Lithium diffusion coefficient in amorphous lithium ... - CyberLeninka

Solid State Ionics 294 (2016) 59–66

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Lithium diffusion coefficient in amorphous lithium phosphate thin films measured by secondary ion mass spectroscopy with isotope exchange methods Naoaki Kuwata a,⁎, Xiaoli Lu a, Takamichi Miyazaki b, Yoshiki Iwai a, Tadao Tanabe a, Junichi Kawamura a a b

Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577, Japan School of Engineering, Tohoku University, 6-6-11 Aramaki-aza Aoba, Aoba-ku, Sendai, 980-8579, Japan

a r t i c l e

i n f o

Article history: Received 10 May 2016 Received in revised form 27 June 2016 Accepted 28 June 2016 Available online 18 July 2016 Keywords: Diffusion coefficient Thin-film battery Pulsed laser deposition Haven ratio

a b s t r a c t Lithium diffusion coefficients in amorphous lithium phosphate (a-Li3PO4) thin films were determined by secondary ion mass spectroscopy (SIMS), using 7Li and 6Li stable isotopes. The diffusion couples were prepared by an ion-exchange method using liquid electrolyte and a mask method based on thin-film deposition. The tracer diffusion coefficient, DLi⁎, was evaluated by analyzing the isotope profiles obtained by SIMS in the temperature range of 25–160 °C. The diffusion coefficient of a-Li3PO4 was 6.0 × 10−13 cm2/s at 25 °C, while the activation energy was 0.58 eV, as measured for the samples prepared by using the ion-exchange method. The conductivity diffusion coefficient, Dσ, was calculated from the thin film ionic conductivity, which was determined by impedance spectroscopy. The correlation factor, HR, was 0.55 ± 0.20 in the measured temperature range, which indicated the cooperative motion of lithium ions in lithium phosphate glasses. © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction The determination of the diffusion coefficient of lithium ions in solids is critical for understanding the ionic transport mechanism in solid-state lithium batteries. However, owing to the absence of suitable radioactive isotopes, only a few experimental studies have been reported on the lithium self-diffusion coefficient in battery materials [1–5]. Here, we present a new method to study the lithium diffusion coefficient in a thin film of a lithium ion conductor. Amorphous lithium phosphate (a-Li3PO4) is widely used in thin-film batteries as a solid electrolyte with wide electrochemical window [6,7] and negligible interface resistance [8,9]. Thin-film solid-state batteries have shown excellent cycle stability and high operating voltages [6,8]. The radioactive isotope of lithium, 8Li, has a very short half-life of 0.84 s. Nevertheless, measurements of 8Li tracer diffusion coefficient (DLi⁎) were performed in β-LiGa [10] and amorphous Li3·4V0.6Si0·4O4 thin films [11,12] by using 8Li beam generated by a radioactive ion accelerator facility. On the other hand, the stable isotopes, i.e., 6Li and 7 Li, can also be used for evaluating DLi⁎. Takai et al. measured the DLi⁎ value in Li4Ti5O12, Li2+2xZn1−xGeO4, La2/3−xLi3xTiO3, and LiMn2O4 by neutron radiography [3,13–15]. However, this method requires largescale facilities as a neutron source. Secondary ion mass spectroscopy ⁎ Corresponding author. E-mail address: [email protected] (N. Kuwata).

(SIMS) is capable of measuring the accurate isotope ratio of lithium (6Li and 7Li) as well as distinguishing the isotopes. Lithium diffusion measurements using SIMS analysis were early reported by Coles and Long for single crystal LiF in 1974 [1]. Okumura ~ Li ) in LixMn2O4 thin et al. reported the chemical diffusion coefficient (D films by using SIMS depth measurements [16]. Recently, Rahn et al. reported the diffusion coefficient in single crystal LiNbO3 [17,18]. A similar method, i.e., laser ablation inductively coupled plasma mass spectrometry, has been applied to lithium tracer diffusion measurements in LiAlSi2O6 [4] and Li2O-SiO2 glasses [5]. SIMS analysis was also utilized to measure the diffusion of lithium in a thin film of a Li-W-O coating layer by Hayashi et al. [19]. In the present study, DLi⁎ was determined in a thin-film solid electrolyte by adopting ion-exchange and SIMS techniques. We prepared the diffusion couples by using two different kinds of processes, namely, ion-exchange and mask methods. The combination of the two techniques and SIMS measurements was applied to a-Li3PO4 thin films to determine DLi⁎. 2. Experimental Polycrystalline lithium phosphate (Li3PO4) with 6Li isotope was synthesized by solid-state reaction. Lithium-6 carbonate (6Li2CO3, 95% 6Li, 5% 7Li, Cambridge Isotope Laboratories) and NH4H2PO4 (Wako Pure Chemical) were mixed and calcined at 700 °C for 6 h. The sample was

http://dx.doi.org/10.1016/j.ssi.2016.06.015 0167-2738/© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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Fig. 1. Schematic diagram of sample preparation methods: (a) ion-exchange method using natLiClO4/PC electrolyte and (b) mask method. The surface concentration of 6Li and 7Li was measured by secondary ion mass spectroscopy line analysis.

crushed in an agate mortar, pressed under the uniaxial pressure of 178 MPa, and sintered at 750 °C for 12 h. The 6Li3PO4 target was 23.7 mm in diameter and 4.4 mm in thickness, and had a density of 1.92 g/cm3. The relative density was 81% of the theoretical density of 6 Li3PO4 (2.37 g/cm3). X-ray diffraction (XRD) analysis was conducted to confirm the crystal structure of γ-Li3PO4 (PDF#01-074-0358). Thin films of a-6Li3PO4 were prepared by pulsed laser deposition (PLD) [6,8,20]. The PLD system consisted of a main vacuum chamber (PLAD-221, AOV Co., Ltd.) and an ArF excimer laser (COMPexPro 205, Coherent). The vacuum chamber was evacuated to 1 × 10−4 Pa; then, high-purity oxygen was introduced, and the pressure was maintained at 0.2 Pa. The ArF excimer laser (λ = 193 nm) was focused onto the surface of the 6Li3PO4 target with pulse energy of 150 mJ, pulse frequency of 10 Hz, and laser fluence of 0.85 J/cm2. Thin films of a-Li3PO4 were grown on Pt (200 nm) coated SiO2 glass substrates at room temperature. The deposition rate was 500 nm/h. The thicknesses of the thin films, measured by a surface profilometer, were controlled to be ~450 nm. Morphology of the thin films was observed by a field emission scanning electron microscope (FE-SEM, SU6600, Hitachi). The operating voltage was 15.0 kV. For cross-section view, the substrate was cut and the fracture surface was observed. Surface roughness of the film was measured by a laser microscope (VK-9710, Keyence) and the surface profilometer (SE-3500, Kosaka Lab.). Two different types of diffusion couples were prepared by using two different techniques, as shown in Fig. 1. The first method (Fig. 1(a)) is called “ion-exchange method”. The a-6Li3PO4 thin film was immersed in a solution of 1 mol/L lithium perchlorate (natLiClO4) in propylene carbonate (PC), which has a natural isotope composition (92.4% 7Li, 7.6% 6 Li). When the sample was immersed in the solution for 10 h at room temperature, 6Li in the film contacting the solution was completely exchanged with natLi. A glass beaker cell sealed with grease (Demnum grease L-65, Daikin Industries, Ltd.) was used for ion exchange. The beaker cell was airtight to avoid evaporation of the solvent. After ion exchange, the sample was washed with dimethyl carbonate, and dried in an Ar-filled glove box. Then, the sample was cut into several pieces. Each of the samples was annealed at different temperatures and times. The isotope profiles of 6Li and 7Li were measured by SIMS, and the DLi⁎ values were obtained by fitting the isotope profiles with the diffusion equation. Fig. 1(b) shows the second procedure, named “mask method”, where an a-natLi3PO4 thin film was deposited on a section of the a-6Li3PO4 film by using a metal mask. The thicknesses of the 6Li and the natLi films were ~ 400 nm. Initially, these films contain 95% and 7.6% of 6Li, respectively. After sufficient time had passed, the average isotope composition, 51% of 6Li and 49% of 7Li, was obtained

owing to mutual diffusion. Due to variation of the film thickness, the experimental results show 51 ± 5% of 6Li. Then, the samples were annealed at different temperatures for the SIMS measurements. The analysis of the diffusion profiles was performed by using the double-focusing magnetic sector SIMS (IMS-7f, CAMECA) available at Tohoku University. The line profile analysis was conducted by using a Cs+ primary ion beam operating at 15 keV and 1 nA. The spot size of Cs+ ion beam was 1 μm. The minimum distance between two points was set to 13 μm for line analysis. Mapping was measured in a range of 200 × 200 μm2 with 2 μm spatial resolution. As the 6Li and 7Li isotopes have the same chemical properties, ionization and detection efficiencies remain nearly constant. The quantitative isotope ratios were directly calculated from the counting rates of the 6Li and 7Li isotopes. The ionic conductivity of thin films was measured by impedance spectroscopy. The a-6Li3PO4 films were deposited on interdigitated array Pt electrodes (ALS Co., Ltd.). The intervals between Pt electrodes were 2 μm. The length was 2.4 mm, and the number of repetitions

Fig. 2. Morphology of an a-6Li3PO4 thin film observed by FE-SEM; (a) surface and (b) cross-section. The thin film was deposited on a Pt/Cr/SiO2 substrate.

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Fig. 3. Isotope mappings of 6Li/7Li for a-Li3PO4 thin films prepared by ion-exchange method; (a) as-prepared and (b) annealed at 120 °C for 24 h. The scan range was 200 × 200 μm2.

was 129. The area was 1.8 × 10−3 cm2 when the film thickness was 590 nm. The cell constant for conductivity measurement was calculated to be 0.11 cm−1. The sample was placed in an O-ring sealed copper cell purged with dry Ar. Impedance spectra were collected using an impedance/gain-phase analyzer (SI 1260, Solartron) in the frequency range of 10−2–106 Hz. The temperature ranged from 25 to 160 °C. The ionic conductivity was determined from the frequency-independent plateau in the impedance spectra [20,21]. 3. Results and discussion Fig. 2 shows the morphology of a-6Li3PO4 thin films observed by FESEM. The film surface and cross-section images show dense and homogeneous morphology without any cracks, pores or grain boundaries. The homogeneity is a characteristic of an amorphous film. Owing to the dense and homogeneous nature, the a-Li3PO4 film has been used as the electrolyte of various kinds of thin-film batteries [6,8,22]. Submicron droplets, which were formed by liquid splashing processes during PLD [21], were observed on the film surface. The surface roughness (Ra) was

0.009 ± 0.003 μm for the a-6Li3PO4 film. The slightly large Ra is due to the droplets on the surface. The film density, which was calculated from the film thickness and weight measurements, was 2.2 ± 0.2 g/cm3 as an average of eight samples. The weight, the thickness and the area of the films were 120 ± 10 μg, 440 ± 50 nm and 1.19 cm2, respectively. The sample prepared by using the ion-exchange method showed no change in appearance when observed by optical microscope and FESEM. However, the isotope profile was clearly revealed by the SIMS analysis. Fig. 3 shows an example of isotope mapping of the diffusion couple prepared by adopting the ion-exchange method. The bottom half of the sample was immersed in the liquid electrolyte for 10 h to replace 6Li with 7Li. The boundary between 6Li and 7Li for the as-prepared diffusion couple is shown in Fig. 3(a). The width of the boundary region where the isotope ratio varied was smaller than 10 μm. When the asprepared sample was annealed at 120 °C for 24 h, broadening of the boundary region occurred, due to lithium diffusion (Fig. 3(b)), and the transition region became larger than 100 μm in width. The isotope profiles were analyzed by the diffusion equation to determine DLi⁎ as described below. SIMS mapping requires a smooth thin-film surface, as

Fig. 4. Surface 6Li concentration ratio in a-Li3PO4 thin films, measured by secondary ion mass spectroscopy line analysis. The diffusion couples were prepared by the ion-exchange method. The annealing temperatures were (a) 80 °C, (b) 100 °C, (c) 140 °C, and (d) 160 °C for 24 h. The solid line shows the fitting curve obtained by using Eq. (1).

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Table 1 Experimental data for tracer diffusion experiments. T (°C)

t (h) ion-exchange

t (h) mask

DLi⁎ (cm2/s) ion-exchange

DLi⁎ (cm2/s) mask

25 40 60 80 100 120 140 160

2928 2740 24 24 24 24 24 24

792 840 164.5 240 96 48 24 12

6.00 × 10−13 1.01 × 10−12 1.20 × 10−11 2.58 × 10−11 5.91 × 10−11 1.63 × 10−10 2.75 × 10−10 5.60 × 10−10

6.85 × 10−13 1.10 × 10−12 1.14 × 10−11 1.56 × 10−11 6.64 × 10−11 1.77 × 10−10 2.94 × 10−10 5.72 × 10−10

the ionization efficiency might be disturbed at the edge, or by the roughness, of the surface. Thus, the ion-exchange method was found to be more suitable and accurate for SIMS mapping than the mask method. Fig. 4 shows the line profile of the isotope ratio of the a-Li3PO4 thin film. The isotope ratio, 6Li/(6Li + 7Li), is shown as a function of the lateral distance. The isotope composition of the a-Li3PO4 film without ion-exchange comprised 95% 6Li and 5% 7Li, which was the same as that of the 6Li3PO4 target. After the sample was immersed in the liquid electrolyte (natLiClO4/PC) for 10 h, the isotope composition changed to 9% 6Li and 91% 7Li, which was closer to the natural abundance. This result demonstrated that most of the 6Li+ ions in the a-Li3PO4 film were replaced by 7Li+ ions in the electrolyte solution within 10 h. The SIMS line profiles of the ion-exchanged samples annealed at different temperatures between 80 and 160 °C for 24 h are shown in Fig. 4 (a)–(d). The width of the transition region between 6Li and 7Li in the

SIMS profile depended on the annealing temperature and duration. The SIMS profiles were analyzed by conventional diffusion equations [23,24]. Under the assumption of a concentration-independent diffusion coefficient, which is allowed for the 6Li/7Li couple investigated here, the solution of Fick's second law for one-dimensional diffusion between semi-infinite media is given by [23,24]: cðx; t Þ−c0 1 ¼ 2 c1 −c0

   x ffi 1−erf pffiffiffiffiffiffiffi 2 D t

ð1Þ

where c(x, t) is the concentration at distance x, c0 and c1 are the initial concentrations in each region of the diffusion couple, D⁎ is the tracer diffusion coefficient, and t is the annealing duration. The isotope ratio 6Li/ (6Li + 7Li) was used as a concentration variable. The x-axis of Eq. (1) can be inverted by using the relation erf(−x) = − erf(x). To evaluate D⁎Li, the 6Li/(6Li + 7Li) isotope profile was fitted by using Eq. (1). The boundary position (x = 0) was also determined by fitting. The experimental data and theoretical fitting curves were in excellent agreement at each temperature, as shown in Fig. 4. The D⁎Li values are summarized in Table 1 along with the annealing temperatures and durations. At room temperature (25 °C), DLi⁎ was experimentally obtained to be 6 × 10−13 cm2/s. If the sample is kept at room temperature for 10 days, pffiffiffiffiffiffiffiffi the diffusion length, approximately calculated by using D t , becomes 7.2 μm, which is still less than the point interval (13 μm) used in the line analysis. Therefore, in this study, for the heat-treated samples, we ignored the room temperature diffusion occurring between the sample preparation and the SIMS experiments.

Fig. 5. Results of numerical simulations. (a) Initial arrangement of the model of the diffusion couple. Three-dimensional plot of 7Li concentration vs. thickness and lateral distance after (b) 1000 s, (c) 3600 s, and (d) 24 h. The diffusion coefficient D was set to 10−12 cm2/s.

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Fig. 6. Time evolution of 6Li surface concentration estimated from the numerical analysis. The model is shown in Fig. 5(a). The solid line represents the concentration obtained from the approximate Eqs. (3) and (4).

Regarding the contact between the a-Li3PO4 film and LiClO4/PC electrolyte, meniscus height can be estimated by the following equation [25]:

h¼

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2γ ð1− sinθE Þ ρg

ð2Þ

where h is the meniscus height, γ is the surface tension, θE is the contact angle, ρ is the density of the electrolyte, and g is the gravitational acceleration. The contact angle was measured to be 66°. The density of the electrolyte was 1.3 g/cm3. The surface tension of the electrolyte was 44 mN/m [26]. Thus, the meniscus height was calculated to be 0.77 mm. When the meniscus height and the border is compared, the boundary region between 6Li and 7Li (~10 μm) was much narrower than the meniscus height. Thus, in the present experiment, the ion exchange can be completed up to the upper limit of the meniscus. Compared with the depth analysis, the present SIMS line analysis has the advantage to avoid problems known as knock-on effect and sample

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charging in SIMS measurements. The knock-on effect is a mixing of atoms due to the sputtering process, which usually distorts the shape of the SIMS depth profile. Sample charging also distorts the depth profile, owing to the migration of mobile ions promoted by the electric field. The SIMS line profile is not influenced by these effects because there is no concentration gradient in depth of the sample. Therefore, it is possible to measure accurate isotope profiles and diffusion coefficients. In the case of the mask method, the fitting equation needs to be modified because the film thickness is different across the boundary line. To find an approximate expression, we performed a numerical analysis of the diffusion equation. An explicit finite-difference method was employed for the numerical analysis by using MATLAB R2015b. The model for the calculation is shown in Fig. 5(a), where the thicknesses of the 6Li3PO4 and 7Li3PO4 films were both equal to 500 nm, and the lateral length was 20,000 nm. Discrete space and time was necessary for the calculation; the thickness step was 70 nm, the lateral step was 200 nm, and the time step was 10 s. The diffusion coefficient D⁎ was set to 10−12 cm2/s for the calculation. Fig. 5(b) – (d) shows the results of the numerical analysis. The 7Li concentration gradient decreased rapidly in the thickness direction. While a gradient along the thickness direction exists after 1000 s (Fig. 5(b)), it disappears after 3600 s, owing to lithium diffusion pffiffiffiffiffiffiffiffi (Fig. 5 (c)). This result is reasonable, as the diffusion length D t reaches 600 nm at t = 3600 s. The diffusion along the lateral direction progresses to 10 μm after 24 h, as shown in Fig. 5(d). After sufficient diffusion time (N24 h), the variation of the isotope profile in the lateral direction can be detected by the spatial resolution of the SIMS line analysis. Fig. 6 shows the surface 6Li concentration obtained from the numerical analysis. The diffusion length increased with the diffusion time. The maximum concentration was 1, whereas the minimum was 0.5. At the midpoint, the concentration was not exactly half, but one third of the difference. This was because the volume of the 7Li region was twice that of the 6Li region. The results can be approximately expressed by the following equations. If x b 0, cðx; t Þ−c0 1 ¼ 3 c1 −c0

   x ffi 1 þ erf pffiffiffiffiffiffiffi  2 D t

ð3Þ

Fig. 7. Surface 6Li concentration ratio measured by secondary ion mass spectroscopy line analysis. The diffusion couples were prepared by the mask method. The annealing temperatures and durations were (a) 25 °C for 792 h, (b) 60 °C for 165 h, (c) 100 °C for 96 h, and (d) 160 °C for 12 h. The solid line shows the fitting curve obtained by using Eqs. (5) and (6).

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the SIMS mapping, the relative isotope ratio is not affected by the edge effect. The temperature dependence of the diffusion coefficient in the Arrhenius plot in Fig. 8 exhibits a linear behavior. In the same plot, the diffusion coefficients obtained from the two different experiments, i.e., ion-exchange and mask methods, are shown. The activation energy Ea and pre-exponential factor D0 were calculated by using the Arrhenius equation:   Ea DLi ¼ D0 exp − kB T

Fig. 8. Arrhenius plot of the lithium diffusion coefficient DLi⁎ in a-Li3PO4 thin films.

   cðx; t Þ−c0 2 x 1 ffi − 1 þ erf pffiffiffiffiffiffiffi ¼ 3 3 c1 −c0 2 D t

ð4Þ

Fig. 6 shows the concentration gradient along the film, as calculated by using Eqs. (3) and (4). The results obtained from the numerical calculation and approximate expressions are in good agreement, validating Eqs. (3) and (4). When the diffusion length was small (3 and 7 days in Fig. 6), there was a deviation between numerical values and approximate expressions, as the concentrations over the surface and an average volume were different during the initial state. At larger diffusion length, the deviation became negligible, and the numerical values were well expressed by Eqs. (3) and (4). If the thicknesses of the 6Li and 7Li films are different, the equations can be modified by using the thickness ratio r = z2/z1, where z1 and z2 are the thicknesses of the 6Li and 7Li films, respectively. If x b 0,    x ffi 1 þ erf pffiffiffiffiffiffiffi 2 D t

ð5Þ

   x r ffi − 1 þ erf pffiffiffiffiffiffiffi  2þr 2 D t

ð6Þ

and if x ≥ 0, cðx; t Þ−c0 1 þ r ¼ 2þr c1 −c0

where kB is the Boltzmann constant and T is the absolute temperature. The activation energies for lithium diffusion were evaluated to be 0.58 eV (ion-exchange method) and 0.57 eV (mask method). The estimated parameters are summarized in Table 2. Fig. 9 shows the temperature dependence of the ionic conductivity, measured by impedance spectroscopy, of the a-6Li3PO4 thin film. The ionic conductivity at room temperature was 2.9 × 10−7 S cm−1. The temperature dependence was fitted by the Arrhenius equation:   Ea σT ¼ σ 0 exp − kB T

and if x ≥ 0,

cðx; t Þ−c0 1 ¼ 2þr c1 −c0

ð7Þ

Fitting of the experimental results was performed by using Eqs. (5) and (6). Fig. 7 shows the experimental results of the mask method. The 6Li and 7Li concentrations were obtained by the SIMS line measurements. The experimental results were well fitted by Eqs. (5) and (6). The estimated D⁎Li values are summarized in Table 1, and are in fairly good agreement with those obtained for the sample prepared by using the ion-exchange method. The facile sample preparation is the main advantage of the mask method, as no contact with the liquid electrolyte is required. This technique is suitable for samples that need high-temperature annealing for isotope exchange. Although the step at the boundary line may distort

ð8Þ

where Ea is the activation energy and σ0 is the pre-exponential factor. The activation energy was estimated to be 0.55 eV, and the preexponential factor was 2.0 × 105 S K cm−1. The present conductivity results agreed with previous experimental data obtained for amorphous lithium phosphate [8]. The relationship between ionic conductivity σ and conductivity diffusion coefficient Dσ is given by the Nernst-Einstein equation: Dσ ¼

kB T nðzeÞ2

σ

ð9Þ

where n is the concentration of mobile ions, z is the valence of the ions, and e is the elemental charge. The lithium concentration (in cm−3) can be calculated from the density and composition of the thin film. We used the density of 2.45 g/cm3 from crystalline γ-Li3PO4. The composition of the a-Li3PO4 film prepared by PLD slightly changed from the stoichiometric composition. The Li/P ratio was 2.9 for the aLi3PO4 thin film [8]. Considering these parameters, n was calculated as 3.73 × 1022 cm−3. Fig. 10 shows the Dσ temperature dependence calculated from Eq. (9), along with the DLi⁎ dependence. A considerable difference is observed between Dσ and DLi⁎, as Dσ is greater than DLi⁎ over the entire temperature range. The activation energy of Dσ was 0.55 eV, which was the same as that obtained from σT. Notably, D⁎Li and Dσ are related by the Haven ratio as follows: HR ≡

DLi : Dσ

ð10Þ

The Haven ratio, HR, is a correction factor of the Nernst-Einstein equation, caused by the correlated charge transport. When HR = 1, individual independent charge transport can be assumed. Besides, HR is known to be b 1 in most of fast ionic conductor glasses [27–29]. Fig. 11 shows the temperature dependence of HR of the a-Li3PO4 thin films. HR was 0.55 ± 0.20 in the temperature range of 25–160 °C. The small

Table 2 Arrhenius parameters obtained by diffusion coefficients and ionic conductivity measurements. Sample

Method

Temperature range (K)

Ea (eV)

D0 (cm2/s)

σ0 (S K cm−1)

a-Li3PO4 a-Li3PO4 a-6Li3PO4

Ion-exchange Mask Conductivity

298–433 298–433 298–413

0.58 0.57 0.55

3.6 × 10−3 3.5 × 10−3 2.9 × 10−3

– – 2.0 × 105

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Fig. 9. Temperature dependence of the ionic conductivity σLi+ in a-Li3PO4 thin films.

value of HR (b1) indicated the correlative motion of Li+ ions in the aLi3PO4 thin film. Furthermore, HR can be also experessed from a microscopic standpoint derived from the Kubo-Green formula as follows [30,31]: X 1 1 ¼1þ HR N

j≠k

Δr j  Δr k

Δr 2

ð11Þ

where N is the total number of mobile ions, 〈Δr2〉 is the mean-square displacement of ions, and 〈Δrj ⋅ Δrk〉 is the average cross-correlation term of different ions [30]. The tracer diffusion coefficient is determined by the mean-square displacement, while Dσ includes the cross correlation of different ions. If there is a positive cross correlation between the different mobile ions, e.g., an interstitialcy mechanism or “caterpillar mechanism” [32], HR will be smaller than 1. The many-body effects on ionic transport in glass are demonstrated in molecular dynamics simulations on alkali silicate glasses as “co-operative jumps” [33]. The dependences of HR on the alkali content for different oxide glasses were reported for Na+, K+, and Rb+ containing glasses [27]. At low mobile ion concentrations, HR was almost 1; however, it decreased to 0.2–0.5 as the alkali content increased, and reached a nearly constant value independent of the concentration. A similar dependence was found in Ag+ ion conducting chalcogenide glasses [29]. The low values of HR at high mobile ion concentrations are caused by a strongly correlated motion of the mobile ions in the glass network.

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Fig. 11. Haven ratio, HR, as a function of the temperature.

Although there are very few data on the HR composition dependence of Li+ ion conductors, HR has been reported for lithium silicate and lithium aluminosilicate glasses; HR values of 0.50 for LiAlSi2O6 [4], 0.27 for Li2Si3O7, and 0.17 for Li2Si6O13 glasses [5] were reported. In the present study, the lithium atomic ratio of the a-Li3PO4 thin film was 37.5%, which was considerably larger than the alkali content in conventional oxide glasses; then, a large correlation between Li+ ions and small HR value was expected. However, the HR value of the a-Li3PO4 was 0.55 ± 0.20, which was slightly higher than that of other alkali-rich glasses [27]. A possible reason for the higher HR value may be the large experimental error in estimating HR. The present HR value may be considered as having the same trend observed for other alkali oxide glasses. The possible reason for the experimental error is as follows. One reason is the variation of temperature, which gives large difference in the conductivity and diffusion coefficient. For instance, ±1 °C error in the temperature gives ±12% error in the conductivity and diffusion coefficient at 40 °C. Another reason is thermal history of the sample. The conductivity of the glassy ionic conductor is influenced by the annealing procedure [34]. Thus, the long annealing duration may cause the difference in the conductivity and diffusion coefficient. Another possibility for the higher HR value is the difference in glass structure, where 4− isolated PO3− 4 and P2O7 units exist in the a-Li3PO4 film [8]. The migration paths of the Li+ ions in the isolated phosphate glass are not limited, as in the case of the chain-like network former. The open path for Li+ migration may decrease the many-particle effects, resulting in the slightly higher HR value. The present study has demonstrated that DLi⁎ in thin-film lithium conductors can be measured by SIMS experiments. The ionexchange method with SIMS line analysis is suitable to measure large diffusion coefficients with values exceeding 10− 11 cm2/s. By contrast, the SIMS depth analysis is valid if the diffusion coefficient is lower than 10− 12 cm2/s until 10− 18 cm2/s [17,18]. The combination of these techniques enables us to measure a wide range of diffusion coefficients in lithium conductors. 4. Conclusions

Fig. 10. Comparison between lithium diffusion coefficients, determined by secondary ion mass spectroscopy experiments, and conductivity diffusion coefficient.

The lithium diffusion coefficients in a-Li3PO4 thin films were measured by SIMS for 6Li/7Li diffusion couples prepared by ion-exchange and mask methods. The isotope profiles were analyzed by the diffusion equation to evaluate DLi⁎. Numerical calculations showed the time evolution of the isotope profile, from which the analytical expression for the mask method was obtained. The diffusion coefficient of a-Li3PO4 films was 6.0 × 10−13 cm2/s at 25 °C, and the activation energy was 0.58 eV as estimated by using the ion-exchange method. Furthermore, HR, calculated from the ionic conductivity and diffusion coefficient, was

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