**2. Vm Quantification by Raman Spectroscopy**

Raman spectroscopy probes the inelastic light scattering from vibrational motions of atoms in a solid, and as such, it is sensitive to any change in the way atoms vibrate, as caused, for instance, by the presence of a different phase. In other words, the Raman spectrum is a fingerprint of the state a solid assumes. In zirconia ceramics, the tetragonal and monoclinic polymorphs present very different spectra [25], and in mixed phases, a superposition between those two spectra appears, the extent of which depends on the volume fraction of the monoclinic phase, Vm, in the investigated area. Various researchers have derived an expression to quantify Vm from the intensity of Raman peaks belonging to tetragonal and monoclinic phases, building upon equations already available for XRD analyses [26]. The equation has the following form [26,27]:

$$\text{V}\_{\text{m}} = \frac{I\_{\text{m}}^{181} + I\_{\text{m}}^{190}}{k \left(I\_{t}^{147} + \delta I\_{t}^{265}\right) + I\_{\text{m}}^{181} + I\_{\text{m}}^{190}} \tag{1}$$

and it differs among the available approaches only for the values of the *δ* and *k* coefficients. *Ii <sup>m</sup>*,*<sup>t</sup>* is the intensity of Raman peaks (at position *i*—in cm−1) belonging to monoclinic and tetragonal phases. The two most used equations for the determination of Vm in THA implants are the one derived by Clarke and Adar (*δ* = 1, *k* = 0.97) [27] and the one derived by Katagiri et al. (*δ* = 0, *k* = 2.2 ± 0.2) [26], whereby the latter has been used in the majority of recent studies concerning the Delta material. Tabares and Anglada [26] recently carried out a systematic study with both Raman and XRD using bulk mixtures of tetragonal and

monoclinic zirconia powders with from 0% to 100% of monoclinic phase content. They calculated Vm using both the Clarke/Adar and Katagiri equations and demonstrated that while Katagiri's equation correctly reproduced the monoclinic content, the Clarke/Adar equation largely underestimated it. XRD results were also in better accordance with the Katagiri equation. They suggested that this discrepancy is related to the localization of the monoclinic polymorph (i.e., the Vm profile) in the material used for calibration by Clarke and Adar: fracture surfaces in ZrO2/Y2O3 specimens, where the monoclinic phase is expected to be present only near the surface. In this case, the penetration depth of X-rays depends on the angle of incidence, and thus it can be suggested that the discrepancy in the Vm calculated with Clarke and Adar's formula is due to a different angle of incidence that Tabares and Anglada used for their XRD measurements, compared to the one used by Clarke and Adar [26]. Hence, according to Tabares and Anglada, the Katagiri equation seems to have universal validity because it has been obtained on bulk mixtures of tetragonal and monoclinic zirconia powders, where the monoclinic content is homogeneous across the whole probed volume by both Raman and XRD. Its validity, however, has neither been systematically demonstrated in materials where a sharp gradient in the monoclinic phase is present, nor in sintered materials. Both aspects clearly apply to in vitro and in vivo aged Delta [3,9,11,28].

Apart from the choice of the equation to calculate Vm, there are many other aspects that could lead to errors and discrepancies between the Vm values reported in the literature:


A comparison between the Clarke/Adar and Katagiri equations using both Raman and XRD on Delta has not yet been reported in the literature, and also a thorough analysis of the aforementioned error sources (even partly) has never been attempted.

#### **3. Materials and Methods**

#### *3.1. In Vitro Aging Study Samples*

Ten Delta heads and ten Delta cup inserts (CeramTec GmbH, Plochingen, Germany) were analyzed by both XRD and Raman spectroscopy in order to independently quantify the monoclinic content. The areas investigated corresponded to the head apex in the heads (polished), and to the center of the bottom (opposite of the cup) in the inserts (ground). The two different surface finishes were selected with the intent to attempt to cover as much of the Vm range, from 0% to 100%, as possible, this way mimicking non-wear and wear zones in real implants, respectively. The aforementioned total hip arthroplasty implant components were tested both before and after extreme hydrothermal aging in an autoclave at 134 ◦C and 2.2 bars for 150 h, which would correspond to more than 300 years in vivo according to the ASTM standard.
