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Abstract
Compared with ordinary uniform lenses, the length and refractive index distribution of gradient refractive index (GRIN) lenses can effectively correct aberration and chromatic aberration. This advantage makes the miniaturization, integration, and lens lightweight possible. Although the visible GRIN lenses based on silicate glass are widely used, the infrared GRIN lenses based on chalcogenide glass are still elusive. This paper introduces a new method for preparing this kind of lens by hot pressing sintering diffusion of chalcogenide glasses. A series of chalcogenide glasses Ge10As22Se68-xSx (x = 4, 7, 10, 14, 24, 28, 34 mol%) with refractive index range from 2.37 to 2.57 (n@8 µm) and similar glass transition temperature (ΔTg < 10℃) were prepared by melt quenching. The relationship between Raman peaks and the refractive index of glasses was studied. Furthermore, the refractive index profile formed by elemental diffusion was characterized by Raman signals. The results show that the diffusion length reaches more than 290 µm, and larger diffusion distances can be achieved by stacking multiple layers. The obtained GRIN glass maintains good transmittance in the whole atmospheric window of 2 ∼ 12 µm.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In order to reduce optical aberration, traditional optical imaging systems, especially multi-light fusion systems, need expensive nonplanar lenses and complex lenses components, which are difficult to miniaturize and lightweight [1]. The appearance of GRIN materials provides a new idea for optical engineering design, using the refractive index change to correct the aberration. In recent years, the development of gradient index optics fully shows that an axial gradient index plate can be equivalent to multiple uniform dielectric plates with different refractive indexes. An axial gradient index spherical lens can be equivalent to the aspherical lens of an ordinary lens in correcting aberration [2]. Moreover, the GRIN optical elements have the characteristics of a large numerical aperture and short focal length, which can significantly reduce the volume and weight of the optical system [3–5]. The GRIN optics have matured in ray tracing, aberration theory, and lens design, but the preparation technology of the infrared GRIN lens is far from mature.
Over the past decade, much attention has been paid to the research of GRIN materials applied to mid-infrared (MIR) bands. The manufacture of MIR GRIN material by technologies such as stacking-diffusion [2,6], ionic exchange [7], electrospray printing [8], crystallization [9], and laser-induced vitrification [10] has been studied. The ion exchange process in chalcogenide glasses (ChGs) is rarely studied for chalcogenide glasses due to the covalent network structure, low glass transition temperature (Tg), and reaction with nitrates. Electrospray printing, crystallization, and laser-induced vitrification have obtained graded refractive index profiles, but they have limitations in fabricating large aperture imaging lenses. The U.S. Naval Research Laboratory prepared MIR GRIN materials through the ChGs sheets stacking-diffusion method. Firstly, 24 kinds of homogeneous glass materials with different components are optimized and developed, and then the refractive index is close to the gradient through long-time thermal diffusion. The glass composition and experimental details were not disclosed. Although the surface of the glass sheet has been polished, it is still impossible to completely fit between the two glass sheets, which seriously affects the progress of diffusion. We use the principle of hot-pressing sintering of powder to promote the sintering between glass sheets through pressure. In the initial stage of hot pressing, the sintering process is the main process, and after the glass is bonded into one, the diffusion process is the main process. The elements in the glass gradually diffuse from the high concentration end to the low concentration end, resulting in a gradient in the refractive index.
The characterization of the refractive index of GRIN materials is of great significance, especially for the long-wave infrared high-refractive-index materials. Traditional methods rely on index matching liquids, which are not available for indexes as high as those found in the chalcogenide glasses (2.4 ∼ 3.2) [11]. Raman spectra contain sharp, molecular-like features associated with local structural elements of the materials [12], which can qualitatively reflect the content of diffusion ions in a location. Therefore, the distribution of Raman peak intensity in spatial is used as an index of diffusion ion concentration, which is related to the spatial change of the refractive index.
Herein, the preparation and characterization of the MIR GRIN glasses by hot-pressing sintering and thermal diffusion method were reported. Firstly, the glass plates were sintered together under high temperature and pressure and then heated and diffused to form GRIN glass. The spatial distribution of the refractive index was characterized by Raman spectra. Moreover, the relationship between element concentration and diffusion coefficient has been discussed.
2. Experiment
2.1 Glass preparation
According to the preparation scheme, the hot pressing process will exert pressure on the glass, so it is necessary to ensure that these ChGs have similar Tg [12], which can ensure that the softening temperature of these glasses is close and avoid damage. Generally, Tg for the glasses possessing the same network connectivity is expected to scale with chemical bond strength. Therefore, Ge-As-S glass should have a higher Tg than Ge-As-Se. However, the relatively narrower glass forming region in Ge-As-S glasses compared with Ge-As-Se glasses shows that the network connectivity in Ge-As-S glasses is worse. Therefore, the lower connectivity of S-based glass will reduce the change in Tg. We chose the Ge-As-Se system and used the element substitution method to keep the mean coordination number of ChGs unchanged [13,14]. Using S instead of Se in Ge-As-Se to form the Ge-As-Se-S quaternary glass system [15]. Then Ge10As22Se68-xSx (x = 4, 7, 10, 14, 24, 28, 34 mol%) can be prepared to meet the requirements [16].
The ChGs were synthesized by the melt-quenching method. High purity starting elements of Ge (5N), As (5N), Se (6N), and S (5N) were weighed and introduced into a quartz ampoule. This ampoule was evacuated to 10−5 Pa, sealed, and heated up in a rocking furnace for 12 h at 800°C. The melt was quenched in water at room temperature. The sample was finally annealed below the Tg for 5 h. Glass samples were then cut and polished for subsequent measurements.
2.2 Hot pressing and heat treatment
The glass sheets were washed with ethanol in an ultrasonic cleaning machine for 20 min, dried, and put into the hot-pressing device, as shown in Fig. 1(a). The glass sheets are generally stacked according to the refractive index from small to large, and the thickness of each glass sheet is 2 mm. As the temperature rose near the softening point, a pressure of 30 MPa was applied to the mold to bond the glass sheets together. Moreover, The softening point is the starting point of the gravitational deformation temperature [17]. In order to prevent damage to the glass, pressure can be applied to the glass after the temperature is higher than the softening point. Then turn off the heating and cooling naturally to room temperature.
Fig. 1. (a) Schematic diagram of the hot-pressing mold. (b) the glass after hot pressing. (c) the glass after heating treatment (the colours represent different refractive indexes at the same wavelength).
The heat treatment process is carried out in the hot-pressing device with pressure is about 10 MPa. After hot pressing and diffusion, the schematic diagrams are shown in Fig. 1(b) and Fig. 1(c). The samples were polished for subsequent measurements.
2.3 Characterization
According to Archimedes’ principle, the density of samples was measured at 20°C in absolute ethanol. Vickers hardness (Hv) was tested on a digital microhardness apparatus (hengyi MH-3). Transmission spectra in the range of 400 ∼ 2500 nm and 2.5 ∼ 20 µm were recorded using a Perkin Elmer Lambda UV-VIS-NIR spectrophotometer and Fourier-transform infrared spectrometer, respectively. The Tg was measured using DSC (TA Q2000) at a heating rate of 10 °C/min with a temperature accuracy of ±1°C. The refractive index of glasses was measured by infrared ellipsometer from 1.7 µm to 15 µm (J.A. Woollam IR-Vase II). Raman spectroscopy was recorded by a confocal micro-Raman spectrometer (Renishaw RM-1000) with a 785 nm LD laser as an excitation source. And the resolution of the spectrometer was about 1 cm−1. All measurements were conducted at room temperature.
3. Results and discussion
3.1 Characterization of glass properties
The series of glasses have high transmittance in both near-infrared and MIR bands, and the highest transmittance is governed by Fresnel reflection law, as shown in Fig. 2(a) and (b). Ge10As22Se68-xSx (x = 4, 7, 10, 14, 24, 28, 34 mol%) samples with the increase of S content from 4 mol% to 34 mol%, and the content of Se decreases accordingly. The short-wave cut-off wavelength blue-shifted from 701 nm to 662 nm. Generally, the short-wave absorption edge of amorphous materials is caused by the excitation of electrons from the upper edge of the valence band to the lower edge of the conduction band, that is, the value of bandgap (Eg) determines the short-wavelength cut-off edge of the glass [18]. The Eg of glass depends on the average electron affinity of anions, the average bond energy, and the average polarization energy of ions [19]. Moreover, S-rich glasses will have high bond energies (200 kJ/mol) [20] and electron affinity, consequently high Eg values. Meanwhile, long-wavelength absorption edges of these samples shift continuously to shorter wavelengths with increasing S content, and some absorption bands in the MIR region are shown in Fig. 2(b). The prominent absorption peak can be attributed to S-H, H2O, OH- and As-O covalent bonds [21].
Fig. 2. (a) Vis-NIR and (b) MIR transmission of the seven glass samples (the thickness is 2 mm). The inset in (a) is an enlarged view of the absorption edge. (c) Density and the average atomic weight of the series of glasses. (d) DSC curve of Ge10As22Se(68-x)Sx series glass
The average atomic weight of each ChG was calculated according to their respective chemical composition, which is shown in Fig. 2(c). Since the relative atomic mass of S (32.06) is less than that of Se (78.96), the average atomic weight of simples must decrease in replacing S with Se. The change of density is positively correlated with the average atomic weight, so it can be inferred that the change of density will bring about the refractive index change.
Figure 2(d) shows the DSC curves of all measured ChGs samples, and the data is in Table 1. We found that Tg fluctuated around 170°C without evident composition dependence, indicating that only using S to replace Se element in the Ge10As22Se68 system will not affect the Tg. It has been well known that the value of Tg closely correlates with the connectivity [22,23] and rigidity [24] of the glass network. It explains that a gradual replacement element scheme can ensure the stability of glass network connectivity and rigidity. Furthermore, the Vickers hardness is almost insensitive under this change, as listed in Table 1 [22].
Table 1. Compositions average atomic weight, density, Vickers hardness, Tg, and Specific wavelength refractive index (n) of Ge10As22Se68−xSx glasses
The infrared refractive index curves of glasses were shown in Fig. 3. The values of refractive index at different wavelengths were listed in Table 1. With the increase of S content, the refractive index decreases gradually. Furthermore, each curve is approximately parallel in the range of 3 ∼ 10 µm, making the difference in the refractive index of the series of glasses constant under the different wavelengths. So that the gradient index glasses prepared later have the same applicability to different bands of light.
Figure 4(a) shows the normalized Raman spectra of the series glasses. All samples were tested in the same batch, and the laser power was 0.5 W. The measured Raman spectra are consistent with those of glass in the similar Ge-As-Se-S system reported by Wang et al. [15]. Since the coordination number of Ge, As, and Se(S) is 4, 3, and 2, respectively [13], the Ge10As22Se68 glass is rich in 15% Se, so the Ge-Ge and As-As bonds can be negligible in the glasses. The sharp peak at 200 cm-1 comes from the vibrations in corner-sharing GeSe4/2 tetrahedra [25,26], and the intensity of this peak decreases with the increase of S content in samples. The band at 342 cm-1 and 365 cm-1 are due to the symmetrical stretching and asymmetric stretching vibration of GeS4/2 [27]. The two characteristic peaks are superimposed, showing an apparent peak position of 350 cm-1 in the Raman spectrum. The intensity of this peak can be used to characterize the S content in the series of glasses. Moreover, the shoulder at 372 cm-1 produced by the vibration of two edge-shared tetrahedra is called the companion band [28]. Two patterns at 225 cm-1and 243 cm-1 are assigned to the AsSe3/2 pyramidal unit. The 250 cm-1 peak is characteristic of Se-rings and the 230 cm-1 peak of Se chains [29]. The Raman peak at 250 cm-1 shifts to 260 cm-1 because with the decrease of Se content, the Seµ long-chain gradually changes to the shorter and stable Se8 chain [30].
Fig. 4. (a) Normalized Raman spectrum of glasses (blue line marks the characteristic peak of 350 cm-1). (b) The refractive index (n@4 µm, 6 µm and 8 µm) and S content as a function of Raman intensity at 350 cm-1.
We choose the characteristic peak at 350 cm-1 to approximately represent the content of S element in glasses. Figure 4(b) shows the refractive index (n@4 µm, 6 µm and 8 µm) and S content as a function of Raman intensity at 350 cm-1. Although some data points are not precisely on the curve, this is due to ellipsometer test errors [31].
3.2 Characterization of samples after heating treatment
Two-layer samples were prepared to explore the thermal diffusion depth under different temperature and time conditions. The results shown in Fig. 5(a) were obtained by processing and Boltzmann fitting the Raman line scan data. The difference between the two inflection points of the curve whose differential is just 0 is defined as the diffusion distance. Moreover, experiments show that the extension of heat treatment time and temperature increase can improve the diffusion depth.
Fig. 5. (a) Concentration diffusion curve of the sample. (b) relationship between diffusion coefficient and S element concentration with different diffusing processes.
Fick's second law is used to predict the distribution of elements in the glass [6]:
and where J is the diffusion flux, D is the diffusivity, C is the concentration, x is the diffusion dimension, and t is time. By introducing Boltzmann Matano theory, a formula for calculating the concentration-dependent diffusion coefficient can be obtained to simplify the relationship [32]:We regarded the whole diffusion process as the diffusion of S element from one end to the other and established a semi-infinite diffusion couple model. The thickness of the sample is large enough relative to the diffusion distance and is in the stage of unsteady diffusion. Then the element content at different corresponding positions can be expressed as [33]:
where ${C_x}$ is the concentration at distance x from the surface, C0 is the original concentration, D is the diffusion coefficient, and t is the diffusion time. It can be concluded that the time required for diffusion is proportional to the square of the diffusion distance x, so to increase the diffusion depth by more than one order of magnitude, a diffusion time of two orders of magnitude is required.In order to improve the diffusion depth, we optimized parameters such as time and temperature (380°C-168 h) and finally obtained the diffusion depth up to 290 µm, as shown in Fig. 6. The line scan results of the left and right sides of the sample cross-section have a high degree of coincidence, which indicates that the sample uniformity is good. Furthermore, the refractive index profile was calculated according to the function in Fig. 4(b).
Fig. 6. The Raman line scanning results after high-temperature diffusion and the refractive index results.
On this basis, deeper diffusion depths can be achieved by stacking of multiple glass sheets. As shown in Fig. 7(a), the gradient distance of the four-layer stacked sample can reach the millimeter level. In order to eliminate inter-layer mutations to achieve a linear gradient, it is necessary to optimize the experimental parameters, especially the thickness of each layer of glass. Therefore, when the thickness of the glass sheet is equal to or less than the diffusion depth, it can obtain a sample with a linear distribution of refractive index with a thickness of more than 1000 µm. Figure 7(b) shows the transmission spectra of the glass samples under different heat treatment times. These samples maintained good IR transmittance after hot pressing and heat treatment.
Fig. 7. (a) Raman scanning results of multi-layer stacking glasses after diffusion, (b) Mid-infrared transmission spectrum of glasses (with different components undergoing different heat treatment times, the thickness of samples is 7 mm).
4. Conclusion
In summary, a series of Ge10As22Se68-xSx glasses with a refractive index span of 0.2 and a substantially unchanged Tg was prepared by gradually replacing Se with S in the Ge-As-Se system. The refractive index distribution of high-refractive-index chalcogenide glass in the micro-region was characterized by normalized Raman characteristic peak intensity. The calculated results of diffusion coefficients show that a higher diffusion temperature and longer diffusion time can effectively increase the diffusion depth. By optimizing the process, the maximum diffusion depth between the two pieces of glass reaches 290 µm within an acceptable time. Furthermore, through multi-layer stacking, a millimeter-level gradient diffusion was achieved. This method has strong universality and can be used to prepare GRIN glass with other systems.
Funding
National Natural Science Foundation of China (61975086, U21A2056); the Key Research and Development Program of Zhejiang Province (2021C01025); the Fundamental Research Funds for the Provincial Universities of Zhejiang (SJLY2022004); K. C. Wong Magna Fund at Ningbo University.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper may be available from the corresponding author upon reasonable request.
References
1. M. Kang, L. Sisken, C. Lonergan, A. Buff, A. Yadav, C. Goncalves, C. Blanco, P. Wachtel, J. D. Musgraves, A. V. Pogrebnyakov, E. Baleine, C. Rivero-Baleine, T. S. Mayer, C. G. Pantano, and K. A. Richardson, “Monolithic Chalcogenide Optical Nanocomposites Enable Infrared System Innovation: Gradient Refractive Index Optics,” Adv. Opt. Mater. 8(10), 2000150 (2020). [CrossRef]
2. D. Gibson, S. Bayya, V. Nguyen, J. Sanghera, M. Kotov, R. Miklos, and C. McClain, “IR-GRIN optics for imaging,” Proc. SPIE 9822, 98220R (2016). [CrossRef]
3. A. M. Boyd, “Optical design of athermal, multispectral, radial gradient-index lenses,” Opt. Eng. 57(08), 1 (2018). [CrossRef]
4. K. A. Richardson, M. Kang, L. Sisken, A. Yadav, S. Novak, A. Lepicard, I. Martin, H. Francois-Saint-Cyr, C. M. Schwarz, T. S. Mayer, C. Rivero-Baleine, A. J. Yee, and I. Mingareev, “Advances in infrared gradient refractive index (GRIN) materials: a review,” Opt. Eng. 59(11), 1 (2020). [CrossRef]
5. M. Li, R. Singh, M. S. Soares, C. Marques, B. Zhang, and S. Kumar, “Convex fiber-tapered seven core fiber-convex fiber (CTC) structure-based biosensor for creatinine detection in aquaculture,” Opt. Express 30(8), 13898–13914 (2022). [CrossRef]
6. D. Gibson, S. Bayya, V. Nguyen, J. Sanghera, M. Kotov, C. McClain, J. Deegan, G. Lindberg, B. Unger, and J. Vizgaitis, “IR GRIN optics: design and fabrication,” Proc. SPIE 10181, 101810B (2017). [CrossRef]
7. C. Fourmentin, X.-H. Zhang, E. Lavanant, T. Pain, M. Roze, Y. Guimond, F. Gouttefangeas, and L. Calvez, “IR GRIN lenses prepared by ionic exchange in chalcohalide glasses,” Sci. Rep. 11(1), 11081 (2021). [CrossRef]
8. S. Novak, P. T. Lin, C. Li, C. Lumdee, J. Hu, A. Agarwal, P. G. Kik, W. Deng, and K. Richardson, “Direct Electrospray Printing of Gradient Refractive Index Chalcogenide Glass Films,” ACS Appl. Mater. Interfaces 9(32), 26990–26995 (2017). [CrossRef]
9. E. Lavanant, L. Calvez, F. Chevire, M. Roze, T. Hingant, R. Proux, Y. Guimond, and X. H. Zhang, “Radial gradient refractive index (GRIN) infrared lens based on spatially resolved crystallization of chalcogenide glass,” Opt. Mater. Express 10(4), 860–867 (2020). [CrossRef]
10. M. Kang, L. Sisken, J. Cook, C. Blanco, M. C. Richardson, I. Mingareev, and K. Richardson, “Refractive index patterning of infrared glass ceramics through laser-induced vitrification Invited,” Opt. Mater. Express 8(9), 2722–2733 (2018). [CrossRef]
11. G. P. Lindberg, R. H. Berg, J. Deegan, R. Benson, P. S. Salvaggio, N. Gross, B. A. Weinstein, D. Gibson, S. Bayya, J. Sanghera, V. Nguyen, and M. Kotov, “Raman and CT scan mapping of chalcogenide glass diffusion generated gradient index profiles,” Proc. SPIE 9822, 98220W (2016). [CrossRef]
12. D. Gibson, S. Bayya, J. Sanghera, V. Nguyen, D. Scribner, V. Maksimovic, J. Gill, A. Yi, J. Deegan, and B. Unger, “Layered chalcogenide glass structures for IR lenses,” Proc. SPIE 9070, 90702I (2014). [CrossRef]
13. R. P. Wang, D. Y. Choi, A. V. Rode, S. J. Madden, and B. Luther-Davies, “Rebonding of Se to As and Ge in Ge33As12Se55 films upon thermal annealing: Evidence from x-ray photoelectron spectra investigations,” J. Appl. Phys. (Melville, NY, U. S.) 101(11), 113517 (2007). [CrossRef]
14. Y. Yang, B. Zhang, A. Yang, Z. Yang, and P. Lucas, “Structural Origin of Fragility in Ge-As-S Glasses Investigated by Calorimetry and Raman Spectroscopy,” J. Phys. Chem. B 119(15), 5096–5101 (2015). [CrossRef]
15. R. Wang, K. Yan, Z. Yang, and B. Luther-Davies, “Structural and physical properties of Ge11.5As24S64.5·xSe64.5·(1−x) glasses,” J. Non-Cryst. Solids 427, 16–19 (2015). [CrossRef]
16. P. Toupin, L. Brilland, J. Troles, and J.-L. Adam, “Small core Ge-As-Se microstructured optical fiber with single-mode propagation and low optical losses,” Opt. Mater. Express 2(10), 1359–1366 (2012). [CrossRef]
17. N. Yin, J. Xu, F. e. Chang, Z. Jian, and C. Gao, “Effect of Te proportion on the properties of Ge25Sb10Se65-xTex chalcogenide glasses,” Infrared Phys. Technol. 96, 361–365 (2019). [CrossRef]
18. S. Ding, S. Dai, Z. Cao, C. Liu, and J. Wu, “Composition dependence of the physical and acousto-optic properties of transparent Ge-As-S chalcogenide glasses,” Opt. Mater. (Amsterdam, Neth.) 108, 110175 (2020). [CrossRef]
19. Z. Yang, L. Luo, and W. Chen, “Red Color GeSe2-Based Chalcohalide Glasses for Infrared Optics,” J. Am. Ceram Soc. 89(7), 2327–2329 (2006). [CrossRef]
20. Y. Yang, Z. Yang, P. Lucas, Y. Wang, Z. Yang, A. Yang, B. Zhang, and H. Tao, “Composition dependence of physical and optical properties in Ge-As-S chalcogenide glasses,” J. Non-Cryst. Solids 440, 38–42 (2016). [CrossRef]
21. V. Shiryaev and M. Churbanov, Preparation of high-purity chalcogenide glasses, Chalcogenide Glasses (2014), Chap.1.
22. M. Micoulaut and G. G. Naumis, “Glass transition temperature variation, cross-linking and structure in network glasses: A stochastic approach,” Europhys. Lett. 47(5), 568–574 (1999). [CrossRef]
23. R. P. Wang, C. J. Zha, A. V. Rode, S. J. Madden, and B. Luther-Davies, “Thermal characterization of Ge-As-Se glasses by differential scanning calorimetry,” J. Mater. Sci.: Mater. Electron. 18(S1), 419–422 (2007). [CrossRef]
24. P. Boolchand, D. G. Georgiev, T. Qu, F. Wang, L. C. Cai, and S. Chakravarty, “Nanoscale phase separation effects near r= 2.4 and 2.67, and rigidity transitions in chalcogenide glasses,” Comptes Rendus Chimie 5(11), 713–724 (2002). [CrossRef]
25. K. Jackson, A. Briley, S. Grossman, D. V. Porezag, and M. R. Pederson, “Raman-active modes of a-GeSe2 and a-GeS2: A first-principles study,” Phys. Rev. B 60(22), R14985 (1999). [CrossRef]
26. P. Tronc, M. Bensoussan, A. Brenac, and C. Sebenne, “Optical-Absorption Edge and Raman Scattering in GexSe1-x Glasses,” Phys. Rev. B 8(12), 5947–5956 (1973). [CrossRef]
27. E. I. Kamitsos, J. A. Kapoutsis, G. D. Chryssikos, G. Taillades, A. Pradel, and M. Ribes, “Structure and Optical Conductivity of Silver Thiogermanate Glasses,” J. Solid State Chem. 112(2), 255–261 (1994). [CrossRef]
28. B. G. Aitken and C. W. Ponader, “Physical properties and Raman spectroscopy of GeAs sulphide glasses,” J. Non-Cryst. Solids 256-257, 143–148 (1999). [CrossRef]
29. R. P. Wang, A. Smith, A. Prasad, D. Y. Choi, and B. Luther-Davies, “Raman spectra of GexAsySe1−x−y glasses,” J. Appl. Phys. (Melville, NY, U. S.) 106(4), 043520 (2009). [CrossRef]
30. W. H. Wei, R.-P. Wang, X. Shen, L. Fang, and B. Luther-Davies, “Correlation between Structural and Physical Properties in Ge-Sb-Se Glasses,” J. Phys. Chem. C 117(32), 16571–16576 (2013). [CrossRef]
31. Y. C. Liu, J. H. Hsieh, and S. K. Tung, “Extraction of optical constants of zinc oxide thin films by ellipsometry with various models,” Thin Solid Films 510(1-2), 32–38 (2006). [CrossRef]
32. P. J. Tumidajski, G. W. Chan, R. F. Feldman, and G. Strathdee, “A BOLTZMANN-MATANO ANALYSIS OF CHLORIDE DIFFUSION,” Cem. Concr. Res. 25(7), 1556–1566 (1995). [CrossRef]
33. J. T. Cahill, V. R. Vasquez, S. T. Misture, D. Edwards, and O. A. Graeve, “Effect of Current on Diffusivity in Metal Hexaborides: A Spark Plasma Sintering Study,” ACS Appl. Mater. Interfaces 9(42), 37357–37363 (2017). [CrossRef]
