Laëtitia Perrin

Johan Spinosi

Laura Chaperon

Sofiane Kab

Frédéric Moisan

PhD. Alexis Elbaz
email: alexis.elbaz@inserm.fr

Epidemiologist Alexis

Pesticides expenditures by farming type and incidence of Parkinson disease in farmers: a French nationwide study Authors

Keywords: Parkinson's disease, incidence, type of farming, pesticides expenditures, farmers

Background: Professional pesticides exposure is associated with PD risk, but it remains unclear whether specific products, which strongly depend on farming type, are specifically involved. We performed a nationwide ecological study to examine the association of pesticides expenditures for the main farming types with PD incidence in French farmers Methods: We used the French National Health Insurance database to identify incident PD cases in farmers (2010)(2011)(2012)(2013)(2014)(2015). We combined data on pesticides expenditures with the agricultural census to compute pesticides expenditures for nine farming types in 2000 in 3,571

French cantons. The association between pesticides expenditures and PD age/sex standardized incidence was examined using multilevel Poisson regression, adjusted for smoking, neurologists' density, and deprivation index.

Results: 10,282 incident PD cases were identified. Cantons with the highest pesticides expenditures for vineyards without designation of origin were characterized by 16% (95% CI=6-28%) higher PD incidence (p-trend corrected for multiple testing=0.006). This association was significant in men and older farmers. There was no association with pesticides expenditures for other farming types, including vineyards with designation of origin.

Conclusions: PD incidence increased significantly with pesticides expenditures in vineyards without designation of origin characterized by high fungicide use. This result suggests that agricultural practices and pesticides used in these vineyards may play a role in PD and that farmers in these farms should benefit from preventive measures aiming at reducing exposure.

Our study highlights the importance of considering farming type in studies on pesticides and PD and the usefulness of pesticides expenditures for exposure assessment.

INTRODUCTION

Parkinson disease (PD) is the second most common neurodegenerative disease after Alzheimer's disease and the neurological disease with the largest increase in age-standardized prevalence between 1990-2015[START_REF] Gbd | Global, regional, and national burden of neurological disorders during 1990-2015: a systematic analysis for the Global Burden of Disease Study 2015[END_REF]. PD etiology is considered as multifactorial, and involves both genetic susceptibility and environmental factors [START_REF] Ascherio | The epidemiology of Parkinson's disease: risk factors and prevention[END_REF].

Among environmental risk factors, professional pesticides exposure is associated with increased PD risk, but it remains unclear whether specific products are more specifically involved due to their large variety and changes over time [START_REF] Van Der Mark | Is pesticide use related to Parkinson disease? Some clues to heterogeneity in study results[END_REF]. Some studies have highlighted herbicides (e.g., rotenone, paraquat), insecticides (e.g., organochlorines), and fungicides (e.g., maneb) [START_REF] Nandipati | Environmental Exposures and Parkinson's Disease[END_REF][START_REF] Tanner | Rotenone, Paraquat and Parkinson's Disease[END_REF]. Most studies used self-reported information to assess exposures, with different levels of detail ranging from a simple occupational history to information on pesticide names, frequency of use, or protective equipment [START_REF] Elbaz | Professional exposure to pesticides and Parkinson's disease[END_REF][START_REF] Moisan | Association of Parkinson's Disease and Its Subtypes with Agricultural Pesticide Exposures in Men: A Case-Control Study in France[END_REF][START_REF] Tanner | Rotenone, Paraquat and Parkinson's Disease[END_REF]. Self-report is prone to recall bias and can induce exposure misclassification and bias association estimates for several reasons [START_REF] Blair | Impact of pesticide exposure misclassification on estimates of relative risks in the Agricultural Health Study[END_REF]: PD mainly occurs after retirement, and farmers have used a large variety of pesticides over a long period of time, often in association, making it also difficult to disentangle their effect; in addition, PD is characterized by some degree of cognitive impairment that may lead to differential recall [START_REF] Bocanegra | Dementia and mild cognitive impairment in Parkinson's disease: a review[END_REF]. One meta-analysis showed that studies that used job titles in combination with expert judgment or job-exposure matrices yielded stronger associations than studies based on self-reported exposures, thus suggesting that exposure misclassification may play a role [START_REF] Van Der Mark | Is pesticide use related to Parkinson disease? Some clues to heterogeneity in study results[END_REF].

Few studies used pesticides expenditures to assess pesticide exposure. This approach is not hampered by recall bias and allows to examine dose-response relationships. It was used to study congenital abnormalities [START_REF] Froes Asmus | Positive correlation between pesticide sales and central nervous system and cardiovascular congenital abnormalities in Brazil[END_REF][START_REF] Markel | Environmental pesticides increase the risk of developing hypertrophic pyloric stenosis[END_REF][START_REF] Schwartz | Congenital limb reduction defects in the agricultural setting[END_REF], human reproductive system disturbances [START_REF] Koifman | Human reproductive system disturbances and pesticide exposure in Brazil[END_REF], and cancers [START_REF] Chrisman Jde | Pesticide sales and adult male cancer mortality in Brazil[END_REF]. To the best of our knowledge, only three studies used this approach to examine the association of pesticides with PD. In rural areas of Quebec (Canada), PD prevalence was correlated with pesticide sales [START_REF] Barbeau | Ecogenetics of Parkinson's disease: prevalence and environmental aspects in rural areas[END_REF]. Based on California (US) pesticide use reporting data, PD mortality was higher in counties with highest pesticide use per square mile [START_REF] Ritz | Parkinson's disease mortality and pesticide exposure in California 1984-1994[END_REF]. In Andalusia (Spain), districts with high pesticide sales were characterized by increased PD prevalence [START_REF] Parron | Association between environmental exposure to pesticides and neurodegenerative diseases[END_REF]. These studies focused on the general population rather than on farmers or agricultural workers. In addition, expenditures and pesticides types differ considerably by type of crops. For instance, vineyards mainly use fungicides, while cereal crops use both fungicides, herbicides, and insecticides, but with lower frequency and intensity. Therefore, crops can contribute to an indirect assessement of exposure to pesticides (Kab et al., 2017b;Moisan et al., 2011b). However, previous studies did not take into account the target of pesticides.

France is the first European consumer of pesticides, with expenditures of ~3 billion euros in 2000 [START_REF] Butault | L'utilisation des pesticides en France : état des lieux et perspective de réduction[END_REF]. After accounting for the number of hectares cultivated, it ranks fourth, behind Portugal, The Netherlands, and Belgium [START_REF] Cemagref | Une utilisation des pesticides élevée mais très mal connue[END_REF]. We performed a nationwide ecological study to examine the association between pesticides expenditures for the main farming types in 2000 with PD incidence (2010)(2011)(2012)(2013)(2014)(2015) in French farmers.

MATERIALS AND METHODS

PD cases

The French National Health Insurance database (Système National des Données de Santé, SNDS) contains individual-level information on health care reimbursements and sociodemographic characteristics, including age, sex, place of residence, and health insurance scheme, for >97% of the French population. Information on health care reimbursements include consultations, medical tests, and drug claims. The latter include type of drugs, purchase date, number of boxes, medication dosage, and specialization of the prescribing physician.

We identified all persons with at least one antiparkinsonian drug reimbursement between 2009-2015, and excluded those <20y, women <50y reimbursed for bromocriptine alone (lactation suppression), persons only on anticholinergics and neuroleptics (druginduced-parkinsonism), and those not living in metropolitan France. We used an algorithm to identify PD cases that was previously validated against a neurological diagnosis (Moisan et al., 2011a). The validation study was based on 1,114 participants (320 with PD, 794 without PD) who used antiparkinsonian drugs. This algorithm allows to estimate the probability that a person is treated for PD based on the annual pattern of antiparkinsonian drugs use (levodopa, dopamine agonists, selegiline/rasagiline, piribedil, anticholinergics, COMT inhibitors), proportion of time treated, number of neurologist/general practitioner's visits, and sex. We used the Youden index to identify the probability cutoff that maximized sensitivity (92.5%) and specificity (86.4%) of the algorithm; antiparkinsonian drug users for whom the algorithm estimated a probability above this cutoff were considered as having PD. Incident cases a given year were persons identified by the algorithm that year and who did not have antiparkinsonian drugs reimbursements the previous year.

For these analyses, we identified persons affiliated with the Mutualité Sociale Agricole (MSA). It guarantees health insurance (including after retirement) for farmers, other agricultural workers, and their spouses if unemployed. In 2015, the MSA covered ~3.3 million people (5% of the French population; 42% farmers, 58% workers). The workers group is a heterogeneous one that includes farm workers (38%) and workers in agricultural cooperatives (16%), administrations (28%) and workers in other areas such as forestry work and green spaces maintenance (18%) (MSA, 2016). A MSA 2010 survey reported that 25% of workers group (farm, cooperatives, administration and others workers) was exposed to pesticides, with around less 50% for agricultural and of green spaces maintenance workers (MSA, 2015). We were able to distinguish farmers from workers, but different types of workers could not be differentiated. Therefore, as the workers group is very heterogeneous, we restricted our analyses to farmers (i.e., farm owners).

Agricultural census

We used data from an exhaustive agricultural census carried out in France by the Ministry of Agriculture that takes place every ~10y [START_REF] Agreste | A propos des recensements agricoles et enquêtes structures des exploitations[END_REF]. Since data on pesticides expenditures were available starting on year 2000, we used the 2000 agricultural census to allow for a latency period ≥10y between exposure assessment and PD incidence.

In the European Union, farms are classified according to their main farming type. A farm is considered to be specialized in a type of farming, if the standard gross production related to that type exceeds two thirds of the farm's total standard gross production (Insee, 2016). The standard gross production is the production value per hectare or animal head. This classification includes 17 farming types (cereals, general crops, fresh vegetables, flowers and ornamental plants, vineyard with designation of origin, vineyards without designation of origin, permanent crops, mixed crops, cattle milk, beef cattle, mixed cattle, sheep and goats, granivore, mixed livestock with herbivore orientation, mixed livestock with granivorous orientation, general crops and herbivore, mixed crops and mixed livestock).

Data were available at the canton-level and included the number of farms for each farming type and the corresponding area or number of animals. Data on pesticide use are not collected in the agricultural census.

Annual pesticides expenditures

Data came from the Farm Accountancy Data Network [START_REF] Agreste | Réseau d'information comptable agricole (RICA)[END_REF]. Since 2000, member states of the European Union carry out an annual survey on a sample of representative farms in terms of region, farming type, and economic size. Although farms of small economic size are not included, the sample covers about 90% of the total agricultural area and agricultural production after sampling weights are taken into account. Data include detailed information on location (region), agricultural activities, and economic and financial information (e.g., value of production of the different crops, sales, purchases) that are used to define farming type (as in the agricultural census). For each farm, pesticides expenditures are available globally, i.e., they are not available for each crop. As for the agricultural census, we used data for France in 2000.

Pesticides expenditures for farms specialized in livestock were considerably lower than for other farming types (less than 100 Euros per hectare) and were similar for different types of animals; in order to reduce the number of variables included in the models from 17 to 9 farming types, we grouped together all types of livestock (cattle rearing -specialist dairying; cattle rearing and fattening; cattle-dairying, rearing and fattening combined; sheep, goats and other grazing livestock; granivores; mixed livestock, mainly grazing livestock; mixed livestock, mainly granivores; field crops-grazing livestock combined; various crops and livestock combined). Alternatively, the two types of vineyards were kept separately because their expenditures were very different. According to European rules, vineyards with a designation of origin are those that originate in a specific geographical location and produce wine whose qualities and characteristics are essentially due to their region of provenance and production method. European wine producing countries have established legal frameworks to guarantee the quality and origin of these wines. Vineyards without a designation of origin correspond to other vineyards.

Annual pesticides expenditures for each farming type in French cantons were determined in two different ways:

-The first approach ("regional expenditures") was based on expenditures at the regional level.

In 22 administrative regions, we determined the weighted median pesticides expenditures per hectare for 9 farming types (cereals, general crops, fresh vegetables, horticulture, vineyards with a designation of origin, vineyards without designation of origin, permanent crops, mixed crops, livestock). Medians were calculated in each region when there were ≥10 farms with the corresponding activity; if there were <10 farms, we used the median national value.

Expenditures were based on regional data for 94.2% of the farms, and on national data for the remaining 5.8%. We then estimated pesticides expenditures in farms from French cantons for each farming type by multiplying the corresponding median expenditures per hectare by the average agricultural area of these farms in each canton.

-In a second approach ("national expenditures"), we took into account farms' size as it can influence pesticides expenditures per hectare. For each farming type, we first performed a weighted linear regression of pesticides expenditures on the agricultural area of the farms.

These analyses were performed at the national level in order to include a sufficient number of farms after removing outliers [START_REF] Blatná | Outliers in regression[END_REF]. We then used the intercept and slope of these models to calculate the average pesticides expenditures per hectare for each faming type in French cantons, using the agricultural area of these farms as explanatory variables. These values were again multiplied by the average agricultural area of each type of farming to obtain average pesticides expenditures per farm for each type of farming in each canton.

For both approaches, the annual average total pesticides expenditures by farms from a canton was calculated by summing expenditures for each type of farming (expenditures multiplied by the agricultural area of these farms) divided by the total number of farms in the canton.

PD incidence rates and standardized incidence ratios

The number of incident cases (corrected for sensitivity/specificity of the algorithm) was computed by sex/5y age groups in each canton according to the place of residence at the time of the first antiparkinsonian drug reimbursement [START_REF] Couris | Method of correction to assess the number of hospitalized incident breast cancer cases based on claims databases[END_REF]. In 2000, there were 3,689 cantons in France, with an average area of 149km². Between 2010-2015, the average number of farmers in each canton was of 261. Since 118 out of 3,689 cantons had no agricultural area, analyses were therefore restricted to 3,571 cantons.

We estimated the number of farmers and the corresponding person-years (by sex/5y age groups), based on the number of farmers with any health-related expense. Analyses were restricted to persons ≥55y because we previously showed that most persons in this age group have at least one health expense per year (correlation with the true number of person-years=0.97; P < 0.001). Below this age, health contacts may be less frequent which would lead to overestimate incidence (Kab et al., 2017a). In addition, PD is very rare below that age Incidence rates were computed by dividing the number of incident cases by the corresponding number of person-years.

To estimate age/sex standardized PD incidence ratios (SIR) in each canton, we used indirect standardization (reference=age/sex-specific French incidence rates).

Statistical analysis

We examined the association between pesticides expenditures and PD incidence among farmers using multilevel Poisson regression with a random intercept per canton and estimated incidence rate ratios (IRR) and 95% confidence intervals (IC). Analyses were performed separately for regional and national expenditures.

We first examined the association of total expenditures with PD incidence. We then included pesticides expenditures for different farming types. Expenditures were included in the models as categorical variables (quintiles); cantons without any expenditure were included in the first quintile. We examined dose-effect relations and tested linear trends by including ordinal variables whose levels were the medians of quintiles divided by 1-standard deviation (SD). Models were adjusted for smoking, neurologists' density, and deprivation (covariates described in Supplementary methods). All covariates were defined at the canton level.

Sensitivity analyses stratified by sex were performed, because men and women have different exposure levels. Second, we stratified analyses by median age at PD incidence (55-74/≥75y) because PD etiology may depend on age. For males and the younger group, we used Poisson regression without random intercept because of small inter-canton variability. We tested interactions by comparing RRs for 1-SD [START_REF] Altman | Interaction revisited: the difference between two estimates[END_REF]. Third, to rule out a potential bias due to under-ascertainment of PD in the oldest age group, we restricted the analyses to the 75-89 years age group. Fourth, we combined the two types of vineyards in a single variable.

Third, models were adjusted for UV-B and vitamin D supplementation. Fourth, as the proportion of cantons without incident PD cases was >20% in some strata, we used binomial negative regression to estimate IRRs.

To take into account multiple comparisons, we used the false discovery rate (FDR) and computed p-values adjusted for multiple testing (q-values) for the trend and interaction tests [START_REF] Benjamini | Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing[END_REF][START_REF] Storey | The positive false discovery rate: a Bayesian interpretation and the qvalue[END_REF].

All tests were two-sided and p-values <0.05 considered significant. Statistical analyses were conducted with SAS 9.4 (SAS Institute, Inc., Cary, NC, USA).

RESULTS

The algorithm identified 17,322 persons as newly treated for PD and affiliated with the Mutualité Sociale Agricole. After correction for the sensitivity and specificity of the prediction model, we identified 14,661 incident PD cases. Of these, 200 did not live in metropolitan France, 417 were <55y, 3,740 were workers, and not farmers, and 22 lived in cantons without agricultural area. Finally, we retained for our analyses, 10,282 incident PD cases among farmers aged ≥55y. There were no incident cases in 654 (18.3%) cantons and the median number of cases in the remaining 2,917 cantons was 2.5 (range=1-24). Supplementary Table 1 presents incidence rates.

Supplementary Figure 1 shows the spatial SIRs distribution.

There was considerable heterogeneity in median pesticides expenditures per hectare across farming types (Table 1): the five types with largest expenditures were fresh vegetables, vineyards with designation of origin, permanent crops, horticulture, and vineyards without designation of origin. Supplementary Table 2 presents median regional expenditures. The regression coefficients from the regression of national pesticides expenditures per hectare on the area devoted to farming types (Table 1) show that expenditures decreased significantly when the area increased for fresh vegetables, vineyards with designation of origin, permanent crops, and vineyards without designation of origin, and increased for cereals and livestock.

Figure 1 show the spatial distribution of total expenditures and expenditures for each farming type. Correlations between expenditures for each farming type were generally weak (Supplementary Table 3), except moderate correlations between livestock and cereals (r=0.482) and between the two types of two vineyards (r=0.459).

Figure 2 presents the associations of total pesticides expenditures with PD incidence in French farmers (regression coefficients in Supplementary tables 4-5); Supplementary table 6 provides cutoffs of quintiles. Using both approaches (regional/national expenditures), total expenditures were not associated with PD incidence neither overall nor in stratified analyses.

Regarding expenditures for farming types, PD incidence increased with increasing expenditures for vineyards without designation of origin, both using regional (q-trend=0.006, Figure 3) and national (q-trend=0.014, Figure 4) expenditures; regression coefficients are shown in Supplementary tables 4-5. PD incidence was 16% higher (IRRQ5=1.16, 95% CI=1.06-1.28) in the fifth quintile compared to the lowest for regional expenditures, and 14% higher (IRRQ5=1.14, 95% CI=1.04-1.25) for national expenditures. Expenditures for other farming types were not associated with PD.

The relation between regional/national pesticides expenditures and PD among farmers was not modified significantly by sex (q-values for interaction≥0.396; Supplementary tables 4-5). In sex-stratified analyses, however, the association of expenditures for vineyards without designation of origin and PD was close to significance in men (regional expenditures, IRRQ5=1.18, 95% CI=1.04-1.33, q-trend=0.067), but not in women (IRRQ5=1.11, 95% CI=0.97-1.27). No tests of linear trend were significant despite some positive associations of PD with mixed crops in men and livestock in women. There was also an inverse association in women for the fifth quintile of national expenditures for vineyards with designation of origin.

Age did not modify the association between regional/national expenditures and PD (qvalues for interaction≥0.27; Supplementary tables 4-5). In age-stratified analyses, there was a positive association for younger farmers in the fourth/fifth quintiles without linear trend.

Regarding expenditures for vineyards without designation of origin, although the interaction was not significant, a significant association was seen in the older group only (regional expenditures: IRRQ5=1.18, 95% CI=1.06-1.31, q-trend=.006; national expenditures: IRRQ5=1.16, 95% IC=1.05-1.28, q-trend=.014), while the association in the younger age groups was weaker and not statistically significant (regional expenditures: IRRQ5=1.09, 95% CI=0.87-1.35, q-trend=.866; national expenditures: IRRQ5=1.05, 95% IC=0.85-1.29, q-trend=.814). Finally, PD incidence was higher in younger farmers in the top quintile of national expenditures for livestock, but without a significant trend. A sensitivity analysis restricted to the 75-89 years age group showed the same positive association between vineyards without designation of origin and PD (regional expenditures: IRRQ5=1.17, 95% IC=1.05-1.30, q-trend=.03; national expenditures: IRRQ5=1.14, 95% IC=1.03-1.27, q-trend=.058). Analyses combining the two types of vineyards did not show a significant association with PD (Figure S2).

Analyses using negative binomial regression or adjusted for UV-B or vitamin D yielded consistent findings (data not shown).

DISCUSSION

Pesticides expenditures in 2000, regardless of farming type, were not associated with PD incidence in French farmers between 2010-2015. However, after distinguishing farming types, cantons with the highest expenditures for vineyards without designation of origin were characterized by a significantly higher PD incidence with a significant trend. In stratified analyses, this association was significant in men and above 75y.

Two previous French studies also highlighted vineyards in relation to PD using alternative exposure assessment methods (Kab et al., 2017b;[START_REF] Moisan | Association of Parkinson's Disease and Its Subtypes with Agricultural Pesticide Exposures in Men: A Case-Control Study in France[END_REF]. In a nationwide ecologic study, PD incidence in the general population increased with the area devoted to agriculture, in particular in cantons with high vineyards density (Kab et al., 2017b). This study ascertained incident PD cases from the general population between 2010-2012 and analyses were conducted overall and after excluding MSA members (farmers and workers). It focused on environmental exposure rather than professional exposure using the area of crops in the cantons of residence as a proxy. In a case-control study (incident and prevalent cases identified in 2006-2007), farmers from 5 regions were interviewed about the crops they had grown and whether they had used pesticides for each of them; farmers who used pesticides for vineyards were at increased PD risk, without association for other crops [START_REF] Moisan | Association of Parkinson's Disease and Its Subtypes with Agricultural Pesticide Exposures in Men: A Case-Control Study in France[END_REF]. In this study, occupational exposure was measured by in-person interview and PD cases were determined by neurological examination to confirm the diagnosis. Our findings are consistent with these studies and extend them to all incident PD cases in French farmers between 2010-2015. In our study, when the two vineyards were combined, the association was no longer significant. The large difference in expenditures between the two types of vineyards explains this finding: 33% of cantons with pesticides expenditures for vineyards without designation of origin were in the first quintile, compared to 5% for vineyards with designation of origin, and few vineyards without designation of origin were included in the fifth quintile that mostly included vineyards with designation of origin.

Our findings demonstrate the importance of considering farming types to study the association between pesticides and PD. Type of products as well as the frequency, intensity, and methods of applications strongly depend on type of crops. Surveys on farming practices show major differences across agricultural activities, with higher pesticide use for vineyards, fresh vegetables, fruit or permanent crops, and flowers and ornamental plants than for other crops [START_REF] Butault | L'utilisation des pesticides en France : état des lieux et perspective de réduction[END_REF]. In France, while vineyards represented ~3% of agricultural land in 2000, they accounted for 20% of pesticides sold, of which fungicides represented 80% [START_REF] Aubertot | Pesticides, agriculture et environnement. Réduire l'utilisation des pesticides et en limiter les impacts environnementaux[END_REF]. In 2005, a wide range of active substances were used in vineyards: >40 insecticides and fungicides and >20 herbicides [START_REF] Aubertot | Pesticides, agriculture et environnement. Réduire l'utilisation des pesticides et en limiter les impacts environnementaux[END_REF]. Fungicides are the most widely used pesticides in vineyards, and their association with PD has previously been reported, both by toxicological studies showing a role of some types of fungicides (dithiocarbamates: maneb, ziram; carbamates: benomyl), and by epidemiological studies [START_REF] Cao | Elucidating Conserved Transcriptional Networks Underlying Pesticide Exposure and Parkinson's Disease: A Focus on Chemicals of Epidemiological Relevance[END_REF][START_REF] Fitzmaurice | Aldehyde dehydrogenase variation enhances effect of pesticides associated with Parkinson disease[END_REF][START_REF] Pouchieu | Pesticide use in agriculture and Parkinson's disease in the AGRICAN cohort study[END_REF][START_REF] Wang | Parkinson's disease risk from ambient exposure to pesticides[END_REF]. A French case-control study in farmers reported an association between PD and duration of exposure to fungicides [START_REF] Moisan | Association of Parkinson's Disease and Its Subtypes with Agricultural Pesticide Exposures in Men: A Case-Control Study in France[END_REF].

A novelty of our study is the distinction between vineyards with and without designation of origin. There are important differences in their practices. Pesticides expenditures per hectare were ~1.5 times greater for vineyards with designation of origin than for those without [START_REF] Agreste | Réseau d'information comptable agricole (RICA)[END_REF][START_REF] Aubertot | Pesticides, agriculture et environnement. Réduire l'utilisation des pesticides et en limiter les impacts environnementaux[END_REF]. Fighting against pests is a quality guarantee for vineyards with designation of origin, which leads them to increase the number of applications. Moreover, the level of technical supervision is higher for vineyards with designation of origin than for those without and it influences methods of application (e.g., use of protective equipment), but also the type of products used [START_REF] Aubertot | Pesticides, agriculture et environnement. Réduire l'utilisation des pesticides et en limiter les impacts environnementaux[END_REF]. In addition, since the turnover is higher for vineyards with designation of origin, more expensive pesticides are used, while mineral products (e.g., sulfur, arsenic, copper) are less likely to be used [START_REF] Viel | Brain cancer mortality among French farmers: the vineyard pesticide hypothesis[END_REF]. One study showed that serum heavy metals (lead, arsenic, nickel, zinc, manganese, copper) levels were much higher in vineyard farmers than unexposed individuals [START_REF] Rocha | Exposure to heavy metals due to pesticide use by vineyard farmers[END_REF]. Heavy metals are known to exert neurotoxic effects, and some pesticides contain metals; for instance, maneb, a fungicide that has been associated with PD [START_REF] Bocchetta | Parkinson's disease and pesticides[END_REF][START_REF] Nandipati | Environmental Exposures and Parkinson's Disease[END_REF], includes manganese.

Exposure to manganese is associated with parkinsonism, copper is implicated in oxidative stress, and zinc affects lysosomal function [START_REF] Montes | Copper and copper proteins in Parkinson's disease[END_REF][START_REF] Tuschl | Manganese and the brain[END_REF]. One study showed higher blood levels of copper and zinc in PD patients than controls [START_REF] Hozumi | Patterns of levels of biological metals in CSF differ among neurodegenerative diseases[END_REF]. However, in epidemiological studies, results on the association between metals and PD are heterogeneous. Available studies do not support association of welding or manganese exposure with PD [START_REF] Mortimer | Associations of welding and manganese exposure with Parkinson disease: review and meta-analysis[END_REF][START_REF] Wirdefeldt | Epidemiology and etiology of Parkinson's disease: a review of the evidence[END_REF]. Other studies are not in favor of an association with cupper or zinc [START_REF] Gorell | Occupational exposures to metals as risk factors for Parkinson's disease[END_REF][START_REF] Lai | Occupational and environmental risk factors for Parkinson's disease[END_REF].

Alternatively, one ecological study showed higher PD incidence rates in US counties with high copper or manganese air concentrations [START_REF] Willis | Metal emissions and urban incident Parkinson disease: a community health study of Medicare beneficiaries by using geographic information systems[END_REF]. Finally, the median area of vineyards without designation of origin (2 ha, interquartile range (IQR)=0.6-8.3) is much smaller than for those with designation (12 ha, IQR=5.6-20.5). Smaller farms are less mechanized, and involve more applications with backpack sprayers (rather than with tractors), leading to greater exposure during pesticide preparation/spraying. In addition, according to the agricultural census, vineyards with designation of origin employed more full-time workers (median=1.7, IQR=1.4-2.2) than those without (median=0.9, IQR=0.6-1.3). Therefore, farmers in vineyards with designation of origin may be less exposed than those without, in particular if workers engage in pesticides applications. An association between pesticides expenditures in vineyards with designation of origin and PD may in fact exist but we were unable to identify it because we only included farmers and not farm workers.

There were no significant differences between men and women for any farming type, but sex-stratified analyses showed that the association with vineyards without designation of origin was restricted to men with a weaker non-significant association in women. The weaker association and lack of significance in women may have several possible explanations: first, PD incidence is lower in women than men and there is less variability in PD incidence across cantons in women than men (data not shown); second, women in this study represent a heterogeneous group that includes farmers and spouses of farmers; third, there are sexdifferences in exposure levels resulting from differences in agricultural tasks, with pesticides mainly prepared/sprayed by men [START_REF] Elbaz | Professional exposure to pesticides and Parkinson's disease[END_REF][START_REF] García | Pesticide exposure and women's health[END_REF][START_REF] Moisan | Association of Parkinson's Disease and Its Subtypes with Agricultural Pesticide Exposures in Men: A Case-Control Study in France[END_REF].

However, the difference between men and women is not large and not statistically significant and should not be over-interpreted.

Regarding age-stratified analyses, the association with vineyards without designation of origin was present only in older farmers. This result is consistent with a previous casecontrol study in farmers [START_REF] Elbaz | Professional exposure to pesticides and Parkinson's disease[END_REF], and an ecologic study in the general population (Kab et al., 2017b). Environmental factors are likely to play a stronger role for cases with later onset, while genetic susceptibility may play a stronger role for younger cases [START_REF] Nalls | Genetic risk and age in Parkinson's disease: Continuum not stratum[END_REF]. Longer exposure in older participants may also play a role, as well as differences in products or application methods. For instance, older persons are more likely to have been exposed to organochlorines or paraquat [START_REF] Elbaz | Professional exposure to pesticides and Parkinson's disease[END_REF][START_REF] Tanner | Rotenone, Paraquat and Parkinson's Disease[END_REF]. Again, the difference between the two age groups is not large and not statistically significant and should not be over-interpreted.

Our study's main limitation is its ecological design. To reduce ecologic bias, we used data aggregated in cantons which represent relatively small areas. In addition, contrary to other studies based on pesticides expenditures, our study is conducted among farmers, rather than the general population, who represent a more homogeneous group [START_REF] Barbeau | Ecogenetics of Parkinson's disease: prevalence and environmental aspects in rural areas[END_REF][START_REF] Cremonese | Pesticide consumption, central nervous system and cardiovascular congenital malformations in the South and Southeast region of Brazil[END_REF][START_REF] Froes Asmus | Positive correlation between pesticide sales and central nervous system and cardiovascular congenital abnormalities in Brazil[END_REF][START_REF] Parron | Association between environmental exposure to pesticides and neurodegenerative diseases[END_REF][START_REF] Ritz | Parkinson's disease mortality and pesticide exposure in California 1984-1994[END_REF]. We also adjusted for a marker of deprivation, smoking, and density of neurologists, with associations in the expected direction. Second, incident PD cases were identified through an algorithm, and were not examined in-person. However, the algorithm has previously been validated with 92.5% sensitivity and 86.4% specificity, and we corrected incidence rates for these estimates [START_REF] Moisan | Prediction model of Parkinson's disease using antiparkinsonian drug claims[END_REF]. Moreover, diagnostic misclassifications is unlikely to depend on the farming type. We were not able to collect clinical information on PD patients (e.g., cardinal signs, severity scales, non-motor symptoms) other than age at PD incidence and sex, and to examine the association between pesticides exposure and different disease phenotypes. Third, a minority of farmers may live and work in different cantons; this is unlikely to represent a major source of exposure misclassification because there is a strong spatial correlation for farming types since neighboring cantons usually have similar farming types (Supplementary Figure 3). Fourth, we were unable to account for migration, and assumed that individuals lived in the same cantons in 2000 and 2010-2015; this is unlikely to represent a major issue for several reasons. We previously showed that the annual rate of migration from one canton to another was small in the general population. In a previous study, we excluded PD cases who moved in the 5y preceding the first reimbursement of PD drugs and results remained similar (Kab et al., 2017b). Moreover, farmers are less mobile than the general population: in 2007, 6.1% of older farmers changed municipality of residence, compared to around 10% for other professional sectors [START_REF] Pistre | Géographies des groupes socioprofessionnels retraités en France métropolitaine : structures spatiales, migrations et trajectoires résidentielles Cahiers de démographie locale[END_REF]. Cantons being geographic areas larger than the municipality (150km² vs 15km²), this percentage is even lower. Finally, our analyses rely on incidence data and it is unlikely that PD patients moved more frequently than the general population before PD onset; therefore, this bias is likely to be non-differential and would bias associations towards the null. Fifth, our analyses are restricted to farmers, and we were unable to examine associations in workers, who include a wide range of occupations that cannot be distinguished using SNDS data. Sixth, the latency period between exposure assessment and PD incidence was quite short (10-15 years), because detailed data on pesticides expenditures were available starting on year 2000. However, summary data from previous years showed that, although pesticides expenditures increased between 1989 and 2000, the same distinctions between crops persisted over time. In addition, the geographic distribution of farming types generally remains stable, in particular for vineyards. In a previous study, we showed a similar distribution of farming types across the French territory in 1988 and 2000 (Kab et al., 2017b). Therefore, cantons with high pesticides expenditures are likely to remain the same over time.

Strengths of our study include its population-based and nationwide design and large size, as well as analysis of incidence rather than prevalence data. We allowed for a long delay between exposure and disease incidence to account for a latency period. Our analyses were adjusted for several potential confounders. We used agricultural data covering all types of farming. Pesticides expenditures, as a means of assessing exposure, are not subject to recall bias and allow to investigate dose-effect relationships. We used two complementary approaches to define pesticide expenditures. While the "regional" approach takes into account that pesticides use depends on regions, the "national" approach takes into account the effect of the farms' area on pesticides expenditures. Both approaches yielded consistent findings for vineyards without designation of origin.

PD incidence in French farmers was higher in cantons with higher pesticides expenditures for vineyards without designation of origin. This result suggests that pesticides used in these vineyards and/or agricultural practices may play a role in PD and that farmers in these farms should benefit from preventive measures aiming at reducing exposure. Additional studies are needed in these farmers to determine which specific products that they are exposed to and to define real-life exposure scenarios relevant for PD [START_REF] Tsatsakis | Toxicology for real-life risk simulation -Editorial preface to this special issue[END_REF]. Our study also highlights the importance of considering farming type in studies on pesticides and PD and the usefulness of pesticides expenditures for exposure assessment. Incidence rate ratios are plotted at the median of each quintile. Test of linear trend: p-values non-adjusted for multiple comparisons; q-values adjusted for multiple comparisons using a false discovery rate (FDR) approach. Incidence rate ratios are plotted at the median of each quintile. Test of linear trend: p-values non-adjusted for multiple comparisons; q-values adjusted for multiple comparisons using a false discovery rate (FDR) approach.

Figure 1 .

 1 Figure 1. Spatial distribution of annual regional pesticides expenditures for all farming types combined (total) and each farming type in French cantons (2000).

Figure 2 .

 2 Figure 2. Association of annual pesticides expenditures (1a. regional, 1b. national) with Parkinson's disease incidence in farmers from French cantons (2010-2015).

Figure 3 .

 3 Figure 3. Multivariable association of annual pesticides regional expenditures for nine farming types with Parkinson's disease incidence in farmers from French cantons (2010-2015).

Figure 4 .

 4 Figure 4. Multivariable association of annual pesticides national expenditures for nine farming types with Parkinson's disease incidence in farmers from French cantons (2010-2015).

Acknowledgements

The authors thank the Ministère chargé de l'agriculture et de l'alimentation.

Financial disclosures: This project was funded by an unrestricted grant from the Plan Ecophyto II, Agence française pour la biodiversité, Ministère de l'environnement. The authors did not receive any additional funding from any institution, including personal relationships, interests, grants, employment, affiliations, patents, inventions, honoraria, consultancies, royalties, stock options/ownership, or expert testimony for the last 12 months.

Author's contribution LP, FM and AE: designed the research; FM and AE: conducted the research; LP: performed statistical analysis and drafted the manuscript; FM and AE: supervised statistical analysis and the writing; LP, JS, LC, SK, FM and AE: contributed to the data interpretation and revised each draft for important intellectual content. All authors read and approved the final manuscript. AE had primary responsibility for the final content, he is the guarantor.

Conflict of interest:

The other authors declare no conflicts of interest. a We regressed pesticides expenditures (PE) per hectare for each type of farming on the average agricultural area of the farms with that type of farming (A, in hectares) (PE = Intercept + Slope × A). Positive slopes indicate that average pesticides expenditures per hectare for a given type of farming increase with the area of farms devoted to that type of farming, while negative coefficients indicate the opposite. * p< .05. 1 Including cereals, oilseed and protein plants, rice. 2 Including field crops, root crops, cotton, tobacco. 3 Including outdoor and under glass fresh vegetables, mushrooms. 4 Including outdoor and under glass flowers and ornemental plants. 5 Including quality wine with label. 6 Including wine other than quality, table grapes. 7 Including fruits, citrus fruits, nuts. 8 Including field crops and horticulture, field crops and permanent crops, field crops and vineyard, horticulture and permanent crops, mixed crops. 9 Including cattle rearing -specialist dairying; cattle rearing and fattening; cattle-dairying, rearing and fattening combined; sheep, goats and other grazing livestock; granivores (e.g. pigs, poultry); mixed livestock, mainly grazing livestock; mixed livestock, mainly granivores; field crops-grazing livestock combined; various crops and livestock combined.


Sen-Jiang Yu

Guillaume Parry

Christophe Coupeau
email: christophe.coupeau@univ-poitiers.fr

Lingwei Li
email: lingwei@hdu.edu.cn

Pressure-induced transition from wavy circular to ring-shaped buckles

Keywords: Thin film, Circular blister, Ring-shaped buckle, Delamination, Stress

We report on buckling structures observed on tantalum films deposited by sputtering on silicon wafers. It is shown that, above a critical diameter, the circular blisters evolve to ring-shaped buckles, whatever the smooth or undulating type of their edges. The experimental results have been compared to finite element simulations. In particular, the polygonal collapsed part at the center of the buckles can be well understood by taking into account the pressure mismatch between the inside and outside parts of the buckles.

Introduction

Thin films and coatings have found widespread technological applications, for instance in optics, microelectronics or microfluidics. Residual stresses are of prime importance to ensure the mechanical stability of the coated substrates and further their lifetime. These stresses may result from different origins, such as the deposition process of the filmitself, the lattice mismatch between the film and its associated substrate, the discrepancy between the thermal expansion coefficients of the film and the substrate, an external mechanical loading, implantation/irradiation processes or environmental parameters like moisture. If the stress is compressive and high enough and if the interface adhesion is comparatively weak, the film may delaminate from its substrate and release the stored elastic energy by buckling, leading to various complex morphologies among which elementary buckles are the straight-sided (SS) [START_REF] Audoly | Secondary buckling patterns of a thin plate under in-plane compression[END_REF]Coupeau et al., Pundt et al., 2003;2004;Yu et al., Cordill et al. 2010;[START_REF] Lu | In situ study of cracking and buckling of chromium films on PET substrates[END_REF]2014;[START_REF] Kleinbichler | Scratch induced thin film buckling for quantitative adhesion measurements[END_REF][START_REF] Coupeau | Interacting straight-sided buckles: an enhanced attraction by substrate elasticity[END_REF]), the circular buckles (CB) [START_REF] Gioia | Delamination of compressed thin films[END_REF][START_REF] Wang | Measurements and analysis of buckling and buckle propagation in compressed oxyde layers on superalloy substrates[END_REF]Moon et al., 2002a;[START_REF] Moon | Buckle delamination on patterned substrates[END_REF][START_REF] Mcdonald | Femtosecond laser induced delamination and blister formation in thermal oxide films on silicon (100)[END_REF][START_REF] Lamri | Estimation of the stress relief induced in CrN thin films by buckling[END_REF][START_REF] Kuznetsov | Hydrogen induced blistering mechanisms in thin coatings[END_REF][START_REF] Chen | Ultra short laser driven stable buckling of blisters in chirped mirror[END_REF][START_REF] Eren | Hydrogen-induced buckling of gold films[END_REF][START_REF] Guo | High temperature brittle film adhesion measured from annealing induced circular blisters[END_REF] or the telephone cord (TC) structures [START_REF] Yu | Buckle formation in vacuum-deposited thin films[END_REF]Moon et al., 2002a;[START_REF] Volinsky | Experiments with in-situ thin film telephone cord buckling delamination propagation[END_REF][START_REF] Cordill | Adhesion measurements using telephone cord buckles[END_REF][START_REF] Abdallah | Buckle morphologt of compressed inorganic thin layers on a polymer substrate[END_REF][START_REF] Abdallah | The effect of moisture on buckle delamination of thin inorganic layers on a polymer substrate[END_REF][START_REF] Peponas | On the post-contamination effect on the delamination of sputtered amorphous carbon nitride films[END_REF][START_REF] Zhang | Telephon cord buckles in wedge-shaped Fe films sputtering deposited on glass substrates[END_REF][START_REF] Grachev | High-throughput optimization of adhesion in multilayers by superlayers gradients[END_REF][START_REF] Faou | How does adhesion induce the formation of telephone cord buckles[END_REF][START_REF] Xiao | Morphological selections and dynamical evolutions of buckling patterns in SiAlNx films: from straight-sided to telephone cord or bubble structures[END_REF][START_REF] Marot | ITER first mirror mock-ups exposed in Magnum-PSI[END_REF][START_REF] Ni | The shape of telephone cord blisters[END_REF]. Note that the TC buckles are the most frequently observed due to the isotropic character of the compressive stresses in most of thin films and coatings [START_REF] Parry | Stability diagram of unilateral buckling patterns of strip-delaminated films[END_REF]. On the other hand, the circular blister usually forms at the early stage of buckling, for instance from film imperfections (Moon et al., 2002b), triggered by indentation [START_REF] Volinsky | Interfacial toughness measurements for thin films on substrates[END_REF] or induced by humidity [START_REF] Moller | Observation of boron nitride thin film delamination due to humidity[END_REF][START_REF] Waters | Stress and moisture effects on thin film buckling delamination[END_REF]. During its growth, its circular edge is destabilized and forms as a result a petal-like pattern all round its circumference [START_REF] Argon | Intrinsic Toughness of Interfaces[END_REF]Hutchinson et al., 1992a;[START_REF] Lee | Wrinkling evolution of a growing bubble: the wonders of petal-like patterns in amorphous silicon membranes[END_REF][START_REF] Yan | Spontaneous wrinkling pattern of a constrained thin film membrane[END_REF]. In particular, it was found by finite elements simulations that the period of the undulating edge decreases with the increasing buckle diameter and with the decreasing film thickness. The axisymmetric growth of the circular blister is thus broken and the petals will gradually evolve to TC buckles, finger branches or complete delamination of the film from its substrate [START_REF] Faou | From telephone cords to branched buckles: a phase diagram[END_REF]. Recently, another fascinating buckles, called ring-shaped structure, have been reported in two independent works. Zhou et al. observed ring-shaped and arc-shaped buckles in cobalt films deposited on glass substrates, which are attributed to the coffee ring effect by evaporation of silicone oil [START_REF] Zhou | Ring-shaped buckles in metal films induced by evaporation of micro-scaled silicone oil droplets[END_REF]. On the other hand, Hamade et al. observed donut-and croissantlike buckles in gold films deposited on silicon substrates. They attributed such buckles to the coupling effect of the external/internal pressure mismatch and the plastic folding of the film [START_REF] Hamade | Effect of plasticity and atmospheric pressure on the formation of donut-and croissant-like buckles[END_REF]. However, many questions are still open on these specific buckling structures. For instance, the observed ring-shaped buckles exhibit smooth edges [START_REF] Hamade | Effect of plasticity and atmospheric pressure on the formation of donut-and croissant-like buckles[END_REF][START_REF] Zhou | Ring-shaped buckles in metal films induced by evaporation of micro-scaled silicone oil droplets[END_REF] while larger circular blisters usually have wavy edges (Hutchinson et al., 1992a). The dynamic process of the formation of ring-shaped buckles is also unrevealed up to now.

In this paper, we report on buckling structures experimentally observed by optical and atomic force microscopies on tantalum films deposited by a sputtering method on silicon wafers. The spontaneous transition from circular to ring-shaped buckles is clearly evidenced experimentally, whatever the edge type of the circular blisters, smooth or wavy. The experimental observations are then compared to finite elements method simulations in order to have a better understanding of the physical parameters controlling this transition.

Experimental results

The tantalum films were deposited on silicon wafers by direct current magnetron sputtering technique at room temperature. The silicon wafers with 10×10 mm 2 size were washed in ethyl alcohol for 10 min and then in deionized water for another 10 min with ultrasound. The tantalum target was 60 mm in diameter and 3 mm in thickness. The distance from target to substrate was about 80 mm. The base vacuum was prior to 2×10 -4 Pa and then pure argon gas was filled into the chamber with the pressure of 0.5 Pa. The sputtering power was 50 W and the deposition time was 8 minutes. The film thickness, measured by a focused ion beam (FIB 200) and a stylus profiler (Dektak XT, Bruker), was estimated to h = 240 nm. The buckle morphologies were investigated by optical microscopy (Leica DMLM) and scanning electron microscopy (SEM, Zeiss Supra 55).

The 3D structures of buckles were determined by atomic force microscopy (AFM, Dimension 3100, Veeco) operated in tapping mode under atmospheric conditions.

The surfaces of the as-prepared Ta thin films were initially smooth but buckling structures spontaneously form under ambient conditions while time is running (sometimes several months after), as shown in Fig. 1a. The frequently observed straight-sided and telephone cord buckles have been extensively studied in the past decades. We focused our attention in the following on the axi-symmetrical ones, especially the ring-shaped structures. The typical blisters investigated by optical microcopy are presented in Fig. 2, for various increasing diameters D. Circular blisters are observed for small diameters (Fig. 2a), lower than approximately D ring ~70 µm, up to which ring-shaped buckles are observed (Fig. 2b). Note that circular blisters and ringshaped buckles are both observed in our experiment for D ranging from 70 to 110 μm.

In addition, the circular blisters exhibit smooth edges when their diameter is small while wavy edges may be observed (Fig. 2c) above a diameter higher than approximately D wavy ~40 µm, leading to a petal-like pattern. Note again that circular blisters with and without edge instability are observed in our experiment in a specific D domain ranging from 40 to 60 μm. Some non-symmetrical (croissant-like) blisters with undulating edges are also sometimes observed (see Fig. 2d-f). At higher diameters, the two phenomena (undulating borders and pushing down in the middle) are combined leading to wavy ring-shaped buckles (see Fig. 2g-i). Finally, a spalling of the Ta film occurs for diameters higher than approximately D spalling ~160 µm. It has been evidenced (not shown here for convenience) by a focused ion beam milling and scanning electron microscopy investigations that the delamination occurs at the interface between the Ta film and the silicon substrate.

The ring-shaped buckles were already reported by the past and result from a collapse of the thin film at their center, down to the substrate. It was demonstrated by finite elements method (FEM) simulations that the outside atmospheric pressure and plasticity at their circumference are the key parameters explaining their formations [START_REF] Hamade | Effect of plasticity and atmospheric pressure on the formation of donut-and croissant-like buckles[END_REF]. An experimental proof of this spontaneous morphological transition is shown in Fig. 3. It is noticed that the edge instability is unchanged during the collapse process. Note also that some buckles are sometimes superimposed one on top of the other, for both the circular and the ring-shaped blisters (see Fig. 1b). It may be interpreted as the signature of plasticity [START_REF] Coupeau | Buckling pattern with rings: an evidence of plastic damage in thin films[END_REF][START_REF] Cordill | The effects of plasticity on adhesion of hard films on ductile interlayers[END_REF] occurring during the buckling-induced delamination process in the Ta films. From a kinetic point of view, the latter case also suggests that, surprisingly, a circular blister may grow by radial delamination even if the edge instabilities already developed at their circumference before. Wavy ring-shaped buckles were almost never mentioned in the literature; one can note the work of [START_REF] Lee | Wrinkling evolution of a growing bubble: the wonders of petal-like patterns in amorphous silicon membranes[END_REF] who reported the collapse of 100 nm thick amorphous Si pressurized blisters. In this work, the gaz and liquid initially inside the circular blisters had diffused out during 24h leading to their collapse to wavy ring-shape blisters. Finally, in the case of ring-shaped buckles with smooth edges previously reported in the literature [START_REF] Hamade | Effect of plasticity and atmospheric pressure on the formation of donut-and croissant-like buckles[END_REF][START_REF] Zhou | Ring-shaped buckles in metal films induced by evaporation of micro-scaled silicone oil droplets[END_REF], the middle internal part pressed down to the substrate was observed to be quite circular.

Surprisingly, the wavy ring-shaped buckles exhibit a polygonal area at their middle, as shown in Fig. 2g-i.

Circular blisters without wavy edges have been studied by using the Föppl-von Karman equations in the framework of the continuum elastic theory. In the elastic buckling model, the blister is treated as a clamped circular elastic plate submitted to an in-plane isotropic compressive stress 𝜎 0 . No effect of the substrate is here considered, assumed as elastically hard compared to the film. In this case, the critical stress c for buckling to occur is given by [START_REF] Yu | Buckle formation in vacuum-deposited thin films[END_REF][START_REF] Evans | On the mechanics of delamination and spalling in compressed films[END_REF]Hutchinson et al., 1992a;Hutchinson et al., 1992b;[START_REF] Lamri | Estimation of the stress relief induced in CrN thin films by buckling[END_REF][START_REF] Chen | Ultra short laser driven stable buckling of blisters in chirped mirror[END_REF][START_REF] Eren | Hydrogen-induced buckling of gold films[END_REF][START_REF] Guo | High temperature brittle film adhesion measured from annealing induced circular blisters[END_REF]:

𝜎 𝑐 = 1.2235 𝐸 1-𝜈 2 ( 2ℎ 𝐷 ) 2 , (1)
with E and  , the elastic modulus and Poisson's ratio of the film, respectively.

The maximum deflection  can be expressed by (Hutchinson et al., 1992a;Hutchinson et al., 1992b;[START_REF] Chen | Ultra short laser driven stable buckling of blisters in chirped mirror[END_REF][START_REF] Guo | High temperature brittle film adhesion measured from annealing induced circular blisters[END_REF]:

𝛿/ℎ = 1 𝑐 1 √ 𝜎 0 𝜎 𝑐 -1, (2)
with c1 = 0.2473(1+)+0.2231(1+  2 ). For ETa = 186 GPa and Ta = 0.35, it leads to c1 ~ 0.58. As h << , 𝜎 0 can be expressed from Eqs. ( 1) and ( 2) by:

𝜎 0 = 1.2235 𝑐 1 𝐸 1-𝜈 2 ( 𝛿 𝐷 ) 2 . ( 3
)
The morphological parameters, i.e. the maximum deflection  and the diameter D, have been determined by AFM. The /D ratio has been reported in Fig. 4a for various increasing D. It is shown that /D does not significantly depend on the blister size, allowing to estimate the internal stress to be constant and approximately equal to  = 1.4 GPa in compression.

The petal number N has been reported in Fig. 4b as a function of the diameter D, for both the circular and the ring-shaped buckles. For the circular blisters, it is shown that N increases step-by-step with the increase of D. Similar trends have been experimentally observed by the past, for instance on mica films (Hutchinson et al., 1992a), boron nitride [START_REF] Moller | Observation of boron nitride thin film delamination due to humidity[END_REF] or amorphous silicon films [START_REF] Lee | Wrinkling evolution of a growing bubble: the wonders of petal-like patterns in amorphous silicon membranes[END_REF][START_REF] Yan | Spontaneous wrinkling pattern of a constrained thin film membrane[END_REF]. In the case of buckling-driven delamination (Hutchinson et al., 1992a), such an incremental increase of N was predicted in the framework of an elastic modeling taking into account a sinusoidal perturbation at the circular crack front (Hutchinson et al., 1992a). In [START_REF] Lee | Wrinkling evolution of a growing bubble: the wonders of petal-like patterns in amorphous silicon membranes[END_REF], the loading configuration of the blisters was also different from ours, as the deflection was predominantly caused by pressure due to the underlying gaseous and liquid droplets inside the blisters rather than internal stresses. This pressure caused membrane tension in the film, the wavelength of the wrinkles forming around the blister being then computed from a minimization of the bending transverse to the folds and the stretching along their length. In contrast, in our configuration, the buckling is clearly due to compressive internal stresses and the pressure mismatch is reversed, i.e. a smaller pressure underneath the blister compared to the outside room pressure. In [START_REF] Yan | Spontaneous wrinkling pattern of a constrained thin film membrane[END_REF], model of circular plate submitted to compressive stress is used, but the difference of pressure underneath and above the blister is not accounted for. One consequence is that the whole family of ring-shaped blister is not present among the computed solutions. It is however worth noting that some of their numerical solutions are close to ours when we will consider small pressure mismatches in our FEM simulations in the following.

Once the circular blisters evolve to ring-shaped buckles, N still increases with the increasing D, even if the incremental increase is no more clearly distinguishable. It suggests that the wavy edge destabilization does not depend on the shape of the buckles, circular or ring-shaped. The wavy blisters have been also characterized by the average period  of the undulation along their circumferences defined as 𝜆 = 𝜋𝐷 𝑁 ⁄ .

 presented in Fig. 4c as a function of D, for both the circular and the ring-shaped buckles. Two different behaviors are evidenced:  steadily decreases for small diameters while it is almost constant for large diameters above 80 µm. The transition seems to be related to the type of buckles, the first (resp. the second) regime being associated with the circular blisters (resp. the ring-shaped buckles). It strongly suggests that the edge destabilization occurring around circular blisters when the diameter is increased does not follow similar mechanisms once the circular blisters have evolved to ring-shaped buckles.

FEM simulations

The simulation box, depicted in Fig. 5, has the shape of a square with edge length L=3D, where D is the circular blister diameter. In order to describe the effect of pressure on the post-buckling regime of the circular blister, a geometrically nonlinear plate model is used in order to describe the thin film. The substrate surface is represented by a rigid plane forbidding the displacement of the plate in the lower half-space (unilateral contact condition). Hence, the elastic deformation of the substrate is not considered.

The whole film, including the circular domain of diameter D where the blister is going to develop, is originally in a planar state with its bottom plane located at the substrate surface. The direction normal to the substrate surface is denoted by (Oz). The displacement components along the axes parallel to 𝑒 ⃗ 𝑥 , 𝑒 ⃗ 𝑦 , and 𝑒 ⃗ 𝑧 are respectively denoted u, v, and w, for any point M(x,y) of the midplane of the plate. The following boundary conditions are imposed: whatever M outside of the disk of diameter D,

u(M)=v(M)=w(M)=0
. This region will be mentioned as 'the bonded part' of the film in the following. In contrast, the region of the disk will be called 'the debonded part'. A rigid contact definition is used between the bottom of the circular patch of plate (free film) and the underneath rigid plane (substrate).

The various buckling patterns are characterized by large values of the out-ofplane displacement component w, such that the calculations must be carried out within the framework of large displacement hypothesis using the Green-Lagrange strain tensor.

The plate is submitted to two successive loading steps:

•

Step 1: Application of the internal stress.

A thermal dilatation strain ε 0 (ε 0 >0) is imposed to the film. As the displacement is blocked in the bonded part of the film, the eigenstrain ε0 generates a compressive stress in the film (because the total strain, which is the sum of the thermal and elastic strains, vanishes), such that σxx=σyy=-E.ε0/(1-ν)≡-σ0 (with σ0>0) and σxy=0. This stress state is generated in the bonded part of the film, but also in the debonded part of the film (the circular patch of diameter D) as long as it is remaining planar. Note that the eigenstrain is maintained during the next step.

•

Step 2: Application of the pressure.

A uniform pressure p is applied, onto the upper surface of the buckled film. The equilibrium can be dramatically modified by this loading, leading to secondary buckling equilibria shapes quite different from the original circular shape in the postcritical regime.

In order to carry out these nonlinear calculations, finite elements simulations have been performed using the software ABAQUS. Quadrilateral shell elements have been used to mesh the film. The element sizes have been chosen in such a way that 40 elements are considered into the film along the diameter. A quasi-static analysis is carried out using the explicit solver. As a matter of fact, due to the presence of two sources of non-linearities (contact and large displacements), an explicit algorithm is preferred to an implicit one even if the analysis is quasi-static. This approach is commonly adopted, imposing for parameters to be chosen carefully so that the kinetic energy always remains very small compared to the strain energy in the elements.

Our study was focused in the following to the case of a Ta film of thickness h = 240 nm, with E = 186 GPa and v = 0.35. For convenience, D was first fixed to 120 µm.

The stable shape of the circular plate is shown in Fig. 6, as a function of both the internal compressive stress 0 and the pressure mismatch p between the outside and inside parts of the buckle. The case p=0 corresponds to the case of an atmospheric pressure inside (i.e. a non-airtight buckle). In this case, only wavy buckles are energetically stable. As described previously, the number of petals N gradually increases with the increase of 0. Increasing p leads to the destabilization of the wavy buckles. For high 0 values, a ring-shaped buckle is observed. The middle part of the circular plate is now in contact with its substrate and adopts a polygonal shape, whose number of sides increases with p. For instance, at 0 = 2.5 GPa, a triangle, a square and finally a pentagon is successively observed for p = 1, 2 and 4 atm respectively. In addition, the type of polygons significantly modifies the shape of the wavy borders. Some 'mexicanhat' undulations are thus observed for triangles or squares. For low stress values, non axi-symmetrical shapes are evidenced. Among the various complex structures, one can note the horseshoe-like (see p = 1 atm and 0 ≤ 1.0 GPa) and the bone-like (see p ≥ 2 atm and 0 = 0.5 GPa) patterns.

It was experimentally demonstrated by the past that a pressure may exist inside the circular blisters, for instance induced by a gaseous environment [START_REF] Parry | About the internal pressure in cavities derived from implantation-induced blistering in semiconductors[END_REF] Some additional experimental results are shown in Fig. 8. The investigations by AFM were carried out on Mo 200 nm thick films deposited by a sputtering technique on Si wafers. After implantation at room temperature with 400 keV Ar ions and for a fluence of around 10 15 ions/cm 2 , the Mo films exhibit circular damage homogeneously dispatched all over the whole sample [START_REF] Goudeau | Ion irradiation effects on the mechanical stability of compressed metallic[END_REF]. Similar buckles were also observed on Au 100 nm thick films on Si wafers after H implantations [START_REF] Eren | Hydrogen-induced buckling of gold films[END_REF]. These circular structures are quite complex but really similar to the ones shown in Fig. 6 (upper left side of the mapping). In this experimental case, D/h ≈ 25 and the initial stresses (i.e. before implantation) were estimated by curvature Stoney method to be approximately 0 = 2 GPa in compression, leading to 0/E = 7.10 -3 . As these structures are energetically stable only for very low 0/E values (see Fig. 7), our numerical results strongly support the idea that the implantation process may also result in a strong decrease of the internal stresses in the films [START_REF] Goudeau | Ion irradiation effects on the mechanical stability of compressed metallic[END_REF].

Conclusions

Circular ring-shaped buckles with undulating edges have been experimentally

observed by optical, atomic force and scanning electron microscopy on Ta 240 nm thick films deposited on silicon wafers. It is shown that these specific buckles (1) are only evidenced for high diameters and (2) exhibit a polygonal area in their middle, those number of sides increases with the increasing diameter. Finite elements simulations confirm that wavy ring-shaped buckles are only energetically favorable above a critical diameter and result from the pressure mismatch between the inside and outside parts of the buckles. An internal stress threshold has been evidenced, below which some more complex non-axi-symmetrical buckles are observed. At a given diameter, the increase of stress decreases the polygonal character (number of sides) of the middle part pressed down to the substrate. Contrary to what was previously shown on smooth (i.e. without edge undulations) circular blisters, plastic events were evidenced by finite element simulations not to be a key-parameter for wavy ring-shaped buckles to appear, even if sometimes experimentally observed. It is believed that the edge undulations play a

Figure captions Figure 1 .

 captions1 Figure captions

Figure 2 .

 2 Figure 2. Characteristic buckles for increasing diameter D. (a) Circular buckle with smooth edges (b) Ring-shaped buckle with smooth edges (c) Circular buckles with wavy edges (d) Bone-like buckles (e,f) horseshoe-like buckles (g-i) Ring-shaped buckles with wavy edges.

Figure 3 .

 3 Figure 3. Spontaneous transition from (a) a wavy circular buckle to (b) a wavy ringshaped buckle. The time interval between is 270 days. The transition is characterized by a collapse of the film at the center of the buckle, down to the substrate.

Figure 4 .

 4 Figure 4. Experimental morphological parameters of the buckles. (a) normalized maximum deflection /D, (b) petal number N and (c) period of the edge undulations , as a function of D.

Figure 5 .

 5 Figure 5. FEM configuration. z is the out-of-plane displacement of the film. D is the diameter of the fixed debonded area between the film and the elastically hard substrate.The size of the box is L x =L y =3D.

Figure 6 .

 6 Figure 6. FEM morphological mapping of a circular plate as a function of the internal stress 0 and the pressure mismatch p, for h = 240 nm, D = 120 µm, E = 186 GPa and  = 0.35.

Figure 7 .

 7 Figure 7. FEM morphological mapping of a circular plate as a function of normalized stress 0/E and normalized diameter D/h, for p = 1 atm and for  = 0.35.

Figure 8 .

 8 Figure 8. Damage circular structures on Mo 200 nm thick films implanted by Ar ions (AFM investigation).

  FIGURE 1

  FIGURE 2

Acknowledgments.

This work was partially supported by the National Natural Science Foundation of China (Grant No. 91963123), the Ten Thousand Talents Plan of Zhejiang Province of China (No. 2018R52003), and the Fundamental Research Funds for the Provincial University of Zhejiang (No. GK199900X022).

 [START_REF] Coupeau | Kinetic evolution of blistering in hydrogen-implanted silicon[END_REF]or associated with liquid droplets [START_REF] Lee | Wrinkling evolution of a growing bubble: the wonders of petal-like patterns in amorphous silicon membranes[END_REF], so that p<0.

A low vacuum pressure may also exist inside closed-airtight buckles [START_REF] Coupeau | Evidence of vacuum between buckled films and their substrates[END_REF]. From an experimental point of view, p may thus also range from 0 to 1. In the following, we restricted our study to the ideal case of p = 1 atm, which means vacuum inside and atmospheric outside. The morphological mapping of the circular plate is shown in Fig. 7, as a function of the normalized stress 0/E and the normalized diameter D/h. Circular buckles are still present, but only for low 0 and low D. As already mentioned previously, increasing 0 results in the destabilization of the blister boundaries. No significant pressure effect is consequently observed for low D, i.e. no collapse of the blister. When D is increased, the wavy buckles stay energetically favorable, but only for high 0 values. At a given stress, the number of petals also increases with increasing D or decreasing h. This behavior is similar to what has been experimentally observed on amorphous Si films, even if it was for pressurized blisters, i.e. for p<0 [START_REF] Lee | Wrinkling evolution of a growing bubble: the wonders of petal-like patterns in amorphous silicon membranes[END_REF]. The stability domain of the wavy ring-shaped buckles is observed for high diameters, whatever the normalized stress ranging here from approximately 5.10 -3 to 13.10 -3 . As experimentally evidenced, the side number of the central polygon decreases with the increasing stress at a given D (see the line at D/h=800). Finally, an intermediate domain is observed at low stresses and medium diameters, for which the bone-like and the horseshoe-like patterns are stable. Note here that the horseshoe-like buckle may exhibit both smooth (see 0/E = 2.7 10 -3 and D/h = 500) and wavy (see 0/E = 8.1 10 -3 and D/h = 450) edges.

The internal stresses in the Ta films were estimated to be 1.4 GPa in compression, which leads to  0 /E = 7.10 -3 . It is expected from Fig. 7 the successive observations of wavy buckles, horseshoe-like and ring-shaped buckles while the diameter D is increased. In addition, the polygon in the middle of the ring-shaped should increase its number of sides. These numerical results are in pretty good agreements with our experimental optical investigations for which the normalized diameters D/h are ranging approximately from 150 to 650 (see Fig. 4b). similar role to stabilize the ring-shaped buckles for high diameters.