阳离子和阴离子掺杂立方氧化锆近临氧离子相互作用的理论模拟_图

1、Theoretical Simulation of the Interaction betweenNeighboring Oxygen Ions for Cation and Anion dopedc-ZrO2Chen Shougang, Wang Daoping, Yin YanshengInstitute of Materials Science and Engineering, Ocean University of China, Qingdao, ShandongProvince 266003, ChinaE-mail:sgchenAbstractTheoretical calcula

2、tions on the interaction between neighboring oxygen ions for selected clusters were performed by density functional method (DFT/B3LYP in order to investigate the stable effect of single and mixed doped c-ZrO2. Mulliken charge population analyses of oxygen ions for undoped, cation-doped, anion-doped

3、and co-doped c-ZrO2 were calculated.Theoretical results, which in good agreement with the experimental data, indicated that the stable ability of doped c-ZrO2 could be described by the Coulomb repulsive force between neighboring oxygen ions (f c. Moreover, the effect of the third phase cation and/or

4、 anion doped zirconia complex materials was expounded by this method, especially on the conductivity decrease of 8YSZ system with increasing SiC content.Keywords: Zirconia, Computer Simulation, Dopant, DFT, Mulliken Charge1IntroductionZirconia, stabilized in the cubic fluorite or tetragonal structur

5、e by the addition of appropriate dopants, is of considerable importance in modern materials technology. The high ion-exchange capacity and redox activities make it useful in many catalytic processes as the catalyst, the supporter and the promoter. In addition, the superior chemical stability, mechan

6、ical strength and ion-exchange capacity are favorable in ceramic toughening, thermal-barrier coating, oxygen sensors and electrolyte in fuel cells16. Pure zirconia has a cubic fluorite structure (c-ZrO2 at high temperatures, > 2650 K. Below this temperature, c-ZrO2 is transformed into a distorted

7、 fluorite structure of tetragonal symmetry (t-ZrO2 and further transformed into monoclinic symmetry (m-ZrO2 at about 1400 K.On the assumption of a hard-sphere approximation, the instability of c-ZrO2 originates from the close-packed oxygen ions in the fluoride structure, because the ionic radii rati

8、o, R Zr4+/R O2- 0.564, 6is small for eightfold coordination, such as the fluoride structure in the MO2-type oxide. Because of the refractory with resistance to thermal shock and phase transformation, many methods have been attempted to stabilize the c-zirconia at low temperature 6-12.As the metastab

9、le tetragonal and cubic ZrO2 have improved mechanical and electrical properties, the effort has been concentrated on stabilizing cubic zirconia with different cation- 1 -substitution, such as MgO, Y2O3, CeO2.7-9 and/or a nanometric grain size is maintained10-12. Generally, three conditions are consi

10、dered to be necessary for stabilization of c-ZrO2. The first one is the addition of a cation, which has a larger ionic radius than that of Zr4+. Doping with such a cation increases the lattice constant of the c-ZrO2 and leads to an obvious increase of the ionic radii ratio 9. Secondly, a more notabl

11、e cubic-stabilizing effect occurs from doping with lower valence cations than that of Zr4+ ions 6-8, 13-15. The doping of zirconia by lower valence cations leads to (i an increase of the number of oxygen ion vacancies, which consequently favors an enhancement of the ionic conductivity, since they ar

12、e mobile, (ii structural changes from monoclinic, tetragonal to cubic phases, and (iii local strains due to short-range interaction between Zr4+ and its dopant, which are expected to be a function of the dopant ionic radius size.16,17 These dopants introduce oxygen vacancies into the lattice and red

13、uce the Zr coordination in the cubic phase with concomitant diminution of the average Zr-O distance in both the tetragonal and cubic phases.Previous theoretical calculation 17-22 and X-ray-absorption fine structure (XAFS measurements23-25 also confirm and support that oxygen vacancies occupy the nea

14、rest neighboring (NN sites with respect to the smaller doped cations whereas oxygen vacancies locate in the next nearest neighboring (NNN sites with respect to larger doped cations.9,13Besides the stabilization by cation substitution, attempts have been made to stabilize cubic zirconia by replacing

15、oxygen through nitrogen or carbon in the anion sublattice 26-30. Lerch 26.27,Cheng 28 and Sharma 29 reported that the stabilization of c-ZrO2 by N3- replace O2-is also attributable to the introduction of vacancies, which are ordered arrangement along the cubic threefold axes in the anion sublattice,

16、 like the adulteration of low valence cations. On the other hand, wang 30,31 reported that carbon element, which mainly locates the octahedral interstitials site by the analysis of density calculation, also has the ability to stabilize c- ZrO2. Meanwhile, Laidani 32 further studied the structure and

17、 stabilization mechanism of carbon element and concluded that the carbon did not substitute the oxygen in the zirconia lattice based on the X-ray photoelectron spectroscopy (XPS analysis, and they predicted that the stabilization effect of c-ZrO2 structure may come from the change of the bulk compre

18、ssive stress.From above analysis, we can classify the stabilization effects of c-ZrO2 into three types by now: the lattice-constant effect, the oxygen-vacancy effect and internal stress change effect. However, some phenomena are not clear and not well explained from the intrinsic nature of- 2 -O R 3

19、+Zr vacancy (a c-(Zr 13O 836+Zr OO Zr R4+(b c-(Zr 11R 2O 738+N vacancy O Zr N (c (d OZr Cf c (zz or f c f c (dd or f c f c (dz or f c Fig. 1 Cluster models and types of O O bonds used in this calculation for c-ZrO 2 solid solutions. (a pure c-ZrO 2, (b c-ZrO 2 with trivalent cation dopant,(c c-ZrO 2

20、 with tetravalent cation dopant,(d c-ZrO 2 with N dopant, (e c-ZrO 2 with c (e c-(Zr 13CO 836+- 3 -c-ZrO 2. Such as although the lattice-parameter changes are larger in the ZrO 2-CeO 2 system than in the ZrO 2-Y 2O 3 system, the stabilization effect of Y 2O 3 doping is bigger than that of CeO 2 dopi

21、ng 9,33; the ZrO 2-Sc 2O 3 and the ZrO 2-C system 30,34, the cubic phase zirconia is stabilized despite the slightly decrease of the lattice parameters. Thus, a comprehensive interpretation on the origins of these phenomena by theoretical or experimental method is needed, especially on the effect of

22、 the anion-doped zirconia. Moreover, to our best knowledge, the interactive effect between neighboring oxygen ions for cation and anion doped c-ZrO 2 has received little attention , so we try to describe the neighboring oxygen interaction by Mulliken charge population aiming to attempt a new idea to

23、 evaluate the stability effect of doped c-ZrO 2.2. Calculation method and Cluster Model2.1 Calculation methodFor zirconia crystal, it can be treated as fully ionic. The effective potentials describing the interatomic forces are expressed by ionic, pair-wise potentials as the following form 35,36:62/

24、exp(4(r C r A r e Z Z r += (1Eq.1 includes a long-range Coulombic interaction and a short-range potential to simulate the repulsions force and van der Waals attraction force between electron charge clouds. The potentials parameters employed in the Eq.1 comes from previous report 36, the O-O short-ra

25、nge interactive energy is very low at r o-o =2.54 Å or so, which is the balanceable distance of c-ZrO 2. Because of the large difference of ionic radii between zirconium and oxygen ions, the neighboring oxygen ions may contact each other in c-ZrO 2. Oxygen ions in t-ZrO 2 would be displaced to

26、decrease the interaction by this contact, the interaction between oxygen ions can be regarded as one of origins of the instability in c-ZrO 2. So the interaction between neighboring oxygen ions can be thought as the prominent effect on the phase stability for c-ZrO 2.Neglecting the short-range poten

27、tial interaction, the interaction between the nearest oxygen ions may be looked as their electron charge clouds repulsive force and Coulomb force (f c , which is simplified from Eq.1 and given by Eq.2:Here, Z and Z are the Mulliken population electron number of the oxygen ions, r represents the dist

28、ance between the nearest oxygen ions, is the dielectric constant in vacuum, e is the electron charge of doped element. N represents the unit for Coulomb force (f c . The Mulliken population electron number was attained by the density functional theory 4(2N r e Z Z r f c =(2- 4 -(DFT in Gaussian 98 c

29、ode 37, specifically the B3LYP 38,39 gradient-corrected method. All kinds of doped zirconia cluster model (Fig.1 were calculated so as to attain the effective oxygen ion charge (Z i. Thereinto, Zr, Y, Sc and Ti atoms are described using Los Alamos LANL2 effective core potentials (ECP and a valence d

30、ouble- basis set 40. Gd, Sm, Gd, Nd and Ce atoms are described using Cep-121G effective core potentials (ECP, which is a triple-split type basis set 41.The O, N and C atoms are described using 6-31G (d basis set 42. The selected calculation method and basis set are appropriate based on previous theo

31、retical simulation 43-46.Table 1 Ion radii and net charge (O(z in each clusterCluster Name Dopant radii (Å6M (mol%O (zc-(Zr13O836+CZr 0.79 0 -1.126c-(Sc2Zr11O738+CZrSc0.81 7.7-1.072 c-(Y2Zr11O738+CZrY 0.92 7.7 -1.010c-(Gd2Zr11O738+CZrGd0.97 7.7-1.067c-(Sm2Zr11O738 +CZrSm 1.00 7.7-1.093c-(Nd2Zr1

32、1O738+CZrNd 1.04 7.7-1.069 c-(Ti2Zr11O836+CZrTi 0.68 15.38 -1.130c-(Ce2Zr11O836+CZrCe0.90 15.38-1.121 c-(Zr13N2O536+CZrN 0.75a15.38-1.080c-(Zr13O8C36+CZrC 0.77a7.7 -1.107a Data come from literature 472.2 Cluster ModelAll kinds of cluster models are shown in Fig.1, where (a is used to describe the pu

33、re c-ZrO2 cluster and (b is used to describe the doped c-ZrO2 clusters with trivalent cations (R3+ = Gd, Sm, Gd, Nd, Sc. An oxygen vacancy, which was introduced to maintain local electrical neutrality, was located at a mutual next-nearest-neighbor site from the dopant cations 9,17-25.(c is used to d

34、escribe the doped c-ZrO2 clusters with tetravalent cations (R4+ = Ti4+ ,Ce4+. Two tetravalent cations were located at nearest neighbor zirconium sites from the center.(d is used to describe doped c-ZrO2 cluster with N3- anion. Two nitrogen atoms substitute two oxygen atoms along the bulk diagonal of

35、 cubic zirconia. An oxygen vacancy was located at nearest-neighbor site from the nitrogen 26-29. (e is used to describe doped c-ZrO2 cluster with C element. The carbon atom was located at the octahedral interstitials in cubic zirconia lattice 30-32.3. Results and DiscussionThe doped content is 15.38

36、 mol% for RO2 and 7.70 mol% for R2O3 in c-ZrO2 cluster according to the atom ratio. Doped ion radii and net charge of oxygen ions (O(z are all shown in- 5 -table 1. All kinds of O-O bond states are also shown in Fig.1. Calculated Coulomb force (f c of all kinds of O-O bonds in doped c-ZrO2 solid sol

37、utions by Eq.2 are shown in Fig.2.Table 2 Ion charge for doped zirconia clusterSystemsIon chargeZr Sc Y C O NN ZrO2-Sc2O3 3.710 2.910 -1.035, 1.019 ZrO2-Sc2O3-Y2O3 3.719 2.882 2.831 -1.023, 0.992 ZrO2-Y2O3 3.712 2.819 -1.037, 0.983ZrO2-Y2O3-C 3.716 2.796 0.549 -1.041,-0.9873.1.Cubic-Zirconia Solid S

38、olutionsIn cation-doped c-ZrO2 solid solutions, two types of oxygen ions exist: oxygen ions bound only with zirconium ions are showed by O(z and oxygen ions are noted with O(d, which are not only bound with doped cations but also with zirconium ions. Therefore, three bonding states in c-ZrO2 represe

39、nt the interactions between O(d O(d, O(z O(z, and O(d O(z, designated as f c(dd, f c(zz, and f c(dz, respectively. However, comparing with cation-doped c-ZrO2, there are different situations for anion-implantation c-ZrO2 solid solutions. For N anion-implantation c-ZrO2, there are only one type of ox

40、ygen ions O(f, which bound with nitrogen atom and oxygen atom. So this cluster has only one bonding state, namely O(f O(f, designated by f c(ff. For carbon-implantation c-ZrO2, we only consider the nearest neighboring and next nearest neighboring oxygen atoms from the implantation of C atom. The nea

41、rest neighboring oxygen atom with carbon atom is showed by O(f, the next nearest neighboring oxygen atom by O(s. Therefore, three bonding states in c-ZrO2 represent the interactions between O (f O (f, O (s O (s, and O (f O (s, designated as f c(ff, f c(ss, and f c(fs, respectively.3.2. Cation dopant

42、The trivalent cation-doped content in the present clusters is 7.70 mol% for R2O3, which is almost equal to that of the c-t phase boundary of the ZrO2-Y2O3 system at room temperature 48. Moreover, experimental and theoretical results have indicated that 8mol % Y2O3 is the minimum content for stabiliz

43、ation of the fluorite phase in the ZrO2-Y2O3 system 9, 20, 49, 50. So we assume that the CZrY cluster should have the lowest O-O repulsive energies and the best stabilization effect based on the present cluster model. This is consistent with our calculated results related to the lowest f c value, as

44、 shown in Fig.2.Because of the similar ionic radius between Sc3+ and Zr4+, the doped effect of Sc3+ ion is- 6 - 5.65.86.06.26.46.66.87.0f c (z z / 109 N ion radii/angstrom 4.04.24.44.64.85.05.25.45.65.86.06.26.46.66.87.0 7.2ion radii/angstrom f c (d d / 109 N 4.85.05.25.45.65.86.06.26.46.66.87.07.2i

45、on radii/angstrom f c (d z / 109 N Fig. 2. Relationship between fc and ion radii used for each cluster of the c-ZrO2solid solutions. Dashed line shows the fc of the pure c-ZrO2.- 7 -relatively complex and the most interesting 17,19,20,49-51. The stability of CZrSc system depends on the balance value

46、 between O-O repulsive force and oxygen ion diffusion barrier. From our calculated results, i t is noted that the dopant of Sc3+ ion produce large O-O repulsive force in CZrSc system, which suggests that this dopant couldnt be used as a good stabilizer. But this material can be used as a good electr

47、olytic material. Since the ionic radius of Sc3+ is much smaller than that of Y3+,Gd3+,Sm3+,Nd3+, the strain from the short-range interaction of charge clouds overlap is also smaller when the oxygen ion diffusion among the nearest neighboring sites of the Sc3+. This fact accords to the experimental r

48、esults in which only 6mol % 8mol % Sc2O3 is needed to stabilize the fluorite phase for good electrolytic materials at room temperature6,51. However, small ionic radii for Sc3+ and low diffusion barrier for oxygen ion make the CZrSc system easily deform with the change of temperature 50. At present,

49、an effective way 18,48 to stabilize the solid solution is to add Y2O3, Yb2O3, or Lu2O3 to the ZrO2-Sc2O3 solid solution in order to increase the diffusion barrier of oxygen ion.The addition of R3+ (R=Gd,Sm,Nd ions have effectively decreased the repulsive forces between neighboring oxygen ions, and t

50、he f c(zz is almost the same as that in CZrGd, CZrSm and CZrNd systems. In this sense, it can be said that R2O3 is more effective for the stabilization of c-ZrO2 However, the f c(zz is lower than that of CZrY system. Because of large ion radii for Gd,Sm,Nd, it is not necessary to stable the c-ZrO2 w

51、ith the 7.70 mol% content of R3+ (R=Gd,Sm,Nd. Higher doping content causes the formation of compounds and dopant-vacancy clustering between bulk vacancy and doped cations and affects the stability. For example, the doping of Gd3+ ion in c-ZrO2 tends to form a pyrochlore-type ordered structure, and i

52、t has been widely applied in solid oxide fuel cells 52-56. Moreover, the f c(dz and f c(dd also have different decrease with the addition of R3+ (R= Gd, Sm and Nd. The Gd3+, whose ionic radii is close to that of Y3+, has fairly favorable stabilization effect comparing to the Sm and Nd from the analy

53、sis of f c(zz, f c(dz and f c(dd. This fact accords well with the previous theoretical results, in which Gd-stabilized ZrO2 was one of the good solid electrolytes for applications requiring high oxygen ion conductivity and high stability 35.To our knowledge there are few reports of ZrO2-Gd2O3 being

54、utilized for electrolyte applications, although Gd3+ is widely used as a dopant in the CeO2-based oxygen ion conductor 57,58.For CZrTi system, f c(zz is slightly larger and f c(dz , f c(dd are slightly lower than that of pure c-ZrO2. Calculated results suggest that the TiO2 is a poor stabilizer for

55、c-ZrO2, and this idea accords well with the similar experimental results on the stabilization with a tetravalent ion like Sn4+ (0.71 is not effective 59. This observation can also be explained in coordinated terms: R Ti4+/R O2- 0.486 is very small for Ti eight coordination than that of Zr. So it is

56、difficult for TiO2 to form CZrTi solid solution. This accords well with the view that Zr4+ is the smallest possible ion- 8 -to maintain the fluorite structure 25,60,61.For CZrCe system, the f c(zz is slightly smaller than that of pure c-ZrO2 , however, the values of f c(dz and f c(dd are obviously l

57、ower than those of pure c-ZrO2 and almost close to the CZrNd system. We concluded that a large tetravalence ion, without introduce oxygen vacancy in c-ZrO2, will distort the surrounding lattice away from the perfect symmetry to a much greater extent than a small ion. Thus, oxygen, connecting with th

58、e oversized doping ions, not only produces the large relaxation, but also decreases the local O-O repulsive force. Although the lattice constant of CZrCe is larger than those of CZrY, CZrSc and CZrGd, the decrease of f c is smaller than those of CZrY, CZrSc and CZrGd, as shown in Fig. 2. These differences cannot be simply ascribed to the difference in the doped ionic radius because of the difference of doped mechanism. Theoretical results also confirm that the ionicity of the oxygen ions is an important element in deciding the