Tantalum and niobium diffusion in single crystalline lithium niobate

Solid State Ionics 259 (2014) 14–20

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Tantalum and niobium diffusion in single crystalline lithium niobate P. Fielitz a,⁎, G. Borchardt a, S. Ganschow b, R. Bertram b, R.A. Jackson c, H. Fritze d, K.-D. Becker e a

Technische Universität Clausthal, Institut für Metallurgie, Robert-Koch-Str. 42, D-38678 Clausthal-Zellerfeld, Germany Leibniz-Institut für Kristallzüchtung, Max-Born-Str. 2, D-12489 Berlin, Germany c Keele University, School of Physical and Geographical Sciences, Lennard-Jones Laboratories, Keele, Staffordshire ST5 5BG, United Kingdom d Technische Universität Clausthal, Institut für Energieforschung und Physikalische Technologien, Am Stollen 19, D-38640 Goslar, Germany e Technische Universität Braunschweig, Institut für Physikalische und Theoretische Chemie, Hans-Sommer-Str. 10, D-38106 Braunschweig, Germany b

a r t i c l e

i n f o

Article history: Received 2 December 2013 Received in revised form 5 February 2014 Accepted 6 February 2014 Available online 4 March 2014 Keywords: Lithium niobate Niobium diffusion Tantalum diffusion SIMS

a b s t r a c t LiNbO3 and LiTaO3 are isomorphous and Nb and Ta have the same valence electron configuration and the same ionic radii. This suggests the use of Ta as a tracer to probe the self-diffusion of Nb in LiNbO3. The diffusion system consisted of a 20 nm layer of LiTaO3 sputter deposited on top of (i) a congruent LiNbO3 single crystal, i.e. (48.3 ± 0.1) mol% Li2O, and on top of (ii) a VTE processed LiNbO3 single crystal with nearly stoichiometric composition, i.e. (49.9 ± 0.1) mol% Li2O. The diffusion anneals (1000 °C ≤ T ≤ 1100 °C) were performed under a constant oxygen partial pressure of 200 mbar. From the resulting SIMS depth profiles of tantalum a constant diffusivity was extracted which can be assumed to reflect the niobium self-diffusivity in LiNbO3. For sub-stoichiometric LiNbO3 the joint discussion of this work and of literature data on the basis of the generally ] = [VLi′], suggests Nb transport in the Li sublattice. For hyper-stoichiometric LiNbO3 accepted defect model, 4[Nb4• h ′ i Li  the defect model 5 V 5Nb ¼ Li•i is derived from the Li3NbO4/LiNbO3 solution reaction of the VTE process designed to obtain Li2O-rich LiNbO3 in accordance with the Li2O–Nb2O5 phase diagram. This model is supported by theoretical calculations of the defect formation energy. Interestingly, the migration enthalpy for the Li vacancy mediated transport of the anti-site defect Nb4• Li in the Li sublattice of congruent, i.e. sub-stoichiometric, LiNbO3 is similar (within a ±10% error) to the one derived for the Nb vacancy mediated transport of Nb in the Nb sublattice of hyper-stoichiometric LiNbO3, i.e. about 3 eV. The significant discrepancies between our results and some earlier literature data can be consistently rationalised if the experimental procedures of those studies are carefully analysed. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Lithium niobate, LiNbO3, has attracted substantial scientific and industrial interest in the last decades because of its excellent electrooptical, piezoelectric and acoustic properties [1]. The production of LiNbO3 and LiTaO3 based components as well as the increasing application of lithium niobate at high temperatures require an understanding of the atomic transport of the constituents [2]. Lithium is generally accepted to be the most mobile species [3–8]. For oxygen diffusion in lithium-deficient single crystalline LiNbO3 there are two controversial data sets available [9,10]. The 18O tracer diffusivity data in reference [9] seem, however, to be debatable because the solid–gas exchange method with mass spectrometric monitoring of the 18O2 concentration of the gas phase is much less reliable than a state-of-the-art SIMS profiling method [10]. More recently, 18O tracer diffusivity measurements were done using VTE processed single crystalline LiNbO3 [11] and were discussed together with the data of lithium-deficient single ⁎ Corresponding author. Tel.: +49 5323 72 2634. E-mail address: peter.fi[email protected] (P. Fielitz).

http://dx.doi.org/10.1016/j.ssi.2014.02.005 0167-2738/© 2014 Elsevier B.V. All rights reserved.

crystalline LiNbO3 [10]. Neglecting the older published oxygen diffusion data in reference [9] one can conclude that the lithium diffusivity is about 4–5 orders of magnitude larger than that of oxygen in the temperature range 800 °C ≤ T ≤ 1100 °C. Regarding the niobium diffusion there exist only three data sets published in 1975 and 1976 [12–14]. Unfortunately, the potentially most interesting publication [12], which applied the radioactive tracer 95Nb, does not allow an unambiguous assessment of the 95Nb tracer diffusion data because of an insufficient presentation of the results. Furthermore, the data presented in [12] deviate strongly from the other two data sets [13,14]. From the published information, it was absolutely not clear whether the reasons for the pronounced discrepancies between the diffusion data sets were due to the materials used (purity, etc.) or due to the analytical techniques applied. Therefore, it appeared necessary to design an experimental procedure suitable to exclude potential errors [11]. To avoid a repetition of the experimental details only the most relevant information on the earlier work [11] will be given in Section 2. The subject of the present work is to study the atomic transport of Nb in LiNbO3. Unfortunately, niobium has only one stable isotope, 93 Nb, and two (comparatively) difficult to handle radioactive isotopes,

P. Fielitz et al. / Solid State Ionics 259 (2014) 14–20

e.g. 91mNb and 95Nb. Therefore, we applied Ta as a diffusion tracer in LiNbO3. This choice was motivated by the fact that LiTaO3 is isomorphous to LiNbO3, and that tantalum replaces niobium up to 100% when introduced into the crystal structure of lithium niobate [15]. Further, the ionic radii of Nb5 + and Ta 5 + proposed by Shannon   [16] are identical r Nb5þ ¼ r Ta5þ ¼ 64 pm; CN ¼ 6 and the atomic mass ratio of the two “isoelectronic” pffiffiffi pentavalent ions should impose a diffusivity ratio of about only 2. Because of the high oxygen activ  ity aO2 ¼ 0:2 throughout the different experimental steps no lower valence states than Nb5 + or Ta5 +, respectively, had to be taken into account [8]. Therefore, a thin LiTaO3 film should be very well suited as a diffusion tracer source for the study of the atomic transport of Nb in LiNbO3. 2. Experimental For our earlier work [11] in 2011, VTE processed single crystals were produced via the vapour transport equilibration (VTE) technique [17] using a large mass of a lithium-rich two-phase mixture (Li3NbO4 and LiNbO3) which acted as a Li2O source during the VTE process. VTE processed samples from the same batch as used in Ref. [11] were employed for the Ta diffusion measurement of this work so that we refer to Ref. [11] for all experimental details of our VTE procedure. For completeness and better readability, the main parameters of the samples [11] are briefly reviewed: Z-cut LiNbO3 wafers (composition: 49.0 mol% Li2O, diameter = 50.8 mm, thickness = 0.5 mm) were purchased from Del Mar Photonics. The chemical analysis by ICP-OES spectrometry (after a microwave assisted conversion with a HNO3/HF mixture into a soluble form) revealed the following impurities (in ppm): Mg (b36), Al (402), Ca (294), Cr (738), Mn (18), Fe (b16), K (b286), Na (b157), and Ti (156). The supplied lithium niobate wafer was cut into two pieces of equal size. One piece was used as reference whereas the other one was used for the VTE process applying a lithium-rich two-phase mixture. Small samples (about 5 × 5 × 0.5 mm3) were cut from the VTE processed LiNbO3 wafer and cleaned with ethanol in an ultrasonic bath. The Li2O content in the VTE processed samples was found to be (49.9 ± 0.1) mol% by measuring the absorption edge according to Ref. [18] using a UV–vis–NIR optical spectrometer (Perkin Elmer Lambda 900). In order to study Ta diffusion in VTE processed, so-called stoichiometric z-cut LiNbO3 as well as in congruent z-cut LiNbO3 (supplied by Del Mar Photonics), we deposited a thin LiTaO3 film on the surface of the samples. The deposition of a 20 nm layer of LiTaO3 at the surface of the LiNbO3 samples was done by 5 keV Ar+ ion beam sputtering. A commercial ion beam coater of Gatan Inc. (IBC 681) was used with a single crystal of LiTaO3 as sputter target, which allowed the deposition of very smooth LiTaO3 layers. In order to avoid contaminations from the metallic target holder during ion beam sputtering the relatively small single crystal of LiTaO3 (about 10 × 10 × 1 mm3) was glued on a larger single crystal of LiNbO3 (about 20 × 20 × 1 mm3). In the case of the VTE processed LiNbO3 (stoichiometric) crystal, Li2O loss during diffusion annealing in 200 mbar 16O2 gas was avoided by placing the samples in a small platinum box (loosely closed by a platinum lid) which contained two sintered tablets of the lithium-rich two-phase mixture used for the VTE process [11]. The filled platinum box was moved into a furnace tube at room temperature and the furnace tube was subsequently evacuated to about 10−3 mbar total pressure for 1 h before filling it with 185 mbar 16O2 gas (which resulted in a pressure of about 200 mbar at annealing temperature in the set-up used for the diffusion runs). In the case of congruent LiNbO3, the samples were simply placed on a small Al2O3 holder which replaced the platinum box. In the next step, the furnace was heated with a heating rate of 12 K/min and held for the annealing time, t, at annealing temperature, T. Thereafter the furnace was cooled to room temperature with a cooling rate of 12 K/min. For finite constant heating

15

and cooling rates one can express the diffusion length, L, by L2 = 2D(t + Δt) where D is the diffusion coefficient and Δt is an effective additional annealing time taking into account diffusion during heating and cooling of the furnace (see Ref. [11] for a detailed description of the evaluation of Δt). Tantalum depth distributions (Fig. 1) were determined by SIMS using a Cameca IMS 3f instrument. Negative 14.5 keV oxygen ions were used as primary beam with 100 nA ion current and a spot size of about 50 μm. The raster-scanned area amounted to 250 × 250 μm 2 and the diameter of the analysed zone was 60 μm. Positive secondary ions were used for the analysis of the samples. Sample charging was prevented by coating the sample surface with a 50 nm thick carbon film. For depth calibration the SIMS crater depth was measured using a surface profiler (Tencor, Alpha Step 500). The apparently lower background signal of the as-prepared sample is due to the fact that in this case the secondary ion intensity was reduced in order to prolong the life time of the electron multiplier (secondary ion detector). After the diffusion anneal, due to the lower Ta concentration at the surface, a different set of ion optics parameters was used, which led to a higher background signal. In order to evaluate the diffusion coefficient from the tantalum depth profiles the solution of the diffusion equation for an instantaneous plane tracer source at position x = 0 on the surface of an infinite volume was used [19]

M x2 cðx; t Þ−c∞ ¼ exp − 1=2 4D t 2ðπDt Þ

! ð1Þ

where M is the total amount of diffusing tracer atoms, D is the constant diffusion coefficient, t is the annealing time and c∞ is the background value for x → ∞. The black solid curve in Fig. 1 shows a leastsquares fit of Eq. (1). Also shown in Fig. 1 is the measured tantalum depth distribution of the sample after deposition of a thin LiTaO 3 layer (about 20 nm thickness). All measured Ta diffusion coefficients of this work are listed in Table 1. It should be noted that the experimentally determined diffusivity is a constant for a given temperature, which indicates that there is one dominant transport mechanism operational in a given material.

Fig. 1. Typical 181Ta SIMS depth profiles (grey curves) of a VTE processed lithium niobate sample (z-cut). The shallow profile (as-prepared) was measured after the preparation of a 20 nm LiTaO3 film on the sample surface. The deep profile was measured after 167 h of annealing at 1048 °C in 200 mbar 16O2 gas.

16

P. Fielitz et al. / Solid State Ionics 259 (2014) 14–20

Table 1 proc. Compilation of Ta tracer diffusion coefficients measured by SIMS depth profiling. DVTE Ta is the Ta diffusion coefficient in VTE processed z-cut LiNbO3 and Dcongruent is the Ta diffusion Ta coefficient in congruent z-cut LiNbO3. T

T

proc. DVTE Ta 2

Dcongruent Ta

proc. Dcongruent /DVTE Ta Ta

2

°C

K

m /s

m /s

1000 1048 1100

1273 1321 1373

5.6 × 10−21 4.4 × 10−20 2.9 × 10−19

2.1 × 10−18 5.3 × 10−18 1.3 × 10−17

375 120 45

For comparison Fig. 2 also shows our recent results [11] for the diffusivity of O (in nominally stoichiometric VTE processed LiNbO3). The special feature of the measured Ta diffusion data (in VTE processed LiNbO3) is that they are directly comparable with the measured 18O tracer diffusion data [11] because VTE processed samples from the same batch were used and annealed with the same equipment. In this way one can clearly recognise that the tantalum diffusivity is generally about 4 orders of magnitude lower than the oxygen diffusivity in VTE processed single crystalline lithium niobate. The activation enthalpy of the oxygen diffusivity is lower than that of Tantalum and amounts to (387 ± 3) kJ/mol [11].

3. Results and discussion 3.1. Comparison with literature data Fig. 2 displays the measured tantalum diffusion coefficients in stoichiometric (VTE processed) z-cut LiNbO3 and in congruent z-cut LiNbO3. They obey the following Arrhenius relations

VTE proc:



2   ð574  15ÞkJ=mol þ6:16 3m exp − ¼ 2:13−1:58  10 RT s

ð2Þ

congruent



2   ð265  3ÞkJ=mol þ0:44 −7 m exp − ¼ 1:57−0:35  10 RT s

ð3Þ

DTa

DTa

where R is the gas constant and T the temperature. In Fig. 2, our results are shown together with the available Nb diffusion data from the literature: 95Nb tracer diffusion coefficients in LiNbO3 [12], Nb diffusion coefficients in LiTaO3 [13], and interdiffusion coefficients from the formation kinetics of LiNbxTa1−xO3 [14], where 0 ≤ x ≤ 1 is the atomic fraction of Nb on the sublattice of the pentavalent cations. The relevant experimental details of the available data on pentavalent (host) ion diffusion in LiNbO3 and LiTaO3 are compiled in Table 2.

Good agreement is observed between our Ta diffusion data in congruent LiNbO3 and the data of Phillips et al. [13] (Fig. 2). These authors used a 160 nm thick film of Nb2O5 on a congruent LiTaO3 single crystalline substrate. Consequently, Phillips et al. [13] measured the Nb diffusion in congruent LiTaO3. This good agreement supports our assumption that a Ta tracer probes the Nb diffusion in LiNbO 3 and that a Nb tracer probes the Ta diffusion in LiTaO3. This conjecture is further backed by the fact that LiNbO3 and LiTaO3 have practically the same homogeneity range and form a complete solid solution at elevated temperature [15]. Because of these similarities, probably the same majority defects (e.g. antisite-defects and Li vacancies for substoichiometric crystals) will be operational for a given Li 2O/ M2O5 ratio (M = Nb or Ta). If one compares the three data sets for congruent LiNbO 3 , i.e. our data, the data of Phillips et al. [13] and the data of Chin et al. [14] (see Fig. 2), one notes that the activation energy determined by Chin et al. [14] is smaller than the ones determined in the two other studies (see Table 2). One reason might be that the samples used by Chin et al. [14] could be contaminated by impurities because the growth of LiNbO 3 films on LiTaO 3 substrates by liquid phase epitaxial techniques, as done by Chin et al. [14], required a flux system. Several flux systems (LiNbO 3 in: K 2WO4, Li2B2O4 , Li2WO4 , WO 3 ) have been shown to be suited to the growth of LiNbO 3 thin films by liquid phase epitaxial techniques [20]. However, it is plausible to assume that the grown LiNbO 3 films may contain traces of the elements (K, B, W) from the flux systems used. Considering ionic radii proposed by Shannon [16] one can conclude that, for a given coordination number, CN, large cations like K + ðr K þ ¼ 138 pm; CN ¼ 6Þ can most probably be discarded as major impurities in the grown LiNbO3 films. However, this will certainly   3+ not be true for smaller cations r B3þ ¼ 27 pm; CN ¼ 6 or  like B 6+ W r W 6þ ¼ 60 pm; CN ¼ 6 . Both of them can be incorporated   5+ on Nb or Ta 5 + rNb5þ ¼ r Ta5þ ¼ 64 pm; CN ¼ 6 or Li + sites  r Liþ ¼ 76 pm; CN ¼ 6 . That is, one can presume in the whole homogeneity range of LiMO3, M = (Nb and/or Ta), incorporation reactions for small cations, e.g. B3 + and W6 +, like (applying the Kröger– Vink notation) 



••

5′

B2 O3 þ 3O″i þ 2LiLi þ 2NbNb ⇌2BLi þ 2V Nb þ 2LiNbO3





5•

5′

WO3 þ LiLi þ NbNb ⇌W Li þ V Nb þ LiNbO3 :

Fig. 2. Arrhenius diagram of Ta diffusivities measured in this work in single crystalline lithium niobate (VTE processed and congruent). For comparison: 18O diffusion in VTE processed LiNbO3 (Fielitz et al. [11]), Nb diffusion in LiTaO3 (Phillips et al. [13]), interdiffusion coefficients from the formation kinetics of LiNbxTa1−xO3 (Chin et al. [14]) and 95 Nb tracer diffusion in LiNbO3 (Lapshin et al. [12]).

ð4Þ

ð5Þ

According to these equations B3+ and W6+ ions would occupy Li+ positions, and the charge is compensated by Nb5+ vacancies, leading to an increased mobility of the pentavalent host ion. (For the sake of simplicity, defect formation reactions for foreign atom doping are written here for LiNbO3 only, but analogous arguments will hold for LiTaO3 or LiNbxTa1−xO3, respectively.) If one compares the Ta diffusion data of this work with the 95Nb tracer diffusion data published in 1976 by Lapshin et al. [12] one finds

P. Fielitz et al. / Solid State Ionics 259 (2014) 14–20

17

Table 2 Compilation of the relevant experimental details of the available data on pentavalent (host) ion diffusion in LiNbO3 and LiTaO3 (see text). SIMS: secondary ion mass spectrometry, EMPA: electron microprobe analysis, VTE: vapour transport equilibration, c-: congruent, s. c.: single crystal. Reference

Set-up

T/°C, atmosphere

Analysis method

D0/m2 s−1

ΔHa/eV

this work

Ta2O5 (20 nm) on LiNbO3, s. c., VTE processed in Li3NbO4/LiNbO3 Ta2O5 (20 nm) on c-LiNbO3, s. c. Nb2O5 (160 nm) on c-LiTaO3, s. c. LiNbO3 (4 μm) on c-LiTaO3, s. c. 95 Nb radiotracer on c-LiNbO3, s. c.

1000, 1048, 1100, 200 mbar O2, aLi2 O fixed (VTE conditions) 1000, 1048, 1100, 200 mbar O2 1100 and 1185, air 1000, 1100, 1200, air 800, 900, 1000, air

SIMS

2.13 × 103

5.95

SIMS EMPA, 1.5° taper section refractive index → concentration Residual activity method, mechanical sectioning

1.57 1.81 5.05 5.24

this work Phillips et al. [13] Chin et al. [14] Lapshin et al. [12]

a significant discrepancy (see Fig. 2 and Table 2). Considering the low activation enthalpy determined by Lapshin et al. [12] one could assume that the (presumably congruent) single crystal was strongly contaminated by (aliovalent cationic) impurities which enhanced the Nb vacancy concentration as discussed above (see Eqs. (4) and (5)). Secondly, if one looks more closely at the work of Lapshin et al. [12] one is confronted with serious deficiencies in the presentation of the experimental data: The self-diffusivity of niobium in LiNbO3 was determined from diffusion profiles obtained by the sectioning method in combination with an appropriate variant of the residual activity method with the radioactive tracer 95Nb, whose (low energy) β− radiation was detected. The radioactive tracer source was deposited onto the polished surface as a thin film of an aqueous solution of salts of oxalic acid. Unfortunately, there is no description of the film deposition procedure and no statement about the resulting film thickness and film roughness. Furthermore, no measured depth distributions of the radioactive tracer 95 Nb are presented and there is no description of the applied sectioning method. As the authors do not show the depth distribution of the radiotracer in an as-prepared sample prior to the diffusion anneal, which could subsequently be compared with the depth distributions after the diffusion annealing, it remains highly questionable whether the broadening of the depth profiles was solely caused by diffusion. Because of these deficiencies in the presentation of the experimental data, doubts are justified whether the data of Lapshin et al. [12] represent reliable data of the Nb tracer diffusion in (congruent) LiNbO3.

3.2. Ta diffusion in congruent and in VTE processed lithium niobate In the VTE process of this work, a mixture of Li3NbO4/LiNbO3 = 3/4 was used with a total mass of 750 g. The VTE processing conditions were 96 h at T = 1100 °C at an oxygen partial pressure of 200 mbar (see [11,17] for a detailed description). According to the Li2O–Nb2O5 phase diagram [21] such a treatment should yield a material with a mole fraction of Li2O of X Li2 O ¼ 0:502  0:001. From optical absorption measurements [18], however, a lower value of X Li2 O ¼ 0:499  0:001 was obtained, which represents the average bulk content of Li2O. This means that there could be a near-surface zone, e. g. 5 μm, in the VTE processed LiNbO3 crystal (with an average bulk concentration given by the corresponding mole fraction X Li2 O ¼ 0:499  0:001 ) which is enriched up to X Li2 O ¼ 0:502  0:001 as given by the Li2O–Nb2O5 phase diagram [21]. According to recent results obtained on VTE processed Li2O-rich samples, at least the surface of the crystals attained a Li2O concentration of (50 ± 0.1)% after 80 h at 1100 °C [22]. Such a Li2O-rich near-surface zone (hyper-stoichiometric with X Li2 O ¼ 0:502  0:001) would be sufficient for a Ta diffusion profile which, as shown by Fig. 1, extends into the crystal by not much more than 1 μm. It is extremely difficult to prove the existence of a thin hyperstoichiometric near surface zone (about 5 μm thickness) with optical methods so that we could not check this hypothesis. In the following discussion we will, therefore, first treat the Ta diffusion in Li2Odeficient LiNbO3 up to the so called nearly stoichiometric composition (X Li2 O ¼ 0:499  0:001) and will then discuss the possibility that Ta

× × × ×

10−7 10−6 10−11 10−11

2.75 3.06 1.72 1.27

diffusion occurred in a hyper-stoichiometric near-surface zone of the (VTE processed) LiNbO3 crystal (with X Li2 O ¼ 0:502  0:001). 3.2.1. Nb diffusion mechanism in lithium-deficient lithium niobate 4• × The standard defect model {[Li× Li]1 − 5x[VLi′]4x[NbLi ]x}NbNbO3 of Li2Odeficient LiNbO3 is well established in the literature [1] so that one has (see Appendix A) x¼

h i 1  4• ¼ NbLi ¼ V ′Li if 4 4X Li2 O −5 2X Li2 O −1

X Li2 O b0:5

ð6Þ

where X Li2 O is the mole fraction of Li2O in the homogeneity range of Li2O-deficient LiNbO3, [Nb4• Li ] = x is the concentration of Nb anti-site defects and [VLi′] the concentration of Li vacancies per formula unit. The electroneutrality condition reads in this case 4[Nb4• Li ] − [VLi′] = 0. This defect model is supported by theoretical work on Li2O-deficient LiNbO3 (see [23] and references therein) which shows that Li2O depletion or Nb2O5 enrichment, respectively, can be realised by several reactions with significantly different formation energies per defect. However, with 3.01 eV/defect [24] the reaction 1 5 4• Nb O þ 5LiLi ⇌4V ′Li þ NbLi þ Li2 O 2 2 5 2

ð7Þ

is the most favourable one for Li-deficient lithium niobate. According to the literature (see e.g. [2,25] and references therein) the Li diffusion coefficient, DLi, in Li2O-deficient LiNbO3 is proportional to the concentration of Li vacancies, [VLi′],     DLi LiLi ¼ Dv V ′Li

ð8Þ

where Dv is the diffusion coefficient of Li vacancies, VLi′. If one assumes that Nb anti-site defects, Nb4• Li , are sufficiently mobile on the Li sublattice and that these defects are in equilibrium with Nb on regular lattice sites, Nb× Nb, one can expect that the Nb diffusion coefficient, DNb, is proportional to the concentration of Nb anti-sites, [Nb4• Li ], (see Appendix B) h i   4• DNb NbNb ≃Da−s NbLi :

ð9Þ

Here Da−s is the diffusion coefficient of Nb anti-site defects, Nb4• Li . × Considering [Li × Li ] = [Nb Nb ] = 1 and Eqs. (6), (8) and (9) one gets DNb/DLi ≃ D a−s/4Dv. That is, because of DNb ≪ DLi (see [2,25]), one has Da−s ≪ Dv. With the assumed Nb diffusion mechanism (Eq. (9)) one can now calculate the theoretical ratio of the Nb diffusivity in congruent LiNbO3, DcNb, and the Nb diffusivity in nearly stoichiometric LiNbO3, Dns Nb, h i  ′ c 4• c NbLi V DcNb ns ¼  ′Lins : ns ≃  4• DNb NbLi V Li

ð10Þ

  If the defect concentration for congruent X Li2 O ¼ 0:483  0:001   and for nearly stoichiometric X Li2 O ¼ 0:499  0:001 LiNbO3 are

18

P. Fielitz et al. / Solid State Ionics 259 (2014) 14–20

calculated (see Eq. (6)) and inserted in Eq. (10), the significant difference of the Ta diffusivities (see Fig. 2) is apparently, at least semiquantitatively, confirmed. But this (apparent) agreement at about 1100 °C is, at best, fortuitous because the temperature dependency of Ta diffusion in the congruent and in the nominally nearly stoichiometric LiNbO3 is very different (see Table 2). It is therefore highly probable that the Ta diffusivity measured in the VTE processed crystal is not representative for nearly stoichiometric LiNbO3, since, for a given composition, the right hand side of Eq. (10) is constant. This implies that the left hand side of this equation should not depend on temperature — which is obviously not the case (see Fig. 2): The observed large difference of the activation enthalpies for the Ta diffusion in congruent and in VTE processed LiNbO3 requires, for the VTE processed LiNbO3 , a diffusion mechanism which is different from the one expressed by Eqs. (9) and (10) for the congruent material and, most probably, for the whole concentration range X Li2 O ≤0:499. This means that in the VTE processed LiNbO3 transport of Nb via the Li sublattice could no longer be the dominating mechanism. The discrepancy under discussion could, however, be rationalised if one recalls the fact that the optical measurements of the Li2O concentration yield an average bulk value only and are unable to detect in a 500 μm wafer a near-surface zone (some μm thick) which is in equilibrium with the LiNbO4/LiNbO5 two-phase mixture of the VTE process, which fixes the mole fraction to X Li2 O ¼ 0:502  0:001 according to the Li2O– Nb2O5 phase diagram [21]. In the following subsection this scenario (Ta/Nb diffusion in a Li2O-enriched near-surface zone) will be used to develop a model for the Ta/Nb transport in hyper-stoichiometric LiNbO3 (with 0:5≤X Li2 O ≤0:502) 3.2.2. Nb diffusion mechanism in lithium-rich lithium niobate The incorporation of excess Li2 O has been briefly described by Donnerberg et al. [24]. For their energetically most favourable reaction Li2O ⇌ Oi″ + 2Li•i with the electroneutrality condition 2[Oi″] = [Li•i ] these authors obtained a formation energy of 4.71 eV/defect. This reaction is, however, unsuitable for the discussion of possible transport mechanisms of Nb. In the present work we consider the Li2O uptake of the crystal in equilibrium with the Li3NbO4/LiNbO3 two-phase mixture (realised during the VTE process and maintained during the diffusion anneal) according to the solution reaction of Li3NbO4 in LiNbO3, 

•

5′

3Li3 NbO4 þ NbNb ⇌5Lii þ V Nb þ 4LiNbO3

ð11Þ

This reaction has not yet been considered before in the literature so that it was necessary to calculate the formation energy of this reaction. The respective lattice energies, EL, and the defect formation energies, E, of reaction (11) are: ELðLiNbO3 Þ ¼ −174:96 eV;  ELðLi3 NbO4 Þ ¼ −208:05 eV  • 5′ E Lii ¼ −7:12 eV; E V Nb ¼ þ127:56 eV:

ð12Þ

These values were calculated using the GULP code [26] and the procedure described in [23]. Essentially, interactions between ions are modelled using interatomic potentials, which, when combined with energy minimisation, allows lattice energies, EL, for LiNbO 3 and Li3NbO4 to be obtained. Defect energies are then calculated by the Mott–Littleton procedure [27], which divides the system into two regions, one surrounding the defect where interactions are treated explicitly, and an outer region which extends to infinity, which is treated as a dielectric continuum. • Taking into account 5[V5' Nb] = [Lii ] and aLiNbO3 ¼ aLi3 NbO4 ¼ 1 the equilibrium constant of reaction Eq. (11) becomes K 11 ðT Þ ¼

h ′ i6 a4LiNbO3  • 5 h 5′ i 5 5 Lii V Nb ¼ 5 V Nb : 3 aLi3 NbO4

ð13Þ

′

5 The formation enthalpy, ΔHNb f , of the niobium vacancy, V Nb , reads therefore

h 0 i1 0 ∂ ln V 5Nb A −kB @ aO ; ∂ð1=T Þ a

p; LiNbO3 ¼ aLi3 NbO4 ¼ 1 2

¼

1 Nb ΔH 11 ¼ ΔH f : 6

ð14Þ

With the calculated lattice energies and the defect formation energies (Eq. (12)) the formation energy becomes ΔE11 =eV ¼ 4ð−174:96Þ þ 127:56 þ 5ð−7:12Þ−3ð−208:05Þ ¼ 16:27 ð15Þ so that the formation enthalpy of a niobium vacancy is given by ΔHNb f = ΔE11/6 = 2.71 eV/defect. According to defect reaction Eq. (11), Nb diffusion occurs in Li2O-rich lithium niobate via Nb vacancies h ′i   5 DNb NbNb ¼ Dv V Nb

ð16Þ

where DNb is the Nb diffusion coefficient and Dv is the diffusion coeffi′ cient of Nb vacancies, V 5Nb . From the Arrhenius plot, DTa(1/T), in Fig. 2 one obtains for the VTE processed LiNbO3 crystal −kB



∂ lnDTa ∂ð1=T Þ aaO ; Ta

¼ ΔH m þ

p; 2 LiNbO3 ¼ aLi3 NbO4 ¼ 1 Ta ΔH f ¼ 5:95 eV

  Ta ¼ ΔH a aLi2 O ¼ max ð17Þ

Assuming DTa ≈ DNb one can now estimate the migration enthalpy of the Ta/Nb diffusion in hyper-stoichiometric LiNbO3, i.e. for the highest possible values of the Li2O activity, aLi2 O ¼ max, as follows NbðTaÞ

ΔH m

  Ta Nb aLi2 O ¼ max ¼ ΔH a −ΔH f ¼ ð5:95−2:71Þ eV

¼ 3:24 eV

ð18Þ

This estimated migration enthalpy for the Ta/Nb diffusion is, on the one hand, hypothetical because we could not directly prove the existence of a hyper-stoichiometric near-surface zone with (optical) analytical methods in the VTE processed LiNbO3 crystal. On the other hand this estimated value is, within a ±10% error, in reasonable agreement with the experimentally determined activation enthalpies of the Ta/Nb transport in congruent LiNbO3 (2.75 eV) and in congruent LiTaO3 (3.06 eV, see Table 2). Because in congruent, i.e. sub-stoichiometric LiNbO3, the Nb4• Li anti-site defect concentration is fixed by the Li2O/Nb2O5 ratio, the experimentally determined activation enthalpy of the Ta(Nb) diffusivity in the sub-stoichiometric crystal consists of the migration term, ΔHm, only. Elaborating this picture further it could be concluded that the transport of the pentavalent host ions occurs in the sub-stoichiometric 4• material via sufficiently mobile anti-site species (Nb4• Li or TaLi , respectively) which are using vacancies on the Li sublattice as the dominant transport “vehicles”. In contrast, the transport of the pentavalent host ions in the hyper-stoichiometric material occurs via vacancies on the ′ ′ Ta(Nb) sublattice (V 5Nb or V 5Ta , respectively) — but in both cases with an essentially comparable migration enthalpy of about 3 eV. 4. Summary In this work we measured Ta diffusion in VTE processed nominally stoichiometric LiNbO3, i.e. (49.9 ± 0.1) mol% Li2O, as well as in congruent, i.e. sub-stoichiometric, LiNbO3 single crystals applying a thin layer of LiTaO3 which was sputter deposited on the surface of the samples. Because VTE processed samples from the same batch like in Ref. [11] were used and annealed with the same equipment we could clearly show that the tantalum diffusivity is about 4 orders of magnitude lower than the oxygen diffusivity in the VTE processed crystals.

P. Fielitz et al. / Solid State Ionics 259 (2014) 14–20

We assume that the measured Ta diffusivity adequately reflects the Nb diffusivity in LiNbO3. This assumption is supported by the reasonable agreement between the results of this work for Ta diffusion in congruent LiNbO3 and the results of Phillips et al. [13] for Nb diffusion in congruent LiTaO3. Therefore, we consider and discuss the measured Ta diffusion data of this work as Nb diffusion data in single crystalline LiNbO3. The results of this work show that, regardless of the exact value of the Li2O/Nb2O5 ratio in the homogeneity range of LiNbO3, the ranking of the self-diffusion coefficients of the host elements (Li, Nb, O) is DLi ≫ DO ≫ DNb. Comparing the results of this work with literature data we conclude that the samples of Chin et al. [14] probably contained impurities from the flux system used. Because of the significant differences to all other available Ta and Nb diffusivity data and because of major deficiencies in the presentation of the measured 95Nb diffusivity data of Lapshin et al. [12] in LiNbO3, it appears questionable whether these data represent reliable results for the Nb tracer diffusion in LiNbO3. If one compares the Ta diffusivity in congruent LiNbO3 crystals with the Ta diffusivity in VTE processed LiNbO3 crystals one finds that the Ta diffusivity in the congruent LiNbO3 crystals is significantly faster. In Li2O-deficient (congruent) lithium niobate, i.e. with (48.3 ± 0.1) mol% Li2O, one can rationalise the diffusion of the highly charged pentavalent host ion, Nb5+(Ta5+), in analogy to the transport of the singly charged ion, Li+, in the framework of the generally accepted defect model for sub-stoichiometric LiNbO3 [1]. In this model one assumes that Nb anti-site cations in lithium niobate, Nb4• Li , are sufficiently mobile to act as transporting defects for Nb ions on regular lattice sites, Nb× Nb, using vacancies on the Li sublattice, VLi′, as the dominant transport “vehicles”. This interpretation of the Ta/Nb diffusion data for congruent, i.e. substoichiometric, material is corroborated by the existing experimental information on the analogous behaviour of Li self-diffusion for a fixed Li2O/Nb2O5 ratio [2,25]. Although the VTE processed crystals with a thickness of 500 μm have an average bulk concentration of “only” (49.9 ± 0.1) mol% Li2O, it must be recognised that the (shallow) Ta/Nb diffusion profile lies in a nearsurface zone of about 5 μm thickness which is in equilibrium with the Li3NbO4/LiNbO3 two-phase mixture of the VTE process. It is concluded that the latter maintains a Li2O activity which induces a Li2O enrichment of up to (50.2 ± 0.1) mol% Li2O according to the Li2O–Nb2O5 phase diagram [21]. The diffusion zone of a VTE processed crystal can thus easily become hyper-stoichiometric. This picture suggests a discussion of the defect formation reaction in Li2O-rich lithium niobate which is based on the experimental procedure of the VTE process, i.e. the solution of Li3NbO4 in LiNbO3. According to the theoretical calculations the • resulting defects, 5[V5′ Nb] = [Lii ], have an energy of only 2.71 eV/defect. It follows from this model that in hyper-stoichiometric lithium niobate Nb diffusion should occur via Nb vacancies. For both the vacancy mediated mechanisms in the congruent as well as in the hyperstoichiometric LiNbO3 a similar migration enthalpy of about 3 eV is observed for the overall mobility of Ta/Nb. The presented results shed light on the interpretation of the chemical diffusion kinetics of the VTE process which are, as yet, not completely understood [3,22,28–30]. The results also suggest future work on the diffusion of the pentavalent host ions in LiNbO3, such as Ta tracer diffusion in Li2O-deficient LiNbO3 as a function of the Li2O/Nb2O5 ratio, and in Li2O-rich bulk samples. In both cases long-term LiNbO3–LiTaO3 interdiffusion runs would supply additional information. Of course, the use of the radiotracers 91mNb or 95Nb in LiNbO3 is, though expensive, a promising option. Acknowledgements We are indebted to J. Rahn for experimental support with ion sputtering of the Ta2O5 layer on LiNbO3 and to E. Ebeling for technical service. The discussion with K. Buse and experimental help of N. Waasem with a Li2O concentration measurement are highly

19

appreciated. Financial support from Deutsche Forschungsgemeinschaft (DFG) is gratefully acknowledged. Appendix A 4• × Because of {[Li× Li]1–5x[VLi′]4x[NbLi ]x}NbNbO3 one gets the relation

½Li2 O ½Li2 O þ ½Nb2 O5    Li ¼     Li   4•  LiLi þ NbNb þ NbLi

X Li2 O ¼

ðA:1Þ

1−5x 1−5x ¼ ð1−5xÞ þ 1 þ x 2−4x   from which x ¼ x X Li2 O is immediately obtained (see Eq. (6)). ¼

Appendix B The concentration profile of the tracer experiment, Fig. 1, shows that there is only one constant tracer diffusion coefficient for Ta as a “tracer” for Nb. Neglecting correlation effects as well as small differences in the jump length, the partial “conductivities” of the theoretically possible    diffusional jumps in the Nb sublattice, NbNb DNb Nb↔Nb, in the Li sublattice, h i     Nb 4• NbLi DNb Li↔Li , from the Nb sublattice to the Li sublattice, NbNb DNb→Li , h i  4• and from the Li sublattice to the Nb sublattice, NbLi DNb Li→Nb , can be averaged as follows 



h i    Nb  4• 4• Nb NbNb þ NbLi DNb ¼ NbNb DNb↔Nb þ NbLi DLi↔Li h i    Nb 4• Nb þ NbNb DNb→Li þ NbLi DLi→Nb

ðB:1Þ

where DNb is the measured tracer diffusion coefficient. On the right hand side of Eq. (B.1) the superscripts on D characterise the diffusing tracer element (i.e. Ta or 95Nb, respectively) and the subscripts indicate the sublattices, in which (or from which to which) the jump under concern occurs. Assuming equilibrium between the two cationic sublattices, one gets h i     Nb 4• Nb NbNb DNb→Li ¼ NbLi DLi→Nb :

ðB:2Þ

4• With [Nb× Nb] ≫ [NbLi ] Eq. (B.1) becomes

h i h i    Nb  4• Nb 4• Nb ½NbNb DNb ¼ NbNb DNb↔Nb þ NbLi DLi↔Li þ 2 NbLi DLi→Nb h i  4• Nb Nb ≃ NbLi DLi↔Li þ 2DLi→Nb

ðB:3Þ

   Nb as the term NbNb DNb↔Nb of Eq. (B.3) can be neglected because of the extremely small value of DNb Nb↔Nb . This can be rationalised because the majority defect concentration of Li2O deficient LiNbO3 is [Nb4• Li ] = [VLi′]/   Nb Nb 4. Denoting the term DLi↔Li þ 2DLi→Nb as the diffusion coefficient of    Nb , one gets Eq. (9). Nb anti-site defects, i.e. Da−s ≡ DNb Li↔Li þ 2DLi→Nb References [1] T. Volk, M. Wöhlecke, Lithium Niobate: Defects, Photorefraction and Ferroelectric Switching, Springer Series in Materials Science, 115, Springer Verlag, Berlin, Heidelberg, 2008. [2] A. Weidenfelder, J. Shi, P. Fielitz, G. Borchardt, K.D. Becker, H. Fritze, Solid State Ionics 225 (2012) 26–29. [3] D.H. Jundt, M.M. Fejer, R.G. Norwood, P.F. Bordui, J. Appl. Phys. 72 (1992) 3468–3473. [4] D.P. Birnie III, J. Mater. Sci. 28 (1993) 302–315. [5] D. Bork, P. Heitjans, J. Phys. Chem. B 105 (2001) 9162–9170. [6] M. Wilkening, D. Bork, S. Indris, P. Heitjans, Phys. Chem. Chem. Phys. 4 (2002) 3246–3251.

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