Jean Michel Guy

Mathew Wilson

Frédéric Schnell

Laurent Chevalier

Jean-Claude Verdier

Sonia Corone

Stéphane Doutreleau

Gaelle Kervio

François Carré
email: francois.carre@univ-rennes1.fr

Incidence of major adverse cardiac events in men wishing to continue competitive sport following percutaneous coronary intervention Incidence des accidents coronariens sévères chez des patients coronariens stentés pratiquants

un sport en competition.

Summary

Background. -The new North American guidelines for participation in competitive sport in patients with coronary artery disease (CAD) are less restrictive than previous guidelines.

Aim. -To evaluate the incidence of major adverse cardiac events (MACE) in men with CAD who practise intensive physical activity after a stenting procedure. MACE included in-stent restenosis (SR), stent thrombosis (ST), new coronary stenosis (NCS), myocardial infarction, heart failure, cardiac arrest or cardiac death.

Methods. -Asymptomatic men with CAD and a coronary stent who practised regular (>4 h/week) sport were included in this retrospective multicentre observational study. All patients presented with left ventricular ejection fraction ≥ 50%, no residual stenosis, and no inducible ischaemia or arrhythmias. Three groups were compared: those undertaking moderate leisure-time sport (MLS), intensive leisure-time sport (ILS) or competitive sport (CS). During follow-up, all patients had a yearly routine cardiology evaluation.

Results. -A total of 108 men with CAD (57.3 ± 9.1 years) were included: 29 MLS, 58 ILS, and 21 CS.

During follow-up (57.6 ± 46.0 months) the incidence of MACE was 15.7% (SR = 5, SR + NCS = 4, ST = 4, NCS = 4) and occurred during physical exertion in 59% of patients. ST was more frequent in the CS (n = 3) than in the MLS (n = 1) or ILS (n = 0) groups, especially in patients with bare-metal stents.

Conclusions. -The incidence of MACE was 15.7%, and only ST was significantly more frequent in CS patients than in MLS or ILS patients. Our data support the new US guidelines for exercise eligibility in men with CAD.

Résumé

Contexte. -Les nouvelles recommandations Américaines du Nord (US 2015) sont plus permissives que les précédentes pour la pratique sportive en compétition par un coronarien.

But de l'étude -Evaluation de l'incidence d'accidents coronariens sévères (ACS) chez des coronariens stentés qui pratiquent un sport intense. Les ACS regroupen, resténose (RS) ou thrombose de stent (TS), nouvelle sténose coronaire significative (NSC), infarctus du myocarde, insuffisance cardiaque, arrêt cardiaque, ou décés de cause cardiaque.

Background

For the health of the coronary circulation, physical activity can act as a "double-edged sword" [START_REF] Möhlenkamp | On the paradox of exercise: coronary atherosclerosis in an apparently healthy marathon runner[END_REF].

Whilst it is well documented that regular, moderate physical activity supports the prevention of coronary artery disease (CAD) by controlling numerous cardiovascular risks factors (CVRFs) [START_REF] Lavie | Cardiac rehabilitation and exercise training in secondary coronary heart disease prevention[END_REF][START_REF] Bruning | Benefits of exercise training on coronary blood flow in coronary artery disease patients[END_REF], vigorous physical exercise may increase the risk of acute coronary events (5.7-fold) in middle-aged "apparently" healthy but untrained men [START_REF] Søholm | Myocardial infarction is a frequent cause of exercise-related resuscitated out-of-hospital cardiac arrest in a general non-athletic population[END_REF]. Moreover, CAD is the leading cause of sports-related cardiovascular events in this population [START_REF] Chevalier | Sports-related acute cardiovascular events in a general population: a French prospective study[END_REF]. Some data report that habitual vigorous activity is not associated with an increased risk of myocardial infarction [START_REF] Yu | Is vigorous physical activity contraindicated in subjects with coronary heart disease? Evidence from the Caerphilly study[END_REF], but a recent prospective epidemiological study demonstrated that daily strenuous physical activity is associated with increased cardiovascular mortality in patients with CAD [START_REF] Mons | A reverse J-shaped association of leisure time physical activity with prognosis in patients with stable coronary heart disease: evidence from a large cohort with repeated measurements[END_REF]. Moreover, Merghani et al. recently examined 152 master (i.e. age >40 years) endurance athletes and 92 controls of similar age, sex and low Framingham 10-year CAD risk scores, with echocardiograms, exercise stress tests, computed tomography coronary angiograms, cardiovascular magnetic resonance imaging (CMR) and 24-h Holter monitoring [START_REF] Merghani | Prevalence of subclinical coronary artery disease in masters endurance athletes with a low atherosclerotic risk profile[END_REF]. Their results showed that male athletes presented a higher prevalence of atherosclerotic plaques than sedentary men. Only male athletes (11.3%) demonstrated a coronary artery calcium score ≥ 300 Agatson units and a luminal stenosis ≥ 50% (7.5%). The number of years of training was the only independent variable associated with the increased risk of coronary artery abnormalities. Lastly, male athletes (14%), but none of the controls, revealed late gadolinium enhancement on CMR; of these, seven had a pattern consistent with previous myocardial infarction.

Consequently, providing physical activity advice for patients with known CAD is difficult, as the potential risk of exercise-induced myocardial ischaemia and adverse cardiovascular events induced by vigorous physical activity are still debated [START_REF] Noël | Can prolonged exercise-induced myocardial ischemia be innocuous?[END_REF]. Recently published Task Force eligibility and disqualification recommendations for competitive athletes with CAD note that it is reasonable for athletes with clinically concealed atherosclerotic CAD to participate in all competitive activities provided that there is good control of CVRFs, the resting left ventricular ejection fraction (LVEF) is ≥ 50%, and there is no inducible ischaemia or electrical instability [START_REF] Thompson | Eligibility and disqualification recommendations for competitive athletes with cardiovascular abnormalities: Task Force 8: Coronary Artery Disease: A scientific statement from the American Heart Association and American College of Cardiology[END_REF]. There are, however, limited longitudinal data to ascertain if these recent Task Force 8 recommendations support this level of clearance for patients with CAD wishing to undertake competitive sport. Accordingly, the aim of this study was to evaluate the incidence of major adverse cardiac events (MACE), including stent restenosis (SR), stent thrombosis (ST), new significant coronary stenosis (NCS), myocardial infarction, heart failure, cardiac arrest or cardiac death in patients with CAD following percutaneous coronary intervention (PCI), who continued to partake in intensive physical activity (including competitive sport) after the procedure.

Methods

This retrospective study involved 19 French cardiology institutions; ethical approval was provided by the Rennes University Hospital Ethics Committee. All patients provided informed consent and gave permission for the anonymous use of their medical data for research purposes. This study was conducted according to the World Medical Association Declaration of Helsinki.

Participants Inclusion criteria

Men with CAD who underwent PCI were eligible for inclusion in the study. Each patient had to be: [START_REF] Möhlenkamp | On the paradox of exercise: coronary atherosclerosis in an apparently healthy marathon runner[END_REF] treated with at least one coronary stent; (2) present with no significant residual stenosis on the main epicardial coronary arteries; (3) be asymptomatic; (4) demonstrate good control of CVRFs; (5) have an LVEF ≥ 50%; and (6) demonstrate no inducible ischaemia or electrical instability [START_REF] Thompson | Eligibility and disqualification recommendations for competitive athletes with cardiovascular abnormalities: Task Force 8: Coronary Artery Disease: A scientific statement from the American Heart Association and American College of Cardiology[END_REF]. Each patient completed a questionnaire that documented physical activity (PA) status (activity type, regularity, frequency, duration and intensity) post-PCI procedure. Only patients who performed ≥ 4 h/week of PA 6 months after the PCI were included. Patients were divided into three groups: (1) those partaking in moderate leisure-time sport (MLS), i.e. PA under the ventilatory threshold; (2) intensive leisure-time sport (ILS), i.e. PA above the ventilatory threshold but not partaking in competitive sport; and (3) those regularly partaking in competitive sport (endurance running, including marathons, road cycling or mountain biking, swimming, basketball, football and racket sports) (CS) [START_REF] Börjesson | ESC Study Group of Sports Cardiology: recommendations for participation in leisure-time physical activity and competitive sports for patients with ischaemic heart disease[END_REF]. Importantly, at each yearly follow-up examination, the attending cardiologist verified that the patient continued to maintain their PA status and thus remained in the allocated group.

Exclusion criteria

Exclusion criteria were incomplete revascularization, coronary artery bypass grafting, abnormal LVEF, atrial fibrillation or complex ventricular arrhythmias, and irregular levels of competitive sport or physical activity (< 4h/week) following the PCI.

Medical evaluation

Only information documented by the attending cardiologist was recorded. Indication for PCI was specified as stable or unstable angina, or myocardial infarction, in accordance with the recommendations provided by the European Society of Cardiology Task Force on the management of stable CAD [START_REF] Montalescot | ESC guidelines on the management of stable coronary artery disease: the Task Force on the management of stable coronary artery disease of the European Society of Cardiology[END_REF]. Details of a post-PCI cardiovascular rehabilitation programme, together with CVRFs, were collected. The CVRFs documented were: (1) cardiovascular disease history in a first-degree relative (father aged < 55 years or mother < 65 years or sibling); (2) active or former (> 3 consecutive years) smoking; (3) obesity; and (4) medical treatment for any of the following (hypertension, diabetes or cholesterol disorder).

MACE incidence and classification

All patients attended all of their yearly examinations during the follow-up period. At each appointment, clinical, 12-lead electrocardiogram, echocardiography and exercise stress test data were recorded, along with information on any MACE events. To corroborate the occurrence of MACE, each patient was contacted by telephone (by GK) to verify the occurrence or absence of any MACE between the annual follow-up examination and data capture closure. Thus, a robust MACE incidence rate could be calculated. MACE was classified as SR, ST, NCS, myocardial infarction, heart failure, cardiac arrest or cardiac death. Incidence of SR or definite ST confirmed by coronary angiography was recorded in accordance with classic definitions [START_REF] Cutlip | Clinical end points in coronary stent trials: a case for standardized definitions[END_REF], together with the incidence of NCS. The incidence of MACE was calculated according to patient PA level (MLS, ILS or CS).

Statistical analysis

Quantitative values are expressed as mean ± standard deviation, with differences between groups analysed using one-way ANOVA. Qualitative values are expressed as number and/or percentages and differences between groups were tested using the χ² test, as appropriate. Fisher's exact test was used to compare MACE incidence between groups. Significance was set at 0.05, with all data analysed using Statistica v8 (Systat Software, Inc. Chicago, IL, USA).

Results

Participants

From 108 patients with CAD (57.3 ± 9.1 years, range 38-78 years), just over half participated in ILS (n = 58, 53.7%), 29 (26.9%) in MLS and 21 (19.4%) in CS. Whilst CS participants were younger than MLS and ILS participants (P < 0.01), no other difference was noted between the groups (Table 1).

Percutaneous coronary intervention

Between 1997 and 2013, 164 stents were inserted into 152 arteries; 97 bare-metal stents (BMS; 1997-2013) and 67 drug-eluting stents (DES; 2003-2013). More DES were implanted in ILS than in MLS or CS participants; no between-group differences were noted for BMS (Table 2). Two patients presented with myocardial infarction as the first coronary event (one MLS and one ILS, P = 0.76).

Fifty-six patients participated in a cardiac rehabilitation programme after PCI, with no difference between groups.

CVRFs and PA status before and after PCI are shown in Table 3. Globally, smoking (P < 0.001) and obesity (P < 0.01) decreased post-PCI. However, no reduction in the prevalence of hypertension, dyslipidaemia or type 2 diabetes was observed. Twenty patients who were sedentary before PCI became physically active after the procedure (MLS n = 18; ILS n = 1; CS n = 1). From those patients who were physically active before their acute CAD event, the number of patients who maintained MLS did not change significantly, but ILS increased (P < 0.001) whilst the number of CS participants decreased (P < 0.05), with 21 men continuing to participate in CS following PCI intervention.

Incidence of adverse cardiac events post-PCI

During the follow-up period (57.6 ± 46.0 months, range 6-192 months), MACE occurred in 17 patients (15.7%; mean age 55.2 ± 8.3 years) (Table 4). There was no statistically significant difference in the incidence of MACE between the groups (P = 0.10). A MACE occurred during physical exertion in 10 of the 17 (58.8%) patients. The remaining seven events were not related to exercise, and included angina (n = 2), abnormal routine maximal exercise tests (n = 3), and during a coronary angiography investigation (n = 1); data were unavailable in one patient. No heart failure episodes, cardiac arrests or cardiac deaths occurred. One MLS patient had a myocardial infarction (not associated with physical activity), and underwent repeat revasculization without complication.

Globally, 4.6% of participants had isolated SR, and 3.7% each had SR plus NCS, ST or isolated NCS. In the four patients (mean age 49.2 ± 8.6 years) with ST, all had a BMS, with MACE occurring 29.2 ± 9.8 months (17-41 months) post-PCI. Stent thrombosis occurred in a greater number of CS than MLS or ILS patients (P ≤ 0.01) (Table 4). Nine patients (55. [START_REF] Mons | A reverse J-shaped association of leisure time physical activity with prognosis in patients with stable coronary heart disease: evidence from a large cohort with repeated measurements[END_REF]

Discussion

The aim of this study was to evaluate the incidence of MACE in CAD patients following PCI who continued to participate in intensive PA post-procedure. The main finding is that from 108 patients followed for 4 years and 9 months, MACE occurred in 15.7%, with no statistically significant difference in the incidence between PA groups. During the follow-up period, ST was significantly more frequent in CS patients than in MLS or ILS patients, , and no other difference was observed concerning ST and NCS. Finally, MACE occurred during physical exertion in 59% of patients; importantly, however, no heart failure episodes, cardiac arrests or cardiac deaths were documented.

To our knowledge, this is the first study to examine the incidence of MACE in patients with known CAD, in relation to their PA status. The question of how intensely a patient with CAD can exercise is a frequent conundrum faced by physicians. Until 2015, previous recommendations for intensive sports clearance in this population were extremely restrictive [START_REF] Börjesson | ESC Study Group of Sports Cardiology: recommendations for participation in leisure-time physical activity and competitive sports for patients with ischaemic heart disease[END_REF]. More recent North American recommendations, however, state that clearance for all competitive sports participation is reasonable in patients with CAD presenting with no inducible ischaemia, no electrical instability, a normal LVEF and good control of their CVRFs [START_REF] Thompson | Eligibility and disqualification recommendations for competitive athletes with cardiovascular abnormalities: Task Force 8: Coronary Artery Disease: A scientific statement from the American Heart Association and American College of Cardiology[END_REF]. The population of patients with CAD who had undergone PCI in this study matched the clearance criteria set out by these recommendations and our data support the exercise eligibility proposed [START_REF] Thompson | Eligibility and disqualification recommendations for competitive athletes with cardiovascular abnormalities: Task Force 8: Coronary Artery Disease: A scientific statement from the American Heart Association and American College of Cardiology[END_REF].

The prevalence of MACE was 15.7% in our study, with stent complications accounting for 77%.

We observed more MACE through BMS complications than through DES complications (75% vs 25%, respectively). This observation concurs with data from the general population [START_REF] Sabaté | The EXAMINATION trial (Everolimus-Eluting Stents Versus Bare-Metal Stents in ST-Segment Elevation Myocardial Infarction): 2-year results from a multicenter randomized controlled trial[END_REF], and underscores the increased risk of MACE with BMS versus DES [START_REF] Valgimigli | Two-year outcomes after first-or secondgeneration drug-eluting or bare-metal stent implantation in all-comer patients undergoing percutaneous coronary intervention: a pre-specified analysis from the PRODIGY study (PROlonging Dual Antiplatelet Treatment After Grading stent-induced Intimal hyperplasia studY)[END_REF].

In the present study, SR was the most frequent MACE (53%). It affected nine patients and 11 stents (BMS n = 7; DES n = 4), with two cases of two simultaneous SR. In one case, the SR (DES) was subacute (1 month). For six patients (BMS n = 5; DES n = 1), the SR was observed at least 12 months after the stent procedure. Intensive sport practise was associated with SR in seven cases (ILS n = 6; CS n = 1). For four patients, the SR was associated with an NCS. In the general population, SR is reportedly more frequently in BMS than DES (10% vs 5%, respectively) [START_REF] Sabaté | The EXAMINATION trial (Everolimus-Eluting Stents Versus Bare-Metal Stents in ST-Segment Elevation Myocardial Infarction): 2-year results from a multicenter randomized controlled trial[END_REF][START_REF] Valgimigli | Two-year outcomes after first-or secondgeneration drug-eluting or bare-metal stent implantation in all-comer patients undergoing percutaneous coronary intervention: a pre-specified analysis from the PRODIGY study (PROlonging Dual Antiplatelet Treatment After Grading stent-induced Intimal hyperplasia studY)[END_REF][START_REF] Zhang | In-stent restenosis is associated with neointimal angiogenesis and macrophage infiltrates[END_REF].

SR is the most feared complication after stent implantation. In the general population, the early (< 1 year) incidence of ST ranges from 0.6% to 3.4% and the incidence of early and late ST appears similar between DES and BMS [START_REF] Claessen | Stent thrombosis. A clinical perspective[END_REF][START_REF] Bangalore | Outcomes with various drug-eluting or bare metal stents in patients with ST-segment-elevation myocardial infarction: a mixed treatment comparison analysis of trial level data from 34 068 patient-years of follow-up from randomized trials[END_REF][START_REF] De Man | Stent thrombosis in real-world patients: a comparison of drug-eluting with bare metal stents[END_REF]. Whilst the present study observed one patient who was noncompliant with his antiplatelet treatment, the mean time between PCI and the ST event was greater than 2 years. Data from a large registry suggested that very late ST may occur with an annual rate of 0.4-0.6% after implantation of a first-generation DES [START_REF] Bangalore | Outcomes with various drug-eluting or bare metal stents in patients with ST-segment-elevation myocardial infarction: a mixed treatment comparison analysis of trial level data from 34 068 patient-years of follow-up from randomized trials[END_REF]. In our patients, all ST concerned BMS, with an annual rate of 0.57% for all stents. Thus, the incidence of ST in our population appears to be similar to that in the general population. Classically, ST may be symptomatic or asymptomatic [START_REF] Valgimigli | Two-year outcomes after first-or secondgeneration drug-eluting or bare-metal stent implantation in all-comer patients undergoing percutaneous coronary intervention: a pre-specified analysis from the PRODIGY study (PROlonging Dual Antiplatelet Treatment After Grading stent-induced Intimal hyperplasia studY)[END_REF]. For all of our patients, ST presented with acute angina and in all cases new PCI was successful.

The pathophysiological mechanism proposed for ST is a fast and unexplained development of instent neoatherosclerosis [START_REF] Koskinas | Role of endothelial shear stress in stent restenosis and thrombosis: pathophysiologic mechanisms and implications for clinical translation[END_REF]. A plaque rupture associated with increased endothelial shear stress, together with neoatherosclerosis, likely accounts for most ST events [START_REF] Koskinas | Role of endothelial shear stress in stent restenosis and thrombosis: pathophysiologic mechanisms and implications for clinical translation[END_REF]. Based on the predisposing factors for both early and late BMS, thrombosis due to non-compliance with antiplatelet agents and acute exercise are proposed [START_REF] Lepor | Primary prevention, treatment, and secondary prevention of late and very late stent thrombosis[END_REF]. Although the role of acute exercise in ST is not clear, exercise training during cardiac rehabilitation is safe (1.2/1000 patients or 0.8/10 6 patient-hours of exercise) for CAD patients after PCI [START_REF] Iliou | Exercise training is safe after coronary stenting: a prospective multicenter study[END_REF].

The risk of vigorous exercise acting as a triggering mechanism for late ST has been previously considered, but mainly in untrained patients [START_REF] Zwart | Vigorous exercise as a triggering mechanism for late stent thrombosis: a description of three cases[END_REF]. Three mechanisms are proposed: (1) the balance between coagulation and fibrinolysis; (2) endothelial stress due to haemodynamic alterations; and (3) hormonal and dehydration changes. During strenuous exercise, a transitory hyperreactivity of platelets is associated with a biphasic change in the fibrinolysis rate, which increases upon exercise initiation and rapidly decreases afterwards [START_REF] Brun | Alterations of blood rheology during and after exercise are both consequences and modifiers of body's adaptation to muscular activity[END_REF][START_REF] Cooper | Temporal changes in tPA and PAI-1 after maximal exercise[END_REF]. In healthy untrained subjects, the balance between coagulation and fibrinolysis appears to be well maintained [START_REF] Li | Platelet activity, coagulation, and fibrinolysis during exercise in healthy males: effects of thrombin inhibition by argatroban and enoxaparin[END_REF]. However, in patients with CAD, the equilibrium between fibrinolysis and coagulation during peak exercise appears to be disturbed in favour of coagulation, especially during post-exercise recovery, which may favour the occurrence of stent occlusion [START_REF] Cooper | Temporal changes in tPA and PAI-1 after maximal exercise[END_REF]. In the present study, all cases of ST presented with symptoms after intense sport practise.

A beneficial effect of moderate endurance training on the red cell deformability during exercise is observed in sedentary people as well as in patients with CAD [START_REF] Brun | Alterations of blood rheology during and after exercise are both consequences and modifiers of body's adaptation to muscular activity[END_REF]. However, the increase in endothelial shear stress associated with intense exercise may traumatize the inner intimal vascular layer, making them prone to rupture [START_REF] Dash | Delayed coronary occlusion after successful percutaneous transluminal coronary angioplasty: association with exercise testing[END_REF]. Intense and/or long duration exercise is associated with a high concentration of catecholamines in the blood; combined with dehydration, this environment may favour vasoconstriction of coronary artery stenosis and cause endothelial injury [START_REF] González-Alonso | Separate and combined influences of dehydration and hyperthermia on cardiovascular responses to exercise[END_REF]. In conclusion, a combination of coagulation perturbations, increased arterial wall stresses, dehydration and catecholergic changes due to intensive exercise, could favour ST occurrence. For the population examined in the present study, the role of collateral circulation can be considered. Indeed, the beneficial effect of physical training on coronary collateralization has been reported [START_REF] Heaps | Effects of exercise training on coronary collateralization and control of collateral resistance[END_REF], although a subsequent meta-analysis proposed that it could be associated with an increased risk of both ST and SR [START_REF] Meier | Coronary collaterals and risk for restenosis after percutaneous coronary interventions: a meta-analysis[END_REF].

Regular and moderate endurance exercise is recommended as a safe and inexpensive way to prevent and treat CAD [START_REF] Bruning | Benefits of exercise training on coronary blood flow in coronary artery disease patients[END_REF]. Our study demonstrated that few athletes had additional MACE following initial PCI, despite regular PA and good control of CVRFs. We observed a significant NCS in a new arterial location in eight patients (7.2% of the whole population), with a yearly incidence of 1.8%. This observation confirms that regular PA does not confer immunity against the development of CAD in middle-aged trained men. Indeed, compared with sedentary men of similar age and a similarly low atherosclerotic risk profile, master's athletic men present a higher prevalence of high coronary artery calcium scores and a greater number of significant atherosclerotic plaques [START_REF] Merghani | Prevalence of subclinical coronary artery disease in masters endurance athletes with a low atherosclerotic risk profile[END_REF].

Limitations

We note two main limitations. This was a retrospective observational study involving a relatively small number of men with CAD due to the restrictive clearance criteria set out by the US recommendations [START_REF] Thompson | Eligibility and disqualification recommendations for competitive athletes with cardiovascular abnormalities: Task Force 8: Coronary Artery Disease: A scientific statement from the American Heart Association and American College of Cardiology[END_REF] and to the relatively high level (≥ 4 h/week) of PA requested for participation. However, we feel our results help support physicians when advising men with CAD who wish to undertake intensive (competitive and non-competitive) sport. No untrained CAD control cohort was studied, but the scientific literature provides enough data concerning the incidence of MACE in this population.

Conclusion

Méthodes. -

 - Abbreviations: CAD, coronary artery disease; CS, competitive sport; CVRF, cardiovascular risks factor; ILS, intensive leisure-time sport; MACE, major adverse cardiac events; MLS, moderate leisure-time sport; NCS, new coronary stenosis; PA, physical activity; SR, stent restenosis; ST, stent thrombosis.

  ± 8.5 years) had an SR, alone or in combination with an NCS, occurring in 11 stents (BMS n = 7 and DES n = 4) after 13.2 ± 15.6 months (1-52 months). For eight patients, an NCS was observed, with SR in four patients, and a double SR observed in two patients (ILS n = 1; CS n = 1); four patients (60.0 ± 4.5 years) had an NCS without associated SR, occurring after 42.5 ± 54.7 months (4-121 months). Each case required a new angioplasty.

Table 1

 1 MACE occurred in 15.7% of men during follow-up, with no significant difference in the incidence of MACE between MLS, ILS or CS physical activity groups. Stent thrombosis was significantly more frequent in CS participants than in MLS or ILS participants; especially in those with a BMS. MACE occurred during physical exertion in 59% of patients, but there were no heart failure episodes, no cardiac arrests and no cardiac deaths documented. Our data supports the Task Force 8 exercise eligibility recommendations in patients with CAD with no inducible ischaemia, no electrical instability, a normal LVEF and a good control of their CVRFs, who wish to partake in intensive competitive sport. Baseline characteristics of men with CAD included in the study

	Characteristic		Overall population	MLS	ILS	CS	P
			n = 108	n = 29	n = 58	n = 21
	Age (years)		57.3 ± 9.1	61.3 ± 7.5	57.1 ± 9.2	52.2 ± 8.0	< 0.01
	BMI (kg/m²)		25.1 ± 2.9	25.0 ± 3.1	24.8 ± 2.6	25.9 ± 3.4	0.39
	LVEF (%)		59.9 ± 6.9	59.7 ± 7.3	59.4 ± 7.0	61.6 ± 6.2	0.56
	Cardiovascular risk factor
	Smoking		6 (5.6)	1 (3.5)	5 (8.6)	0	0.25
	Hypertension		42 (38.9)	12 (41.4)	21 (36.2)	9 (42.9)	0.88
	Dyslipidaemia		52 (48.2)	18 (62.1)	25 (43.1)	9 (42.9)	0.34
	Type 2 diabetes		10 (9.3)	3 (10.3)	7 (12.1)	0	0.53
	Obese (BMI ≥ 30 kg/m	2 )	7 (6.5)	3 (10.3)	1 (1.7)	3 (14.3)	0.21
	Cardiac medications
	Beta-blocker		90 (83.3)	24 (82.8)	48 (82.8)	18 (85.7)	0.97
	Antiplatelet a		107 (99.1)	29 (100)	58 (100)	20 (95.2)	0.95

Data are expressed as mean ± standard deviation or number (%). P values indicate the inter-group comparison. BMI: body mass index; CS: competitive sport group; ILS: intensive leisure-time sport group; LVEF: left ventricular ejection fraction; MLS: moderate leisure-time sport group. a For the recommended treatment duration.

Table 2

 2 Coronary history and procedural data of the study cohort. Data are expressed as mean ± standard deviation or number (%). BMS: bare-metal stent; DES: drugeluting stent; MLS: moderate leisure-time sport group; ILS: intensive leisure-time sport group; CS: competitive sport group. * P < 0.05, ILS DES group compared with MLS and CS groups.

	Variable	Global population	MLS	ILS	CS
		(n = 108)	(n = 29)	(n = 58)	(n = 21)
	First coronary event
	Stable angina	42 (38.9)	6 (20.7)	26 (44.8)	10 (47.6)
	Unstable angina	28 (25.9)	6 (20.7)	16 (27.6)	6 (28.6)
	Myocardial infarction	41 (38.0)	18 (62.1)	18 (31.0)	5 (23.8)
	Mean number of	1.5 ± 0.8	1.3 ± 0.5	1.6 ± 0.9	1.5 ± 0.8
	stents/patient
	Number of stents implanted
	(n=164)
	One	68 (63.0)	20 (69.0)	35 (60.3)	13 (61.9)
	Two	30 (27.8)	8 (27.8)	16 (27.6)	6 (28.6)
	Three or more	10 (9.3)	1 (3.4)	7 (12.1)	2 (9.5)
	Type of stent
	BMS	97	32	41	24
	DES	67	7	52*	8
	Location of stent (n=152)
	Left anterior descending	85/108 (78.8)	23	51	11
	artery
	Circumflex artery	27/108 (19)	6	16	5
	Right coronary artery	42/108 (38.9)	11	18	13
	Left main artery	2/108 (1.9)	0	0	2

Table 3

 3 Evolution of cardiovascular risk factors and sports practise after the stenting procedure (n = 108).

	Variable	Before stenting	After stenting	P
	Risk factor
	Smoking	41 (37.9)	6 (5.6)	< 0.001
	Hypertension	30 (27.8)	42 (38.9)	0.08
	Dyslipidaemia	52 (48.1)	52 (48.1)	0.77
	Type 2 diabetes	6 (5.6)	10 (9.3)	0.29
	Obesity	19 (17.6)	7 (6.5)	< 0.01
	Sports practise
	No sport	20 (18.5)	0	< 0.001
	MLS	22 (20.4)	29 (26.9)	0.26
	ILS	31 (28.7)	58 (53.7)	< 0.001
	CS	35 (32.4)	21 (19.4)	< 0.05

Data are expressed as number (%). The P values concern the inter-group comparison. CS: competitive sport; ILS: intensive leisure-time sport; MLS: moderate leisure-time sport.

Table 4

 4 Occurrence of major adverse coronary events during a mean follow-up of 57.6 ± 46.0 months. Data are expressed as number (%). The P values concern the inter-group comparison. CS: competitive sport group; ILS: intensive leisure-time sport group; MACE: major adverse cardiac events;

	Event	Global	MLS	ILS	CS	P
		population (n =	(n = 29)	(n = 58)	(n = 21)
		108)
	All MACE	17 (15.7)	5 (17.2)	7 (12.1)	5 (23.8)	0.10
	Isolated SR	5 (4.6)	1 (3.5)	3 (5.2)	1 (4.8)	0.24
	SR + NCS	4 (3.7)	1 (3.5)	3 (5.2)	0	0.12
	ST	4 (3.7)	1 (3.5)	0	3 (14.3)	0.01
	Isolated NCS	4 (3.7)	2 (6.9)	1 (1.7)	1 (4.8)	0.46

MLS: moderate leisure-time sport group; NCS: new coronary stenosis; SR: stent restenosis; ST: stent thrombosis.

Acknowledgments

The authors acknowledge André Gabriel, Jean Gauthier, Aude Girard-Girod, Jacques Gueneron, Andre Heraudeau, Jean Jacques Louchart, Jean-Philippe Mathieu, Jacques Mourot, Bernadette Nivoix, Gerald Phan, François Passard François, Philippe Poinson Philippe and Cecile Ramseyer for their participation in the patient-inclusion phase.

Sources of funding

This study received the Fabrice Salenson fellowship, a grant from the Club des Cardiologues du Sport.

Contribution of authors

J.M.G., L.C. and F.C. contributed to the conception or design of the work. J. M. G., F. S., L. C., S. C., J.C.V. and S.D. contributed to the acquisition and analysis of data for the work. J. M. G., G. K., and 13 F.C. drafted the manuscript. M.G. and F.S. critically revised the manuscript. All authors gave final approval and agree to be accountable for all aspects of work ensuring integrity and accuracy.

Disclosure of interest

None.


Olivier Torresin

Mario Borz

Julien Mauchain

Ivan Blum

Victor I Kleshch

Alexander N Obraztsov

Angela Vella

Benoit Chalopin
email: benoit.chalopin@irsamc.ups-tlse.fr

Conduction mechanisms and voltage drop during field electron emission from diamond needles

We report results of experimental investigation of field electron emission from diamond nanoemitters. The measurements were performed with single crystal diamond needles fixed at tungsten tips. The voltage drop along diamond needles during emission was revealed and measured using electron energy spectroscopy. The observed linear dependence of the voltage drop in diamond on voltage applied to the tungsten tip is explained in the frame of a simple macroscopic electrical model combining Poole-Frenkel conduction along the diamond tip and Fowler-Nordheim tunneling at the diamondvacuum junction. Experimental evidences of electron emission sensitivity to laser illumination are discussed for possible modification of diamond emitter characteristics and voltage drop.

I. INTRODUCTION

Diamond attracted a lot of interest over the last decades as alternative to conductive metallic and semiconducting cold cathodes [1][2][3][4][5][6][7][8][9]. Attempts to build diamond-based and diamond-like emitter arrays, to function as field emission displays, were ultimately commercially unsuccessful, but the potential for using a diamond nanocrystal to act as a point-electron source was not systematically explored in this earlier work. High mechanical robustness, thermal conductivity and chemical inertness intrinsically possessed by diamond, could be key factors providing a desirable stability of electron source. Most studies with electric fields in the range of 1MV/m were performed previously on polycrystalline diamond films or composites of nanostructured diamond species with doped or defective diamond. Recently, Kleshch et al. [10] first demonstrated the use of a single-crystal diamond needle as a point electron source. One of their findings was a saturation phenomenon of electron emission manifested in deviation of current-voltage curve from the Fowler-Nordheim dependence at high voltages. The current in the saturation region follows a Poole-Frenkel mechanism and is associated to a voltage drop detected in the measurement of kinetic energy spectra of the emitted electrons. The formation of a depletion zone near the diamond tip apex, which is typical for semiconductor emitters [11], may happen in the saturation regime. This saturation of current may also be explained by a reduction of the field enhancement factor (see. e.g. [12]) because of a voltage drop along the emitter as it has also been observed by Groening et al. [7] for diamond films and discussed recently by Forbes [13]. He argues that this effective "saturation" of Fowler-Nordheim plots can come from a voltage-divider effect. This paper extends on that idea and investigates the conduction and emission properties of diamond needles (representing a kind of diamond nanoemitters), where the voltage drop is substantial. In the following, we present measurements of electron emission from a diamond nanotip which confirm and extend previous results obtained for similar diamond crystallites [10]. We use kinetic energy spectra of emitted electrons to characterize the conduction mechanisms as a combination of Poole-Frenkel conduction in the diamond and Fowler-Nordheim tunneling at the diamondvacuum junction. At this stage in our investigation of electron emission from diamond needles, we focus on the experimental results revealing the main practical aspects of the emission and on the simplest modeling of the data from which general characteristics of the sample could be extracted. Even though some microscopic considerations will be discussed, the aim of this article is to get a macroscopic view on conduction mechanisms on this object but not to discuss the microscopic aspects of the electrons transport and the electric field distribution inside the diamond needle. Section II describes the diamond needles used in our experiment, section III presents the results of electron emission measurements, section IV describes an electrical model used to account for the two different conduction mechanisms, and section V shows the possibilities to control electron emission by laser illumination of the tip apex.

II. SINGLE-CRYSTAL DIAMOND NEEDLES

The diamond needles used in our experiments are (001) oriented single crystals, created by chemical vapor deposition (CVD) and selective thermal oxidation. The fabrication process is described in Ref. [14] and the needles have been investigated on several different aspects: in terms of structural properties [15], field emission [10], optical response in electron emission [16], photolumi-FIG. 1: SEM images of a single-crystal diamond needle mounted on a tungsten nanotip using FIB (a) and close-up on the apex (b) from which the radius is estimated.

nescence and cathodoluminescence [17][18][19][20]. They were welded on a tungsten nanotip using Focused Ion Beam (FIB). The diamond needles macroscopically have a pyramidal shape (while shape of near apex lost the geometrically perfect form), with a length of 50 to 100 µm, and a apex radius of 10 to 50 nm. This dimension is similar to a typical tungsten nanotip used for cold field emission, which justifies the comparison of their field emission properties. Several diamond needles have been used. The sample used in the experiment presented here is shown in Fig. 1 III. ELECTRON FIELD EMISSION Fig. 2(a) shows a sketch of the experimental appara-tus for electron emission, adapted from [21,22]. Diamond tips and their tungsten holder are mounted inside an ultra-high vacuum chamber designed for field and laser-induced electron emission with a pressure of 2 × 10 -10 mbar. Tips are biased with a voltage V DC . The total emitted current is measured with a picoammeter, plugged on the tip at high voltage and isolated from ground. This measurement comes with a noise of a few tens of pA. The electron kinetic energy spectrum is measured with a retarding field spectrometer at zero potential with an entrance pinhole of 200 µm, counting electrons with a multi-channel plate. The latter has a resolution of approximately 1 eV within our operating parameters. A typical spectrum is shown in Fig. 2(b) in which the width is limited by the low-resolution of the spectrometer. We can therefore not measure precisely the features of the spectrum but only the mean kinetic energy of the emitted electrons. The spectrometer is a few millimeters away from the tip apex and is mounted on translation stages in order to perform field-emission microscopy (FEM) (Fig.

2(c))

. A femtosecond laser (wavelength λ = 1030 nm, 300 fs pulse duration, variable repetition rate from 1 kHz to 2 MHz) can be focused on the apex with a beam size of a few micrometres, allowing the illumination of the apex only. Taking into account the submicrometer transverse dimension of the needle near the apex, the laser beam power illuminating of the needle may be estimated as about 10% of the incident power. Before they are used as electron sources, the needles are cleaned using a combination of the application of a 2.5 kV positive applied voltage for three minutes, and focused laser illumination for an hour with a mean power of a 120 mW. We observed that strong emission currents or high laser intensities can cause modification of the needles' shape and their emission properties. However with moderate currents and laser intensities, which were used in this work, no substantial damage was observed on the diamond needles. This corresponds to our expectations based on the high optical transparency of diamond in the visible range.

The kinetic energy of emitted electrons is not equal to eV DC because of the voltage drop ∆V between both ends of the diamond needle. Since the voltage between the tip apex and the grounded counter-electrode is V DC -∆V , we write this energy as E kin = e(V DC -∆V ) where e is the elementary positive charge.

We measured the field-emission current as well as the voltage drop ∆V as a function of the applied voltage V DC (Fig. 3) using the picoampermeter and the spectrometer. The current rises exponentially and we reach currents of a few nA for applied voltage between 400 V and 1.5 kV. The picoammeter has a resolution of about 10 pA. Hence, we were not able to measure current below 100 pA which corresponds to applied voltage below 400V. At these currents we observed substantial voltage drop of several hundreds of volts, similarly to previously reported results [10] which were obtained in the current saturation region. The voltage drop however behaves linearly as a function of the applied voltage V DC with a non-zero intercept of -134 V and a slope of 0.53.

IV. CONDUCTION MODEL FOR ELECTRONS

To explain the evolution of the current and the voltage drop as a function of the applied voltage, we introduce a simple macroscopic electrical model for the conduction of electrons between the tungsten holder and the spectrometer. This macroscopic model aims at explaining the dependence of current and voltage drop as a function of applied voltage. Two conduction mechanisms are simultaneously happening. We model them as differential resistances connected in series with the same electrical current I (Fig. 4). First in the diamond, the conduction in the saturation region is best described with the Poole-Frenkel mechanism [10, 23-25] associated with a voltage ∆V which scales as :

I = A ∆V e B √ ∆V (1)
where A and B are constants depending on the tip characteristics and temperature (described later). This mechanism can be understood as thermally stimulated emission of charges over a potential-energy barrier reduced by the Schottky effect. It is important to notice here that this macroscopic point of view can apply to both surface conduction and bulk conduction. Although a microscopic description of the conduction could provide a better understanding of the role of the various parameters, the macroscopic model we use here is proving sufficient to model the experimental data. Then at the diamond-vacuum junction, electrons are emitted through field emission, with a Fowler-Nordheim behaviour [26][27][28] associated to a local electrostatic field of magnitude E F N . As in the case for cold field emission from metallic nanotips, we can link this electric field to the potential at the tip apex. But in this case, the potential at the tip apex differs from the applied voltage V DC by the voltage drop. Hence, in the same spirit as for conductive emitters, we can write

E F N = β(V DC -∆V ). β (in m -1
) is a parameter that describes field enhancement at the tip apex. In the following, we make the assumption that β is constant and does not depend on V DC or ∆V . This strong hypothesis is an approximation because of a possible field penetration to the emitter tip, especially when the depletion region is formed [24,29], as well as because of the non linearity of PF conduction. This non-linearity makes the field profile in diamond non-homogenous, and the shape of the iso-potential lines at the apex (which β depends on) should therefore depend on the applied voltage or current. A more detailed microscopic analysis of the field profile versus PF current would be necessary to determine the exact dependance with the applied voltage. But this is outside the scope of this article and from there on, we consider β to be constant. We can therefore write:

I = C(V DC -∆V ) 2 e - D V DC -∆V (2)
where C and D ∝ φ 3/2 /β are approximately constants depending on the workfunction φ and the voltage-to-field β factor.Considering that the PF and FN currents must be equal in the static regime, we write:

I = A ∆V e B √ ∆V = C(V DC -∆V ) 2 e - D V DC -∆V (3)
Using equations ( 1) and ( 2), we can fit the current using both the PF (ln I ∆V vs ∆V ) and FN (ln

I (VDC-∆V ) 2 vs
1 VDC-∆V ) coordinates as shown in Fig. 5. The PF fit gives A 0 = 3.04 ± 0.03 × 10 -5 nA/V and B 0 = 0.239 ± 0.001 V -1/2 , and the FN fit gives C 0 = 7.49 ± 0.09 × 10 -5 nA/V 2 and D 0 = 1.895 ± 0.012 × 10 3 V. For this set of parameters A 0 , B 0 , C 0 and D 0 , equation ( 3) can be numerically solved to find the expected value of ∆V as a function of V DC . The results are shown in Fig. 3 (solid lines) alongside the direct measured values (I and ∆V versus V DC ) and in Fig. 5 in reduced coordinates. They agree well with the measurements for both the current I and voltage drop ∆V versus V DC . Little discrepancies are visible in Fig. 5, which could be due to variations in the value of the beta factor, which are not taken into account in Eq. 2. The plots we present here seem to differ from other results in diamond [10] or semiconductors [30,31] where strong saturations of the FN plots are observed. This is partly due to the fact that in these cases, larger values of applied voltage are used spanning over regions with more different physical behaviours.

From the values of parameters B 0 and D 0 we can retrieve numerical values for some of the physical parameters of the diamond tip. The Poole-Frenkel mechanism leads to a current I that scales as

I ∝ ∆V exp   e 3 ∆V π 0 r d -E a k B T   ( 4
)
where r is the relative permittivity of diamond, d is the field penetration length inside the diamond, k B the Boltzmann constant, T the temperature, and E a an activation energy (or trap energy) that is related to the trap potential of impurities inside the diamond. This means

B 0 = e 3
π 0 r d /k B T . E a has been measured for diamond needles in [10] and is on the order of 0.2 eV. In diamond films, earlier studies reported similar values for the trap energy [5,8]. The value of B 0 given by the fit leads to long, but its surface can be partially covered by carbon amorphous conductive layers.

On the other hand, the Fowler-Nordheim parameter D is equal to 4 √ 2m 3 e φ 3/2 v(y) 1 β with m the electron mass, φ the workfunction and v(y) a slowly varying special mathematical function [27] of the parameter y = e 3 β(VDC-∆V ) 4π 0 /φ. Many modern experimental papers on field emission use a simplified form in which the factor v(y) does not appear. This is equivalent to taking v(y) = 1, and causes error in the current density prediction by a factor of 100. Here we use the value v(w) = 0.6, which is similar to the value used for a metallic field emitter [32]. Taking D = D 0 = 1895 V from the fit and a workfunction φ of 5 eV (from [7] for instance), we get β = 2.4 × 10 7 m -1 . The value of beta can also be estimated from the geometry of the emitter. In the first approximation it depends only on the radius of the emitter r as β = 1/(kr) with the coefficient k approximately equal to 5 [START_REF] Gomer | Field emission and field ionization[END_REF]. From the SEM image, we got r = 25 nm and β = 0.8 × 10 7 m -1 which is much lower than the value obtained from FN plot fit. The discrepancy can be explained by the fact that within our voltage range, the current is saturated due to the field penetration effect. In [10], it was shown that at smaller currents where there is no saturation the I-V curve in FN plot bends downward i.e. its slope becomes higher. This means that β, estimated from the fit of FN plot, will be smaller in this region and should be closer to its value determined from the geometry of the emitter.

In our experiments, the linear dependence of the voltage drop with a slope of 0.53 shows that with an applied voltage V DC between 500 and 1500 V, the current limitation is rather balanced between the PF and the FN mechanisms, both contributing to current limitation with differential resistances of the same order. This differential resistances can be defined as However, the behavior is different for other values of V DC . At low applied voltage, the voltage drop is close to zero, meaning that the PF conduction in the tip is not relevant and the PF resistance is much smaller than the FN resistance. At higher V DC (above 2000 V for our parameters) numerical calculations shown in Fig. 6 show that the PF resistance decreases slower, indicating that the FN mechanism is taking over again.

R P F = ∆V /I = 1/Ae -B √ ∆V and R F N = (V DC -∆V )/I = 1 C(V DC -∆V ) e D V DC -∆V

V. INFLUENCE OF THE EXPERIMENTAL PARAMETERS ON THE VOLTAGE DROP

From this model, it is clear that modifying the diamond tip parameters will change the values of the four relevant parameters A, B, C and D and will modify the balance between the PF and FN mechanisms. This can be observed either in the current or the voltage drop dependence on the applied voltage. Experiments performed in [10] showed that the PF mechanism is indeed affected by temperature through a modification of the B parameter. We were not able to reproduce these experiments that require the tip to be cooled down or heated by several hundreds of Kelvin. However, our model shows that this would translate into a modification of the slope of the linear part of the voltage drop dependence. This variation is shown in Fig. 7 (left) where the voltage drop and the slope are plotted for various values of the B parameter. As expected, at high temperature, the PF mechanism is dominant for higher voltage, since the associated resistance is very low. A similar interpretation can be made for the influence of the D parameter. Calculations of ∆V for various values of D is shown in Fig. 7 (right). For a single diamond tip, the value of D cannot be modified easily since it depends on the tip shape and material. However, laser illumination can lead to an increase in the emission current by various physical mechanisms, which is equivalent to a reduction of the FN differential resistance. This experiment has been performed with femtosecond pulses (300 fs duration, 1030 nm wavelength, 1 MHz repetition rate ) and a focal spot of a few micrometres on the apex of the biased diamond tip. This experiment differs from what has been studied by Porshyn et al. [16] and Borz et al. [START_REF] Borz | 2017 30th International Vacuum Nanoelectronics Conference (IVNC)[END_REF]. The main difference is that in our experiment, only the apex is illuminated thanks to a very tight laser focus. This means that the PF conduction inside the diamond is not affected, and only the emission process at the apex is modified. We observed a transition in the emission regime when the laser power is increased. The voltage drop changes when passing through a critical FIG. 8: Measurement of ∆V as a function of V for DC and DC+laser field emission for different laser powers (corresponding to different shaped symbols). Above a critical laser power, the voltage drop changes, following a linear behavior versus applied voltage V DC , with a similar slope compared to the static emission, but with a different intercept, close to zero. The lines correspond to two different fits which gives different values of the D parameter.

laser power of about 50 mW as shown in Fig. 8. Below the critical power, the voltage drop behaves as it would without laser illumination. Above it, the voltage drop increases linearly with V DC with an intercept close to 0. This decreases the parameter D and therefore the FN resistance. Fitting the ∆V versus V DC under laser illumination gives a new value of the D parameter, which drops to 73 V, which is more than twenty times smaller than the value obtained in static measurements. The fit is however not as precise and also shows that the decrease of D is associated with a decrease of the C parameter as well. If we assume that the D parameter can still be written as 4 √ 2m

3 e φ 3/2 v(y) 1 β , then the drop of D can be a consequence of a change in either the workfunction φ, the voltage-to-field factor β or even the v(y) function. A more precise interpretation of these findings requires essentially a microscopic analysis which is out of the scope of the present study and requires intensive investigations which are in progress now.

VI. CONCLUSION

In conclusion, we have presented experimental measurements of current and voltage drop versus V DC in diamond nanoemitters acting as a point electron source in vacuum. We confronted these measurements to a macroscopic electrical model, that is able to accurately fit the data, including the linear dependence of the voltage drop with a negative intercept. This model combines Poole-Frenkel conduction and Fowler-Nordheim tunneling which are both contributing to the measured current and voltage drop. We showed how laser illumination on the tip apex only can shift up the voltage drop and keep the slope constant. This study also explains how using the reduced voltage at the apex V DC -∆V , the Fowler-Nordheim plots show much less saturation than with regular coordinates. From this work onward, it becomes necessary to carry out further investigations to reveal in more details the microscopic mechanisms so that it becomes possible to optimize samples and experimental conditions to obtain results which may be greatly attractive for both applied and fundamental perspectives.

FIG. 2 :

 2 FIG. 2: (a) Experimental setup for electron emission investigation (see text for details). (b) Typical energy spectrum recorded by the retarding field spectrometer, from which the voltage drop ∆V is measured. (c) Typical field emission microscopy image.

FIG. 3 :

 3 FIG. 3: Top: Measured current I as a function of the applied voltage V DC (triangles) in semilog scale. In solid lines is the computed value resulting from equation 3 using parameters from the fits of equations 1 and 2. Inset shows a current versus V DC in usual FN coordinates ln I V 2 DC versus 1 VDC . Bottom: Measurement of the voltage drop ∆V as a function of V DC (triangles) and corresponding computed value from equation 3 (solid line).

FIG. 4 :

 4 FIG. 4: Conduction model for the emission current: the Poole-Frenkel and Fowler-Nordheim dipoles are in serial so that the emission current should obey both the Poole-Frenkel and Fowler-Nordheim laws with a corresponding potentiel difference ∆V and (V DC -∆V ) respectively.

  FIG. 5: Top: Poole-Frenkel plot of the measured current as a function of the potential difference ∆V between both ends of the diamond tip. The solid line represent the curve obtained for the combined fit of I and ∆V versus V DC . Bottom: the same current is plotted as a function of V DC -∆V which corresponds to the electric field at the diamond-vacuum junction.

Fig. 6

 6 Fig. 6 shows the voltage divider as a function of the applied voltage V DC . It is indeed almost constant for an applied voltage between 1000 V and 2000 V.

FIG. 6 :

 6 FIG. 6: Normalized resistances (voltage divider)of Poole-Frenkel and Fowler-Nordheim R P F /(R P F + R F N ) and R F N /(R P F + R F N ) calculated from I and ∆V as a function of V DC .

FIG. 7 :

 7 FIG. 7: Evolution of the Voltage drop as a function of the applied voltage for different values of the parameters B and D. Top left is a series of plots of ∆V vs V DC for values of B ranging from 0.3 * B 0 to 10B 0 . Bottom left shows the slope of the linear dependence of ∆V as a function of B/B 0 . Top right is a series of plots of ∆V vs V DC for values of D ranging from 0.1 * B 0 to 3B 0 . Bottom right shows the vertical intercept of the linear dependence of ∆V as a function of D/D 0 .

ACKNOWLEDGMENTS

This work was supported by Programme Investissements d'Avenir under the programs ANR-11-IDEX-0002-02, reference ANR-10-LABX-0037-NEXT, ANR-13-BS04-0007-01 and ANR-10-LABX-09-01, LabEx EMC3, by the European Union with the European Regional Development Fund (ERDF) and the Regional Council of Normandie. ANO and VIK are grateful for financial support from Russian Foundation for Basic Research (grant # 18-29-19071).


K Gajavalli

M Barrachin

P Benigni

J Rogez

G Mikaelian

E Fischer

Determination of Solution Enthalpy of Zirconium in Liquid Aluminum

The work presented in this paper is the continuation of our earlier publication (Barrachin et al. [1]) where the literature data on the calorimetric measurements of the zirconium dissolution in liquid aluminum at temperatures around 1000 K were carefully analyzed. In this previous study, we showed that these different data were erroneously interpreted by their authors in terms of dissolution enthalpies. In our interpretation, the measured thermal effects rather resulted from the initial complete transformation of Zr into Al 3 Zr, due to the quick diffusion of aluminum towards the zirconium sample core. In this scenario, the subsequent dissolution of the aluminide particle in the melt, which is very slow at this temperature, was likely to remain undetected in the calorimetric experiments. To overcome these difficulties, the partial drop-solution enthalpy of zirconium at infinite dilution is indirectly derived from Al 3 Zr dissolution in liquid aluminum at 1173 K. It is found to be ∆ ds H

∞,1173K

Zr,298K =-130±9 kJ.mol -1 . The corresponding partial mixing enthalpy of Zr at the liquid state is ∆ mix H ∞,1173K Zr =-175±10 kJ.mol -1 . This value is consistent with the results obtained by various authors having performed calorimetric experiments at temperatures higher than 1700 K. It can hence be concluded that the zirconium partial mixing enthalpy at infinite dilution does not depend on temperature between 1173 K and 2045 K.

Introduction

Molten aluminum was used as a solvent in many high temperature solution calorimetry studies around 1000 K in order to measure the standard enthalpy of formation of zirconium-based binary compounds, e.g. in the Cu-Zr [2, 3], Ni-Zr [3-5], Co-Zr [6, 7], U-Zr [8] , and Ag-Zr [9] systems. In these studies, dissolution of zirconium, of the March 8, 2019

second metallic element (i.e. Cu, Ni, Co, U and Ag respectively) and of the compound of interest in liquid aluminum are conducted in three separate experiments. The partial drop solution enthalpies of the elements and of the compound are first extrapolated at infinite dilution and then combined in a thermodynamic cycle to yield the standard enthalpy of formation of the compound.

In a previous paper [1], we critically reviewed the different experimental data related to the partial drop solution enthalpy of zirconium in liquid aluminum at infinite dilution around 1000 K. We demonstrated that there is an incompatibility between the durations of the thermal effects reported by the different authors and the durations which can be estimated from a dissolution kinetic model. As a consequence, we concluded that, contrary to the authors expectations, the zirconium samples were likely to be not fully dissolved in these experiments.

The main reason is linked to the formation of an Al 3 Zr layer, Al 3 Zr being the richest Al stoichiometric compound in the Al-Zr phase diagram, at the liquid/solid metal interface at the beginning of the "dissolution" reaction. Once this layer created, the direct contact between the pure zirconium sample core and the aluminum liquid is prevented. The kinetics of the dissolution process then becomes essentially governed by two competing mechanisms, firstly, the aluminide layer dissolution by liquid aluminum and secondly, the growth of this layer towards the sample core. Kidson [10] showed that solid-state diffusion of aluminum across Al 3 Zr at temperatures between 800 and 900 K is much faster than the one of zirconium. The Al (fcc) and Al 3 Zr (D0 23 ) structures presents similarities in terms of interatomic distances which makes the Al diffusion through the aluminide easier, leading to a quick growth of the Al 3 Zr layer, to the exclusion of the growth of other Al-Zr compound. Extrapolating this experimental observation to the liquid aluminum/solid zirconium interaction during calorimetric experiments around 1000 K, a more or less a complete transformation of the zirconium sample into the aluminide is expected. Large Al 3 Zr precipitates, having typical size of several 10 µm, are effectively observed in our experiments [10]. They were probably not formed when the aluminum bath, after being extracted from the calorimeter, was cooled down to room temperature, but rather in situ, at the calorimeter temperature. Moreover, we put in evidence that the enthalpy values consistently measured in these different experiments including ours [2-9, 11, 12] could quantitatively match with our formation of Al 3 Zr scenario.

At this stage, the measurement of the standard formation enthalpy of Zr-based compounds by high temperature solution calorimetry seemed to be compromised and required, in order to enhance the dissolution kinetics, either to change the solvent and/or to increase the measurement temperature, keeping in mind that our Tian-Calvet calorimeter is not designed to work above 1373 K1 . An alternative possibility would be to use a stirring device to promote liquid aluminum convection during the experiment. Such a technique has been implemented by Maciag [14] and used to dissolve zirconium in liquid aluminum at 1073 K in the frame of calorimetric experiments aiming at determining the standard formation enthalpy of various Al-Zr compounds. His results will be discussed in detail in this paper.

From our side, the possibility to dissolve zirconium in other metallic solvents was firstly investigated. In liquid tin, Zr partial mixing enthalpies values in the liquid at infinite dilution were reported by Bouhajib et al. [15] at 1173 K, and at higher temperatures by Valishev [16] at 1973 K and by Sudavtsova et al. [17] at 1889 K. These literature results suggested that, in spite of the large discrepancy between the different measurements, liquid tin could be a potential solvent for Zr. Our preliminary tests, at 996 K as well as at 1173 K, have shown such a large dispersion that deriving a reliable value of the partial mixing enthalpy of zirconium in liquid tin was impossible. The zirconium samples were suspected to be floating on the bath, due to the lower density of solid Zr compared to the liquid tin one, preventing an efficient dissolution process. To our best knowledge, no test was performed before in liquid indium. In our experiments at 996 K and at 1173 K, previous difficulties related to the unfavorable ratio between the densities of the solvent and the solute, were also identified. The dissolution process was similarly found to be erratic with the impossibility to derive an accurate value of the Zr partial mixing enthalpy. An additional reason could be the strongly reduced driving force for Zr dissolution because of the extremely low zirconium solubility in liquid indium at these temperatures [START_REF] Dieva | Izd. Ural'sk. Nauch. Tsentra Akad[END_REF].

Scoping dissolution tests of zirconium in liquid aluminum were also performed at 1173 K, i.e. more than 150 K higher than the temperature of our previous experiments [9]. Once again, the measured drop-solution heats were largely scattered preventing the determination of a reliable value at infinite dilution. Moreover, the inconsistency between the duration of the observed thermal effect and the dissolution time calculated with our kinetic model was an additional indication that the aluminide formation could not be excluded at this temperature. The driving force of the dissolution process is the zirconium concentration difference between the solid/liquid interface, which is equal to the zirconium solubility in liquid aluminum, and the bulk of the liquid. In this case, the increase of the calorimeter temperature was not sufficient to significantly increase this driving force.

In the above described scenario of the competition between aluminide formation and aluminide dissolution, the dissolution of the aluminide principally occurs after the complete conversion of zirconium into aluminide. This dissolution is expected to take place during the experiments but, unfortunately, detection of the associated thermal effect proved to be difficult, the main reason being that the dissolution kinetics is much slower than the heat release linked to the aluminide formation and can easily be hidden in baseline fluctuations of the calorimetric signal. After very deep inspection of some thermograms, an endothermic signature, likely associated to the aluminide dissolution, could be identified unambiguously (Figure 1) before a complete return of the signal to the baseline. However, in many thermograms, such identification remained unclear and the quantitative measurement of the heat associated to this process was not reliable. To overcome these difficulties, it was later tried to directly measure the partial drop-solution enthalpy of Al 3 Zr samples in liquid aluminum. This value was then used to derive the partial drop-solution enthalpy of zirconium in liquid aluminum by a thermodynamic cycle.

Experimental

Instrumentation and experimental procedure

The instrumentation and the calorimetric method already described in detail in [9] for Zr is applied for Al 3 Zr drop-solution experiments.

The calorimeter temperature was set to 1173 K. Aluminum (Alfa Aesar, Table 1) was used as solvent and calibration material. The protective atmosphere in the calorimeter was argon gas (Air Liquide, Table 1) with a pressure equal to 0.11MPa. For each run, a mass around 8.4-8.5 g of Al was loaded in a graphite crucible. At the beginning of the experiment, the calorimeter was calibrated by four Al drops. Then, small fragments of Al 3 Zr slugs (zirconium aluminide Al 3 Zr, CAS 12004-83-0, D0 23 , Alfa Aesar, Table 1) were successively dropped into the bath until a target final concentration was reached. The differential signal of the calorimeter was continuously monitored and recorded during the process. The next addition was triggered once the signal has returned to the baseline. The final concentration of the bath was chosen to ensure that the concentration in zirconium was not exceeding the solubility limit in liquid aluminum [19] at the calorimeter temperature.

The processing of the acquisition data file consists in computing the area of each peak by numerical integration after having subtracted the baseline from the calorimetric signal. The main source of error arises from the choice of the baseline which is made to compute the area of each individual peak. The worst case corresponds to a peak of small height and a fluctuating baseline for which different equally probable baseline selections may affect the computed area by several percent.

Al 3 Zr dissolution experiments in liquid aluminum at 1173 K

Three runs of Al 3 Zr dissolution in liquid aluminum measurements were performed at 1173 K.

Within one run, each drop of δn moles of aluminide in the bath containing N moles of Al and M moles of Zr corresponds to the following reaction:

δn < Al 3 Zr > 298K + ((NAl, MZr)) 1173K → (((3δn + N)Al, (δn + M)Zr)) 1173K (1)
The associated heat effects Q 1 which have been measured, are reported under the heading

∆ ds H 1173K Al 3 Zr,298K (x Al 3 Zr ) = Q 1 /δn in Table 1.
The typical thermogram recorded during the drop of an Al 3 Zr fragment is portrayed in Figure 2. Two successive endothermic peaks are seen. The first sharp one is due to the fast heating of the fragment upon entering the aluminum bath while the second smeared peak results from its subsequent slower dissolution.

In the investigated composition range, ∆ ds H 1173K Al 3 Zr,298K (x Al 3 Zr ) was found to be independent on x Al 3 Zr . Hence, the partial drop-solution enthalpy of Al 3 Zr at infinite dilution in liquid aluminum, ∆ ds H ∞,1173K Al 3 Zr,298K , was simply calculated by taking the average of the 10 measurements reported in Table 1.

∆ ds H ∞,1173K Al 3 Zr,298K is equal to 173±7 kJ.mol -1 .
The uncertainty reported here is an expanded uncertainty with a coverage factor of 2. It combines the standard uncertainty on the calorimeter calibration coefficient and the standard uncertainty on the Al 3 Zr dissolution heats. In assessing the uncertainty of the calibration coefficient, it was further assumed that the uncertainty on the heat increment of pure aluminum calculated with the SGTE data [20] was 1% at 1173 K. From the standard enthalpy of formation of Al 3 Zr reported by Meschel et al. [21], the drop-solution enthalpy of zirconium at infinite dilution in liquid aluminum at 1173 K can be calculated with the following expression:

∆ ds H ∞,1173K Zr,298K = ∆ f H 298K Al 3 Zr -3∆H 1173K Al,298K + ∆ ds H ∞,1173K Al 3 Zr,298K (2)
with

∆ f H 298K Al 3 Zr =-193.6±5.2 kJ.mol -1 [21]
, and ∆H 1173K Al,298K =36.4 kJ.mol -1 [20], the aluminum heat increment from 298 K to 1173 K.

The partial drop-solution enthalpy of zirconium, ∆ ds H

∞,1173K

Zr,298K , at 1173 K in liquid aluminum calculated according to ( 2) is equal to -130±9 kJ.mol -1 with the following reference states : solid zirconium at 298 K and liquid aluminum at 1173 K.

Using the heat increment of Zr between the solid state at 298 K and the supercooled liquid state at 1173 K, ∆H 1173K

Zr,298K = 44.7 kJ.mol -1 calculated with the SGTE data [20], it is then possible to derive the partial mixing solution of zirconium at infinite dilution in aluminum at 1173 K, ∆ mix H ∞,1173K Zr which is equal to -175±10 kJ.mol -1 with the following reference states : liquid zirconium and aluminum at 1173 K. It is worth noting that the uncertainty on this value is very difficult to assess because it depends on the standard uncertainty of the heat increment of liquid Zr, 955 K below its melting point. This standard uncertainty which is unknown has been assumed to be 10% of its SGTE value in the present work.

Discussion

Partial drop-solution enthalpy of zirconium in liquid aluminum

The partial drop-solution enthalpy of zirconium in liquid aluminum at infinite dilution at 1073 K has been very recently reported by Maciag [14]. The value, -244.5±5.4 kJ.mol -1 , is rather consistent with the previous measurements [2-9, 11, 12] at similar temperatures (Table 3) even if it can be underlined that this value is the most negative of the data set. This value is in strong disagreement with the value determined in this paper, -130±9 kJ.mol -1 .

In the past experiments, as mentioned in the introduction, it was suspected that the thermal effects were erroneously interpreted in terms of Zr dissolution. It was shown that they more likely corresponded to the zirconium transformation into Al 3 Zr. If we assume that such a process occurs in Maciag's experiments, the associated heat, ∆H 2 , can be estimated from the heats involved in the following reactions:

                         < Zr > 298K +3 < Al > 298K →< Al 3 Zr > 298K ∆ f H 298K Al 3 Zr < Al 3 Zr > 298K →< Al 3 Zr > 1073K ∆H 1073K Al 3 Zr,298K < Al > 298K → ((Al)) 1073K ∆H 1073K Al,298K (3)
The heat involved , ∆H 2 , can be written:

∆H 2 = ∆ f H 298K Al 3 Zr + ∆H 1073K Al 3 Zr,298K -3∆H 1073K Al,298K (4)
with, for the Maciag's experimental conditions,

∆ f H 298K Al 3 Zr =-193.6±5.2 kJ.mol -1 [21], ∆H 1073K
Al,298K =33.3 kJ.mol -1 [20], and ∆H 1073K Al 3 Zr,298K =79.7±0.4 kJ.mol -1 [1]. The calculated value, ∆H 2 , equal to -213.8±5.3 kJ.mol -1 , is not far from the Maciag's value (Table 3) in such a way that the hypothesis of aluminide formation in the calorimeter cannot be fully excluded.

In our previous article [1], a dissolution kinetic model was developed in order to estimate the duration of the thermal effect expected in a dissolution process driven by diffusion and natural convection induced by the density difference between zirconium and aluminum. The dissolution process of a solid sample in liquid aluminum is described by the Nernst-Shchukarev equation (commonly used, see e.g. [22,23]) :

dC(t) dt = K S V [C s -C(t)] (5)
where C(t) is the concentration of the dissolved metal in the liquid bulk at time t, C s , the metal concentration in the liquid at saturation as given by the Al-Zr phase diagram, t(s) the dissolution time, S (m 2 ) the sample surface area , V (m 3 ) the melt volume, and K (m.s -1 ), the mass transfer coefficient. Equation ( 5) of the evolution of the zirconium concentration in the liquid is expressed under the following form :

dC(t) dt = S V B 0 [C s -C(t)] + S V B 1 [C s -C(t)] 5/4 ( 6
)
with the following definitions for B 0 , and B 1 :

               B 0 = 3.47D 0 S 1/2 B 1 = 0.51 D 0 S 1/2 A 1 gS 3/2 D 0 ν 1/4 (7)
where :

A 1 = ρ l,Zr -ρ l,Al ρ l,Al C s + ρ l,Zr (1 -C s ) (8)
with g (m.s -2 ) is acceleration due to gravity, d (m) the diameter of the sphere, ρ l,i (kg.m -3 ) the density of i at the liquid state, ν (m 2 .s -1 ), the kinematic viscosity, D 0 (m 2 .s -1 ) the diffusion coefficient of solute in liquid, and S the sample surface. The numerical values of these different parameters can be found in [1]. Under our experimental conditions at 1173 K, we have firstly simulated (Figure 3) the dissolution of the first dropped aluminide sample of Run 3 (whose thermogram can be seen in Figure 2). The calculation shows that the sample should be dissolved in ≈ 2000 s. This value is consistent with the duration of the thermal effect which can be estimated from the thermogram.

To make our model consistent with the stirring mechanism adopted in the Maciag's experiments, the mass transfer coefficient, K, should be modified to take into account the forced convection. Nevertheless it can be underlined that the masses of the zirconium dropped samples in his experiments are about 0.36 g [24] for an initial aluminum bath of 50 g, i.e. a zirconium content about 0.2 at.%. After the first drop, the zirconium concentration in the bath is very close to the solubility limit at 1073 K [19]. In these conditions, the dissolution kinetics becomes extremely reduced, even in case of forced convection, due to the very small difference between the zirconium concentration in the bath and the solubility limit. These conditions are favorable to the transformation of the zirconium sample into aluminide.

The large negative values of the standard enthalpies of formation of Al-Zr compounds determined by Maciag can be explained by his large negative value of ∆ ds H ∞,1073K Zr,298K . It is the case for Al 3 Zr and Al 2 Zr, with values which are respectively 13 kJ.mol -1 and 15 kJ.mol -1 more negative than other experimental determinations by Meschel [21] using high temperature direct synthesis calorimetry for Al 3 Zr and by Klein et al. [13] using acid solution calorimetry for Al 2 Zr.

A more general tendency can be obtained by comparing the standard enthalpies of formation obtained by Maciag for Al 3 Zr, Al 2 Zr, Al 3 Zr 2 , AlZr, Al 2 Zr 3 , AlZr 2 , and AlZr 3 with the consistent set of DFT standard enthalpies of formation from Duan et al. [25] and selected by Fischer et al. [26] in their Calphad assessment of the Al-Zr phase diagram. Table 4 shows that the discrepancy between the two sets of values tends to increase from Al 3 Zr to AlZr 3 . It also indirectly validates the assumption that Maciag's value of the drop-solution enthalpy of zirconium is too negative.

Assuming only an incorrect value for the drop-solution enthalpy of zirconium in the Maciag's study and a reliable set of DFT values from [25], a linear variation of the discrepancy between the Maciag's and Duan's compound standard enthalpies of formation with the zirconium content, x of the compound written under the form AlZr x , should be expected. The observed variation deviates from this tendency (Figure 4). It could take its origin in the measured heats of dissolution of the compounds themselves. For Al 3 Zr, a direct comparison with our measurement is possible. From the values of ∆ f H 298K Al 3 Zr =-206.4± 9.2 kJ.mol -1 and ∆ ds H

∞,1073K

Zr,298K =-244.5± 5.4 kJ.mol -1 reported by Maciag, ∆ ds H ∞,1073K Al 3 Zr,298K measured in his experiments and not reported in his article can be inferred2 , 61.8 kJ.mol -1 . It is in strong disagreement with our value, even if both values were obtained at two temperatures 100 K apart. Using the heat increment of Al 3 Zr from 298 to the calorimeter temperature 1073 K, 79.7 kJ.mol -1 [1] and the melting enthalpy of Al 3 Zr (≈ 88 kJ.mol -1 [27]), it is deduced that the partial mixing enthalpy of Al 3 Zr (liquid state) at infinite dilution in liquid aluminum at 1073 K is a strongly exothermic process (≈ -106 kJ.mol -1 ) according to Maciag's data. By contrast, we put in evidence a slightly exothermic process 3 , about ≈ -6.2 kJ.mol -1 . Such discrepancy cannot be accounted for by the difference of the calorimeter temperatures in both datasets. As in zirconium drop-solution experiments, Maciag [24] used rather large masses of Al 3 Zr (≈0.4 g). Under these experimental conditions, the dissolution process could have been drastically slowed after the first drop.

Plotting the convex hull at 298 K from Maciag's results in Figure 4, it can be seen in the region of compositions lower than 50%Zr that Al 2 Zr and Al 3 Zr 2 should be less stable than mechanical mixtures of Al 3 Zr and AlZr. This conclusion contradicts the state of the art of the Al-Zr phase diagram [28] and the DFT calculations from [25].

Partial zirconium mixing enthalpy at liquid state

We have reported in Table 3 and on Figure 6, the existing data related to the partial mixing enthalpies of zirconium at infinite dilution in liquid aluminum.

They can be divided into two groups, the low temperature data, obtained between 984 K and 1073 K, are between -243 and -285 kJ.mol -1 while the high temperature data, obtained between 1693 K and 2045 K, give much less exothermic values in the range -139 to -177 kJ.mol -1 .

The partial zirconium mixing enthalpy in liquid aluminum at 1173 K obtained in this paper, -175±10 kJ.mol -1 , correlates well with the high temperature measurements of Witusiewicz et al. [29], Esin et al. [30] and Sudavtsova et al. [31]. This good correlation would suggest that Zr partial mixing enthalpy at infinite dilution in liquid Al does not depend on temperature in the range 1173-2045 K.

Comparing now our partial zirconium mixing enthalpy with the low temperature data, a variation between 67 and 109 kJ.mol -1 , depending on the considered value in the data set [2-9, 11, 12, 14], can be calculated over a temperature interval less than 200 K. Variation of this magnitude over such a narrow temperature interval would be very surprising, even more if we consider that most of these data have been obtained under rather similar experimental conditions. This unexpected enthalpy variation can be discussed in terms of excess heat capacity of Al-Zr liquid. In the recent assessment of the Al-Zr phase diagram [26], Fischer et al. choose a composition dependency Redlich-Kister polynom of second degree to model the Gibbs energy of the liquid phase in the Al-Zr system. The analysis of the experimental data relative to the mixing enthalpy of the liquid phase (Figure 3 of [26]) shows that the regular solution model can be considered as a rather good approximation to describe the mixing enthalpy. Within this framework, the excess mixing enthalpy can be written as:

∆ mix H liq,xs (x Zr , T ) = ζ(T )x Zr (1 -x Zr ) (9)
where ζ(T ), the interaction parameter. The zirconium partial mixing enthalpy in liquid aluminum takes the following expression :

∆ mix H T Zr = ζ(T )(1 -x Zr ) 2 ( 10
)
where ζ(T ), appears to be the zirconium partial mixing enthalpy at infinite dilution. The excess heat capacity can be written as:

C liq,xs p (x Zr , T ) = x Zr (1 -x Zr ) dζ(T ) dT (11)
Using our measured values at 996 K from [9] and 1173 K from this work, the mean excess heat capacity of Al-Zr liquid in the temperature range [996 K-1173 K] can be roughly estimated by the following expression:

C liq,xs p (x Zr , 1084.5K) ≈ x Zr (1 -x Zr ) ζ(1173) -ζ(996) 1173 -996 (12)
or:

C liq,xs p (x Zr , 1084.5K) ≈ 474 x Zr (1 -x Zr ) J.mol -1 .K -1 (13)
The previous expression of C liq,xs p yields 118.5 J.mol -1 .K -1 at the average temperature of 1084.5 K and at the equimolar composition. At the same composition and temperature, the ideal heat capacity of liquid, C liq,id p , according to the Neumann-Kopp rule 4 , is equal to 32.7 J.mol -1 .K -1 . Considering that the excess heat capacity in most cases contribute only little to the heat capacity of a metallic liquid, the excess heat capacity derived from the measurements at 996 K can be considered as unrealistic.

Fischer and Colinet [26] underscored that the Calphad modelling of the Al-Zr system is very constrained by the standard enthalpies of formation of the numerous intermetallic compounds in order to guarantee their stability at 298 K. In this context, Fischer and Colinet gave more weight to Witusiewicz et al. liquid enthalpy data [29] in their optimization process and obtained a good fit of the phase diagram in the aluminum-rich region.

In their modelling, the mixing enthalpy of the liquid phase, ∆ mix H, is not temperature dependent. The partial enthalpy of mixing of zirconium at infinite dilution can be derived from the assessed interaction parameters of the liquid using the following equation:

∆ mix H ∞ Zr = lim x Zr →0       ∆ mix H -x Al ∂∆ mix H ∂x Al T,p       = -156.7 kJ.mol -1 (14)
Our experimental value, -175±-10 kJ.mol -1 is in the [-120;-180 kJ.mol -1 ] range of the values of the Zr partial enthalpy of mixing at infinite dilution in liquid Al measured by calorimetry at the highest temperatures [29][30][31][32][33]. Morevover, our value is also in reasonable agreement with the value calculated from the parameters assessed by Fischer et al. [26], the magnitude of the difference, roughly 20 kJ.mol -1 , being comparable to the experimental scattering affecting Witusiewicz's data, as shown in Fig 4 of [26]. Being aware of the ability of the Calphad approach to test the compatibility between phase diagram data and thermodynamic functions of individual phases, this agreement can be considered as an additional indirect validation of our measurement.

Conclusion

In the past, several consistent values for the partial drop-solution enthalpy of zirconium in liquid aluminum around 1000 K were reported. In a previous study, we showed , with the heat capacities of Al and Zr taken from [20].

that these different data have to be rather interpreted in terms of transformation of Zr into Al 3 Zr.

To overcome these difficulties, in this work, the zirconium partial drop-solution enthalpy at infinite dilution is indirectly derived from Al 3 Zr drop-solution experiments in liquid aluminum at 1173 K. It is found to be ∆ ds H

∞,1173K

Zr,298K =-130±9 kJ.mol -1 . The corresponding zirconium partial mixing enthalpy at infinite dilution in liquid aluminum is ∆ mix H ∞,1173K Zr =-175±10 kJ.mol -1 . This value is consistent with literature data obtained by calorimetric experiments performed at temperatures higher than 1700 K and likely indicates that the partial mixing enthalpy of Zr at infinite dilution in liquid Al does not depend on temperature between 1173 K and 2045 K. Al 3 Zr,298K )=7kJ.mol -1 , combined expanded uncertainty on the average of 10 measurements with a coverage factor of 2. The subscript c denotes a combined uncertainty according the nomenclature in [START_REF] Taylor | Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results[END_REF]. 3 Indicative value, not considered as reliable, due to difficulty of the baseline choice. Not taken into account in the average for the calculation of ∆ ds H ∞,1173K Al 3 Zr,298K . The differential signal of the calorimeter is plotted vs. time. The mass of the dropped Al 3 Zr fragment is 9.52 mg. Interpretation of the thermal event is as follows. The first sharp endothermic deviation corresponds to the heating of the fragment and is followed by its slower dissolution which is also endothermic, before the signal final return to the baseline. The linearly interpolated baseline is plotted as a red dashed line. 3, 5 th column). The references states are liquid zirconium and liquid aluminum at the calorimeter temperature.

x i = Σ i-1 j=1 n j + n i 2 Σ i-1 j=1 n j + n i 2 + n Al (15)

This work

2

 2 Uncertainties : u(T )=1K, u(p)=10kPa, u c (M init Al )=0.000045g, u c (δm Al 3 Zr )=0.00002g, u c (δn Al 3 Zr )=0.00012mmol, u c (x Al 3 Zr )=0.000001. U c (∆ ds H ∞,1173K

Figure 1 :Figure 2 :

 12 Figure 1: Representative thermogram of the "dissolution" of a Zr sample in liquid aluminum at 1173 K.The differential signal of the calorimeter is plotted vs. time. The mass of the dropped Zr fragment is 12.23 mg. Interpretation of this complex thermal event is as follows. The very first small endothermic deviation corresponds to the heating of the fragment which is quickly counterbalanced by a large exothermic deviation due to the Al 3 Zr formation reaction. Subsequent Al 3 Zr endothermic dissolution is only seen at greater magnification in the figure inlay, in which the linearly interpolated baseline is plotted as a red dashed line.

Figure 3 :

 3 Figure 3: Calculated evolution of the dissolved mass fraction of Al 3 Zr for Run 3 conditions, first dropped sample.

Figure 4 :

 4 Figure 4: Difference between the standard enthalpies of formation of the different Al-Zr binary compounds measured by Maciag [14] and calculated by Duan [25] as function of x, zirconium composition of the compound of formula AlZr x (see Table4)

Figure 5 :

 5 Figure 5: Standard enthalpies of formation of the different Al-Zr binary compounds as measured by Maciag [14], as calculated by Duan [25] and as assessed by Fischer and Colinet [26]. In dashed red line, the convex hull at 298 K from Maciag's results shows that, according his values, Al 2 Zr and Al 3 Zr 2 should be less stable than mechanical mixtures of Al 3 Zr and AlZr.

Figure 6 :

 6 Figure 6: Partial mixing enthalpy of zirconium at infinite dilution in liquid aluminum vs. temperature according to different authors (see values in Table3, 5 th column). The references states are liquid zirconium and liquid aluminum at the calorimeter temperature.

Table 1 :

 1 Element purities H 2 O<3 ppm mole, O 2 < 2 ppm mole, C n H m <0.5 ppm mole according to Air Liquide data. 11

	Chemical name	Source	Commercial	Initial	Purification
			grade	purity	method
	Al	Alfa Aesar	-	0.9999 (mass)	None
	Al 3 Zr	Alfa Aesar	-	0.99 (mass)	None
	Ar	Air Liquide Alphagaz 1 0.99999 (mole) 1	None

1

Table 2 :

 2 Partial drop-solution enthalpy (kJ.mol -1 ), ∆ ds H 1173K Al 3 Zr,298K (x Al 3 Zr ), of Al 3 Zr in liquid aluminum at T =1173 K -The experimental pressure is p =0.11MPa. The references states are solid Al 3 Zr at T =298 K and liquid aluminum at T =1173 K. M init Al and δm Al 3 Zr in g, δn Al 3 Zr in mmol. M init Al is the sum of the bath mass plus the masses of the 4 aluminum calibration samples. x Al 3 Zr 1 is the molar fraction of Al 3 Zr. The uncertainties are indicated below the Table2. For the i th drop of n i moles of Al 3 Zr in the aluminum bath containing initially n Al moles of pure Al, the molar fraction of Al 3 Zr, x i , corresponding to the measured partial enthalpy, is calculated according to :

	M init Al	δm Al 3 Zr	δn Al 3 Zr	x Al 3 Zr	∆ ds H	1173K Al 3 Zr,298K (x Al 3 Zr )
	Run 1 8.45740
		0.01317 0.076495 0.00012201		168
		0.01501 0.087182 0.00038296		184
		0.02496 0.144974 0.00075286		173
	Run 2 8.56149
		0.01060 0.061568 0.00009701		184
		0.01143 0.066388 0.00029855		173
		0.01432 0.083174 0.00053403		166
		0.01600 0.092932 0.00081116		175
	Run 3 8.50833
		0.00952 0.055295 0.00008767		164
		0.01009 0.058605 0.00026820		179
		0.01096 0.063659 0.00046192		(147) 3
		0.01150 0.066795 0.00066853		160
	1

Table 3 :

 3 Partial drop-solution and mixing enthalpies,of zirconium in liquid aluminum at infinite dilution, ∆ ds H respectively in kJ.mol -1 . The references states are solid zirconium at 298 K and liquid aluminum at the calorimeter temperature (T cal ) for ∆ ds H ∞,T cal Zr,298K . The references states are liquid zirconium and liquid aluminum at the calorimeter temperature for ∆ mix H ∞,T cal Zr . x Zr is the maximum zirconium molar fraction reached in the different experiments. ( * ) The more recent values of Turchanin et al., according to the authors [3], are considered to be a refinement of the previously published ones.( * * ) n.r. : not reported.

	∞,T cal Zr,298K , and ∆ mix H	∞,T cal Zr
	Authors	T cal (K)	x Zr	∆ ds H	∞,T cal Zr,298K	∆ mix H	∞,T cal Zr
	Ansara et al. [4]	984	≤ 0.0014	-212.4	-250.8
	Nagarajan et al. [8]	991	≤ 0.0267 -220.3±9.5	-258.9±9.5
	Decreton et al. [9]	996	≤ 0.0022 -221.5±5.8	-260.3±5.8
	Turchanin et al. [2, 3]	1022	≤ 0.0055 -235.0±4.3 *	-274.7±4.3
	Turchanin et al. [5, 11, 12]	1026	≤ 0.0044 -217.4±8.5	-257.2±8.5
	Gomozov et al. [6, 7]	1030	≤ 0.0006 -203.3±4.9	-243.2±4.9
	Maciag [14]	1073	n.r. * *	-244.5 ±5.4 -285.9 ±5.4
	Sudavtsova et al. [32]	1693	n.r. * *	-76.2	-140.0
	Batalin et al. [33]	1773	≤ 0.09	-52.6±1.3	-119.5±1.3
	Sudavtsova et al. [31]	1790	≤ 0.18	-102.4±20.0	-170±20.0
	Esin et al. [30]	1970	≤ 0.60	-91.7	-166.5
	Witusiewicz et al. [29]	2045	≤ 0.54	-99.4±10.1 -177.3±10.1
	This work	1173	≤ 0.001	-130±9	-175±10

,

Table 4 :

 4 Standard enthalpies (kJ.mol -1 ) of formation measured by drop-solution calorimetry[14] and calculated by DFT[25]

		AlZr 1/3	AlZr 1/2	AlZr 2/3	AlZr	AlZr 3/2	AlZr 2	AlZr 3
	Maciag [14] (1)	-68.8 ±1.6 -84.5±3.3 -99.3±4.0 -142.6±8.8 -122.5±7.8 -168.3±9.3 -174.4±9.2
	Duan et al. [25] (2)	-62.4	-77.4	-83.1	-89.8	-95.7	-102.7	-116.0
	∆(1 -2)	-6.4	-7.1	-16.2	-52.8	-26.8	-65.6	-58.4

The zirconium dissolution at room temperature was shown to be feasible by Klein et al.[13] using an acid mixture containing hydrofluoric acid. This technique will be not discussed in this paper.

The heat increment of Al from 298 to 1073 K is taken from[20] and is

33.3 kJ.mol -1 .3 The heat increment of Al 3 Zr from 298 to calorimeter temperature 1173 K is 91.2 kJ.mol -1[1].