1. Introduction

Zirconia is among the most biocompatible materials widely used in medical applications [1, 2]. Since seventies, zirconia has known several applications as implants, but recently in the dentistry domain for crowns and fixed partial dentures [3]. Especially, Tetragonal zirconia doped with 3 % mol of yttria (3Y-TZP) is used because of its high strength and fracture toughness [4]. Zirconia crystal structure knows three phases depending on temperature: the monoclinic phase (m), the tetragonal phase (t) and the cubic phase (c). During aging of 3Y-TZP dental implants tetragonal to monoclinic phase transformation occurs due to the environment humidity. In this phenomenon known as low temperature degradation (LTD), the transformation from tetragonal to monoclinic phase begins at the surface and spreads inside the implant causing microcracks and mechanical properties degradation. The hydrothermal degradation was reported first by Kobayashi et al [5] and was widely documented in previous works [6, 7]. Artificial LTD on zirconia is studied to predict implants degradation by aging. In this case, monoclinic phase fraction is measured as a function of temperature and time of humidity exposure. Several techniques for zirconia transformation study were reported: transmission electron microscopy, X-ray diffraction, optical interferometry and AFM [8, 9]. But, they are limited to the surface analysis or involve the sample section. Raman microspectroscopy is an alternative technique for a local analysis of tetragonal to monoclinic phase transformation [10, 11]. Quantitative analysis are obtained from tetragonal and monoclinic phases spectra, by measuring the Raman band intensity of each phase, which depends directly on their relative concentration. Different ways of quantification of monoclinic/tetragonal proportions in zirconia samples was proposed using Raman spectroscopy always on cross-sections [12, 13]. Raman confocal microspectroscopy (RCMS) offers a supplementary advantage in zirconia transformation analysis. Its high axial resolution (2 μm) permits to probe samples with a resolution depending on the zirconia optical properties (absorption and scattering) by using optically conjugate pinhole diaphragms [14]. The depth profile has been calibrated by using optical properties of excitation wavelength and objective numerical aperture [15, 16]. However, few is reported on probing tetragonal to monoclinic phase transformation in depth because of sample preparation (sample sectioning) [17]. For in-depth studies by RCMS technique, the optical sectioning is more suitable for transparent samples. Recently, correction of depth profiles considering diffraction and refraction in polymers was reported [18, 19]. In this study, RCMS is used to probe tetragonal to monoclinic phase transformation of different aging times of 3Y-TZP samples without any sample sectioning by using different pinhole sizes. A theoretical model is proposed based on the optical properties of the excitation laser (wavelength), the objective characteristics (numerical aperture, magnification) and the zirconia optical properties (refraction index, absorption and scattering coefficients). Experimental and theoretical zirconia transformation curves are compared and transformation factors are provided by using a totally non-destructive method for in-depth analysis.

2. Materials and methods

Experimental zirconia transformation curves were obtained on (20×4×2) mm³ specimens with a pure tetragonal crystalline structure assessed before aging by Raman spectroscopy. The samples were exposed to in vitro aging in Ringer solution at 130°C and 0.6 MPa for 25h and 90h. Raman spectra of transformed zirconia were recorded using a Labram Raman spectrometer (Horiba Jobin Yvon, Kyoto, Japan). The excitation laser was a HeNe laser (633 nm) with 1 mW power. The Raman spectrometer was combined to a confocal microscope (Olympus LX71).

In this study, an objective 10×, NA 0.25 was used. Considering the refraction index of zirconia (n=2.2), the effective numerical aperture (NA_eff) as described in [20] is NA/n=0.11. This gives an axial resolution due to the refractive effect of 70μm ( ${\mathit{FWHM}}_z=1.4\lambda /{\mathit{NA}}_{\mathit{eff}}^2$).

Combining the objective with gradually enlarged confocal pinhole apertures, from 30 to 300 μm, allows the control of the probe size and thus of the collection depth (z_exp). Pinhole function as rejecting out-of focus signals, enables thin optical sectionning within thick samples [21].

The principle of the confocal microprobe method is illustrated in Fig. 1. Pinhole size variation leads to different optical slice sizes described theoretically in transparent media by Eq. (1) [22]:

 

Fig. 1 Schematic presentation of confocal detection principal in the confocal Raman micro-spectroscopy.

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Moreover, zirconia is also a highly scattering medium whereas the absorption coefficient of 3Y-TZP can be neglected (μ_a = 0.135cm⁻¹), in front of the reduced scattering coefficient (μ′_s = 100cm⁻¹ from [23]). The optical slice described previously in transparent media should then be modified according to this scattering effect. The study of in-depth variation in scattering media as phantoms was reported [20, 24]. To determine this scattering effect, a calibration of the optical slice sizes is necessary depending on the pinhole size. In case of zirconia, the calibration of collection depth was conducted on a highly-polished knife-shaped specimen as reported by the authors and based on the protocol previously described in [10]. In this study, we have compared the theoretical and experimental optical depths obtained in zirconia.

Figure 2 (left) shows the calculated axial optical slices (z_opt) in non-scattering media given by Eq. (1) and the measured experimental depths by knife-edge technique obtained for different pinhole sizes. The ratio between experimental (z_exp) and theoretical (z_opt) optical slices is due to the scattering effect. In Fig. 2 (right), we see that this ratio is fitted by an exponential law as Beer-Lambert law which describes this scattering effect (I(z) = I₀e^−μz where I(z) is the intensity axial profile). Since the absorption is neglected in zirconia, only the scattering coefficient (μ′_s = 0.01μm⁻¹) is present. A factor of 2 is added in the fit curve due to the fact that, the scattering is considered twice: one time for excitation laser scattering and a second time for Raman diffusion scattering.

 

Fig. 2 Calculated optical slice thickness given by the optical objective and measured axial depths in zirconia for each pinhole size (left) Ratio between calculated and measured depths.

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After depth penetration calibration, Raman spectra were collected from three randomly selected points on the surface of each aged specimen. Raman spectra were measured in 22 probes following the same protocol. The purity of the tetragonal phase was assessed in the control samples. Close to 800 spectra were collected and analyzed. Raman peak positions and intensities were obtained by fitting the Raman spectra with Lorentzian curves. From each spectrum, the monoclinic volume fraction V_fm was calculated. Noise in Raman spectra was very low and the bands picks fittings give errors bars in V_fm calculations which were presented on the experimental graphs.

The spectra of the tetragonal and of the monoclinic phases are sufficiently different to enable qualitative analysis. Each structure exhibits specific features that can be assigned to actual spectral signature of the studied phases. In the tetragonal phase, the most characteristic bands are a sharp band at 142 cm⁻¹ and a broader one at 256 cm⁻¹, whereas, in the monoclinic phase, a doublet is seen at 178 and 190 cm⁻¹. Raman spectra of aged zirconia were reported by the authors in [10]. The zirconia degradation occurs during the tetragonal to monoclinic transformation, which is estimated by calculating the monoclinic volume fraction, V_fm, using Eq. (2) [10, 11]. The calibration constant of 0.33 included in the ratio between the intensities of the monoclinic and tetragonal peaks taken in this work was widely discussed [13], and used to calculate the monoclinic fraction volume:

 

Fig. 3 Measured and calculated averaged monoclinical fraction in depth.

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3. Results and discussion

Theoretically, the monoclinic fraction measured depends on the laser intensity Gaussian profile ( $e^{-\frac{z^2}{0.4D_z^2}}$ with D_z, the axial resolution of the objective), the optical properties of zirconia (described by Beer-Lambert law: e^−μ′_sz) and a sigmoid model describing the theoretical monoclinic volume fraction F(z) in depth as proposed by [7] (see Fig. 4 (left)). The optically modified fraction profile includes the contribution of optical parameters (excitation and beer-Lambert law with zirconia optical parameters) to the real transformation profile described in Eq. (2). This optically modified monoclinic fraction profile OF(z) is then described by Eq. (3):

 

Fig. 4 Calculated monoclinic fraction in depth for two different aging times.

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A simulation program based on Eq. (3) was developed using Igor software (WaveMetrics, Portland, USA). This program provide a theoretical curve, matching closely to the experimental averaged monoclinic fraction shown in Fig. 3 by variating the parameters: V₀, T and z₀.

In fact, these experimental curves represent the average monoclinic fraction (AF) measured from the surface down to the depth z for each pinhole size. Indeed, as it was shown, the optical slices represent the collected signal from the surface down to optical depths (z) that are collected by each pinhole size. Thus, the average monoclinic fraction (AF) corresponds to the ratio between the collected monoclinic fraction (OF) and the optical slice thickness (z_exp). Theoretically, the experimental design with progressive enlargement of pinhole diameter enables the measurement of monoclinic volume fraction in increasing thickness of material AF (z), which can be written:

The average fraction (AF) is the theoretical description of the measured transformation profiles (V_fm calculated using Eq. (2)) by confocal Raman micro-spectroscopy for each optical slice defined for each pinhole size. Figure 3 shows the experimental zirconia transformation AF(z) for two aged times. These experimental curves are compared to the theoretical averaged monoclinic volume fraction inside the collected depth AF(z) obtained by simulation program. Thus, to have the closest profiles, the simulation program fixes the transformation parameters V₀, T and z₀, such as T=1.1 μm⁻¹ for both aging times, whereas, z₀ = 30μm and V₀ = 78% for 90h and z₀ = 20μm and V₀ = 45% for 25h aging time.

This means that the real transformation profile (F(z)) can be determined precisely directly from the simulation of the AF(z) curve and the fit of the experimental AF(z) curve. Figure 4 shows the result of the calculated monoclinic fraction axial profile for the theoretical monoclinic fraction (F(z)) and the optically modified monoclinic fraction (OF(z)) using Eq. (3) depending on pinhole sizes. The transformation parameters, V₀, T and z₀ have been fixed by the simulation program. In this work, the theoretical monoclinic volume fraction curves (F(z)) are calculated without any sample cross section and are very close to profile curves obtained by sample cut reported before [7]. F(z) is integrated and averaged in the confocal depth to obtain finally the calculated averaged monoclinic fraction (AF(z)), which corresponds closely to the experimental one measured by confocal Raman microspectroscopy. The transformation parameters (V₀, T and z₀) are obtained for zirconia hydrothermal degradation in depth which allows the prediction of LTD for different other aging times.

4. Conclusion

In this study, the evolution of transformation (LTD) of 3Y-TZP is simulated and compared with experimentally measured LTD by confocal Raman micro-spectroscopy. The experimental method and the simulation model that we have proposed allow optical sectioning in depth by using different pinhole sizes to avoid any mechanical sectioning. The optical sectioning microscope was used to study a highly scattering media as zirconia used in dental crowns. The developped simulation program allows depths corrections and LTD factors estimation. This leads to the prediction of real transformation factors and profiles for any aging times without any mechanical sectionning which could induce some additional degradations. In addition, this simulation will be useful to model hydrothermal degradation in different dental materials based on zirconia using Raman confocal micro-spectroscopy.