Improving the High-Pressure Sensing Characteristics of Y₂MoO₆:Eu³⁺ Using a Machine Learning Approach

Abstract

In this study, we explore the potential of applying machine learning (ML) to enhance high-pressure luminescence sensing. We investigate the luminescence behavior of Y₂MoO₆:Eu³⁺, synthesized via a self-initiated, self-sustained reaction. Emission spectra were collected under varying pressures using a 405 nm laser diode and an AVANTES AvaSpec 2048TEC USB2 spectrometer. An analysis of the pressure-dependent curve, based on the intensities of two key peaks, indicates a possible crystal phase transition or another underlying physical phenomenon. Moreover, the non-unique relationship between pressure and peak intensity limits its effectiveness for precise sensing. To overcome this challenge, we employ an ML-based approach, combining Uniform Manifold Approximation and Projection (UMAP) for data visualization with a deep neural network to estimate pressure directly from the full luminescence spectrum. This strategy significantly extends the usable pressure range of Y₂MoO₆:Eu³⁺ up to 12 GPa, representing a marked improvement over conventional methods.

1. Introduction

The growing interest in using luminescent materials for high-pressure measurement, often doped with rare earths, highlights their potential in various industrial and scientific applications where the monitoring of this crucial physical parameter is essential [1,2,3,4,5,6,7,8,9].

This paper reports on a machine learning analysis of the high-pressure luminescence properties of Y₂MoO₆:Eu³⁺. The material, known for its excellent thermal and chemical stability due to the presence of Eu³⁺ ions in non-centrosymmetric sites [10,11,12], was prepared using a self-initiated and self-sustained reaction method, as detailed in a previous study [13]. Both the Y₂MoO₆:Eu³⁺ material and the R1 emission line of ruby can be excited by blue light, which makes Y₂MoO₆:Eu³⁺ a promising candidate for high-pressure measurements.

According to the Judd–Ofelt (J-O) theory, materials doped with the Eu³⁺ ion are excellent candidates for optoelectronic devices because the luminescence of Eu³⁺ is highly sensitive to its local crystal environment [8,10,14,15]. For this reason, the Eu³⁺ ion is frequently used as a probe to monitor subtle changes in a material’s crystalline structure [8,16].

The unique properties of the Eu³⁺ ion are a direct result of its $4f$ electrons. In a centrosymmetric structure, the outer shell electrons shield the $4f$ electrons from the environment, which forbids $f-f$ electric dipole transitions and allows only magnetic dipole transitions. Conversely, in a non-centrosymmetric structure, electric dipole transitions can occur due to an interaction with an odd-parity crystal field [8,14,15].

High-pressure techniques offer a powerful way to systematically alter a crystal’s structure by changing interatomic bond lengths, bond angles, and atomic positions [17]. As Halevy et al. proposed, increasing external pressure has a similar effect on the host’s crystal structure as when increasing temperature [18]. This manipulation of the crystal field directly impacts the luminescence properties of the material, which is why high pressure is used as a tool to study and tune these characteristics [8,16].

Since the discovery of pressure measurement via the luminescence shift of ruby (Cr³⁺:Al₂O₃) [19], the ruby sensor has become a widely used pressure gauge in a variety of experiments. Although proposed long ago, the ruby sensor is still being analyzed and improved. In [20], the authors propose a calibration of ruby, samarium-doped strontium tetraborate (Sm²⁺:SrB₄O₇), and samarium-doped yttrium aluminum garnet (Sm³⁺:YAG) using Raman and fluorescence spectra, with measurements conducted over the temperature range of 296–850 K and pressure range of 0–55 GPa. In [21], the authors measured the luminescence shifts of the ruby’s R1- and R2-lines and the line of (⁵D₀ → ⁷F₀) from Sm²⁺:SrFCl corresponding to the melting pressure of mercury.

A comprehensive review and comparison of various high-pressure sensors is provided in [22], which clearly demonstrates that the search for improved high-pressure sensors is still ongoing. The high thermal and chemical stability of Y₂MoO₆:Eu³⁺ is a necessary performance feature for its use as a pressure sensor, since such sensors are often employed under extreme conditions.

While recent studies in high-pressure sensing have largely concentrated on developing new luminescent probes, advancements in spectral data analysis methods have been comparatively limited. This gap highlights a promising opportunity for machine learning (ML) algorithms, which have seen a surge of interest for investigating various scientific and social data sources in recent publications [23,24,25,26] and the references therein.

Machine learning (ML) is increasingly being employed to analyze luminescence, near-infrared, and other spectral data [27,28,29,30,31,32,33,34,35,36]. Traditional analysis methods, however, typically rely on a single, empirically chosen spectral parameter. While this approach is widely used for remote thermometry, publications on high-pressure measurements using luminescence are less numerous. Both fields, however, often share this same calculation method, highlighting a common limitation in their analytical techniques.

The advantage of the ML approach lies in its ability to account for all features of the measured signal within the selected spectral range, including peak intensity, intensity ratios, and spectral shifts. In this sense, regardless of the material analyzed, ML offers a more comprehensive solution compared to individual calculation techniques.

While our previous research on the SrCeO₄:Eu³⁺ phosphor [37] successfully used a single spectral feature (e.g., intensity ratio or spectral shift) for thermometric and high-pressure measurements, this approach inherently limits accuracy and resolution by only partially utilizing the available spectral data. The method was effective in that specific case because the phosphor did not undergo a phase transition.

However, a similar single-parameter approach is insufficient for the Y₂MoO₆:Eu³⁺ phosphor studied here, as a simple calibration curve fails to provide accurate results across the full measurement range.

In contrast, the deep learning neural network approach developed by the authors of [36] demonstrates the potential to fully exploit temperature-dependent spectral data by extracting multiple features, an approach that is necessary to overcome the challenges presented by our current material.

Our study investigates the pressure effects on the optical properties of a Y₂MoO₆:Eu³⁺ nanophosphor, with a focus on improving the accuracy of high-pressure measurements using a machine learning (ML) approach. To our knowledge, this is the first time ML has been applied to enhance high-pressure measurements in this manner. For our analysis, we used the Uniform Manifold Approximation and Projection (UMAP) method for initial data visualization and a deep learning artificial neural network to predict pressure intensity based on luminescence spectral data.

2. Materials and Methods

The Y₂MoO₆:Eu³⁺ powder was synthesized using a self-initiated and self-sustained reaction method [13]. To ensure full crystallinity, the material was then calcined at different temperatures, as detailed in [13]. The Y₂MoO₆ examined in this study was doped with 5 at.% Eu³⁺ and sintered at 800 °C. The resulting material exhibits an average grain size of 30–50 nm, and all synthesized samples correspond to single-phase monoclinic Y₂MoO₆ (JCPDS card 00-057-0517) [13]. The photoluminescence emission spectrum was recorded using a 405 nm laser diode for excitation and an AVANTES AvaSpec 2048TEC USB2 spectrometer (Lafayette, CO, USA) for detection, providing a wavelength resolution of 0.11 nm. Measurements were acquired with an integration time of 30 ms and averaged over five scans, and all spectra were radiometrically corrected. The spectrometer features a 12-bit analog-to-digital resolution. The laser output power was 5 mW, with an estimated 3 mW reaching the sample. Given a spot size of 10 µm, the corresponding power density was approximately 7639 W/cm². The pressure dependence of the Y₂MoO₆:Eu³⁺ emission spectrum was then measured, and a pressure-dependent plot was constructed based on the intensity ratio of two prominent peaks.

While the experimental setup for luminescence measurements as a function of temperature and pressure is described in [37], we will now focus specifically on the setup used for high-pressure measurements.

2.1. Experimental Setup for High-Pressure Measurements

High pressure was generated using a Membrane Diamond Anvil Cell (MDAC) manufactured by BETSA, which featured a $300$ μm culet diameter which employed two 300 micron culet diameter diamonds (see Figure 1). The fundamental principle of a Diamond Anvil Cell (DAC) is to create very high pressures by applying a reasonable mechanical force to a tiny surface area (the culet). While earlier DAC models used a screw to apply this force, the MDAC achieves fine control and adjustment through pressurized helium, which presses a circular membrane against a piston.

The powdered sample, along with a pressure transmitting fluid and a small ruby sphere, was placed inside a metal gasket. The gasket was pre-indented between the diamond anvils to create a secure, leak-proof seal. The gasket diameter is D = 100 μm and thickness t = 60 μm. The ruby sphere has a diameter of 10 μm. We used a 4:1 mixture of methanol and ethanol as the pressure transmitting medium to ensure a uniform pressure distribution on the sample.

Since the diamond anvils are optically transparent in this pressure range, we were able to perform optical measurements on the pressurized sample. The applied pressure was accurately determined by measuring the redshift of the ruby R1 luminescence line. In our experimental setup, the pressure-induced red shift of ruby luminescence is shown in Figure 2. The ruby pressure scale was originally established decades ago [19], and in this work, we adopt the calibration provided in Figure 1 of [38]. We assume a linear dependence of wavelength shift on pressure, with a coefficient of 0.3246 nm/GPa, and an associated uncertainty of approximately 5% as reported in [38].

2.2. Machine Learning Analysis

To perform our machine learning (ML) analysis, we used the Solo+Mia software package (Version 9.1, Eigenvector Research Inc., Manson, WA, USA) [39,40]. This user-friendly software was chosen for its accessibility, allowing individuals without programming expertise to analyze data.

Early on, we determined that our number of measurements was insufficient for effective ML training. To overcome this, we employed an image data augmentation technique, as surveyed in [41], to expand our training dataset. Specifically, we generated new data by adding random noise to the original measured samples, a method we successfully utilized in a previous study [42]. Numerous techniques exist to achieve pattern recognition that is robust to variations in lighting, viewing angles, and distances. In contrast, spectral data recognition is considerably simpler; therefore, we introduced only random noise.

3. Results

To analyze how high pressure affects the photoluminescence emission of the Y₂MoO₆:Eu³⁺ nanophosphor, we measured its spectral responses at various pressures. The resulting luminescence spectra are presented in Figure 3. The green lines in Figure 3 indicate the region of interest for calculating the intensity ratio. From the outset, we selected the peak at 578 nm (at atmospheric pressure) for all calculations due to its higher intensity. Accordingly, the intensity ratio was calculated using the peaks at 578 nm and 614 nm (referenced to their positions at atmospheric pressure), and their intensities were tracked as they shifted under pressure.

Rare earth ions are well known for their high sensitivity to local symmetry, which makes any change in the crystal structure observable in their luminescence spectra [43]. The paper by Zhang et al. [8] provides a detailed explanation of how pressure-induced phase transitions in a crystal structure affect the luminescence of the ${\mathrm{Eu}}^{3+}$ ion.

Specifically, as pressure increases, two key changes occur in the luminescence spectrum:

–

Red shift of emissions: This is attributed to the expansion of the ${\mathrm{Eu}}^{3+}$$4f$ orbital [8].

–

Change in relative intensity ratio: This variation is caused by a change in the crystal field, which is a direct consequence of the applied pressure [8].

Both of these effects could be seen in Figure 3.

Pressure-induced changes to the crystal lattice parameters also disturb the energy level positions, particularly those of the ⁵D₁ and ⁵D₀ states. This variation, along with changes in the charge transfer region, increases the probability of non-radiative transitions. As shown in Figure 3, the applied pressure predominantly affects the ⁵D₀ level.

The exact positions of the luminescence peaks used for calculating intensity ratios are at 578 nm (⁵D₀ → ⁷F₀) and 614 nm (⁵D₀ → ⁷F₂) at atmospheric pressure. A slight variation in the intensity of the most prominent ⁵D₀ → ⁷F₂ transition line can also be observed in Figure 3. The resulting intensity ratios of the emission lines from the ⁵D₀ states are presented in Figure 4.

The spectra shown in Figure 3 clearly exhibit peak shifts. For calculating the intensity ratio, we used the peaks at 578 nm and 614 nm (corresponding to their positions at atmospheric pressure) and tracked their intensities as they shifted under pressure.

A change in the luminescence spectrum, such as a deformation or discontinuity, indicates that a single physical behavior model is insufficient to describe the data. Such discrepancies become evident when the measured points cannot be accurately fitted with a single curve, suggesting that different segments of the data correspond to distinct physical models.

As shown in Figure 4, the intensity ratio calibration data for the Y₂MoO₆:Eu³⁺ nanophosphor exhibits these discrepancies across the measured pressure range. Consequently, the resulting curve lacks a unique and consistent relationship between the peak intensities and pressure, making it unsuitable for a reliable calibration method.

To enhance our analysis, we applied machine learning techniques to the data. For a clearer visualization of the results from the UMAP [44] and deep learning methods, we employed a color-coding system. Figure 5 shows the specific color scheme used to represent the different measured pressures of the Y₂MoO₆:Eu³⁺ sample. The training data is structured as a matrix, with each row representing a spectrum measured at a specific pressure.

To evaluate the effectiveness of the constructed training set and the actual diversity of the data, we applied several visualization techniques. These visualization techniques are based on dimensionality reduction in the data. The best results were obtained using UMAP, so only UMAP clustering is presented here.

Figure 6 shows the UMAP clustering of the high-pressure data for the Y₂MoO₆:Eu³⁺ sample. The data points are clearly grouped, with a strong correlation between the proximity of points in the intensity ratio data (from Figure 4) and their arrangement in the UMAP embeddings plot. While it is important to note that UMAP, unlike methods such as Principal Component Analysis, does not have a direct physical analogy, we have consistently found it to be the most effective visualization method for this type of spectral data in both this and our previous studies.

After successfully visualizing our data with UMAP, we began using a deep learning neural network to model the measured spectra. If the data points are not well clustered in Figure 6, training the deep learning artificial neural network would be ineffective.

3.1. Model and Training Configuration

The deep learning artificial neural network (ANNDL) implementation in SOLO can utilize either the SciKit or TensorFlow Python 3.9.13 packages. In our study, we selected TensorFlow, which leverages GPU acceleration for highly efficient computations.

The core concept of high-pressure estimation using ANNDL involves training the network with sample spectra paired with corresponding pressure measurements. During training, the network iteratively minimizes the error between predicted and actual pressures. Since the region of interest in the measured spectra spans 575.05–640.08 nm, and given the resolution of the spectrometer, the input layer of the deep learning network contains 548 nodes. The output node provides predicted pressure.

Following a period of trial and error, we found that a network with two hidden layers, each containing 100 neurons, provided the best results.

After extensive experimentation, we configured our deep learning model using the Relu activation function. We found that the Adam and Adamax optimizers performed best, with Adamax showing a slight edge in performance. Based on the learning curves in Figure 7 and Figure 8, we set the number of epochs to 60 for the Adam optimizer and 50 for Adamax. The learning curve for Adamax demonstrated a slightly more consistent and stable convergence pattern compared to the one for Adam.

We used a Venetian blind cross-validation method [40] with a 10-fold split, meaning 90% of the data was used for training and 10% for validation in each sub-validation experiment. The data structure is shown in Figure 5. After augmentation [41], each pressure value is represented by 10 spectra, resulting in a total of 130 spectra. Each test set was determined by selecting every tenth spectrum from the dataset, starting with spectrum number 1 and continuing through all spectra. In practice, 10% of the data (corresponding to the same pressure) (corresponding to one spectrum per pressure, i.e., 13 spectra) was treated as unknown, while the remaining 90% was used for training. In each of the 10 sub-validation experiments, a different 10% of the data was set aside as unknown to the computer. This is a standard feature of the SOLO machine learning software, designed for situations of this kind. After further testing, we selected a batch size of 10, a value different from the default setting in the Solo software (Version 9.1).

3.2. Data Preprocessing

Before training, the data underwent a two-step preprocessing procedure using built-in options in the SOLO software. First, 1-Norm (area = 1) normalization was applied to the dataset. The data was then smoothed using a Savitzky–Golay filter with a width of 5, a polynomial order of 0, and weighted tails.

Figure 9 and Figure 10 display the deep learning model’s predictions versus the measured pressures for the Adam and Adamax optimizers. The performance metrics for Adam are RMSEC (root mean standard error of calibration) = 0.106 GPa and RMSECV (root mean standard error of cross-validation) = 0.312 GPa. The Adamax optimizer demonstrated superior performance, achieving a slightly better RMSEC of 0.105 GPa and a significantly lower RMSECV of 0.150 GPa. This indicates that while both optimizers behaved similarly on the training data, Adamax showed a marked advantage in its ability to generalize and make accurate predictions on new, unseen data. These errors are quite satisfactory, as visually confirmed by the plots.

To further visually analyze the model’s accuracy, the residuals—which represent differences between the pressures used for training and the pressures predicted by the deep learning network—are shown in Figure 11 and Figure 12. The high residuals correspond to data outside the training set.

4. Discussion

Although the Y₂MoO₆:Eu³⁺ nanomaterial employed in this study exhibits a narrower measurement range than some host–dopant systems reported in the literature [1,3,5,6,7,8,9], its performance is somewhat superior to others [2,4]. Nevertheless, our primary objective was not to maximize the measurement range, but rather to develop a method that leverages the full information contained in the measured spectra, allowing for a more comprehensive and accurate analysis within the material’s effective range.

It should be noted that the comprehensive review and comparison of high-pressure sensors presented in [22] indicates that there are many sensors superior to the Y₂MoO₆:Eu³⁺ nanomaterial. At the same time, this review highlights that the search for improved high-pressure sensors is still ongoing. Moreover, it inspired the idea of using a streak camera, as employed in our previous publications, to determine the pressure dependence of the lifetime for candidate high-pressure sensors.

We did not include plots of the material’s behavior during decompression. It is known that some Eu³⁺-doped materials do not preserve their cycling characteristics [45,46,47]. We acknowledge the possibility of differing behavior during decompression; however, as shown in our earlier work [37], the compression and decompression curves are nearly identical. Since no hysteresis was observed in the high-pressure calibration curves during decompression, this data was neither recorded nor incorporated into the ML analysis.

We also considered the hydrostatic limit of the 4:1 methanol–ethanol pressure medium, which is around 10–11 GPa [48]. Consequently, it is unclear whether the observed change at 9 GPa reflects the onset of a phase transition or arises from non-hydrostatic effects. In addition, only a single ruby sphere was used, preventing us from evaluating potential stress gradients by comparing measurements from multiple ruby spheres placed at different positions within the diamond anvil cell.

In a previous study [49], the authors reported that monoclinic Y₂MoO₆ shows no phase transition up to 34.5 GPa. We do not have the technical capabilities to verify the crystalline phase at higher pressures. As shown in Figure 4, around 9 GPa, the intensity ratio changes, which we interpret as a possible structural transformation. According to [8], such transformations are not abrupt, and there exists a pressure range where two phases coexist. It is also worth noting that [49] employed the same 1:4 ethanol–methanol mixture as a pressure-transmitting medium, which could be used beyond 10–11 GPa if stress gradients were monitored using multiple ruby spheres. Finally, our Y₂MoO₆:Eu³⁺ sample was sintered at 800 °C, whereas in [49], the material was sintered at 1400 °C; this difference may explain the variation in observed behavior.

5. Conclusions

In this study, we successfully demonstrated the potential of using machine learning (ML) to improve high-pressure luminescence sensing. The UMAP visualization method confirmed that our augmented experimental data could be effectively grouped by pressure, validating its suitability for ML analysis. We then showed that a deep learning neural network could accurately predict the applied pressure based on the measured luminescence spectra. To our knowledge, this is the first study to present such a machine learning-based improvement for high-pressure sensing.

While the Y₂MoO₆:Eu³⁺ nanomaterial used in this research has a more limited measurement range compared to some other hosts and dopants in the literature [1,3,5,6,7,8,9], its performance is slightly superior to others [2,4]. Our primary goal, however, was not to maximize the measurement range but to provide a method that fully utilizes all available information from the measured spectra, enabling a more complete and accurate analysis within the working range of the material.

We employed a machine learning (ML) approach to improve high-pressure measurements from the optical spectra of Y₂MoO₆:Eu³⁺. This method moves beyond the conventional technique of using only the intensity ratio or spectral shift of select spectral peaks. Instead, we trained a computer model to recognize the complete spectral signature associated with different pressures, which allowed us to incorporate both peak intensity ratios and spectral shifts. This advanced analysis successfully extended the useful pressure range of the Y₂MoO₆:Eu³⁺ material to 12 GPa, representing a significant improvement over traditional methods.