Rachna Bhoonah
email: rachna.bhoonah@minesparis.psl.eu

Alice Maury-Micolier

Olivier Jolliet

Integrated empirical and modelled determination of the human health impacts of building material VOCs

Introduction

Indoor air quality (IAQ) is of crucial concern since humans spend more than 90% of their time indoors [START_REF]Report to Congress on indoor air quality[END_REF] and are directly exposed to substances that can be harmful to their health. These substances, called pollutants, are either in the form of gases or are adsorbed to particulate matter (PM) and are either emitted directly by indoor sources (materials used in construction and furniture, human activities and humans themselves) or transferred from the outdoor environment through ventilation, infiltration and airing. Since people spend a lot of their time and get most of their intakes indoors, it is crucial to assess indoor pollutant concentrations and to identify their main sources in order to limit IAQ-related intake and health damage.

Materials have been identified as important continuous sources of chemicals present in indoor environments [START_REF] Huang | Chemicals of concern in building materials: A highthroughput screening[END_REF][START_REF] Shaw | Investigation of building materials as VOC sources in indoor air[END_REF][START_REF]Why Indoor Chemistry Matters[END_REF], which can directly affect human health or react with other substances such as ozone to form new harmful substances in the gas or particle phase [START_REF]Why Indoor Chemistry Matters[END_REF].

Thus, a high number of studies have measured the emission of volatile organic compounds (VOCs) from specific materials [START_REF] Shaw | Investigation of building materials as VOC sources in indoor air[END_REF][START_REF] Wilke | VOC-and SVOC-emissions from adhesives, floor coverings and complete floor structures[END_REF][START_REF] Won | A Comprehensive VOC emission database for commonly-used building materials[END_REF][START_REF] James | Emissions of Volatile Organic Compounds from Several Green and Non-Green Building Materials: A Comparison[END_REF]. Furthermore, since 2011, it is mandatory for manufacturers to measure VOC emissions of construction, wall and flooring materials under the regulatory labelling scheme in France [START_REF]relatif à l'étiquetage des produits de construction ou de revêtement de mur ou de sol et des peintures et vernis sur leurs émissions de polluants volatils[END_REF]. However, measured data are only available and valid at a few specific points in time, during a restricted timespan of a few days to a few weeks. In order to obtain a complete emission profile and assess the cumulative intake of these VOCs, concentrations have to be extrapolated. Linear extrapolations cannot be applied since emissions themselves vary with the time dependent mass of the substance left in the material. Simple fit of decay exponential curves has also limited validity to reflect the potential increase of initial air concentration. Moreover, air chamber measurements and emissions depend on the actual ventilation rate and surfaces to volume ratio, and therefore need to be scaled up to real building usage conditions [START_REF] Xu | A general model for analyzing single surface VOC emission characteristics from building materials and its application[END_REF][START_REF] Rackes | Do time-averaged, whole-building, effective volatile organic compound (VOC) emissions depend on the air exchange rate? A statistical analysis of trends for 46 VOCs in[END_REF][START_REF] Zhou | Alternately airtight/ventilated emission method: A universal experimental method for determining the VOC emission characteristic parameters of building materials[END_REF]. Thus there is a need to couple measurements with more elaborated emission models to determine the emission and resulting concentration profiles as a function of time.

Emission models of VOCs from materials are based on the mass balance of the substance emitted from the material and depend on chemical, material and building parameters. Two main parameters characterize the combined influence of material and chemical properties and are unique to each material-chemical combination: 1) the diffusion of these substances through the material, determined by the diffusion coefficient, and 2) the material-air partition coefficient, , which is the ratio at equilibrium of the concentration of the chemical at the surface of the material and in the boundary air layer at material surface.

QPPRs (Quality Property-property Relationship) have been developed to compute materialspecific properties such as and , for multiple material types from chemical properties more commonly available such as molecular weight and [START_REF] Huang | A quantitative property-property relationship for the internal diffusion coefficients of organic compounds in solid materials[END_REF][START_REF] Huang | A quantitative structure-property relationship (QSPR) for estimating solid material-air partition coefficients of organic compounds[END_REF]. Developed from large datasets of about 1000 measurements, these QPPRs reference values can be used to simulate average indoor concentrations when no specific emission data are available, but are associated with relatively large uncertainties of a factor 10 to a 100. Another key parameter is the mass fraction of volatile substances in the material, , which determines the amount that can be emitted in air. Material compositions are often unknown, except for the average values that can be found for some material categories in e.g. the Pharos database, aggregating information on chemicals in building materials and associated human and environmental health hazards [START_REF]Pharos -About. Pharos -Healthy Build Netw[END_REF].

Measurements do not represent real-life occupied indoor environments and are only available at specific points in time, while models contain uncertainties and unknowns. The combination of the measurements to emission models could take advantage of the respective strengths of these approaches and help to predict more precisely the evolution of indoor VOC concentrations. Furthermore, since VOCs can have serious adverse effects on health, it is beneficial to model intake and health damages on building occupants in order to make First, we will present the framework developed to calibrate an emission model with emission data. The framework will then be applied to two mono-layered materials: gypsum board and bamboo flooring. In a case study, we will evaluate the health damages related to the intake of VOCs emitted by the gypsum board and bamboo flooring.

Material and methods

In this study, the driving input parameters of an emission model will be adjusted using available measured concentrations from chamber experiments to simulate continuous VOC emissions from materials. The framework will be applied to two materials: gypsum board and bamboo flooring. The main steps are summarised in Figure 1.

Figure 1: Methodology for extrapolating VOC emission data with an emission model: calibration, application and validation on different materials with measured data and determination of health damages from exposure

From a test chamber measurement pool of N substances emitted by the material under study, a minimum of 2 and maximum of N-1 substances are selected and coupled with an existing emission model and reference coefficient values in order to estimate the optimal diffusion and material-air partition coefficients unique to the material that best fit the measurements. The initial mass fraction, , of each substance, specific to each material, that yield the lowest error of the predicted compared to the measured concentrations are then derived. The framework is validated by comparing the predicted concentrations to measured data for all N substances. Using the determined optimal parameters, the inhalation exposure to material VOCs can be determined by the model and combined with exposure-response data to evaluate corresponding health damages.

Measured air concentration data in test chamber

Air concentration measurements of different substances emitted at different points in time by materials, for instance by material manufacturers. Since these measurements are made in test chambers, the following chamber characteristics are considered: 1) the chamber walls are made of very low absorption or emission materials such as glass or stainless steel, in order not to interfere with the tested material and 2) only one face of the material emits substances, the other being covered by an impermeable material. The ventilation rate and temperature during measurements must also be known.

In this study, we used data on two mono-layered materials: gypsum board and bamboo flooring. Air concentration data are available at 3 days ( ) and/or 28 days ( ) for the two materials from the manufacturer's data sheet (created in response to the regulatory labelling scheme [START_REF]relatif à l'étiquetage des produits de construction ou de revêtement de mur ou de sol et des peintures et vernis sur leurs émissions de polluants volatils[END_REF]), with no uncertainty range available. For all two materials, the tests were carried out with an air change rate of 0.5 vol.h -1 at 23 °C and a relative humidity of 50 %. A summary of relevant information is presented in Table 1. Out of the total number of chemicals measured, only those having two measurement points (at and ) were chosen for calibration and validation: 5 for gypsum board and 3 for bamboo flooring. Calibration substances were selected based on their emission dynamics, defined by their diffusion (m²/s) and material-air partition (-) coefficients, as explained in paragraph 2.3: hexanal, toluene and n-hexadecane for gypsum board, and acetic acid and phenol for bamboo flooring.

Table 1: Main characteristics of the measurement of VOCs emissions from gypsum board and bamboo flooring

Emission model and main parameters of influence

The multi-layered material emission model used in this paper has been developed by Yan et al. [START_REF] Yan | Simulation of VOC emissions from building materials by using the state-space method[END_REF], modified by Guo [START_REF] Guo | A Framework for Modelling Non-Steady-State Concentrations of Semivolatile Organic Compounds Indoors -I: Emissions from Diffusional Sources and Sorption by Interior Surfaces[END_REF], and further adjusted by Micolier [START_REF] Micolier | Development of a methodology for a consistent and integrated evaluation of the health, energy and environmental performance of residential building design solutions[END_REF]. The material is divided into several layers. Each layer is considered to have a uniform substance concentration and is represented by a single node. The emission rate is obtained from the mass balance of substances at different nodes within the material and in air, as a function of the initial mass fraction of the substance in the material, (kg chemical /kg material ). The mass balance equations for each node are given in SI S.1. VOC emissions are driven by two major parameters, i.e. the diffusion coefficient on and the material partition coefficients and this emission can be limited by its diffusion through the material (D-limited) or by its partition from the material to the boundary layer (K-limited).

These two parameters have been estimated from material and substance specific coefficients [START_REF] Huang | A quantitative property-property relationship for the internal diffusion coefficients of organic compounds in solid materials[END_REF][START_REF] Huang | A quantitative structure-property relationship (QSPR) for estimating solid material-air partition coefficients of organic compounds[END_REF] as follows:

(

(2)

(

Selection of substances for main parameter calibration

In order to optimise the parameters (material-specific coefficient for diffusion) and

(material-specific coefficient for partition), a calibration is realised for each material using data for part of N substances for which measurements at two points in time ( and ) are known, the other substances (at least one) being kept for the validation step. Excluding one substance for validation (from N-1), we select at least two and up to four substances for calibration, with the broadest range possible in their diffusion ( ) and partition coefficients to cover various emission dynamics: the substance having the highest and highest , and the one with the lowest and lowest are chosen. If more than one substance remains, up to two additional substances are selected: the one(s) having the highest absolute difference between and . Any remaining substance is kept for validation. A detailed description of the selection process is given in SI section S.2.

Parameters calibration

and are first varied within their range of uncertainty using a 50 x 50 grid, yielding 2500 combinations of D and K. For each of these combinations -, we perform the following iterative process: a) We first back-calculate the initial mass fraction of the substance under study 1 that correctly predicts the concentration at time , . b) We then evaluate for each -combination the deviation ( between the log of observed and predicted ratios of calculated as :

(3) c) We calculate for each -combination, the mean deviation across all calibration substances d) We also determine for each b-β combination a penalty for diverging from the reference and values is applied to each -couple, calculated as: 1 This step only serves the purpose of calibration. The actual mass fraction of the substance in the material is determined later based on all available measurements (see section below).

(4)

The optimal -combination is selected as the one minimizing the sum of the obtained average deviation plus the penalty :

(5)

Mass fraction and resulting air concentration

Since initial mass fractions of substances inside the measured materials ( ) are usually unknown, we use the optimal parameters from the calibration step to determine as the mass that minimizes the root mean squared log error (RMSLE) on all concentrations for all times (i=1,n) and substances (s=1,x):

We then apply the emission model from Micolier (2019) to yield predicted air concentrations.

Health impacts calculation

Health impacts (DALY) are calculated in DALYs (disability-adjusted life years), a measure of the number of healthy life years lost due to sickness or premature death recommended by the World Health Organisation (Murray et al. 1996), currently used as an endpoint indicator in life cycle assessment (LCA), from the severity factor (DALY/cases), effect factor (cases/kg intake ), product intake fraction (kg intake /kg in product ) and the initial mass of substance in the material (kg in product ).

With

Where (1/s) is the exposure factor representing the fraction of the air volume that is taken in by the occupants per time unit.

Case study

We selected as a case study a room with of 38.75 m² gypsum-covered walls and 15 m² bamboo flooring. The room is ventilated at 1 ACH and occupied by 3 persons 8 hours per working day and indoor temperature is set at 20°C.

Applicability and assumptions

The framework is applicable under the following conditions: 1) data is available on test chamber conditions, namely volume, air change rate and temperature, 2) dimensions of the material are known and 3) at least two measurement points for at least three substances are available, since emission data for at least two substances are used for calibration and the model is validated with at least one other substance.

The model is applied under the following assumptions: 1) the concentration of the substance is initially identical for all layers of the same material, 2) the concentration of the substance in each layer is uniform at any point in time, 3) the substances emitted are volatile, 4) and are unique to all layers of the same material and 5) emissions occur under stable atmospheric conditions with constant pressure, relative humidity and temperature.

Results

Deviation of predicted values from measured values

The above framework is applied to the two mono-layered materials with available measurement data: gypsum board and bamboo flooring. Hexanal, toluene and n-hexadecane were selected for the calibration of the gypsum board parameters whereas acetic acid and phenol were used for bamboo flooring calibration. Figure 2 presents for each of these chemicals-material combinations the deviation between the log of observed and predicted ratios of concentrations , as calculated by equation (3). The optimal parameters and minimize the average deviation across chemicals as determined by equation ( 5) (black-outlined red dots in Figure 2 and for bamboo flooring are -5.75 and 0.29, thus with a factor 10 lower on the material air partition coefficient from the default reference value of -5.61 and 1.36.

Predicted vs measured VOC air concentrations

For each substance, the optimal parameters are used to determine based on equation ( 6) are applied to the model, and obtain the air concentration of different emitted substances as a function of time. The volatile nature of the considered substances is reflected in the decrease in mean concentrations with increasing time frame. Since the first measured point is higher, its squared difference to the model tends to be higher as well and the concentration curves tend to be closer to this first measured value, within a factor 1.4.

(a) (b) (c) (d) (e) (f)

Uncertainties

The model is validated against the test substances calibration, estimating the percentage error, the root mean squared log error (RMSLE) and the mean absolute log deviation (MALD). Since predicted concentration different substances can vary over orders of magnitude, selecting the error on the log of concentrations gives equal importance to relative errors across the entire range of concentration and avoids a bias towards substances with higher concentrations. Figure 4 compares the predicted and measured air concentration, with circle markers for the gypsum board and triangles for the bamboo flooring mono-layered material.

Figure 4: Measured v/s predicted concentrations for 3-day (bigger markers) and 28day (smaller markers) measurements from gypsum board (circle markers) and bamboo flooring (triangle markers) for all substances with both measurements known. The substances with a black-outlined marker have been selected for the calibration process

Figure 4 shows good agreement between measured and modelled data for both the calibration data and for the test data with less than a factor two for the test substances pentadecane and nonanal (cyan and brown circles) in the gypsum flooring and for 2-ethyl 1hexanol in the bamboo flooring (orange triangle).

Table 2 summarises the errors (percentage error, RMSLE and MALD) for the substances divided into three categories: all substances, only test substances and only substances selected for the calibration process. As expected, the error indicators are lower for substances used in the calibration procedure whereas, prediction remains within max a factor 2 of the observed value for the test substances. Relative error, for all substances and all measurements, on the predicted values is of 22%, corresponding to average errors on air concentration measurements, generally around 20%, but which could range from 5% to 25% [START_REF] Wilke | Investigations for the Improvement of the Measurement of Volatile Organic Compounds from Floor Coverings within the Health-Related Evaluation of Construction Products[END_REF][START_REF] Jia | Variability of indoor and outdoor VOC measurements: An analysis using variance components[END_REF].

For the bamboo flooring, the predicted initial mass fractions of 7.6 x 10 -7 for phenol and 8.4 x 10 -8 for toluene respectively 2 and 6 orders of magnitude lower than reported ones in Pharos. Lower predictions could be explained by the difference between the composition of the product under study and those referenced in Pharos. Calculated mass fractions correspond to the amount of substance in the material at the beginning of chamber tests. Thus, low-end values could also come from the time elapsed between the manufacture and the chamber tests, and, consequently, partial emission of substances (especially highly volatile ones) before measurements are taken.

Application to the case study

The case study parameters, optimal and and mass fractions calculated previously for both materials are applied to the model for substances studied (those with two measured data). For point with single measured data, is back-calculated from the measured concentration using the same optimal and as for the other substances. The intake fractions are calculated from equation ( 8) using concentrations and exposure fractions and the consequent health damages are evaluated using equation [START_REF] James | Emissions of Volatile Organic Compounds from Several Green and Non-Green Building Materials: A Comparison[END_REF]. Figure 5 shows that the differences between short, medium and long-term exposures to acetaldehyde emitted from gypsum board or acetic acid from bamboo flooring are not significant since these substances are highly volatile and rapidly emitted. For some substances

such as n-hexadecane emitted from gypsum board, the short-term impacts can be lower but long-term impacts higher than certain substances such as n-pentadecane, since their emission dynamics are different.

It can also be noted that impacts can be different for similar intake quantities, or that they can be higher for substances with lower intake quantities since there can be substantial variations between effect factors of different substances. For example, the intake quantity of acetic acid from bamboo flooring is of 1.90 x 10 4 µg while for phenol it is of 1.24 x 10 3 µg.

Their respective health damages are 1.91 µDALY and 2.50 µDALY. Despite having over 10 times the intake quantity of phenol, acetic acid is responsible for less health impacts due to its lower effect factor. It can also be noted that the differences between the health damage from different substances are several orders of magnitude high and that the substances of concern in each material can be different. In the case of gypsum board, tetrachloroethylene is responsible for 53% of the total damage from VOC emissions, toluene for 19% and formaldehyde 17%. For bamboo flooring, phenol has the highest contribution, accounting for 52% of health impacts and acetic acid 48%. Table 3 summarises the health damages related to the exposure to VOCs emitted by the three materials for short, medium and long-term exposures. The equivalent damage for 1 m² flooring area per year is also given based on the long-term exposure. From Table 3, it can be noted that, for the functional unit of 1 m² floor area, gypsum board leads to more health damage on occupants than bamboo floor.

Conclusion

A framework was developed to calibrate a material VOC emission model depending on parameters having relatively high uncertainties (factor 10 to 100), and to calculate unknown VOC mass fractions using measured air concentration data. It allows to extrapolate measurements, only valid at few points in time and for short time spans, scale concentrations to real building contexts, and calculate full exposure and long-term health impacts on occupants. The framework was tested on two mono-layered materials, yielding an uncertainty factor of 1.1 (RMSLE) and a relative error of 22% between measurements and predictions, corresponding to typical VOC air concentration measurement uncertainties. Calculated parameters were applied to a case study of an office to calculate short, medium and long-term health impacts from the exposure to VOCs: 24 µDALY, 61 µDALY and 66 µDALY respectively. This framework, by providing full concentration profiles, can help manufacturers to devise material treatment strategies that aim at lowering impacts related to VOC off-gassing (e.g. artificial ageing). It can also help in decision-making process in the building sector: choice of low-impact materials and adequate ventilation rates to evacuate pollutants. The present method is dependent on emission data, but these are often confidential or incomplete. Due to regulations and growing concern regarding health implications of material VOCs, these data are expected to become more readily available in the future. Health impacts are possibly underestimated since toxicity data are lacking for a number of substances and should be updated when available, and also because, in real building contexts, gypsum board is often covered in paint which can lead to additional VOC emissions. Finally, chemical reactions in indoor air can consume existing chemicals or produce new ones and should be considered in IAQ health impact assessments [START_REF]Why Indoor Chemistry Matters[END_REF].

  judicious choices right at the design stage. The present paper therefore aims to propose and apply a framework combining measured emission data with a mass balance model of VOCs emission from materials. More specifically, the different objectives are: 1. Develop a framework to use multi-layered emission model for interpreting and generalising measured emission data from building materials 2. Perform a parameter optimisation and evaluate the quality of the approach based on sets of chemicals in gypsum board and bamboo flooring 3. Determine long-term chemical intakes and related human health impacts and compare across chemicals

  g/mol) is the molecular mass of the substance, (K) is the absolute temperature of the room and , (K) and are material-specific coefficients, (J/mol) the enthalpy of vaporisation and is the chemical's dimensionless octanol-air partition coefficient at 25 °C. Coefficients and have several reference values as a function of the type of material independently of the considered chemical. These values have been obtained by Huang et al. (2017) and Huang and Jolliet (2019) based on the analysis of more than 1000 measured diffusion coefficients and material-air partitioning coefficients, with high R², but still substantial remaining uncertainties: SE on and amount to + 2.30 and + 1.22 respectively, corresponding to uncertainty factors of 200 and 17. It is therefore interesting to take advantage of the measured concentrations to calibrate these parameters within their uncertainty range to the specific considered material.

Figure 2 :

 2 Figure 2: Heat maps of the deviation between the log of observed and predicted ratios of concentrations for (a) hexanal, (b) toluene, (c) n-hexadecane emissions from gypsum board and (d) acetic acid,(e) phenol from bamboo flooring as a function of the material coefficient b for diffusion and  for material-air partition. The reference default values of b and  are indicated by a yellow dot at the centre and optimal values by a larger red dot. The scale of deviation, from -1 to 1, is given on the right side of (e).

  and therefore fall in the lightgreen or light blue areas that correspond to values that make the model best agree with measurements and yield smallest deviations. For the gypsum board, the deviation primarily depends on the diffusion coefficient , with deviation of up to a factor 10 ( , dark blue area) between modelled and measured concentrations of hexanal and toluene at low diffusion coefficient. The optimal and combination is obtained for and  , which is close (within a factor 2 for the diffusion coefficient) to the reference values of -5.77 and 1.26.For the bamboo flooring, emissions are sensitive to both diffusion and material-air partition coefficients when considering acetic acid and phenol. The low-deviation (light green) regions are quite limited. Based on the deviation and penalty, the optimal solutions of

Figure 3 Figure 3 :

 33 Figure 3: Evolution of the predicted concentrations for (a) n-hexadecane, (b) npentadecane, (c) nonanal emitted by gypsum board, and (d) acetic acid, (e) 2-ethyl 1-hexanol, (f) phenol emitted by bamboo flooring: The mean predicted concentrations over 10, 100 and 10000 days are presented by red, light blue and green lines respectively.

Figure 5

 5 Figure 5 presents the intake (µg) and health impacts (µDALY) of substances emitted by gypsum board and bamboo flooring over short, medium and long-term exposure corresponding to 10, 100 and 10000 days respectively. 18 out of 21 substances emitted by gypsum board and 4 out of the 11 substances emitted by bamboo flooring have known toxicity data (effect factors).

Figure 5 :

 5 Figure 5: Intake quantities (µg) for (a) 17 substances emitted by gypsum board and (b) 6 substances emitted by bamboo flooring and health impacts for different substances emitted by (c) gypsum board and (d) bamboo flooring over 10, 100 and 10000 days

Table 2 :

 2 Relative error, Root Mean Squared Log Error, and Mean Absolute Log Deviation (MALD) for all substances, only validation points and only substances selected for the calibration

		All substances	Only test substances	Only calibration
	% Error	22%	32%	16%
	% Error 3d	18%	29%	11%
	% Error 28d	26%	35%	20%
	RMSLE	0.02	0.05	0.02
	RMS uncertainty factor	1.05	1.13	1.04
	MALD	0.19	0.30	0.13
	MALD uncertainty factor	1.56	1.99	1.34

Table 3 :

 3 Health damages related to the intake of substances with known toxicity data for gypsum walls and bamboo floor for the office (3 persons in 15 m 2 ) over three exposure periods, per unit floor area per year and per kg of material

	Health impacts	Gypsum walls	Bamboo floor
	10 days (µDALY)	23.18	1.16
	100 days (µDALY)	57.60	3.60
	10000 days (µDALY)	61.97	4.43
	10000 days (µDALY/m²/year)	0.15	0.01
	10000 days (µDALY/kg)	0.11	0.01

Data availability

The ED10 and ED50 data used to support the findings of this study are included within the supplementary information files.

Acknowledgement

The authors would like to thank the financial support by the Chair ParisTech VINCI Eco-design of buildings and infrastructure.

Conflicts of interest

The authors declare that there is no conflict of interest regarding the publication of this paper.

Supplementary Materials

The multilayered emission model is described in supplementary material S.1. Detailed description for the selection of substances based on their emission dynamics are given in S.2.

In S.3. the equations used for the calculation of exposure factors and effect factors are

given. The data used for the calculation of are given in Table S1 in S.4.


Jiaqi Sun

Yan Yang

Zhongping Wang

Qunke Xia

Impact of fluorine on the thermal stability of phlogopite

Keywords: Fluorine, water, thermal stability, phlogopite, mantle

Knowledge of volatile cycling is vital to understand evolution of the planet and the life it supports. Although it is gradually accepted that the mantle is a vast store house of H 2 O and other volatiles, the impact of co-existing volatiles on the thermal stabilities of OH and the lattice of the host mineral is still poorly understood.

Phlogopite is one of the few hydrous minerals capable of carrying both water and halogens into the mantle. Previous observations from both experiments and textural relationships in natural samples have indicated that F-rich phlogopite can be stable under ultra-high-temperature conditions. Here, the impact of F on the thermal stability of phlogopite was investigated via XRD, Raman, and IR spectroscopy from room temperature to 1000 to 1200 °C. Based on the experimental results from a F-poor and a F-rich natural phlogopites, we show that about 4 wt% F can increase the breakdown temperature of phlogopite by 100 °C under ambient pressure. The impact mechanism mainly involves preventing OH and lattice softening at high temperatures. This study reveals the links between F and the behavior of OH and phlogopite lattice, which is important for constraining volatile cycling as well as F's role in the physical and chemical properties of the upper mantle.

INTRODUCTION

Volatiles (e.g., hydrogen, nitrogen, carbon, and halogens) are not only present on the surface of the Earth, but also in the deep Earth. Volatile exchange between the surface and mantle plays a critical role in the evolution and habitability of the Earth.

Although a large number of studies have investigated volatile cycling in the deep Earth, it is still unclear how these volatiles are transported. Volatile transport in the deep Earth mainly depends on the thermal stabilities of the host minerals [START_REF] Van Keken | Subduction factory: 4. Depth-dependent flux of H 2 O from subducting slabs worldwide[END_REF].

Most hydrous minerals are not only important water carriers, but carry also other volatiles such as nitrogen and the halogens [START_REF] Williams | Diagenesis of ammonium during hydrocarbon maturation and migration, Wilcox Group, Louisiana[END_REF][START_REF] Bebout | Nitrogen isotope tracers of high-temperature fluid-rock interactions: Case study of the Catalina Schist, California[END_REF][START_REF] Hall | Ammonium in granites and its petrogenetic significance[END_REF][START_REF] Sadofsky | Ammonium partitioning and nitrogen-isotope fractionation among coexisting micas during high-temperature fluid-rock interactions: examples from the New England Appalachians[END_REF][START_REF] Yokochi | Nitrogen in peridotite xenoliths: Lithophile behavior and magmatic isotope fractionation[END_REF][START_REF] John | Dehydration of subducting serpentinite: Implications for halogen mobility in subduction zones and the deep halogen cycle[END_REF][START_REF] Palya | Storage and mobility of organic nitrogen and carbon in the continental crust: Evidence from partially melted metasedimentary rocks, Mt. Stafford, Australia[END_REF][START_REF] Kendrick | Subduction zone fluxes of halogens and noble gases in seafloor and forearc serpentinites[END_REF][START_REF] Halama | Nitrogen recycling in subducted mantle rocks and implications for the global nitrogen cycle[END_REF][START_REF] Pagé | Halogen (F, Cl, Br, I) behaviour in subducting slabs: A study of lawsonite blueschists in western Turkey[END_REF]Grützner et al. 2017a). Few studies have paid attention to the possible links between the volatiles when evaluating volatile transport by the host minerals. It has been noticed that fluorine (F) substituting for hydroxyl (OH) can extend the pressure-temperature stability field of the hydrous minerals such as amphibole, talc, and clinohumite [START_REF] Foley | High-pressure stability of the fluor-and hydroxy-endmembers of pargasite and K-richterite[END_REF][START_REF] Chibisov | Effect of Fluorine Additions on the Stability of Mg 3 Si 4 O 10 (OH) 2 : Computer Simulation[END_REF]Grützner et al. 2017a). Recent studies have also pointed out the intimate links between nitrogen and hydrogen diffusion in phengite [START_REF] Yang | The fate of ammonium in phengite at high temperature[END_REF][START_REF] Liu | Intimate link between ammonium loss of phengite and the deep Earth's water cycle[END_REF], providing new insights into water release in the Earth's interior. Therefore, exploring the effects of specific volatiles on water release from the host hydrous minerals is greatly needed in order to understand the associated cycling of volatiles and H 2 O.

Phlogopite is a sheet silicate frequently found in mantle nodules brought to the Earth's surface mainly by alkaline basalt and kimberlite lavas [START_REF] Frey | Ultramafic inclusions from San Carlos, Arizona: Petrologic and geochemical data bearing on their petrogenesis[END_REF][START_REF] Erlank | Evidence for mantle metasomatism in peridotite nodules from the Kimberley pipes, South Africa[END_REF][START_REF] Fritschle | Petrological characterization of the mantle source of Mediterranean lamproites: Indications from major and trace elements of phlogopite[END_REF]. Fluorine has been experimentally proven to be compatible in phlogopite, with a F partition coefficient between phlogopite and melt larger than 1 [START_REF] Flemetakis | Constraining the presence of amphibole and mica in metasomatized mantle sources through halogen partitioning experiments[END_REF]. Thus, phlogopite acts as an important reservoir and carrier of water and F in the upper mantle despite the fact that it is volumetrically insignificant when compared to olivine and pyroxenes [START_REF] Frost | The Stability of Hydrous Mantle Phases[END_REF]). Many studies have 3 focused on the P-T stability field of phlogopite in different systems. Most importantly, observations from both experiments and textural relationships in natural samples have shown that F-rich phlogopite can be stable up to ultra-high-temperature conditions [START_REF] Peterson | The effects of fluorine on the vapor-absent melting of phlogopite + quartz; implications for deep-crustal processes[END_REF][START_REF] Dooley | Fluid-absent melting of F-rich phlogopite + rutile + quartz[END_REF][START_REF] Motoyoshi | F-rich phlogopite stability in ultra-high-temperature metapelites from the Napier Complex, East Antarctica[END_REF].

However, the impact of F on the stability of phlogopite has never been explored further and many unknowns still exist. For instance, what is the relationship between the proportion of F (F/(F+OH) ratio) in phlogopite and the breakdown temperature down to the atomic level? In addition, it has been reported that dehydrogenation could happen at low temperatures, such as 500 °C, before the breakdown of phlogopite [START_REF] Chon | Structural changes and oxidation of ferroan phlogopite with increasing temperature: in situ neutron powder diffraction and Fourier transform infrared spectroscopy[END_REF][START_REF] Ventruti | High-temperature treatment, hydrogen behaviour and cation partitioning of a Fe-Ti bearing volcanic phlogopite by in situ neutron powder diffraction and FTIR spectroscopy[END_REF][START_REF] Zema | Kinetics of Fe-oxidation/deprotonation process in Fe-rich phlogopite under isothermal conditions[END_REF]. But it remains unclear whether F has an impact on the dehydrogenation of phlogopite. These unknowns limit a full understanding of volatile release from phlogopite.

In this study, we systematically investigate the effect of F on the thermal stability and dehydrogenation of phlogopite, using high temperature Raman spectroscopy and X-ray diffraction (XRD) to monitor the breakdown processes of the lattice, and high temperature Fourier transform infrared (FTIR) spectroscopy to reveal the behavior of OH with increasing temperature.

MATERIALS AND METHODS

Samples

The two starting samples are phlogopite crystals from two different localities described in [START_REF] Li | Fluorine follows water: Effect on electrical conductivity of silicate minerals by experimental constraints from phlogopite[END_REF]. The F-rich phlogopite is a 10 × 5 mm, golden-brown crystal from Franklin, New Jersey, United States. The F-poor phlogopite is a 70 × 50 mm, reddish-brown crystal from Badakhshan, Afghanistan. The chemical compositions were obtained using a shimadzu electron probe microanalyzer (EPMA 1720) at 15 kV and 10 nA beam with a 5 μm beam diameter. Counting time was 10 s on the peak and 10 s on the background for all elements except F, which was 60 s on peak and 30 s on background. Four to seven points were measured on each phlogopite grain. The average chemical compositions of the two samples are listed in Table 1. Structure formula was calculated on the basis of 22 cation charges, assuming an anion framework of 10 oxygens and 2(OH+F+Cl), and all Fe as Fe 2+ [START_REF] Dymek | Titanium, aluminum and interlayer cation substitutions in biotite from high-grade gneisses, West Greenland[END_REF][START_REF] Rieder | Nomenclature of the micas[END_REF]. ] for the F-poor phlogopite (X F = 0.026).

X-ray diffraction spectroscopy (XRD)

To monitor the breakdown processes of the two samples, high temperature X-ray diffraction measurements were carried out on a PANalytical X'Pert PRO Multipurpose Diffractometer (MPD), powered by a Philips PW3040 generator and equipped with an X'Celerator detector using CuKα radiation (λ=1.5406 Å). The measurements were operated at 40 kV and 40 mA with 2θ ranging from 7 to 70°. Both samples were finely pulverized in an agate mortar for over 3 h and then passed through a 74 μm sieve.

Powders were mounted on a platinum resistive heating stage and placed in an evacuated chamber. For each run, the temperature was increased from room temperature to 1100 °C at 100 °C intervals and with a heating rate of 10 °C/min. The temperature was monitored by a TCU1000N (2604 unit) controller with a temperature error of less than 1 °C. The XRD spectra were collected at each temperature. Each 100 °C temperature step consisted of a 15 min dwell time and a 30 min detection time. All data were analyzed using the Jade 6 software.

Raman spectroscopy

To further characterize phlogopite breakdown processes, high temperature Raman spectra of the phlogopites in the frequency range 50 to 1200 cm -1 were collected using a LABRAM-HR spectrometer with an 1800 grooves/mm grating. The sample was excited by a 532 nm green light from a Spectra Physics Ar ion laser for a total time of 5 100 s for each data point. Single-crystal silicon was used as the reference spectrum.

High temperatures were produced by a Linkam TS1500 heating stage, equipped with a resistance heater and a S type thermocouple. Temperatures were determined with an uncertainty of less than 1 °C. The powder samples (grain size < 74 μm) were heated while continuously purged by Ar and held for 30 min at the desired temperatures of 900, 1000, 1100, and 1200 °C. Raman spectra were measured on the samples after they have been quenched to room temperature. In order to investigate the evolution of lattice vibrations as a function of increasing temperature, temperature-dependent Raman spectra, from room temperature to 1000 °C, were measured on crystal samples in the heating stage. The heating rate was set to be 10 °C/min, and an idle time of 5 min was applied to each experimental temperature.

Fourier transform infrared (FTIR) spectroscopy

To reveal the behavior of OH and dehydrogenation in the two samples at high temperatures, thin cleavage flakes perpendicular to the (001) plane with a thickness of 50 to 130 μm were used for the temperature-dependent FTIR measurements. Polarized and unpolarized FTIR spectra in the frequency range 1000-4000 cm -1 were collected with an IR beam direction perpendicular to the (001) plane (i.e., to the layers) using a Nicolet iS50 FTIR spectrometer coupled with a Continuμm microscope. A KBr beam-splitter and a liquid-nitrogen cooled MCT-A detector were applied. A total of 128 scans were accumulated for each spectrum at a 4 cm -1 resolution. The aperture size was set to 50 × 50 μm.

High temperatures were produced using an Instec HS1300 heating stage with CaF 2 windows, equipped with a resistance heater and a S type thermocouple. The phlogopite grains were placed on a sapphire plate in the heating stage continuously purged with N 2 gas. The sample temperature was determined with an uncertainty of less than ±1 °C.

The FTIR measurements were performed from room temperature to 100 °C and then 1000 °C using an interval of 100 °C. Samples were heated at a rate of 10 °C/min and held at the desired temperature for 5 min. Background spectra and sample spectra were collected on the same selected area, respectively, for each grain and each temperature.

RESULTS

Stability of F-rich and F-poor phlogopites at high temperatures

Studies on the stabilities of phlogopite in complex systems have long been carried out (Frost 2006 and references therein). They proposed that the stability field and decomposition products depend on the initial chemical compositions of the systems. In this study, the focus is on the role of F during the breakdown of individual phlogopite crystals.

X-ray diffraction patterns at elevated temperatures are shown in Figure 1. With increasing temperature, the intensities of the original diffraction peaks ( 005) and ( 003)

of the phlogopite decrease, whereas the intensities of the diffraction peaks for forsterite, such as ( 222), ( 031) and ( 120), grow concomitantly (Figs. 1c-d). Both phlogopite samples began to decompose at 1000°C, as indicated by the appearance of the forsterite diffraction peaks. Moreover, most of the phlogopite diffraction peaks disappear at 1100 °C for the F-poor phlogopite, whereas the sharp diffraction peaks (005) and ( 003) persist for the F-rich phlogopite, indicating the different degrees of breakdown for the two samples. Comparison of the XRD patterns from the two samples before and after the run shows more clearly the different degrees of breakdown (Fig. 1e). These X-ray diffraction results demonstrate that breakdown starts at 1000 °C for both samples, but the F-poor phlogopite completely decomposes at 1100°C, whereas the F-rich phlogopite has only partly decomposed at the same temperature. The breakdown process of the two phlogopites was further characterized by Raman spectra from the quenched powder samples after annealing at different temperatures (Fig. 2). In accordance with observations from the XRD results, the Raman spectra show that both phlogopites start to decompose at 1000 °C as illustrated by the appearance of the characteristic peaks of forsterite at 825 and 857 cm -1 . But the breakdown degrees were different between the two samples. After annealing at 1100 °C, the F-poor phlogopite completely decomposed as indicated by the disappearance of the initial characteristic peaks of phlogopite, while there still exist remnants of these peaks for the F-rich phlogopite. By 1200 °C, the F-rich phlogopite had completely decomposed, according to the Raman spectra in Figure 2, indicating that the breakdown process is faster for the F-poor phlogopite than for the F-rich one.

Lattice of the F-rich and F-poor phlogopites at various temperatures

The thermal behavior of the crystal lattice for the two samples were investigated using temperature-dependent Raman spectra in the range of 50-1200 cm -1 up to 1000°C (Fig. 3). Raman modes of the two phlogopite samples are similar to those observed in previous studies [START_REF] Loh | Optical vibrations in sheet silicates[END_REF][START_REF] Clemens | Phlogopite: High temperature solution calorimetry, thermodynamic properties, Al-Si and stacking disorder, and phase equilibria[END_REF][START_REF] Tlili | A Raman Microprobe Study of Natural Micas[END_REF][START_REF] Mckeown | Raman spectra and vibrational analysis of the trioctahedral mica phlogopite[END_REF][START_REF] Tutti | High-temperature study and thermal expansion of phlogopite[END_REF], but minor differences exist in band positions of some modes (Fig. 3a).

The predominant modes are 193, 281, 327, 358, and 682 cm -1 for the F-poor phlogopite, and 193, 277, 320, and 682 cm -1 for the F-rich phlogopite. Modes at 193, 277 to 281, 320 to 327, and 682 cm -1 appear to correspond to the same modes in both phlogopites.

The intensity of the 358 cm -1 mode is much stronger for the F-poor phlogopite than the F-rich one, which is in agreement with the fact that it has only been reported in the synthetic pure OH phlogopite [START_REF] Clemens | Phlogopite: High temperature solution calorimetry, thermodynamic properties, Al-Si and stacking disorder, and phase equilibria[END_REF]). Modes at frequencies less than 350 cm -1 are generally classified as the lattice modes where long-range T 4 O 10 sheet motions can mix with M2 and (F, OH) displacements. Modes between 350 and 850 cm -1 have bond stretch and bend motions with the T 4 O 10 sheets and M2 octahedra. The mode at 682 cm -1 is assigned to O3-T-O1 band, which reflects motion along the z(c) direction in the structure [START_REF] Mckeown | Raman spectra and vibrational analysis of the trioctahedral mica phlogopite[END_REF].

No new band in the spectra appears nor disappears at elevated temperatures (Figs.

3b -c). Most lattice modes shift continuously toward lower wavenumbers without apparent turning points, except for some small accidents around 400 to 500 °C for the 193 and 682 cm -1 modes (Figs. 3d-h). These small breaks do not support any structural phase transitions occurring during the heating process, although phlogopite has been found to undergo a structural phase transition at temperatures of around 400 °C [START_REF] Tutti | Temperature-induced phase transition in phlogopite revealed by Raman spectroscopy[END_REF]. Similarly, [START_REF] Zhang | Optical phonons, OH vibrations, and structural modifications of phlogopite at high temperatures: An in-situ infrared spectroscopic study[END_REF] found that the phonon modes of phlogopite all exhibited gradual changes with increasing temperature except for the Al-O and Si-O stretching vibrations, which show a discontinuity near 327 °C. This was suggested by the authors to be related to the alteration of the OH environment. The small accidents around 400 to 500 °C for the 193 and 682 cm -1 modes observed in this study could be related to dehydrogenation processes, which is evidenced by the behavior of OH at elevated temperatures (Fig. 4).

Behavior of OH in F-rich and F-poor phlogopites as a function of temperature

Figures 4a-b show the temperature-dependent unpolarized IR spectra of OH vibrations in the 3500 to 3750 cm -1 range up to 1000 °C for the F-rich and F-poor phlogopites. For both samples, the absorptions of OH stretching bands recorded through IR beam perpendicular to the (001) plane have isotropic properties, thus, the spectra with polarizer rotating to different angles are similar (Fig. 4c). Some differences in OH wavenumbers between the two samples can nevertheless be observed.

For the F-poor phlogopite, there are mainly three OH bands at 3714, 3671, and 3621 cm -1 . In contrast, three OH bands at 3707, 3665 and 3599 cm -1 are shown in the IR spectra of the F-rich phlogopite. [START_REF] Vedder | Correlations between infrared spectrum and chemical composition of mica[END_REF] divided the OH bands in phlogopite into three groups: type N band (normal) corresponding to OH bonding to three octahedrally coordinated divalent cations, type I band (impurity) related to OH bonding to two divalent and one trivalent cations, and type V band (vacancy) due to an OH adjacent to an octahedral vacancy. All previous studies assign the bands at 3714 and 3707 cm -1 to the type N OH [START_REF] Vedder | Dehydroxylation and rehydroxylation, oxidation and reduction of micas[END_REF][START_REF] Zhang | Optical phonons, OH vibrations, and structural modifications of phlogopite at high temperatures: An in-situ infrared spectroscopic study[END_REF]). Bands at 3671 and 3665 cm -1 were assigned to the type I OH, relating to Mg 2 (Al, Fe 3+ )-OH species [START_REF] Robert | Generalization of the correlation between hydroxyl-stretching wavenumbers and composition of micas in the system K 2 O-MgO-Al 2 O 3 -SiO 2 -H 2 O: a single model for trioctahedral and dioctahedral micas[END_REF][START_REF] Ventruti | High-temperature treatment, hydrogen behaviour and cation partitioning of a Fe-Ti bearing volcanic phlogopite by in situ neutron powder diffraction and FTIR spectroscopy[END_REF][START_REF] Zhang | Optical phonons, OH vibrations, and structural modifications of phlogopite at high temperatures: An in-situ infrared spectroscopic study[END_REF]. The bands at 3621 and 3599 cm -1 are generally associated with the type V OH, corresponding to a vacancy with two divalent ions in the octahedral sheet and a vacancy with one divalent ion and one trivalent ion, respectively [START_REF] Vedder | Correlations between infrared spectrum and chemical composition of mica[END_REF]. The relative intensity of the type N OH to the other two groups is larger for the F-poor phlogopite than the F-rich phlogopite, which is consistent with the conclusion that F prefers to substitute for the type N OH based on analyses of synthetic F-rich phlogopites [START_REF] Papin | Intersite OH-F distribution in an Al-rich synthetic phlogopite[END_REF].

Since the IR spectra exhibit isotropic features independent of the polarizer orientation in (001) plane, we used only unpolarized IR spectroscopy to study the OH in phlogopite at elevated temperatures. Comparison between the IR spectra of the F-poor phlogopite before heating and after quenching shows no evident decrease of the absorbance for the type N OH (3714 and 3707 cm -1 ), and a small decrease for the type I OH (3671 and 3665 cm -1 ), while the type V OH (3621 and 3599 cm -1 ) almost disappears. These variations in the absorbances suggest dehydrogenation, especially for the type V OH (Figs. 4a-b). We could not tell from the spectra whether dehydrogenation happened at elevated temperatures for the F-rich phlogopite, because the spectrum of the quenched sample from 1000 °C is seriously distorted. But dehydrogenation could be inferred from the evolution of the OH band wavenumbers with temperature. The three OH band groups shift to lower wavenumbers with increasing temperature, but with discontinuities at 400 to 500 °C for the type I OH and the type V OH bands (Fig. 4d). The abrupt shift in the temperature-induced OH wavenumber for type I OH and type V OH, observed around 400 to 500 °C, occurs in the temperature range where dehydrogenation is generally observed in phlogopite (e.g., [START_REF] Vedder | Dehydroxylation and rehydroxylation, oxidation and reduction of micas[END_REF][START_REF] Tutti | High-temperature study and thermal expansion of phlogopite[END_REF][START_REF] Zhang | Optical phonons, OH vibrations, and structural modifications of phlogopite at high temperatures: An in-situ infrared spectroscopic study[END_REF]). Thus, both phlogopites experienced dehydrogenation of type I OH and type V OH at around 400 to 500 °C during heating, further confirming the IR spectra before heating and after quenching, although we cannot confirm it with the spectrum from the quenched F-rich phlogopite. The effects of F on the thermal stability of phlogopite It has already been documented that F may markedly extend the thermal stability of phlogopite. For example, the experimental study by [START_REF] Hensen | Experimental Study of Dehydration Melting of F-Bearing Biotite in Model Pelitic Compositions[END_REF] demonstrated that synthetic phlogopite with about 6 wt% F decomposed at 1045 °C and 9 kbar. Moreover, Dooley and Patiño Douce (1996) found that the synthetic phlogopite with 8.7 wt% F can be stable at 1263 °C at 10 kbar. Accordingly, F-rich phlogopite was reported as a stable constituent in ultra-high-temperature rocks [START_REF] Motoyoshi | F-rich phlogopite stability in ultra-high-temperature metapelites from the Napier Complex, East Antarctica[END_REF]. To reveal the relationship between F and the breakdown temperature of phlogopite, we plotted the breakdown temperature to proportion of F (F/(F+OH) ratio)

DISCUSSION

in Figure 5 based on the data from this study and previous studies. It shows that addition of F can increase the breakdown temperature, confirming the higher stabilities of F-rich phlogopites previously observed. The F-poor and F-rich phlogopite samples start to decompose at 1000 °C under ambient pressure. But the breakdown process is faster for the F-poor phlogopite compared to the F-rich phlogopite, since the complete breakdown temperature is at least 100 °C lower for the F-poor phlogopite compared with the F-rich phlogopite.

It should be noted that in addition to F, the chemical compositions of these two phlogopites differ. Previous studies have suggested that Ti can stabilize biotite both at high P-T and at low H 2 O activity [START_REF] Henry | The Ti-saturation surface for low-to-medium pressure metapelitic biotites: implications for geothermometry and Ti-substitution mechanisms[END_REF][START_REF] Harlov | The role of advective fluid flow and diffusion during localized, solid-state dehydration: Sondrum Stenhuggeriet, Halmstad, SW Sweden[END_REF][START_REF] Hansen | Whole-rock, phosphate, and silicate compositional trends across an amphibolite-to granulite-facies transition, Tamil Nadu, India[END_REF]. As basically the Mg endmember of the biotite series, phlogopite should also be stabilized by Ti. To check the effect of Ti on the thermal stability of phlogopite, we plotted the Ti contents vs. the breakdown temperatures of the samples from Figure 5 in the supplementary material (Fig. S1). Indeed, a high Ti content can increase the thermal stability of phlogopite as well. Although the F-poor phlogopite contains more Ti than the F-rich phlogopite, F content still plays an important role in phlogopite stability as shown in Figure 5. Therefore, the actual effect of F on phlogopite could be even stronger if the Ti content was the same in both phlogopite samples. On the other hand, pressure effect on the mineral stability is also important. To check the effect of F on the breakdown temperature of phlogopite under different pressures, compiled data previously reported for phlogopite and other hydrous minerals at high pressure is plotted in Figure 5. It is shown that F generally plays an important role on the thermal stabilities of the host minerals at the same pressure. For phlogopite, the breakdown temperature increases with the increasing F content no matter whether at ambient pressure or at 7 to 15 kbar. Moreover, the breakdown temperatures of phlogopites with the same amount of F are higher at ambient pressure than at high pressures. Considering the impact of Ti on the phlogopite samples with higher Ti contents used in experiments at 7 to 15 kbar, the breakdown temperatures may be even lower than those shown in Figure 5. Thus, it seems that pressure plays a negative role in the thermal stability of phlogopite, which is the reverse of F effect. However, this pressure effect for phlogopite is not applicable to other minerals. For example, for clinohumite, with a F fraction of 0.5, can be stable up to 1100 °C at 30 kbar (Fig. 5), and up to 1600 °C at 10 GPa as inferred from Grützner et al. (2017).

The effects of F on the breakdown process at high temperatures

With increasing temperature, most Raman modes shift toward lower wavenumbers (Figs. 3d-h), indicating a temperature-induced softening of the phlogopite lattice for the two samples. So far, no one has reported the effect of F on the lattice vibrations of phlogopite at high temperatures. To investigate this, Figure 6a compares the temperature-induced shifts of the main Raman modes of the F-poor phlogopite and the F-rich one. It is seen that F has an impact on the temperature-induced shifts of the modes around 320 and 682 cm -1 . The shifted amplitudes of these modes are drastically reduced for the F-rich sample. This suggests that incorporation of F retards the lattice softening at high temperatures.

Fluorine appears to have an impact on the thermal behavior of OH in phlogopite. It can be observed that wavenumbers of the three groups OH bands in the F-rich phlogopite are generally lower than those in the F-poor phlogopite (Fig. 4d).

Relationship between the OH wavenumbers for the three groups of OH bands and Al content has been reported by [START_REF] Robert | Generalization of the correlation between hydroxyl-stretching wavenumbers and composition of micas in the system K 2 O-MgO-Al 2 O 3 -SiO 2 -H 2 O: a single model for trioctahedral and dioctahedral micas[END_REF]. According to them, micas with higher Al contents show lower OH wavenumbers for the type N and I OH bands, which is in contrast with our study that the F-poor phlogopite with a higher Al content has a higher OH wavenumber for all the types of OH bands. Therefore, the Al content alone cannot explain the differences in OH wavenumbers between the two samples.

Another factor may be the higher Fe content in the F-rich phlogopite which will decrease the OH wavenumber [START_REF] Vedder | Correlations between infrared spectrum and chemical composition of mica[END_REF]). In addition, the impact of F on the OH wavenumber has been reported for mica, amphibole, and talc [START_REF] Robert | Fluorine in micas: crystal-chemical control of the OH-F distribution between trioctahedral and dioctahedral sites[END_REF][START_REF] Robert | Near-infrared study of short-range disorder of OH and F in monoclinic amphiboles[END_REF][START_REF] Rywak | The crystal chemistry and thermal stability of sol-gel prepared fluoride-substituted talc[END_REF], which is not difficult to understand considering the stronger electronegativity of F than oxygen [START_REF] Pauling | The nature of the chemical bond. IV. The energy of single bonds and the relative electronegativity of atoms[END_REF]). Thus, it may be expected that F substitution for OH in phlogopite will strengthen the hydrogen bonding (O-H•••F), thereby reducing the OH wavenumber [START_REF] Libowitzky | Correlation of O-H stretching frequencies and O-H•••O hydrogen bond lengths in minerals[END_REF]. This has been seen in the F-induced OH band shift to lower wavenumbers in apatite (e.g., [START_REF] Tacker | Hydroxyl ordering in igneous apatite[END_REF]). To explore the correlation between F incorporation and hydrogen bonding strength, we plot wavenumbers of the type N OH against the F content represented by their X F values in Figure 6b, based on the data from this study and a compilation of data from literature. Although the data are somewhat scattered, mainly due to different chemical compositions besides F, the negative relationship is obvious. Consequently, with increasing F substitution, the strength of hydrogen bonding in phlogopite will be enhanced. This strengthened hydrogen bonding may influence the thermal stability of OH, which is seen in the different thermal behavior of OH for the F-poor phlogopite vs.

F-rich phlogopite. With increasing temperature, the OH bands all become broader, and shift towards lower wavenumbers, suggesting temperature-induced OH softening (Figs. 4a-b). There also exist some differences in the amplitudes of the temperature-induced wavenumber shifts of the OH bands between the two samples. The shift amplitudes are generally larger for the F-poor phlogopite than for the F-rich one (Fig. 6c). In other words, despite the fact that a higher temperature induces OH softening for all the phlogopite samples, phlogopite will experience less softening with addition of F. Thus, dehydrogenation may be more difficult for the F-rich phlogopite, and this needs to be verified by dehydrogenation kinetics studies in future.

From the vibrational spectra, the isobaric Grüneisen parameters of the lattice and OH modes in the two samples are calculated via the equation

 iP = -   i ( 𝜕 i

𝜕T

) P , where  iP is isobaric Grüneisen parameter of a mode ( i ), and  is the thermal expansion coefficient. Since there has been no report of the effects of F on the thermal expansion coefficient of phlogopite, we here refer to the thermal expansion coefficient of 6.26 × 10 -5 K -1 from [START_REF] Tutti | High-temperature study and thermal expansion of phlogopite[END_REF]. The calculated isobaric Grüneisen parameters of the two samples are listed in Tables 2 and3. The parameters are generally larger for the F-poor phlogopite than the F-rich phlogopite, indicating that the OH and lattice of the F-poor phlogopite are more sensitive to temperature. Therefore, our study reveals that both OH and the lattice of F-rich phlogopite have a higher thermal stability, compared with those of the F-poor phlogopite. Hydrogen diffusion from the lattice has been suggested to control the stability of muscovite [START_REF] Gaines | Dehydroxylation of muscovite[END_REF]. The impact of F on the lattice and the OH are thus probably responsible for the different breakdown processes of the F-rich and F-poor phlogopites at high temperatures. To date, one study has reported on the high-pressure Raman spectra of phlogopite [START_REF] Williams | The high-pressure behavior of micas: vibrational spectra of muscovite, biotite, and phlogopite to 30 GPa[END_REF].

They reported that both OH and lattice stiffened with increasing pressure, whereas the impact of F is unknown. Considering that pressure is another important parameter, future experimental work should focus on high pressures to explore the effects of F on the behavior of OH and the lattice of the phlogopite.

IMPLICATIONS

Because of the size similarity between F and OH, it is generally supposed that the incorporation of F into both nominally hydrous and anhydrous silicate minerals is mainly through the substitution for OH (e.g., [START_REF] Robert | Near-infrared study of short-range disorder of OH and F in monoclinic amphiboles[END_REF][START_REF] Crépisson | Clumped fluoride-hydroxyl defects in forsterite: Implications for the upper-mantle[END_REF]; [START_REF] Roberge | Is the transition zone a deep reservoir for fluorine?[END_REF][START_REF] Beyer | Fluorine partitioning between eclogitic garnet, clinopyroxene, and melt at upper mantle conditions[END_REF]Grützner et al. 2017b;[START_REF] Yoshino | Fluorine solubility in bridgmanite: A potential fluorine reservoir in the Earth's mantle[END_REF][START_REF] Hughes | Fluorine partitioning between humite-group minerals and aqueous fluids: implications for volatile storage in the upper mantle[END_REF]. This substitution inevitably causes variations in the structure and property of the phlogopite. The data from this study demonstrates that increasing the F substitution in phlogopite can prevent O-H bonding weakening and lattice softening at high temperatures, and consequently stabilize the phlogopite, which has an impact on the stability of phlogopite at high temperatures.

Roberge

It is well known that the mantle is a major water reservoir in the Earth because of the storage of hydrogen defects in nominally anhydrous mantle minerals such as olivine (e.g., [START_REF] Bell | Water in Earth's Mantle: The Role of Nominally Anhydrous Minerals[END_REF][START_REF] Pearson | Hydrous mantle transition zone indicated by ringwoodite included within diamond[END_REF]. Recent studies have also indicated that the mantle has acted as a reservoir for F (e.g., [START_REF] Beyer | Fluorine partitioning between eclogitic garnet, clinopyroxene, and melt at upper mantle conditions[END_REF][START_REF] Grützner | The effect of fluorine on the stability of wadsleyite: implications for the nature and depths of the transition zone in the Earth's mantle[END_REF][START_REF] Yoshino | Fluorine solubility in bridgmanite: A potential fluorine reservoir in the Earth's mantle[END_REF]. A close association between F and OH has been demonstrated via their coupled incorporation mechanism in olivine [START_REF] Crépisson | Clumped fluoride-hydroxyl defects in forsterite: Implications for the upper-mantle[END_REF]). To date, only one study has reported on the impact of F on nominally anhydrous mantle minerals, mainly focusing on F storage and phase stability [START_REF] Grützner | The effect of fluorine on the stability of wadsleyite: implications for the nature and depths of the transition zone in the Earth's mantle[END_REF]. Phlogopite is a F-rich and hydrous key mineral in the upper mantle. Experimental studies have suggested that F concentrates preferentially in phlogopite compared to other minerals [START_REF] Edgar | Fluorine-bearing phases in lamproites[END_REF]. The F contents in mantle phlogopites are mostly from 0 to ~5 wt% and some are up to ~8-9.5 wt% [START_REF] Li | Unusually high electrical conductivity of phlogopite: the possible role of fluorine and geophysical implications[END_REF]. Figure 5 indicates that X F > 0.5 can increase the breakdown temperature of phlogopite to over 100 °C under ambient pressure.

Considering the high-pressure conditions in the upper mantle and the impact of other elements, such as Ti, the specific breakdown temperature for phlogopite would be affected. For example, a phlogopite with 8 wt% F (X F = 0.9) is expected to be stable up to 1350 °C under ambient pressure, while it is expected to be stable up to a temperature lower than 1300°C at 7-15 kbar (Fig. 5). Indeed, high-Ti phlogopite containing 8 wt% F has been found in an ultra-high-temperature (UHT) metamorphic terrane (980-1120 °C, below 9 kbar) [START_REF] Motoyoshi | F-rich phlogopite stability in ultra-high-temperature metapelites from the Napier Complex, East Antarctica[END_REF] suggesting that F-rich samples can be stable at higher temperatures at ambient pressure than at a higher pressure. Consequently, the increased stability and hydrogen bonding of F-bearing phlogopite makes it an excellent candidate for the storage and transport of both H 2 O and the halogens in the upper mantle. In the lithospheric mantle, F can be stored both in hydrous minerals and nominally anhydrous minerals. Although amphibole, phlogopite, and apatite are accessory mantle phases, they are dominant F carriers because F is likely a compatible element in these minerals [START_REF] Klemme | Halogens in the Earth's Mantle: What We Know and What We Don't[END_REF]. Furthermore, the transport of F in the mantle is dependent on the thermal stabilities of F-bearing minerals. Previous studies showed that phlogopite can be stable up to 1100 °C under 6 GPa, amphibole (K-richterite) can be stable up to 1300 °C, and apatite can be stable up up to 1100 °C under 6 to 8 GPa [START_REF] Konzett | The stability of hydrous potassic phases in lherzolitic mantle-an experimental study to 9.5 GPa in simplified and natural bulk compositions[END_REF][START_REF] Konzett | The high PT stability of apatite and Cl partitioning between apatite and hydrous potassic phases in peridotite: an experimental study to 19 GPa with implications for the transport of P, Cl and K in the upper mantle[END_REF]. Since F plays an important role in stabilizing phlogopite, amphibole, and apatite (e.g., Frost 2006), F-bearing phlogopite, amphibole, and apatite act as important repositories of F in the mantle, dependent on their distributions in some regional zones.

The effect of F on the hydrogen bonding may have some implications on the dehydrogenation and electrical conductivity of phlogopite. Although it has been reported that dehydrogenation will occur before phlogopite breaks down (e.g., [START_REF] Vedder | Dehydroxylation and rehydroxylation, oxidation and reduction of micas[END_REF][START_REF] Tutti | High-temperature study and thermal expansion of phlogopite[END_REF][START_REF] Zhang | Optical phonons, OH vibrations, and structural modifications of phlogopite at high temperatures: An in-situ infrared spectroscopic study[END_REF], our study shows that the addition of F may make dehydrogenation more difficult. Furthermore, [START_REF] Li | Fluorine follows water: Effect on electrical conductivity of silicate minerals by experimental constraints from phlogopite[END_REF] has reported that increasing the F content can significantly enhance the electrical conductivity of phlogopite. Our study shows that F incorporation can prevent O-H bonds from weakening at high temperatures, which may impede hydrogen mobility.

Therefore, the contribution of hydrogen conductivity should decrease with increasing F content in phlogopite. literature. Phlogopite at ambient pressure: [START_REF] Rimsaite | Structural formulae of oxidized and hydroxyl-deficient micas and decomposition of the hydroxyl group[END_REF][START_REF] Rimsaite | DTA, TG, IR and isotopic analyses and properties of phlogopite, biotite muscovite and lepidolite in temperature range of metamorphic reactions[END_REF], [START_REF] Prost | Far-infrared study of potassium in micas[END_REF], [START_REF] Hammouda | Synthesis of fluorphlogopite single crystals. Applications to experimental studies[END_REF], [START_REF] Ogorodova | Thermodynamic properties of natural tetraferriphlogopite[END_REF]. Phlogopite at high pressures: [START_REF] Hensen | Experimental Study of Dehydration Melting of F-Bearing Biotite in Model Pelitic Compositions[END_REF], Dooley and Patiño Douce (1996). Pargasite: [START_REF] Holloway | Fluid-absent melting of the fluoro-hydroxy amphibole pargasite to 35 Kbar[END_REF], [START_REF] Oba | Experimental study on the tremohte-pargasite join at variable temperatures under 10 kbar[END_REF]. K-richterite: [START_REF] Foley | High-pressure stability of the fluor-and hydroxy-endmembers of pargasite and K-richterite[END_REF]. Clinohumite: [START_REF] Weiss | Clinohumites, a field and experimental study[END_REF]. The open square represents the poorly constrained breakdown temperature of fluorphlogopite in [START_REF] Hammouda | Synthesis of fluorphlogopite single crystals. Applications to experimental studies[END_REF]. It is probably higher than 1403 °C because it completely melts without breakdown at this temperature. The red and blue filled squares represent F-poor and F-rich phlogopites in this study, respectively. Wavenumbers of the type N OH at ambient conditions versus X F . Two data are from this study, and the others are from previous studies [START_REF] Vedder | Correlations between infrared spectrum and chemical composition of mica[END_REF][START_REF] Prost | Far-infrared study of potassium in micas[END_REF][START_REF] Xu | Mineralogical study on fluorphlogopite from the Bayan Obo ore deposit[END_REF][START_REF] Chon | Structural changes and oxidation of ferroan phlogopite with increasing temperature: in situ neutron powder diffraction and Fourier transform infrared spectroscopy[END_REF][START_REF] Piccinini | Synchrotron radiation FT-IR micro-spectroscopy of fluorophlogopite in the O-H stretching region[END_REF][START_REF] Scordari | Ti-rich phlogopite from Mt. Vulture (Potenza, Italy) investigated by a multianalytical approach: substitutional mechanisms and orientation of the OH dipoles[END_REF][START_REF] Ventruti | High-temperature treatment, hydrogen behaviour and cation partitioning of a Fe-Ti bearing volcanic phlogopite by in situ neutron powder diffraction and FTIR spectroscopy[END_REF][START_REF] Lacalamita | Substitution mechanisms and implications for the estimate of water fugacity for Ti-rich phlogopite from Mt. Vulture, Potenza, Italy[END_REF][START_REF] Zhang | Optical phonons, OH vibrations, and structural modifications of phlogopite at high temperatures: An in-situ infrared spectroscopic study[END_REF]. (c)

Temperature-induced wavenumber shifts of the OH bands. Since there exist

Figure captions :

 captions Figure captions:

Figure 2 .

 2 Figure 2. Comparisons of Raman spectra of lattice vibrations between the initial and

Figure 4 .

 4 Figure 4. (a) Unpolarized IR spectra of OH stretching vibrations from the F-poor

Figure 5 .

 5 Figure 5. Breakdown temperature of phlogopite and other hydrous minerals (pargasite,

Figure 6 .

 6 Figure 6. (a) Temperature-induced wavenumber shifts of the lattice modes. (b)

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  Mg 2.723 Fe 0.026 Al 0.111 Mn 0.001 Ti 0.062 Cr 0.002 Ni 0.001 )(Si 2.955 Al 1.045 )O 10 [F 0.053 C l 0.002 OH 1.945

	This	results		in	the	following		formula
	(K 0.963 Na 0.015 )(Mg 2.677 Fe 0.166 Al 0.059 Mn 0.002 Ti 0.015 Cr 0.009 Ni 0.003 )(Si 3.067 Al 0.933 )O 10 [F 0.905 C
	l 0.016 OH 1.079 ]	for	the	F-rich	phlogopite	(X F	=	0.45),	and
	(K 0.911 Na 0.047 )(

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Table 1 .

 1 Chemical compositions of the two phlogopite samples (in wt%, dash = below 0.01 wt%).Note: *H 2 O and OH estimated on the basis of 22 cation charges, assuming 10 oxygen and 2(OH+F+Cl)[START_REF] Rieder | Nomenclature of the micas[END_REF]. is the peer-reviewed, final accepted version for American Mineralogist, published by the Mineralogical Society of America. The published version is subject to change. Cite as Authors (Year) Title. American Mineralogist, in press. DOI: https://doi.org/10.2138/am-2022-8051. http://www.minsocam.org/ Always consult and cite the final, published document. See http:/www.minsocam.org or GeoscienceWorld

			This
		F-poor phlogopite (from Badakhshan)				F-rich phlogopite (from Franklin)
		Phl1	Phl2	Phl3	Phl4	Average	SD	Phl5	Phl6	Phl7	Phl8	Phl9	phl10	phl11	Average	SD
	SiO 2	42.39	43.23	42.67 42.31	42.65	0.42	43.16	43.68	43.51	43.69	43.87	43.41	43.52	43.55	0.23
	TiO 2	1.15	1.13	1.24	1.20	1.18	0.05	0.33	0.42	0.18	0.25	0.24	0.23	0.21	0.27	0.08
	Al 2 O 3	14.31	14.18	14.14 14.03	14.16	0.11	12.16	11.84	11.87	12.00	12.13	11.85	11.77	11.95	0.15
	FeO	0.48	0.47	0.41	0.48	0.46	0.04	2.80	2.47	2.70	2.73	2.86	2.98	3.17	2.82	0.22
	MnO	-	0.04	-	0.06	0.02	0.03	0.01	0.04	0.01	0.09	0.03	-	0.05	0.03	0.03
	MgO	26.62	26.34	26.02 26.48	26.37	0.26	25.77	25.58	25.88	25.59	25.06	25.36	25.29	25.50	0.29
	CaO	-	0.01	-	-	-	-	-	-	-	-	-	-	-	-	-
	Na 2 O	0.30	0.39	0.36	0.35	0.35	0.03	0.07	0.09	0.14	0.10	0.12	0.12	0.15	0.11	0.03
	K 2 O	10.36	10.27	10.22 10.41	10.31	0.09	10.76	10.77	10.70	10.63	10.71	10.69	10.76	10.72	0.05
	F	0.23	0.26	0.24	0.24	0.24	0.01	3.98	4.10	4.10	4.01	3.97	4.03	4.24	4.06	0.09
	Cl	-	0.03	0.04	0.02	0.02	0.02	0.12	0.12	0.13	0.14	0.16	0.17	0.14	0.14	0.02
	Cr 2 O 3	0.03	-	0.08	0.04	0.04	0.03	0.20	0.14	0.13	0.15	0.16	0.14	0.16	0.15	0.02
	NiO	-	-	-	0.05	0.01	0.03	0.07	-	0.05	0.04	0.05	0.08	-	0.04	0.03
	H 2 O*	4.22	4.23	4.19	4.19	4.21		2.34	2.28	2.28	2.33	2.34	2.29	2.20	2.30
	Subtotal 100.08 100.57 99.60 99.85	100.03		101.77 101.52 101.66 101.75 101.70 101.36 101.65	101.63
	O=F,Cl	0.10	0.12	0.11	0.11	0.11		1.70	1.75	1.76	1.72	1.71	1.74	1.81	1.74
	Total	99.99	100.45 99.49 99.74	99.92		100.06	99.77	99.90	100.03	99.99	99.62	99.84	99.89

Table 2 .

 2 Evolutions of wavenumbers of the lattice modes (cm -1 ) with temperature and the isobaric Grüneisen parameters. The data in italics are the uncertainties.This is the peer-reviewed, final accepted version for American Mineralogist, published by the Mineralogical Society of America.The published version is subject to change. Cite as Authors (Year) Title. American Mineralogist, in press. DOI: https://doi.org/10.2138/am-2022-8051. http://www.minsocam.org/

	Temperature	F-poor phlogopite
	(°C)	Lattice mode (cm -1 )

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Table 3 .

 3 Evolutions of wavenumbers of the three groups of OH bands (cm -1 ) with temperature and the isobaric Grüneisen parameters of the OH modes. The data in italic are the uncertainties. This is the peer-reviewed, final accepted version for American Mineralogist, published by the Mineralogical Society of America.The published version is subject to change. Cite as Authors (Year) Title. American Mineralogist, in press. DOI: https://doi.org/10.2138/am-2022-8051. http://www.minsocam.org/

	Temperature (°C)	F-poor phlogopite OH wavenumber (cm -1 )

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(41972038), the Zhejiang Province Natural Science Foundation of China (LY18D020001), and the Fundamental Research Funds for the Central Universities (K20210168). Can Rao and Suwen Qiu are thanked for the analysis of F using EPMA.

ACKNOWLEDGMENTS

This work is supported by the National Natural Science Foundation of China

This is the peer-reviewed, final accepted version for American Mineralogist, published by the Mineralogical Society of America. The published version is subject to change. Cite as Authors (Year) Title. American Mineralogist, in press. DOI: https://doi.org/10.2138/am-2022-8051. http://www.minsocam.org/ 698 This is the peer-reviewed, final accepted version for American Mineralogist, published by the Mineralogical Society of America. The published version is subject to change. Cite as Authors (Year) Title. American Mineralogist, in press. DOI: https://doi.org/10.2138/am-2022-8051. http://www.minsocam.org/ Always consult and cite the final, published document. See http:/www.minsocam.org or GeoscienceWorld This is the peer-reviewed, final accepted version for American Mineralogist, published by the Mineralogical Society of America. The published version is subject to change. Cite as Authors (Year) Title. American Mineralogist, in press. DOI: https://doi.org/10.2138/am-2022-8051. http://www.minsocam.org/ Always consult and cite the final, published document. See http:/www.minsocam.org or GeoscienceWorld This is the peer-reviewed, final accepted version for American Mineralogist, published by the Mineralogical Society of America. The published version is subject to change. Cite as Authors (Year) Title. American Mineralogist, in press. DOI: https://doi.org/10.2138/am-2022-8051. http://www.minsocam.org/ Always consult and cite the final, published document. See http:/www.minsocam.org or GeoscienceWorld This is the peer-reviewed, final accepted version for American Mineralogist, published by the Mineralogical Society of America. The published version is subject to change. Cite as Authors (Year) Title. American Mineralogist, in press. DOI: https://doi.org/10.2138/am-2022-8051. http://www.minsocam.org/ Always consult and cite the final, published document. See http:/www.minsocam.org or GeoscienceWorld This is the peer-reviewed, final accepted version for American Mineralogist, published by the Mineralogical Society of America. The published version is subject to change. Cite as Authors (Year) Title. American Mineralogist, in press. DOI: https://doi.org/10.2138/am-2022-8051. http://www.minsocam.org/ Always consult and cite the final, published document. See http:/www.minsocam.org or GeoscienceWorld This is the peer-reviewed, final accepted version for American Mineralogist, published by the Mineralogical Society of America. The published version is subject to change. Cite as Authors (Year) Title. American Mineralogist, in press. DOI: https://doi.org/10.2138/am-2022-8051. http://www.minsocam.org/ Always consult and cite the final, published document. See http:/www.minsocam.org or GeoscienceWorld This is the peer-reviewed, final accepted version for American Mineralogist, published by the Mineralogical Society of America. The published version is subject to change. Cite as Authors (Year) Title. American Mineralogist, in press. DOI: https://doi.org/10.2138/am-2022-8051. http://www.minsocam.org/ Always consult and cite the final, published document. See http:/www.minsocam.org or GeoscienceWorld

discontinuities in the wavenumber evolutions of some lattice modes and OH bands, the 697 dotted squares indicate the temperature range of the linear fit.