr is favorable for the formation of Schottky defects,
1. Introduction It is known that corundum structured a-Al2O3 is the most thermodynamically stable phase among the eight isomerides of alumina, and thus it finds widespread applications in optical devices, electronic substrates, catalyst supports, thermal and tritium permeation barrier coatings, etc.1–6 However, these applications may encounter some difficulties, since the properties of a-Al2O3 depend on its defect chemistry, which has been widely studied in the last three decades.5–10 Therefore, it is essential to understand the basic defect chemistry of a-Al2O3 both for scientific and technologic interests. Recently, based on first-principles plane-wave pseudopotential calculations, we studied the six types of isolated intrinsic point defects in pure a-Al2O3, and then proposed a new perspective for the process of intrinsic point defects in a-Al2O3.11 As a matter of fact, experimentally, it is practically an unachievable task to prepare a perfect pure a-Al2O3 specimen, and trace impurity even at a magnitude of ppm will manipulate the defect chemistry, especially the defect concentration in a-Al2O3.8 The variation of charge state, existing form and atomic transport etc. of intrinsic point defects with impurities in a-Al2O3, however, have seldom been investigated by previous studies. These must, however, be clearly understood, since they are undoubtedly a vital fundamental scientific issue in the practical applications of a-Al2O3 based materials and devices. Natural corundum-structured a-Al2O3 can contain up to 1.81 wt% Cr2O3 beside Fe2O3 and other impurities.12 On the other hand, Cr can be observed experimentally in Al2O3 coatings as thermal or tritium permeation barriers because of the thermal Institute of Materials, China Academy of Engineering Physics, Mianyang, 621908, China. E-mail: [email protected]; Fax: +86 81636 25900; Tel: +86 81636 26483
This journal is © the Owner Societies 2016
diffusion of Cr from steel substrates during the coating preparation.13–15 It thus can be said that Cr is a commonly existing impurity element in Al2O3, which may exert some impact on the properties of Al2O3. Take corundum for example, it will turn from colorless or transparent to red after a certain amount of Cr is introduced. Doping with Cr was also shown to alter the structural, electronic and reactive properties of the a-Al2O3 (0001) surface.12 Therefore, it is anticipated that the defect chemistry of a-Al2O3 will be affected by Cr impurity, no matter whether it is naturally existing or unintentionally doped. For this reason, to focus mainly on the process of intrinsic point defects, the firstprinciples method is used to investigate the influence of Cr addition on the defect chemistry of a-Al2O3 in the present work. The results are anticipated to be meaningful not only to understand the interaction of external impurities with intrinsic defects in a-Al2O3, but also to parameterize multi-scale models of the defect kinetics for oxide ceramics under growth and working environments.
2. Computational method and model All the present first-principle calculations were performed with the DMol316 package in the Materials Studio of Accelrys Inc. For the exchange–correlation potential, the generalized gradient approximation (GGA) given by Perdew and Wang (PW91)17 was used. As for the core treatment, the frameworks of all electron18 and double numerical plus polarization (DNP)19 were employed. The Brillouin-zone was integrated by a 2 2 1 k-point mesh created by the Monkhorst–Pack20 scheme. A thermal orbital occupation of 0.008 Ha incorporated with a global cutoff of 4.3 Å were used for all calculations without considering the spin polarization. The convergence criteria of the energy, force, displacement and self-consistent field (SCF) used in the present
Phys. Chem. Chem. Phys.
View Article Online
Published on 09 February 2016. Downloaded by University of Pennsylvania Libraries on 21/02/2016 14:42:32.
Paper
work were the same as those in our previous work,11 giving an energy convergence within 2 meV per atom. In order to study the Cr effect on the process of intrinsic point defects in a-Al2O3, a 36-layer (2 2 2) a-Al2O3 supercell was firstly built in this work. After full geometry optimization, a Cr atom was introduced to create a Cr interstitial or substituent nearby the geometry center of the supercell. By comparing the total energies of Cr-containing a-Al2O3 supercells after geometry optimization, the preference for Cr occupation, i.e. substitution (CrAl, CrO), and interstitial (Cri) could be determined. Thereafter, the crystal lattice of the most stable optimized Cr-containing supercell was constrained, and all atoms except for those in both the upper and bottom ten layers were relaxed during defect calculations. Then, an isolated intrinsic point defect of vacancy (VAl, VO), interstitial (Ali, Oi) and antisite atom (AlO, OAl) was generated within different atomic distances (1 NN–8 NN, NN stands for the nearest neighbor) from the Cr atom by removing, introducing and substituting a corresponding atom in the a-Al2O3 supercell, respectively. After geometry optimization, the defective supercell with minimum total energy was selected to determine the most stable site for each defect species in Cr-doped a-Al2O3. Taking the interstitial Al atom as an example, as shown in Fig. 1(a), within different atomic distance from the CrAl substituent, an Al atom was placed in the center of an octahedral interstitial site in the supercell, and the relative total energies of these supercells are shown in Fig. 1(b). It can be seen that the most stable site for Ali locates in the 1 NN interstitial site from the CrAl atom. With the same method, the most stable sites for Oi can also be determined, i.e. in the 1 NN interstitial site from the CrAl substituent. The formation energies of isolated intrinsic point defects in Cr-containing a-Al2O3, obtained from the total energy differences between the supercells with and without defects, were firstly calculated to determine the Cr occupation, thermodynamical stable charge state of each defect, and the relative stability of all defect types within the Fermi level. Specifically, the formation
PCCP
energy was calculated by the following equation based on the standard formalism proposed by Zhang et al.:21 X f tot tot ECr;def ðXÞ ¼ ECr;def ECr þ Dni mi þ qEF (1) i
Etot Cr,def
Etot Cr
and are the total energies of the Cr-containing where supercell with and without defects, respectively. The changed atom number Dni of atom species i (Al or O) in the supercell, the atomic chemical potential mi of element i, the charge state q of defect X, and the Fermi level EF in eqn (1) have the same meanings as those described in our previous work,11 and were also treated in the same way in this work.
3. Results and discussion 3.1
Cr occupation in a-Al2O3
Fig. 2 shows the formation energies of Cr-related defects in various charge states in a-Al2O3 as a function of the Fermi level EF under the two extreme conditions of O-rich (oxidation limit) and O-deficient (reduction limit). In this Figure, only results of the most stable charge states of individual defects are exhibited. It is clearly shown that, compared with Cri and CrO, CrAl has the lowest formation energy over the entire Fermi level under O-rich conditions, that is, CrAl is the most stable species among the Cr-related defects in this situation, as shown in Fig. 2(a). On the other hand, as illustrated in Fig. 2(b), under O-deficient conditions, CrAl is more stable than Cri and CrO within a much wider range of Fermi level (EF 4 2.01 eV). Obviously, Cr prefers to occupy the lattice site of the Al atom to form a CrAl substituent under both the O-rich and O-deficient conditions, consistent with previous theoretical12,22 and experimental results.22 The Cr occupation in a-Al2O3 can be related to the isostructure of the two oxides of a-Al2O3 and Cr2O3, since the +3 charged Cr ion has an identical charge and a similar ionic radius to Al3+ (0.755 and 0.675 Å, respectively), resulting in similar crystal lattices of the two metal oxides (4.931 and 4.760 Å accordingly), which is also beneficial for Cr substitution in a-Al2O3.12
Fig. 1 (a) Side view of the Cr-containing (2 2 2) a-Al2O3 supercell (only the relaxed layers are shown). The grey ball depicts a Cr atom, and red and purple ones denote oxygen and aluminum atoms, respectively. The letters I1–I8 indicate possible interstitial sites of Al or O atoms within different atomic distances from the doped Cr atom; (b) relative total energies of the supercells containing a CrAl substituent and an Ali atom within different atomic distances from the CrAl atom.
Phys. Chem. Chem. Phys.
This journal is © the Owner Societies 2016
View Article Online
Published on 09 February 2016. Downloaded by University of Pennsylvania Libraries on 21/02/2016 14:42:32.
PCCP
Paper
Fig. 2 Formation energies of Cr-related defects in various charge states in a-Al2O3 as a function of the Fermi level EF under (a) O-rich and (b) O-deficient conditions.
For the CrAl substituent, the most stable charge state depends on the EF position, either under O-rich or O-deficient conditions, as shown in Fig. 2. When EF locates near the top of valence band, the stable charge state is CrAl3+, and then will change to CrAl2+ and CrAl1+ at higher EF level. The neutral state i.e. Cr0Al will remain at EF Z 2.4 eV. Obviously, over the entire EF range, the neutral state will dominate. By contrast, the formation energies of CrAl in each charge state under the conditions O-deficiency are much larger than those under O-rich conditions, up to about 2.5 eV, indicating that CrAl forms more easily under O-rich conditions. In any case, Cr0Al dominates the substituent, that is, the +3 charged Cr ion substitutes for Al3+ in a-Al2O3. Therefore, only the neutral charge state was considered as the CrAl substituent in the following calculations both under the O-rich and O-deficient conditions. 3.2
Cr effect on isolated intrinsic point defects in a-Al2O3
Fig. 3 plots the formation energy variation of six types of isolated intrinsic point defects in various charge states with the Fermi level EF in Cr-doped a-Al2O3 under O-rich and O-deficient conditions. In this Figure, only the most stable charge states for each defect within the whole Fermi level range are exhibited. It can be
seen that the charge states and their variation tendencies of each defect species in Cr-doped a-Al2O3 are dependent on the EF position, consistent with the most recent theoretical predictions in pure a-Al2O3.5,11,23 However, within the EF range, 2 and 3 charged states are not stable states for OAl in Cr-doped a-Al2O3 under both O-rich and O-deficient conditions, while they will be readily present in pure a-Al2O3.11 Moreover, after Cr doping, the relative stability of intrinsic point defects in a-Al2O3 under O-rich conditions is VAl 4 OAl 4 Oi 4 VO 4 Ali 4 AlO over a fairly wide EF range (Fig. 3(a)), similar to that in pure a-Al2O3.11 The main difference emerges for the more stable EF range of VAl and OAl. In pure a-Al2O3, VAl has a wider (41.6 eV) stable EF range than in Cr-doped a-Al2O3. On the other hand, the relative defect stability in a-Al2O3 will be significantly affected by Cr. As shown in Fig. 3(b), near the bottom of the conduction band, the relative stability in Cr-doped a-Al2O3 is OAl 4 VAl 4 Oi 4 VO 4 AlO 4 Ali, while in pure a-Al2O3 it is VAl 4 OAl 4 Oi 4 VO 4 Ali 4 AlO;11 and at the position of gap center, the relative stability in Cr-doped a-Al2O3 is VO 4 VAl 4 Ali 4 AlO 4 Oi 4 OAl, yet it will change to VAl 4 VO 4 Oi 4 Ali 4 OAl 4 AlO in pure a-Al2O3.11 Therefore, the doped Cr has exerted an influence on the defect chemistry in a-Al2O3.
Fig. 3 Formation energies of isolated intrinsic point defects in various charge states in Cr-doped a-Al2O3 as a function of the Fermi level EF under (a) O-rich and (b) O-deficient conditions.
This journal is © the Owner Societies 2016
Phys. Chem. Chem. Phys.
View Article Online
Published on 09 February 2016. Downloaded by University of Pennsylvania Libraries on 21/02/2016 14:42:32.
Paper
PCCP
Fig. 4 Comparison of formation energies of isolated intrinsic point defects in a-Al2O3 before and after Cr doping under (a) O-rich and (b) O-deficient conditions.
Interestingly, the formation energies of each defect species in a-Al2O3 will be significantly affected by Cr, as shown in Fig. 4. Under the O-rich conditions, over the entire Fermi level, the formation energies of VO, Ali, Oi, AlO and OAl in a-Al2O3 will be reduced by Cr to different extents (Fig. 4(a)), indicating that Cr is favorable for the formation of these defects; while for the defect of VAl, Cr is also beneficial at a small EF range (0–3.89 eV), but unfavorable for defect formation at a larger EF range (43.89 eV). On the other hand, a similar phenomenon will be present under O-deficient conditions, yet Cr will have a negative effect on the formation of VAl over a wider EF range (42.56 eV), as shown in Fig. 4(b). Therefore, depending on the O environment, Cr has great influence on the formation, charge state and relative stability of isolated intrinsic point defects in a-Al2O3. However, under convenient circumstances the constraint of electroneutrality must be satisfied in these materials. For Cr-doped a-Al2O3, the +3 charged Cr ion substitutes for Al3+, leading to no extra charge, neutralizing the charged isolated intrinsic point defects formed in the material. Consequently, the intrinsic point defects in Cr-doped a-Al2O3 cannot be isolated, but exist in charge-neutral combinations, resulting in the formation of Schottky defects, Frenkel defects or antisite pairs; that is, the so-called defect process in materials. Since Cr has great influence on the isolated intrinsic point defects in a-Al2O3, it is anticipated that Cr will definitely exert some effect on the defect process in this material. 3.3
Cr effect on Schottky defect in a-Al2O3
The Schottky defect in a-Al2O3 consists of several VAl and VO, under the constraints of charge neutrality and stoichiometry. Seen from Fig. 3, after Cr doping, the main stable defect form for VAl is VAl3, accompanied with a much smaller proportion of VAl2, VAl1 and V0Al; while for VO, the main defect form is V0O, with a small percentage of 2 and 1 charged states. Therefore, the Schottky defect in Cr-doped a-Al2O3 can be expressed as {mVOp+:nVAlq} (mp = nq, p = 0–2, q = 0–3). According to our previous work, vacancies to form Schottky defects in a-Al2O3 should be sufficiently separated and have no interactions.11 Consequently, following the method proposed by Çakır et al.,24
Phys. Chem. Chem. Phys.
the positively charged part of a Schottky defect will have an identical formation energy to the negatively charged one, i.e. EF(mVOp+) = EF(nVAlq), and thus the average formation energy of the Schottky defect could be determined from 2EF(mVOp+)/(m + n). In earlier studies,25,26 the Schottky defect in a-Al2O3 was directly considered as a quintet i.e. {2VAl3 + 3VO2+}, since Al2O3 is constituted of Al3+ and O2 ions. However, this case will be totally different. Fig. 5(a) plots the formation energies of mVO and nVAl at each charge state in Cr-doped a-Al2O3 as a function of the Fermi level under O-rich conditions. When the formation energy variation line of a negatively charged nVAl intersects with a positively charged mVO line, a possible Schottky defect will form. It thus can be seen that there are three types of possible Schottky defect formed in Cr-doped a-Al2O3 under O-rich conditions, i.e. {VO2+:2VAl1}, {VO2+:VAl2}, {3VO2+:2VAl3}, and the average formation energies are 1.62, 2.71 and 3.92 eV, respectively. Obviously, the most stable Schottky defect is {VO2+:2VAl1} for its smallest average formation energy, and such a small formation energy enables defect formation at room or higher temperatures. The situation is a little different from that in pure a-Al2O3.11 By contrast with pure a-Al2O3, one less type of possible Schottky defect i.e. {VO1+:VAl1} will form in Cr-doped a-Al2O3. As for the same types of Schottky defects, the formation energies will be decreased after Cr doping. Especially for the most stable Schottky defect {VO2+:2VAl1}, the formation energy decrease is up to about 1.6 eV. Therefore, Cr is favorable for the formation of Schottky defects in a-Al2O3 under O-rich conditions. Moreover, the formation energy differences of these three types of Schottky defects in Cr-doped a-Al2O3 are much larger (41.0 eV) than those in pure a-Al2O3 (o1.0 eV), indicating that {VO2+:2VAl1} will dominate among the Schottky defects in a-Al2O3, yet {VO2+:VAl2} and {3VO2+:2VAl3} will only share much smaller proportions after Cr doping, while not a single Schottky defect could be absolutely dominant in pure a-Al2O3.11 In a word, Cr has great influence on the Schottky defects in a-Al2O3 under O-rich conditions. Similarly, as shown in Fig. 6(b), under O-deficient conditions, there are six types of possible Schottky defects in Cr-doped a-Al2O3, i.e. {3VO1+:VAl3}, {2VO1+:VAl2}, {3VO2+:2VAl3}, {VO2+:VAl2},
This journal is © the Owner Societies 2016
View Article Online
Published on 09 February 2016. Downloaded by University of Pennsylvania Libraries on 21/02/2016 14:42:32.
PCCP
Paper
Fig. 5 (a) Formation energies of VAl and VO in various charge states, some of which are multiplied by a factor, and (b) possible Schottky defect configurations formed in Cr-doped a-Al2O3 under O-rich conditions.
Fig. 6 (a) Formation energies of VAl and VO in various charge states, some of which are multiplied by a factor, and (b) possible Schottky defect configurations formed in Cr-doped a-Al2O3 under O-deficient conditions.
{VO1+:VAl1} and {VO2+:2VAl1}, which is consistent with the case in pure a-Al2O3.11 The corresponding average formation energies are 2.59, 2.82, 3.92, 5.19, 3.99 and 4.05 eV. Obviously, the most stable Schottky defect is {3VO1+:VAl3}, for which such a small formation energy allows defect formation under convenient circumstances, also consistent with that in pure a-Al2O3.11 Moreover, the formation energies of Schottky defects except {VO2+:VAl2} will decrease to different extents after Cr doping, suggesting that Cr is generally beneficial for the formation of Schottky defects in a-Al2O3 under O-deficient conditions. Considering the small formation energy differences (o1.0 eV) between the first two types of defects, and much larger differences (41.0 eV) between these two and other four types of defects, it is clear that {3VO1+:VAl3} and {2VO1+:VAl2} will be dominant in Cr-doped a-Al2O3 under the conditions of O-deficiency; while in pure a-Al2O3, one more type of Schottky defect i.e. {3VO2+:2VAl3} will also be dominant.11 Therefore, the Schottky defects in a-Al2O3 under O-deficient conditions will be readily affected by Cr. By contrast, there are three more types of Schottky defects formed in Cr-doped a-Al2O3 under O-deficient conditions than that under O-rich conditions. For the same three defect types
This journal is © the Owner Societies 2016
({VO2+:2VAl1}, {VO2+:VAl2} and {3VO2+:2VAl3}), the formation energy of the first one under O-deficient conditions is B2.4 eV higher than that under O-rich conditions, about 0.6 eV smaller than that in pure a-Al2O3.11 As for the second one, ({VO2+:VAl2}), the formation energy difference under both conditions is twice as large as that in pure a-Al2O3.11 The last one, ({3VO2+:2VAl3}), shares an identical formation energy under both conditions, yet is about 0.3 eV smaller than that in pure a-Al2O3.11 Obviously, Cr has significant influence on Schottky defects in a-Al2O3, and the influence extent depends on the O environment. 3.4
Cr effect on Frenkel defects in a-Al2O3
The Frenkel defect in a-Al2O3 incorporates an interstitial atom and a corresponding identically charged vacancy. As shown in Fig. 3, after Cr doping, four types (3, 2, 1 and 0) of charge states exist for VAl, and three types (0, +1, +2) for VO. Therefore, the cation Frenkel defect can be expressed as {Aliq+:VAlq} (q = 0–3), while the anion one can be described as {Oip:VOp+} ( p = 0–2). When a Frenkel defect forms, the defect constituent of the interstitial and vacancy will have an equal formation energy, which could also be determined as the average formation energy of the Frenkel defect.
Phys. Chem. Chem. Phys.
View Article Online
Published on 09 February 2016. Downloaded by University of Pennsylvania Libraries on 21/02/2016 14:42:32.
Paper
PCCP
Fig. 7 Possible cation (a and b) and anion (c and d) Frenkel defects formed in Cr-doped a-Al2O3 under O-rich (a and c) and O-deficient (b and d) conditions.
Generally, the two types of Frenkel defects in a-Al2O3 are considered to be {Ali3+:VAl3} and {Oi2:VO2+},23,25,26 inconsistent with our previous work.11 Following the statements in Section 3.2, the case must have some difference in Cr-doped a-Al2O3. Fig. 7 plots the formation energies of interstitials and vacancies in each charge state in Cr-doped a-Al2O3 as a function of the Fermi level under O-rich and O-deficient conditions. When the formation energy variation line of a negatively charged interstitial (vacancy) intersects with a positively charged vacancy (interstitial) line, a possible Frenkel defect will form. It thus can be seen that there are two types of possible cation Frenkel defects formed in Cr-doped a-Al2O3 under O-rich conditions (Fig. 7(a)), i.e. {Ali2+:VAl2} and {Ali3+:VAl3}, and the average formation energies are 4.47 and 4.78 eV, respectively, for which the defect formation can be realized at temperatures a little higher than convenient circumstances. Considering the small formation energy difference (0.31 eV), the main Frenkel defect {Ali2+:VAl2} will not dominate, and {Ali3+:VAl3} will also share a big proportion in Cr-doped a-Al2O3. However, only one type of Frenkel defect i.e. {Ali3+:VAl3} with a little higher formation energy forms in pure a-Al2O3 under O-rich conditions,11 indicating that Cr is beneficial for the formation of Frenkel defects in a-Al2O3. On the other hand, three types of possible cation Frenkel defects will form in Cr-doped a-Al2O3 under O-deficient conditions (Fig. 7(b)), i.e. {Ali1+:VAl1}, {Ali2+:VAl2} and {Ali3+:VAl3}, which is consistent with that in pure a-Al2O3.11 Nevertheless, the corresponding
Phys. Chem. Chem. Phys.
formation energies (5.93, 4.47 and 4.78 eV, respectively) are smaller than that in pure a-Al2O3,11 which could be attributed to the doped Cr. Moreover, the defect {Ali1+:VAl1} has a much higher formation energy (41.0 eV) than {Ali2+:VAl2} and {Ali3+:VAl3}, suggesting that the latter will dominate in Cr-doped a-Al2O3, while only {Ali3+:VAl3} will dominate in pure a-Al2O3.11 Obviously, the cation Frenkel defect in a-Al2O3 will be greatly affected by Cr under both O-rich and O-deficient conditions. As for the anion Frenkel defect, there are two possible defect types i.e. {Oi1+:VO1} and {Oi2+:VO2} formed in Cr-doped a-Al2O3 under both O-rich and O-deficient conditions, and the corresponding average formation energies are 5.24 and 5.57 eV in each condition, suggesting that the anion Frenkel defects in Cr-doped a-Al2O3 are independent of the oxygen environment, consistent with the case in pure a-Al2O3.11 Moreover, such formation energies can enable defect formation at temperatures a little higher than a convenient environment. Obviously, the most stable anion Frenkel defect is {Oi1+:VO1} for its lower formation energy; yet a big proportion of {Oi2+:VO2} will also be present in Cr-doped a-Al2O3 because of the rather small formation energy difference (0.33 eV) of the two types of Frenkel defects, which is similar to the case for pure a-Al2O3.11 By contrast, however, the formation energies of {Oi1+:VO1} and {Oi2+:VO2} in a-Al2O3 will be, respectively, reduced by 0.61 and 0.84 eV after Cr-doping, indicating that Cr is favorable for the formation of anion Frenkel defects in a-Al2O3. Therefore, the doped Cr will have some impact on the anion Frenkel defects in a-Al2O3.
This journal is © the Owner Societies 2016
View Article Online
Published on 09 February 2016. Downloaded by University of Pennsylvania Libraries on 21/02/2016 14:42:32.
PCCP
Paper
Fig. 8 (a) Formation energies of antisite atoms in various charge states, and (b) possible antisite defect combinations formed in Cr-doped a-Al2O3 under the O-rich conditions.
3.5
Cr effect on antisite pairs in a-Al2O3
The antisite pair in a-Al2O3 combines two antisite atoms i.e. OAl and AlO, which can be expressed as {AlOq+:OAlq} (q = 0–5). When an antisite pair forms, the two antisite atoms will have identical formation energies. Fig. 8 plots the formation energies of OAl and AlO in all charge states in Cr-doped a-Al2O3 as a function of the Fermi level under O-rich conditions. When the formation energy variation line of a negatively charged OAl defect intersects with a positively charged AlO line, a possible antisite pair will form. It thus can be seen that there are three types of possible antisite pairs formed in Cr-doped a-Al2O3 under O-rich conditions (Fig. 8(b)), i.e. {AlO3+:OAl3}, {AlO4+:OAl4} and {AlO5+:OAl5}, and the average formation energies are 9.53, 9.35 and 11.82 eV, respectively. Obviously, the most stable antisite pair is {AlO4+:OAl4} for its lowest formation energy. This situation is different from what in pure a-Al2O3, in which the most stable antisite pair is {AlO3+:OAl3}.11 By contrast, the formation energies of each antisite pair in Cr-doped a-Al2O3 are a little lower than those in pure a-Al2O3,11 indicating that Cr is somewhat favorable for the formation of antisite pairs in a-Al2O3, although such large formation energies mean that they are still very unlikely to form in Cr-doped a-Al2O3 at conventional conditions as in pure a-Al2O3.
Therefore, Cr has some influence on the antisite pairs in a-Al2O3 under O-rich conditions. On the other hand, there are five possible antisite pairs formed in Cr-doped a-Al2O3 under O-deficient conditions i.e. {AlO1+:OAl1}, {AlO2+:OAl2}, {AlO3+:OAl3}, {AlO4+:OAl4} and {AlO5+:OAl5} (Fig. 9), and the formation energies are 8.81, 8.57, 9.53, 9.35 and 11.81 eV, respectively. Thus the most stable antisite pair is {AlO2+:OAl2}, also different from the case in pure a-Al2O3.11 Moreover, the formation energies of each antisite pair in Cr-doped a-Al2O3 are correspondingly smaller than that in pure a-Al2O3, indicating that Cr is favorable for the formation of antisite pairs in a-Al2O3. Obviously, Cr will exert some influence on the antisite pairs in a-Al2O3 under O-deficient conditions.
4. Conclusions The effect of Cr on the process of intrinsic point defects in a-Al2O3 has been studied based on first-principle calculations. The results obtained can be summarized as follows: (1) Cr prefers to occupy the lattice site of the Al atom to form a CrAl substituent in a-Al2O3.
Fig. 9 (a) Formation energies of antisite atoms in various charge states, and (b) possible antisite defect combinations formed in Cr-doped a-Al2O3 under O-deficient conditions.
This journal is © the Owner Societies 2016
Phys. Chem. Chem. Phys.
View Article Online
Published on 09 February 2016. Downloaded by University of Pennsylvania Libraries on 21/02/2016 14:42:32.
Paper
(2) Depending on the O-conditions, Cr has great influence on the formation, charge state and relative stability of isolated intrinsic point defects in a-Al2O3, and thus will exert some effect on the defect process in this material. (3) The possible Schottky defect types and their relative proportions under both O-rich and O-deficient conditions will be changed by Cr, and Cr is favorable for the formation of Schottky defects in a-Al2O3. (4) The main cation Frenkel defect in a-Al2O3 will be changed from {Ali3+:VAl3} to {Ali2+:VAl2} after Cr doping, yet the anion Frenkel defect will remains as {Oi1+:VO1}, and both the formation energies will be reduced. (5) Cr has a positive effect on the formation of antisite pairs, though this will alter the main possible defect types in a-Al2O3. (6) Based on the above results, Cr has a significant influence on the process of intrinsic point defects in a-Al2O3, and the extent of the influence depends on the O-conditions. Generally speaking, Cr is favorable for the formation of Schottky defects, Frenkel defects and antisite pairs in a-Al2O3.
Acknowledgements This work is supported by the National Magnetic Confinement Fusion Science Program (No. 2013GB110006B) and the National Natural Science Foundation of China (No. 21471137 and 11275175).
Notes and references 1 R. H. Doremus, Alumina, in Ceramic and Glass Materials: Structure, Properties and Processing, ed. J. F. Shackelford and R. H. Doremus, Springer, 2008, pp. 1–26. 2 H. Heuer, D. B. Hovis, J. L. Smialek and B. Gleeson, J. Am. Ceram. Soc., 2011, 94, s146. 3 K. Shirvani, S. Mastali, A. Rashidghamat and H. Abdollahpour, Corros. Sci., 2013, 75, 142. 4 J. K. Bristow, D. Tiana, S. C. Parker and A. Walsh, J. Mater. Chem. A, 2014, 2, 6198. 5 G. K. Zhang, Y. J. Lu and X. L. Wang, Phys. Chem. Chem. Phys., 2014, 16, 17523.
Phys. Chem. Chem. Phys.
PCCP
6 J. Cai, Y. Li, J. M. Wu and G. P. Ling, Oxid. Met., 2014, 81, 253. ¨ger, Solid State Ionics, 1984, 12, 189. 7 F. A. Kro ¨f and R. W. Grimes, Acta Mater., 1998, 8 K. P. D. Lagerlo 46, 5689. 9 K. P. Muthe, K. Sudarshan, P. K. Pujari, M. S. Kulkarni, N. S. Rawat, B. C. Bhatt and S. K. Gupta, J. Phys. D: Appl. Phys., 2009, 42, 105405. 10 S. Ikeda and T. Uchino, J. Phys. Chem. C, 2014, 118, 4346. 11 X. Xiang, G. K. Zhang, X. L. Wang, T. Tang and Y. Shi, Phys. Chem. Chem. Phys., 2015, 17, 29134. 12 J. Baltrusaitis, C. Hatch and R. Orlando, J. Phys. Chem. C, 2012, 116, 18847. 13 L. Xing, Y. Zheng, L. Cui, M. Sun, M. Shao and G. Lu, High Temp. Mater. Processes, 2011, 30, 99. 14 H. G. Yang, Q. Zhan and W. W. Zhao, J. Nucl. Mater., 2011, 417, 1237. 15 Q. Zhan, H. G. Yang, W. W. Zhao, X. M. Yuan and Y. Hu, J. Nucl. Mater., 2013, 442, S603. 16 B. Delley, J. Chem. Phys., 2000, 113, 7756–7764. 17 J. A. White and D. Mbird, Phys. Rev. B: Condens. Matter, 1994, 50, 4954–4957. 18 B. Delley, J. Chem. Phys., 1990, 92, 508–517. 19 J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865–3868. 20 H. J. Monkhorst and J. D. Pack, Phys. Rev. B: Solid State, 1976, 13, 5188. 21 S. B. Zhang and J. E. Northrup, Phys. Rev. Lett., 1991, 67, 2339. 22 E. Gaudry, D. Cabaret, P. Sainctavit, C. Brouder, F. Mauri, J. Goulon and A. Rogalev, J. Phys.: Condens. Matter, 2005, 17, 5467. 23 N. D. M. Hine, K. Frensch, W. M. C. Foulkes and M. W. Finnis, Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 79, 024112. 24 D. Çakır, G. A. de Wijs and G. Brocks, J. Phys. Chem. C, 2011, 115, 24429. 25 N. D. M. Hine, K. Frensch, M. W. Finnis, W. M. C. Foulkes and A. H. Heuer, Int. Conf. on QMC, April 6, 2009, Apuan. 26 K. Matsunaga, T. Tanaka, T. Yamamoto and Y. Ikuhara, Phys. Rev. B: Condens. Matter, 2003, 68, 085110.
This journal is © the Owner Societies 2016
