Nina Kreuzberger
email: nina.keuzberger@gmail.com

Basile Chaix
email: basile.chaix@iplesp.upmc.fr

Julie Méline
email: julie.meline@irsn.fr

Tarik El

Transport-Related Noise Exposure in a Representative Sample of Île-de-France Residents: A Data-Enrichment Approach

1

Transport-Related Noise Exposure in a Representative Sample of Île-de-France

Residents: A Data-Enrichment Approach

INTRODUCTION

Noise is an environmental stressor which has been linked to various adverse health outcomes [START_REF] Babisch | Cardiovascular effects of noise[END_REF] such as hearing loss [START_REF] Lie | Occupational noise exposure and hearing: a systematic review[END_REF], stress hormone imbalance [START_REF] Selander | Saliva cortisol and exposure to aircraft noise in six European countries[END_REF], hypertension [START_REF] Van Kempen | The quantitative relationship between road traffic noise and hypertension: a meta-analysis[END_REF], sleep disturbance [START_REF] Hume | Effects of environmental noise on sleep[END_REF], long-term elevated risk of stroke [START_REF] Halonen | Road traffic noise is associated with increased cardiovascular morbidity and mortality and all-cause mortality in London[END_REF] and diabetes [START_REF] Dzhambov | Long-term noise exposure and the risk for type 2 diabetes: a meta-analysis[END_REF]. To minimize the negative impact of noise on health, daily average levels below 50-55 dB(A) are recommended for the general population (European Environment Agency, 2010).

Many of the associations between noise and health were either assessed in occupational settings [START_REF] Skogstad | Systematic review of the cardiovascular effects of occupational noise[END_REF] or were based on residential assessments of outdoor noise from modeled noise exposure of selected sources, typically road traffic, railway systems, and aircrafts [START_REF] Sørensen | Road traffic noise and incident myocardial infarction: a prospective cohort study[END_REF][START_REF] Floud | Exposure to aircraft and road traffic noise and associations with heart disease and stroke in six European countries: a cross-sectional study[END_REF]. However, noise exposure is not limited to a unique source or a single environment, as people move between places for activities. Therefore, stationary assessment might not accurately reflect personal noise exposure, in particular during the day.

Recent studies took the movement between different microenvironments into account and described personal exposure by following individuals continuously with a noise dosimeter (Taimisto et al., 2013[START_REF] Kraus | Individual daytime noise exposure in different microenvironments[END_REF][START_REF] Neitzel | Noise levels associated with New York City's mass transit systems[END_REF]. A study done by [START_REF] Kraus | Individual daytime noise exposure in different microenvironments[END_REF] showed that one of the environments with high noise levels was traffic (mean equivalent sound levels (L Aeq ) between 74.0 and 78.3 dB(A) depending on the transport mode. The average values during transport exceeded the noise level of 70 dB(A) which was established for prevention of hearing loss, indicating room for improvements in the protection of the general population during transport in metropoles. More extensive information on the intensity, duration, and frequency of exposure to noise in a variety of settings would be needed to estimate average daily exposures of a population and evaluate the impact that different scenarios of intervention may have. Unfortunately, studies that deploy noise dosimeters and thus offer very precise information on noise exposure over multiple environments usually result in small sample sizes due to high costs and work-load in data collection and analysis.

To circumvent the limitations of both large-sample residential noise studies based on modelled maps and small studies based on noise dosimeters, the current study proposes a dataenrichment approach to estimate noise levels for a large representative sample from a smaller study sample of the same background population with available noise dosimeter data. A similar approach has been successfully applied to physical activity during transportation by [START_REF] Brondeel | Associations of socioeconomic status with transportrelated physical activity: combining a household travel survey and accelerometer data using random forests[END_REF]. The objectives of the present study were a) to describe personal noise exposure during daily trips with different transport modes in the Île-de-France region, b) to specify a model that predicts personal noise exposure in the dosimeter-based RECORD MultiSensor study, c) to cross-validate this model with a train-test set procedure and d) to apply the developed and validated model to a larger, representative dataset of the same background population (Enquête Globale Transport -EGT) in order to estimate transport-related noise exposure of Île-de-France residents.

MATERIALS AND METHOD

RECORD MultiSensor Study

Sample

As described elsewhere [START_REF] Chaix | Cohort profile: residential and non-residential environments, individual activity spaces and cardiovascular risk factors and diseases -the RECORD cohort study[END_REF], the participants of the RECORD study were recruited in 2007-2008 during free preventative health checkups offered by the French National Health Insurance System for Salaried Workers (CNAMTS) at four different sites in the Île-de-France region affiliated with the IPC medical Center. The Île-de-France region is the most populated of the 18 regions in France and contains the city of Paris. Inclusion criteria were a) being born between 1928 and 1979, b) residing in one of 112 a priori selected municipalities, and c) being able to complete the questionnaires of the study in French with minimal help. The same participants were followed up and new participants were invited in a second wave of the RECORD study (2011)(2012). During this second wave, 286 participants were invited to participate in the RECORD MultiSensor study from September 2013 to June 2015. Written informed consent was obtained from all participants. The RECORD MultiSensor study was approved by the French Data Protection Authority.

Data collection and processing

For the RECORD study, sociodemographic variables were obtained during the health checkup where participants filled in the IPC medical questionnaire and the RECORD questionnaire.

Household income needed to be recoded from a categorical to a continuous variable to be comparable with the EGT income variable. Educational level was summarized in three categories (No diploma of secondary education, diploma of secondary or lower tertiary education, diploma of higher tertiary education). The location of residence was indicated as inner city (Paris), inner suburbs or outer suburbs.

During the MultiSensor study, the participants carried several sensors (wearable class II dosimeter Wed007, ACOEM; GT3X+ accelerometer, ActiGraph; and BT-Q1000XT GPS receiver, QStarz) from day of inclusion up to day eight. Measurements from day one, 03:00 am up to day eight, 03:00 am were used for analysis. The GPS data of each participant was automatically pre-processed in order to identify visited places and start and end time of each trip stage [START_REF] Wolf | Eighty weeks of Global Positioning System traces: approaches to enriching trip information[END_REF], which is the portion of a trip undertaken with a single transportation mode. These pre-processed GPS tracks were consolidated during a phone mobility survey with the participants, resulting in a detailed timetable of visits at activity places and trips segmented into trip stages for the 7 days of observation, as described in more detail in [START_REF] Brondeel | Associations of socioeconomic status with transportrelated physical activity: combining a household travel survey and accelerometer data using random forests[END_REF] and [START_REF] Chaix | Active transportation and public transportation use to achieve physical activity recommendations? A combined GPS, accelerometer, and mobility survey study[END_REF].

Participants were instructed to wear the dosimeter at their belt and the microphone close to the ear, and to charge the device during night. Noise was measured continuously as Aweighted equivalent sound level (L Aeq,1s ) per second in a range of 40 to 120 dB(A). All L Aeq,1s values of a trip stage were extracted and summarized average L Aeq which is defined as follows: , = 10 log ∑ 10

Where:

L Aeq,T = Averaged equivalent noise level Li Aeq = Equivalent noise level for each second n = The total number of one second intervals from i to n per trip stage

In total, 78 participants of the MultiSensor study carried all devices necessary for inclusion in the prediction model (i.e., the noise dosimeter). However, observations of one participant were excluded due to dosimeter failure.

Global Transport Survey

The global transport survey (EGT; STIF -OMNIL -DRIEA, 2012) is a household survey investigating travel behavior in the Île-de-France region every ten years to assess transport usage in the region, with the latest available data from 2010. Each member of randomly selected households was interviewed face-to-face with regard to all trips performed on the day preceding the interview, resulting in 42,529 surveyed persons. Trips with multiple transport modes were separated into trip stages. The locations of the start and end points of each trip were defined within a grid with a spatial resolution of 100 m x 100 m squares, hereafter called tiles. For the current analysis, the age range was limited to the age range of the participants of the RECORD study who carried noise dosimeters (34-74 years old at the date of investigation), resulting in a sample of 18,929 out of 35,511 participants with trips during the past day. A comparison of demographics of the two samples can be found in Table 1. The mean age in the EGT sample retained for the analysis was 51.6 years (sd = 10.9). The RECORD MultiSensor study included relatively more men, more people with higher education and more people living in intramural Paris and the inner suburbs.

Noise map

To comply with the Environmental Noise Directive, the non-governmental organization Bruitparif is responsible for integrating modelled noise databases of Île-de-France municipalities.

A noise map for the years 2007 to 2011 was constructed to represent the yearly averaged indicator for day, evening and night sound levels (L den ) per transport-related noise source (road, railway and air traffic), starting at 55 dB(A) in classes of 5 dB(A). Additionally, the original noise layers were gathered and processed to obtain a map that covers the noise range between 30-80 dB(A) [START_REF] Méline | Road, rail, and air transportation noise in residential and workplace neighborhoods and blood pressure (RECORD Study)[END_REF][START_REF] Méline | Transportation noise and annoyance related to road traffic in the French RECORD study[END_REF].

The three traffic source layers were combined to produce one integrative noise layer which was used to compute yearly averages of noise levels at the start and end location of each trip stage at a resolution of 100 m x 100 m tiles in both the RECORD MultiSensor and the EGT studies. ArcMap 10.5 Geographic Information System (ESRI, 2016) and ArcGIS python scripts (Python version 3.4) were used to intersect the required tiles with the polygons of the final noise layer. The process is illustrated in Supplemental material A. For each tile, the mean and quartiles of noise level and the percentage of surface covered by noise levels equal to or higher than 75 dB(A) were calculated using the R software, Version 3.3.2 (R Core Team, 2016). These indicators are hereafter referred to as noise map predictors.

Statistical analysis

The 77 RECORD MultiSensor study participants considered in the present study undertook 2537 trips consisting of 4365 trip stages. After exclusion of trip stages that used rare transport modes (e.g., skateboard), crossed or were out of the Île-de-France department border, missed more than 50% of one-second noise L Aeq values or lasted for less than one minute, 3729 trip stages remained in the dataset for analysis.

To ensure consistency with the literature and the Environmental Noise Directive, L Aeq,T values were used as the outcome for the prediction models per transport mode. A multilevel model (MLM) was specified to predict trip stage level personal noise exposure from trip stage variables. A random intercept was specified at the individual level to account for the hierarchical structure of the data with various trip stages per participant, while variables at the trip stage level were added as fixed effects. Person level variables such as sex, age and educational level were excluded due to the small sample size.

For the cross-validation of MLM, the dataset was randomly split in half 10,000 times at the person level to generate pairs of independent datasets, hereafter called train and test sets. The random intercepts that were estimated for each participant in a train set could not be used for the corresponding test set, because participants of one dataset were excluded from the other. Instead, the estimated overall population intercept was used (which is called marginal prediction andused when the final aim is to conduct inference towards a wider population; [START_REF] Welham | Prediction in linear mixed models[END_REF].

Based on the success of a previous data-enrichment approach by [START_REF] Brondeel | Associations of socioeconomic status with transportrelated physical activity: combining a household travel survey and accelerometer data using random forests[END_REF], the non-parametric machine learning algorithm 'Random Forests' (RF) with 1000 trees per forest was used in addition to the MLM. RF consist of an ensemble of decision trees that are created by introducing two sources of randomness to the CART algorithm, bagging of observations and subsampling of variables at each tree node [START_REF] Breiman | Random forests[END_REF]. Bagging refers to the construction of each tree based on a bootstrapped subset of approximately two thirds of the unique observations, while at the same time only one-third of model predictors are used per node in the decision trees. An example and more information on RF can be found in Supplemental material B and publications by e.g. [START_REF] Tan | Introduction to Data Mining[END_REF], [START_REF] Strobl | An introduction to recursive partitioning: rationale, application and characteristics of classification and regression trees, bagging and random forests[END_REF][START_REF] James | An Introduction to Statistical Learning: with Applications in R[END_REF]. The algorithm is more robust against overfitting than single decision trees and has an internal validation mechanism, the out-of-bag R 2 , i.e., an R 2 that is estimated by predictions for each trip stage using every tree for which this trip stage was not used in developing the model. It has been found that the out-of-bag R 2 can be overestimated when the data is clustered, because trip stages of each given individual are split between those used to grow the forest and those in the out-ofbag sample [START_REF] Karpievitch | An introspective comparison of random forest-based classifiers for the analysis of cluster-correlated data by way of RF++[END_REF]. Therefore, as a more robust validation procedure, the RF models were then cross-validated by splitting the dataset 100 times into a train and test set, containing 70% and 30% of the randomly sampled participants, respectively. The number of splits was lower for RF than for MLM due to the complex algorithm which requires longer computation times.

As a performance indicator for both model types, the proportion of variance explained (R 2 ) by the full models in the train sets and test sets were calculated with the following formula to allow comparability:

= 1 - ∑ -! ∑ -"!
The denominator represents the total variation of the response variable y from the mean, while the numerator represents the variation of y from the predicted outcome. R 2 can take negative values for MLM and RF which indicate that the prediction of the fitted model is worse than the horizontal line drawn through the overall mean noise exposure across all trip stages. Our a priori strategy was to apply the prediction model calibrated from the RECORD MultiSensor Study to the EGT dataset only if the model fit could be considered as good and the predictions accurate.

The multilevel model was built with the R package 'nlme' [START_REF] Pinheiro | nlme: Linear and Nonlinear Mixed Effects Models[END_REF]. Random forests were built with 'randomForest' R package [START_REF] Liaw | randomForest' -Breiman and Cutler's Random Forests for Classification and Regression[END_REF] which implements Breiman's RF [START_REF] Breiman | Random forests[END_REF].

RESULTS

Personal dosimeter and map-based assessments of noise

A summary of personal noise exposures according to demographic and trip stage variables can be found in Table 2. The mean duration of a trip stage was 9.7 minutes. The overall average personal noise exposure across all trip stages for L Aeq,T was 71.6 dB(A) (sd = 8.6 dB(A)).

Noise exposure was not very variable between age groups (range: 69.9 -72.4 dB(A)) and was on average 2 dB(A) higher for men than for women. Personal noise values were on average higher in the second half of the week as compared to the beginning of the week and highest during summer compared with other seasons. Expected differences in exposure between transport modes were recorded, with motorbike showing the highest exposure followed by subway trip stages, and then by tram and bike trip stages. Lower personal exposures were documented for car, train, walking and bus trip stages. percentile; p75 = 75 th percentile; a Regional TER and SNCF trains

Multilevel model

Model on the full dataset

A comparison of the empty model to predict L Aeq,T with and without participant-level random effects justified the choice of a multilevel model (χ 2 = 568.73, df = 1, p < 0.0001; ∆BIC = 560.74). The variance partition coefficient of the multilevel model without fixed effects was 0.20, indicating that around 20% of the variance in noise exposure can be attributed to betweenperson variation.

The coefficients for the fixed effects and corresponding 95% confidence intervals (95% CI) of the multilevel model can be found in Table 3. The full model with random intercepts could explain 25.4% of the overall variance in L Aeq,T , while the model that ignored random intercepts resulted in an R 2 of 0.10. Several transport modes, i.e. motorbike, car and metro, showed higher noise exposures than walking. The predicted personal noise exposure L Aeq,T increased by 2.6 dB(A) (95% CI: 0.61 to 4.58 dB(A)) and 3.13 dB(A) (95% CI: 1.15 to 5.11 dB(A)), respectively for a 0 to 100% change of the noise map predictor. It was found that trip stages starting in the outer suburbs compared to intramural Paris were associated with higher personal noise exposure. Trip stages on Thursdays and Fridays exposed participants to more personal noise compared with Sundays. Afternoons and evenings showed higher exposure than mornings (β = 1.19 dB(A), 95% CI: 0.63 to 1.76 dB(A) and β =1.38, 95% CI: 0.48 to 2.28 dB(A), respectively). Each kilometer increase in straight-line distance from start to end of a trip stage resulted in an increase of a bit less than 0.1 dB(A). All other variables were not associated with personal noise exposure. 95% CI: 95% confidence interval, dB(A): A-weighted decibels; a percentage of surface within start and end tile of departure covered by polygons representing noise exposure equal to or higher than 75dB(A); b 7:00h-9:00h and 16:00h-19:00h

Cross-validation.

With a division into train and test set at the person level, the average R 2 of the 10,000 models on the train sets when using random intercepts was 0.27 (range: 0.14 to 0.40). When using the population intercept instead for a prediction in the train set, the average R 2 was 0.12 (range: 0.02 to 0.24). In contrast, the average R 2 that was obtained by applying each train set model to its corresponding test set was 0.01 (range: -0.77 to 0.14), indicating a very low predictive ability for other participants than those based on which the model was estimated. For further post-hoc examination, multilevel models were also estimated in each test set, and the regression coefficients for the transport modes and noise map predictors were compared between each train and test set pair of models.

Random Forests

Model on the full dataset

Two versions of RF were built, one including and one excluding person level variables (sex, age, occupation, educational level, household income, and number of people living in a household).

Several noise map predictors were entered into the models (mean, median, 25 th and 75 th percentile of the proportion of the 100 m tiles at the start and end of trip stages covered by noise polygons), as random forests are able to deal with multicollinearity of the predictors [START_REF] Hayes | Using Classification and Regression Trees (CART) and random forests to analyze attrition: results from two simulations[END_REF][START_REF] Strobl | Conditional variable importance for random forests[END_REF]. As RF result in slightly different predictions for each run due to the randomness introduced by bagging and random selection of variables at each tree node, RF were checked for consistency of prediction accuracy by iterating each version (one with and one without person level variables) 50 times. The model including person level variables obtained an average out-of-bag R 2 of 0.37 (range: 0.37 to 0.37) and an average train set fit of 0.84 (range: 0.84 to 0.84). Excluding the person level variables, the model was still able to result in a prediction accuracy of 0.27 (range: 0.26 to 0.27) for the out-of-bag R 2 and 0.81 (range: 0.81 to 0.81) of variance explained for the dataset itself. However, it should be noted that the out-of-bag observations originated from the same participants as the observations used to build the trees.

Cross-validation

To test if RF can predict noise exposure for new participants, the dataset was split 100 times randomly into a train set (70% of the sample) and a test set at the person level. For the train set, the RF procedure automatically estimated an R 2 based on out-of-bag observations. In addition, we recalculated R 2 for the whole train set and for the test set. The average and range of the outof-bag R 2 , the whole train set R 2 , and test set R 2 per version of the model are shown in Table 4.

The model including the person level variables achieved an out-of-bag R 2 of 0.39 (range: 0.26 to 0.48) and a good average fit on the train dataset. However, the average R 2 for predictions on the test set (for participants that were not considered to grow the model) was 0.01, ranging from -0.12 to 0.10. Similarly, the predictions for the test sets of the model with only trip stage variables resulted in an R 2 of -0.02 (range: -0.15 to 0.10). The predictive ability of the model was thus close to zero and its range was very broad. Based on these results, the estimated models were not applied to obtain noise level estimates in the EGT dataset. predictions can therefore explain as much of the variance in the data as our model. Although the non-parametric RF can describe the train data itself very well, the out-of-bag R 2 (estimated from trip stages from the same participants as those used to derive the model) indicated that RF performed better than MLM but worse than expected. RF estimates were not better than MLM estimates when applied to other participants than those used to derive the models. These inaccurate predictions did not allow us to apply the model to the EGT dataset, therefore objective d could not be realized.

Interpretation and limitations

The idea for the current study was based on the successful application of RF for the prediction of the number of minutes spent in moderate-to-vigorous physical activity during trips [START_REF] Brondeel | Using GPS, GIS, and accelerometer data to predict transportation modes[END_REF][START_REF] Brondeel | Associations of socioeconomic status with transportrelated physical activity: combining a household travel survey and accelerometer data using random forests[END_REF]. Even though comparable datasets and partly the same methodology were used, there are substantial differences in the predicted outcomes which require a different set of predictors. Unfortunately, a limitation inherent to the data-enrichment approach, here from a detailed dosimeter study to a large representative household study, is the necessity to use only predictors available in both datasets. Some potentially relevant factors for noise exposure may have been missed due to the unavailability in either one or both datasets. For example, if we were interested only in the RECORD MultiSensor study participants, additional variables such as the travel speed, the exact distance covered, and information based on more precise coordinates such as GPS tracks in combination with the noise map could have been entered as predictors to allow for more efficient use of data. Although the predictors used in the current MLM were associated with the personal exposure, the coefficient of 3.1 was small for an increase from 0 to 100% of the surface of the tile exceeding 75 dB(A). We expected the RF to account for the unequal importance of the noise map predictors for the different transport modes (e.g., outdoor road, air, and railway traffic noise may not be meaningful to predict the personal exposure for the underground subway trip stages). In addition, the specific map we used represented the annual average noise exposure without any daily, weekly or seasonal variation.

Due to the relatively small participant number, some variables contained numerous factor levels. One of these variables was the specific transport line covered in each of the public transport trips; however, many of these lines occurred with low frequencies in our sample and could thus not be entered into the model, but may have implicitly incorporated information on speed, crowding, environmental factors, and type and age of vehicles typically. For instance, train and subway noise levels are influenced by the presence of squealing noises and public audio system, train type and external (Tabacchi et al., 2011, Soeta and[START_REF] Soeta | The impact of external environments on noise inside a train car[END_REF], while car noise differs by car type, opening of windows, type of road, number of intersections, etc. For the same reason, person level demographic variables were excluded, which could contain valuable information on behavioral aspects linked to noise exposure. The person-level clustering

indicates that there may be some factors at the individual level that influence noise exposure and may explain the non-generalizability of estimated associations to participants who were unknown to the model. One major influence potentially arose from speech because some participants may preferably perform their trips in the company of friends or relatives, and contribution of speech to overall noise levels is dependent on the background levels [START_REF] Ryherd | Influence of a wearer's voice on noise dosimeter measurements[END_REF], increasing unpredictability of the measurements. Other sources of person level variation, dependent on the transport mode, may be route and speed preferences, population density and other characteristics of areas commonly visited, vehicle type, sound system usage, and driving style [START_REF] Mikulec | Noise exposure in convertible automobiles[END_REF]. Future prediction models based on a larger dataset may show if the transport line and person level predictors can capture some of the variability in noise exposure.

Due to this person level variation, RF were tested for prediction because they are known to capture complex interactions without explicit specification and are commonly used for clustered data [START_REF] Karpievitch | An introspective comparison of random forest-based classifiers for the analysis of cluster-correlated data by way of RF++[END_REF]. Therefore, the huge difference between the out-of-bag estimate and the test set prediction (on independent participants) was unexpected. [START_REF] Martin | Efficiently exploring multilevel data with recursive partitioning[END_REF] showed that random forests based on the CART algorithm performed poorly in his simulated condition with a high intra-class correlation of 0.30 and a small sample size (20 clusters with 15 observation each) [START_REF] Martin | Efficiently exploring multilevel data with recursive partitioning[END_REF], resulting in negative values for R 2 . The explanation of his results adapted to our findings may sound as follows: the trip stages undertaken by a given participant resemble each other more than when compared with the trip stages by other participants. Therefore, when a tree in a forest is exposed to trip stages of a participant, its knowledge is higher for other trip stages of this participant than for trip stages of other participants. As a consequence, the RF majority vote is more adapted to the participants used for forest construction than for new participants [START_REF] Martin | Efficiently exploring multilevel data with recursive partitioning[END_REF].

Predictions for the known participants was not outstanding, possibly due to the lack of specificity of the predictors as outlined before, but potentially also due to the way noise exposure was summarized. We chose the L Aeq,T due to its comparability with current regulations.

However, noise exposure expressed as a single value may not describe the variation of soundscapes between microenvironments sufficiently, as the L Aeq,T can take the same value for different patterns of exposure. It is possible that different transport modes have very diverse patterns of noise exposure in regard to the frequency bands, rhythm, and noise level peaks. Noise

Table 1 : Overview of the demographic characteristics of the RECORD MultiSensor and EGT study samples Variable RECORD MultiSensor EGT Sample size

 1

	Number of participants
	Number of trips
	Number of trip stages

RECORD = Residential Environment and CORonary heart Disease study cohort, MultiSensor branch; EGT = Global Transport Survey

Table 2 : Descriptive statistics for average equivalent sound levels (L Aeq,T in dB(A)) of trip stages in RECORD, overall and separated by participant and trip stage characteristics

 2

		N Trip		Mean (sd) L Aeq,T	P25 -p75 L Aeq,T
	Overall		3729	71.6 (8.6)	68.0 -76.8
	Age	34-43 years	1097	72.0 (9.7)	68.1 -77.5
		44-53 years	1205	72.4 (6.6)	68.4 -76.6
		54-63 years	806	69.9 (8.9)	66.8 -75.2
		64-74 years	605	71.5 (9.4)	68.4 -77.4
	Sex	Female	1466	70.4 (10.0)	67.0 -76.5
		Male	2247	72.4 (7.5)	68.4 -76.9
	Transport	Walking	2,061	70.5 (8.6)	66.9 -75.6
	Mode
		Bike	143	73.5 (7.2)	70.7 -77.6
		Motorbike	155	79.5 (10.3)	74.7 -84.8
		Car	720	71.2 (8.3)	67.4 -76.1
		Bus	143	70.2 (6.7)	67.9 -73.3
		Tram	46	73.8 (4.6)	72.1 -75.8
		Metro	332	75.1 (7.6)	72.9 -79.3

RECORD: Residential Environment and CORonary heart Disease study cohort, MultiSensor branch; N Trip = Number of trip stages per factor level; L Aeq,T = Time-averaged equivalent sound level; sd = Standard deviation; p25 = 25 th

Table 3 : Fixed effects of two-level regression model with trip stage variables as fixed effects and person identifier as random effect on the full dataset to predict average equivalent sound levels (L Aeq,T ) in dB(A) from personal dosimetry

 3

		Coefficient	95% CI
	Intercept	67.02	[65.22; 68.83]
	Mode: Walking	Reference
	Mode: Bike	1.42	[-0.08; 2.92]
	Mode: Motorbike	5.95	[4.24; 7.65]
	Mode: Car	1.23	[0.44; 2.02]
	Mode: Bus	-0.42	[-1.76; 0.93]
	Mode: Tram	1.83	[-0.49; 4.15]
	Mode: Metro	3.68	[2.71; 4.64]
	Mode: Train	-0.82	[-2.48; 0.83]

Table 4 : Average and range of the out-of-bag R 2 estimated in the train set (%), of the R 2 estimated in the whole train set R 2 (%) and of the test set R 2 (%) per version of the model predicting the noise outcome L Aeq,T Model Out-of-bag R 2 R 2 train set R 2 test set not

 4 considered to derive the model. These negative values indicate that the mean across all

DISCUSSION

Summary of the results

The current study aimed to describe noise exposure during daily trips, to build a model that can predict this noise exposure, and to apply the model to a larger sample that comes from the same source population. In line with previous findings in different locations [START_REF] Kraus | Individual daytime noise exposure in different microenvironments[END_REF], Taimisto et al., 2013[START_REF] Neitzel | Noise levels associated with New York City's mass transit systems[END_REF], noise exposure summarized as the L Aeq,T on average exceeded the recommended level of 70 dB(A) for all transport modes. With an average transport time of 93.2 minutes per participant per day, personal transport is a considerable source of noise exposure.

The multilevel model showed that approximately 20% of the variance in noise exposure in our sample was at the person level. Around 9.6% of the variance could be explained by the fixed effects, where transport mode, day of the week and time of the day, the noise map predictor, the straight-line distance between start and end tiles were found to be important predictors. The R 2 , and thus the predictive ability of the models, was relatively low even when estimated for the participants who were used to derive the models. However, our cross-validation procedure splitting the trip stages at the participant level showed that the prediction accuracy was even lower and included negative values when models were applied to the participants who were summary measures with different meanings are for example the number of noise events or percentiles of one-second interval L Aeq values such as L A95 and L A5 [START_REF] Can | Comparison of noise indicators in an urban context[END_REF]. More detailed noise data will be available from a currently ongoing study (MobiliSense) in our lab, which may allow for more discriminable summary measures in the future. Data and scripts can be provided upon request.

Conclusion

In line with previous studies, the current study found that noise exposure during daily travels is in general high for all transport modes. While models with moderate prediction ability for the participants used to develop the models could be built based on both MLM and RF, the prediction accuracy for other participants was low. Accordingly, we decided to not conduct a prediction of noise levels for the trip stages of the large representative EGT sample. The results may be explained by limitations in the predictors that were used, by the small sample size of the model development set, and by the way noise was summarized.

Supplemental Material

A. Distribution of combined road, rail and air traffic noise in the Île-de-France region.

A shows an overview of the noise distribution and is zoomed towards the inner suburbs (departments 92, 93, 94) and This decision tree is constructed for illustrative purposes only, built with the package 'rpart' [START_REF] Therneau | Package 'rpart': Recursive Partitioning and Regression Trees[END_REF] using the ANOVA method for continuous outcome variables and default parameters. Predictors: sex, transport mode, employment status, educational level. Outcome: L Aeq,T in dB(A), at trip-stage level. The values in each node represents the estimated for the subgroup.


Patrice Berthod
email: patrice.berthod@centraliens-lille.org

Mira Khair
email: mira.kheir@hotmail.com

Thermodynamic and Experimental Study of Cobalt-based Alloys designed to contain TiC carbides

Keywords: Cobalt alloys, TiC, High temperature microstructures

Two alloy compositions, {Co(bal.)-25Cr-0.25C-1Ti} and {Co(bal.)-25Cr-0.50C-2Ti}, were studied using Thermo-Calc. In parallel the corresponding real alloys were elaborated by foundry and their microstructures, in their as-cast state or after a long stage at 1000 or 1200°C, were characterized. Thermodynamic calculations and real experiments were globally in good agreement. They both demonstrate that the two alloys are highly refractory, that solidification starts by the crystallization of the alloy matrix in all cases and that all titanium carbides precipitate at the end of solidification and belong to a {matrix + TiC} eutectic compound. The TiC carbides remain stable during long exposure at elevated temperature, for both temperatures for the {0.50C-2Ti}-alloy but only at 1000°C for the {0.25C-1Ti}-alloy. This observation suggests potential high mechanical properties of the {0.50C-2Ti}-alloy at elevated temperature. Many of the collected experimental data -temperature range of melting or solidification, microstructures stabilized at high temperature (natures, fractions and chemical compositions of the phases) -will be of interest for testing and improving databases.

Introduction

Superalloys are refractory metallic alloys used for high temperature applications, such as static or rotating blades in aero-engines and energy-generation turbines [START_REF] Sims | The Superalloys[END_REF][START_REF] Bradley | Superalloys: A Technical Guide[END_REF].

Among the most modern ones there are the nickel-based gamma / gamma prime single crystal alloys [START_REF] Donachie | Superalloys : A Technical Guide[END_REF] which are certainly the best ones in term of mechanical [START_REF] Donachie | Superalloys : A Technical Guide[END_REF] and chemical [START_REF] Kofstad | High Temperature Corrosion[END_REF][START_REF] Young | High Temperature Oxidation and Corrosion[END_REF] resistances at elevated temperatures. However γ/γ' single crystals cannot be easily shaped for obtaining compact pieces. Conventionally cast pieces constituted of equi-axed superalloys remain of great interest. Some attention must be focused on recent formulae of chromium-rich cobalt-based alloys, involving interdendritic scriptlike shaped TaC [START_REF] Berthod | [END_REF] or HfC [7]. Such interdendritic carbides which form a eutectic compound with matrix at the end of solidification and which remain stable at elevated temperature, possess additionally a morphology which is recognized as particularly efficient for strengthening alloys at high temperature [8]. This was recently demonstrated by the observation of significant creep resistance at temperatures as high as 1200°C [9]. Unfortunately such elements (Ta, Hf…) are rather expensive and their high atomic masses tend increasing the density of alloys, which is harmful for transportation applications as well as for industrial pieces in high speed rotation during working.

TiC is also a MC-type carbide. It is formed from an element which is not so refractory as Ta or Hf. Indeed the melting point of Ti is 1725°C against 2996°C for Ta or 2205°C for Hf [START_REF] Shaffer | High-Temperature Materials -N°1 Materials Index[END_REF]. TiC is however a very refractory compound, with a melting point of more than 3000°C [START_REF] Samsonov | High-Temperature Materials -N°2 Properties Index[END_REF]). Titanium is an element which is rather cheap and profuse on earth and the MC carbides which can be obtained from Ti is of a rather low density (4.93 g cm -3 for TiC against 12.6 and 14.3 for HfC and TaC respectively [START_REF] Samsonov | High-Temperature Materials -N°2 Properties Index[END_REF]). The titanium monocarbide is thus potentially very interesting and it is judicious to investigate how it may appear in chromium-rich cobalt-based alloys, where in the microstructure and with which morphology, and how it behaves at high temperature for long-time exposures.

In this work two Co-based compositions involving rather high amounts in titanium and carbon were first studied using thermodynamic calculations to obtain preliminary data about the appearance or not of TiC during solidification and, if TiC can be present, to value the stability of this carbide at high temperature. Thereafter elaborations by casting under inert atmosphere were carried out to obtain the two alloys. Their melting ranges were measured and their microstructures, in their as-cast state or after 46 hours isothermally spent at 1000, 1100 and 1200°C, were characterized. Comparisons will be done between the results of thermodynamic calculations and the real experiments.

Experimental method

Thermodynamic calculations

Preliminary thermodynamic calculations were carried out using the Thermo-Calc (version N) software [START_REF]Foundation for Computational Thermodynamics[END_REF] working with a database based on the SSOL commercial one [START_REF]SGTE Solutions Database[END_REF] especially enriched by Sylvain Michon [START_REF] Michon | Metallurgical and mechanical optimization of cobalt-based superalloys for glass-forming at 1200[END_REF] for the needs of his doctoral research. This database contains the descriptions of the Co-Cr [START_REF]SGTE Solutions Database[END_REF], Co-C [START_REF]SGTE Solutions Database[END_REF], Cr-C [START_REF]SGTE Solutions Database[END_REF], Co-Ti [START_REF] Cacciamani | [END_REF], Cr-Ti [16] and Ti-C [17] binary systems as well of the Co-Cr-C [START_REF]SGTE Solutions Database[END_REF], Co-Ti-C [18] and Cr-C-Ti [19] ternary systems. Calculations were carried out at successive temperatures between 2000 and 1000K, interval covering the temperature range of solidification or melting and the solid state temperature range in which diffusion and transformation rates are known to be reasonably possible for usual practical cooling rates. The number of the phases existing at each temperature step, their natures and their mass fractions were noted.

Additional calculations were done at 1000 and 1200°C for specifying more extensively the metallurgical states of the alloys, for specifying again the natures and mass fractions of the different existing phases, and also their chemical compositions (essentially liquid and matrix). These mass fractions were converted into volume fractions according to equation (1) in order to allow thereafter comparisons with the experimental surface fractions measured in the aged samples:

[ ] [ ] [ ] ∑ = i i w j w j v i f j f f ) / ( / ) / ( φ φ ρ φ ρ φ φ (1)
in which fv [ϕj], fw [ϕj] and ρϕj are respectively the volume fraction, the mass fraction and the density of the phase ϕj. The values taken for the densities were 4.93 g cm -3 for the TiC carbides, 6.95 g cm -3 for the chromium carbides (Cr7C3 and Cr23C6 are almost of the same density), and 8.34, 8.14 and 8.19 g cm -3 for the matrixes of the Co-25Cr-0.25C-1Ti and Co-25Cr-0.50C-2Ti alloys respectively. The densities of the alloys were calculated from the mass and dimensions of very regular parallelepipeds accurately cut and measured in the two ingots. The densities of the matrixes were assumed to be very close to the ones of the alloys.

Synthesis of the alloys

The two alloys were elaborated by high frequency induction foundry (CELES furnace, France) from small parts of pure elements: Co, Cr, Ti, and graphite (Alfa Aesar, all >99.9wt.% in purity). In each case the parts were placed in a copper crucible internally cooled by room temperature water circulation. A silica tube was placed surrounding the crucible and inside the copper induction coil (also cooled by internal water circulation) to isolate the crucible and the metallic parts from outside. Pumping until reaching about 0.03 millibars was realized three times, each time followed by introduction of pure argon until reaching about 300 millibars. After final pumping, an atmosphere of 300 millibars of argon was present in the fusion chamber. The voltage was increasingly applied until reaching the temperature level which was demonstrated by the preliminary thermodynamic calculations as compulsory for the fusion of the considered alloys as well as for the steady molten state of the obtained liquid alloy. The voltage was maintained at this value (5kV, frequency: about 110kHz) during five minutes. The cooling at the end of the isothermal stage cooling was realized, with a rate defined by the rate of power decrease. This procedure led to two ingots of a compact shape, each weighing about 40 grams.

Microstructure characterization of the as-cast state

The ingots were cut using a Delta Buelher saw. A part from each of them was embedded in a cold resin mixture (resin CY230 and hardener HY956 from ESCIL, France). The mounted samples were thereafter ground with SiC papers, for grade varying from 80 to 4000. They were immersed in water and ultrasonically cleaned.

Final polishing was realized using a textile disk enriched with 1µm diamond particles, until obtaining a mirror-like state. The alloys were observed using Scanning Electron Microscopy (SEM, JEOL JSM-6010A) in Back Scattered Electrons mode (BSE). The general chemical composition of the alloys was verified by Energy Dispersion Spectrometry (EDS) using the EDS device equipping the SEM. Spot EDS measurements were additionally carried out to specify the chemical compositions of the present phases: accurate composition of matrix but only qualitative composition of the different types of particles (too small size to be accurately analyzed). The particles containing especially high contents in carbon and titanium were assumed to be TiC carbides and the ones appearing particularly rich in carbon and chromium were supposed to be chromium carbides (but without further information about their stoichiometry).

Isothermal exposures of the alloys and metallographic characterization

In both ingots a small parallelepiped was cut in order to carry out differential thermal analysis using a SETARAM TG-DTA apparatus, respecting the following cycle: heating from the ambient temperature up to 1200°C at +20K/min, heating from 1200 to 1470°C at +5K/min, cooling down to 1200°C at -5K/min then at -20K/min. The temperatures of heat absorption start and end and the temperature of heat release start and end were noted on the obtained curves (temperatures at which the heat flow curves took off from the base line -or tangent line -or at which they rejoined again the base line).

Isothermal exposures of the alloys and metallographic characterization

In each ingot two additional parts were cut for performing the isothermal exposures in high temperature resistance tubular furnace. Their approximate dimensions were 10 mm × 10 mm × 3 mm. After heating at +20K min -1 they were maintained at two high temperatures (1000 and 1200°C) for 46 hours in each case. Post-isothermal cooling was realized at -5K min -1 down to room temperature. Thereafter, these different aged samples were prepared (cutting, embedding, grinding, polishing) and characterized (SEM/BSE observations and photographs, EDS identification of the different types of particles and spot analyses of the chemical composition of the matrix) as previously described for the as-cast alloys. The microstructure characterization was completed by the measurements of the surface fractions of the phases using the image analysis tool of the Photoshop CS software (Adobe).

Hardness measurements

The as-cast alloys as well as the aged ones were all subjected to Vickers indentation under a load of 10kg, in order to correlate with the observed carbides surface fractions and to qualitatively anticipate about their possible mechanical potential at high temperature. The used apparatus was a Testwell Wolpert macro-indentor.

Results and discussion

Thermodynamic calculations

The first results of thermodynamic calculations are presented in Figure 1 and in This first stage of crystallization is expected to be a little longer for the first alloy than for the second one since the temperature range is broader in the first case than in the second one. Qualitatively one can think to a more developed pre-eutectic dendrite network for the {0.25C-1Ti}-alloy than for the {0.50C-2Ti}-alloy. Inversely the later alloy will probably contain a more extended interdendritic domain composed of the {matrix + TiC} eutectic than the former one. Indeed, the eutectic precipitation of matrix and TiC carbides which will effectively take over from the pre-eutectic crystallization of matrix, will take place during a cooling over a much wider temperature range (more than 200K against only several tens K for the {0.25C-1Ti}-alloy. After total solidification the metallurgical state can be double-phased (matrix + TiC) for these two alloys with equal atomic contents between carbon and titanium. During the subsequent solid state cooling of the Co-25Cr-0.25C-1Ti alloy, M23C6 carbides would start precipitating after several hundreds of Kelvin under the end of solidification. Its next solid state transformation should be the allotropic change of the austenitic FCC matrix into a hexagonal compact HCP one. This is globally the same scenario for the Co-25Cr-0.50C-2Ti. 1 POSITION OF FIGURE 2 The theoretic solidifications and the solid state transformations at temperatures still high are represented more quantitatively for the two alloys in Figure 3 (Co-25Cr-0.25C-1Ti) and Figure 4 (Co-25Cr-0.50C-2Ti). In each case the top graph concerns all phases while the bottom graph, enlarged version of the previous one, only concerns carbides. One logically finds confirmation that the first carbide to appear is the titanium one (TiC, FCC_A1#2), while chromium carbides may precipitate in solid state more 200K lower than the appearance of the titanium carbides. TiC carbides initially precipitate during the eutectic part of solidification until reaching a little more than 0.5 mass.% for the {0.25C-1Ti}-alloy and almost 2 mass.% for the {0.50C-2Ti}-alloy. In both cases titanium carbides stay alone before the solid state precipitation of the chromium carbides, directly Cr23C6 for the first alloy and seemingly with a short transition of Cr7C3 before Cr23C6 for the second one. The predicted mass fractions in chromium carbides are lower than the TiC ones but of the same order of magnitude. 3 POSITION OF FIGURE 4

POSITION OF FIGURE

POSITION OF FIGURE

As-cast microstructures of the obtained alloys

After elaboration of the alloys by high frequency induction melting and metallographic preparation of parts cut in the obtained ingots, microstructure examination in electron microscopy was carried out to have a look to the as-cast microstructures. Two micrographs, presented in Figure 5, illustrate the microstructure of the as-cast {0.25C-1Ti}-alloy, with two magnifications. This alloy is obviously composed of a dendritic matrix (solid solution of Co containing Cr and a part of Ti and of C) and of interdendritic dark particles. These ones are rich in titanium and in carbon.

The same type of microstructure is presented by the {0.50C-2Ti}-alloy (Figure 6), with more interdendritic particles. In this second alloy these particles are either rich in Ti and C, or in chromium and C. Because of the too low surface fraction of these precipitates and of their too low size, even in the second alloy, neither X-ray diffraction nor spot chemical analysis by energy dispersion spectrometry and by wavelength dispersion spectrometry allowed to accurately specify the nature of these particles. They were only identified as being rich in Ti and C for some of them and in Cr and C for the other ones. 5 POSITION OF FIGURE 6

POSITION OF FIGURE

Melting temperature range of the obtained alloys

In parallel with the preparation of the metallographic samples small parallelepipeds were cut in the ingots to perform differential thermal analysis. The obtained DTA curves are displayed in Figure 7 and Figure 8, for respectively the {0.25C-1Ti}-alloy and the {0.50C-2Ti}-alloy. The first alloy starts melting at about 1370°C and finishes melting above 1460°C. It starts solidifying at about 1400°C, obviously after an important undercooling as suggested by the sudden crystallization releasing a great quantity of heat over a small temperature range. It finishes its solidification near 1350°C. The melting of the second alloy starts at a temperature lower than for the first one, at about 1270°C, and finishes at about 1450°C. An undercooling is also observed prior to the start of its solidification, revealed by a jump in released heat at about 1420°C. The end of solidification happens just below 1300°C. 7 POSITION OF FIGURE 8 The exact values of melting and solidification starts and ends determined by DTA for the {0.25C-1Ti}-alloy are given in Table 1, with the corresponding values of solidus and liquidus temperatures issued from thermodynamic calculations. One can note that the calculated solidus and liquidus are in good agreement with the one deduced from the DTA results.

POSITION OF FIGURE

POSITION OF TABLE 1

In contrast, the calculated and experimental results are not consistent for the {0.50C-2Ti}-alloy (Table 2). The calculated solidus temperature is much higher than the melting start's and solidification end's ones, as well as the average of the two. The calculated liquidus temperature is significantly lower than the melting end's temperature, the solidification start's one and the average value.

POSITION OF TABLE 2

Aged microstructures

The microstructure behaviors of the two alloys when isothermally exposed at high temperature were studied at 1000 and 1200°C during 46 hours. The highest temperature was considered as possible according to the DTA measurements which previously demonstrated that none of the two alloys risks melting. The aged microstructures were analyzed following the same protocol of preparation and characterization as the as-cast samples. By looking to the micrographs presented in Figure 9 it appears that, during the stay at 1200°C, the {0.25C-1Ti}-alloy has become almost single-phased. Indeed it has lost almost all its initial carbides, obviously dissociated and their constitutive elements dissolved in the solid solution. One can see here and there some rare TiC carbides as isolated blocky particles. After 46 hours spent at 1000°C, the carbides are still here but they obviously coalesced. One can distinguish black/dark gray TiC carbides and pale gray chromium carbides, for the chosen contrast and brightness settings. During the same tests the {0.50C-2Ti}-alloy behaved differently (Figure 10). For both temperatures the surface fraction of carbides was not so lowered. The TiC carbides were a little fragmented and coalesced after exposure at 1200°C while chromium carbides are difficult to see or do not exist anymore. Both carbides are still present after exposure at 1000°C. The dark TiC carbides obviously staid script-like shaped. The chromium carbides are dispersed as rare blocky pale particles. 9 POSITION OF FIGURE 10

POSITION OF FIGURE

Metallurgical state comparison between calculations and experiments

The theoretic results issued from thermodynamic calculations and the ones issued from metallographic characterization may be compared in the fields of carbides natures, carbides fractions and matrixes chemical compositions. This was done for the {0.25C-1Ti}-alloy in Table 3 and for the {0.50C-2Ti}-alloy in Table 4.

POSITION OF TABLE 3 POSITION OF TABLE 4

Concerning the first alloy rather good agreement is found concerning the chemical composition of the matrix. The calculated and measured chromium contents are very close to one another. In contrast, the titanium content measured by EDS seems being a little higher in the aged alloys than the predicted values. This suggests that a lower fraction of TiC carbides remain stable in the microstructure by comparison with predictions. This is exactly the case: the TiC are effectively less present in the aged samples than anticipated by calculations. This is particularly true for 1200°C, temperature at which TiC were expected to be still present with rather high fraction (1.4 vol.%), just a little less than for 1000°C: only less than 0.3 vol.% of TiC staid in the 1200°C-aged {0.25C-1Ti}-alloy. Concerning the chromium carbides, excellent agreement appears between calculations and experiment for 1200°C: they are totally absent according to calculations and to metallography. Differences appear for 1000°C but the fractions in chromium carbides are close to 0 in both cases.

The same good correspondence of the chromium content in matrix and the same type of difference in titanium content as for the first alloy is found again concerning the chemical composition of the matrix of the second alloy after aging at 1200 and 1000°C: the Cr contents are almost equal and the Ti content tends to be higher in the real alloy than the calculated values. Curiously, the volume fractions of the TiC carbides are higher in the aged real alloy than the calculated values. The same hierarchy is found for the chromium carbides at 1000°C: their surface fraction in the microstructure is higher than their calculated volume fraction. For 1200°C, calculations and metallography led to the same results: total absence of chromium carbides.

Hardness

The average and standard deviation values of the five indentation results obtained for each {alloy, state] couple are given in Table 5. The aging at 1000°C transformed the {0.25C-1Ti}-alloy in a harder material, seemingly thanks to the previously observed coalescence of the carbides occurred during the aging. Inversely, the hardness falls under the as-cast alloy value after aging at 1200°C, consecutively to the disappearance of all carbides. For all states the {0.50C-2Ti}-alloy is harder than the first one. The equivalent hardness for the as-cast state and for the 1000°C-aged state can be easily related to the unmodified carbide network. The softening observed after 46 hours at 1200°C can be also easily explained by the decrease in carbide fraction and by the fragmentation of the TiC carbides. The hardness of the 1200°C-aged {0.50C-2Ti}-alloy nevertheless remains higher than the one of the as-cast {0.25C-1Ti}-alloy.

POSITION OF TABLE 5

Discussion

Titanium, as many other MC-former elements, is stronger in this role than chromium, according to the carbides' Ellingham diagram [20][21][22]. This was thus not a surprise to note that TiC formed at the expense of chromium carbides in the alloys considered in this work, observations here predicted in a first time with thermodynamic calculations and directly done on really elaborated alloys in a second time.

However, this was not self-evident as earlier seen in the case of tantalum carbides in nickel-based alloys. Indeed, TaC carbides were effectively present at the expense of chromium carbides in cobalt-chromium alloys [START_REF] Berthod | [END_REF] while they were replaced by chromium carbides in nickel-chromium alloys [23]. A problem of lack of thermodynamic stability of TiC in presence of chromium was encountered in nickelbased alloys, for example in [24]. It was thus not sure that TiC is able to compete with chromium carbides in the present alloy, even if a cobalt-base previously favored another MC carbide (TaC, [START_REF] Berthod | [END_REF]) at the detriment of chromium carbides in contrast with what occurred in nickel-based alloys [20].

The preliminary calculations performed here suggested the successful formation of TiC carbides during solidification and their high stability at elevated temperature.

During cooling from the liquid state they are the second solid phase to crystallize (after the matrix), and the single carbide phase to appear during solidification. Chromium carbides are expected to appear in a second time, at lower temperatures, by solid state precipitation. This theoretic succession of phase transformations during cooling is common to the two alloys. The main difference concerns the quantities of carbides which are not the same (logically higher for the second alloy than for the first one, regarding their respective contents in C). These previsions are globally confirmed by the as-cast microstructures: dendritic matrix (thus necessarily the first phase to crystallize) and eutectic shape of the TiC carbides (script-like mixed with matrix). The chromium carbides look like solid state precipitates. After isothermal exposure at high temperature long enough to expect the reaching of the thermodynamic equilibria, it appeared that the TiC carbides became and remained the single carbide present at 1200°C and the two carbides still existed after exposure at 1000°C. Calculations and experiment results thus appeared as qualitatively consistent. Image analysis allowed to possibly give quantitative confirmation of this good agreement. This was not really the case since the volume fractions of the two types of carbides issued from the mass fractions issued from thermodynamic calculations and the ones deduced from the surface fractions measured by Adobe Photoshop corresponded to one another more or less imperfectly.

The fineness of the script-like eutectic TiC and the small size of the chromium carbides, as well as the proximity of the tint of the later ones with the matrix, may be responsible of this mismatch. It is true that, in spite of the care with which the threshold was rated, the surface fractions of carbides were measured without a high accuracy. Some of the standard deviation values witness of these difficulties. Another significant lack of consistency between calculations and experimental measurements was found concerning some of the DTA results. This was the case of the {0.50C-2Ti}-alloy for which the melting or solidification range was more extended that the difference of the calculated solidus and liquidus temperatures. This suggests that the database merits to be improved for the C-richest Ti-richest part of the diagram at high temperature. For instance, the description of the Co-Cr-Ti ternary system, which is currently lacking in our database, may be incorporated rather shortly since first results concerning this system start to be available, as the ones obtained by P. Zhou et al rather recently published [25]. Anyway one must consider that, in its present state, this database is globally performing enough to give very useful indication on the microstructure of Ticontaining Cr-rich cobalt-based alloys containing carbon for forming carbides.

Conclusions

Cobalt-based alloys elaborated by classical foundry keep significant interest for many applications at high temperature and, besides solid solution strengthening, the necessity to strengthen grain boundaries and to consolidate the inter-dendrites cohesion leads to favor the long term presence of particles such as script-like shaped eutectic carbides. TiC carbides, which correspond to these requirements, may be more interesting than other MC carbides thanks to their lower density and for the availability of titanium much more extended than the one of other MC-former elements. Although obtaining successfully stable TiC carbides was previously showed as not possible in nickel-chromium alloys, both by thermodynamic calculations and real experiments, the same types of investigations undertaken in the present study both just demonstrate that this is totally different in cobalt-chromium alloys. With the two alloys of this type considered in the present work, preliminary calculations, carried out using a home-made database, suggested in a first time that obtaining eutectic TiC carbides is possible. In a second time, the elaboration of real alloys led to as-cast microstructures with predominant TiC carbides. Furthermore these ones did not accidentally precipitated during the rather fast solidification (and thus in non-equilbrium conditions) since they remained stable at high temperature as showed by isothermal aging applied on rather long time. This is true that this is essentially the alloy with 050wt.%C and 2wt.%Ti which staid really stable in these conditions. The rather high room temperature hardness of this alloy in its as-cast state as well as after several days spent at high temperatures suggests interesting mechanical properties at elevated temperatures. Unfortunately, with its current chemical composition this alloy obviously starts melting at a temperature a little too low to expect high creep resistance at elevated temperature. This is probably due to the presence of some rare chromium carbides that the respect of the atomic equality of titanium and carbon did not succeed to totally avoid the formation of these carbides responsible of low melting point of the grain boundaries. However, by considering the isopleth sections presented in the first figures of this manuscript, it seems possible to suppress the chromium carbides for example by increasing the Ti content up to 2.4 wt.% for the same C content (0.50wt.%).

However one must be careful with such deductions made from the current database since, even if good predictions were made by using it for the thermodynamic calculations, this one may lead to slight discrepancies, as the ones observed in the

Figure 2 .

 2 Figure 2. Figure 1 allows knowing qualitatively the solidification and solid state

Fig. 1 .Fig. 2 .Fig. 4 . 9 Fig. 5 .

 12495 Fig. 1. The {25wt.%Cr-1wt.%Ti}-section computed with Thermo-Calc with position of the low carbides alloy

Fig. 6 .Fig. 7 .Fig. 8 .

 678 Fig. 6. The as-cast microstructure of the Co-25Cr-0.50C-2Ti alloy (top: general view, bottom: detailed view)

Table 1 .

 1 Comparison of the calculated liquidus and solidus temperatures and the measured ones for the Co-25-0.25C-1Ti alloy

	Thermo-Calc	Differential thermal analysis	Consistent ?
		Fusion end's temperature (°C)
	Liquidus temperature (°C)	Average value (°C)	Yes / No
		Solidification start's temperature
		(°C)
		1464
	1419	1432	YES
		1399
		Fusion start's temperature (°C)
	Solidus temperature (°C)	Average value (°C)	Yes / No
		Solidification end's temperature
		(°C)
		1375
	1358	1365	YES
		1354

Table 2 .

 2 Comparison of the calculated liquidus and solidus temperatures and the measured ones for the Co-25-0.50C-2Ti alloy

	Thermo-Calc	Differential thermal analysis	Consistent ?
		Fusion end's temperature (°C)
	Liquidus temperature (°C)	Average value (°C)	Yes / No
		Solidification start's temperature
		(°C)
		1447
	1394	1438	NO
		1428
		Fusion start's temperature (°C)
	Solidus temperature (°C)	Average value (°C)	Yes / No
		Solidification end's temperature
		(°C)
		1278
	1351	1284	NO
		1290

Table 3 .

 3 Comparison of the metallurgical states at 1200 and 1000°C of the Co-25Cr-0.25C-1Ti alloy as calculated by Thermo-Calc (Th.-Calc) and as really obtained (Exp.)

	Temperature	FCC Co-based	TiC carbide	M23C6 carbide
		matrix
	Source: Th.-Calc	Exp.	Th.-Calc	Exp.	Th.-Calc	Exp.
	1473.15K	Chem.	Wt.% in	0.832	average
	(1200°C)	compo:	Cr and	mass.%	± std dev
		74.365 Co 25.192 Cr	Ti: Bal. 25.4 ±0.5	i.e. vol.% 1.400	(surf.%) ± 0.07 0.26	/	/
		0.345 Ti	0.6 ±0.1
		0.098 C	Not
			meas.
	1273.15K	Chem.	Wt.% in	0.933	average	0.637	average
	(1000°C)	compo:	Cr and	mass.%	± std dev	mass.%	± std dev
		74.801 Co 24.896 Cr	Ti: Bal. 24.7 ±0.3	i.e. 1.566 vol.%	(surf.%) 1.37 ± 0.17	i.e. 0.758 vol.%	(surf.%) 0.17 ± 0.30
		0.260 Ti	0.4 ±0.2
		0.043 C	Not
			meas.

Table 4 .

 4 Comparison of the metallurgical states at 1200 and 1000°C of the Co-25Cr-0.50C-2Ti alloy as calculated by Thermo-Calc (Th.-Calc) and as really obtained (Exp.)

	Temperature	FCC Co-based	TiC carbide	a M7C3 or b M23C6
		matrix			carb.
	Source: Th.-Calc	Exp.	Th.-Calc	Exp.	Th.-Calc	Exp.
	1473.15K	Chem.	Wt.% in	2.145	average
	(1200°C)	compo:	Cr and	mass.%	± std dev
		74.081 Co 25.497 Cr	Ti: 25.7 ±0.2 Bal.	vol.% 3.512 i.e.	± 0.28 6.11 (surf.%)	/	/
		0.314 Ti	0.5 ±0.1
		0.108 C	Not
			meas.
	1273.15K	Chem.	Wt.% in	2.189	average	b 0.983	average
	(1000°C)	compo:	Cr and	mass.%	± std dev	mass.%	± std dev
		74.679 Co 25.017 Cr	Ti: Bal. 25.0 ±0.3	i.e. 3.577 vol.%	(surf.%) 4.55 ± 1.05	i.e. 1.139 vol.%	(surf.%) 1.99 ± 1.82
		0.261 Ti	0.8 ±0.3
		0.043 C	Not
			meas.

Table 5 .

 5 Room temperature hardness of the two alloys in their three states (as-cast or aged at one of the two temperatures)

	Vickers 10kg	Co-25Cr-0.25C-1Ti	Co-25Cr-0.50C-2Ti
	(10 indentations)
	After 46h at 1200°C	263 ± 12	317 ± 5
	After 46h at 1000°C	331 ± 12	362 ± 13
	As-cast	306 ± 21	364 ± 12

present study, notably in the case of this {0.50C-2Ti}-alloy. It is preferable to improve the accuracy of this database prior using it for designing new TiC-containing cobaltchromium alloys, notably by using the presented metallographic data obtained in this work. These ones are also available to test other databases and to serve as references for improving them for better predictions if necessary.