Luiz C Cotovicz

Bastiaan A Knoppers

Loris Deirmendjian

Gwenaël Abril

Sources and sinks of dissolved inorganic carbon in an urban tropical coastal bay revealed by δ 13 C-DIC signals

Keywords: δ 13 C-DIC signatures, coastal eutrophication, carbon cycling, Guanabara Bay

Dissolved inorganic carbon (DIC), its stable isotope composition (δ 13 C-DIC) and ancillary parameters of the water column were investigated in a eutrophic tropical marine-dominated estuary surrounded by a large urban area (Guanabara Bay, Rio de Janeiro, Brazil). Most negative δ 13 C-DIC signatures (down to -6.1‰) were found in polluted regions affected by direct sewage discharges where net heterotrophy induces high partial pressure of CO2 (pCO2) and DIC concentrations. Keeling plot was applied to this polluted region and determined the δ 13 C-DIC sewage signature source of -12.2‰, which is very consistent with isotopic signature found in wastewater treatment plans. These negative δ 13 C-DIC signatures (i.e., DIC depleted in 13 C) were restricted to the vicinity of urban outlets, whereas in the largest area of the bay δ 13 C-DIC signatures were more positive (i.e., DIC enriched in 13 C). The most positive δ 13 C-DIC signatures (up to 4.6‰) were found in surface waters dominated by large phytoplankton blooms, with positive correlation with chlorophyll a (Chl a). In the largest area of the bay, the preferential uptake of the lighter stable carbon isotope ( 12 C) during photosynthesis followed the Rayleigh distillation, and appeared as the most important driver of δ 13 C-DIC variations. This reveals an important isotopic fractionation (ε) by phytoplankton due to successive algal blooms that has turned the remaining DIC pool enriched with the heavier stable carbon isotope ( 13 C). The calculated diel apparent ε showed higher values in the morning (18.7‰ to 21.6‰) and decreasing in the afternoon (6.8‰ to 11.1‰). ε was positively correlated to the pCO2 (R 2 = 0.88, p = 0.005) and DIC concentrations (R 2 = 0.73, p = 0.02), suggesting a decline in carbon assimilation efficiency and decreasing uptake of the lighter carbon under CO2 limiting conditions. The eutrophic coastal waters of Guanabara Bay have δ 13 C-DIC signatures well above that found in estuaries, shelf and ocean waters worldwide.

Introduction

The coastal zone is one of the most biologically active areas of the biosphere, and plays an important role in the global carbon cycle [START_REF] Gattuso | Carbon and carbonate metabolism in coastal aquatic ecosystems[END_REF]. Estuaries are considered prominent coastal environments, which receive large amounts of organic matter from land, and exchange material with the adjacent ocean and the atmosphere [START_REF] Borges | Carbon Dioxide and Methane Dynamics in Estuaries[END_REF][START_REF] Chen | Air-sea exchanges of CO2 in the world's coastal seas[END_REF]). The most recent global estimation of estuarine CO2 emissions to the atmosphere is about 0.1 Pg C yr -1 [START_REF] Chen | Air-sea exchanges of CO2 in the world's coastal seas[END_REF]). These emissions occur because in estuaries the consumption of organic carbon exceeds net primary production, and the net heterotrophy in the ecosystem leads to high pCO2 levels [START_REF] Gazeau | The European coastal zone: characterization and first assessment of ecosystem metabolism[END_REF]; [START_REF] Borges | Carbon Dioxide and Methane Dynamics in Estuaries[END_REF], together with lateral CO2 inputs from tidal wetlands (Cai and Wang 1998., [START_REF] Bouillon | Inorganic and organic carbon biogeochemistry in the Gautami Godavari estuary (Andhra Pradesh, India) during pre-monsoon: The local impact of extensive mangrove forests[END_REF]; Bouillon et al. 2011) and rivers [START_REF] Gattuso | Carbon and carbonate metabolism in coastal aquatic ecosystems[END_REF]Hunt et al. 2011;Joesoef et al. 2017). However, it must be highlighted that the high diversity of estuarine morphological types and associated ecosystems creates strong local and regional differences that hinders the extrapolation of results for global estimations, which remain uncertain [START_REF] Borges | Do we have enough pieces of the jigsaw to integrate CO2 fluxes in the coastal ocean? Estuaries[END_REF].

The δ 13 C-DIC is a helpful tool understanding biogeochemical cycling and tracing the sources, sinks and transformations of carbon in aquatic ecosystems [START_REF] Gillikin | Stable carbon isotopic composition of Mytilus edulis shells: relation to metabolism, salinity, δ 13 CDIC and phytoplankton[END_REF][START_REF] Burt | Carbon sources in the North Sea evaluated by means of radium and stable carbon isotope tracers[END_REF]). During photosynthesis, plants use preferentially the lighter stable carbon isotope ( 12 C) than the heavier stable carbon isotope ( 13 C). This carbon stable isotope discrimination leads to an isotopic fractionation and, thus, organic carbon in marine plants and algae are depleted in 13 C relative to their DIC source [START_REF] Burkhardt | Effects of growth rate, CO2 concentration, and cell size on the stable carbon isotope fractionation in marine phytoplankton[END_REF]. Therefore, aquatic primary production tends to leave the water rich in 13 C, increasing δ 13 C-DIC signatures [START_REF] Zeebe | CO2 in Seawater: Equilibrium, Kinetics, Isotopes[END_REF]). On the other hand, the degradation of organic carbon by respiring heterotrophic organisms, either in pelagic or in benthic compartments, produces CO2 with approximately the same isotopic signature of the respired organic matter, decreasing δ 13 C-DIC signatures [START_REF] Kendall | Stable isotope applications in hydrologic studies[END_REF][START_REF] Miyajima | Export of inorganic carbon from two Southeast Asian mangrove forests to adjacent estuaries as estimated by the stable isotope composition of dissolved inorganic carbon[END_REF]; Bouillon et al. 2011;[START_REF] Bhavya | Spatiotemporal variation in δ 13 CDIC of a tropical eutrophic estuary (Cochin estuary, India) and adjacent Arabian Sea[END_REF]).

The freshwater δ 13 C-DIC endmember in estuaries could present very different values, and related to distinct isotopic signatures from the major sources and sinks, including biogenic and lithological sources, air-water CO2 exchanges, and in situ metabolism [START_REF] Mook | Stable carbon isotopes in rivers and estuaries[END_REF][START_REF] Campeau | Multiple sources and sinks of dissolved inorganic carbon across Swedish streams, refocusing the lens of stable C isotopes[END_REF]. This large heterogeneity leads to freshwater end-members generally ranging between -5‰ and -25‰, depending on the intensity of the different δ 13 C-DIC sources and sinks [START_REF] Kendall | Stable isotope applications in hydrologic studies[END_REF][START_REF] Finlay | Stable isotope tracing of temporal and spatial variability in organic matter sources to freshwater ecosystems[END_REF]. This results in marked changes in the stable isotope carbon composition across estuarine salinity gradients from freshwater to the sea [START_REF] Fry | Conservative mixing of stable isotopes across estuarine salinity gradients: A conceptual framework for monitoring watershed influences on downstream fisheries production[END_REF]. Very negative δ 13 C-DIC signatures (down to -20‰ or range), which shows a strong depletion of 13 C in the DIC pool, were documented in several estuaries, especially at low salinity regions, which are usually highly heterotrophic [START_REF] Bouillon | Biogeochemistry of the Tana estuary and delta (northern Kenya)[END_REF]; Bouillon et al. 2011). Contrary to low salinity regions, the marine-dominated regions of estuaries exhibit higher δ 13 C-DIC signatures that are usually in the range of -2‰ to +2‰ (mean approaching 0‰) due to a predominance of marine DIC and a limited influence of DIC from terrestrial sources [START_REF] Mook | Stable carbon isotopes in rivers and estuaries[END_REF][START_REF] Chanton | Plankton and Dissolved Inorganic Carbon Isotopic Composition in a River-Dominated Estuary: Apalachicola Bay, Florida[END_REF][START_REF] Gruber | Spatiotemporal patterns of carbon-13 in the global surface oceans and the oceanic Suess Effect[END_REF]. Generally, the stable isotope signature of DIC in estuaries follows mixing process between marine and freshwater end-members [START_REF] Mook | Stable carbon isotopes in rivers and estuaries[END_REF], attesting that DIC levels are mainly controlled by physical processes [START_REF] Wang | Controls on the sources and cycling of dissolved inorganic carbon in the Changjiang and Huanghe River estuaries, China: 14 C and 13 C studies[END_REF]). However, deviation from mixing curves are frequently reported [START_REF] Coffin | Stable Isotope Analysis of Carbon Cycling in the Perdido Estuary, Florida[END_REF][START_REF] Bouillon | Inorganic and organic carbon biogeochemistry in the Gautami Godavari estuary (Andhra Pradesh, India) during pre-monsoon: The local impact of extensive mangrove forests[END_REF]; [START_REF] Gillikin | Stable carbon isotopic composition of Mytilus edulis shells: relation to metabolism, salinity, δ 13 CDIC and phytoplankton[END_REF]; [START_REF] Miyajima | Export of inorganic carbon from two Southeast Asian mangrove forests to adjacent estuaries as estimated by the stable isotope composition of dissolved inorganic carbon[END_REF]; Bouillon et al. 2011;[START_REF] Bhavya | Spatiotemporal variation in δ 13 CDIC of a tropical eutrophic estuary (Cochin estuary, India) and adjacent Arabian Sea[END_REF]). The δ 13 C-DIC data below conservative mixing suggest prevalence of respiration that adds depleted δ 13 C-DIC [START_REF] Bouillon | Inorganic and organic carbon biogeochemistry in the Gautami Godavari estuary (Andhra Pradesh, India) during pre-monsoon: The local impact of extensive mangrove forests[END_REF]Bouillon et al. 2011). On the other hand, in estuaries with important levels of photosynthesis, deviation above to the mixing curve can occur due to the preferential uptake of the lighter stable carbon isotope [START_REF] Coffin | Stable Isotope Analysis of Carbon Cycling in the Perdido Estuary, Florida[END_REF][START_REF] Zeebe | CO2 in Seawater: Equilibrium, Kinetics, Isotopes[END_REF][START_REF] Gillikin | Stable carbon isotopic composition of Mytilus edulis shells: relation to metabolism, salinity, δ 13 CDIC and phytoplankton[END_REF]). In addition to the metabolic controls (respiration and photosynthesis), the δ 13 C-DIC dynamic is also affected by physical controls such as the CO2 exchange with the atmosphere and dissolution/precipitation of carbonate minerals [START_REF] Finlay | Stable isotope tracing of temporal and spatial variability in organic matter sources to freshwater ecosystems[END_REF]. It is important to point out that when DIC reaches the equilibrium with atmospheric CO2 concentrations, the δ 13 C-DIC becomes close to the value of 0‰ (Bouillon et al. 2011). However, there is an important temperature-dependent equilibrium isotope fractionation of δ 13 C-DIC [START_REF] Zhang | Carbon isotope fractionation during gas-water exchange and dissolution of CO2[END_REF], and this can causes regional deviations from 0‰ depending on aquatic and atmospheric temperatures.

In addition to the high natural variability of δ 13 C-DIC values in estuaries and coastal zones, the isotopic signature of the DIC can change in response to anthropogenic forcing [START_REF] Finlay | Stable isotope tracing of temporal and spatial variability in organic matter sources to freshwater ecosystems[END_REF][START_REF] Yang | Treated Wastewater Changes the Export of Dissolved Inorganic Carbon and Its Isotopic Composition and Leads to Acidification in Coastal Oceans[END_REF]. Human activities, such as land-use changes, wastewater discharges, and wetlands destruction, are altering carbon sources, sinks, cycling and budgets [START_REF] Bauer | The changing carbon cycle of the coastal ocean[END_REF]. Although the use of δ 13 C-DIC is well established for investigations of ecosystem metabolism and water mixing processes in estuaries, this parameter has been rarely used to describe the occurrence of anthropogenic perturbations such as eutrophication. In the tropics, the development of coastal megacities with inefficient treatment of wastewaters, combined with enhanced biological activity due to specific climatic features, leads to drastic modifications of the regional carbon cycle [START_REF] Carreira | Changes in the sedimentary organic carbon pool of a fertilized tropical estuary, Guanabara Bay, Brazil: An elemental, isotopic and molecular marker approach[END_REF][START_REF] Cotovicz | A strong CO2 sink enhanced by eutrophication in a tropical coastal embayment (Guanabara Bay, Rio de Janeiro, Brazil)[END_REF], which should impact the isotopic signature of the DIC. Here, we present the first measurements of δ 13 C-DIC in a tropical coastal embayment that receives large amounts of untreated wastewaters from surrounding urban areas, which hosts a population of about 9 millions of inhabitants. Large inputs of domestic effluents into the bay enhanced the levels of aquatic primary production [START_REF] Rebello | Avaliação da produtividade primaria e da disponibilidade de nutrientes na Baia de Guanabara[END_REF], and turned the bay into a marked sink of CO2 [START_REF] Cotovicz | A strong CO2 sink enhanced by eutrophication in a tropical coastal embayment (Guanabara Bay, Rio de Janeiro, Brazil)[END_REF]. We hypothesized that these human perturbations of the estuarine system will have important impacts on the isotopic signature of the DIC that need a detailed characterization. We also expected uncommon isotopic signatures of these coastal waters compared to other estuarine and marine environments.

Materials and Methods

Study Area

Guanabara Bay (22°41-22°58 S and 43°02-43°18 W) is a tropical coastal embayment located at the SE-Brazilian coast (Fig. 1). The surface area is 384 km 2 , the mean depth is 5.7 m, and the water volume is about 1870 x 10 6 m 3 . The bay has a microtidal regime, and is a partially mixed estuary [START_REF] Kjerfve | Oceanographic characteristics of an impacted coastal bay: Baia de Guanabara, Rio de Janeiro, Brazil[END_REF]), but under conditions of high solar incidence and high freshwater discharge the bay could present a strong vertical thermohaline stratification [START_REF] Cotovicz | A strong CO2 sink enhanced by eutrophication in a tropical coastal embayment (Guanabara Bay, Rio de Janeiro, Brazil)[END_REF]. The annual freshwater inputs by the rivers is only about 100 m 3 s -1 [START_REF] Kjerfve | Oceanographic characteristics of an impacted coastal bay: Baia de Guanabara, Rio de Janeiro, Brazil[END_REF]. The large difference between the high water volume and the low amount of freshwater inputs are reflected in high salinities along the Bay (averaging 29.5 ± 4.8), with few lower values (down to 15) at the vicinity of the small river mouths. Considering the bay as a whole, more than 85% of the water volume corresponds to seawater, whereas only 15% is attributed to freshwaters (Costa-Santos, 2015). The average time necessary to renew 50% of the total water volume with the tidal movements is 11.4 days, but with significant spatial differences, especially at the most confined regions [START_REF] Kjerfve | Oceanographic characteristics of an impacted coastal bay: Baia de Guanabara, Rio de Janeiro, Brazil[END_REF]). Guanabara Bay is located in the intertropical zone, and the climate is characterized by a warm and wet summer, and a cooler and drier winter [START_REF] Bidone | The use of DPSIR framework to evaluate sustainability in coastal areas, case study: Guanabara Bay Basin, Rio de Janeiro, Brazil[END_REF]. The annual freshwater input to the bay is approximately 100 ± 59 m 3 s -1 , and modest compared to the bay's water volume, which contributed to the predominance of polyhaline to euhaline waters. The bay is one of the most polluted coastal systems in the world that receives large inputs of untreated domestic and industrial effluents at approximately 25 m 3 s -1 [START_REF] Kjerfve | Oceanographic characteristics of an impacted coastal bay: Baia de Guanabara, Rio de Janeiro, Brazil[END_REF][START_REF] Bidone | The use of DPSIR framework to evaluate sustainability in coastal areas, case study: Guanabara Bay Basin, Rio de Janeiro, Brazil[END_REF]. We compartmentalized the bay into five domains (sectors 1, 2, 3, 4, and 5) as described by [START_REF] Cotovicz | A strong CO2 sink enhanced by eutrophication in a tropical coastal embayment (Guanabara Bay, Rio de Janeiro, Brazil)[END_REF]2018a) for the treatment, computations and interpretation of the data (Fig. 1).

Experimental Design, Sampling Procedures and Laboratory Analysis

In 2013 and 2014, nine sampling campaigns were conducted for the analysis of δ 13 C-DIC and ancillary parameters of the water column in Guanabara Bay. The water parameters were sampled in continuous on-line and/or discrete procedures. Continuous measurements were performed to analyze the water temperature, salinity, DO and pCO2, as described by [START_REF] Cotovicz | A strong CO2 sink enhanced by eutrophication in a tropical coastal embayment (Guanabara Bay, Rio de Janeiro, Brazil)[END_REF]. Briefly, one submersible water pump was positioned at the side of the boat (depth of 0.5 m), providing continuous water flow to a measurement system located inside the boat. The continuous measurements of pCO2 followed the equilibration technique using a marble-type equilibrator coupled to a non-dispersive infrared gas detector (LICOR 820) [START_REF] Frankignoulle | A new design of equilibrator to monitor carbon dioxide in highly dynamic and turbid environments[END_REF]Cotovicz et al. 2016a). The equilibrator had a response time lower than 4 minutes, and, as the boat speed during measurements was about 6 km h -1 , pCO2 measurements were averaged over approximately 300m of the boat's track. One calibrated YSI 6600 V2 multiparameter probe measured continuously the water temperature, salinity and DO. Discrete water samples were taken for δ 13 C-DIC, chlorophyll a (Chl a), pheo-pigments, total alkalinity (TA), and dissolved inorganic phosphorus (PO4 3-), accounting to about 16-19 stations distributed across the bay, except in December 2013, when only 8 stations could be sampled. Subsurface water samples were collected at 0.5 m depth with a Niskin bottle, and conditioned (i.e. fixed and/or kept on ice in the dark) for further chemical analysis at the laboratory. The comparison between surface and bottom waters in terms of δ 13 C-DIC concentrations and other physico-chemical parameters were performed at some stations, during the summer period, and during conditions of maximal vertical stratification at summer period in sectors 3, 4, and 5 (Cotovicz et al. 2016b).

The water was filtered with whatman GF/F glass-fibre filters (porosity 0.45 μm) followed by determination of suspended particulate material (SPM), Chl a and pheo-pigments. The filters were pre-combusted (at 500° C during 6 hours) and pre-weighted before utilization. After filtration, filters were dried in an oven at 50°C and then weighed. SPM was determined gravimetrically. Chl a and pheo-pigments were extracted in 90% acetone and quantified spectrophotometrically before and after acidification of the samples, according to [START_REF] Strickland | A practical handbook of seawater analysis[END_REF]. PO4 3-was quantified by the colorimetric method as in [START_REF] Grasshoff | Methods of seawater analysis[END_REF]. For the stable isotope composition of the DIC, the water was sampled and transferred directly to 150 mL serum vials, which were poisoned by adding 0.2 mL of a solution saturated with HgCl2 and carefully sealed, taking care that no air remained in contact with samples. Vials were also stored in the dark to prevent photo oxidation. In the laboratory, the δ 13 C-DIC signature was determined following the protocol of [START_REF] Bouillon | Biogeochemistry of the Tana estuary and delta (northern Kenya)[END_REF]. We injected 40 mL of helium gas inside the bottles to create a headspace, maintaining the bottles bottom-up and simultaneously expelling water by a second needle.. Then, 0.2 mL of ultrapure and concentrated H3PO4 was introduced to convert all inorganic carbon to CO2. Samples were shaken vigorously and kept 12h in the dark at a controlled temperature of 25°C. The δ 13 C of CO2 in the headspace was determined by injecting between 0.5 mL and 1 mL of the headspace gas in an isotopic ratio mass spectrometer (IRMS, Micromass IsoPrime), equipped with a manual gas injection port. δ 13 C-DIC was calibrated using a laboratory standard, which was prepared adding 45 mg of Na2CO3 in a sealed vial flushed with helium and dissolved with 3 mL of 85% H3PO4, as described in [START_REF] Deirmendjian | Carbon dioxide degassing at the groundwater-streamatmosphere interface: isotopic equilibration and hydrological mass balance in a sandy watershed[END_REF]. This standard was calibrated against certified standard (NBS19, -1.96%) using a dual-inlet IRMS. The isotopic value of the Na2CO3 standard was -4.5±0.2‰. The obtained δ 13 C values were corrected for the partitioning of CO2 between the gaseous (headspace) and water phase in each sample using the algorithm of [START_REF] Miyajima | Determining the stable isotope ratio of total dissolved inorganic carbon in lake water by GC/C/IIRMS[END_REF]. The repeatability of the analysis was approximately 0.1‰. The δ 13 C-DIC signatures are reported in ‰ relative to the standard Vienna Pee Dee Belemnite (V-PDB) scale. TA was measured on 70 mL of filtrate samples, by the classical Gran titration method [START_REF] Gran | Determination of the equivalence point in potentiometric titrations[END_REF]) using an automated titration system (Mettler Toledo model T50). The reproducibility of the titration was ± 3 µmol kg -1 (n = 5), and the accuracy was estimated at ± 5 µmol kg -1 (inferred from certified material reference, CRM, provided by A. G. Dickson, Scripps institution of Oceanography). To compare the pCO2 with discrete sampling, we used the value of pCO2 exactly the moment of the discrete sampling at the fixed station (after achievement of equilibration). As such, we obtained the values of pCO2 and TA at same time and place. DIC concentrations were calculated from the values of pCO2 and TA, and were very consistent with the DIC calculated from the values of measured pH and TA [START_REF] Cotovicz | A strong CO2 sink enhanced by eutrophication in a tropical coastal embayment (Guanabara Bay, Rio de Janeiro, Brazil)[END_REF]. Calculations of DIC were made using the carbonic acid constants proposed by [START_REF] Mehrbach | Measurements of the apparent dissociation constants of carbonic acid in seawater at atmospheric pressure[END_REF] refitted by [START_REF] Dickson | A comparison of the equilibrium constants for the dissociation of carbonic acid in seawater media[END_REF] as implemented in the CO2Calc V 4.0.9 program (Robbins et al. 2010).

Calculation of DIC and δ 13 C-DIC addition or loss

Guanabara Bay did not present a marked saline gradient (Tab. 1; range was 14 to 35). Instead, this bay presents salinities generally higher than 30, and the low salinity waters are restricted to locations close to the river water and effluent discharges. When the river DIC inputs are weak or negligible, the conservative mixing of DIC (DICmixing) can be calculate using the marine endmember as follows [START_REF] Jiang | A comparative study of carbon dioxide degassing in river-and marine-dominated estuaries[END_REF]):

DICmixing = Si/Socean*DICocean (1)
Where Si is the measured salinity, Socean the salinity of the ocean end-member, and DICocean the DIC concentration of the ocean end-member. The DICmixing is the DIC concentration after the ocean end-member is diluted by a zero DIC freshwater; however, this equation also includes possible DIC inputs from river [START_REF] Jiang | A comparative study of carbon dioxide degassing in river-and marine-dominated estuaries[END_REF]).

The excess of DIC (ΔDICexcess) is defined as the DIC addition or loss relative to the conservative mixing [START_REF] Jiang | A comparative study of carbon dioxide degassing in river-and marine-dominated estuaries[END_REF], and can be expressed as:

ΔDICexcess = DICi -DICmixing (2)
Where DICi is the measured DIC. In the same way, the excess of total alkalinity (ΔTAexcess) can be calculated as the deviation from the conservative mixing:

ΔTAexcess = TAi -TAmixing (3)
In a similar approach developed by [START_REF] Yang | Treated Wastewater Changes the Export of Dissolved Inorganic Carbon and Its Isotopic Composition and Leads to Acidification in Coastal Oceans[END_REF], the difference between the δ 13 C-DIC of the sample (δ 13 C-DICi) and the δ 13 C-DIC of the marine end-member (δ 13 C-DICocean) represent the stable isotopic deviation from the marine end-member (Δδ 13 C-DIC) linked to local processes, as follows:

Δδ 13 C-DIC = δ 13 C-DICi -δ 13 C-DICocean (4)
When DIC is altered by processes of organic carbon degradation, primary production, and/or airwater exchanges, its isotopic composition is also altered, following mass balance equations (complete set of equation can be found in [START_REF] Yang | Treated Wastewater Changes the Export of Dissolved Inorganic Carbon and Its Isotopic Composition and Leads to Acidification in Coastal Oceans[END_REF]). The simplified equation is: 13 Cexcess-δ 13 Cocean) [START_REF] Bhavya | Spatiotemporal variation in δ 13 CDIC of a tropical eutrophic estuary (Cochin estuary, India) and adjacent Arabian Sea[END_REF] The δ 13 Cexcess represent the stable isotopic composition of the added or lost DIC whereas the δ 13 Cocean is the stable isotopic composition of the marine end-member. In coastal waters with limited river inputs, the DICi and DICocean are approximately the same. Then, the equation 5 can be adjusted to:

Δδ 13 C-DIC = ΔDICexcess/DICi*(δ
Δδ 13 C-DIC = ΔDICexcess/DICocean*(δ 13 Cexcess-δ 13 Cocean) [START_REF] Bidone | The use of DPSIR framework to evaluate sustainability in coastal areas, case study: Guanabara Bay Basin, Rio de Janeiro, Brazil[END_REF] This equation above means that ΔDICexcess/DICocean and Δδ 13 C-DIC are linked and linearly related. In this way, the slope of this relationship can be used to infer the isotopic composition of the added or lost DIC and the ocean end-member value [START_REF] Yang | Treated Wastewater Changes the Export of Dissolved Inorganic Carbon and Its Isotopic Composition and Leads to Acidification in Coastal Oceans[END_REF]).

The δ 13 C signature of the added or lost DIC due to the organic carbon production or respiration was taken as the average of δ 13 C-POC value in the bay, which is about -20‰ [START_REF] Kalas | Molecular and isotopic characterization of the particulate organic matter from an eutrophic coastal bay in SE Brazil[END_REF]). The fractionation factor (αCO2) due to outgassing of CO2 was calculated following the procedures described by [START_REF] Alling | Degradation of terrestrial organic carbon, primary production and out-gassing of CO2 in the Laptev and East Siberian Seas as inferred from δ13C values of DIC[END_REF] and [START_REF] Samanta | Dissolved inorganic carbon (DIC) and its δ 13 C in the Ganga (Hooghly) River estuary, India: Evidence of DIC generation via organic carbon degradation and carbonate dissolution[END_REF]. We applied the equation of [START_REF] Rau | A model of photosynthetic C-13 fractionation by marine phytoplankton based on diffusive molecular CO2 uptake[END_REF] to estimate the fractionation factor (α) between DIC and the dissolved CO2 in water, according to: δ 13 C-CO2 = δ 13 C-DIC + 23.644 -9701.5/T [START_REF] Borges | Do we have enough pieces of the jigsaw to integrate CO2 fluxes in the coastal ocean? Estuaries[END_REF] This equation gives the equilibrium fractionation factor (ɛCO2), which is the difference between δ 13 C-CO2 and δ 13 C-DIC. This calculation provides a value of ɛCO2 of -9.2‰, representing the averaged found in the sector 2 (the only sector that is a net source of CO2 to the atmosphere). Defining fCO2 as the fraction of DIC remaining in the water after outgassing of CO2, we can calculate the DIC concentration after CO2 loss (DICF, which is equivalent to the measured DIC, DICi), according: DICF = fCO2 * DICI [START_REF] Borges | Carbon Dioxide and Methane Dynamics in Estuaries[END_REF] where DICI represents the initial DIC concentration before outgassing, which is equivalent to the calculated DIC based on equation 1, DICmixing. The 13 C/ 12 C ratio in the remaining waters (RF) will be fractionated during progressive outgassing by the Rayleigh distillation process, according:

RF= RI (fCO2) αCO2-1 (9)
Where RI is the initial 13 C/ 12 C ratio before outgassing. This equation is equivalent to (Alling et al.

2012):

δ 13 CF = δ 13 CI + 10 3 (αCO2 -1) ln(fCO2) [START_REF] Bouillon | Biogeochemistry of the Tana estuary and delta (northern Kenya)[END_REF] If we consider that the amount of DIC that is lost by outgassing is small compared to the total pool of DIC [START_REF] Alling | Degradation of terrestrial organic carbon, primary production and out-gassing of CO2 in the Laptev and East Siberian Seas as inferred from δ13C values of DIC[END_REF][START_REF] Samanta | Dissolved inorganic carbon (DIC) and its δ 13 C in the Ganga (Hooghly) River estuary, India: Evidence of DIC generation via organic carbon degradation and carbonate dissolution[END_REF], the DICF tend to be close to DICmixing (in fact this ratio is close to 1 in Guanabara Bay, and consistent with other studies). In this way, equations 1, 4, 8 and 9 can be combined:

Δδ 13 C-DIC ~ ΔDICexccess (αCO2 -1)10 3 [START_REF] Bouillon | Use of Stable Isotopes to Understand Food Webs and Ecosystem Functioning in Estuaries[END_REF] Considering that αCO2 ~ 0.991 in Guanabara Bay, there is a near linear relationship between Δδ 13 C-DIC and ΔDICexcess, with a slope of -9.2 value of outgassed CO2. As the bay is a net sink of CO2 [START_REF] Cotovicz | A strong CO2 sink enhanced by eutrophication in a tropical coastal embayment (Guanabara Bay, Rio de Janeiro, Brazil)[END_REF], we also calculate a slope representing the uptake of atmospheric CO2. During uptake, αCO2 ~ 0.998 (Siegethaler and Münnich, 1981; [START_REF] Inoue | Carbon isotopic fractionation during the CO 2 exchange process between air and sea water under equilibrium and kinetic conditions[END_REF], giving a slope of approximately -2.0 that represents the process of CO2 uptake.

The average δ 13 C -DIC signature of the wastewater DIC input was calculate with the keeling plot for the most polluted region (Fig. S1, supplementary file), which give a value of -12.2‰. This stable isotopic signature is very consistent with that found in wastewater samples (-12.0‰).

Estimates of the apparent photosynthetic fractionation factor of DIC (ε-DIC)

Photosynthesis leads to the 13 C enrichment of the remaining DIC pool as the phytoplankton uses preferentially the 12 C (Mook 2001). The photosynthetic fractionation factor of DIC consumed (εp-DIC) was calculated using the diurnal variations in the DIC concentrations and its stable isotope composition. In Sep.2013, Jan.2014 and Apr.2014, diurnal variations in water δ 13 C-DIC were estimated within the upper sectors (sector 4 and 5) by performing lateral trajectories back and forth across the sectors from dawn to noon (further referred as morning period) and from noon to dusk (further referred as afternoon period). The stable isotope composition of the DIC used by phytoplankton (δ 13 Cused) from dawn to noon period is likened to the DIC concentrations and its stable isotope composition observed between these two periods considering a simple conservative mixing by a mass balance equation:

δ 13 Cused = (DICdawnδ 13 Cdawn-DICnoonδ 13 Cnoon) /(DICdawn-DICnoon) [START_REF] Brandini | Nutrient behavior in a highly-eutrophicated tropical estuarine system[END_REF] where δ 13 Cdawn and δ 13 Cnoon refer to the stable isotope composition of the DIC at dawn and noon, respectively, and DICdawn and DICnoon refer to their respective concentrations. This formulation was also applied to investigate the stable isotope composition of the DIC used by phytoplankton during the afternoon. Then, this apparent photosynthetic fractionation of DIC (εp-DIC) was then estimated as the difference between the initial composition of DIC (δ 13 C-DICi) and the calculated δ 13 Cused for each period (morning and afternoon), as follows:

εp-DIC = δ 13 C-DICiδ 13 Cused (13)

In addition, we calculated the plots of Rayleigh Distillation, where the increase in δ 13 C-DIC was plotted against the consumed DIC at the diel scale, in a similar approach of Dam et al. (2018).

Statistical Analysis

The Shapiro-Wilk test showed that data of pCO2, TA, DIC, δ 13 C-DIC and Chl a did not follow a normal distribution. Consequently, non-parametric statistical tests were performed. The paired Wilcoxon test was used to compare concentrations of the measured parameters between surface and bottom waters. The seasonal differences were analyzed by the Mann-Whitney test. Spearman rank coefficient was used to calculate the coefficient correlations between the measured parameters. Linear and non-linear (second order polynomial) regressions were also calculated. All statistical analysis were based on α = 0.05 and were performed with the GraphPad Prism 6 software.

Data Compilation and Literature Survey

A compilation of δ 13 C-DIC signatures from global databases such as the Institute National des Sciences de L'Univers (INSU-France) and the Carbon Dioxide Information Analysis Center (CDIAC) was carried out to obtain δ 13 C-DIC data of other estuarine, coastal and open ocean waters worldwide. We also used the search engines Google Scholar and Web of Science to compile data from literature. We recorded the available data directly from tables and/or interpolated from figures using the data extraction program PlotDigitalizer. The different δ 13 C-DIC data obtained from this compilation work were ranked according to their salinity in order to compare it with the data obtained in this study.

Results

The 1: Mean (± standard deviation) and ranges of the principal parameters investigated in the waters of Guanabara Bay, separated by sectors.

The δ 13 C-DIC signatures in Guanabara Bay did not present conservative distributions with salinity gradient (Fig. S2; supplementary file). Indeed, DIC in the bay was enriched in 13 C in some parts (mainly sectors 3, 4 and 5) relative to the marine end-member that presented a stable isotopic signature of 1.5‰ (Tab. 1), whereas in some restricted parts the bay showed 13 C depletion (mainly sector 2) (Tab. 1, Fig. 1). Spatially, the sectors 1 and 3 presented the higher averages of δ 13 C-DIC signatures, which were 1.6‰ and 1.7‰, respectively (Tab. 1). However, some extreme high values (δ 13 C-DIC > 3‰) were also present at the most shallow-confined regions of the bay (sectors 4 and 5) (Tab. 1). Sector 2, the most polluted region, presented the lowest average of δ 13 C-DIC, which was 0.4‰ (Tab. 1). Some more negative values of δ 13 C-DIC were also found in sectors 4 and 5 close to the outlet of rivers and urban sewage networks (Tab. 1; Fig. 1). Considering all sectors, the range of δ 13 C-DIC signature in the entire bay was -6.1‰ (Sector 2) to 4.6‰ (Sector 3). Temporally, the δ 13 C-DIC also showed important seasonal variations, especially between winter and summer periods (Fig. 1). Significantly (Mann-Whitney test, p < 0.001), the summer period (considered the months of Apr. 2013, Jul. 2013, Aug. 2013, Sep. 2013 and Ap. 2014) presented more positive δ 13 C-DIC signatures than the winter period (Oct. 2013, Dec. 2013, Jan. 2014 and Feb. 2014). Indeed, the average signatures of δ 13 C-DIC for the entire bay in winter and summer were respectively 1.0‰ ± 1.4‰ and 1.5‰ ± 1.7‰. Moreover, the differences between surface and bottom waters for δ 13 C-DIC during summer were of high statistical significance (p < 0.001; Wilcoxon test). DIC pool was significantly enriched in 13 C at the surface layer, as δ 13 C-DIC averaged at 1.8‰ ± 0.6‰ in surface waters and 1.2‰ ± 1.0‰ in bottom waters (Tab. S1, supplementary file). The Spearman correlation matrix was calculated for all the parameters considered in this study: δ 13 C-DIC, salinity, temperature, Chl a, DIC, pCO2, DO, photosynthetically active radiation (PAR), suspended particulate material (SPM), and particulate organic carbon (POC) (Tab. S2, supplementary file). The values were established with averages for each sampling campaign. Interestingly, δ 13 C-DIC was significantly and positively correlated to temperature, Chl a, PAR, DO, SPM and POC concentrations, while negatively correlated to pCO2 levels and DIC concentrations. Fig. 2 showed the calculated diel photosynthetic fractionation factor (ε-DIC) plotted against the discrete values of pCO2 and DIC concentrations. This approach was applied only at the diel scale, assuming that the phytoplankton blooms realized isotopic fractionation by incorporating preferentially the lighter stable carbon isotope. We compare the fractionation between the morning and the afternoon. The isotopic fractionation was higher during the morning, ranging from 18.7‰ to 21.6‰ whereas lower fractionations occurred during the afternoon, and ranged between 6.8‰ to 11.1‰ (Fig. 2). The photosynthetic fractionation factor was strongly and positively correlated to the concentrations of DIC (R 2 = 0.73, p = 0.02) and pCO2 (R 2 = 0.88, p < 0.005) (Fig. 2). Fig. 3 showed the plots of Rayleigh distillation that aimed to better analyze the diel isotopic fractionation dynamic. The increase of δ 13 C-DIC was related to a given change in the fraction of consumed DIC. The diel cycles of production and respiration caused δ 13 C-DIC to vary between 2.1‰ and 2.8‰ (Fig. 3). The increase of δ 13 C-DIC signatures along the day was proportional to the decrease of DIC concentrations (Fig. 3). The relationship between δ 13 C-DIC and the Chl a concentrations was plotted using the sector-averaged values for each sampling survey (Fig. 4). This figure shows a positive relationship between the phytoplankton biomass and δ 13 C-DIC, especially at the most productive regions of Guanabara Bay (sectors 3, 4 and 5), where the extreme positive δ 13 C-DIC signatures occurred in dense phytoplankton blooms with Chl a concentrations above 50 µg L -1 (Fig. 4). The comparison of δ 13 C-DIC signatures of Guanabara Bay with other ecosystems worldwide was provided in Fig. 5. Guanabara Bay showed an inverse tendency between δ 13 C-DIC and pCO2 values (Fig. 5a), where phytoplankton-dominated waters presented the highest δ 13 C-DIC and the lowest pCO2 values. The values of pCO2 in Guanabara Bay were generally lower than the compiled data, whereas δ 13 C-DIC signatures were much higher (Fig. 5a). This comparison of Guanabara Bay with other coastal and open ocean waters worldwide was also performed considering the salinity (Fig. 5b and5c). These graphs showed a high scattering in the distributions of the δ 13 C-DIC according to salinity. For a same salinity, the δ 13 C-DIC may exhibit variation up to 20‰. The range of δ 13 C-DIC was higher in low salinity regions and decreased progressively when freshwaters mixed with ocean waters. The salinity range between 20-30 presented the highest δ 13 C-DIC enrichment in Guanabara Bay compared to the data from other estuaries and coasts, with a difference of about 3.20‰, on average (Fig. 5b). Compared to mangrove-dominated estuaries with salinities ranging from 15 to 20, Guanabara Bay showed an significant (Mann Whitney test, p < 0.0001) increase in δ 13 C-DIC of 6.75‰ (Fig. 5b). As a coastal embayment dominated by saline waters, the inputs of freshwater to Guanabara Bay are very low compared to its water volume [START_REF] Kjerfve | Oceanographic characteristics of an impacted coastal bay: Baia de Guanabara, Rio de Janeiro, Brazil[END_REF]). Taking account this hydrological characteristic, we calculated the sinks and sources of DIC and TA to the system for a special case, i.e., when the freshwater inputs are weak, following the procedures described by [START_REF] Jiang | A comparative study of carbon dioxide degassing in river-and marine-dominated estuaries[END_REF]. Thus, it is possible to infer the gains and losses of DIC (ΔDICexcess) and TA (ΔTAexcess) relative to the conservative mixing (see materials and methods for details). The maximum values of ΔDICexcess and ΔTAexcess were coincident with the highest values of pCO2 and no related to salinity (Fig. S2; supplementary file). Oversaturation of pCO2 in the bay was restricted to sites close to the small river mouths and sewage channels [START_REF] Cotovicz | A strong CO2 sink enhanced by eutrophication in a tropical coastal embayment (Guanabara Bay, Rio de Janeiro, Brazil)[END_REF]. These polluted sites present occasional occurrence of hypoxia and anoxia events, sustaining heterotrophic metabolism [START_REF] Ribeiro | Anthropogenic influence on the water quality in Guanabara Bay, Rio de Janeiro, Brazil[END_REF][START_REF] Cotovicz | A strong CO2 sink enhanced by eutrophication in a tropical coastal embayment (Guanabara Bay, Rio de Janeiro, Brazil)[END_REF]. Anaerobic processes including ammonification, denitrification and sulphate reduction can contributes to the production of alkalinity [START_REF] Abril | Nitrogen -alkalinity interactions in the highly polluted Scheldt Basin (Belgium)[END_REF][START_REF] Hu | An assessment of ocean margin anaerobic processes on oceanic alkalinity budget[END_REF].

DIC (‰ )

C -DIC (‰)

The spatial distributions of δ 13 C-DIC along Guanabara Bay shows a higher 13 C depletion (down to -6.17‰) only closest to the locations that receive these direct inputs of DIC from effluent discharges (Fig. 1). Fig. 6 shows the plot of ΔDICexcess/DICocean against Δδ 13 C-DIC, and the slopes of this relationship can be used to infer the main biogeochemical processes affecting the distributions of DIC and δ 13 C-DIC (see the figure caption for further explanations). The highest DIC additions occurred closest to Rio de Janeiro city at the northwestern region of Guanabara Bay (Sector 2). These samples from polluted sites fall within the III quadrant of the graph, indicating processes of organic carbon degradation [START_REF] Samanta | Dissolved inorganic carbon (DIC) and its δ 13 C in the Ganga (Hooghly) River estuary, India: Evidence of DIC generation via organic carbon degradation and carbonate dissolution[END_REF][START_REF] Yang | Treated Wastewater Changes the Export of Dissolved Inorganic Carbon and Its Isotopic Composition and Leads to Acidification in Coastal Oceans[END_REF]. For very high pCO2 values, the data in quadrant III follows the theoretical slopes of wastewater contribution (slope = -0.012; vector D) and the degradation of organic carbon (slope = -0.020; vector C), and confirms the DIC inputs more depleted in 13 C. These polluted regions present the highest bacterial and virus contents [START_REF] Fistarol | Environmental and Sanitary Conditions of Guanabara Bay, Rio de Janeiro[END_REF], are sources of CO2 and CH4 [START_REF] Cotovicz | A strong CO2 sink enhanced by eutrophication in a tropical coastal embayment (Guanabara Bay, Rio de Janeiro, Brazil)[END_REF]2016b), and show episodic evidence of corrosive waters with low saturation state of calcium carbonates (Cotovicz at el., 2018b). Similar results were found in the urbanized temperate Jiaozhou Bay-China [START_REF] Yang | Treated Wastewater Changes the Export of Dissolved Inorganic Carbon and Its Isotopic Composition and Leads to Acidification in Coastal Oceans[END_REF]2018), where the authors found an important input of depleted δ 13 C-DIC in waters that receive direct discharge from wastewater plans.

The strong negative correlation (R² = 0.8; p-value<0.001) between δ 13 C-DIC and PO4 3-in sector 2 reinforce the role of wastewaters as the main source of PO4 3-and DIC depleted in 13 C in this region (Fig. S3; supplementary file). Studies have shown that, in general, the PO4 3--P was the dominant limiting nutrient in the bay, presenting sometimes an almost depletion and related to the strong phytoplankton uptake (Costa-Santos 2015; [START_REF] Brandini | Nutrient behavior in a highly-eutrophicated tropical estuarine system[END_REF]). The calculated isotopic signature of the added DIC for the samples located in these polluted regions (excluding the data with Chl a concentrations > 50 µg L -1 ) gives a stable isotopic signature of sewage source of -12.2‰ (Fig. S2). This value is very consistent with that found in wastewater treatment plants in China (average of -12‰; Yang et al. 2018), and with values found in a domestic sewage emissary in another region of Rio de Janeiro city (-13‰; unpublished data). Taking into account this, we quantified the contribution of sewage discharges for the two most polluted regions (sectors 2 and 5; Fig. 1) by applying a simple two-source mixing model [START_REF] Phillips | Uncertainty in source partitioning using stable isotopes[END_REF]. We used the value of -12.2‰ as the δ 13 C-DIC signature of sewage source, and the value of 1.5‰ as the δ 13 C-DIC-signature source of marine source (considered the average δ 13 C-DIC signature of sector 1). The model calculated a sewage contribution of about 10% in sector 2 and 5% in sector 5. The depleted δ 13 C-DIC signature from polluted sources is lost very fast in the bay, confirming the sewage-derived DIC is rapidly degassed and/or assimilated by phytoplankton blooms, as we will discuss in the next section of the manuscript. Important to point that the degassing is a process that turns the water more enriched in the heavier carbon isotope ( 13 C), since that during CO2 emissions the lighter carbon ( 12 C) is preferentially emitted due to the kinetic isotope effect.

Another source of DIC depleted in 13 C to the water column in Guanabara Bay could be the mangrove forest located at the northeastern region (Fig. 1); however, we could not find a clear contribution into the bay (except for one sample collected close to the region, during low tide, which presented a negative δ 13 C-DIC signature of -2.5‰). This value is very far from that found in mangrove-dominated waters, for example, in a tidal creek in Gazi Bay (Kenya) where the δ 13 C-DIC values were very depleted (~ -8‰) even for salinities higher than 30 [START_REF] Bouillon | Biogeochemistry of the Tana estuary and delta (northern Kenya)[END_REF]) (Fig. 5). This low influence of mangrove in Guanabara Bay occurs probably because of low tidal pumping related to the microtidal character of the bay (Cotovicz et al. 2018a). In addition, the less 13 C-enriched sediments were restricted to the area very close to the mangrove forest [START_REF] Carreira | Changes in the sedimentary organic carbon pool of a fertilized tropical estuary, Guanabara Bay, Brazil: An elemental, isotopic and molecular marker approach[END_REF]).

Influence of the phytoplankton fractionation on the δ 13 C-DIC dynamics

Despite the influence of wastewater contribution closest to sites that receive direct sewage discharge, most of δ 13 C-DIC values are positive, indicating an isotopic fractionation of DIC by marine phytoplankton by a preferential use of 12 C during photosynthesis (Fig. 6). Many data points follow the theoretical slope of primary production (represented by vector A) that decreases the ratio ΔDICexcess/DICocean and increases the Δδ 13 C-DIC in the quadrant I (slope of -0.020). The high incidence of PAR, especially during summer, associate with high nutrient availability and formation of thermohaline stratification, increases the rates of primary production [START_REF] Rebello | Avaliação da produtividade primaria e da disponibilidade de nutrientes na Baia de Guanabara[END_REF], associated with development of massive phytoplankton blooms and strong CO2 uptake [START_REF] Cotovicz | A strong CO2 sink enhanced by eutrophication in a tropical coastal embayment (Guanabara Bay, Rio de Janeiro, Brazil)[END_REF]. This uptake of DIC removes preferentially the lighter 12 C, enriching the waters with the heavier stable carbon isotope [START_REF] Mook | Environmental Isotopes in the Hydrological Cycle[END_REF]. Successive algal blooms could consumes more of the DIC pool, and the residual DIC becomes progressively 13 C-enriched due to the isotopic fractionation [START_REF] Finlay | Stable isotope tracing of temporal and spatial variability in organic matter sources to freshwater ecosystems[END_REF]. Guanabara Bay showed persistent phytoplankton blooms in all the sampling campaigns, which spread to the entire bay and cover larger areas during summer months [START_REF] Cotovicz | A strong CO2 sink enhanced by eutrophication in a tropical coastal embayment (Guanabara Bay, Rio de Janeiro, Brazil)[END_REF]. Fig. 4 corroborates this result, with a positive tendency between the δ 13 C-DIC and Chl a concentrations, suggesting that the seasonal variation of the δ 13 C-DIC signature is related to changes in the extension of the phytoplankton dominance. This feature was also reported in the Perdido Estuary (Florida, USA) during periods of higher phytoplankton production [START_REF] Coffin | Stable Isotope Analysis of Carbon Cycling in the Perdido Estuary, Florida[END_REF], in the Scheldt Estuary (Netherlands and Belgium) when the δ 13 C-DIC showed higher signatures during phytoplankton bloom periods [START_REF] Hellings | Dissolved inorganic carbon in a highly polluted estuary (the Scheldt)[END_REF][START_REF] Gillikin | Stable carbon isotopic composition of Mytilus edulis shells: relation to metabolism, salinity, δ 13 CDIC and phytoplankton[END_REF]. Fig. 6 present some points located in the quadrant IV, which represents the carbonate dissolution. The process of carbonate dissolution consumes DIC of the water column, and adds δ 13 C with an isotopic signature closest to that of marine carbonates (0‰), turning the waters enriched in 13 C relative to the conservative mixing [START_REF] Alling | Degradation of terrestrial organic carbon, primary production and out-gassing of CO2 in the Laptev and East Siberian Seas as inferred from δ13C values of DIC[END_REF]). However, this process is unlikely to occur in the bay since that the values of pCO2 in quadrant IV are low and the pH values are high (Cotovicz et al. 2018b). Actually, DIC and δ 13 C-DIC can be subjected simultaneously to more than one process and not just by a specific one [START_REF] Samanta | Dissolved inorganic carbon (DIC) and its δ 13 C in the Ganga (Hooghly) River estuary, India: Evidence of DIC generation via organic carbon degradation and carbonate dissolution[END_REF]. This means that if one sample was subject to degradation of organic carbon (represented by quadrant III) followed by primary production (represented by quadrant I), this sample could finally be located in quadrant IV (the deviation is represented by the blue arrow, which is drawn parallel to vector A). Similarly, if a sample was subject to the DIC uptake by primary production (vector A) and thereafter occurs an intrusion of atmospheric CO2 due to the gradient at the air-water interface (CO2 sink, vector E), this sample could also be deviated to the quadrant IV (green arrow). The red arrow is drawn parallel to vector B, representing the effect of organic carbon degradation followed by outgassing of CO2. This is probably occurring in samples mainly from sector 2 that are located on quadrant IV that present high values of measured pCO2, when the outgassing could be important due to important air-water gradient of CO2. Another example is the quadrant I, where exists two vectors (A and B), representing the slopes of biological production and outgassing, respectively. Both these processes lead to loss of DIC and increase of δ 13 C-DIC. However, the process of outgassing in these samples are unlikely since that the values of pCO2 in this quadrant are highly undersaturated. ). The red, blue and green arrows represent the direction in which the samples will follow if they are subject to more than one process. The red arrow represents the effect of organic matter degradation followed by outgassing of CO2, which is drawn parallel to vector B. The blue arrow represents the effect of degradation of organic carbon followed by biological production, which is drawn parallel to vector A. The green arrow represents the effect of primary production followed by intrusion of atmospheric CO2 due to the air-water gradient, which is drawn parallel to vector E.

The apparent phytoplankton isotopic fractionation (ε-DIC) was higher under conditions of high availability of dissolved CO2, with higher fractionation during the morning than the afternoon (Fig. 2). During morning, the values of pCO2 were higher in Guanabara Bay as the results of the accumulated CO2 respired during the nighttime [START_REF] Cotovicz | A strong CO2 sink enhanced by eutrophication in a tropical coastal embayment (Guanabara Bay, Rio de Janeiro, Brazil)[END_REF]. This suggests that the discrimination against 13 C is higher when the availability of dissolved CO2 is higher. Previous studies showed similar results, both in culture experiments (Fogel and Cifuentes, 1993), and in situ at a Chinese hypereutrophic lake (Van Dam et al. 2018). The δ 13 C-DIC fractionation by phytoplankton in Guanabara Bay follows a Rayleigh distillation (Fig. 3), where the increasing removal of DIC fractions is accompanied by the isotopic fractionation of δ 13 C-DIC, turning the water enriched in 13 C. The values of ε-DIC found during the morning period in Guanabara Bay were about 20‰, a classical value for the marine phytoplankton [START_REF] Fontugne | Organic carbon isotopic fractionation by marine plankton in the temperature range -1 to 31°C[END_REF]Duplessy, 1981, Fogel and[START_REF] Coffin | Stable Isotope Analysis of Carbon Cycling in the Perdido Estuary, Florida[END_REF][START_REF] Mook | Environmental Isotopes in the Hydrological Cycle[END_REF]. Under conditions of low pCO2, the δ 13 C-DIC fractionation decreases during the afternoon, reflecting the decline in carbon assimilation efficiency. This decrease of fractionation under CO2 limitation was showed experimentally for marine diatoms [START_REF] Burkhardt | Effects of growth rate, CO2 concentration, and cell size on the stable carbon isotope fractionation in marine phytoplankton[END_REF]), and it is consistent with results found in a hypertrophic Chinese lake under conditions of CO2 sub saturation (Van Dam et al. 2018). In addition, under low availability of dissolved CO2, the phytoplankton can consumes bicarbonate (HCO3 -) [START_REF] Burns | Utilization of inorganic carbon acquisition by marine microalgae[END_REF], and this could contribute to decrease the isotopic fractionation factor since that the isotope ratio of HCO3 -is about 8‰ more positive than that of dissolved CO2 (Fogel and Cifuentes, 1999). Previous studies suggested an active uptake of HCO3 -in Guanabara Bay due to the enrichment of the δ 13 C-POC pool (δ 13 C-POC reaching -15.1‰; [START_REF] Kalas | Molecular and isotopic characterization of the particulate organic matter from an eutrophic coastal bay in SE Brazil[END_REF][START_REF] Martins | Characterization of particulate organic matter in a Guanabara Bay-coastal ocean transect using elemental , isotopic and molecular markers[END_REF]. Cyanobacteria blooms, which have already been documented in Guanabara Bay, can use bicarbonate under low pCO2 availability [START_REF] Miller | Physiological aspects of CO2 and HCO3 transport by cyanobacteria: A review[END_REF]).

Comparison with other ecosystems worldwide

The plot of δ 13 C-DIC versus pCO2 (Fig. 5a) shows that the blooms-dominated waters present strong pCO2 under-saturation and are as well enriched in 13 C, that is intrinsically related to the extreme levels of primary production. Guanabara Bay presented values of δ 13 C-DIC high above than those of the compiled data in estuaries and coasts, revealing the advanced process of eutrophication in the bay. The compiled data in estuaries presented a high scattering compared to the open ocean waters, especially for values of δ 13 C-DIC lower than 0‰ (Fig. 5c). This reflects a combination of processes such as respiration of terrestrial organic carbon from multiple sources with different δ 13 C signatures, weathering and the contribution of carbonate rocks in the watershed, primary production, gas exchange and water mixing along the land-ocean aquatic continuum [START_REF] Mook | Environmental Isotopes in the Hydrological Cycle[END_REF]. The matrix correlation (Tab. S2) shows that higher values of δ 13 C-DIC are related to high levels of DO, POC, SPM, and Chl a, and low concentrations of DIC. Recent findings in Guanabara Bay showed that the DOC and POC fractions present a large phytoplankton dominance, surpassing the contribution of terrestrial sources (Cotovicz et al. 2018a). Compared to other estuaries, Guanabara Bay presented the highest enrichment of 13 C-DIC in the salinity range between 20 and 30 (Fig. 5b). In Guanabara Bay, this salinity interval is present in confined stratified waters of the sectors 3, 4 and 5, which are net autotrophic and phytoplankton-dominated (Rebelllo et al. 1988;[START_REF] Cotovicz | A strong CO2 sink enhanced by eutrophication in a tropical coastal embayment (Guanabara Bay, Rio de Janeiro, Brazil)[END_REF]2018a). This behavior is in contrast with most of other estuarine studies, which are mostly located in temperate regions and river-dominated ecosystems, where the effects of respiration, either in the water column or in sediments, are often much more pronounced than photosynthesis [START_REF] Mook | Environmental Isotopes in the Hydrological Cycle[END_REF][START_REF] Bouillon | Inorganic and organic carbon biogeochemistry in the Gautami Godavari estuary (Andhra Pradesh, India) during pre-monsoon: The local impact of extensive mangrove forests[END_REF]. The relative enrichment of 13 C-DIC is also important for salinities > 30, suggesting that Guanabara Bay can export 13 C-DIC enriched waters to the coastal ocean. There is a marked depletion of δ 13 C-DIC in estuaries dominated by mangroves. The net inputs of 13 C-depleted DIC in mangroves are attributed to the predominance of respiration in tidal creeks, as this process adds DIC to the water with a signature similar to that of the organic matter being respired (C3 plants with signature ranging between -24‰ to -30‰) [START_REF] Bouillon | Inorganic and organic carbon biogeochemistry in the Gautami Godavari estuary (Andhra Pradesh, India) during pre-monsoon: The local impact of extensive mangrove forests[END_REF]Bouillon et al. 2011;[START_REF] Miyajima | Export of inorganic carbon from two Southeast Asian mangrove forests to adjacent estuaries as estimated by the stable isotope composition of dissolved inorganic carbon[END_REF]).

In open ocean waters, the compiled data of δ 13 C-DIC showed a range between -1.13‰ and 2.31‰, averaging at 0.70‰ ± 0.57‰ (Fig. 5). This range of δ 13 C-DIC is in accordance with previous studies in seawaters with a limited influence from land carbon sources (-2‰ and 2‰; [START_REF] Mook | Stable carbon isotopes in rivers and estuaries[END_REF]. However, the average of 0.71‰ is slightly lower than previous averages reported in literature [START_REF] Kroopnick | The distribution of 13C of Σ CO2 in the world oceans[END_REF][START_REF] Mook | Environmental Isotopes in the Hydrological Cycle[END_REF]. According to [START_REF] Mook | Environmental Isotopes in the Hydrological Cycle[END_REF], the δ 13 C-DIC in seawater varies between +0‰ and +2.5‰, with the majority of data between 1‰ and 2‰. According to [START_REF] Kroopnick | The distribution of 13C of Σ CO2 in the world oceans[END_REF], the δ 13 C-DIC of surface oceanic waters are generally around 2‰. Differences in the averages and ranges of these studies can be attributed to the specific conditions during sampling collection, since that consider regions with distinct biological, air-sea exchange processes and different in situ temperatures, which could alter the δ 13 C-DIC signature. In addition, δ 13 C-DIC could substantially differ considering the differences between surface and bottom waters. δ 13 C-DIC can present vertical stratification attributed to the oxidation of the organic material produced at the surface waters (majority from phytoplanktonic origin) as it falls through the water column and remineralizes at depth, with addition of isotopically light respiratory CO2 to the DIC pool below the pycnocline (Kroopnick, 1985, Koné et Guanabara Bay also present a significant vertical δ 13 C-DIC stratification during summer, with higher values at surface waters, reflecting the enrichment by phytoplankton blooms, and the depletion in bottom waters due to the predominance of respiration of organic matter (Tab. S1).

Conclusion

Our results showed a strong control of δ 13 C-DIC dynamics by biological processes in the highly polluted and eutrophic Guanabara Bay. Indeed, the extreme high Chl a concentrations concomitant with heavier δ 13 C-DIC signatures and low pCO2 values indicate a strong carbon isotopic fractionation by primary production, especially at mid-inner shallow regions of the bay. The isotopic fractionation induced by primary production is accentuated during summer conditions when the vertical thermohaline stratification, the nutrients availability and the photosynthetically active radiation were at their highest. Our calculated apparent phytoplankton fractionation based on diel variations of δ 13 C-DIC signatures and DIC concentrations showed higher 13 C discrimination from morning to noon period, decreasing during afternoon, following a Rayleigh distillation process. Overall, the in situ δ 13 C-DIC concentrations were well above than the values expected in equilibrium with atmospheric CO2 concentrations. The lower/negative δ 13 C-DIC signatures were restricted to the regions under direct influence of domestic effluent discharges, where high inputs of organic matter stimulate the microbial respiration that adds depleted δ 13 C-DIC into the waters. The process of air-water exchange seems also to exert influence on the isotope signatures; however, in a lower magnitude compared to the biological activities. Compared to the compiled data from several estuaries and open ocean waters worldwide, Guanabara Bay showed a marked enrichment of 13 C, increasing δ 13 C-DIC signatures. The highest signature of δ 13 C-DIC in Guanabara Bay reached 4.57‰, and to the best of our knowledge, this is the highest value reported in coastal and open waters worldwide. These results indicate that the eutrophication process can deeply modify the isotopic signature of the dissolved inorganic carbon pool in coastal waters dominated by large algal blooms.

Figure 1 .

 1 Figure 1. Composite maps showing the study area and the spatial distributions of the δ 13 C-DIC signatures in winter period (a) and summer period (b) in surface waters of the Guanabara Bay. The bay was divided into five sectors (S1 to S5). The black dots represent the sampled sites.

Figure 2 .

 2 Figure 2. Calculated apparent diel phytoplankton fractionation of δ 13 C-DIC (ɛ-DIC) plotted against a) pCO2 values and b) DIC concentrations. The blue circles represent the ɛ-DIC for the period from dawn to noon, and the green circles represent the ɛ-DIC for the period from noon to dusk.

Figure 3 .

 3 Figure 3. Plots showing the diel variations of δ13C-DIC and DIC (Rayleigh Distillation), where the increases of δ 13 C-DIC values are equivalent to decreases in the DIC concentrations. Graphs a, b and c are represent the diel surveys (from dawn to dusk) in the months of Sep.2013, Jan.2014 and Apr.2014, respectively.

Figure 4 .

 4 Figure 4. Relationship between δ 13 C-DIC signatures and Chl a concentrations. The graph present the averaged-sector values for each sampling campaign.

Figure 5 .

 5 Figure 5. Comparison of Guanabara Bay with other systems worldwide: a) relationship between δ 13 C-DIC and pCO2 values; b) distributions of δ 13 C-DIC according to salinity intervals; c) distributions of δ 13 C-DIC values against salinity. The references of the compiled data set are provided in the supplementary file.

1

 1 Sewage inputs of depleted δ 13 C-DIC

Figure 6 .

 6 Figure 6. Plot of Δδ 13 C-DIC vs. ΔDICexcess/DICocean in the Guanabara Bay. The origin represents the conservative mixing with sample values equal to the ocean end-member value (see material and methods for further explanation). The four quadrants (I, II, III and IV) indicate additional processes than could influence the DIC and δ 13 C-DIC distributions. The quadrant I represents the primary production / outgassing of CO2, when DIC concentrations increase and δ 13 C-DIC values decrease. The quadrant II represents the calcite precipitation, when DIC concentrations and δ 13 C-DIC values decrease. The quadrant III represents the degradation of organic carbon and inputs from wastewater, when DIC concentrations increase and δ 13 C-DIC decrease. The quadrant IV represents the carbonate dissolution, when the DIC concentrations and the vales of δ 13 C-DIC increase. The vectors A, B, C, D and E represent the slopes of specific processes affecting the DIC and δ 13 C-DIC distributions, that are, respectively, primary production (slope = -20.0‰), the outgassing of CO2 (slope = -9.2‰), degradation of organic carbon (slope = -20.0‰), wastewater input of DIC (-12.2‰) and intrusion of atmospheric CO2 (slope = -2.0‰). The red, blue and green arrows represent the direction in which the samples will follow if they are subject to more than one process. The red arrow represents the effect of organic matter degradation followed by outgassing of CO2, which is drawn parallel to vector B. The blue arrow represents the effect of degradation of organic carbon followed by biological production, which is drawn parallel to vector A. The green arrow represents the effect of primary production followed by intrusion of atmospheric CO2 due to the air-water gradient, which is drawn parallel to vector E.

  al. 2009; Eide et al. 2017). Lower δ 13 C-DIC values in bottom waters were reported in several estuarine, coastal and open ocean waters (Chou et al 2007; Burt et al 2016; Humphreys et al. 2016; Filipsson et al. 2017).

Table

  Table1showed the average concentrations with standard deviations as well as the ranges of the main water parameters analyzed in this study, separated by sectors. The upper sectors of the bay (sectors 4 and 5) presented lower salinities (27 ± 4.3 and 27.2 ± 3.5, respectively) and higher temperatures (26.8 ± 2.6 °C and 26.7 ± 2.2 °C, respectively), associated to waters with longest residence times (Tab. 1). To the contrary of upper sectors, sector 1 which is located near the mouth of the bay, showed lower temperatures (23.8 ± 1.7 °C) and higher salinities (32.2 ± 2.1) as expected due to the major influence of shelf waters.

		Sector 1	Sector 2	Sector 3	Sector 4	Sector 5
	Temperature	23.8 ± 1.7	25.5 ± 2.2	25.4 ± 2.1	26.8 ± 2.6	26.7 ± 2.2
	(°C)	(21.0 -29.3)	(22.1 -32.4)	(22.1 -31.5)	(22.0 -32.3)	(22.6 -33.9)
	Salinity	32.2 ± 2.1	30.3 ± 2.4	29.8 ± 3.0	27.0 ± 4.3	27.2 ± 3.5
		(25.4 -34.9)	(17.7 -33.7)	(15.1 -33.8)	(14.6 -33.2)	(16.6 -32.9)
	δ 13 C-DIC	1.59 ± 0.84	0.43 ± 1.93	1.68 ± 1.25	1.15 ± 1.50	(0.99 ± 1.66)
	(‰)	(-0.02 / 3.03)	(-6.17 / 3.24)	(-1.88 / 4.57)	(-2.50 / 3.81)	(-4.87 / 3.71)
	pCO2	411 ± 145	711 ± 561	286 ± 157	307 ± 256	272 ± 293
	(ppmv)	(104 -747)	(50 -3715)	(41 -660)	(29 -2222)	(22 -2203)
	pH	8.20 ± 0.16	8.15 ± 0.32	8.35 ± 0.23	8.34 ± 0.29	8.44 ± 0.31
	(NBS)	(7.90 -8.71)	(7.33 -8.96)	(7.88 -8.96)	(7.39 -9.01)	(7.51 -9.23)
	TA	2240 ± 92	2291 ± 99	2168 ± 177	2045 ± 369	2137 ± 166
	(μmol.kg -1 )	(1942 -2320)	(1890 -2488)	(1507 -2500)	(2111 -3920)	(1479 -2314)
	DIC	1985 ± 120	2044 ± 268	1847 ± 257	1658 ± 259	1758 ± 264
	(μmol.kg -1 )	(1720 -2127)	(1526 -2523)	(1332 -2290)	(1095 -2118)	(1198 -2190)
	DO	103 ± 29	97 ± 59	138 ± 51	142 ± 62	160 ± 69
	(%)	(48 -221)	(2 -263)	(56 -357)	(30 -361)	(46 -370)
	Chl-a	19.1 ± 22.0	46.2 ± 51.4	57.6 ± 90.0	69.2 ± 60.2	107.7 ± 101.8
	(μg.L -1 )	(2.0 -128.0)	(3.3 -212.9)	(1.6 -537.2)	(13.1 -288.8)	(1.5 -822.1)
	PO4 3--P	1.11 ± 0.60	5.28 ± 3.88	1.51 ± 1.07	1.10 ± 0.79	2.23 ± 2.17
	(μM)	(0.11-2.44)	(0.17 -20.79)	(0.17 -1.10)	(0.03 -2.96)	(0.02 -8.72)

Acknowledgments This study was supported by the No Frontier Sciences Program of the Brazilian National Council of Research and Development (CNPq-PVE No 401.726/2012-6), by the Carlos Chagas Foundation for Research Support of the State of Rio de Janeiro (FAPERJ; proc. no. E-26202.785/2016), and by the Coordination for the Improvement of Higher Education Personnel (CAPES). Luiz C. Cotovicz Jr. is a postdoctoral researcher of FAPERJ (FAPERJ; proc. no. E-26202.785/2016); B. A. Knoppers is a senior scientist of CNPq (proc. no. 301572/2010-0). We are grateful to Nilva Brandini and Suzan J. Costa Santos for their support during field sampling, and to Karine Charlier for her support with IRMS analytical procedures.


Guillaume Riquet
email: guillaume.riquet@ensicaen.fr

Sylvain Marinel

Yohann Breard

Christelle Harnois

Sintering mechanism and grain growth in CaCu3Ti4O12 ceramics

Keywords: CaCu3Ti4O12, Sintering, Microstructure, Grain growth

In this work, a study of the densification of CaCu3Ti4O12 (CCTO) ceramics during conventional sintering process is presented. Dilatometric study was conducted in detail to find out which diffusion mechanism is responsible for densification. Based on the shrinkage curves, it was shown that densification is mostly controlled by grain boundary diffusion. The microstructure evolution of CCTO during conventional sintering was studied through the sintering trajectory, which corresponds to a unique relationship between grain size and density. According to SEM analysis, it was shown that abnormal grain growth takes place for samples sintered at high temperature stage with density > 80% of the theoretical density. Finally, the Master Sintering Curve (MSC) method was also used to characterize the densification process of CCTO and estimate the apparent sintering activation energy (Q=730 kJmol -1 ).

Introduction

In the last years, the research of materials having high dielectric constant with good temperature stability has raised significant attention because of their interest in many potential applications. The cubic double distorted perovskite like structure of CaCu3Ti4O12 (CCTO) (SG Im3; a = 7.393 Å), which contains square-planar Cu atoms on A site inducing the tilt of TiO6 octahedra, has attracted much attention [START_REF] Subramanian | High Dielectric Constant in ACu3Ti4O12 and ACu3Ti3FeO12 Phases[END_REF][START_REF] Ramirez | Giant dielectric constant response in a copper-titanate[END_REF]. In terms of dielectric properties, CCTO ceramic has a high relative dielectric permittivity at room temperature of εr~10 5 at 1 kHz with good temperature stability on a wide temperature range [100K, 400K] and no phase transition. The IBLC model has often been reported to explain this apparent high dielectric permittivity in CCTO ceramics. This model suggests the presence of an Internal Barrier Layer Capacitor, consisting of semiconducting grains separated by thin insulating grain boundaries [START_REF] Sinclair | CaCu3Ti4O12: One-step internal barrier layer capacitor[END_REF][START_REF] Schmidt | Effects of sintering temperature on the internal barrier layer capacitor (IBLC) structure in CaCu3Ti4O12 (CCTO) ceramics[END_REF].

In addition, below 100K, a drastic decrease of the permittivity down to 100 has been reported [START_REF] Lunkenheimer | Nonintrinsic origin of the colossal dielectric constants in CaCu3Ti4O12[END_REF][START_REF] Ferrarelli | Comment on the origin(s) of the giant permittivity effect in CaCu3Ti4O12 single crystals and ceramics[END_REF].

A literature survey has clearly reported that CCTO dielectric properties are strongly correlated to its microstructure, therefore it is necessary to pay attention to the processing conditions from which microstructure highly depends. Recently, Riquet et al. [START_REF] Riquet | Direct and hybrid microwave solid state synthesis of CaCu3Ti4O12 ceramic: Microstructures and dielectric properties[END_REF] has successfully synthesized CCTO by conventional and microwave heating conducting to different initial average grain sizes, i.e. 1µm and 400 nm, respectively. After conventional sintering of the two powders in air at 1050 °C for 2h, they observed similar microstructures with large grains up to 30 µm and inter/intra porosity, indicating that abnormal grain growth occurs during sintering. Fang et al. [START_REF] Fang | Mechanism for Developing the Boundary Barrier Layers of CaCu3Ti4O12[END_REF] have also observed discontinuous grain growth for different samples sintered from 1035°C to 1065°C, and that for different sintering times in air. In their experimental conditions, grain size was remaining practically constant for heat treatment duration lower than 8h at 1035°C or lower than 3h at 1065°C. According to the literature, this sudden grain growth is correlated to the apparition of a Cu-rich intergranular phase at the high temperature stage [START_REF] Kim | Microstructural evolution and dielectric properties of Cu-deficient and Cu-excess CaCu3Ti4O12 ceramics[END_REF]. These microstructures changes may have an impact on the dielectric properties of CCTO. For instance, Adams et al. [START_REF] Adams | Giant Barrier Layer Capacitance Effects in CaCu3Ti4O12 Ceramics[END_REF] have measured an increase of the permittivity value, measured at 10 kHz, from 9000 to 280 000 , for ceramics sintered, respectively, at 1100°C for 3h and 24h. While density for both samples were almost identical, the average grain sizes were very different i.e., 6 µm and 100 µm respectively, showing the high dependence of the permittivity of CCTO on the microstructure. Therefore, it is well established that dielectric properties of CCTO highly depend on the sintering conditions. So far, only the presence of abnormal grain growth at high temperature stage has been reported. Nonetheless there is a lack of information regarding the sintering mechanisms involved during the overall sintering process of CCTO. Therefore, the aim of this paper is to bring new insights into the densification behavior of CCTO material during conventional sintering. Dilatometric study was conducted in detail to find out which diffusion mechanism is responsible for densification. Based on this dilatometric data, the Master Sintering Curve (MSC) was also determined. This method was originally developed by Su and Johnson [START_REF] Su | Master Sintering Curve : a practical approach to sintering[END_REF] and is a powerful tool to predict and characterize the densification process of ceramics and to estimate the apparent sintering activation energy. Finally, the microstructure evolution of CCTO during conventional sintering was studied through the sintering trajectory. This trajectory corresponds to a unique relationship between grain size and density, being given a starting powder and one sintering process.

II. Experimental 1. Powder synthesis and materials shaping

The solid state synthesis of CCTO was performed using highly pure CaCO3 (99,95% Alfa Aesar), CuO (99,7% Alfa Aesar) and anatase-TiO2 (99,9% Materion) as starting materials. The precursors were mixed and grounded by ball milling during 16 min (Fritsch Pulverisette 6 planetary mill) with respect to the stoichiometry of CaCO3-3CuO-4TiO2. The mixed precursor powder was subsequently heated three times in air in a tubular furnace using the following thermal cycle: heating up to 900°C at 2.5 °C min -1 with a dwell of 10h. An organic binder (PVA -1 wt%) was used to ensure a good cohesion of the compacted green samples. The CCTO powder was shaped into disks by uniaxial pressing at 5 MPa (6 mm in diameter, 6 mm thick) followed by an isostatic pressing step at 200 MPa. The binder was removed by a heat treatment in air at 400°C for 2h. The green sample density was close to 61 % of the theoretical value (5.05 g cm -3 ).

Sintering conditions and characterizations

The samples were conventionally sintered in air at temperatures ranging from 1000°C to 1100°C with different dwell times using two different furnaces: (i) in a Thermo-Mechanical Analysis chamber (TMA) with heating and a cooling rate of 5°C min -1 to record the shrinkage during the heating process. (ii) In a conventional tubular furnace with a heating rate of 5°C min -1 , which allows quenching samples from the high temperature stage to room temperature. The samples were then quenched in air to observe the evolution of the microstructure as the sintering process progressing. For the construction of the Master Sintering Curve (MSC), seven samples were sintered using the TMA furnace at 1050°C for 2h using different heating rates: 5°C min -1 , 7.5°C min -1 , 10°C min -1 , 12.5°C min -1 , 15°C min -1 , 17.5°C min -1 and 20°C min -1 .

Based on these dilatometric curves and assuming isotropic shrinkage, the sample density can be calculated as a function of the temperature from the shrinkage value, by using the following equation:

= (1)
where ρ(T) is the instantaneous relative density (g.cm -3 ), ρArchi the final density measured by Archimedes's method in absolute ethanol (g.cm -3 ), St the instantaneous vertical shrinkage (µm), Sf the final vertical shrinkage (µm) and hf the final height of the sample (µm). The X-Ray Diffraction (XRD) measurements were performed on a Theta-Theta PANalyticalX'Pert Pro diffractometer with a CuKα (λ=1.54059 Å) radiation. The Rietveld method using Fullprof program was used for the structural refinement. The microstructural characterizations were carried out using a scanning electron microscope (SEM Zeiss Supra 55), equipped with an Energy Dispersive Spectroscopy (EDS) System. The average grain size was estimated by linear intercept method over 200 grains of different micrographs to ensure a good reliability. [START_REF] Mendelson | Average grain size in polycrystalline ceramics[END_REF] 3

. Construction of the Master Sintering Curve (MSC)

The master sintering curve is obtained by separating the sintering parameters into: (i) those related to the microstructure (ii) those related to the thermal history of the material. According to Su

and Johnson [START_REF] Su | Master Sintering Curve : a practical approach to sintering[END_REF], these parts are related to each other experimentally and the temperature dependent side can be expressed as:

θ = exp ( 2
)
where c is the heating rate, T0 the starting temperature, Tm the maximum reached temperature and Q the apparent activation energy for densification.

The curves of the density (ρ) versus the log(θ) parameter are constructed for each heating rate.

The mean ρ=f(log(θ)) curve can be calculated, and the convergence of data is quantified through the calculation of the mean residual square obtained from the experimental data points and the mean curve. If we can find a Q value for which all ρ=f(log(θ)) curves coincide regardless the heating rates (and so that minimizes the value of the mean residual squares), then this single ρ versus θ curve is called the master sintering curve of the densification process and this particular Q value represents the apparent sintering activation energy. In such a case, the grain size is independent of thermal history and it is only a function of density.

III. Results and discussions

Sintering mechanisms

Figure 1 shows the XRD pattern and the SEM microstructure of the as-synthesized CCTO powder, with a narrow average particle size distribution centered at 800 nm. According to the structural refinement, apart some weak diffraction peaks characteristic of CuO (1%) and CaTiO3 (1%) which are observed at extremely low amounts, all the diffraction peaks can be attributed to CCTO phase. Figure 2 represents the variation of the linear shrinkage and relative density of a CCTO sample versus temperature, for the following temperature cycle: heating up to 1100°C at 5°C min -1 with a dwell time of 2 hours. The relative densities were calculated using Eq [START_REF] Subramanian | High Dielectric Constant in ACu3Ti4O12 and ACu3Ti3FeO12 Phases[END_REF]. During solid state sintering of ceramics, several diffusion mechanisms may be involved but only volume and grain boundary diffusion cause material to migrate from inside the particles to the neck surface, resulting in material densification. To determine the dominant diffusion mechanism controlling the densification, the shrinkage equations during isothermal sintering can be used [START_REF] Bernache-Assollant | Chimie-physique du frittage[END_REF]. Assuming that grain growth is negligible, which is a reasonable assumption during the initial stage of sintering; the linear shrinkage equation (in isothermal condition) can be expressed as follows:

Grain boundary diffusion:

!" " # = $ #% & ' & ( ) * +, - . . 0 (3)
Volume diffusion:

!" " 1 = $ 23' 4 ( ) * , . . 0 (4)
where ΔL is the linear shrinkage, L0 the initial thickness of the sample, δG is the thickness of the grain boundary, DG is the grain boundary diffusion coefficient, γSV represents the solid-vapor surface energy of the solid, Ω is the molar volume of the solid, DJ represents the lattice diffusion coefficient, r is the grain size, R the universal gas constant, T is the temperature and t the time. By plotting the logarithm of the shrinkage versus the logarithm of the time (in isothermal condition), a linear equation can be obtained and the slope value can be used to determine the dominant diffusion mechanism leading to densification: ½ for volume diffusion and ⅓ for grain boundary diffusion.

The experimental isothermal shrinkage curve measured at 1000°C is shown on figure 3a. The final density of the sintered sample was 73% of the theoretical value. Experimentally, the ln(ΔL/L0)=f(ln(t)) plot is shown in figure 3b., and represents a straight line with a slope value b=0.31 which clearly indicates that grain boundary diffusion mechanism is the dominant diffusion mechanism for densification during the CCTO initial stage of sintering. To check that no grain growth occurs during the initial stage of sintering, samples were heated (up to 4% of relative shrinkage) and quenched in air.

Figure 3b also shows a SEM microstructure of CCTO at the end of the initial step of sintering, with a density of ρ=67.9% and an average grain size of 850 nm. This confirms that grain growth is negligible during the initial stage of sintering. Otherwise, those data confirm the validity of isothermal equations previously used. For several density, the average grain size of CCTO samples was estimated and is represented in figure 4. It is shown that the grain size remains nearly constant for density ranging from 60% to 80%. As shown in figures 3b and 5(a,b,c), the average grain size slightly increases from 800-850 nm during the initial stage sintering (60-68% density range) to 1.3 µm (78.9% of density), showing that grain growth is very limited for this density values range. However, figures 4 and 5 show that exaggerated grain growth occurs beyond ρ = 80 % of the theoretical density. Figure 5g shows SEM micrograph using an AsB detector to reveal composition contrasts on the image. Coupling with EDS mapping of grains and grain boundaries in figure 6, it reveals that a Cu-rich phase is present and segregates at grain boundaries. This microstructural evolution of CCTO is consequently in good agreement with already reported abnormal grain growth phenomenon. This latter mechanism was often explained by the presence of a small amount of CuO which segregates at triple point site and grain boundaries at high temperature [START_REF] Fang | Mechanism for Developing the Boundary Barrier Layers of CaCu3Ti4O12[END_REF].

Application of the Master Sintering Curve

It must be kept in mind that several conditions must be fulfilled to properly use the MSC concept. First the MSC can be applied only to samples shaped with the same powder, green-body process and green density. Another assumption is that microstructural evolution depends only on density and that one diffusion mechanism dominates in the sintering process. Practically, deviations from these assumptions can be observed. As previously seen, the grain size-density trajectory has shown an abrupt grain size increasing at density >80%, indicating the initiation of the exaggerated grain growth phenomenon. Therefore, it makes sense not to include data taken in this density range in the initial MSC analysis to avoid confusion during the process of minimization of the sums of residual squares.

Different values of activation energy Q were tested, and the ρ=f(log(θ)) curves for all heating profiles were plotted using Eq. ( 1) and Eq. ( 2). The convergence of the data can be quantified through the sum of the residual squares. When the best estimate of Q is found, all the data should converge to a single curve and the mean residual squares is a minimum. The minimum was reached at ~ 730 kJ mol -1 , as shown in figure 7a, and represents the apparent sintering activation energy for CCTO. The resulting MSC is given (figure 7c) and shows that the ρ=f(log(θ)) curves from the different heating rates have merged onto a single curve but only over the medium density range, up to 80% of the theoretical density.

Over the range 60% -80 % of the theoretical density, the master sintering curve was obtained and no deviation was observed. This confirms that the solid state sintering of CCTO is taking place with one dominant diffusion mechanism during the sintering process in this density range, which was found to be grain boundary diffusion. Nonetheless, the high apparent sintering activation energy, Ea = 730 kJ mol -1 , suggests a difficult densification of the material during the early stage of sintering. To understand this high value of the sintering activation energy, it is worthy to pay attention on the microstructure evolution between the green shaped compact (see figure 5a) and the same microstructure on the sintered compact at 1080°C with no dwell time (figure the 5c). Actually, just after synthesis, necks between particles are partially formed (see the arrow) showing that the early stage of sintering has already started (x/r ≠ 0). After sintering at 1080°C (fig. 5.c), the x/r value has slightly increased but its value remains low, showing that the diffusion through the grain boundary is taking much energy (high value of Ea). Over this stage, the densification takes place through the sintering of the agglomerates and the homogenization of the microstructure.

Beyond 80% of the theoretical density, abnormal grain growth in CCTO occurs, which explains the clear discrepancy on figure 7c on the MSC curves. The same phenomenon has already been observed for some materials such as TiO2-doped Al2O3 [START_REF] Su | Master Sintering Curve : a practical approach to sintering[END_REF][START_REF] Mendelson | Average grain size in polycrystalline ceramics[END_REF][START_REF] Bernache-Assollant | Chimie-physique du frittage[END_REF][START_REF] Wang | Estimate of the activation energy for boundary diffusion from rate-controlled sintering of pure alumina and alumina doped with zirconia or titania[END_REF] for which the sintering data points do not converge for high values of density. On this study, they reported an abrupt increase of the grain size for densities higher than 95% of the theoretical value, indicating the initiation of exaggerated grain growth.

A similar behavior is observed on CCTO. As the sintering temperature increases, it is shown that a Cu-rich phase segregates at grain boundaries, as clearly observed on the figure 6. This Cu rich phase is most likely at the liquid state [START_REF] Yuan | Investigation on the decomposable process and the secondary liquid phase effect on the dielectric properties of CaCu3Ti4O12 ceramics[END_REF][START_REF] Adams | Decomposition Reactions in CaCu3Ti4O12 Ceramics[END_REF] during the high temperature stage as this phase seems to coat the grains. Therefore, the abnormal grain growth results from this liquid phase which promotes the dissolution-diffusion-precipitation process, known as Ostwald ripening mechanism [START_REF] Singh | Modification of interface anisotropy and its effect on microstructural evolution during ostwald ripening[END_REF]. The consequence is that small grains disappear to the benefit of very large grains. Figure 8 proposes a scheme to summarize this grain growth mechanism through the Ostwald ripening phenomenon for densities higher than 80 % of the theoretical value. This scheme also shows what is happening for density lower than this threshold value.

IV. Conclusion

In this work, the densification behavior of CaCu3Ti4O12 during conventional sintering has been deeply investigated. Sintering trajectory (grain size vs density) and Master Sintering curves have been determined and can be divided in two distinct regions. From 60% to 80 % of the theoretical density, the densification mostly takes place and the grain size remains constant and close to 1.1 µm. Based on the linear shrinkage equation, it was also shown that the dominant diffusion mechanism leading to densification during the initial stage of sintering is the grain boundary diffusion. For this mechanism, the apparent sintering activation energy, determined by using the MSC model, was found to be ~730 kJ.mol -1 . This relatively high value can be correlated to the quite low variation of the sintering advancement over this sintering stage (x/r value evolution). For higher densities (>80%), grain size increases exponentially, indicating the initiation of the exaggerated grain growth due to the presence of a Cu-rich liquid phase at grain boundaries. This liquid phase promotes the dissolution-diffusionprecipitation mechanism known as Oswald Ripening phenomenon. Further investigations using transmission electron microscopy are in progress to probe the origin of the Cu-rich phase and the nanoscale compositional variations in the grain and grain boundary regions of CCTO ceramics. Relative density (%)

Figure 1 :Figure 2 :

 12 Figure 1: X-Ray diffraction patterns (λ = 1.594 Å) recorded at 300K and SEM micrographs of CaCu3Ti4O12 powder obtained by conventional synthesis. Experimental: red crosses. Calculated: black line. Difference: green line. The blue vertical bars are the positions of the reflections allowed by CaCu3Ti4O12. The black set of vertical bars is correlated to the secondary phase CaTiO3, while the orange vertical bars indicate the reflections allowed by the phase CuO.

Figure 3 :Figure 4 :

 34 Figure 3: (a) Relative shrinkage vs dwell time at 1000°C -(b) Linear shrinkage equation during initial stage of sintering and SEM micrographs of CCTO sample at the end of the initial stage sintering.

Figure 5 :Figure 6 :

 56 Figure 5: SEM micrographs of sintered samples at different densities (a) ρ=60.8 % (b) ρ=72.4 % (c) ρ=78.9 % (d) ρ=81.1 % (e) ρ=83.2 % (f) ρ=88.5 % (g) ρ=91.7 %

Figure 7 : 1 dFigure 8 :

 718 Figure 7: (a) Estimation of the apparent sintering activation energy. Application of the "Master Sintering Curve" model using different activation energies: (b) 300 kJ mol -1 (c) 730 kJ mol -1 (d) 1200 kJ mol -1 .

Acknowledgments 10

The authors thank the French Ministry of Research for the financial support. The authors are also thankful to Jerome Lecourt and Christelle Bilot for their help in conducting the experimental work.