Colinge Jacques

Lambert Philippe

Amouyal Michel

Clary Bernard

PERSONNEL ENSEIGNANT Garcia Marc

Lucie Barateau

Bastide Physiologie

Sophie

Benoit Lattuca

Cardiologie

Guillaume Sarrabay

Génétique

PROFESSEURS DES UNIVERSITES

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Montpellier, c'est parce que vous faites partie des meilleurs de l'internat que vous êtes là et cela se ressent.!

ADV :

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Merci

Perpignan :

Merci à toute l'équipe pour ce semestre où j'ai beaucoup appris notamment en interventionnel.

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Clinique Beausoleil :

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Merci à toute l'équipe que je n'ai pas la chance de connaître encore.

Lap Os :

Même si je n'ai pas encore eu la chance de passer dans votre service, merci à Catherine, Yann, Marie Pierre, Arthur et William.

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Results:

Sixty four patients were reviewed, 33 with bowel occlusion (mean age 65 +/-20 yo) and colitis (mean age 49+/-22 yo).

The maximum CNR value was observed at 60 keV in the 2 groups with respectively no significant difference between the different levels except between 70 and 60 keV (-4.7% and p<0.05) for bowel occlusion and significant difference with 40 and 70 levels for colitis..

The subjective evaluation showed a superiority of 60keV images compared to the others mono energetic levels and mixed images for all criterions.

Inter-observer agreement for the analysis of the different criteria showed a kappa of 0.95 for noise, 0.89 for smoothing, 0.88 for overall quality, 0.91 for diagnostic quality and 0.99 for diagnostic confidence.

Conclusions:

60keV seems to be the most suitable mono energetic level for analyzing the digestive tract since subjective evaluation found less noise and better appreciation of image quality and objective evaluation found a maximum CNR.

Keywords: Dual Energy CT; Virtual monoenergetic images; Abdomen;

Digestive tract; Emergency

Introduction

During the last ten years, dual energy CT (DECT) has seen its applications and its use grow particularly for abdominal region (1). This technique is based on the use of two spectra of X-rays, one at low energy and other at high energy. These spectra are used by material decomposition algorithms to characterize tissues according to two or three basic materials including those with a low atomic number (e.g., water) and those with a high atomic number (e.g., iodine) (1,2).

Most manufacturers now offer scanners capable of obtaining dual-energy images using different acquisition or detection techniques with different performances [START_REF] Papadakis | Fast KVp-Switching Dual Energy Contrast-Enhanced Thorax and Cardiac CT: A Phantom Study on the Accuracy of Iodine Concentration and Effective Atomic Number Measurement[END_REF][START_REF] Greffier | Performance of Four Dual-Energy CT Platforms for Abdominal Imaging: A Task-Based Image Quality Assessment Based on Phantom Data[END_REF][START_REF] Jacobsen | Intermanufacturer Comparison of Dual-Energy CT Iodine Quantification and Monochromatic Attenuation: A Phantom Study[END_REF]. One of them is the dual source CT (DSCT) with two X-ray tubes associated to two detectors mounted orthogonally (90° or 95° depending on the generation) [START_REF] Greffier | Impact of Dose Reduction and the Use of an Advanced Model-Based Iterative Reconstruction Algorithm on Spectral Performance of a Dual-Source CT System: A Task-Based Image Quality Assessment[END_REF]. Each tube deliver one kVp, tube « A » for low kVp (100 kVp) and tube « B » for high kVp (140kVp) associated to tin filter. Several type of images are generated, in addition to the low kVp and high kVp images that can be viewed separately, mixed images are also generated from low and high kVp images to produce images equivalent to that of a conventional acquisition at 120 kVp. Virtual monochromatic images (VMIs) are calculated as a linear combination of the basis material images using attenuation coefficients that approximate the energy dependence of the photoelectric and the Compton effects [START_REF] D'angelo | Dual energy computed tomography virtual monoenergetic imaging: technique and clinical applications[END_REF] . These images are useful for improving iodine contrast, using low energy level values (40 to 70 keV) and reducing image artifacts with high energy level values [START_REF] Jagoda | Comparison of Metal Artifact Reduction in Dual-and Single-Source CT: A Vertebral Phantom Study[END_REF]. Material specific images are generated such as iodine maps to quantify iodine concentration in lesions [START_REF] Dabli | Optimization of Image Quality and Accuracy of Low Iodine Concentration Quantification as Function of Dose Level and Reconstruction Algorithm for Abdominal Imaging Using Dual-Source CT: A Phantom Study[END_REF][START_REF] Yu | Dual-Energy CT-Based Monochromatic Imaging[END_REF][START_REF] Lourenco | Dual-Energy CT Iodine Mapping and 40-KeV Monoenergetic Applications in the Diagnosis of Acute Bowel Ischemia[END_REF][START_REF] Potretzke | Early Small-Bowel Ischemia: Dual-Energy CT Improves Conspicuity Compared with Conventional CT in a Swine Model[END_REF]. Finally, virtual non constrast (VNC)

images could be generated to obtain images virtually without iodine. These images are still evaluated inferior for some indications (13) but presents similarity to traditional non contrast acquisitions, for example for characterization of adrenal incidentalomas [START_REF] Ananthakrishnan | Spectral Detector CT-Derived Virtual Non-Contrast Images: Comparison of Attenuation Values with Unenhanced CT[END_REF][START_REF] Virarkar | Virtual Non-Contrast Imaging in The Abdomen and The Pelvis: An Overview[END_REF].

Several studies have demonstrated the interest value of dual energy acquisitions and their post-processing reconstruction, particularly for vascular or oncological analysis [START_REF] Leithner | Virtual Monoenergetic Imaging and Iodine Perfusion Maps Improve Diagnostic Accuracy of Dual-Energy Computed Tomography Pulmonary Angiography With Suboptimal Contrast Attenuation[END_REF][START_REF] Albrecht | Assessment of an Advanced Monoenergetic Reconstruction Technique in Dual-Energy Computed Tomography of Head and Neck Cancer[END_REF]. Optimization of iodine attenuation also allows the injection of less contrast medium, which is beneficial in patients with renal or cardiac insufficiency [START_REF] Noda | Advantages and Disadvantages of Single-Source Dual-Energy Whole-Body CT Angiography with 50% Reduced Iodine Dose at 40 KeV Reconstruction[END_REF] Several studies on phantoms sowed that VMIs are associated with an increase of CNR (1) and detectability [START_REF] Greffier | Impact of Dose Reduction and the Use of an Advanced Model-Based Iterative Reconstruction Algorithm on Spectral Performance of a Dual-Source CT System: A Task-Based Image Quality Assessment[END_REF][START_REF] Greffier | Impact of Four KVp Combinations Available in a Dual-Source CT on the Spectral Performance of Abdominal Imaging: A Task-Based Image Quality Assessment on Phantom Data[END_REF].

Most of the studies concerning abdominal and pelvic applications of DECT were devoted to the detectability and characterization of solid organ lesions, in particular hepatic [START_REF] Robinson | Dual Source Dual Energy MDCT: Comparison of 80 KVp and Weighted Average 120 KVp Data for Conspicuity of Hypo-Vascular Liver Metastases[END_REF], renal [START_REF] Mileto | Dual-Energy MDCT for Imaging the Renal Mass[END_REF] or pancreatic [START_REF] Macari | Dual-Source Dual-Energy MDCT of Pancreatic Adenocarcinoma: Initial Observations with Data Generated at 80 KVp and at Simulated Weighted-Average 120 KVp[END_REF].

But few studies have been devoted to the diagnostic contribution of dualenergy CT in the context of emergency pathologies and in spite of the potential of DECT, its applications are little or not used by physicians [START_REF] Punjabi | Multi-Energy Spectral CT: Adding Value in Emergency Body Imaging[END_REF][START_REF] Yeh | Dual-Energy and Low-KVp CT in the Abdomen[END_REF].

The purpose of this study was to compare the objective (noise, contrast and CNR) and subjective (noise, smoothing, overall image quality and diagnostic quality) image quality of four monoenergetic levels of VMIs and mixed images obtained with DECT. This, in order to determine the most suitable image type for the the digestive tract in context of emergency pathologies.

Materials and methods

Design and study population

Data of all adult patients who received a portal time-injected abdominal-pelvic CT scan in dual-energy mode on the dedicated emergency double-tube scanner between February 2019 and February 2020 were screened from the Dosimetry Archiving and Communication System (DACS).

A retrospective analysis of the reports was performed to identify pathologic CT with pathology visualized on portal acquisition. All pathologic CTs have been verified thereafter. Patients with a pathology of the digestive tract and with a total number of patients greater than or equal to 30 over the study period were included (except for diverticulitis and appendicitis). Two indications were included in the study: intestinal obstruction and colitis. Figure [START_REF] Lestra | Applications of Dual Energy Computed Tomography in Abdominal Imaging[END_REF] shows the flowchart for the selection of the included patients.

Acquisition and reconstruction parameters

The CT acquisitions were performed on a SIEMENS Somatom Force Dual-Source scanner equipped with the latest generation of ADMIRE (Advanced modeled iterative reconstruction) algorithm. The acquisitions were performed at portal time by injecting 90 ml of Xenetix 300 contrast medium at a flow rate of 2 or 3 ml/s.

The portal acquisitions were performed using the voltage couple 100/Sn150 kVp, a rotation time of 0.5 s, a pitch of 0.6 and a collimation of 128x0.6 mm. Intensity modulation was enabled (CareDose4D) with a reference effective charge (mAsref) of 190 mAs on tube A and 95 mAs on tube B.

Images were reconstructed using a soft kernel (Br40), a slice thickness of 1 mm, and a slice interval of 1 mm with level 3 of the ADMIRE algorithm (A3). Mixed images were generated with a weighting factor of 0.8 as well as single-energy virtual images (VMI) at 4 energy levels 40, 50, 60 and 70 keV.

Dosimetric analysis

CTDIvol values expressed for a 32-cm IEC phantom and PDL were collected on the DACS. In the absence of patient weights and heights, a dose estimation taking into account the morphology of the patients (SSDE) was performed according to the method of AAPM 204 [START_REF] Burton | Evaluation of AAPM Reports 204 and 220: Estimation of effective diameter, waterequivalent diameter, and ellipticity ratios for chest, abdomen, pelvis, and head CT scans[END_REF]. For this, the effective diameter (Diameff) was calculated for each patient according to the formula below:

With : Diam_AP the diameter of the abdomen according to the anteroposterior incidence and Diam_LAT the diameter of the abdomen according to the lateral incidence. The SSDE was calculated using formula below: with f a correction factor according to the extract from Table 1 of the AAPM 204 report.

The mean values of CTDIvol , PDL and SSDE were calculated for each indication. The mean values of CTDIvol and PDL were compared to the diagnostic reference levels (DRL) and guidance reference level (GRL) of the order of 23/05/2019 [START_REF]Arrêté du 23 mai 2019 portant homologation de la décision n° 2019-DC-0667 de l'Autorité de sûreté nucléaire du 18 avril 2019 relative aux modalités d'évaluation des doses de rayonnements ionisants délivrées aux patients lors d'un acte de radiologie, de pratiques interventionnelles radioguidées ou de médecine nucléaire et à la mise à jour des niveaux de référence diagnostiques associés[END_REF].

Objective evaluation of image quality.

For each patient and each type of images (mixed or VMI), the HU and noise values (with their standard deviation) were measured on the images by placing a region of interest (ROI) of 1 cm² surface with the SyngoVia software.

A ROI was placed on the pathological area of the digestive tract (occlusion or colitis) and another in the background (fat). The value of the contrast to noise ratio (CNR) was calculated for each image using the formula below: CNR = (HU digestive wall -HU fat) / SD fat with SD = standard deviation of subcutaneous fat representing the imagenoise.

The contrast to noise ratio values were compared between the different images for each indication.

Subjective evaluation of image quality

The quality of mixed and VMI images at the 4 single-energy levels was evaluated by two radiologists, one experienced (more than 5 years of experience) and one junior (less than 5 years of experience). Both radiologists were blinded to the type of image during the evaluation. Images were scored on 4 image quality criteria according to a scale described in Table [START_REF] Lestra | Applications of Dual Energy Computed Tomography in Abdominal Imaging[END_REF].

For each indication, the mean value of the scores of each VMI image were compared with the score of the mixed images. The diagnostic quality of images completed the criterion of pure global image quality only based on noise level and smoothing. An image may be judged to have low overall quality but sufficient to make the diagnosis. A score of less than 3 on this criterion indicates that the image is not clinically usable.

Statistical analysis

Statistical analyses were performed for each indication using theGMRC Shiny Stat. The overall agreement between the scores of the two radiologists was calculated with the Cohen's Kappa test and classified as poor 1.4Results

1.4.1Study population

Table [START_REF] Jacobsen | Dual-Energy CT: Lower Limits of Iodine Detection and Quantification[END_REF] shows the description of the patient population included for both pathologies.

Patients with intestinal obstruction were of mean age 65 years ± 20. (range from 18 to 95 years). 51.5% of the patients were women. 75,5% of patients were referred for a clinical obstructive syndrome (gas and material obstruction, abdominal meteorism, vomiting, etc.). The other patients (24,5%) were referred for, epigastric pain, abdominal pain and hypotension, non-systematized pain, abdominal pain without signs of occlusive syndrome. Finally, 48.5% of the patients were hospitalized and 51.5% were referred by the emergency department.

Patients with colitis were of mean age 49 years ± 22.Women represented 51.6% of the patients. Among these patients, 74.2% presented with abdominal pain or tenderness. Other symptoms observed were diarrhea (38.7%), fever (29%), biological inflammatory syndrome with or without fever (38.7%) and patients with rectal bleeding or septic shock (12.9%). The emergency department referred the majority of the patients included.

Dosimetric analysis

Table ( 3 ) shows the results of the dosimetric data for the two groups of patients. The mean CTDIvol and PDL values were lower than the DRL value(13 mGy and 625 mGy*cm, respectively) and GRL (11 mGy and 525 mGy*cm) for an abdomen-pelvis examination.

The mean CTDIvol for obstruction examinations was significantly higher than that for colitis (+34.2%±1.5). Similar results were observed for DLP (40.4% ±1.3), SSDE (9.5% ±1.3), and effective diameter (18.9% ± 5.1).

The difference between the CTDIvol and SSDE was higher for patients with colitis (37.5%) than for patients with obstructions(12.3%).

Objective evaluation of image quality

Figure [START_REF] Jacobsen | Dual-Energy CT: Lower Limits of Iodine Detection and Quantification[END_REF] represents the variation of noise, contrast and CNR as function of the single energy levels and for mixed images for the two groups.

For patients with obstructions, the noise and contrast decreased significantly as function of energy level from 40 to 70 keV (-47.2% and -56.3% respectively) and was similar between 70 and the mixed images (6.5% with p = 0,53 for noise and 0.9% with p = 0.36 for contrast). The maximum CNR value was observed at 60 keV but no significant difference was observed between the different energy levels except between 70 and 60 keV (-4.7% and p<0.05). No significant difference was observed between the singleenergy levels and the mixed images (mean difference of 2.2%±1.2).

Similar results for noise and contrast were found for colitis with a decrease in noise and contrast between 40 and 70 keV of -50.4% and -56.2% respectively. Noise and contrast were similar between 70 keV and the mixed images (11.2% and 5.7%). For CNR, the maximum value for VMIs was observed at 60 keV but the difference was only significant with 40 and 70 keV levels. The difference between VMIs and mixed images was significant for all single-energy levels with an average difference of -6.6% ±4.1.

Subjective evaluation of image quality

Concordance

The results showed a good inter-observer agreement for the analysis of the different criteria with a calculated kappa index of 0.95 for noise, 0.89 for smoothing, 0.88 for overall quality, 0.91 for diagnostic quality and 0.99 for diagnostic confidence

Noise

The variation of the mean noise score for both pathologies are depicted on For patient with colitis, similar results were found with the maximum score at 60 keV and no significant difference between mixed images and 70 keV level score (p=0.066).

Smoothing

Figure [START_REF] Greffier | Performance of Four Dual-Energy CT Platforms for Abdominal Imaging: A Task-Based Image Quality Assessment Based on Phantom Data[END_REF] shows the smoothing image score for the two groups.

For obstruction the maximum smoothing score was reported at 60 keV. It increased significantly between 40 and 60 keV and decreased significantly at 70 keV. The mixed image score was significantly higher than for images at 40, 50 and 70 keV but not significant for 60 keV (p = 0.119).

For colitis , similar results were observed with the maximum score at 60 keV and no significant difference between the mixed images and 60 keV level score (p=0.888).

Overall quality

Figure [START_REF] Jacobsen | Intermanufacturer Comparison of Dual-Energy CT Iodine Quantification and Monochromatic Attenuation: A Phantom Study[END_REF] shows the global image quality scores as function of the energy levels and mixed images.

For the two groups, the maximum score for global image quality was observed at 60 keV. It increased significantly from 40 to 60 keV and significantly decreased at 70 keV. The mixed image score was significantly lower than the score at 60 keV and significantly higher that at 40 and 50 keV, except for colitis where the difference was not significant at 50 keV (p=0.162). The difference between mixed images and images at 70 keVwas not significant for the two groups.

Diagnostic quality

Figure [START_REF] Greffier | Impact of Dose Reduction and the Use of an Advanced Model-Based Iterative Reconstruction Algorithm on Spectral Performance of a Dual-Source CT System: A Task-Based Image Quality Assessment[END_REF] depicts the score of diagnostic quality according to the energy levels for both VMIs and mixed images. Examples of quality and attenuation differences are shown on figure [START_REF] D'angelo | Dual energy computed tomography virtual monoenergetic imaging: technique and clinical applications[END_REF] for colitis, liver on figure [START_REF] Jagoda | Comparison of Metal Artifact Reduction in Dual-and Single-Source CT: A Vertebral Phantom Study[END_REF] and intestinal obstruction on figure [START_REF] Dabli | Optimization of Image Quality and Accuracy of Low Iodine Concentration Quantification as Function of Dose Level and Reconstruction Algorithm for Abdominal Imaging Using Dual-Source CT: A Phantom Study[END_REF].

All p-values are shown on table ( 4 ) for patients with intestinal obstruction and table [START_REF] Jacobsen | Intermanufacturer Comparison of Dual-Energy CT Iodine Quantification and Monochromatic Attenuation: A Phantom Study[END_REF] for patients with colitis.

Discussion

In The results showed that the maximum CNR was observed on VMI images at 60 keV compared to other VMI images and mixed images but without statistical significance. The subjective evaluation showed that the 60 keV VMI images had the best noise, smoothing, overall quality and diagnostic quality scores with a significant difference compared to the other images except for the smoothing between 60 keV and mixed images which was considered similar for both pathologies.

The CTDIvol results showed that the average CTDIvol and PDL of the acquisitions were lower than the DRL and GRL [START_REF]Arrêté du 23 mai 2019 portant homologation de la décision n° 2019-DC-0667 de l'Autorité de sûreté nucléaire du 18 avril 2019 relative aux modalités d'évaluation des doses de rayonnements ionisants délivrées aux patients lors d'un acte de radiologie, de pratiques interventionnelles radioguidées ou de médecine nucléaire et à la mise à jour des niveaux de référence diagnostiques associés[END_REF]. This reflects optimized practices and protocols in Dual-energy CT as well as conventional CT acquisitions. The mean CTDIvol of intestinal obstruction patients was significantly higher than that of colitis patients. This is essentially due to patients corpulence. Indeed, in the absence of the weight and height of the patients, the calculation of the effective diameter shows that patients with intestinal obstruction had a significantly higher Deff than that of the colitis. The use of the intensity modulation system therefore increases the mAs for these patients in order to maintain sufficient image quality. This is also confirmed by the difference observed between the SSDE and CTDIvol which was lower for occlusions compared to colitis (37%) because of an effective diameter (26.77 cm) further from the diameter of the standard dosimetry phantom (32 cm) compared to the occlusions case (31.83).

Concerning the objective evaluation of the images, a decrease in iodine contrast and noise when the monoenergetic level increased was observed.

This result is equivalent to that reported in several studies on phantom and patients [START_REF] Booij | Assessment of Iodine Contrast-To-Noise Ratio in Virtual Monoenergetic Images Reconstructed from Dual-Source Energy-Integrating CT and Photon-Counting CT Data[END_REF][START_REF] Kang | Value of Virtual Monochromatic Spectral Image of Dual-Layer Spectral Detector CT with Noise Reduction Algorithm for Image Quality Improvement in Obese Simulated Body Phantom[END_REF]. This behavior is explained by the strong attenuation of low keV X-rays due to the increased contribution of the photoelectric effect.

This increases the contrast between the iodine and the surrounding tissue at low keV but also increases the noise. The difference in contrast and noise between the VMIs at 70 keV and the mixed images was not significant. This can be explained by the fact that the 70 keV energy is close to the average energy of the X-ray spectrum of a conventional acquisition at 120 kVp represented by the mixed images in this case. Nevertheless, the comparison of the CNRs showed a trend toward a maximum value at 60 keV but the differences were not significant between the different monoenergetic levels and between these levels and the mixed images. This result is different from those reported in several phantom studies showing a maximum CNR at 40 keV and a decrease with monoenergetic levels [START_REF] Tao | Improving Iodine Contrast to Noise Ratio Using Virtual Monoenergetic Imaging and Prior-Knowledge-Aware Iterative Denoising (Mono-PKAID)[END_REF]. However, other patient studies have also reported a non-significant difference in CNR between monoenergetic levels on VMIs [START_REF] Dabli | Optimization of Image Quality and Accuracy of Low Iodine Concentration Quantification as Function of Dose Level and Reconstruction Algorithm for Abdominal Imaging Using Dual-Source CT: A Phantom Study[END_REF][START_REF] Patino | Virtual Monochromatic Dual-Energy Aortoiliac CT Angiography With Reduced Iodine Dose: A Prospective Randomized Study[END_REF]. Indeed, the inter-patient variability makes this observation more complex compared to the phantom which is standardized and fixed without movements. Indeed, the decrease in contrast when the monoenergetic level increases is compensated by the decrease in noise in the same proportions.

The results of the subjective evaluation showed that the noise score increased between 40 and 60 keV and then decreased at 70 keV. The score for those levels were similar to that of the mixed images. These results are consistent with the objective noise assessment except between 60 and 70 keV where the objective noise difference showed lower noise. For image smoothing, the radiologists considered the best noise texture to be on the 60 keV images for VMIs and for both pathologies and no significant difference was observed between these images and the mixed images. This result is equivalent to that reported by Greffier et al [START_REF] Greffier | Impact of Dose Reduction and the Use of an Advanced Model-Based Iterative Reconstruction Algorithm on Spectral Performance of a Dual-Source CT System: A Task-Based Image Quality Assessment[END_REF] who found an increase in the average frequency of the noise spectrum between 40 and 60 keV and then a decrease at 70 keV which reflects a finer noise texture. The best overall image quality (compromise between noise and smoothness) was observed on the VMIs at 60 keV for both pathologies. This score reflects the best compromise between noise and smoothing for the visualization of intestinal obstruction and colitis. Several studies have reported similar results for other abdominal pathologies in patients [START_REF] Hokamp | Assessment of Arterially Hyper-Enhancing Liver Lesions Using Virtual Monoenergetic Images from Spectral Detector CT: Phantom and Patient Experience[END_REF][START_REF] Mcnamara | Multireader Evaluation of Lesion Conspicuity in Small Pancreatic Adenocarcinomas: Complimentary Value of Iodine Material Density and Low KeV Simulated Monoenergetic Images Using Multiphasic Rapid KVp-Switching Dual Energy CT[END_REF][START_REF] Patel | Energy-Specific Optimization of Attenuation Thresholds for Low-Energy Virtual Monoenergetic Images in Renal Lesion Evaluation[END_REF][START_REF] Martin | Noise-Optimized Virtual Monoenergetic Dual-Energy Computed Tomography: Optimization of Kiloelectron Volt Settings in Patients with Gastrointestinal Stromal Tumors[END_REF]. In addition, similar results were observed in a phantom study using advanced image quality metrics including detectability index (34) on the same DECT platform. This study showed that detectability was maximal at 70 keV for lesions simulated with blood+iodine contrast at 2 mg/mL. The difference observed between this phantom study and the results of our study can be explained by a higher contrast of iodine in occlusions and colitis compared to the simulated contrast in the study.

The diagnostic quality was also judged better at 60 keV compared to the other monoenergetic levels and compared to the mixed images. These were judged to be equivalent to those of the VMIs at 70 keV. Some of the VMI images at 40 and 50 keV were judged to be of insufficient diagnostic quality (24% of patients at 40 keV and 12% at 50 keV for occlusions and 13% and 3% respectively for colitis). The trade-off between noise and smoothing associated with image aspects, clear visualization of edges and structures of diagnostic interest thus justified the better quality on VMIs at 60 keV compared to other monoenergetic levels and mixed images.

Thus, several studies have reported the interest of low-energy VMIs in enhancing the contrast of iodine and consequently improving the visualization of enhanced lesions, particularly in the abdominal region. The monoenergetic levels reported vary between 40 and 70 keV for different abdominal pathologies [START_REF] D'angelo | Dual energy computed tomography virtual monoenergetic imaging: technique and clinical applications[END_REF]. However, the increase in noise at low keV limits the use of VMIs in certain cases. It is therefore important to adapt the monoenergetic level according to the clinical objective (pathology, iodine contrast, ..).

Moreover, studies evaluating the performance of different dual-energy CT (DECT) platforms have shown that the optimal monoenergy level may differ from one platform to another for the same clinical task [START_REF] Greffier | Performance of Four Dual-Energy CT Platforms for Abdominal Imaging: A Task-Based Image Quality Assessment Based on Phantom Data[END_REF][START_REF] Jacobsen | Intermanufacturer Comparison of Dual-Energy CT Iodine Quantification and Monochromatic Attenuation: A Phantom Study[END_REF][START_REF] Dabli | Optimization of image quality and accuracy of low iodine concentration quantification as function of kVp pairs for abdominal imaging using dual-source CT: A phantom study[END_REF][START_REF] Sellerer | Dual-Energy CT: A Phantom Comparison of Different Platforms for Abdominal Imaging[END_REF] .

This study allowed us to propose the optimal monoenergy level for the visualization of digestive occlusions and colitis on the 3rd generation dual source CT platform. Beyond the improvement of the image quality, the definition of this level allows to optimize the DECT image workflow by generating VMIs at 60 keV systematically for the examinations concerning occlusions and colitis.

Finally, this study has some limitations, the first of is the monocentric aspect making the generalization of these results to all centers difficult. The study concerns a single scanner model and the analysis was done retrospectively. Finally, the absence of patient's weight and height is also a limitation but this was compensated for by the calculation of the SSDE.

Conclusions

Our study showed the interest of using VMIs on the evaluation of intestinal obstruction and colitis in the emergency setting. The use of the monoenergetic level of 60 keV could allow a better image quality in terms of noise, image texture and diagnostic quality than the other monoenergetic levels and mixed images. ). Among them, 535 were pathological using DE on portal acquisition, including 213 digestive pathologies (except diverticulitis and appendicitis) Among these patients, 33 had gastrointestinal obstruction and 31 had colitis and were included in the study for a total of 64 patients.

  Maxime, le meilleur bro depuis maintenant un bon moment. Mon premier coloc et le dernier j'espère, c'était très fatiguant. T'es devenu un de mes meilleurs amis et je n'ai aucun doute sur le fait que ça sera pour une grande partie de ma vie, alors merci. Merci d'être toujours prêt à blaguer mais en même temps d'être toujours de bon conseil car tu en sais beaucoup sur beaucoup de choses. J'ai bien fait de te sauver de l'incendie de la patate dans notre coloc. J'espère qu'on travaillera ensemble un jour, ça serait une belle façon de conclure tout ce chemin parcouru côte à côte. A Quentin, Docteur House, un très bon ami et un très bon radiologue. Le covoiturage et les débriefing de MAPR me manquent. Même si t'as pas les os très solides (fais une ostéodensitométrie mec) t'es un gars en or et surtout ne change rien. J'ai hâte d'être ta demoiselle d'honneur au mariage. A Benoit, tu m'as beaucoup appris, toujours dans la bonne humeur grâce à tes anecdotes. Merci de m'avoir permis d'approcher la radiologie interventionnelle. J'ai envie de refaire un stage à Perpignan rien que pour refaire un semestre avec toi. A Julien, mon meilleur compagnon pour la cantine. Merci mon pote pour ces bons moments de rire lors de nos stages à ADV et à Nimes, j'espère qu'on aura l'occasion de faire d'autres semestres ensemble. Quand tu veux on retourne au Couperet .

  dans la bonne humeur, tu es un exemple à suivre. Merci pour les merguez, les soirées coupe d'Europe chez toi et les Fifa. A Maxime, d'une compétence et d'une cool attitude infinie. A Ana, merci pour ta gentillesse, pour la promenade en RS5 et pour tous les Nutella Be-Ready A Aymeric, pour sa vision des choses, son humour, j'attends toujours pour essayer ta Tesla. A Sabine, Philippe, Sandra, Nicolas, Jean Louis, Aurélie, Paul, pour avoir su partager leurs connaissances. A Mohamed, Ian, Yvan et Vincent, pour leur formation en radiologie interventionnelle.

Figure ( 1 )

 1 below shows an example of the measurement of the AP and Lat diameters.

(

  κ=0.00-0.20), low (κ=0.21-0.40), moderate (κ=0.41-0.60), good (κ=0.61-0.80), or excellent (κ=0.81-1.00). The mean contrast to noise ratio values and the mean score values of each image quality criterion of the VMIs were compared with the score of the mixed images using the Mann-Whitney U test for paired sample.

Figure ( 3 )

 3 Figure[START_REF] Papadakis | Fast KVp-Switching Dual Energy Contrast-Enhanced Thorax and Cardiac CT: A Phantom Study on the Accuracy of Iodine Concentration and Effective Atomic Number Measurement[END_REF]. For patient with obstruction the maximum noise score was

For

  obstructions, the maximum diagnostic image quality score was obtained at 60 keV. It increased significantly between 40 and 60 keV and decreased significantly compared to 70 keV and to mixed images. The mixed images score was significantly higher than 40 and 50 keV energy levels scores but similar than 70 keV level (p=0.459). The number of images scored ≥ 3 was 25, 29, 33, 33 and 33 at 40, 50, 60, 70 and on mixed images respectively. For colitis, the maximum score was at 60 keV as well. The difference with the other monoenergetic levels was significant. The difference between VMIs and mixed images was not significant at 50 keV (p=0.190) and 60 keV (p=0.663). The number of images scored ≥ 3 was 27, 30, 31, 31 and 31 at 40, 50, 60, 70 and on mixed images respectively.

  this study, an objective and subjective comparison of image quality of VMIs at 40, 50, 60 and 70 keV as well as mixed images generated by the Dual-source CT platform for the diagnosis of intestinal obstruction and colitis in the emergency setting was performed. The images of 64 patients were analyzed by measuring noise, contrast and calculating CNR and a subjective evaluation by two radiologists of noise, smoothing, overall quality (noise+smoothing) and diagnostic quality was performed.

Figure 1 :

 1 Figure 1 : AP and LAT mesures, to determine effective diameter and SSDE.

Figure 2 :

 2 Figure2: Flow chart 1527 CT were performed in dual energy in our Department during the study period (February 2019, February 2020). Among them, 535 were pathological using DE on portal acquisition, including 213 digestive pathologies (except diverticulitis and appendicitis) Among these patients, 33 had gastrointestinal obstruction and 31 had colitis and were included in the study for a total of 64 patients.

Figure 2 :

 2 Figure 2 : variation of noise, contrast and CNR as function of energy levels and mixed images for obstructions (a,b,c) and colitis (e,f,g).

Figure 3 :Figure 4 :Figure 5 :

 345 Figure 3 : variation of mean noise score as function of energy levels and mixed images (a. intestinal obstruction and b. colitis)

Figure 6 :

 6 Figure 6 : Variation of mean diagnostic quality score as function of energy levels and mixed images (a. Intestinal obstruction and b. Colitis).

Figure 9 :

 9 Figure 9 : Example of intestinal obstruction differences between VMI and 120KvP reconstruction (A: 40KeV ; B : 50 KeV ; C : 60 KeV ; D : 70 KeV ; E : 120 KvP ) each on standard abdominal window (W 370 C 60).

Figure 8 :

 8 Figure 8 : Example of noise differences on the liver between VMI and 120KvP (A: 40KeV ; B : 50 KeV ; C : 60 KeV ; D : 70 KeV ; E : 120 KvP ) each on a window suitable for interpretation.

Figure 7 :

 7 Figure 7 : Example of colitis differences between VMI and 120KvP reconstruction (A: 40KeV ; B : 50 KeV ; C : 60 KeV ; D : 70 KeV ; E : 120 KvP ) each on standard abdominal window (W 370 C 60).

2022 PERSONNEL ENSEIGNANT Maîtres de Conférences des Universités - Praticiens Hospitaliers MCU-PH Hors classe -Echelon Exceptionnel

	GIANSILY-BLAIZOT Mu-	Hématologie ; transfusion
	DADURE Christophe PASQUIE Jean-Luc PROFESSEURS ASSOCIES -Médecine Anesthésiologie-réanimation et médecine péri-Cardiologie riel
	opératoire Chirurgie infantile MEUNIER Isabelle (Ophtalmologie) DAUVILLIERS Yves KALFA Nicolas Physiologie JUNG Boris Médecine intensive-réanimation MCU-PH de BESSIS Didier (Dermato-vénéréologie) 2 éme classe
	DE TAYRAC Renaud DE VOS John DAUVILLIERS Yves DE TAYRAC Renaud LACHAUD Laurence LALLEMANT Benjamin BERGOUGNOUX MULLER Laurent (Anesthésiologie-réanimation et médecine péri-opératoire) Gynécologie-obstétrique, gynécologie médicale Histologie, embryologie et cytogénétique Physiologie Gynécologie-obstétrique, gynécologie médicale Parasitologie et mycologie Génétique Anne MCU-PH de 1 re classe Oto-rhino-laryngologie LE QUINTREC DON-CHIRIAC Anca Immunologie PERRIGAULT Pierre-François (Anesthésiologie-réanimation et médecine péri-Néphrologie opératoire) BERTRAND Martin Anatomie NETTE Moglie LETOUZEY Vincent Gynécologie-obstétrique ; gynécologie médicale DE JONG Audrey Anesthésiologie-réanimation et médecine péri-QUANTIN Xavier (Pneumologie) BOUDOUSQ Vincent Biophysique et médecine nucléaire opératoire
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	DUCROS Anne MENJOT de CHAMP-COSSEE Mireille DUPEYRON Arnaud FESLER Pierre GARREL Renaud GENEVIEVE David GUILLAUME Sébastien GUIU Boris HAYOT Maurice HOUEDE Nadine FLEUR Nicolas MILLET Ingrid GIRARDET-BESSIS HERRERO Astrid MURA Thibault NAGOT Nicolas OLIE Emilie PANARO Fabrizio PARIS Françoise Anne LAVIGNE Géraldine LESAGE François-Xavier MARTRILLE Laurent MATHIEU Olivier HUBERLANT Stéphanie KUSTER Nils MAKINSON Alain PANTEL Alix ANNEE UNIVERSITAIRE 2021 -RICHARD Bruno Radiologie et imagerie médicale Génétique Neurologie Médecine physique et de réadaptation Médecine interne ; gériatrie et biologie du vieillis-sement, médecine générale, addictologie Oto-rhino-laryngologie Génétique Psychiatrie d'adultes ; addictologie Radiologie et imagerie médicale Physiologie Chirurgie viscérale et digestive Biochimie et biologie moléculaire Radiologie et imagerie médicale Biostatistiques, informatique médicale et technolo-gies de la communication Biostatistiques, informatique médicale et technolo-gies de la communication Psychiatrie d'adultes; addictologie Chirurgie viscérale et digestive Biologie et médecine du développement et de la reproduction ; gynécologie médicale Hématologie ; transfusion Médecine et Santé au Travail Médecine légale et droit de la santé Pharmacologie fondamentale ; pharmacologie cli-Gynécologie-obstétrique ; Gynécologie médicale Biochimie et biologie moléculaire Maladies infectieuses, Maladies tropicales Bactérologie-virologie ; hygiène hospitalière nique ; addictologie PERS Yves-Marie Thérapeutique; addictologie Médecine palliative MOUZAT Kévin Biochimie et biologie moléculaire Cancérologie ; radiothérapie KLOUCHE Kada Médecine intensive-réanimation PELLESTOR Franck Histologie, embryologie et cytogénétique SEGONDY Michel ROUBILLE Ca-Médecine interne ; gériatrie et biologie du vieillis-Bactériologie-virologie ; hygiène hospitalière PANABIERES Catherine Biologie cellulaire mille sement ; addictologie
	KOENIG Michel KOUYOUMDJIAN Pascal PEREZ MARTIN Antonia POUDEROUX Philippe MCU-PH Hors classe RAVEL Christophe SZABLEWSKY	Génétique Chirurgie orthopédique et traumatologique Chirurgie vasculaire ; médecine vasculaire (option Gastroentérologie ; hépatologie ; addictologie Parasitologie et mycologie médecine vasculaire) Anatomie et cytologie pathologiques
	LAVABRE-BERTRAND Thierry RIGAU Valérie BADIOU Stéphanie SCHUSTER-BECK Iris	Histologie, embryologie et cytogénétique Anatomie et cytologie pathologiques Biochimie et biologie moléculaire Physiologie
	LAVIGNE Jean-Philippe RIVIER François BOULLE Nathalie STERKERS Yvon	Bactériologie-virologie ; hygiène hospitalière Pédiatrie Biologie cellulaire Parasitologie et mycologie
	LE MOING Vincent ROSSI Jean François LECLERCQ Florence ROUBILLE François CACHEUX-RATABOUL Valère THEVENIN-RENECéline	Hématologie ; transfusion Maladies infectieuses ; maladies tropicales Cardiologie Cardiologie Génétique Immunologie
	MATECKI Stéfan SEBBANE Mustapha CARRIERE Christian	Physiologie Médecine d'urgence Bactériologie-virologie ; hygiène hospitalière
	MORANNE Olivier CHARACHON Sylvie	Néphrologie Bactériologie-virologie ; hygiène hospitalière
	MOREL Jacques	Rhumatologie
	NAVARRO Francis cale FABBRO-PERAY Pas-	Chirurgie viscérale et digestive Epidémiologie, économie de la santé et prévention
	NOCCA David	Chirurgie viscérale et digestive

Maîtres de Conférences des Universités -Médecine Générale MCU-MG de 1 re classe

	Maitres
	COSTA David
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de Conférences des Universités Maîtres de Conférences hors classe Maîtres de Conférences de classe normale

	BIRON-ANDREANI	COLIN Olivier		GALMICHE Sophie		MEROUEH Fadi
	Christine
	BLANC Brigitte	CONSEIL Mathieu Remerciements : GENY Christian		MEYER Pierre
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	vie	PH chargés d'enseignements
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	LADRET Véronique Davide		Mathématiques appliquées et applications des mathé-IERE Gilles
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	BENEZECH Jean-	santé CATHALA Philippe	FAUCHERRE		LUQUIENS Aman-
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	MORITZ-GASSER Sylvie BENNYS Karim CAZABAN Michel Neurosciences FILLERON Anne		MANZANERA Cyril
	MOUTOT Gilles BERNARD Natha-	Philosophie CHARBIT Jonathan FITENI Frédéric		MARGUERITTE
	PASSERIEUX Emilie lie	Physiologie		Emmanuel
	RAMIREZ Jean-Marie Ivan BERTCHANSKY CHEVALLIER Thierry Histologie	FOURNIER Philippe		MARTIN Lucille
	BIBOULET Phi-	CHEVALLIER-MICHAUD
	lippe	Josyane

Aux membres du jury : A Monsieur le professeur Jean Paul Beregi :

	C'est un honneur de vous avoir en président du jury aujourd'hui. Merci de
	m'avoir accompagné et de m'avoir guidé dès le début de cette thèse. J'ai
	beaucoup appris à vos côtés, et vos enseignements m'ont permis d'avoir
	une nouvelle approche de la radiologie et de la médecine de manière géné-
	rale.
	A

Madame la Professeure Ingrid Millet:

	Merci de me faire l'honneur de participer au jury de cette thèse. Votre répu-
	tation vous précède et c'est une véritable chance de vous présenter mon tra-
	vail. Je suis impatient de travailler à vos côtés lors de mon prochain stage.

A Monsieur le Docteur Jean Goupil:

	A ma famille :
	A mes parents, merci de m'avoir accompagné lors de ce long voyage. Je ne jours de bonne humeur et toujours partante pour aider notamment lors de
	serai jamais arrivé là sans vous. Votre soutien lors de mes études et lors de nos travaux.
	mes concours est d'une valeur inestimable et a été inconditionnel et pour A René Claude et Sandrine, merci pour ces bons moments dans mon en-
	cela vous aurez ma reconnaissance éternelle. Même si je suis parti récem-fance, je regrette qu'on ne se voit pas aussi souvent qu'il le faudrait.
	ment de la maison (certes je ne suis pas parti très loin), je resterai toujours à
	vos côtés. A Gabri, Graziella, Adri et Nino, merci pour ces incroyables moments de
	convivialité, c'est toujours un plaisir de vous retrouver tous ensemble lors
	Maman, merci pour tes conseils au quotidien, tu n'imagines pas la chance des fêtes de famille.
	que j'ai d'avoir une mère qui sait toujours tout. Je ne sais pas où j'en serais
	sans toi. Merci pour tout ma mère je t'aime. A mes cousins, même si ces derniers temps il est vrai qu'on se voit peu,
	quelle idée de faire autant d'enfants.
	Papa, merci pour ton amour infaillible et ton soutien au quotidien. Merci
	pour les petits déjeuners, merci pour tes conseils. Merci pour tout mon père A Chloé, merci pour ton soutien depuis le concours de l'internat, tu as tou-
	je t'aime. jours été là pour moi et je serai toujours là pour toi. Tu es à la fois ma chérie
	et ma meilleure amie, je ne m'ennuie jamais avec toi et c'est tellement pré-
	A mes grands-parents : cieux. Merci d'être toi, je n'y serai jamais arrivé sans toi , je t'aime. !
	A Mamie, tellement de bons souvenirs à tes côtés, merci pour ces moments
	de convivialité et ces repas pantagruéliques.
	A Papi, merci pour ces souvenirs d'enfance, ces parties de pêches et surtout
	Merci de me faire l'honneur de juger ce travail et merci de m'avoir accom-pour les casses croutes de pâté sur le bateau.
	pagné lors de l'élaboration de ce dernier. Vous êtes un mentor et un ami, A Nonna, merci pour ces beaux moments durant mon enfance, même si je
	merci d'être là aujourd'hui. ne comprenais pas toujours ce que tu me disais, je sais que c'était toujours
	pour mon bien.
	A Nonno, je regrette de ne pas avoir eu la chance de plus te connaître mais
	les histoires que tes enfants ont pu me raconter m'ont permis de savoir que
	tu étais quelqu'un d'exceptionnel.
	A mon grand frère, mon exemple, merci d'avoir toujours été là pour moi.
	Merci pour tes conseils et merci d'être toujours disponible quand ton frère,
	ce boulet, ne sait pas quoi faire. Félicitations pour la maison, j'ai hâte de la
	voir.

A mes amis : A Jules, mon

  meilleur ami. Je te connais depuis près de 10 ans et tu ne peux pas savoir combien je suis heureux que tu aies choisi la même spécialité que moi. 10 ans c'est long mais ce n'est que le début et j'ai hâte de voir la suite, car crois moi mon ami, je serai toujours là. Vers le Nord ! A Roman, on s'aime autant qu'on se déteste et c'est bien pour ça que notre amitié est si précieuse. D'innombrables bons moments passés à tes côtés depuis le lycée, merci pour les fous rires mais merci également pour ces moments de sincérité et de confidence. Je serai toujours là pour toi mon ami.

Article Determination of the most suitable mono energetic level of virtual monochromatic images in Dual source CT to analyze the digestive tract in context of emergency 1.1 Abstract Objective:

  To compare objective and subjective image quality between virtual monoenergetic images (VMI) and mixed images (120kvP) in patients with colitis or bowel obstruction in the emergency department.

	Table des matières
	1.
	1. Article
	1.1. Abstract
	1.2. Introduction
	1.3. Materials and methods
	1.3.1. Design and study population
	1.3.2. Acquisition and reconstruction parameters Methods: Retrospective monocentric analysis of patients with bowel obs-
	1.3.3. Dosimetric analysis truction and colitis in different mono energetic levels (40, 50, 60 and 70-
	1.3.4. Objective analysis of image quality
	1.3.5. Subjective analysis of image quality
	1.3.6. Statistical analysis
	1.4. Results
	1.4.1. Study population
	1.4.2. Dosimetric analysis
	1.4.3. Objective analysis of image quality
	1.4.4. Subjective analysis of image quality
	1.5. Discussion
	1.6. Conclusion
	2. Références
	3. Annexes

keV) and mixed images (120kvP) in portal time abdominopelvic CT. Objective criterias (CNR) and subjective criterias like noise, smoothing, overall quality and diagnostic quality were evaluated.

Table 4

 4 En présence des Maîtres de cette école, de mes chers condisciples et devant l'effigie d'Hippocrate, je promets et je jure, au nom de l'Etre suprême, d'être fidèle aux lois de l'honneur et de la probité dans l'exercice de la médecine. Respectueux (se) et reconnaissant (e) envers mes Maîtres, je rendrai à leurs enfants l'instruction que j'ai reçue de leurs pères.

shows all p-values for subjective evaluation of image quality for patients with intestinal obstruction *Represents statistically significant difference (p<0,05) SERMENT " " Je donnerai mes soins gratuits à l'indigent et n'exigerai jamais un salaire au-dessus de mon travail. " Admis (e) dans l'intérieur des maisons, mes yeux ne verront pas ce qui s'y passe, ma langue taira les secrets qui me seront confiés, et mon état ne servira pas à corrompre les moeurs, ni à favoriser le crime.

"

Résumé :

Determination en scanner double énergie du niveau mono énergétique le plus adapté à l'analyse du tube digestif dans le cadre des pathologies d'urgence.

Objectif:

Comparer


Abir Hizi

Alexis Front

Moncef Said

Fabienne Berthier

Guy Tréglia

Christine Mottet
email: mottet@cinam.univ-mrs.fr

Tight-binding Ising modeling of the interplay between bulk ordering and surface segregation in Pt-Ag nanoalloys

Keywords: Alloys Surfaces, Nanoalloys, Surface segregation, chemical ordering, Monte Carlo simulations, Tight-Binding Ising model

.

I. INTRODUCTION

Pt-Ag systems have been recently reinvestigated both in bulk alloys [2] and in nanoalloys [1,3,4] because of fundamental and applied interests. Pt-based alloys play an important role in catalytic applications [4][5][6] and notably in fuel cells [7][8][9] where it is necessary to decrease the amount of platinum in the cathodes to reduce the cost. From a fundamental point of view, Pt-Ag system displays a quite atypical phase diagram [2,10,11] with a large miscibility gap between two solid solutions at temperature between 1470 and 1170 K : one Pt-rich with a few percent of Ag up to 15% at 1470 K and the other Ag-rich with up to 40% at 1470 K. Below 1170 K there is an ordered stoechiometric compound, around the equiconcentration, precisely at Ag 47 Pt 53 . It is ordered according to the L1 1 structure which is an alternation of pure atomic layers in the (111) orientation (CuPt-type structure). First principles calculations of the Ag-Pt system coupled with a cluster variational method show that the cluster interactions have to be expanded beyond the second nearest neigbors in order to stabilize the miscibility gap between the two solid solutions at high temperature [11] and the L1 1 ordered structure as in the CuPt ordered compound [12]. The specifity of the Pt-Ag alloy is to display both phase separation and ordering tendency in the same system. This implies to use a theoretical model where the Effective Paire Interactions (EPIs) strongly depend on the concentration.

We use a quite simple theoretical model based on a Tight-Binding Ising Model (TBIM) [13] on a rigid lattice where the Effective Pair Interactions (EPIs) are fitted to ab-initio, semiempirical Tight-Binding interatomic potential calculations or experimental data. We vary the EPIs as a function of the concentration in the alloy in order to take into account the specificity of the Pt-Ag system which presents both a miscibility gap and an ordered phase.

Variation of the EPIs has already been used in Fe-Cr alloys to take into account shortrange-order reversal as a function of concentration evidenced by diffuse-neutron-scattering and resistivity measurements [14]. Numerical simulations are performed using Monte Carlo simulations in canonical and semi-grand canonical ensembles in order to describe systems at a given concentration (canonical) or at a given difference of chemical potential (semi-grand canonical) enabling to vary the concentration and temperature to describe phase diagrams.

We also apply the Widom method in order to connect the two statistic ensembles.

The chemical ordering and surface segregation are crucial to control catalytic properties [4][5][6][7][8][9]. Nanoalloys represent systems of choice for catalytic applications since they optimize surface atoms as compared to the total weight of metal catalyst. However their structure and morphology vary sensibly as compared to bulk stucture [START_REF]Nanoalloys: From Theory to Application[END_REF][16][START_REF]Nanoalloys, Synthesis, Structure and Properties[END_REF]. Therefore a lot of studies are needed to characterize experimentally the nanoparticles and theoretically predict chemical arrangement notably at the surface where experimental results are still very scarce [1].

We use the semi-empirical SMA (Second Moment Approximation) potential developped for the Pt-Ag nanoalloys [1] and compared to ab initio calculations on small cluster sizes to fit a more simple energetic model on rigid lattice with variable EPIs as a function of the concentration. It is made to reproduce qualitatively the bulk phase diagram in the solid state part which means the L1 1 typical ordered phase and the phase separation between the two solid solutions at high temperature. Then we use it to characterize the surface segregation profile at the vicinity of the surface and we apply it to clusters of different sizes in the truncated octahedral shape.

The paper is divided in five parts including introduction and conclusion. The second part gives a description of the theoretical energetic model and atomistic simulations. The third and fourth parts describe the results respectively on the bulk and on the alloy surfaces and nanoalloys.

II. TIGHT-BINDING ISING MODEL AND MONTE CARLO SIMULATIONS

A. Concentration dependent Tight-Binding Ising Model

The Tight-Binding Ising Model (TBIM) [13,[START_REF] Tréglia | [END_REF] has been developped to study chemical ordering effects in metallic alloys and surface segregation effects in semi-infinite [19] or finite systems [20,21]. It is developped according to a Tight-Binding Hamiltonian, on a rigid lattice, where order/disorder phenomena are well treated. The rigid lattice assumption is partially compensated by adding a relaxation correction taking into account the lattice misfit that we fit using a tight-binding second moment approximation (TB-SMA) interatomic potential. The hamiltonien writes in terms of effective pair interactions (EPI) V nm between atoms at sites n and m, and occupation factors p n with an Ising character which means p n = 1 if the site n is occupied by an atom of type A or p n = 0 if not (i.e. the site n is occupied by a B-type atom):

H T BIM = n,m p n p m V nm + n p n (∆h coh n + ∆h size n ) (1)
where the EPI V nm = 1 2 (V AA + V BB -2V AB ) characterizes chemical ordering. The second term corresponds to a local contribution to the energy induced by inequivalent geometrical environments in inhomogeneous systems like surfaces or clusters. It is composed of a cohesive term (∆h coh n ) due to the cohesion difference of the two metals, and a relaxation term (∆h size n ) due to size mismatch between the two elements, which is added to correct the rigid lattice assumption. They are nonzero for sites n which belong to the surface. ∆h coh n is equal to the difference of surface energies of the two elements (promoting the element with the lowest one to segregate). They are calculated using the many-body SMA interatomic potential [1] on each different sites of a truncated octahedron cluster of 1289 atoms. We checked that the values obtained on the cluster facets are the same as the one obtained on infinite surfaces in order to use the same parameters for clusters and infinite surfaces. ∆h size n are also calculated in the framework of the SMA potential by taking an impurity which differs from the matrix only by its atomic radius and corresponds to the difference in energy for a system with the impurity at the surface (infinite surface or cluster surface) as compared to the impurity in the bulk (or in the core of the cluster). The systems are quenched at 0 K by quenched molecular dynamic simulations. The values are listed in Tab. I.

The determination of the EPIs is more tricky. In the face centered cubic structure (fcc), it has been shown [22] that first neighbours interactions V 1 (for sites n and m first neighbours) dominate as compared to the following V 2 , V 3 , V 4 . Therefore in general, we consider only first neighbours pairs V 1 . However, at equiconcentration, to stabilize the L1 1 phase of the PtAg alloy with respect to the L1 0 or A 2 B 2 ones, it is necessary to go at least to the second neighbours EPIs. The corresponding ground states on fcc lattice is shown on Fig. 1 [12,[START_REF] Ducastelle | Order and Phase Stability in Alloys, Cohesion and Structure[END_REF]. This phase diagram results from the description of each phase in terms of pair interactions.

The stability domain for the L1 1 phase involves V 2 > 0 and

V 2 > V 1 /2 if V 1 > 0, or V 2 > -V 1 if V 1 < 0 (
as illustrated by the diagram on Fig. 1). V 1 and V 2 EPIs can be fitted to the mixing enthalpies of the L1 1 and L1 0 phases calculated either by density functional theory (DFT) calculations or semi-empirical potentials.

The ab-initio calculations are performed within the density functional theory (DFT) and the generalized gradient approximation (GGA) using the Perdew and Wang [START_REF] Perdew | [END_REF] exchange and correlation functional and the projector augmented wave (PAW) [25,26] interaction potential between the ions and the electrons, using the VASP code. The s and d valence electrons are considered for each metal with a cutoff energy equal to 600eV for plane wave basis set. The Brillouin zone integration is performed with the Monkhorst-Pack scheme with k-point mesh comprising 12 to 19 subdivisions along each reciprocal lattice vector.

The cohesive energy and lattice parameter of pure Ag and Pt, and the formation energies of the L1 1 and L1 0 ordered phases have been optimized. The results are shown in Tab. II and compared to the same quantities obtained with the semi-empirical potential developped by Pirart et al. in ref. [1]. We check first that the formation energies of the alloy ordered phases calculated by DFT [11] are quite similar with the present ones. Our calculations are lower in energy but the difference between the two phases is comparable (90 to 100 meV).

The large discrepancy comes from the TB-SMA calculations for which the formation energy of the L1 1 phase has been intentionally overestimated as compared to the L1 0 one in order to stabilize the L1 1 phase in bulk phase diagram [1,27].

Beside the equiconcentration we need to describe all the concentration range between Ptpure and Ag-pure systems. For that purpose we determine the EPIs by comparing energy of systems with impurity pair far separated versus neighboring. The energy difference between two impurities in first or second neighbors and the two impurities far away in the metal corresponds to V 1 or V 2 respectively. In Table III are listed the EPIs in bulk for the first (V 1 ) and second (V 2 ) neighbors in the two diluted limits and for the equiconcentrations as deduced from the formation energy of the ordered phase. We notice that they vary sensibly between the Pt-rich and the Ag-rich phases when calculated by TB-SMA whereas their variations are much smaller but still there in DFT, with a change of sign of V 1 in DFT as in TB-SMA and a positive value of V 2 in DFT even if much lower than in TB-SMA. As mentioned before, knowing that the formation energy of the L1 1 is overestimated in TB-SMA in order to stabilize the phase, this can explain the difference between DFT and TB-SMA calculations. In such a case we chose to fit the EPIs to the TB-SMA values. Then we take into account their variations by fitting a polynomial function with the three EPIs values in order to use appropriate value according to the concentration in silver of the system leading to the concentration dependence illustrated in Fig. 2. We also checked that the EPIs values at equiconcentration respect the criteria to stabilize the L1 1 ordered phase.

The symmetry breaking at surfaces implies that the EPIs are modified at the surface [13,28]. They have been determined by TB-SMA calculations in the same way as for the bulk but for sites located at the surface (the last atomic layer before the vacuum). We distinguish parallel interactions V i where the two atoms are neigbouring in the surface layer, and perpendicular interactions V ⊥ i for which the two atoms are neigbouring between two atomic layers perpendicularly to the surface. V i is the energy difference between a slab where two impurities are located in-plane in first or second neighbour distance and a slab with the two impurities in-plane but far away one from the other. V ⊥ i is the energy difference between a slab where two impurities are located out-of-plane with the same conditions. The values are reported in Tab. IV. We use a similar polynomial function as in the bulk to take into account their variations as a function of the concentration (see Fig. 2). Because we do not determined specific EPIs for the edge and vertex sites of the clusters, we take the same EPIs as the (100) surface sites. They appear in the following expression of the difference in energy between a surface site "p" and a bulk site for what concerns the alloying effect:

∆E alloy p = (Z 1 + 2Z ′ 1 )V 1 + (Z 2 + 2Z ′ 2 )V 2 -(Z 1 V 1 + Z ′ 1 V ⊥ 1 ) -(Z 2 V 2 + Z ′ 2 V ⊥ 2 ) (2)
where Z 1 and Z 2 are the first and second neighbors in the p plane and Z ′ 1 and Z ′ 2 , the same out of plane.

It follows that the TBIM presents three phenomenological effects to control the surface segregation: the alloying effect which, at least in case of first neighbours interactions, favours the segregation of the minority element when V < 0, or the majority element with an oscillating profile when V > 0, but here with V 2 of the same order of V 1 this usual prediction does not strictly applied; the cohesive effect (∆h coh ) which promotes the segregation of the element with the lowest cohesive energy; and the size effect (∆h size ) which promotes the segregation of minority atom when it is the biggest one.

We performed Monte Carlo simulations in canonical (N Ag , N P t , P and T constant) and semi-grand canonical ensembles (∆µ = µ P t -µ Ag , N tot =N P t +N Ag , P and T constant) where atoms exchange (exchange the position of two atoms of different nature), respectively atoms permutations (permute the nature of one atom: A in B or B in A), are proposed and accepted according to a Metropolis sampling [29] insuring to reach a Boltzmann distribution of the chemical configurations at equilibrium. In canonical ensemble, the concentration remains constant whereas in the semi-grand canonical ensemble, the concentration varies and the difference of the chemical potential of the two elements remains constant. In each case we keep the same number of atoms in the simulation box.

To check the equivalence of the two statistical ensembles we can determine in canonical ensemble the chemical potential for a given concentration according to the Widom method [30].

We propose virtual permutations (Pt in Ag or Ag in Pt) to evaluate the averaged chemical potential at constant concentration, "virtual" because the system is unchanged as if there was no permutation. It is only made to evaluate the variation of the energy after the permutation and to deduce the chemical potential: For a permutation of Pt in Ag:

∆µ P t->Ag = µ Ag -µ P t = -k B T ln{( 1 N Ag + 1 )( M Ag M P t ) P t atoms e -∆E P t->Ag k B T } (3)
and for a permutation of Ag in Pt:

∆µ Ag->P t = µ P t -µ Ag = -k B T ln{( 1 N P t + 1 )( M P t M Ag ) Ag atoms e -∆E Ag->P t k B T } (4)
where N P t and N Ag are the total numbers of Pt and Ag atoms, M Ag , M P t their masses and ∆E P t->Ag the variation in energy. In our model with rigid lattice the masses are not taken into account so that

M Ag M P t = 1.
Then we restore the system in its initial state and we proceed that way a large number of times (around 20000) to perform ensemble averages and get the equilibrium ∆µ value. At equilibrium the ∆µ P t->Ag and ∆µ Ag->P t must be equivalent. This method has been used in different studies [31,32] to connect the semi-grand canonical ensemble with the canonical ensemble.

For such simulations, we performed ten to twenty thousands macrosteps after leaving the system being equilibrated during two to five thousands macrosteps. Each macrostep consists in proposing randomly to any atom of the box a chemical exchange (exchange or permutation). For bulk systems, periodic conditions are applied in each cristallographic direction whereas in surfaces they are applied only in two directions and for clusters there are no periodic conditions.

It is important to notice that the calculation of the energy difference between two configurations which comes into the exponential in the probabilities calculation, even if it concerns only two atoms over a few thousands, is very sensitive to the variation of the EPIs when they are not constant as in our present model. Therefore it is necessary to calculate at each step the total energy of the system instead of a partial one which concerns only a sphere of atoms located around the permuting or exchanged atoms, as it is usually done in Monte Carlo simulations to save computer time.

III. PT-AG BULK PHASE DIAGRAM

We first perform semi-grand canonical Monte Carlo simulations to determine isotherms along the whole composition range starting from Pt-pure system up to Ag-pure system or reversely. The curves in Fig. 3 show the equilibrated concentration when we vary the chemical potential difference ∆µ up and down. We notice a large hysteresis between upward and downward curves in the semi-grand canonical ensemble for temperatures below 7000 K.

The upward curve starts with a quasi Pt-pure phase which changes to an Ag-rich solid solution. The downward curve starts with the Ag-rich phase containing up to 60% of Pt (as compared to 40% in the upward curve) creating a large and asymmetric hysteresis between the two curves. The instability domain with two coexisting phases increases when the temperature decreases. We use the Widom method in canonical ensemble to better characterize the transition and determine the exact critical concentrations in order to plot the phase diagram. First we notice that outside the phase coexisting domain the curves obtained within the two ensembles are fully superimposed which confirms that the statistical calculations are well converged. Inside the phase coexisting domain, the canonical ensemble explores instable states whereas semi-grand canonical ensemble explores both stable and metastable states. To extract the stable states and define the domain limits of each phase we determine the critical chemical potential in the canonical curve with the "s" curve. The critical concentrations are deduced from the s-curve (shown in red in Fig. 3) where we divide the area on both side of the "s" in two equal parts as illustrated by the Figure 4. After defining the critical ∆µ it is easy to extract the corresponding concentrations in Pt-rich (c 1 ) and Ag-rich (c 2 ) phases that will be reported on the bulk phase diagram. We get a very asymmetric miscibility gap with a quasi Pt-pure phase (c 1 around zero) and a solid solution where Ag is majoritary, which is a result of the variation of the EPIs as a fonction of the concentration.

When increasing the temperature up to 7000 K (Fig. 3 for increasing or decreasing temperatures. Due to the strong asymmetry of the Pt-Ag system, the L1 1 phase is not centered on the equiatomic composition but rather at 60% of silver which characterizes the critical order/disorder temperature equal to 2200 K. To characterize the concentration domain of the L1 1 phase we performed Widom canonical simulations where the permutations are virtual but we explore all the composition range at constant temperature. In Fig. 6 we show the variation of the global Ag composition as a function of the chemical potential together with the four sublattices occupations. The s-curve of the canonical Widom simulation illustrates the phase coexistence between the quasi-pure Pt phase with c 1 almost equal to zero and the ordered L1 1 phase at c ′ 1 around 0.5. This limit is obtained by the same rule as performed at high temperature via the critical chemical potential corresponding to the separation of the instable domain in two equal areas. With the corresponding sublattices occupation (equally occupied two by two) we can characterize the L1 1 phase in coexistence with the Pt-rich solid solution. The second limit of the L1 1 phase domain is not characterized by an "s" loop on the canonical curve which means this second transition is continuous going progressively from a very strongly overstoechiometric L1 1 phase (near 75% of silver) to a Ag-rich disordered solid solution. The limit is then characterized by the separation of the four sublattices equally occupied two by two in the grand canonical simulations.

In the experimental phase diagram [2,10,11] the ordered L1 1 phase transforms into a coexistence domain between two solid solutions at 1200 K. Our model reproduces the miscibility gap but at a higher temperature (2100 K) than the experimental one (Fig. 7).

Our model has also the tendency to underestimate the solubility limit in the Pt-rich domain and to overestimate the solubility limit in the Ag-rich domain. Finally the domain of the L1 1 ordered phase is much more broaden in our model. Nevertheless, using a quite simple model, we get a qualitatively satisfying bulk phase diagram for solid phases as compared to the experimental one, with notably a nice anisotropy thanks to the variations of the EPIs.

IV. (111) AND (100) PT-AG ALLOYS SURFACES

Because of the very large difference between the cohesive energy of the two elements (see Table I), we expect to get a quite substantial silver surface segregation on the Pt-Ag alloys surfaces in order to minimize the total energy of the system. We will see in the following how the surface segregation influences the chemical configuration at the vicinity of the two most compact surfaces: (111) and (100). Depending on the temperature, we will also study how the surface segregation takes place with the different chemical ordering tendencies present in the bulk phase diagram i.e. phase separation between 2000 K and 7000 K and ordering with the L1 1 phase below 2000 K.

The Monte Carlo simulations in the semi-grand canonical ensemble are performed at different temperatures on slabs constituted by 40 atomic layers with about one hundred of atoms each (exactly 100 atoms for the (111) orientation and 72 atoms for the (100) one).

We checked that the results we show are independent of the size of the slab as soon as the thickness of the slab is sufficiently large (more than 30 atomic layers) in order to get the bulk conditions in the middle of the slab.

We will consider in the next sections the (111) and (100) infinite surfaces at high temperature (above the ordering temperature for the L1 1 phase) and at room temperature. coexistence between a quasi Pt-pure bulk with only the top surface layer Ag-pure, and the L1 1 phase. The stable domain of this ordered phase starts at equiconcentration up to 80% of Ag. By increasing the Ag concentration, the core of the slab is made of the Ag-rich solid solution with still the Ag pure surface layer. As in the bulk, there is a large miscibility gap between the quasi Pt-pure solid solution and the L1 1 ordered phase. The L1 1 ordered phase starts to nucleate near the surface because of the presence of the Ag surface segregation by a continuation of the alternate staking of Ag and Pt pure layers.

C. (100) Pt-Ag surface at 300 K At low silver concentration, before the filling of the whole surface as in the (111) orientation, the (100) Pt-Ag surface starts with a surface superstructure with silver atomic rows in the < 110 > direction leading to the (1x2) surface structure (see Fig. 10-(a)). Then we get the pure Ag surface layer on top of the Pt quasi-pure phase (Fig. 10-(b)), as in the (111) surface, and just after, a second pure Ag sub-surface layer (Fig. 10-(c)). The miscibility gap represents a coexistence of two phases: the purely segregated configuration and the Ag segregated one with the L1 1 ordered phase beneath. This structure is displayed on Fig. 10-(d). The up and down curves are not fully superimposed because of the phase coexistence: the structure Fig. 10-(c) appears in the "up" simulation only and the structure Fig. 10-(d) only in the down simulation. Also in the down curve we notice a continuous variation of the concentration of the sub-surface layer (c 1 ) up to the mixte composition of the plane. This composition of 50% corresponds to the (2x1) ordering which forms the L1 1 ordered phase according to the (100) orientation. As for the (111) surface, the miscibility gap is delimited by the Ag surface segregation limit on the left and the occurence of the L1 1 phase on the right. This domain is nicely comparable to the one of the bulk phase diagram (Fig. 7).

To conclude for the infinite surfaces compared to bulk phase diagram, the infinite systems behave essentially as the bulk except that a part of the phase separation concerns the Ag surface segregation. In the next section, concerning alloys clusters, we will see the effect of the finite size of the system, particularly the finite reservoir of silver matter and the morphology of the cluster, on the chemical arrangement of the nanoalloys.

We study truncated octahedron (TOh) clusters of 1289 and 2951 atoms with both (111) and (100) facets and compare the segregations on these facets to the surface segregation of related infinite surfaces. We also study the behaviour of the miscibility gap for the finite size cluster system as compared to the other infinite systems (bulk and surfaces).

TOh are made of ( 111) and (100) facets connected by edges and vertices at the surface and we will consider all the other sites as core sites. We perfomed semi-grand canonical Monte Carlo simulations as in the infinite surfaces at different temperatures.

A. Pt-Ag nanoalloys at high temperature

In the Figure 11 we have reported the segregation isotherms of the 1289-atoms TOh cluster at high temperatures as for the (111) and ( 100) surfaces (Fig. 8). By comparison of the cluster facets with the corresponding infinite surface, we notice that the surface segregation (c 0 in Fig. 8) is the same as the cluster facet ones (( 111) and (100) facets in Fig. 11) on the condition of considering the segregation isotherms plotted as a function of the core concentration (c core ) (right column of Fig. 11). The finite matter effect (limited quantity of Ag) in clusters is remarkable when the site concentrations are plotted as a function of the global concentration since all the silver atoms segregate to the surface, the core remaining Pt-pure up to a global concentration of 40% of Ag (of course depending on the cluster size). First the vertex, then the edge sites are occupied by Ag atoms, followed closely by the (100) and (111) facets sites. The hierarchy of occupation of the different types of surface sites on the cluster follows the broken bonds except for the facets since the (111) facets are slightly more enriched in Ag than the (100) ones. This is counter intuitive because it does not follows the hierarchie of broken bonds. However a similar reversal of segregation concerning the (100) and (111) facets had been observed in Cu-Ag clusters [20] rather due to a coupling between the edges with the facets. Here there can be two effects: the inversion can be intrinsec to the system because as in the Cu-Pt system [19], the chemical ordering with positive V 2 can influence the segregation differently and in small clusters there can be some influence of the edges. Anyway the anisotropy is rather weak. When all the surface sites are occupied by Ag atoms, which represents around 40 % of the total number of sites in the TOh 1289 cluster, then the core of the cluster begins to be populated by Ag atoms, forming a disordered solid solution because of the high temperature (higher than the critical order/disorder temperature).

Finally, one notices the absence of miscibility gap in the cluster below 7000 K, at the difference with the bulk phase diagram (Fig. 7) or the infinite surfaces (Fig. 8).

B. Pt-Ag nanoalloys at 500 K By decreasing the temperature below 2000 K, we get the L1 1 ordered phase around 70 % of silver in the cluster, which is clearly characterized by the sublattice occupation illustrated in the bottom graph of Fig. 12 and Fig. 12-(c). Just before the complete ordering of the core with the four sublattices two-by-two occupied, we notice that the four sublattices are not fully randomly distributed but two over the four are partially ordered i.e. one is enriched in Ag, the other is pure in Pt. Clearly the definition of these sublattices is not appropriate to characterize a new ordering but looking at the chemical arrangement in Fig. 12-(b) we observe that the structure is made of concentric atomic layers alternatively occupied by Ag and Pt atoms. Everything happens as if one L1 1 ordered phase nucleates beneath all the (111) facets. This structure is effectively stabilized in our model in a composition range between 60 and 70 % of silver. Then one perfect L1 1 domain occupies all the cluster core focusing on one (111) facet orientation. This is in agreement with the experimental and modelisation with interatomic SMA potential of small Pt-Ag nanoclusters [1]. However, the SMA potential predicted the formation of at most three alternated concentric atomic layers in the vicinity of the surface. Such interatomic potential allows atomic relaxations which is not the case in our TBIM rigid model. Within SMA potential, the subsurface Pt segregation forming the first concentric layer below the surface is due to the lattice mismach between Ag and Pt and to the inward surface relaxation of the cluster surface, inducing a subsurface stress in compression which can be released by putting smaller atoms below the surface. In the present study, because of the rigid lattice assumption, we cannot get surface relaxation effects leading to specific subsurface segregation. However we demonstrate here that the chemical EPIs interactions lead to the formation of these two kinds of ordering depending on the concentration, one with concentric pure atomic layers alternating Ag and Pt, the other with the L1 1 ordered phase along one of the (111) orientation of the clusters, as illustrated on Fig. 12.

We also notice that the hierarchy of segregation of the different sites of the cluster respect the same as at high temperature (see Fig. 11, and the shifts are even enhanced by lowering the temperature. This leads to a structure where all the verteces and edges are occupied by Ag atoms whereas the facets are rather rich in Pt before 20 % of silver in the cluster and between 30 and 40 % of silver, only the (111) facets are populated by Ag whereas the (100) have around 30 % of Ag atoms. However we must recall that the (100) facets contain only 9 sites, so that 30 % of Ag atoms corresponds to the (2x1)(100) surface reconstruction.

Finally we show the finite size and matter effect on the width of the miscibility gap in the clusters of 1289 and 2951 atoms (Fig. 13). The larger the size of the cluster, the wider the miscibility gap between the core-shell structure and the ordered one starting with the concentric alternated layers. This confirms that by increasing the size, the cluster should behave like the bulk phase diagram. Moreover, in the clusters, at the difference with the infinite surfaces, we notice another miscibility gap between the first surface site occupation up to 0.05 % of Ag and the almost complete core-shell structure. This means that the core-shell structure driven by the strong Ag surface segregation is too much concentrated in silver to be compatible with the Pt-rich solid solution so that there are some forbidden phases around 20 % of silver in the cluster. These are very new and surprising results which show the specificities of the nanoalloys as compared to systems with infinite reservoirs.

VI. CONCLUSIONS

Using a quite simple Tight-Binding Ising model, on rigid lattice, with variable EPIs as a function of the concentration, we successfully reproduce the asymmetric and original bulk phase diagram of the Pt-Ag system where both separated and ordered phase are present depending on temperature and concentration. We applied our model to (111) and (100) surfaces and truncated octahedron clusters of 1289 and 2951 atoms. All the systems show a strong silver surface segregation and then a chemical ordering according to the L1 1 bulk ordered phase. In the (111) surface, this structure is just the surface termination of the alternate staking of Ag pure, Pt pure layers. In the (100) case, after the filling of the first surface layer with silver atoms, the L1 1 phase grows in the second and following alternate staking of Pt and Ag atomic planes along the (111) direction. In the clusters case, the surface segregation of one atomic plane corresponds to a core-shell structure whereas the chemically ordered L1 1 phase appears in two different ways: at lower silver concentration, the L1 1 ordering appears below each (111) oriented facets leading to a pure onion-shell structure alternating Ag pure and Pt pure concentric layers; at higher concentration, we observe a single oriented L1 1 phase with a silver pure surface shell as in the experiments [1]. We also analyzed the evolution of the miscibility gap domains in the clusters, as compared to the surfaces and bulk and show the effect of finite size and finite matter on the phase diagrams of nanoalloys. Such study is a step towards the characterization of nanoalloys phase diagrams.

A simple model as the TBIM is further promising in order to study kinetics and aging of nanoalloys.

(eV/at.) Vertex Edge (100) (111) (eV/at.)

γ P t
V (111) 1 V ⊥(111) 1 V ⊥(111) 2 V (100) 1 V (100) 2 V ⊥(100) 1 V ⊥(100) 2
Pt(Ag) -0.026 -0.081 0.062 -0.048 0.032 -0.112 0.045 Ag(Pt) 0.002 0.003 0.115 0.075 0.115 0.002 0.100

  ) we notice that the semi-grand canonical Monte Carlo curve becomes continuous, similar to the canonical curve and the hysteresis disappears. Above 7000 K the phase diagram displays a solid solution along the whole composition range. At low temperature, below 2000 K, the chemical structure becomes ordered according to the L1 1 phase around the equiconcentration as shown in Fig. 5. This phase is characterized by the sublattices occupation illustrated on Fig 5 where on each consecutive (111) layer the sublattices are occupied alternatively by Ag and Pt atoms. To characterize the order/disorder transition we performed canonical simulations at constant concentration and

FIG. 1 .

 1 FIG. 1. Ground state diagram of an Ising model for Effective Pair Interactions (EPIs) on fcc lattice at first and second neighbors [12, 23, 27].

FIG. 3 .FIG. 4 . 6 FIG. 5 .

 3465 FIG.3. Bulk isotherms determined via semi-grand canonical Monte Carlo simulations with increasing (dashed line) and decreasing (straight line) ∆µ from pure Pt metal (on the left) to pure Ag metal (on the right) or via canonical Monte Carlo simulation using the Widom method (virtual permutations) (red line).

FIG. 6 .FIG. 7 .

 67 FIG. 6. Top left, the global Ag concentration as a function of the chemical potential at 1000 K from semi-grand canonical Monte Carlo (in black) and canonical Widom Monte Carlo simulations with virtual permutations (in red) as in Fig. 3. The corresponding sublattices occupations plotted as a function of the chemical potential ∆µ (bottom left) and as a function of the global Ag concentration (top right). The critical ∆µ which separates the "s" loop in two equal areas allows to characterize the concentration c ′ 1 limiting the phase coexistence domain (instability domain in canonical simulation) and the pure L1 1 phase characterized by the sublattices equally occupied two by two. The c 2 between the L1 1 and the Ag-rich solid solution is deduced from the grand canonical curves (GCMC down) whit the separation of the sublattices occupation two by two as compared to the equal occupation for the Ag-rich solid solution.

FIG. 8 .FIG. 9 .

 89 FIG.8. Segregation isotherms at (111) and (100) surfaces at 7000K, 5000K and 3000K where we plot the top surface c 0 , the subsurface c 1 and the following c 2 and c 3 atomic layers concentrations in silver by increasing (up) or decreasing (down) the chemical potential.

TABLE III .

 III of one impurity at surface site n as compared to the same impurity in the bulk, the impurity being distinct of the matrix only by its atomic radius (see text). Calculations are performed with the tight binding TB-SMA interatomic potential. a( Å) E coh (eV/at) ∆H L1 1 ∆H L1 0 Effective pair interactions (EPI) extended to first V 1 and second V 2 neighbors for different concentrations: impurity of Ag in Pt "Pt(Ag)" and impurity of Pt in Ag "Ag(Pt)" in the bulk calculated by DFT (GGA) and semi-empirial (TB-SMA).

	EPI (eV/at.)	Pt(Ag)	PtAg	Ag(Pt)
	n γ Ag n ∆h coh n ∆h size n Pt(Ag) -0.10 -0.12 -0.13 -0.10 0.60 0.50 0.67 0.51 1.06 0.86 0.38 0.3 -0.44 -0.36 -0.29 -0.21 Vertex Edge (100) (111) Ag(Pt) -0.002 0.008 0.02 0.01 TABLE I. TBIM on site parameters related to surface segregation driving forces: cohesion effect ∆h coh n which is the difference in surface site energies(γ M etal n ) between Pt and Ag metals, n being either a site of cluster surface (facets) or infinite surfaces, and size effect ∆h size n which is the DFT-GGA 4.16 -2.725 TB-SMA 4.16 -2.725 Exp. 4.09 -2.950 Pt TB-SMA 3.98 -5.53 Exp. 3.92 -5.86 AgPt DFT-GGA -0.051 0.041 DFT-GGA [11] -0.039 0.063 V 1 DFT-GGA -0.012 -0.013 0.007 TB-SMA -0.086 -0.016 0.002 V 2 DFT-GGA 0.034 0.027 0.001 difference in energy Ag DFT-GGA 3.98 -5.53 TB-SMA 0.007 0.087 0.106
	TB-SMA		-0.213 0.063

TABLE II. DFT (GGA) and semi-empirical (TB-SMA) calculations of the formation enthalpies (in eV/at.) of the AgPt ordered phases compared to other DFT calculations

[11]

and experimental data (Kittel, Wiley, New York, 1996). The formaton enthalpies of the ordered (L1 1 and L1 0 ) phases are defined as the energy difference between the ordered system and the demixed one without interface which means pure Pt and pure Ag metals. The TB-SMA potential has been fitted to reproduce the DFT values of the lattice parameter and cohesion energy of the pure metals

[1]

.

TABLE IV .

 IV Effective pair interactions (EPIs) at the (111) and (100) surfaces calculated with TB-SMA potential.

ACKNOWLEDGMENTS

This work was granted access to the HPC resources of IDRIS under the allocation 2017-096829 made by GENCI. The authors would like also to acknowledge support from the International Research Network -IRN "Nanoalloys" of CNRS.

A. ( 111) and (100) Pt-Ag surfaces at high temperature The infinite (111) and (100) surfaces present a strong silver surface segregation for each temperature up to 7000K where the system becomes fully disordered in the bulk. At lower temperatures (5000K or 3000K) there is a miscibility gap between the two solid solutions as in the bulk phase diagram. The segregation isotherms are illustrated on Fig. 8 for the (111) and (100) surfaces. We observe a slight oscillation profile in the (111) surface because of the alternation of (111) atomic layers that recalls the L1 1 ordered phase even for temperatures higher than the order/disorder transition. This is a signature of the ordering tendency of the Pt-Ag system which is consistent with the (111) surface orientation and not with the (100) where only the top surface layer in enriched with silver, then very slightly the second one.

We could have expected a more important segregation for the (100) orientation as compared to the (111) one because of the effect of the broken bonds, the more open the surface the more important the segregation. This was not the case for a similar system, the Cu-Pt alloys [19], where a very unusual anisotropy was found: in that case, the Cu surface enrichment was stronger for the close-packed (111) surface than for the more open (100) one, contrary to usual arguments based on the anisotropy of surface energy. In Pt-Ag, at high temperature, the surface anisotropy is negligeable. We will see in the following by comparing cluster facets that a slight anisotropy exists and the segregation is slightly stronger on the (111) facets as compared to the (100) ones, in agreement with the results reported on Cu-Pt system [19].

B. (111) Pt-Ag surface at 300 K

The (111) Pt-Ag surface at room temperature is made of a silver pure atomic surface layer, for any composition larger than a limit concentration of Ag which is linked to the thickness of the slab. It corresponds to a system with a quasi Pt pure bulk (core of the slab) and two Ag surface layers on each side (the slab presenting two surfaces). This limit concentration c * Ag = 2/n p , where n p is the number of atomic layers in the slab, tends naturally to zero for an infinite number of layers. Typically, in the results presented on Fig. 9,c 12. Segregation isotherms of TOh 1289 cluster at 500 K with the same legends as in Fig. 11 and the associated structures.