Alkali ion diffusion and structure of chemically strengthened TiO 2 doped soda-lime silicate glass

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Introduction
The industrial transition towards sustainable development requires more efficient processes and ways to use our resources better [1].Glass is used in a wide variety of applications in our society that calls for improved properties [2,3], such as thin glass which is widely used as cover glass in electronic handheld devices [4,5].Other large scale applications, are architectural [6,7], automotive [8] and solar energy [9] glass which are produced in billions of square meter per annum [10].Therefore, making glass thinner and stronger could aid to reduce its environmental footprint by using less raw materials and consuming less energy for melting, and also increase its life-span.
Chemical strengthening (CS) is frequently used to strengthen thin glasses.CS of glass is based on ion exchange of larger ions from a molten salt into glass.Both the ion and counter ion are conventionally monovalent alkali ions.Larger ions typically penetrate a few tenths of micrometers into the glass surface.CS of glasses has recently been reviewed by several authors [11][12][13][14][15]. Three distinct CS processes can be identified: (i) ion exchange and ion diffusion, (ii) build-up of compressive stresses, and (iii) relaxation of stresses.These processes are not necessarily directly linked to each other.The CS process was first discovered by Kistler [16] and Acloque and Tochon [17].Although the CS process has been investigated for about 60 years, it is still not fully understood [18].The current understanding of CS is excellently described in recent literature [19,20].A typical well-performing composition for CS is achieved using alkali aluminosilicate (ALS) glass [14,15] with Al(IV) charge-balancing the non-bridging oxygens.Al 2 O 3 , as a component in glass, is an intermediate glass-former that increases the melting temperature and the viscosity [21].Thus, it requires high energy to melt.It is therefore relevant to look for alternative glass components for chemical strengthening, e.g., B 2 O 3 [22], P 2 O 5 [23] or ZrO 2 [24].Soda-lime silicate (SLS) glasses, from which the vast majority (about 90 %) of the glass produced today is derived, are generally poor candidates for CS in comparison to the ALS glass [25].However, the SLS glass is developed with the main purpose to be cost-effective [26].Therefore, it is interesting to investigate how to improve the SLS glass with respect to chemical strengthening [27].CS of SLS glass has been recently studied [28][29][30].A recent study of the simulation of stress relaxation of glasses has revealed that SLS is subject to significantly more relaxation than ALS glass [19].
TiO 2 is a widely used intermediate glass former due to its favourable optical properties [31].It has recently received attention for its mechanical, thermal and structural effects on glass [32][33][34][35][36].In addition, TiO 2 is frequently used as a nucleation agent [37] to make transparent glass-ceramics [38].It is also used for shifting the UV absorption edge [31], which can be of particular importance in low iron-containing glasses, e.g., for transparent glass containers [39], or glass for photovoltaics [40].Although it is widely used in the glass industry, the effect of TiO 2 on CS has not been scientifically investigated.It is known from previous studies that TiO 2 has a slightly reducing effect on the viscosity and melting temperature [41,42].Hence, it can reduce energy consumption in glass production [43].
In the present paper, we investigate the ion exchange kinetics using X-ray Photoelectron Spectroscopy (XPS), the structural properties by Raman Spectroscopy, and the optical properties by means of spectrophotometric analysis of K + ion-exchanged TiO 2 -doped SLS glasses.In a relating paper are the indentation surface mechanical properties studied [44].

Glass preparation and ion exchange treatment
SLS glasses with different additions of TiO 2 were synthesized.The glass compositions investigated in the present study are presented in Table 1.The glass melting procedure and the material properties have been presented elsewhere [31,32].The samples were cut into pieces of about 1 × 1 cm 2 and polished to approximately 1 mm thickness before being cut into five smaller pieces using a diamond cutter.
The ion exchange procedure was performed for 5 h at four different temperatures below T g (350, 400, 450 and 500 • C).In detail, the synthesis of the procedure was as follows.First, 5 g of KNO 3 (ACROS Organics 99% purity, melting point 334 • C [45]) was added to a small ceramic porcelain crucible with a bottom diameter of 3 cm, which was enough to keep the glasses fully immersed in the salt upon melting.The crucible with the salt was heated in a muffle furnace (Nabertherm P330).The furnace was programmed to reach the given temperature in 1 hour to avoid thermal shock.After reaching the given temperature, the glasses were immersed in the molten salt, and the temperature was held for 5 h.The crucible with the glass was removed from the furnace and was air-cooled for 10 min.The crucible was quenched to room temperature by adding deionized water.The glass samples were cleaned with deionized water and ethanol, and the side exposed to the melt was marked with a marker.

X-ray photoelectron spectroscopy
The following three samples were prepared and analyzed by X-ray Photoelectron Spectroscopy (XPS): (1) SLS, (2) 4.7% TiO 2, and (3) 9.9% TiO 2 (see Table 1).Before XPS measurements, the samples were wetetched using hydrofluoric (HF) acid to produce samples with six different etching depths.The procedure was conducted in the following manner: The glass samples were cleaned in a detergent solution: H 2 O (100%) / H 3 PO 3 (99%) / CH 3 COOH (≥ 99%) / HNO 3 ≥ 65%) with the relative proportions: 700/800/50/50 mL for 10 min.To ensure high cleanliness of the glass samples, a Tepla 300 plasma stripper was used to remove remaining organic residues on the glass surface for 20 min.The edges of the glass samples in direct contact with the molten salt in the ion exchange process were masked with a cathode tape.A 1 µm thick Mo hard mask was deposited using a von-Ardenne CS 730 S magnetron sputter on the masked sample.The deposition was conducted at 1000 W with a deposition time of 4 min.The cathode tape was removed, and the glass samples were treated in 2 vol% HF for 10 min per etch depth.This was repeated six times.After the treatment, the samples were rinsed with deionized water to remove the acid.The etch depths were measured with a Bruker DektakXT surface profilometer.
The XPS measurements were performed using a Phi Quantera II spectrometer.A monochromated Al Kα X-ray source was used with a photon energy of 1486.6 eV and a focus at a 45 • angle relative to the samples.Pass energies of 224 eV and 55 eV with a step resolution of 0.5 eV and 0.2 eV were used for the survey and the high-resolution spectra, respectively.Before each measurement, the samples were sputtered with an argon ion gun for 2 min with an acceleration voltage of 4 kV.A flood gun with an emission current of 500 µA was used to neutralize the samples.Since no adventitious carbon could be detected in some measurements, the argon peaks resulting from the sputtering were used to calibrate the binding energies.The XPS measurements were used to obtain chemical profiles of the glass samples, and served as raw data for calculating the alkali ion diffusion coefficients and the activation energy for diffusion.The atomic concentration of species x, C x , was calculated according to where S i (S x ) represents the sensitivity factor of element i (x).n is the number of atoms per cm 3 of the material, and I is the intensity, i.e., the number of counts per second of a specific spectral peak.The accuracy of the determined elemental composition is estimated to be ± 2 at.%, similar to the estimation of Pintori and Cattaruzza [46].The alkali ion diffusion coefficient D K− Na (cm 2 s − 1 ) was calculated using lC(x, t) = C s erfc where C(x, t) is the concentration, x is the depth, t is the time, and C s is the surface concentration of either K or Na.The concentration profiles provided by the XPS analysis (q.v.Eq. 1) were used to calculate the alkali diffusion coefficient D K− Na .For the complementary error function solution, a plot of the inverse error function of 1 − (C(x, t)/C s ) versus the depth x of six data points was shown to yield straight lines.From the slope, 1/2 ̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ̅ D K− Na t √ , the diffusion coefficient D K− Na was extracted.A linear regression curve was fitted to the data points to obtain the slopevalue and the error estimation.The activation energy for alkali ion diffusion was calculated from the Arrhenius equation, where D 0 is a temperature-independent pre-exponential constant, R is the universal gas constant (JK − 1 mol − 1 ), T is the temperature (K), and E a is the activation energy for alkali diffusion in the glass (J/mol).A plot of ln D K− Na versus 1000/T yields a straight line with slope E a /R and intersection point lnD 0 .

Raman spectroscopy
Confocal Raman spectroscopy was performed with a Renishaw in Via Raman spectrometer using a frequency doubled Nd: YAG laser 532 nm excitation source employing 50% laser power.The Raman scattered light was detected in the backscattering configuration employing linear polarization and 2400 lines/mm grating, and a 100x objective lens.Depth profile spectra were collected at six different depths of 0, 10, 20, 30, 40, and 50 µm for each glass sample, employing 12 scans with a 10 s exposure time for each scan.The actual "average" focus position of the laser was calculated based on the refractive index, numerical aperture, and origin of the Raman scattering, following the methodology of Everall [47], which is further explained in the supplementary materials and the Matlab code for the analysis has been published elsewhere [48].
The depth profile parameters for the different glass samples are shown in Table 2.

Spectrophotometry
Spectrophotometric measurements were conducted before and after K + /Na + ion-exchange treatmeatment for 5 h at 500 • C. Spectra were collected between 300 and 2500 nm using a Perkin Elmer Lamda900 instrumet with a spectral resolution of 5 nm.The absorption coefficient, α(λ), was calculated according to Hong's absorption equation [49], where d is the sample thickness, R(λ) is the reflectance and T(λ) the transmittance.The value of T(λ) was not instrument corrected but as the diffuse reflectance is low for glass we assume T(λ) ≈ T cor (λ).R(λ) was calculated according to the Fresnel equation for normal incidence, R = (    samples (n glass ) as given in [31].For the refractive index of air, n air = 1, was used.It was thus assumed that the reflectance R(λ) was the same for all wavelengths.

XPS depth profile measurements and ion exchange kinetics
Fig. 1 shows the ion exchange concentration profiles obtained from the XPS depth profile measurements at different treatment temperatures for the SLS, the 4.7 and 9.9% TiO 2 doped glasses.The data displays an exponentially decreasing K + /Na + concentration ratio as a function of depth.Furthermore, the K + /Na + concentration ratio increases as the temperature increases.Therefore, only the concentration changes of K + as a function of depth is displayed, but it follows from the ion-exchange process that a decrease in K + results in a directly proportional increase in the Na + concentration.From Fig. 1, it can be deduced that Na + is not completely exchanged at the surface except for the SLS treated at 450 and 500 • C and the 4.7 and 9.9% TiO 2 doped glass treated at 500 • C. Due to the relatively small diffusion depths obtained at the lowest treatment temperature for all samples (as well as the 400 • C treatment temperature for the 9.9% TiO 2 glass), only one data point with a non-zero concentration of K + was acquired (the surface concentration).These data points were therefore excluded from calculations of the diffusion coefficients.
Using Eq. 2, a plot of the inverse error function of 1 − (C(x, t) /C s ) versus the depth x for the XPS data shown in Fig. 1 was shown to be well fitted by straight lines, demonstrating Fickian diffusion.From the slopes of these curves, 1/2 ̅̅̅̅̅ Dt √ , D K− Na was extracted.Fig. 2 shows the Arrhenius plot, the activation energy and the D K− Na as a function of temperature for SLS, 4.7% and 9.9% TiO 2 doped SLS glasses.The value of D K− Na for the SLS glass, was found to be close to previously reported values in the literature, which shows that the methodology of extracting the alkali diffusion coefficient from depth-resolved XPS analysis is accurate [29,[50][51][52][53].As can be seen from Fig. 2c, a slight decrease of D K− Na is observed as the TiO 2 content is increased.This is also evidenced by the Arrhenius analysis in Fig. 2a, where an increase of the activation energy for diffusion, E A (as calculated using Eq.3), is seen to increase as a function of TiO 2 dopant concentration in the SLS glass, see Fig. 2c.

High-resolution XPS
Fig. 3a and b show the Ti 3+ /Ti 4+ ratio (left y-axis) and the Na + /K + concentration ratio (right y-axis) as a function of depth for the 4.7 and 9.9% TiO 2 glass at the four different treatment temperatures.The Ti 3+ / Ti 4+ ratio was obtained from the deconvolution of the high-resolution Ti peaks Fig. 3c and 3d display the total Ti 3+ concentration in at.% (left yaxis) and the Na + /K + concentration ratio (right y-axis) as a function of depth for the 4.7 and 9.9% TiO 2 glasses treated at the same four different temperatures.
The data reveals higher concentration of Ti 3+ for the 9.9% TiO 2 glass (~ 14% Ti 3+ /Ti 4+ ) compared to the 4.7% TiO 2 glass (~ 8%).It is noted that although the Ti 3+ /Ti 4+ ratio is significant in both glasses, the total Ti 3+ concentration is small, considering all glass components.No distinct colouration of the glasses can thus be expected due to the strong blue/violet colour of Ti 3+ , even at low concentrations.Significant  concentration of Ti 3+ is expected only at the surface and decreases rapidly within a few micrometers.This is roughly seen in Fig. 3, but a plateau-like region is also discerned close to the surface, which we associate with the retarded alkali diffusion in the TiO 2 modified glasses (q.v.Fig. 2) that pins the alkali to Ti-O groups in the glass.The results shown in Fig. 3 suggest that Ti 3+ species are associated with the retarded alkali diffusion and interact with the K + ions, possibly forming unsaturated Ti-O species.

Raman spectroscopy and structure of TiO 2 doped SLS glass
Raman spectra of the different ion exchange treatment temperatures measured at the surface for SLS, 4.7 and 9.9% TiO 2 glass samples are shown in Fig. 4. In general, Raman spectra of silicate glasses can be divided into three regions: (i) the low frequency region (10-200 cm − 1 ), originating from low-lying optical and high-lying acoustic modes, as well as vibrations emerging from cation movements relative to the silicate structure [54], (ii) the intermediate frequency region (300-800 cm − 1 ), revealing information about T-O-T rocking and bending modes (where T = Si, Ti) and structural characteristics of larger ring distributions, and (iii) the high-frequency region (800-1200 cm − 1 ), provides information about highly localized T-O-T and T-O − non-bridging oxygen stretching modes [55].Since the bands in the low-frequency region do not bear any structural information of the glass network, only the bands in the intermediate-and high-frequency regions were analyzed in this paper.The Raman spectrum of SLS glass was deconvoluted into twelve individual bands, see Fig. 4a.Two additional bands emerged at 898, and 991 cm − 1 for the 4.7 and 9.9% TiO 2 glasses, while the band at 612 cm − 1 concommitantly disappeared, see Fig. 4b and c.
For SLS glass, a broad asymmetric band can be seen at around 1106 cm − 1 in Fig. 4a, and its non-Gaussian shape suggests an overlap of more than one band.Therefore, the peak deconvolution procedure proposed by Mysen and Neuville [56] was adopted.The deconvolution was done by separating the broad 1100 cm − 1 band into three bands located at 1054, 1106 and 1145 cm − 1 .The idea that the 1145 cm − 1 shoulder shares the same origin with the 1106 cm − 1 band is supported by the previous study of Matson et al. [54], where alkali-silicate compositions (R 2 O-SiO 2 , where R=Li, Na, K, Rb or Cs) were investigated.The band at 1106 cm − 1 is widely accepted to originate from asymmetric stretching vibrations of Q 3 groups.Fig. 5 schematically illustrates the bridging oxygen (BO) and non-bridging oxygen (NBO) Si-O species designed Q 1 , Q 2 , Q 3 and Q 4 .Therefore, the shoulder at 1145 cm − 1 most likely corresponds to either the stretching vibrations, or a Q 3 band with a slightly shorter bond length than the main Q 3 band at 1106 cm − 1 .Matson et al. argued that if the shoulder corresponds to the stretching vibrations of Q groups, a direct correlation to the intensities of the 472 cm − 1 Q 4 band in the intermediate frequency region of the investigated alkali-silicate glasses should be observed, which was not the case.Instead, the intensity ratios were approximately equivalent for the two bands at and 1145 cm − 1 for the different TiO 2 glasses.Moreover, for alkali contents approaching the di-silicate composition (R 2 O-2SiO 2 ), the cm − 1 band appeared to merge with the 1106 cm − 1 band, which makes the assignment as another Q 3 band most likely.The 949 cm − 1 band appearing in the base silicate glass has been assigned to the Si -O − stretching vibrations in Q 2 units [56].

Temperature dependence
Three clear trends can be seen for the 574, 817 and 1106 cm − 1 bands in the Raman spectra of SLS glass (q.v., Fig. 4a).Since the bands in the high-frequency region originate from highly localized Si-O stretches within the silicate tetrahedra, a shift in band position signifies a change of the internal Si-O bond length.A shift towards higher wavenumbers (blue-shift) corresponds to a decrease of the internal Si-O bond length with the only exception for Q 4 units [57].The reduction of the internal Si-O bond length reveals the presence of compressive stresses in the glass generated from the ion-exchange process, i.e., from the CS process [58].The blue shift of 1106 cm − 1 band indicates the presence of increasing surface compressive stresses as the treatment temperature is increased.A distinct shift of the 817 cm − 1 band towards lower Raman shifts is also observed for the SLS.Similar shifts have been observed previously, both in ion-exchanged glasses [57,59,60] and in mixed-alkali glasses [60][61][62].However, the reason for this red-shift is not clear in the literature.We hypothesize that it could be an indication of differentiations in the O-Si-O − or O-Ti-O − bending vibration that are charge balanced with R (Na + or K + ) resulting from a higher degree of Na + being replaced by K + .
In the titano-silicate glasses, the most distinct changes are displayed by the 574 and 1106 cm − 1 bands.The 574 cm − 1 band shifts to lower wavelengths as the treatment temperature increases (see Fig. 6).In contrast, the 1106 cm − 1 band shifts to higher wavenumbers with increasing treatment temperature.When comparing the band shifts of the different titania-silicate glasses, a significant decrease in the relative band shifts is observed as SiO 2 is substituted for TiO 2 .As seen in Fig. 4c, the relative shifts are so small for the 9.9% TiO 2 glass, and they cannot be displayed satisfactorily in the offset plots.If we instead consider the band shift of the 574 cm − 1 bands, it is known that bands emerging in the intermediate frequency region are related to the Si-O-Si bond angle, where a shift towards lower wavenumbers is indicative of an increase of the angle.The results in Fig. 6 suggest an increased Si-O-Si bond angle as the treatment temperature is increased [57].
In the titania-silicate glasses shown in Fig. 4b and c, the mode due to the Q 2 stretching band is replaced by a new band emerging at around 991 cm − 1 , which has been assigned as Ti-O-Si asymmetric bridging oxygen vibrations [32].Furthermore, in the titania-silicate glasses, an additional high-intensity band appears at about 898 cm − 1 , whose origin is unclear.It was assigned to Ti-O, a bridging oxygen vibration by Mysen and Neuville [56], while Reynard and Webb [63] associated it with titanyl bonds (T=O) in TiO 5 .Recently, Limbach et al. [32] found that the band displays a linear increase with increasing TiO 2 content.Furthermore, as the TiO 2 content increased at the expense of CaO, or SiO 2 , a shift towards either higher wavenumbers or lower wavenumbers was observed in the latter study, which was suggested to be due to the presence of two different network structures.Henderson et al [64].previously argued that a more flexible glass structure promoted the formation of [TiO 4 ] tetrahedra, while a more rigid glass structure favoured the formation of [TiO 5 ] polyhedra.Hence, they proposed that the  band at 898 cm − 1 could be composed of two individual bands corresponding to TiO 4 and TiO 5 polyhedra populations.However, in the present paper, we have not observed any significant shifts of the 898 cm − 1 band from the depth profile measurements and have therefore fitted the band with a single Gaussian peak.Lastly, a broad band at about 817 cm − 1 can be seen, which was previously assigned to as silicate cage or Si-O-Si bending modes by McMillan [65].
The intermediate frequency region was deconvoluted into five   bands.The band at 346 cm − 1 was previously assigned to the Ti-O asymmetric bending in [TiO 6 ] [66].However, its assignment is questionable as the amount of [TiO 6 ] is expected to be negligible for the investigated titanium silicate glasses [32], and the band is also observed in the SLS glass.The bands emerging at 472 and 574 cm − 1 can be assigned to Si-O-Si bridging oxygen vibrations.The delocalized nature of this band means that it carries information about the three-dimensional network structure, and hence can be used to evaluate the alkali distribution characteristics [36,67].The bands at 505 and 612 cm − 1 in the base silicate band are the defect bands and correspond to oxygen-breathing vibration in four-and three-membered silica rings [68].As seen from the titania-silicate glasses, the band at 612 cm − 1 is reduced by the addition of TiO 2, and for the 9.9% TiO 2 glass, the band has totally disappeared.The higher fractional exchange of Na + resulting from a higher treatment temperature (q.v.Fig. 1) can be considered to be directly proportional to the magnitude of the compressive stresses (at a given treatment temperature) if relaxation stresses are disregarded.However, as we increase the treatment temperatures, alkali diffusion increases, but also the viscous relaxation is likely to become more pronounced, especially after prolonged time [19,20].Previous studies reported that TiO 2 had a slight suppressing effect on the viscosity [41,42].The glasses were here ion-exchanged for 5 h.Thus, the viscous relaxation should be apparent at the higher temperatures, but not have relieved all compressive stresses.From our data we tentatively associated the red-shift of the 574 cm − 1 band with increasing temperature as being due to an increasing Si-O-Si bond angle induced by viscous relaxation.Systematic experiments employing heat treatments at different times and temperatures should be performed to elucidate the degree of viscous relaxation to confirm this assertion Table 4. summarizes the Raman band assignments based on the discussion above.

Depth dependence
Depth profiles of the 4.7 and 9.9% TiO 2 glasses are shown in Fig. 7.The main trend that can be discerned from the depth-resolved Raman spectra is a slight shift of the band at 1106 cm − 1 towards higher wavenumbers at a depth of 10 µm for all measurements except those conducted at 350 • C, see Fig. 8a for the Raman shifts depth profile data for 500 • C. As mentioned above, this shift is indicative of the presence of increasing compressive stresses and the absence therefrom at the surface is anticipated to be due to surface stress relaxation [69].At higher depths, no shift, or slightly negative shifts, of the 1106 cm − 1 band relative to the surface measurement was found, corresponding to a relaxed glass.The shallow stress profile, along with the relatively low penetration depth of K + , suggests a relatively low magnitude of residual compressive stresses in the TiO 2 glasses.However, this will need to be confirmed by systematic surface stress and viscous relaxation measurements, as noted in Section 4. In the depth-resolved Raman spectra, the intensity of the 898 cm − 1 band is significantly higher at the surface for  9.9% TiO 2 compared to the 4.7% TiO 2 glass sample, see Fig. 8. From 10 µm depth and deeper both samples then follow the same trend.Since we expect that the 898 cm − 1 band originates from either Ti-O bridging oxygen vibrations or titanyl bonds, we interpret this observation to a K + rich surface that triggers a chemical change in the surface region upon ion exchange.

Spectrophotometry of TiO 2 doped SLS glass
Fig. 9 shows absorptance spectra and absorption coefficients for SLS and TiO 2 modified glasses.A sharp UV absorption edge is observed at around 340 nm for the 4.7% TiO 2 glass and about 350 nm for the 9.9% TiO 2 glass, while the SLS glass has a sharp absorption edge at around 320 nm.All glasses have the same thicknesses.Therefore, it can be concluded that the shift of the absorptance edge for the titania-silicate glasses towards longer wavelengths is due to the presence of Ti 4+ ions in the glass [70].
The presence of Ti 3+ is confirmed by the wide d-d band with the optical transition appearing in the visible region at about 450 nm [71], which gives the glasses a dark blue/ violet colouration at high Ti 3+ concentration [72], and which here is seen as as a shoulder at the absorption edge.The absorptance spectra show the presence of Ti 3+ even before the ion-exchange, even though at low amounts, and only small changes of the d-d bands can be observed after the treatment, which suggests that the ion-exchange has a small impact on the overall Ti 3+ concentration in the glasses, in agreement with the XPS analysis above.This is not surprising since the width of the ion-exchanged layer (order of μm) can be regarded as negligible compared to the width of the samples (order of cm).Consequently, the optical bulk properties of the glass obtained from the spectrophotometric analysis reveal the presence of Ti 3+ in the titania-silicate glasses, although in relatively small amounts, which must be the consequence of a redox equilibrium given by the conditions during manufacturing.The SLS glass also displays d-d band transitions in the visible region, although not as pronounced as those of the titania-silicate glasses.The weak d-d band transition coincides well with Fe 3+ [73].Fe 2 O 3 is a common impurity in the sand [74].The absence of any pronounced absorptance maximum in the NIR region at around 1050 nm corresponding to Fe 2+ indicates a ferric/ferrous redox ratio close to 1 (Fe 3+ /Fe 2+ ), or more likely a low impurity level of Fe, see Fig. S2 in the supplementary materials.Since this d-d band is located within the same wavelength span as the band corresponding to Ti 3+ , the d-d transitions displayed for the SLS glass may be also present in the titania-silicate glasses, and thus a superimposition of the two.Similar to the SLS glass, the titania-silicate glasses do not have an absorption band corresponding to Fe 2+ so a similar Fe 2+ /Fe 3+ redox ratio would be expected for the titania-silicate glasses.
By comparing the redox potentials of Fe and Ti ions in glass melts [70], one can see that Ti 3+ /Ti 4+ has a lower redox potential than Fe 2+ /Fe 3+ .This means that the oxidized states of Ti (Ti 4+ ) will become reduced by the presence of any reduced states of Fe (Fe 2+ ) according to the following charge-transfer reaction: Fe 2+ + Ti 4+ → Fe 3+ + Ti 3+ .As seen from the charge-transfer reaction, iron impurities in the glass could explain the observed presence of Ti 3+ in the titania-silicate glasses.It would also explain the low concentration of Ti 3+ as it would be proportional to the amount of Fe 2+ impurities in the glass.Another interesting aspect is the colouration effect arising from this charge-transfer reaction.Fe 3+ gives a yellowish colour, and Ti 3+ a dark blue/violet colour, which is each other's complementary colours.Thus, the colour effect is cancelled but typically gives a greyish or brownish colour, explaining the reduced transparency in this type of glasses [31].
Based on the features of the absorption spectra, five gaussian peaks was used to deconvolute the spectra of the 4.7 and 9.9% TiO 2 glasses, see Fig. 10a and b, respectively.The three absorption bands found at the highest wavelengths are attributed to Ti 3+ ions [75].The band with its maxima located in the spectral region of 420-440 nm corresponds to Ti 3+ ions in an octahedral environment, and the two succeeding bands are believed to be a consequence of Jahn-Teller distortion, i.e., a distortion of the octahedral environment where the two axial bonds are of different length than the four equatorial bonds.According to crystal field theory, a Jahn-Teller distortion for the quintuple energy level of the 3d 1 electron of Ti 3+ should result in three absorption bands corresponding to 2 B 2g -2 E g , 2 B 2g -2 B 1g and 2 B 2g -2 A 1g transitions, see energy diagram in Fig. 11.The weak spin-orbital interaction of the d 1 orbital results in splitting the quintuple energy level into one 2 A 1g -and two 2 E g levels.Thus two optical absorptions should be observed from distorted Ti 3+ apart from the absorption arising from the octahedral environment of Ti 3+ .The magnitude of the tetragonality is less than unity (unit cell dimensions c/a < 1) since no resonance is expected from the exact cancelling of spin and orbital contributions to the angular momentum when the tetragonality of the distorted octahedron is larger than unity.Thus, Ti 3+ is coordinated in an octahedron compressed in the direction of the z-axis [75].
Table 5 displays the relative concentrations of the absorption bands calculated from the band areas obtained from the deconvolution.The relative concentration of Ti 4+ and Ti 3+ was in very good agreement with the values obtained from the XPS analysis.Similar to the XPS results, where a plateau region of the Ti 3+ /Ti 4+ concentration was observed, the optical data also indicate a fairly constant Ti 3+ /Ti 4+ concentration Fig. 9. (a) Absorptance spectra in the visible region before and after ion exchange and absorption coefficient before and after ion exchange in the (b) 4.7, and (c) 9.9% TiO 2 glasses, respectively.
F. Bengtsson et al. within the penetration depth (~ 1-7 mm).Also, similar to the XPS analysis, the concentration of Ti 3+ was higher in the 9.9% TiO 2 glass compared to the 4.7% TiO 2 glass.For the 4.7% TiO 2 glass, the ionexchange was found to cause an increase in the overall Ti 3+ concentration, for which the contributions from all three optical transitions of Ti 3+ experience an increase.For the 9.9% TiO 2 glass, the ion-exchange was found to have the opposite effect, namely a decrease in the Ti 3+ concentration.In this case, the 2 B 2g -2 B 1g transition was the only transition experiencing an increase.We cannot rule out that the Fe concentration in the different glasses differs due to the different amounts of raw materials, and the redox ratio could be slightly different.

Optical basicity analysis
The optical basicity describes the ability of oxygen to donate, or obtain electrons from surrounding cations, commonly referred to as probe ions (e.g., Ti 4+ in this study).In glasses with strong covalent interactions between O 2-and the surrounding cations, the oxygen is less able to donate charge to the probe ionmeaning lower optical basicity.If optical basicity is high, the free O 2-are practically uninfluenced by surrounding cations.An increase in optical basicity is usually obtained from an increase of the concentration of non-bridging oxygens, related to a modification of the valence state of the probe ion, in this case, Ti 4+ [76].Therefore, it can be a valuable tool to predict the local glass structure.
For multicomponent glass, the basicity parameter, B is described as: where n i is the molar fraction of glass component i and B i is the basicity parameter of glass component i. Fig. 12 shows the basicity parameter as a function of depth in relation to the Ti 3+ /Ti 4+ ratio for the 4.7 and 9.9% TiO 2 glasses at the four different treatment temperatures.The basicity parameters were calculated using the basicity values from Table 3 in Morinaga et al. [71], and the molar fractions in Table 1.
Due to the higher basicity parameter of K 2 O compared to Na 2 O, a decrease in the basicity parameter as a function of depth is observed.We assume that the change in basicity is solely affected by the Na + /K + exchange.The basicity parameter is directly related to the concentration profiles in Fig. 1.The result from the deconvolution of the absorption spectra reveals an increase in Ti 3+ for the 4.7% glass but a decrease for the 9.9% TiO 2 glass.Hence, it seems that there is no straightforward explanation for the change in Ti 3+ concentration upon ion-exchange.The optical basicity could possibly be one of the driving factors behind the equilibrium change, see Fig. 12.The structural differences of the 4.7% TiO 2 glass compared with the 9.9% TiO 2 glass may cause the optical basicity to have the opposite effect on the two glasses.Morinaga et al [71] found that the relative proportion of Ti 3+ increases in silicate glasses with decreasing basicity, which is the opposite of our results in Fig. 12.
Other possible reasons to why Ti 3+ would increase because of the ion exchange treatment may be found from the SLS glass manufacturing process.From the raw material information given in [31], NaNO 3 was used as an oxidizer.Thus it is plausible that the equilibrium is shifted to Ti 4+ when making the glasses.Another possible reason could be impurities (e.g., Fe 2+ ) in the porcelain crucible used as the salt bath contained   c,d) represent an estimated error of 15% on the Ti 3+ /Ti 4+ ratio and the dashed lines in all graphs are guides for the eye.

Table 3
Alkali diffusion coefficients (D K-Na ) and activation energies (E A ) for the SLS, 4.7 and 9.9% TiO 2 doped SLS glasses.Estimated errors of D K-Na and E A are about 7% for SLS and about 15% for 4.7 and 9.9% TiO 2 as given from the root mean square error in Fig. 2a. in the ion exchange treatment.If Fe 2+ has been dissolved in the salt, Fe 2+ ions could be exchanged with Ca 2+ .

Summary and conclusions
A series of chemically strengthened titania-doped SLS glasses were investigated using depth-resolved XPS and confocal Raman spectroscopy, and spectrophotometry.Alkali ion diffusion is slightly decreased in soda-lime silicate glass subjected to Na + -K + ion exchange and TiO 2 doping, as TiO 2 replaces CaO and SiO 2 .The physical reasons for this is likely to be due to the structural arrangement, where SiO 4 and TiO 4 coexist with NBO species located at the SiO 4 groups (for TiO 2 < 9 mol%).From the depth analysis of the ion exchanged TiO 2 doped glasses it is clear that the ion exchange affects the 898 cm − 1 band which was assigned to Ti-O bridging oxygen vibration or titanyl bonds (T=O) in TiO 5 groups.The alkali ions are assumed to have higher affinity to SiO 4 groups than for TiO 4 groups that are clustered in isolated groups, giving rise to lower alkali ion diffusion in the K + enriched glasses, which is evident from the calculated alkali diffusion coefficients, D K− Na , and the associated activation energy that slightly increases with increasing TiO 2 content.From XPS analysis, the alkali ion diffusion coefficient was found to decrease (and the corresponding activation energy increase) with increasing TiO 2 content in the glass.The obtained values for the diffusion coefficient and activation energy were determined to be in the range 3.3×10 − 12 -4.5×10− 11 cm 2 s − 1 and 101-106 kJmol − 1 , respectively, consistent with the previous studies.
XPS analysis also shows that Ti 3+ exists as a minor species in the glasses.Analysis of the absorption spectra in the near UV-range confirms the XPS findings.The results clearly show Jahn-Teller compressed distortion of the Ti 3+ octahedral coordination.Furthermore, it was shown that for 4.7% TiO 2 , the relative proportion of Ti 3+ increases, while for 9.9% TiO 2 , it decreases.The reason for this is not conclusive and can be either due to the ion exchange, optical basicity, the different structure of the samples, or impurities of the salt bath container.Minor concentrations of Ti 3+ in the surface region of the glass was confirmed by spectrophotometric analysis.While Ti 3+ is present in the TiO 2 doped glasses, K + ion exchange treatment gives a higher relative Ti 3+ content in the surface region.Assuming that the ion exchange gives the glass an optical basicity it gives an opposite trend to the conventional Ti 3+ /Ti 4+ equilibrium.The presence of Ti 3+ in the glass is linked to the Fe 2 O 3 content and as the Ti 3+ and Fe 3+ absorb in complementary colours their optical appearance give a greyish tone which results in a slightly reduced transmittance similar to what was observed in a previous study [31].The close connection between the Ti 3+ and the Fe 2 O 3 content necessitates that Fe impurities in the glass must be considered in the ion exchange process.
Raman spectroscopy analysis reveals that stretching vibrations due to Q 3 NBO groups at 1106 cm − 1 are blue-shifted to 1145 cm − 1 because of a shorter bond length that is attributed to induced compressive stresses as K + replaces Na + as charge compensator in the glass.A redshift was observed for the 817 cm − 1 band and was observed both in ion exchanged and mixed-alkali glasses, while compression instead is expected to give a blue-shift [58].Therefore, we hypothesize that the red shift of 817 cm − 1 originates from the bending vibration of O-Si-O − or O-Ti-O − that are charge balanced by Na + .As Na + is replaced by K + it gives rise to a red-shift.Analysis of Raman spectra showed evidence of Q 3 -silicate non-bridging oxygen Si-O species with different bond lengths and bond angles, which were attributed to induced surface compressive stresses by the ion exchange.The 574 cm − 1 band is an indication of the Si-O-Si bond angle and is a signature of the compressive stresses in the chemically strengthened glass.As the temperature is increased the band is subjected to a red-shift and an increase of the bond angle which we interpret is due to an increased viscous relaxation of the compressive stresses even if the alkali ion diffusion also increases.From the calibration curve in [57] we estimate the Si-O-Si bond angle to be about 135 • and upon increasing the ion exchange temperature it increases to about 136 • for SLS and 4.7% TiO 2 and 137 • for 9.9% TiO 2 .Systematic experiments employing heat treatments at different times and temperatures should be perfomed to elucidate K + induced stress in the glass and the degree of viscous relaxation that counteracts the build up of stress in the surface region of the ion exchanged glass, and the extent of retardation of viscous relaxation due to TiO 2 doping.
The compressive stress was found to be attenuated after increasing glass pre-treatment temperatures due to viscous relaxation.TiO 2 doping of soda lime silicate glass is found to decrease alkali diffusion and to maintain the compressive stress in the sub-surface region of the ion exchanged glass, but also enhance temperature induced viscous relaxation.

n glass − nair n glass +nair ) 2
using the refractive index (n d ) values for the different glass

Fig. 1 .
Fig. 1.Concentration profiles obtained from the XPS depth profile measurements depicting the K + /Na + concentration ratio as a function of depth for the four different treatment temperatures.Concentration profiles for (a) the SLS, (b) 4.7, and (c) 9.9% TiO 2 glasses.The dots in the graph illustrates the different data points and its size is approximately the error of the analysis as indicated by one added error bar (q.v., Section 2.2).The dashed line represent steady state diffusion, i.e., assuming ∂c/∂x = constant and the solid are guides for the eye.

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Fig. 2 .
Fig. 2. (a) Arrhenius plot of lnD K-Na as a function of 1000/T for SLS, 4.7 and 9.9% TiO 2 where the lines are linear fits of the data (b) Activation energy, E A , as a function TiO 2 concentration added to the SLS glass, as calculated from the Arrhenius plots.(c) Alkali Diffusion coefficients (D K-Na ) as a function of temperature, T, for SLS, 4.7 and 9.9% TiO 2 .The error bars represent the estimated error from the root mean square analysis of (a).

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Fig. 3 .
Fig. 3. (a, b) Relative and (c, d) absolute Ti 3+ concentration as a function of depth for 4.7 (a, c) and 9.9% TiO 2 (b, d) glasses treated at 350, 400, 450 and 500 • C ion exchange temperatures.The error bars represent an estimated error of 15% on the Ti 3+ /Ti 4+ ration and 10% on at%.The dashed lines represent the K + /Na + ratio and are guides for the eye as taken from Fig. 1.

Fig. 4 .
Fig. 4. Raman spectra offset plot and deconvolution of (a) the SLS, (b) the 4.7%, and (c) the 9.9% TiO 2 glasses for the different ion exchange treatment temperatures as measured at the surface.The dashed lines are guides for the eye.

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Fig. 5 .
Fig. 5. (a) Description of Q-group concept in silicate glasses and the charge-balancing of NBO by (b) Na + , and (c) K + after ion exchange.

Fig. 6 .
Fig. 6.Raman shift of the 574 cm − 1 band as a function of ion exchange temperature.The dashed lines are guides for the eye.

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Fig. 7 .
Fig. 7. Raman depth profile spectra of (a) the SLS, (b) 4.7% and (c) the 9.9% TiO 2 glass as a function of depth.The dashed lines are guides for the eye.

Fig. 8 .
Fig. 8. Band intensity of (a) the 898 cm − 1 and (b) 1105 cm − 1 band for the 4.7 and 9.9% TiO 2 glasses as a function of depth for 500 • C ion exchange treatment temperature.The dashed lines are guides for the eye.

Fig. 11 .
Fig. 11.Energy diagram displaying the energy levels of 3d 1 electron (Ti 3+ ) in two kinds of octahedral environments due to Jahn-Teller distortion.(i) regular octahedral environment, (ii) distorted octahedral environment with a tetragonality less than unity.

Fig. 12 .
Fig. 12.The basicity parameter B as a function of depth for the glass with (a) 4.7, and (b) 9.9% TiO 2 as well as the Ti 3+ /Ti 4+ ratio as a function of depth for (c) 4.7 and (d) 9.9% TiO 2 .The error bars in (c,d) represent an estimated error of 15% on the Ti 3+ /Ti 4+ ratio and the dashed lines in all graphs are guides for the eye.

Table 2
Data of the Z-distance moved by the objective table to obtain laser focus at the different depths taking into material and scattering geometry parameters.The absolute errors of the Z-distance movement were ≤ 0.1 µm.

Table 4
[56]ary of vibrational band assignment of Raman peaks for the SLS and TiO 2 modified SLS glasses.Si-O -stretching of BO in [SiO 4 ] of at least one NBO[56]

Table 5
Concentrations of the absorption bands calculated from the relative band areas obtained from deconvolution of absorption spectra.Based on the assumption of Gaussian peaks in the deconvoluted fit we have estimated the error to be ±0.1%.