Abou Maher

Ekaterina Karam

Nils Mukhina

Isabelle Daras

Hélène Rivals

Wafa Pillet

Nathanaël Skalli

Yohan Connesson

Pierre-Yves Payan

Rohan

Karam

Ekaterina Mukhina

Nils Daras

Isabelle Rivals

Helene Pillet

Wafa Skalli

Nathanaël Connesson

Yohan Payan

Pierre-Yves Rohan

Reliability of B-mode ultrasound and shear wave elastography in evaluating sacral bone and soft tissue characteristics in young adults with clinical feasibility in elderly

Keywords: pressure ulcer, sacrum, medial sacral crest, elderly, ultrasound, shear wave elastography, elasticity, reliability B-mode, Brightness mode, CI, confidence interval, CT, Computed tomography, FE, Finite element, HT, Hypodermis thickness, hSWE, hypodermis shear wave elastography, HE, Medial sacral crest height, ICC, intraclass correlation coefficient, IT, ischial tuberosity, MRI, Magnetic resonance imaging, MSC, Medial sacral crest, mSWE, muscle shear wave elastography, OA, Medial sacral crest opening angle, PSIS, Posterior superior iliac spine, PU, Pressure ulcer, ROC, Medial sacral crest radius of curvature, ST, Skin thickness, SWE, Shear wave elastography, sSWE, Skin shear wave elastography, US, ultrasound

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Tissue morphology, mechanical properties, physiology, and repair properties can all change over time as a result of aging, lifestyle, chronic injury, or disease. Over a bony prominence, these changes -associated with a mechanical load -can lead to a localized injury known as a "pressure ulcer" [START_REF] Pppia | Prevention and Treatment of Pressure Ulcers/Injuries: Clinical practice Guideline. The International Guideline[END_REF].

The prevalence of this lesion ranges between 9% [START_REF] Moore | Pressure ulcer prevalence and prevention practices in care of the older person in the Republic of Ireland[END_REF] and 15% [START_REF] Børsting | Prevalence of pressure ulcer and associated risk factors in middle-and older-aged medical inpatients in Norway[END_REF] in long term care or hospitalized patients , and is most frequently observed over the sacrum or the heel. Two thirds of PU are observed in patients above 70 years of age [START_REF] Agrawal | Pressure ulcers: Back to the basics[END_REF]. The occurrence of PU is associated with significant increase in hospital costs, length of stay and, most importantly, an increased risk of death. [START_REF] Allman | Pressure ulcers, hospital complications, and disease severity: impact on hospital costs and length of stay[END_REF]- [START_REF] Moore | Risk assessment tools for the prevention of pressure ulcers[END_REF].

While numerous and efficient therapies have been developed, prevention remains the center of interest of all healthcare professionals and thus of researchers [START_REF] Agrawal | Pressure ulcers: Back to the basics[END_REF]. However, current practices in PU prevention are far from satisfactory with more than 85% lack in documented repositioning care plan. This is majorly due to the lack of staff and time [START_REF] Moore | Pressure ulcer prevalence and prevention practices in care of the older person in the Republic of Ireland[END_REF]. PU prevention protocols are based on risk assessment tools or scales (Norton scale, Braden scale…) [START_REF] Balzer | The Norton, Waterlow, Braden, and Care Dependency Scales: comparing their validity when identifying patients' pressure sore risk[END_REF]. The impact of these tools on the incidence of PU remains uncertain and fail to meet the needs of all patients in different clinical settings [START_REF] Moore | Risk assessment tools for the prevention of pressure ulcers[END_REF].

The process of aging is associated with physiological changes including sarcopenia, osteoporosis, progressive increase in blood glucose and skin atrophy [START_REF] Boss | Age-Related Physiological Changes and Their Clinical Significance[END_REF]. The decrease in muscular power has a high impact on the performance of daily activities even in healthy older persons leading to increased immobility [START_REF] Harms | Exercise physiology of normal development, sex differences, and aging[END_REF]. In consequence, the elderly are considered at risk of developing PU and therefore, a target group for preventive screening protocols. Several bedside technologies combined with assessment tools were investigated for early detection of PU, especially in long term care facilities. High frequency ultrasound (HFUS) was particularly studied, given its accessibility and capacity to detect preclinical superficial skin changes, mainly the presence of fluid/oedema at different levels of the skin [START_REF] Oliveira | Accuracy of ultrasound, thermography and subepidermal moisture in predicting pressure ulcers: a systematic review[END_REF]. However, a randomized controlled trial [START_REF] Grubbs | The Effect of High Frequency Ultrasound on the Prevention of Pressure Ulcers in Long-term Care Patients[END_REF] failed to demonstrate that HFUS was an effective strategy for predicting the development of Category/Stage I PU s of the heel or sacrum compared with a focused physical assessment. Also, a systematic review [START_REF] Scafide | Bedside Technologies to Enhance the Early Detection of Pressure Injuries: A Systematic Review[END_REF] evaluated HFUS among other technologies. Despite giving meaningful and consistent results, it could not be recommended due to lack of reliability of protocols, being limited to detecting macroscopic level tissue damage, and its training requirements for image interpretation.

In terms of etiology/pathophysiology, studies based on both in vitro (cell models) and in vivo (animal models) approaches have demonstrated that at least two damage mechanisms, are involved in the development of PU: first, compression damage due to tissue ischemia/reperfusion initiated by local, moderate and persistent mechanical loads; secondly, direct deformation damage above a threshold level related to shear strain; even for a short period of time (during transfer from bed to a wheelchair for example) [START_REF] Oomens | How does lateral tilting affect the internal strains in the sacral region of bed ridden patients? -A contribution to pressure ulcer prevention[END_REF]. These results suggest the presence of a direct link between mechanical determinants and biological processes leading to tissue damaging and, in fine, necrosis.

Based on the rationale that elucidating the relationship between external loads and internal local stresses and strains within loaded soft tissues has the potential of improving the management and prevention of PUs, several Finite Element (FE) models of the buttocks have been proposed in the literature. Models are mostly based on the segmentation of MRI or CT scan sequences [START_REF] Levy | An air-cell-based cushion for pressure ulcer protection remarkably reduces tissue stresses in the seated buttocks with respect to foams: Finite element studies[END_REF]- [START_REF] Linder-Ganz | Assessment of mechanical conditions in sub-dermal tissues during sitting: A combined experimental-MRI and finite element approach[END_REF]. However, the use of MRI and CT scans is limited due to cost, accessibility, and time [START_REF] Akins | Feasibility of freehand ultrasound to measure anatomical features associated with deep tissue injury risk[END_REF]. In this perspective, brightness mode (B-mode) ultrasound (US) imaging was proposed as an alternative to MRI or CT-scan. Feasibility, reproducibility, and its use for personalized FE models were investigated mainly over the ischial tuberosity [START_REF] Akins | Feasibility of freehand ultrasound to measure anatomical features associated with deep tissue injury risk[END_REF]- [START_REF] Macron | Is a simplified Finite Element model of the gluteus region able to capture the mechanical response of the internal soft tissues under compression?[END_REF].

Recent studies [START_REF] Akins | Feasibility of freehand ultrasound to measure anatomical features associated with deep tissue injury risk[END_REF], [START_REF] Gabison | Ultrasound imaging of tissue overlying the ischial tuberosity: Does patient position matter?[END_REF], [START_REF] Sonenblum | Seated buttocks anatomy and its impact on biomechanical risk[END_REF] proposed B-mode US for the evaluation of biomechanical risk of PU in a seated position by assessing, among other parameters, tissue thickness changes in different positions. On the other hand, ultrasound elastography, a relatively new method that shows structural changes in tissues following application of physical stress can be used in the examinations of musculoskeletal system [START_REF] Paluch | Use of Ultrasound Elastography in the Assessment of the Musculoskeletal System[END_REF]. Shear wave elastography (SWE) uses focused ultrasonic beams, to remotely generate mechanical vibration sources radiating low-frequency, shear waves inside tissues [START_REF] Bercoff | Supersonic shear imaging: a new technique for soft tissue elasticity mapping[END_REF]. It allows a bedside evaluation of the local mechanical properties of soft biological tissues by assessing shear modulus [START_REF] Deprez | On the potential of ultrasound elastography for pressure ulcer early detection[END_REF]- [START_REF] Sigrist | Ultrasound Elastography: Review of Techniques and Clinical Applications[END_REF]. Experiments demonstrated that ultrasound elastography is a promising technique for PU detection, especially at an early stage of the pathology, when the disease is still visually undetectable [START_REF] Deprez | On the potential of ultrasound elastography for pressure ulcer early detection[END_REF].

Previous studies investigating the combination of B-mode US and SWE elastography in the context of PU prevention focused on potential changes of tissue stiffness during prolonged loading [START_REF] Schäfer | Using ultrasound elastography to monitor human soft tissue behaviour during prolonged loading: A clinical explorative study[END_REF] or tissue characteristics in different body postures [START_REF] Mansur | Ultrasound elastography reveals the relation between body posture and soft-tissue stiffness which is relevant to the etiology of sitting-acquired pressure ulcers[END_REF].

The current study aimed to propose and test a bedside B-mode US and SWE protocol that can be used as a risk assessment tool for sacral PU in elderly. The protocol was designed for the evaluation of bone geometry, tissue morphology and mechanical characteristics over the sacrum. Reliability and reproducibility of our protocol were tested on a healthy young adults group. The protocol was then applied on a group of healthy older people to assess for clinical feasibility.

Materials and methods

Data Collection

The current study was approved by the ethics committee (

Ultrasound acquisition protocol

B-mode US images and shear wave elastography (SWE) videos were obtained using a commercial device (SupersonicMach30, SuperSonic Imagine, France). Two probes were used, the curvilinear (SuperCurved C6-1X) with low frequency (1 to 6 MHz allowing increased depth visualization) and large field of view, and the linear (SuperLinear L10-2) probe with a higher frequency (2 to 10 MHz allowing superficial layers visualization). The general mode and penetration optimization were chosen for all acquisitions.

A standardized -tissue and musculoskeletal US/SWE over the sacral region -protocol was developed and was first pilot tested on a sample of three healthy young volunteers, consequently, adjustments were made. The definitive protocol is described thoroughly in Appendix 1.

Acquisitions were taken in the lying prone position. After anatomic palpation of the two posterior superior iliac spines (PSIS), the curvilinear probe was first used in B-mode to recognize the anatomic region of interest: the MSC. An image was captured to assess bone anatomy and the skin was marked with a tape. Switching to the linear probe, the second image captured the skin and hypodermis at the level of the MSC. The third part, also using the linear probe at the marked skin level, was a series of three videos (of 10 seconds each) in SWE mode with a region of interest (ROI) including both skin and hypodermis. For the fourth and last part, three SWE videos of the gluteus maximus muscle were taken lateral to the sacro-coccygeal region at the lower part of the sacrum. The images/videos using the linear probe were taken with minimal applied pressure, using a thick gel layer and making sure it was visible on the US image. A summary of the acquisition protocol and images are shown in figure 1.

Parameter estimation

To reduce acquisition time, processing and measurements for images/videos were done separately using a custom software written in Matlab (R2019a) (MathWorks, Inc, Natick MA). In total 8 parameters were measured using the images/videos captured during each acquisition. First, the bone anatomy image (fig. 1a) was used to measure the MSC radius of curvature (ROC), opening angle (OA), and height (HE). Then, the second image (fig. 1b) was used to measure the skin thickness (ST) and the hypodermis thickness (HT). For the SWE videos of the third (fig. 1c) and fourth (fig. 1d) part of the acquisition, images were extracted and processed using a separate written code [START_REF] Vergari | Intervertebral disc characterization by shear wave elastography: An in vitro preliminary study[END_REF]. The average value of the images of each video was calculated and then, the average of the three videos determined the shear wave velocity of one acquisition for: the skin (sSWE), the hypodermis (hSWE), and gluteus maximus muscle (mSWE). Details about the definitions and recommendations for these measurements are reported in table 1.

Method Evaluation

Sample size and Reliability assessment

All the data were analyzed with the IBM SPSS for Windows (Version 27.0. Armonk, NY: IBM Corp).

The reliability study was conducted on the young, healthy group by two operators: a physician and an engineer. Both operators received extensive training consisting of two phases: first, measurements were repeated until reaching adequate reproducibility compared with an expert sonographer then, deviations were assessed, and possible problems were determined and corrected.

The operators were asked to repeat the protocol three times on each subject, i.e., captured three images for each of the bone geometry parameters and tissue morphology, and nine SWE videos for each tissue stiffness parameter.

The reliability of our protocol was assessed by calculating the intra class correlation coefficient (ICC) for withinoperator and between-operator for the young subjects group [START_REF] Mcgraw | Forming Inferences About Some Intraclass Correlation Coefficients[END_REF]. The minimum sample size required for this testretest reliability study was estimated based on the recommendations made in Bujang et al [START_REF] Bujang | A simplified guide to determination of sample size requirements for estimating the value of intraclass correlation coefficient: A review[END_REF]. With three observations per subject, a minimum sample size of 15 is required to detect an ICC value of 0.5 with power of 90% when taking a type I error risk of 5% (table 1a of [START_REF] Bujang | A simplified guide to determination of sample size requirements for estimating the value of intraclass correlation coefficient: A review[END_REF]).

Given that ultrasound acquisition is highly operator dependent, and that the processing/measurement of a given image/video (i.e. definitions of parameters) might also differ from one operator to another, we decided to quantify the variability first at processing level, and then at both processing and acquisition level. First, the two operators processed and measured one acquisition conducted by the physician on all subjects. Each operator repeated measurement of the same image/video three times, allowing an intra-image analysis [START_REF] Hebert | A systematic review of the reliability of rehabilitative ultrasound imaging for the quantitative assessment of the abdominal and lumbar trunk muscles[END_REF]. For this analysis, the ICC model 3 (2-way mixed)

was chosen for within-operator reliability, and ICC model 2 (2-way random) for between-operator reliability with absolute agreement type and single measure [START_REF] Koo | A Guideline of Selecting and Reporting Intraclass Correlation Coefficients for Reliability Research[END_REF]. For between operator reliability, values of one of the three measurement, chosen randomly for each operator, was used. Then, each operator processed and measured their own acquisitions allowing an inter-image analysis [START_REF] Hebert | A systematic review of the reliability of rehabilitative ultrasound imaging for the quantitative assessment of the abdominal and lumbar trunk muscles[END_REF]. The same model and type for within-operator ICC (2-way mixed and absolute agreement) were used with single measure, and for between-operator reliability also the ICC model 2 was used but with consistency agreement type and single measure since different images are compared. Also, for between operator reliability, values of one of the three measurements, chosen randomly for each operator, was used.

This procedure was conducted for each parameter and the ICC with 95% confidence interval was reported. Values less than 0.5, between 0.5 and 0.75, between 0.75 and 0.9, and greater than 0.90 indicated poor, moderate, good, and excellent reliability, respectively [START_REF] Koo | A Guideline of Selecting and Reporting Intraclass Correlation Coefficients for Reliability Research[END_REF].

Agreement assessment

The modified Bland Altman plot analysis for continuous measures [START_REF] Jones | A graphical method for assessing agreement with the mean between multiple observers using continuous measures[END_REF] was used as a measure of the level of agreement within and between operators for both the intra-image and inter-image analysis. In the absence of a gold standard, the value of each measurement was compared to the average of all measurements for one subject (bias line equal to zero).

The difference between each observer and the overall mean for a subject is estimated. The 95% level of agreement with the mean is estimated as ±2 x Standard deviation (SD), where SD represents the square root of the variance of the differences.

Healthy young adults vs healthy elderly

The same protocol was conducted once (one acquisition and measured once) on the older group by one operator: the physician. For the young adults group data, the measurements of one of the three acquisitions collected by the physician were chosen randomly. Normality was checked with the Shapiro-Wilk test and the equality of variance was assessed with the Levene's test. If both normal distribution and equality of variance of the different groups could be assumed, data were reported per parameter and per group as mean ±1 SD and groups (young versus old) were compared using the student t-test. In case the normality or equality of variance assumption was violated, groups were compared with the Wilcoxon test. For all the tests, the significance level was set at 0.05 a priori.

Results

Reliability assessment

Within operator and between operator ICC with the 95% confidence interval, for both the intra and inter-image analysis for all parameters, are reported in table 2. First in the intra-image analysis, all ICC confidence interval values showed good to excellent reliability for within operator, except for the ROC, and the OA of the MSC for the physician with moderate to excellent reliability. For between operator ICC the following parameters: HE, hypodermis thickness, SWE skin, SWE hypodermis, SWE muscle, showed good to excellent reliability. The ICC for the OA and the skin thickness showed moderate to excellent reliability. For the inter-image analysis, within operator ICC showed excellent reliability for the hypodermis thickness parameter for both operators. The physician (operator 1) showed good to excellent reliability for the ROC and HE. For the SWE skin parameter he showed moderate to excellent reliability; for the opening angle parameter moderate to good reliability; for the remaining parameters poor to good reliability. The to claim that the distributions were not normal or that the variances were not equal. Based on the results of the student t-test, we concluded that there is a statistically significant difference only for the mSWE (2.11 ± 0.27 m/s for the young adults group vs 1.70 ± 0.17 m/s for the elderly, p-value = 0.001). Because of the relatively small sample size, the sample means for each parameter were also compared using the Wilcoxon signed rank test. The conclusions were the same i.e., there is a statistically significant difference only for the mSWE.

Images reported in figure 2 show observations for the older group subjects that diverged from the group. The upper and lower limits for skin and hypodermis SWE were found in a 62-year-old male subject with a BMI of 39.1 kg/m² (fig. 2a) and a 67-year-old male with a BMI of 27.4 kg/m² (fig. 2b), respectively. A 62-year-old female elderly with a BMI of 22.3 kg/m² (fig. 2c) showed a heterogeneous distribution of hypodermis thickness over the MSC.

Discussion

This study aimed to evaluate the use of B-mode US and SWE in the assessment of bone geometry, tissue morphology and tissue stiffness in the context of sacral PU prevention in elderly. A protocol was developed to evaluate the region over the MSC. It was tested for reliability on a group of 19 healthy young subjects by two operators: a physician and an engineer. Afterwards, the protocol was tested on a group of 11 healthy older people by the physician only. The parameters evaluated by our protocol were: the radius of curvature (ROC), opening angle (OA), and height (HE) of the MSC for the bone geometry; the skin thickness (ST), and hypodermis thickness (HT) for the tissue morphology; skin shear wave velocity (sSWE), hypodermis shear wave velocity (hSWE), and muscle shear wave velocity (mSWE) for tissue stiffness.

Reliability study

The intra-image analysis was first conducted to assess the operators understanding and reliability of measuring each parameter. Within-operator ICC was good to excellent for all parameters for the engineer. For the physician, most parameters showed good to excellent reliability except for the ROC (CI 0.68-0.94) and OA (CI 0.66-0.94), showing moderate to excellent reliability. This might be due to an unclear definition of these two parameters. While the ROC is measured by placing points on the tip of MSC, the position of the start and ending points are not always clear.

Between operator ICC, for the intra-image analysis, showed good to excellent reliability for all parameters except ROC, OA, ST with moderate to excellent reliability. These results also highlight the difficulty in choosing the points for the ROC and OA. For the ST parameter, although the skin is a continuous layer over the hypodermis, both stratum corneum : the most superficial layer of the epidermis, and the reticular layer: the lower part of the dermis, are wavy layers and thus might affect ST measurement depending on the part of the image chosen to assess ST [START_REF]Junqueira's Basic Histology Text and Atlas, 16e[END_REF]. The interimage analysis aimed to test whether operators are capable of successfully repeating an acquisition three times and reproducing the acquisition protocol. Because acquisitions measured were not the same, ICC results were expected to have lower values. The discussion will involve only the parameters that showed good to excellent reliability on the intra-image analysis. First the HE parameter, within operator reliability was good to excellent for the physician but low to good for the engineer. A possible explanation might be that the acquisitions were not taken at the same level over the MSC. Another explanation is the fact that, in terms of anatomy, the sacrum is the most variable portion of the spine. In fact, the MSC is formed by the fusion of the spinous processes of the first three to four sacral vertebrae, and therefore bone morphology might differ from a level to another [START_REF] Cheng | Anatomy of the sacrum[END_REF]. In this perspective, an emphasis should be on taking the acquisition at the level of the two PSIS, since it is a fixed, palpable and US visible anatomic landmark (using the curvilinear probe). Also, the only study, that the authors found in the literature, that included US and SWE tissue evaluation of the sacral region reported neither the protocol of measurement nor the US anatomic landmark used during acquisition [START_REF] Schäfer | Using ultrasound elastography to monitor human soft tissue behaviour during prolonged loading: A clinical explorative study[END_REF]. The authors think that this biased the results since the anatomy of the sacrum is complex and irregular [START_REF] Cheng | Anatomy of the sacrum[END_REF], [START_REF] Baron-Sarrabère | Sacrum, coccyx, articulations sacro-iliaques : technique radiologique et aspects normaux[END_REF].

For the shear wave velocity: within operator and between operator ICCs showed moderate to excellent reliability for the skin; low to good reliability for hypodermis and muscle for both within and between operator ICCs. Possible reasons include signal instability and inhomogeneity associated with tissue depth and operator's experience. Another reason might be tissue anisotropy, therefore tissue SWE signal depends on the orientation of the probe relative to the layer tested. Also, this affects much more muscular fibres since they're organised with a geometric alignment compared with the less structured adipose tissue or skin [START_REF] Serafin-Król | Diagnostic errors in musculoskeletal ultrasound imaging and how to avoid them[END_REF]. This explains the larger gap observed in the CI of between operator ICC for the mSWE (table 2).

The agreement plots were drawn to assess clinical significance of difference between measurements even when a parameter showed good reliability [START_REF] Jones | A graphical method for assessing agreement with the mean between multiple observers using continuous measures[END_REF]. In the absence of a gold standard imaging tool in our study the level of agreement necessary for confident usage remains uncertain. However, we hypothesized that the clinical difference between different groups is significantly higher than the uncertainty of the measurements. For the bone geometry parameters, previous studies focused on ischium morphology and its impact on internal soft tissue strain thus on the occurrence of PU using mainly FE models [START_REF] Macron | Is a simplified Finite Element model of the gluteus region able to capture the mechanical response of the internal soft tissues under compression?[END_REF], [START_REF] Gefen | Risk factors for a pressure-related deep tissue injury: a theoretical model[END_REF]. Our aim was to combine the three bone parameters : ROC, OA, and HE to differentiate a sharp tip from a flat tip [START_REF] Candadai | Stress distribution in a physical buttock model: Effect of simulated bone geometry[END_REF]. For our knowledge, no research was conducted on the impact of the shape of the MSC on surrounding tissue deformation. In fact, reliability of bone morphology assessment using ultrasound is controversial: Akins et al [START_REF] Akins | Feasibility of freehand ultrasound to measure anatomical features associated with deep tissue injury risk[END_REF] found good between operator reliability for ischial tuberosity (IT) radius of curvature but they only reported the average ICC = 0.712 , while Swaine et al [START_REF] Swaine | Adaptation of a MR imaging protocol into a real-time clinical biometric ultrasound protocol for persons with spinal cord injury at risk for deep tissue injury: A reliability study[END_REF] found poor reliability for estimating inferior curvature of the IT in both its short and long axis. The methodology for our protocol combining an intra-image and-inter image analysis seemed promising but, with lack of reliability in the results and no clinical baseline for the MSC morphology, no interpretation could be given to the agreement plots reported in figure 2 for these parameters.

For tissue morphology parameters, skin thickness showed low reliability and a 95% CI of agreement with the mean of ±1.04 mm for the inter-image analysis. With a maximum skin thickness reported in the literature of 4mm [START_REF]Junqueira's Basic Histology Text and Atlas, 16e[END_REF] this parameter needs further investigation before clinical use. A possible solution might be to tell operators to measure the ST directly over the MSC. In this perspective and since the linear probe is limited in depth and field of view, the first acquisition using the curvilinear probe is crucial for identifying and marking the level of the MSC, but also its exact position over the spine midline. In fact, previous studies investigating the inter-operator reliability of tissue thickness measurement over IT showed : excellent reliability for total thickness with an average ICC=0.948, also without reporting the confidence interval [START_REF] Akins | Feasibility of freehand ultrasound to measure anatomical features associated with deep tissue injury risk[END_REF] ; moderate to excellent reliability (0.60-0.95) for skin and fat thickness [START_REF] Swaine | Adaptation of a MR imaging protocol into a real-time clinical biometric ultrasound protocol for persons with spinal cord injury at risk for deep tissue injury: A reliability study[END_REF]. To our knowledge, no study investigated the reliability of measuring tissue thickness using US over the sacrum. On the other hand, hypodermis thickness parameter showed excellent reliability and a 95% CI of agreement with the mean of ±1.4mm for the inter-image analysis. Since hypodermis thickness is variable, and mainly related to body mass index [START_REF] Gibney | Skin and subcutaneous adipose layer thickness in adults with diabetes at sites used for insulin injections: implications for needle length recommendations[END_REF] with a value exceeding sometimes 50 mm over lumbar spine [START_REF] Lee | Fat Thickness as a Risk Factor for Infection in Lumbar Spine Surgery[END_REF], the clinical significance of this agreement seems plausible. However, the interpretation depends on another factor: the homogeneity of the distribution of the hypodermis over the sacrum. This is going to be discussed in the next section.

For tissue stiffness parameters, although reliability was not satisfactory for all three parameters: skin, hypodermis, and muscle; the 95% CI level of agreement with the mean of the inter-image analysis of ±0.33 m/s; ±0.29 m/s; ±0.25 m/s respectively, was minimal. In fact, previous studies investigating changes of shear wave velocity values in specific circumstances or disease showed: with prolonged loading in elderly, shear wave velocity of superficial region (mainly skin + hypodermis) over IT varied form 2.5 m/s to 3.3 m/s [START_REF] Schäfer | Using ultrasound elastography to monitor human soft tissue behaviour during prolonged loading: A clinical explorative study[END_REF]; contracture strips of the gluteal muscle showed a shear wave velocity of 7.23 m/s vs 1.84 m/s for a healthy muscle at the same position [START_REF] Guo | Shear-wave elastography assessment of gluteal muscle contracture[END_REF]. Because the aim of this evaluation is to point out subjects who significantly diverge from normal values, the SWE values for the three regions remain interesting to report. Nevertheless, interpretation should be taken with caution and further investigations are needed to increase reliability. Possible solutions might include operator's training, and taking SWE videos in the transverse and vertical directions, especially for muscle stiffness, since the properties parallel to the fibers are quite different from loading perpendicular to the fibers [START_REF] Escobar | Mechanical Characteristics of Muscle, Skin and Fat -Elastic Moduli for Finite Element Modeling of Limbs[END_REF].

Young adults vs healthy elderly

The following discussion will highlight observations noted when comparing parameters of the young adults group and the healthy older people for the acquisitions conducted only by the physician. The interpretations cannot be generalized since reliability of measurements was not satisfactory.

For bone parameters, aging is associated with structural, geometric and bone volumetric density changes [START_REF] Riggs | Population-Based Study of Age and Sex Differences in Bone Volumetric Density, Size, Geometry, and Structure at Different Skeletal Sites[END_REF]. It is unclear how that might affect the external shape of the MSC; the similar median values in the boxplot, and the absence of statistical significance of differences between the means for the three parameters might suggest that there are no US changes observable. Therefore, the estimation of these parameters aims to evaluate the impact of bone geometry on tissue deformation independently from age difference.

For the tissue morphology parameters, the median values for both ST and HT were lower for the older group, but no statistical difference was noted between means. In fact, studies have shown that thinning of the skin, associated with age, is observed in subjects with more than 70 years [START_REF] Lasagni | Echographic assessment of age-dependent variations of skin thickness[END_REF] while our older age group had a mean age of 65 ± 2.4 yrs.

Nevertheless, the mean ST of the young adults group 3.61 ± 0.55 mm was close to values previously reported for the skin over the sacrum like, for example, Yalcin et al [START_REF] Yalcin | Skin thickness on bony prominences measured by ultrasonography in patients with spinal cord injury[END_REF] found a mean of 3.2 ± 0.5mm. Also studies comparing tissue thickness differences between SCI patients without vs with history of PU showed total thickness average of 15.3 mm vs 9.5 mm over the apex of IT [START_REF] Sonenblum | Seated buttocks anatomy and its impact on biomechanical risk[END_REF]. Thus, the difference is quantifiable, but the challenge remains to determine a risk threshold value at high-risk patients. On the other hand, an observation, not reported in the literature to our knowledge, was noted for the hypodermis thickness distribution over the sacrum. One subject (fig. 2b) clearly showed thinning of HT from the lateral to medial spine. Possible causes might be a spinal deformation causing a shift in the hypodermis layer while the skin, loosely bonded to subjacent organs, can slide over and maintain the same thickness [START_REF]Junqueira's Basic Histology Text and Atlas, 16e[END_REF]. This highlights the importance of measuring the HT directly over the tip of the MSC instead of the thickest region as mentioned in our protocol. In fact, HT is considered as an important parameter affecting internal soft tissue response to load [START_REF] Macron | Is a simplified Finite Element model of the gluteus region able to capture the mechanical response of the internal soft tissues under compression?[END_REF] and thus, PU risk.

For the tissue stiffness parameters, median shear wave velocity for skin, hypodermis, and muscle was lower for the elderly group. Only for the muscle the difference showed statistical significance (p=0.001). In fact, physiologic aging is associated with a loss of muscle mass starting at the age of 30 [START_REF] Harms | Exercise physiology of normal development, sex differences, and aging[END_REF]. This might be caused by the infiltration of fat tissue and connective tissue into skeletal muscle [START_REF] Mccormick | Age-related changes in skeletal muscle: changes to life-style as a therapy[END_REF]. Previous studies suggest that this is associated with an increase in muscle stiffness [START_REF] Rahemi | The effect of intramuscular fat on skeletal muscle mechanics: implications for the elderly and obese[END_REF] and, with continuous compression, a further increase in muscle stiffness leading to injury [START_REF] Gefen | In Vivo Muscle Stiffening Under Bone Compression Promotes Deep Pressure Sores[END_REF].

While our results seem contradictory, since we noted a decrease in shear wave velocity between the young and the elderly group, the signal was collected closer to the proximal attachment of the gluteus maximus (lateral to the sacrococcygeal region) rather than the muscle belly. Moreover, most studies, evaluating tissue stiffness and PU, focused on the variation of stiffness with loading [START_REF] Schäfer | Using ultrasound elastography to monitor human soft tissue behaviour during prolonged loading: A clinical explorative study[END_REF], [START_REF] Gefen | In Vivo Muscle Stiffening Under Bone Compression Promotes Deep Pressure Sores[END_REF], [START_REF] Linder-Ganz | Strains and stresses in sub-dermal tissues of the buttocks are greater in paraplegics than in healthy during sitting[END_REF]. The complexity and duration of the exam, especially for highrisk subjects, makes it impossible to evaluate a large number in a loading position. That is why we proposed in our study to evaluate tissue characteristics in an off-loading position and determine normal ranges within homogenous groups. While studies suggest that aging is associated with a decline in skin stiffness [START_REF] Boss | Age-Related Physiological Changes and Their Clinical Significance[END_REF], [START_REF] Luebberding | Mechanical properties of human skin in vivo: a comparative evaluation in 300 men and women[END_REF] making it more susceptible to PU, there is no specific threshold value proposed for increased risk. On the other hand, sustained pressure application was associated with an increase in tissue stiffness [START_REF] Schäfer | Using ultrasound elastography to monitor human soft tissue behaviour during prolonged loading: A clinical explorative study[END_REF], [START_REF] Gefen | The biomechanics of sitting-acquired pressure ulcers in patients with spinal cord injury or lesions[END_REF], [START_REF] Shoham | Deformations, mechanical strains and stresses across the different hierarchical scales in weight-bearing soft tissues[END_REF].

Limits and perspectives

The lack of reliability of measures is the main limit of our study. This is mainly related to: difficulty in repeating acquisitions on the same anatomic level, definition of parameters, lack of signal stability, and ultrasound expertise.

Also, the patient's prone position might be problematic for higher risk subjects. The sample size and the number of operators is also a limitation of this study. However, the protocol we developed is clinically feasible and can be easily proposed to evaluate patients at bedside. The relatively easy palpation of the anatomic landmark (PSIS) allows the exam to be conducted by any physician or nurse. The perspectives include a review of the protocol to increase reliability and an evaluation of higher risk elderly in nursing homes. Also, this protocol can quantify all layers' characteristics including bone, muscle, hypodermis, and skin using only US and SWE. This might serve in -patient specific -finite element modeling since quantifying tissue strain and stress distribution over a bony prominence is essential in determining an injury threshold [START_REF] Macron | Is a simplified Finite Element model of the gluteus region able to capture the mechanical response of the internal soft tissues under compression?[END_REF], [START_REF] Linder-Ganz | Strains and stresses in sub-dermal tissues of the buttocks are greater in paraplegics than in healthy during sitting[END_REF], [START_REF] Loerakker | The effects of deformation, ischemia, and reperfusion on the development of muscle damage during prolonged loading[END_REF].

Conclusion

In this study, we developed a protocol using US and SWE to assess bone and tissue characteristics over the sacrum in the context of PU prevention in elderly. It is the first protocol that combines assessment of all layers over bony prominences using only one imaging technique.

The protocol's reliability was evaluated on a sample of young adults and then tested on a group of healthy older subjects. We provided a thorough description of anatomic landmarks on palpation and US visualization to ensure reproducibility and real clinical application. However, reliability was not satisfactory and further improvements of the protocol are needed. The results comparing the young to healthy older age group suggested that changes related only to age might affect tissue thickness and elasticity more than bone morphology, but this cannot be generalized or quantified before increasing reliability and sample size. On the other hand, an observation in one of the subjects of the elderly group was not found in the literature: a heterogeneous distribution of the hypodermis thickness over the sacrum. In order to evaluate the use of this tool for PU risk assessment, it is essential to test it on a high-risk sample like elderly in nursing homes or long hospital stay.

Finally, our recommendations for the scientific community -when using US and SWEare:

anatomic palpation and US recognition using the curvilinear probe.

report exact anatomic region and provide proof on the US image.

when measuring thickness and SWE ensure that acquisition is taken pressure free directly over the bone prominence and not in the surrounding region.

results cannot be generalized before testing for reliability.

Table 2 .

 2 180 engineer (operator 2) showed moderate to excellent reliability for the ROC, SWE skin, SWE hypodermis, and SWE 181 muscle parameters. For the opening angle parameter, the engineer showed moderate to good reliability; for the HE, 182 skin thickness poor to good reliability. The between operator ICC also showed excellent reliability for the hypodermis 183 thickness. The ICC for SWE skin parameter showed moderate to excellent reliability. The ICC of the remaining Reliability assessment results with Intraclass correlation coefficient ICC for both intra-image and inter-image analysisThe modified Bland Altman agreement plots for both the intra and inter image analysis are reported in figure2. The 95% limits of agreement with the mean varied from the intra to the inter-image analysis as follows: for the ROC from ±0.83 mm to ±1.1 mm; for the opening angle from ±15.8 degrees to ±24.8 degrees; for the HE from ±1.4 mm to ±6.1 mm; for the skin thickness from ±0.43 mm to ±1.04 mm; for the hypodermis thickness from 0.57 mm to 1.4 mm; for the SWE skin from ±0.03 m/s to ±0.[START_REF] Vergari | Intervertebral disc characterization by shear wave elastography: An in vitro preliminary study[END_REF] m/s; for the SWE hypodermis from ±0.06 m/s to ±0.29 m/s; and for the SWE muscle from ±0.08 m/s to ±0.25 m/s. The results of means, normality tests and Student's t-test test are reported in table 3. There was insufficient evidence

	184
	185	parameters showed poor to good reliability.
	186 187 188 189	for both operators: 1 the physician and 2 the engineer.

Table 3

 3

			Young adults	Healthy elderly	Student's
	Parameter	Mean ± SD	Shapiro Wilk test p-value	Mean ± SD	Shapiro Wilk test p-value	t-test p-value
	Bone	OA (°)	80.32 ± 21.06	0.628	79.54 ± 19.19	0.509	0.920
	anatomy
		HE (mm)	10.39 ± 4.45	0.119	8.20 ± 2.94	0.293	0.159
	(MSC)
		ROC (mm)	2.90 ± 1.21	0.191	2.19 ± 0.17	0.550	0.088
	Tissue	ST (mm)	3.61 ± 0.55	0.982	3.30 ± 0.53	0.215	0.147
	morphology	HT (mm)	8.67 ± 5.21	0.380	6.08 ± 3.56	0.457	0.156
		sSWE (m/s)	2.27 ± 0.28	0.087	2.22 ± 0.55	0.295	0.800
	Tissue stiffness	hSWE (m/s)	2.06 ± 0.16	0.497	1.98 ± 0.33	0.437	0.465
		mSWE (m/s)	2.11 ± 0.27	0.128	1.70 ± 0.17	0.758	0.001

. Mean of each parameter for the young adults group and healthy elderly, normality using Shapiro-wilk test and comparison using Student's t-test.

  close to values reported in the literature (2.5 m/s and 1.8 m/s respectively) for a similar sample of nine healthy volunteers with a mean age of 70.1 ± 4.8 years[START_REF] Schäfer | Using ultrasound elastography to monitor human soft tissue behaviour during prolonged loading: A clinical explorative study[END_REF].

	The two subjects presenting
	maximum and minimum skin/hypodermis baseline shear wave velocity in the elderly group (fig2.a; fig2.b) were
	overweight (BMI > 25 kg/m²). It is known that BMI values have an impact on the biomechanical behavior of tissues

[START_REF] Sopher | Exposure to internal muscle tissue loads under the ischial tuberosities during sitting is elevated at abnormally high or low body mass indices[END_REF]

,

[START_REF] Elsner | Is obesity a risk factor for deep tissue injury in patients with spinal cord injury?[END_REF]

, further investigations are needed to evaluate changes in tissue elasticity associated with BMI changes. Also the mean values of sSWE and hSWE over the sacrum of the elderly group (2.22 ± 0.55 m/s and 1.98 ± 0.33 m/s respectively) are

Acknowledgement

This project has received funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 811965.

Conflict of interest

None APPENDIX 1

Ultrasound and SWE protocol

Position and anatomic landmarks

The volunteer is asked to lie down in the prone position with a cushion under the pubis to reduce lumbar lordosis. The examiner inspects the skin to identify any redness/swelling over the sacral region. Then, he palpates the posterior superior iliac spine (PSIS) and recognizes the continuation of intergluteal cleft representing the midline of the spine.

Curvilinear probe

The curvilinear probe allows a large field of view and better visualization of deep layers. After applying gel on the skin or the probe, the examiner scans the sacral region between the two PSIS in B-mode transverse view. The MSC appears as a reverse V-shaped hyperechoic contour (fig. 1a). Sliding the probe lateral to the midline allows the recognition of the round shaped PSIS (fig. 1a). An image is captured showing the MSC and PSIS. The region is marked over the skin with a marker or medical tape.

NB: if PSIS is not visible on US the use of sagittal view of the sacrum allows to recognize the anatomic site of the MSC. The examiner can align the site in the middle of the US image and then rotate the probe 90 degrees to return to transverse view.

Linear probe

The linear probe is used to assess the superficial layers over the MSC. A thick layer of gel is applied directly on the midline of the marked level. The probe is then applied in the transverse B-mode view with minimum pressure.

Artefacts from air bubbles appear as a linear hypoechoic signal perpendicular to skin layers. The examiner eliminates air bubbles using the probe or by adding and spreading the gel again. An image is captured showing the skin and adipose tissue, and the thick layer of gel over the skin (fig. 1b).

The linear probe is also used in SWE mode at the same level with a thick gel layer and minimum pressure. The region of interest (ROI) covering the skin and adipose tissue is chosen, and the examiner waits for a homogeneous signal on the screen, increasing/decreasing elasticity range matching tissue stiffness. One measurement is three videos in SWE of 10 seconds each (or more if signal fluctuates). The last acquisition in SWE mode, for the gluteus maximus muscle, is taken lateral to the sacro-coccygeal region using the same procedure. The anatomic landmark is the sacral horns and sacro-coccygeal ligament described as the "frog sign". The muscle fibers are described as horizontal echoic lines under the skin and hypodermis (fig1.c).

List of figures

List of tables


M Akhlaghi

E Camposilvan

Z Goharibajestani

S Khabbaz Abkenar

C W Ow-Yang

Y Jorand

L Gremillard

V Garnier

J Chevalier
email: jerome.chevalier@insa-lyon.fr

yttria stabilized zirconia obtained by pressure-less sintering

Keywords: Yttria stabilized zirconia, Pressure-less sintering, Nanograin, Transparent ceramics

This work describes the development of transparent high-strength Yttria-Stabilized Zirconia (YSZ) ceramics with ultra-fine grain size utilizing conventional pressure-less densification. Starting with nanoparticles with diameter < 10 nm, it was possible to achieve full densification (>99.5% of theoretical density) at a sintering temperature of 1100-1200 °C. The average grain size of the resulting dense ceramics was 75 nm in 3 mol. % YSZ and 85 nm in 8 mol. % YSZ, showing in-line light transmission of 38% and 51% at a wavelength of 800 nm and average biaxial strength (piston on three balls test on samples of diameter 12 mm and thickness 1 mm) of 1980 MPa and 680 MPa, respectively. The nano-grained structure, absence of color centers, and miniaturization of residual pores enable the excellent light transmission. The high biaxial strength is attributed to the refined microstructure, but also to the martensitic tetragonal-to-monoclinic phase transformation that remains active even in nano-sized zirconia grains.

Introduction

Polycrystalline transparent ceramics are of great interest due to their unique combination of physical, mechanical, and optical properties. These high performance materials enable variety of applications such as infrared (IR) and heat resistant windows [START_REF] Serivalsatit | Synthesis, processing, and properties of submicrometer-grained highly transparent yttria ceramics[END_REF], lasers [START_REF] Du Merac | Increasing fracture toughness and transmittance of transparent ceramics using functional low-thermal expansion coatings[END_REF], [START_REF] Goldstein | Transparent ceramics at 50: progress made and further prospects[END_REF], ballistic armors [START_REF] Klimke | Transparent tetragonal yttria-stabilized zirconia ceramics: influence of scattering caused by birefringence[END_REF] etc. Fabrication of transparent ceramics generally requires high temperatures and long densification times to eliminate residual pores as the main light scattering centers. Light scattering is a function of pore size and content and depends on the wavelength [START_REF] Pabst | Light scattering models for describing the transmittance of transparent and translucent alumina and zirconia ceramics[END_REF]. Consolidation conditions give rise to grain growth which also favors transparency but at the expense of the mechanical properties [START_REF] Serivalsatit | Synthesis, processing, and properties of submicrometer-grained highly transparent yttria ceramics[END_REF]. Recent findings revealed that the scattering efficiency of residual pores substantially declines with size in nano-range [START_REF] Krell | Transparent compact ceramics: inherent physical issues[END_REF], [START_REF] Yamashita | Transmission properties of translucent polycrystalline alumina[END_REF]. As grain boundaries have less impact on transparency of ceramics compared to residual porosity [START_REF] Klimke | Transparent tetragonal yttria-stabilized zirconia ceramics: influence of scattering caused by birefringence[END_REF], [START_REF] Zhang | Optimization of highpressure sintering of transparent zirconia with nano-sized grains[END_REF], reducing the grain size of polycrystalline ceramics to < 100 nm and consequently, miniaturization of the residual pores can provide simultaneous transparency and higher mechanical performance compared to micron grain-sized counterparts [START_REF] Yamashita | Light scattering by residual pores in transparent zirconia ceramics[END_REF], [START_REF] Zhang | Making yttria-stabilized tetragonal zirconia translucent[END_REF].

Yttria Stabilized Zirconia (YSZ) can be the material of choice for the fabrication of nanocrystalline transparent ceramics. YSZ has attracted considerable attention in a promise of merging, in a single system, materials with outstanding mechanical properties (i.e. 3 mol. % YSZ with a strength of more than 900 MPa and fracture toughness of 5-10 MPa•m 1/2 ) and others with optical transparency (i.e. 8 mol. % YSZ) [START_REF] Xiong | Dynamic pore coalescence in nanoceramic consolidated by twostep sintering procedure[END_REF], [START_REF] Meyers | Mechanical properties of nanocrystalline materials[END_REF], [START_REF] Lach | From nanometric zirconia powder to transparent polycrystal[END_REF]. 3 mol.% YSZ has been predominantly an opaque material mainly due to birefringence of the tetragonal phase and thus, optical anisotropy at the grain boundaries [START_REF] Alaniz | Optical properties of transparent nanocrystalline yttria stabilized zirconia[END_REF]. On the other hand, 8YSZ-fully cubic zirconia offers an isotropic refractive index, which promotes transparency, but the absence of the stress-induced phase transformation in cubic zirconia significantly lowers the mechanical properties of 8YSZ (i.e., <400 MPa and <1.5 MPa•m 1/2 ) [START_REF] Yamashita | Light scattering by residual pores in transparent zirconia ceramics[END_REF]. Currently, consolidation of ceramic powders to nano-crystalline transparent structures can be achieved only by high-pressure (e.g., 1 GPa) sintering methods such as hot isostatic pressing (HIP) or spark plasma sintering (SPS) [START_REF] Lu | Sintering of nanoceramics[END_REF], [START_REF] Maglia | Densification and properties of bulk nanocrystalline functional ceramics with grain size below 50nm[END_REF]. Zhang et al. [START_REF] Zhang | Optical properties and microstructure of nanocrystalline cubic zirconia prepared by high-pressure spark plasma sintering[END_REF] and Klimke et al. [START_REF] Klimke | Transparent tetragonal yttria-stabilized zirconia ceramics: influence of scattering caused by birefringence[END_REF] have shown an increase of transparency with YSZ of ~100 nm grain size consolidated by SPS and HIP, respectively. Anselmi et al. [START_REF] Anselmi-Tamburini | Transparent nanometric cubic and tetragonal zirconia obtained by high-pressure pulsed electric current sintering[END_REF] further demonstrated the feasibility of 20% and 50% Real In-line Transmission (RIT) in the visible range (i.e., wavelength of 400-800 nm) for 3YSZ and 8YSZ, respectively, through obtaining fully-dense structures (thickness of 1 mm) with grain size of 50 nm after SPS and annealing in air. However, color centers and residual carbon generated by the reducing environment [START_REF] Xiong | Dynamic pore coalescence in nanoceramic consolidated by twostep sintering procedure[END_REF], as well as production cost, limited product size, and essential post-sintering annealing [START_REF] Drazin | Pressureless low temperature sintering of nanocrystalline zirconia ceramics via dry powder processing[END_REF], [START_REF] Krell | Fine-grained transparent spinel windows by the processing of different nanopowders[END_REF], raise questions about practicality of such non-conventional consolidation methods in commercial production [START_REF] Mazaheri | Densification and grain growth of nanocrystalline 3Y-TZP during two-step sintering[END_REF].

Given the limitations of the high-pressure sintering methods, using conventional pressure-less sintering is obviously preferable for densification of ceramics. In this approach, size and distribution of residual pores in dense bodies are directly influenced by powder features and green body preparation [START_REF] Binner | Processing of bulk nanostructured ceramics[END_REF], [START_REF] Szepesi | A critical assessment of nanometer-scale zirconia green body formation by pressure filtration and uniaxial compaction[END_REF]. With the goal of obtaining crack-free transparent bulk ceramics with a final grain size of less than 100 nm, the initial nanopowders should have a much smaller particle size. Under these circumstances, controlling the powder characteristics (e.g. size and agglomeration), green body formation (e.g., density, pore size, and pore size distribution), and sintering process becomes quite challenging. No such material has been obtained by pressure-less sintering so far.

In this study, 1.5-8 mol. % YSZ green bodies obtained from optimized nano-dispersions with an average primary particle size of 8 nm were characterized and densified by conventional pressure-less sintering in air. As reliable experimental data on both transparency and mechanical properties of nano-crystalline YSZ are scarce, we focused on the effect of microstructure on both optical properties (real in-line and total forward transmission) and mechanical performance (biaxial strength, hardness and fracture toughness) of nano-crystalline YSZ ceramics.

Experimental section 2.1. Starting materials and sample preparation

Aqueous colloidal suspensions of yttria-doped zirconia nanoparticles were prepared by Mathym SAS (Champagne-au-Mont-d′Or, France). In a typical synthesis, an aqueous solution of a zirconyl chloride octahydrate (ZrOCl2.8 H2O, 0.471 M) and yttrium chloride hexahydrate (YCl3.6 H2O, 0.033 M) were prepared, mixed for 1 h, and the mixed hydroxides were precipitated in an ammonium hydroxide solution (NH4OH, 3 M). After agitating for 1 h to break soft agglomerates, the resulting hydroxides were kept uninterrupted for 5 min to separate out the sediments. The supernatant was replaced by deionized water until a constant conductivity was achieved (displacement washing, typically 7 times). Subsequently, tetramethylammonium hydroxide pentahydrate solution (TMAOH, 10%) was added dropwise and the mixture was placed into a modified hydrothermal vessel with a Teflon lining and equipped with a propeller. Heat treatment was applied at 200 °C for 1 h under propeller rotation of 180 rpm and 10-12 bar pressure. Fig. S1 shows the particle size and particle size distribution, measured by digital image analysis, of the nanoparticles present in the initial dispersions, indicating an average particle size of 8 ± 1 nm.

After cooling down the hydrothermal vessel, triammonium citrate and polyvinyl alcohol based binder were added to the batch. After homogenization by bath sonication for 2 h, pressure filtration was applied at 10-80 bar over a Whatman Cyclopore polycarbonate membrane with pore size of 100 nm to obtain wet bodies, followed by demolding at humidity-controlled home-made green house (90% relative humidity) and drying in humidity controlled chamber at a rate of 15% humidity decrease per day to reach ambient condition.

The green bodies (Fig. S2) were ground by sandpaper (Grit 400-800) to reduce the thickness to 3 mm and characterized in terms of apparent density and pore size. The samples were then debinded at 600 °C for 2 h (with temperature ramp of 0.5 °C/min), and finally densified: 1.5-2YSZ at 1100 °C for 2 h, 3YSZ at 1150 °C for 2 h, and 4-8YSZ at 1200 °C for 1 h. Heating and cooling rates at this stage were fixed at 3 °C/min for all samples. All sintered samples were ground to 1 mm thickness with 120-1200 grit paper and then mirror-polished with diamond pastes down to 1-μm for further characterizations. Some of 3YSZ green bodies were used for Hot Isostatic Pressing (HIP, Type ASEA pressure systems Model N°QIH3 with graphite chamber) for comparison. To keep grain growth at minimum, green body discs with 3 mm thickness were pre-sintered in air at 950 °C for 1 h at a rate of 10 °C/min. The material was then subjected to HIP at 1100 °C under argon atmosphere and a pressure of 200 MPa for 10 h.

Methods

Light transmission measurements were conducted in a Jasco V-670 UV-Visible/NIR spectrophotometer using standard illuminant D65 on samples of 1 mm thickness. The spectrophotometer was also equipped with a 60 mm integrating sphere for total forward transmission measurement. The transparency was determined in the center of the pellet (spot size 5 mm). RIT measurements were conducted using a shield with an appropriate aperture placed between the sample and the detector to avoid scattered light with angle > 0.5°, and the distance between the sample and the detector was ~1 m.

Biaxial strength was measured with a piston-on-three-balls fixture (universal electromechanical testing machine-Instron 8563), according to ISO 6872 recommendations on the testing procedure, using 10-20 samples per group with diameter of 12.0 ± 0.5 mm and thickness of 1.00 ± 0.02 mm. Few samples were slightly smaller than the ISO 6872 specifications on dimensions (e.g. 11.5 mm in diameter or 0.98 mm in thickness).

Hardness and indentation fracture toughness tests were performed using a Vickers indenter (Vickers hardness tester FV-700) and an applied load of 3 kg for cubic and 10 kg for tetragonal YSZ samples. Results were reported as the average of at least 30 measurements from three different samples. The KIC values were estimated from the formula proposed by Anstis [START_REF] Anstis | A critical evaluation of indentation techniques for measuring fracture toughness: I, direct crack measurements[END_REF] as 0.016

× 𝐹 𝐶 3 2 ⁄ × ( 𝐸 𝐻 𝑉 ) 3 2 ⁄
, where E is Young modulus (210 GPa), F is load (N), Hv is hardness (GPa), and c is half length of the crack generated by indentation (m). It is understood that KIC measured by this technique and calculated from the Anstis equation are only estimations and should rather be considered as 'indentation crack resistance' and not 'real toughness' (Single Edge Notched Beam tests should be preferred). However, we were limited by the size of our samples and we used the values mostly for comparison purposes. Standard 3YSZ (Future-Tech, Japan) with average grain size 0.4 µm was used as a reference, showing a calculated Hv of 12.8 ± 0.3 GPa and KIC of 3.9 ± 0.2 MPa•m 1/2 . SEM observations were conducted on Zeiss Supra 55VP field emission scanning electron microscope, without gold-coating, at acceleration voltage of 1 KeV and working distance of 1 mm. To measure the size of grains, all mirror-polished specimens were further polished by vibratory polishing machine (Vibromet Buehler) for 12 h with a super finishing colloidal silica suspension (0.03 µm, Presi-SPM).

To analyze the vicinity of cracks, Vickers indentation was applied on the selected vibratory polished specimens before SEM observation.

X-Ray Diffraction (XRD) patterns were collected by a Bruker AXS diffractometer (Cu Kα-0.154 nm). The content and composition of cubic and tetragonal phases were calculated by Rietveld analysis via the software Topas 4.0.

The Brunauer-Emmett-Teller (BET) specific surface (SBET) and Barrett-Joyner-Halenda (BJH) profile were determined on the green bodies before and after thermal treatment at different temperatures by analyzing the standard nitrogen sorption isotherms at 77 K using a surface area and porosity analyzer (TriStar II 3020, Micrometrics). All samples were dried at 120 °C for 12 h under vacuum prior to the measurement.

Dilatometry analysis was performed on green bodies from room temperature up to 1300 °C using a Setsys evolution-Setaram thermo-mechanical analysis platform with heating rate of 1 °C/min.

The density of dried and sintered samples was measured according to the Archimedes principle in deionized water using MettlerToledoAE100 balance equipped with density determination kit at 25 ± 1 °C. Green bodies were coated by a thin layer of acrylate base adhesive before the measurement.

Thermogravimetric analysis combined with micro gas chromatography and mass spectrometry was conducted on Mettler Toledo TGA-DSC2-μGC operating over a temperature range from 25 °C to 1200 °C with heating rate of 5 °C/min. The emitted gas molecules were separated by molecular sieve (OV1 and Poraplot U columns) and identified by the mass spectrometer.

Electron Energy Loss Spectroscopy (EELS) measurements were performed by using a post-column energy filter spectrometer (Gatan GIF Quantum ER) attached to a spherical aberration-corrected scanning transmission electron microscope (JEM-ARM 200CF; JEOL, Tokyo, Japan), operated at 200 kV. The entrance aperture of the spectrometer was 5 mm, and a camera length of 20 mm was used, resulting in a collection semi-angle of 83 mrad. To acquire spectra, a dispersion of 0.25 eV/channel was used, leading to a FWHM of 0.75 eV of the zero-loss peak. The local elemental distribution with nano-scale spatial resolution within the crystalline grains was analyzed by an energy-dispersive x-ray spectrometer (Centurio, JEOL) in STEM mode. The thin lamella for the analyses was prepared by Focused Ion Beam milling (FIB) on an SEM platform, (JIB 4601 F Multi-Beam, JEOL Ltd.) with a 30 kV ion energy. Ion milling with different ion beam currents (from 10 nA, down to 100 pA) was applied until an electron-transparent foil of ca. 100 nm-thickness was obtained. For the in-situ lift-out step, the thinned lamella was mounted to a supporting half copper grid by using a micromanipulator.

Results and discussion

Microstructure

Residual pores are the main source of light scattering that limit transparency in ceramics. The size and total volume of these residual pores are controlled by the pore characteristics (i.e., fraction, size, and distribution) of green bodies. Complete densification in subsequent sintering process is expected when green bodies benefit from high density, small pore size, and narrow pore size distribution [START_REF] Mazaheri | The effect of conformation method and sintering technique on the densification and grain growth of nanocrystalline 8 mol% yttria-stabilized zirconia[END_REF]. Indeed, uniform particle coordination impedes locally different shrinkages and restricts pore coarsening during consolidation [START_REF] Yoshida | Fabrication of translucent tetragonal zirconia by gelcasting of thin zirconia nano-slurry[END_REF]. Colloidal processing generally allows the reduction of size and number of pores in green bodies by providing particles freedom to arrange themselves in packingefficient configurations [START_REF] Binner | Processing of bulk nanostructured ceramics[END_REF], [START_REF] Santacruz | Preparation of high solids content nanozirconia suspensions[END_REF]. Nevertheless, fine nanoparticles (e.g., <15 nm) tend to form agglomerates, owing to their high surface area (e.g., SBET of 3YSZ nanoparticle as 117 m 2 /g in this work) and reactivity [START_REF] Hotza | Obtaining highly dense YSZ nanoceramics by pressureless, unassisted sintering[END_REF]. Consequently, the formation of uniform green bodies without coarse heterogeneities demands effective powder processing and shaping methods.

Green bodies that were formed at pressures lower than 10 bar required higher sintering temperatures (e.g., >1250 °C) for full densification and as a result, the final grain size was beyond 100 nm (e.g., 110-180 nm, Fig. S3). On the other hand, green bodies filtered at pressures > 40 bar (T.D. >52%) were more prone to cracking during drying, debinding, or sintering (Fig. S4). Among green bodies tested and irrespective of yttria content, samples that were filtered at 20 bar (showing 52% > T.D. > 50%) were fully densified (>99.5% T.D.) at temperature of 1100-1200 °C (T.D. of 1.5 YSZ as 6.15 g/cm3, 3YSZ as 6.09 g/cm3, and 8YSZ as 5.95 cm3). Thus, 50.5 ± 0.5 T.D. was considered as the criteria to use the green samples throughout the rest of the work. Fig. 1a represents the pore size evolution of 3YSZ filtered samples as a function of thermal-treatment temperature. The Barrett-Joyner-Halenda (BJH) profile demonstrates a nearly symmetrical distribution of interconnected pores with average diameter of 4.2 nm in green bodies. As temperature increases during sintering, uniform growth is noticeable and the average pore diameter reaches 8.7 nm at 800 °C. This uniform change in pore size is also manifested by a single narrow peak of shrinkage rate in the dilatometry curve (Fig. 1b) implying the presence of a narrow pore size distribution with no agglomerate across the sample [START_REF] Durán | Preparation, sintering, and properties of translucent Er2O3-doped tetragonal zirconia[END_REF]. It is worth noting that the two peaks at temperature < 400 °C are related to dehydroxylation of nanoparticles and organic burn-out (Fig. S5 and Table S1).

Increasing temperature beyond 900 °C breaks the interconnected porosity network and forms individual pores (Fig. S6). As a result, pore analysis by N2 sorption is no longer applicable. In order to assess the size of residual pores as well as size of grains after sintering, the samples were characterized by SEM (Fig. S7). Typical microstructures of 3YSZ and 8 YSZ ceramics are shown in Fig. 2, confirming the high degree of densification with average grains size of 75 nm and 85 nm, respectively. In both cases, residual pores with a maximum diameter of < 15 nm could be detected at the triple points of some grains (Fig. 2c). These results support the miniaturization of residual pores to diameters of < 15 nm and grains of < 85 nm, which was found also valid in all zirconia ceramics obtained with sintering temperatures ranging from 1150 °C to 1200 °C.

Optical properties

In the visible domain and when birefringence is significant, apart from residual pores, grain boundaries are the main source of light scattering in non-cubic ceramics. Scattering by grain boundaries (GBs) depends on the grain size (= GBs density) in relation with the wavelength used (for infrared light, grains with a size of about 500 nm will be invisible). Furthermore, a non-cubic ceramic like alumina with very low birefringence (about 0.007) will be less sensitive to light scattering. The Rayleigh approximation [START_REF] Klimke | Transparent tetragonal yttria-stabilized zirconia ceramics: influence of scattering caused by birefringence[END_REF] can be used as a straight-forward model to estimate the real in-line transmission (i.e, RIT, as a measure of transparency) of a high purity, dense (no pore), and non-cubic ceramic in which RIT is inversely proportional to the average birefringence and grain size at a fixed thickness (Eq. 1).

𝑇 𝐼𝑛-𝑙𝑖𝑛𝑒 = (1 -𝑅)𝑒𝑥𝑝 {-( 128𝜋 4 𝑟 3 18𝜆 4 ) [ Δ𝑛 𝑎𝑣𝑒 (2𝑛+Δ𝑛 𝑎𝑣𝑒 ) 2 ] 2 𝑡}
Eq. 1

Δnave is the average birefringence, 2r is the grain size, t is the thickness, n is the refractive index (e.g., 2.19 and 2.15 for 3YSZ and 8YSZ, respectively at λ of 633 nm), λ is the wavelength of the incident light, and R= 1-2 n/(n2 +1) is the reflection loss at two surfaces of a sample. In our case, the band gap of YSZ is high enough for considering no absorption in Eq. 1. Taking into account the criterion for Rayleigh scattering (2πrn/λ < 1), the model is valid for grain size of 50-110 nm in 3YSZ ceramics [START_REF] Krell | Transparent compact ceramics: inherent physical issues[END_REF], [START_REF] Zhang | Making yttria-stabilized tetragonal zirconia translucent[END_REF], and is consistent with the grain size of our specimens. From Klimke et al. [START_REF] Klimke | Transparent tetragonal yttria-stabilized zirconia ceramics: influence of scattering caused by birefringence[END_REF], given the birefringence of 0.03-0.04 in 3YSZ, an RIT greater than 20% in the visible range necessitates a grain size of < 80 nm in a sample of 1 mm thickness in the direction of the optical path. On the other hand, when Δnave= 0 (cubic zirconia, e.g., 8YSZ), the RIT becomes independent of grain size and loss of transmitted light is only attributed to the reflection at the surfaces. In the absence of other source of light scattering such as impurities, pore, secondary phases, and coloring centers, the maximum RIT of a dense YSZ ceramic can be estimated as ~76% of the incident light for entire visible spectrum [START_REF] Klimke | Transparent tetragonal yttria-stabilized zirconia ceramics: influence of scattering caused by birefringence[END_REF]. Based on the size of residual nano-pores, nano-grained microstructure, and high purity of our samples-no coloring centers and impurities (Table S2), we anticipated a high degree of translucency/transparency in our samples. Fig. 3 confirms this hypothesis by showing the optical spectra as well as appearance of 1-mm thick specimens with average grain size of 75 ± 5 nm. The 8YSZ presents a maximum in-line transmittance of 51% at 800 nm with gradual decrease to 25% at λ = 380 nm. In a similar way, the transmission of 3YSZ is above 10% for λ > 580 nm with a maximum of 38% at 800 nm wavelength. Interestingly, the light transmission of 8YSZ and 3YSZ here is higher than the reported values for samples manufactured by HIP-SPS with even smaller grain size (e.g., 50 nm) [START_REF] Klimke | Transparent tetragonal yttria-stabilized zirconia ceramics: influence of scattering caused by birefringence[END_REF], [START_REF] Lach | From nanometric zirconia powder to transparent polycrystal[END_REF], [START_REF] Anselmi-Tamburini | Transparent nanometric cubic and tetragonal zirconia obtained by high-pressure pulsed electric current sintering[END_REF], [START_REF] Dash | Transparent tetragonal-cubic zirconia composite ceramics densified by spark plasma sintering and hot isostatic pressing[END_REF].

To gain insight into the high RIT of YSZ samples, we first characterized them by Total Forward Transmission (TFT) and then, calculated the diffuse transmission (Tdiffuse=TTFT -TRIT). As shown in Fig. 3b, both TFT and RIT increase with λ and yttria content. TFT increase partly correlates with the decreasing refractive indices as a function of the wavelength of the incident light. [START_REF] Krell | Transparent compact ceramics: inherent physical issues[END_REF] RIT increase is directly linked to the content of cubic phase which inherently promotes transparency (Fig. S8 and Table S3). A significant difference between TFT and RIT can be noticed in tetragonal zirconia, especially in the shorter wavelength range. By contrast, cubic zirconia shows a similar trend for inline and total forward transmission and the diffuse transmission is less sensitive to the wavelength compared to that of 3YSZ (Fig. 3c). Considering the absence of birefringence in cubic zirconia, this wavelength independence suggests that the loss of RIT in 8YSZ stems from residual nano-pores.

Although scattering efficiency of pores markedly decreases in the nano-range, total pore volume still plays a key role in diffuse transmission. Numerical studies reveal further details about the correlation between RIT and pore size-volume. For RIT loss below 20% in cubic zirconia with pore size of 10-15 nm, the relative density of 99.7% is required (Vpore< 3000 ppm) [START_REF] Yamashita | Light scattering by residual pores in transparent zirconia ceramics[END_REF], [START_REF] Wang | Transparent ceramics: processing, materials and applications[END_REF]. This result is in agreement with density of our samples (5.94 ± 0.01 g/cm 3 ) and supports the fact that the high RIT of 8YSZ in the entire spectrum originates from miniaturization and elimination of residual pores.

In the case of tetragonal zirconia, grain boundaries also scatter light and both residual porosity and size determine the extent of diffuse scattering. Ultra-fine grains with a size of < 30 nm would be practically invisible to the incident visible light. As grain size increases, the interaction between grains and light intensifies. Light with shorter wavelengths can be effectively scattered in 3YSZ with an average size of 75 nm [START_REF] Zhang | Making yttria-stabilized tetragonal zirconia translucent[END_REF], whereas scattering becomes less pronounced at longer wavelengths owing to the direct correlation between RIT and λ (Eq. 1). Therefore, as opposed to nano-pores, the dependency of Tdiffuse and λ in this range of grain size makes the diffuse transmission behavior elliptic (as a function λ) and promotes the loss of RIT in 3YSZ (Fig. 3c). The effect of scattering centers on RIT was further explored by synthesis of a fully dense 3YSZ (99.9% of T.D.) with an average grain size of 50 nm (Fig. S9), densified by HIP (referred to HIP50). The light transmission of HIP50 after annealing in air (Fig. S10) is consistent with that of reported by Anselmi-Tamburini et al. [START_REF] Anselmi-Tamburini | Transparent nanometric cubic and tetragonal zirconia obtained by high-pressure pulsed electric current sintering[END_REF] However, surprisingly, both RIT and TFT of 3YSZ with grain size of 75 nm (pressure-less sintered) are still higher than those of HIP50. The development of high concentrations of point defects, in the form of oxygen vacancies, was suggested as the origin of significant light absorption in the latter [START_REF] Anselmi-Tamburini | Transparent nanometric cubic and tetragonal zirconia obtained by high-pressure pulsed electric current sintering[END_REF].

To test this conjecture, we investigated the local environment (e.g. oxygen coordination) of Zr cations by analyzing the Energy Loss Near Edge Structure (ELNES) fingerprints of the characteristic Zr-M ionization edges in nano-grains of 3YSZ and HIP50 specimens. This is possible as subtle changes in the number and spatial arrangements of the atoms in the first nearest neighbor shell around the ionized atom in electron energy loss spectroscopy (EELS) result in characteristic differences in the shape of ELNES features [START_REF] Keast | Electron energy-loss near-edge structure -a tool for the investigation of electronic structure on the nanometre scale[END_REF].

Fig. 4 shows a comparison between representative EELS spectra after background subtraction by a power-law model and removal of multiple scattering by Fourier-ratio deconvolution. The EELS spectrum of the stoichiometric ZrO2 standard sample (JEOL, Tokyo, Japan) is also presented as the reference spectrum for comparison. The ionization peaks in the range of 180-250 eV, 340-360 eV, and 540-550 eV are associated with the Zr-M2,3, Zr-M4,5, and O-K ionization edges, respectively [START_REF] Ni | Quantitative EELS analysis of zirconium alloy metal/oxide interfaces[END_REF].

The identical ELNES features of the Zr-M and O-K edges in samples are indicative of a similar local environment and bonding of zirconium to the oxygen. We did not notice significant differences in local oxygen coordination of Zr 4+ cations in other point analyses that could be correlated with the reducing atmosphere of HIP. This shows the efficiency of an annealing in air to recover oxygen stoichiometry. On the other hand, a pronounced C-K edge at 280 eV was observed in the EELS spectrum of HIP50. Carbon centers (C-centers) were also detected by energy dispersive X-ray spectroscopy (EDS) with evidence of accumulation in grain boundaries (~1.8 at%, Table S4, Fig. S11). These observations indicate that optical properties of HIP50 are controlled by the presence of C-centers in significant amounts and not by oxygen vacancies. Therefore, the high RIT of 3YSZ in this work is directly attributed to the reduced size of grains and residual pores while avoiding the formation of other sources of light absorption such as C-centers and impurities that are difficult to avoid or suppress with HIP or other pressure-assisted methods such as SPS with graphite dies.

Mechanical properties

The strong chemical bonds and the consequent limited dislocation mobility govern the strong resistance to plastic deformation in ceramics. Like in metals, grain boundaries (GBs) act as additional obstacles for movement of dislocations, resulting in an exceptionally high stress needed for plasticity in polycrystalline ceramics. The effect of grain size on yield strength and hardness, often referred to as Hall-Petch relation, is described by the linear dependence between the hardness (or yield strength) and the inverse square root of grain size [START_REF] Bokov | Size-induced grain boundary energy increase may cause softening of nanocrystalline yttria-stabilized zirconia[END_REF], [START_REF] Muche | Colossal grain boundary strengthening in ultrafine nanocrystalline oxides[END_REF], [START_REF] Wollmershauser | An extended hardness limit in bulk nanoceramics[END_REF], [START_REF] Yang | Grain boundary strengthening in nanocrystalline zinc aluminate[END_REF]. In addition to dislocation motion, tetragonal zirconia ceramics may exhibit transformation-induced plasticity under stress field [START_REF] Garvie | Ceramic steel?[END_REF]. This sudden rearrangement from meta-stable tetragonal to stable monoclinic phase (t→m transformation) is accompanied by ~4% volumetric expansion and also by twinning and formation of shear bands in the structure. The latter can be microscopically observed as surface corrugations [START_REF] Zhang | Understanding specimen-and grain-size effects on nanoscale plastic deformation mechanisms and mechanical properties of polycrystalline yttriastabilized tetragonal zirconia nanopillars[END_REF], [START_REF] Lange | Transformation toughening[END_REF], [START_REF] Zeng | Crystal orientation dependence of the stressinduced martensitic transformation in zirconia-based shape memory ceramics[END_REF]. The stability of tetragonal phase is dependent on doping content and grain size. The lower yttria content and larger grain size, favoring the t→m transformation [START_REF] Binner | Processing of bulk nanostructured ceramics[END_REF], [START_REF] Bravo-Leon | Fracture toughness of nanocrystalline tetragonal zirconia with low yttria content[END_REF], determine the extent of plastic deformation and, thus, mechanical properties of tetragonal zirconia ceramics.

The biaxial strength (σf), hardness (Hv) and indentation fracture toughness (KIC) of zirconia samples with grain size of 75 ± 5 nm are plotted as a function of composition in Fig. 5. The cubic zirconia (8YSZ) shows strength of 680 ± 60 MPa, hardness of 14.3 ± 0.2 GPa, and KIC of 1.5 MPa•m 1/2 . Biaxial strength of YSZ gradually improves by decreasing yttria content, in the region 8-3.5 mol.%. Below this value, a significant increase to ~2 GPa is first showed for 3YSZ, followed by a further rise with lower yttria contents, finally reaching a value as high as ~2.6 GPa for 1.5YSZ. The abrupt increase in biaxial strength at ~3 mol. % yttria coincides with a slight drop in hardness from 14.2 ± 0.2 to 13.2 ± 0.2 GPa. Variation in KIC as a function of yttria content is also similar to that of biaxial strength. However, the sudden change occurs at lower yttria content (from 2YSZ to 1.5YSZ) and it is concurrent to the second decrease in hardness from 13.0 ± 0.2 to 12.2 ± 0.1. The analysis of vicinity of indentation cracks is useful to gain deeper understanding about the mechanism behind these observations. Fig. 6a andb show the tip of indentation cracks in 8YSZ samples with average grain size of 160 nm and 80 nm, respectively. The former was produced from same green bodies but specifically heat treated at 1250 °C for 3 h to obtain submicron grain size. Fracture path shifts from mostly transgranular in the 'large grain' (dgrains=160 nm) samples to mostly intergranular in fine grain (dgrains=80 nm) microstructures showing deflection, bridging, and wedging of cracks. Comparing the σf and Hv values with micron grain-sized 8YSZ [START_REF] Yamashita | Light scattering by residual pores in transparent zirconia ceramics[END_REF], [START_REF] Hotza | Obtaining highly dense YSZ nanoceramics by pressureless, unassisted sintering[END_REF] (bending strength of 250-400 MPa and hardness of 11.8-12.3 GPa in samples with grain size of 17-70 µm), the effect of nano-grained structure on improving strength and hardness of zirconia ceramics correlates with the small defect size and impeding effect of GBs on dislocation movement [START_REF] Serivalsatit | Synthesis, processing, and properties of submicrometer-grained highly transparent yttria ceramics[END_REF], [START_REF] Launey | On the fracture toughness of advanced materials[END_REF]. Biaxial strength of zirconia samples increases with decreasing yttria content (from 8 mol. % to 3.5 mol. %) in the structure. This change is consistent with the experimental and molecular dynamics simulations of single crystal YSZ, demonstrating that higher the yttria content, higher the local weak points which facilitate the dislocation motion [START_REF] Zhang | Effects of specimen size and yttria concentration on mechanical properties of single crystalline yttria-stabilized tetragonal zirconia nanopillars[END_REF], [START_REF] Otsuka | Dislocation-enhanced ionic conductivity of yttria-stabilized zirconia[END_REF]. On the other hand, direct relation between hardness and yttria composition is attributed to the variation in content of cubic phase (Table S3) which is inherently a harder phase owing to the stabilizing effect yttria as well as non-transformability of tetragonal phase with yttria > 4 mol. % [START_REF] Cousland | Mechanical properties of zirconia, doped and undoped yttria-stabilized cubic zirconia from first-principles[END_REF]. Once the structure is fully transformable (tetragonal, 3YSZ Table S3), martensitic phase transformation becomes active (Fig. 6c). Activation of the t→m transformation as the second plastic deformation mechanism decreases the hardness of YSZ. On the other hand, it can synergize with nano-grained structure by reducing the stress-intensity at the crack tip [START_REF] Mcmeeking | Mechanics of transformation-toughening in brittle materials[END_REF] and interfere with crack propagation (Fig. S12 and [START_REF] Meyers | Mechanical properties of nanocrystalline materials[END_REF], [START_REF] Zhang | Competing mechanisms between dislocation and phase transformation in plastic deformation of single crystalline yttria-stabilized tetragonal zirconia nanopillars[END_REF]) and consequently, alludes to the high strength of tetragonal zirconia. Decreasing the yttria content to 1.5 mol. % changes the dominant mechanism of energy dissipation from intergranular cracking to transgranular phase transformation (Fig. 6d) and further improves the strength of YSZ. Dominancy of t→m transformation mechanism is also manifested by observing the second drop in hardness and significant growth in KIC. Fig. 7 shows the vicinity of indentation cracks in tetragonal YSZ at lower magnification. The t→m transformation in 3YSZ is limited to few grains in front of the crack (Fig. 7a) and deflection/bridging during intergranular fracture (Fig. 6c) is still active as crack-tip shielding mechanism [START_REF] Launey | On the fracture toughness of advanced materials[END_REF]. As the yttria content decreases, the transform-zone around the crack-tip increases (Fig. 7b) and the t→m transformation becomes the primary source of toughening in 1.5 YSZ (Fig. 7c and Fig. S13). Therefore, the pronounced strength and hardness of tetragonal YSZ compared to micron grain-sized samples is directly linked to the grain refinement and activation of stress-induced phase transformation, even in this range of grain sizes.

Summary and conclusion

We report on the preparation of nano-grain YSZ ceramics with density > 99.5% T.D. through conventional pressure-less sintering. Green body density > 50% T.D., narrow pore size distribution centered at ~4 nm, and use of highly reactive nanoparticles with primary particle size of < 10 nm are crucial to reduce the densification temperature to 1100-1200 °C (with dwell time of 1-2 h) and thus, obtain nano-crystalline structures. Decreasing the grain size to < 85 nm significantly improves light transmission and biaxial strength of YSZ compared to both nano-crystalline zirconia ceramics synthesized by high pressure sintering techniques such as HIP/SPS and micron/sub-micron grain-size zirconia counterparts (Table S5). The pronounced light transmission of 3YSZ and 8YSZ in this work is directly related to the nano-grains and both miniaturization and elimination of residual pores while avoiding formation of other source of light scattering such as carbon contaminations and impurities. High strength and hardness correlate with microstructure refinement in cubic zirconia and activation of both intergranular deformation and martensitic phase transformation which is still active even in nano-sized tetragonal zirconia. These results will potentially open up venues for preparation of transparent ceramics while keeping high strength through simple, scalable, and producible route.

Figure 1 :

 1 Figure 1: a) Pore size distribution as a function of temperature of densification; 120 °C (□), 500 °C (○), 600 °C (Δ), and 800 °C (◇) and b) effect of temperature on the linear shrinkage and relative density (dash line shows the shrinkage rate) of samples with a green density 50.5 ± 0.5 T.D. All samples here are formed from 3YSZ with primary particle size of 8 nm. Inset in (a) shows the average pore size of samples as a function of temperature.

Figure 2 :

 2 Figure 2: SEM image of fully dense a) 3YSZ and b) 8YSZ sintered at 1150 °C and 1200 °C, respectively. Representative SEM (c) and high-angle annular dark-field image in STEM (d) of 3YSZ at higher magnification showing the nanoscale range of residual pores (size of <15 nm) and fully densified structure, respectively. The nanopores in (c) are not prevalent as the density of the samples is 6.06 ± 0.01 g/cm 3 .

Figure 3 :

 3 Figure 3: Optical spectra of 1 mm-thick polished samples with grain size of 75 ± 5 nm; a) RIT, b) TFT, and c) diffuse transmission, and d) appearance of discs with diameter of 12.0 ± 0.5 mm and thickness of 1.00 ± 0.02 mm under transmitted light. Images were captured under same illumination and background conditions. The dashed line in (a) shows the maximum theoretical RIT of a dense YSZ ceramic estimated as ~76%. The 1.5YSZ and 6YSZ samples are reported for comparison.

Figure 4 :

 4 Figure 4: EELS spectra of a) stoichiometric ZrO2, b) nanograin 3YSZ, and c) HIP50 after annealing in air.

Figure 5 :

 5 Figure 5: Biaxial strength (Δ), hardness (○), and, indentation fracture toughness (□) of YSZ with grain size 75 ± 5 nm as a function of yttria content.

Figure 6 :

 6 Figure 6: Vicinity of indentation cracks in a) 8YSZ with grain size of 160 nm and b) 8YSZ with grain size of 80 nm, c) 3YSZ with grain size of 80 nm, and d) 1.5YSZ with grain size of80 nm. Dash-lines are added to (a) to highlight GBs. Arrows in (b) show bridging, wedging, and deflection of the crack from left to right. Arrows in (c) and (d) show exemplary twinning and surface corrugations resulted from t→m transformation.

Figure 7 :

 7 Figure 7: Vicinity of indentation cracks in tetragonal YSZ with grain size of 75 ± 5 nm; a) 3YSZ, b) 2YSZ, and c) 1.5YSZ. Dash-lines in (a) and (b) highlight the boundary of transformed zone around the crack. Arrows in (c) shows the width of transformed zone around the crack.

Figure S3 .

 S3 Figure S3. Samples with average grain size of left) 156 nm and right) 110 nm in two magnifications and with associated grain size distribution. Green bodies presented an apparent density of 47.7-48.5% T.D and were sintered at 1300-1350 °C for 2h.

Figure S4 .

 S4 Figure S4. Representative image of samples that were cracked during sintering in a) transmission and b) reflection mode. Green bodies presented an apparent density of 52.6% T.D. and were sintered at 1150 °C for 2h.

Figure S5 .

 S5 Figure S5. Results of μGC-TG on a green body of 3YSZ sample filtered at 20 bar and after drying (all curves are upward except DTG)

Figure S12 .

 S12 Figure S12. Vicinity of indentation cracks in 3YSZ with a grain size of 250 nm. Arrows show intergranular crack propagation in a grain without (left) and with (right) t→m transformation.

Figure S13 .

 S13 Figure S13. Optical images with polarized light from the vicinity of indents in left) 1.5 YSZ and right) 2YSZ. Scale bars show 100 μm. Lines of stress-induced phase transformation are visible as surface corrugation (transformation bands) in (left).

Table S1 .

 S1 Maximum volatile counts and associated temperatures in the μGC-TG test

	Volatile	H2O	CO2	CO	NH3
	Maximum count	10400	4580	301	29
	Tmaximum count(°C)	99.6	307	333	294

Table S2 .

 S2 Representative ICP results of 3YSZ green body filtred at 20 bar and after drying

	ZrO2	Y2O3	HfO2	Fe2O3	Al2O3	SiO2	CaO	Na2O	Cr2O3	TiO2
	(wt.%)	(wt.%)	(wt.%)	(ppm)	(ppm)	(ppm)	(ppm)	(ppm)	(ppm)	(ppm)
	91.09	5.90	1.96	<5	<5	112	51	30	<5	<5

Table S3 .

 S3 Rietveld analysis of dense-YSZ ceramics with different yttria compositions

	Material	Phase Name	wt.%	Yttria in phase (wt. %)	Total yttria (mol.%)	a (Å)	c (Å)	Rwp	R Bragg
	1.5YSZ	Tetragonal Monoclinic	95.55 4.45	1.81	1.81	3.6011	5.1816	8.266	4.231 3.774
	2YSZ	Tetragonal	100	2.27	2.27	3.6031	5.1793	11.235	2.07
	3YSZ	Cubic Tetragonal	2.96 97.04	6.44 3.60	3.62	5.1280 3.6102	5.1716	9.938	2.26 2.13
	5YSZ	Cubic Tetragonal	34.45 65.55	6.42 4.94	5.45	5.1354 3.6174	5.1638	9.102	1.77 2.60
	6YSZ	Cubic Tetragonal	59.87 40.13	6.67 5.26	6.11	5.1363 3.6191	5.1619	9.109	2.00 2.81
	8YSZ	Cubic	100	8.61	8.61	5.1433		12.394	5.55

Table S4 .

 S4 The results of quantitative analysis of interior grains and grain boundaries (GBs) by energy dispersive spectroscopyfor 3YSZ and HIP50 after annealing in air

	Specimen		C	Elemental Distribution (at%) O Y	Zr
	3YSZ	Interior GBs	<0.01 <0.01	52.9 51.8	3.2 3.6	43.9 44.6
	HIP50	Interior GBs	0.3 1.8	64.2 63.2	2.6 3.3	32.9 31.7

Table S5 .

 S5 Light transmission and biaxial strength of nanograin zirconiain this work in comparison to micron grain-size commercial counterparts and YSZ synthesized by HIP/SPS

Funding:

The authors declare no competing financial interest

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary materials