Stéphanie Lachaud-Martin

Corinne Marache

Mikaël Julie Mcintyre

Guardians of Trade Secrets. Brokers and Wine

authorities levied heavy excise duties on wine, payable by consumers and retailers. In order to control the collection of these taxes, an artificial (and unworkable) distinction between wholesalers, semi-retailers and retailers had been introduced 5 .

Unlike wine-producing countries, and especially France, where some in-depth research has been conducted on the history of wine brokerage, 97 the profession has attracted hardly any attention in the Netherlands 6 . Some studies on Dutch trade history, however, do contain a chapter on brokerage in general [START_REF] Gelderblom | Cities of Commerce: The Institutional Foundations of International Trade in the Low Countries, 1250-1650[END_REF] . Unfortunately, most of these are, as Velinov has recently pointed out, largely based on regulation, whereas documents reflecting commercial practice have hardly been studied [START_REF] Velinov | Parasites ou abeilles ? Le rôle des courtiers dans les marchés médiévaux et modernes (Bruges, Anvers, Amsterdam, XIVe-XVIIIe siècle)[END_REF] . Historians have moreover exclusively focused on Amsterdam wholesale trade. Transaction cost analysis is the dominant explicative framework.

Instead of compressing the object in a preconceived model, this research on the contrary, makes a case for an empiricist study of the praxis of wine brokerage, based on merchant letters, books and bills. I will investigate why semi-retailers hired wine brokers, even though this was not compulsory. The first section discusses the main features of the Dutch wine market and the organization of the brokers' profession in the foremost distribution centers: Amsterdam, Rotterdam, Middelburg and the inland port of Dordrecht. The second and third parts examine the circumstances under which specialized wine merchants appealed to a broker. The backgrounds and careers of these intermediaries in trade are also discussed here. Finally, special attention is given to the brokers' role in the provision of information, as this has always been a central aspect of wine brokerage.

Brokerage and wine distribution in the United Provinces

In the 18 th century, the Dutch wine market had some stable features, but also went through a number of significant changes. In the first half of the century, the United Provinces were the chief market for French wine and conversely French wines had an overwhelming share of the Dutch wine trade. Outside periods of war, the vast majority of Dutch maritime wine imports (70 to 90% depending on the year) came from France. High tolls were levied at the Rhine, preventing Rhine and Mosel wines from gaining a large market share 9 .

Amsterdam and Rotterdam were the main ports for imports of wine in Holland, the former increasingly surpassing the latter. The town of Middelburg in Zeeland, which had dominated maritime wine imports up to the first decades of the 17 th century, still played a second-rate role, with a share of approximately 15%. The former staple of Dordrecht controlled part of the distribution of German wines, a greatly reduced branch of trade.

Over the course of the century, several independent phenomena such as the falling purchasing power of the middle classes and the increasing profitability of Dutch and French West-Indian trade, contributed to a decrease in wine imports in the United Provinces. However, at the same time, the increasingly complex structure of the Dutch wine market may have furthered the need for specialized intermediaries. Around the middle of the century, elite consumer preferences shifted from the sweet white wines of the Garonne Valley and the Bergerac area to the red wines of Médoc, Cahors, Languedoc and Spain. Improvements in conservation techniques encouraged wine aging, and producer names and regional brands became ever better known among regular consumers. Diversification also occurred at the lower end of the market. There was a strong demand for cheap processed wines (for instance from Poitou), softened by the addition of sugar syrup and also for locally produced Ersatz. Small consumers, whose daily drink consisted of beer and tea, attached great Above the door: "'t maekelaers comptoir" ("The brokers' hall"). Above the upper window : "Vryheid is voor geen geld te koop" ("Freedom is not for sale").

© Anne Wegener Sleeswijk, 2019. importance to drinking "wine" at special occasions: christenings, weddings, funerals and the annual fair.

Given the dominant position of Amsterdam in imports, it seems logical that this city had the largest number of wine brokers. Around 1720, according to Jean-Pierre Ricard, sixty to eighty brokers -both official and illicit-specialized in the wine and brandy trade10 . However, 100 some of them hardly practiced, because they were either too old or combined wine brokerage with other activities. The 1730 official brokers' directory for Amsterdam mentions twentythree names of professionals who considered the wine and brandy trade as their specialization 11 . In Rotterdam, the number of official wine brokers was at least eleven in 1735 12 . Eight sworn wine brokers were active in Middelburg in 1648; in 1754 they were only four [START_REF]Ordonnantie voor de makelaars van de wijnen binnen de stad Middelburg in Zeeland, met aanvullingen tot 1723[END_REF] . In Dordrecht, the number of brokers allowed to mediate in any trade except for grain was set at six in 1726 14 . Newspaper advertisements show that Dordrecht brokers did not specialize and those involved in the wine trade also settled transactions in other goods and services [START_REF]Advertisements for wine and timber auctions in Dordrecht[END_REF] .

In all four cities, brokers were required to join the local brokers' guild. Whereas the Middelburg wine brokers formed a separate guild from 1648 onward, with its own ordinance and guild house, the Amsterdam, Rotterdam and Dordrecht wine brokers belonged, to the general brokers' guilds. In other respects there were also major differences between the four cities. Brokerage rates for wine varied considerably for instance from one city to another. They were the highest in Amsterdam, but hardly ever exceeded 3% of a wine's value [START_REF] Sr | Dossier van het geschil tussen wijnkooplieden en makelaars[END_REF] . 101

Brokers were responsible for two major commercial institutions that held a key position in the provision of commercial information. The Dean and the Council of the Amsterdam brokers' guild were in charge of the publication of the commodity price lists, the Amsterdamsche Prijscourant, which had appeared weekly or bi-weekly since 1585 [START_REF] Cusker | The Beginnings of Commercial and Financial Journalism[END_REF] . Every week, the Amsterdam wine brokers had to transmit current wholesale prices. They also selected the types of wine to be mentioned, changing the classification several times in the course of the century. Between the end of the 17 th and the end of the 18 th century, the Prijscourant thus mentioned the wholesale prices of sixteen to twenty-eight categories of French wine, three to fourteen Spanish and Portuguese wines and occasionally an Italian wine. German wines were not included as they were imported by wine merchants and generally sold without brokers' intermediation.

In all four cities, brokers also had the privilege of organizing voluntary auction sales of merchandize, under the supervision of a city official. Wine was one of the goods most frequently sold. Around 1720, in Amsterdam, about a quarter of all imported wine was sold at the auction. Most sellers were wholesalers; the buyers were mostly wine merchants, distillers and institutions such as trading companies and old people's homes. Only sellers at the auction were obliged to hire a broker, but buyers also often did so. In Amsterdam, Rotterdam and Dordrecht, wine auctions took place in specialized inns, whereas the Middelburg auctions were organized at the wine merchants' guild house 18 .

While regulation gives an idea of the contours of the wine brokers' profession, correspondence between wine merchants and their brokers provides more insight into the position of these intermediaries in distribution networks.

Formal representatives and troubleshooters

In January 1750, the Dordrecht wine merchant Matthijs Marshal wrote to his Rotterdam broker, Pieter van Overzee, that he had received in good order, the six hogsheads of new Bergerac wine that the latter had 102 shipped to him. He also asked him to buy some barrels of a red Bordeaux from the 1748 vintage, preferably of a cru that he had previously sampled, provided that the wine was "clean" and not too expensive. Finally, he enquired how his broker valued the latest "vin du Haut-Pays". Had he already tasted these wines? Where they "good and sweet" and at what prices did they sell19 ? Pieter van Overzee was Marshal's regular Rotterdam broker. Purchase orders and information on prices and on the quality of wines formed the main subjects of their correspondence.

Matthijs Marshal was born in Dordrecht in 1705. In spite of his English sounding last name, he was probably of German descent: he spoke and wrote German fluently and belonged to the Lutheran congregation. He learned the wine trade with his father20 . Only one archival piece has survived for his enterprise, a messy copybook of outgoing correspondence for the period 1745 to 1762, also containing some copies of bills. Marshal was well-to-do: he owned several houses and warehouses in his hometown, and possessed a carriage and a country house near Wieldrecht, where he enjoyed spending the weekend. He belonged to "De Veertigen", the council of representatives of the guilds that compiled the lists from which the Dordrecht aldermen and the town councilors were chosen 21 . By the end of his life, Marshal was appointed Dean of the wine merchants' guild 22 .

As a "wijnkoper", Marshal specialized in semi-retailing. However, like many of his Dordrecht colleagues, he also imported Rhine and Mosel wines on his own account. He had a stable network of suppliers in the German hinterland including merchants and producers from Trier, Trarbach, Bingen-am-Rhein, Mainz and Cologne (fig. 2). His German correspondents acted as commission agents, but he also regularly merchants in other cities of the United Provinces with German wine. In 1760, he even made an attempt to export Rhine and Frontignan wine to Batavia, but this proved unsuccessful [START_REF][END_REF] . The volume of his wine sales is only known for one year: from November 1745 to October 1746 they amounted to approximately 47 thousand liters.

Marshal mainly used brokers in two cases: when he sold Rhine or Mosel wines at the auction in his hometown and when he bought French or Spanish wine in Amsterdam or Rotterdam. As his dealings with Dordrecht brokers have proved to be difficult to document, we will concentrate on his metropolitan brokers.

Between 1745 and 1762, Marshal maintained exclusive and long-term relationships with one Rotterdam broker and one Amsterdam broker. The two men had very different backgrounds. Pieter van Overzee from Rotterdam belonged to a prosperous and influential brokers' clan. He had been active as a broker since at least 1723, but like his father, he focused initially on the timber trade 28 . He started to specialize in wine from the 1730s, probably as a consequence of his marriage, in 1733, to a daughter of Florens Eilbracht, one of the foremost Rotterdam wine brokers [START_REF] Sr | Pieter van Overzee[END_REF] . Van Overzee's career is interesting because it shows that in 105 Holland a successful wine broker was not necessarily in the first place a wine expert.

Usually, Van Overzee bought batches of four to eight hogsheads of wine for Marshal. Before carrying out his assignment, the broker would send sample bottles of different producers and vintages. Sometimes, Marshal also traveled to Rotterdam himself (about 18 kilometers from Dordrecht) to taste wines in the company of his broker. It is noteworthy that Marshal even appealed to his metropolitan brokers when purchasing wine with importers he knew quite well himself. He seems to have hired his brokers not in the first place to reduce search costs, nor to enforce contracts. He essentially turned to them because they provided him with a "package" of services. They had barrels cleaned up if necessary, took care of payment and import taxes and also acted as shipping agents [START_REF] Rad | MML, Letter to Pieter van Overzee[END_REF] .

From 1748 on, Marshal also employed an Amsterdam broker, Arent van Eldick [START_REF]Letter to Arent van Eldick[END_REF] . At the time, Van Eldick, who seems to have established himself in Amsterdam around 1730, worked as an illicit broker. He only obtained a license in 1758 after a long career [START_REF]Lyste der naamen en woonplaatsen van de makelaars[END_REF] . Initially, there was some confusion about his position, as Marshal's German correspondent had presented him as "an Amsterdam wine commissioner" 33 . However, Van Eldick charged a broker's fee and not a commission (a percentage) and acted in every respect as a broker [START_REF]Letter to Arent van Eldick[END_REF] . This confusion is remarkable because it bears witness both to the proliferation of all sorts of middlemen in 18 th century trade and to the blurring of boundaries between official and illicit brokerage. Young brokers often worked as illegal brokers before obtaining an office. Moreover, although strictly forbidden, official and illicit wine brokers regularly collaborated. Attitudes towards illegal brokerage changed considerably in the course of the 18 th century. In the 17 th century and at the beginning of the 18 th century, the Amsterdam city council had enacted many laws to counter this practice [START_REF] Stuart | De Amsterdamsche makelaardij. Bijdrage tot de geschiedenis onzer handelswetgeving[END_REF] . However, from the first decades of the 18 th century on, the 106 brokers' guild filed fewer and fewer procedures against the so-called "beunhazen" 36 . At the same time, illegal brokers increasingly declared themselves as such in public. In 1742, on the occasion of the "personele quotisatie", a one-off tax on income and property, several well-todo illicit wine brokers such as Wiggert Winter and Justus de Rolder even officially stated "beunhaas" as their profession [START_REF] Oldewelt | Kohier van de Personeele quotisatie te Amsterdam over het jaar 1742[END_REF] .

Marshal contacted Van Eldick with a special purpose: to get rid of an unsalable lot of wine, which he had exceptionally received as a commission from his correspondent Adolf Böcking from Trarbach in the Palatinate [START_REF] Rad | MML, Letter to Arent van Eldick[END_REF] . In September 1748, Böcking had sent Marshal about 30 pieces of old low-quality Mosel wine 39 . At the time of shipment, Marshal had expected a quick sale to the States army, which was stationed close to Dordrecht to fight the War of the Austrian Succession (1740-1748). However, due to all kinds of setbacks, transport took more than two months and when the wine finally arrived in Holland, peace had been signed and most army units had been demobilized [START_REF]War ended on 18 October 1748 with the signing of the Peace of Aix-la-Chapelle. RAD, 1390 MML[END_REF] .

Marshal then asked a Dordrecht broker to sell the wine at the local auction. The brokers' auction was often successfully used when a quick sale was required, for example because wine started to spoil, or because a merchant needed cash. However, this particular auction became an outright failure: although advertisements were published to announce the sale, not a single potential buyer from outside town showed up. The main part of the wine therefore went unsold and had to be stored again in Marshal's cellar.

A year later, after having incurred substantial costs, Marshal and Böcking at last decided to ship the wine to Amsterdam and charge Van Eldick with its sale 41 . The remaining barrels were sold to four Amsterdam wine merchants, including Jan Bols, a relative of the famous distiller 107 Lucas Bols, whose company still survives today [START_REF][END_REF] . Prices were so low, that it seems likely that the wine was indeed only suitable for distillation.

Marshal's small brokers' network was thus characterized by sustainable personal relationships. His brokers had different backgrounds and may not have been knowledgeable wine experts. In addition to purchasing wine for him, they provided a wide range of other (paid) services, and can best be regarded as all-round metropolitan business agents. They also kept Marshal informed about prices and vintages, a role that appears even more clearly in the brokers' correspondence of the Middelburg wine merchants Van

Information from the brokers' auction

In the third quarter of the 18 th century, Andries van der Poest was a considerable Middelburg wine merchant 43 . He had started out in business with his father-in-law and established his own company around 1750 [START_REF]Extract uit de resolutien ten raade der stad Middelburg in Zeeland[END_REF] . Elected Dean of the wine merchants' guild shortly thereafter, he also held various offices [START_REF] Naamwyzer | aantonende alle de namen en woonplaatsen van de Edele achtbare magistraat der stad Middelburg in Zeeland. Verder alle de hooge en aanzienlijke amptenaren[END_REF] . He was related to the "French" families of Middelburg and for a long time, he was an Elder in the Walloon church 46 .

Around 1775 -possibly to secure his old age-, Van der Poest hired Johan Clement as a bookkeeper. The young Clement had studied law 108 and in addition to being a wine merchant, he also worked as a lawyer. In 1781, Clement became a partner in the company. After the death of Van der Poest in 1783, Clement continued the firm with his widow. Deeply involved in the revolutionary patriot movement, the wine trade however soon became secondary among his activities [START_REF] Augustinus Van Cauwenberg | Omstandig verhaal van het voorgevallene te Middelburg in Zeeland, bij gelegenheid der revolutie in den jaare 1787[END_REF] .

Van der Poest and Clement traded in all sorts of wine, but mostly in French wines from Bordeaux, Bergerac and (from the late 1760's onward) Languedoc. Like Marshal, they were not only involved in distribution, but also imported wines themselves. Over the period 1766-1793, they had suppliers in Nantes, Bordeaux, Bayonne, Marseille, Sète and Toulon (fig. 3). They purchased German wine, Champagne and Burgundy from colleagues from Liège, Namur, Maastricht and Dordrecht. However, sometimes they also ordered wines from trading houses in Reims and Beaune and occasionally, they imported from Cologne, Frankfurt-am-Main, Düsseldorf and Mainz. In peak years, the volume of their imports was up to about 25.000 liters of wine, which was substantial for a semi-retailer, but modest when compared to wholesalers.

Van der Poest and Clement had a diverse clientele. Customers in Middelburg were numerous, but remain largely invisible in the outgoing correspondence. Letters occasionally mention them though, as in 1791, when Clement wrote to a Rotterdam supplier that he needed wine must for Middelburg innkeepers and operators of music halls for the production of piquette, as their clients wanted to drink white wine but could not pay much for it [START_REF] Za | [END_REF] occasional 53 . Van Raalt practiced as a broker for nearly thirty years until his death in 1785 [START_REF]Advertisements for wine auctions[END_REF] . Throughout his life, he collaborated intensively with his brother Nicolaas, a wine merchant who lived near him at Wijnhaven 55 . Cooperation between brokers and relatives who were wine merchants or wholesalers was common and allowed brokers to circumvent the strict regulations that forbade private trade to brokers.

Van der Poest regularly hired Gerard Verboom from 1771 to 1775. Their relationship was often tense, the merchant needing to remind his broker repeatedly, that his letters had remained unanswered or that he was late in executing his modest purchase orders 56 . In the 1760s to 1780s, Verboom regularly sold huge quantities of wine at the Rotterdam auction, up to two hundred casks at a time, on behalf of the main "French" wine importers of Rotterdam, such as Jouhanneau, Laregnère and Cornelis Balguerie 57 . It seems that Verboom largely focused on the Rotterdam bulk trade at the expense of provincial wine merchants such as Van der Poest.

A serious crisis of confidence arose in 1773, on the occasion of a purchase order of six hogsheads of five year-old red Cahors wine, for which the choice had been based on test bottles that Verboom had sent to Middelburg. On delivery, the wine turned out to be totally different than 111 the sample. Van der Poest hence blamed his broker, for not having tasted the wine himself, supposing that he certainly would have noticed that at least half of it was of the latest vintage, and not even from Cahors 58 ! In accordance with breach of contract law, Van der Poest then sent the wine back to Rotterdam at the broker's expense. This affair shows that wine brokers were not always as sincere and committed as they had promised when taking the oath.

Between 1775 and 1793, Van der Poest and Clement employed Jacobus van Overzee as a broker, a son of Pieter van Overzee, who had worked for Marshal some twenty years earlier. In the course of the 18 th century, brokers' dynasties seem to have become increasingly widespread 59 . Van Prior to the auctions, wine brokers typically placed advertisements in newspapers and had posters printed to announce the sale (figure 4). Through these ads, which mentioned factual as well as subjective information, wine knowledge also reached a larger number of people.

However, the brokers' auction was not a transparent market. Brokers shared private information with befriended clients and frequently colluded. In 1735, for example, Marshal's Rotterdam broker, Pieter van Overzee and his father-in-law Florens Eilbracht were involved in a major scandal. They were accused of forming a bidding ring to keep prices low. Evidence brought against them blatant, but they were maintained in office, as they had strong personal ties with members of the urban government 68 . Wine brokers and their auctions were indeed not just cost saving and trade facilitating devices. 114

Official and illicit wine brokers occupied an important place in 18 th -century wine distribution in the United Provinces. Wine brokers were employed by wholesalers who were often of foreign origin and who were not allowed to sell in semi-retail for fiscal reasons. 68 Specialized wine merchants also often hired brokers. Close investigation into the affairs of two of these semi-retailers, Matthijs Marshal from Dordrecht and Van der Poest & Clement from Middelburg, reveals that wine brokers commonly acted as their general metropolitan business agents. They were at the same time informants, consultants, problem solvers, network builders, legal representatives and matchmakers.

Many Amsterdam and Rotterdam wine brokers no doubt got only a small part of their income from the modest fee they received for their mediation between individual sellers and buyers. They also earned from the organization of auctions, the storage and handling of wines and from their mediation in insurance and payments and they combined wine brokerage with other (trade) activities.

Unlike their colleagues in wine producing countries, Dutch wine brokers were not always wine experts. Some of them were more specialized than others, depending on their training and on the possibility of collaboration with relatives involved in the wine trade. The degree of specialization also differed from one city to another, urban regulation explaining for example the absence of specialized wine brokers in Dordrecht.

Dutch wine brokers constituted an exceptionally heterogeneous group. They had different social backgrounds, though many came from families involved in wine trade or in brokerage. The scale of their activities varied greatly. Some brokers mainly worked for wholesalers while others chiefly carried out purchase orders for semi-retailers.

The brokers' auctions largely contributed to the supply of information on prices, the quality of wines and the activity in trade. The brokers' privilege regarding the organization of commercial auctions also allowed them to control part of the market. The study of wine brokers' correspondence indeed reveals that practice was sometimes at odds with the model of the neutral mediator in charge of a public service under the supervision of local authorities that emerges from ordinances. For most brokers, however, sincerity and loyalty to their clients were the guiding principles in their business and this undoubtedly largely explains the sustainability of their relationships.

  Lachaud-Martin, Corinne Marache, Julie McIntyre, Mikaël Pierre ( Eds.), Wine, Networks and Scales. Intermediation in the Production, Distribution and Consumption of Wine, Bruxelles, Peter Lang, 2021, p. 95-114.

  Lachaud-Martin, Corinne Marache, Julie McIntyre, Mikaël Pierre ( Eds.), Wine, Networks and Scales. Intermediation in the Production, Distribution and Consumption of Wine, Bruxelles, Peter Lang, 2021, p. 95-114. 99 Fig. 1. The Amsterdam brokers' guildhall, built in 1633

  Lachaud-Martin, Corinne Marache, Julie McIntyre, Mikaël Pierre ( Eds.), Wine, Networks and Scales. Intermediation in the Production, Distribution and Consumption of Wine, Bruxelles, Peter Lang, 2021, p. 95-114.

  Lachaud-Martin, Corinne Marache, Julie McIntyre, Mikaël Pierre ( Eds.), Wine, Networks and Scales. Intermediation in the Production, Distribution and Consumption of Wine, Bruxelles, Peter Lang, 2021, p. 95-114.

  Pre-print Dans: Stéphanie Lachaud-Martin, Corinne Marache, Julie McIntyre, Mikaël Pierre ( Eds.), Wine, Networks and Scales. Intermediation in the Production, Distribution and Consumption of Wine, Bruxelles, Peter Lang, 2021, p. 95-114. 103 Fig. 2. Wine supply network of Matthijs Marshal, Dordrecht, 1745-1762 23 traveled to Germany to purchase wine on the spot. He imported a wide range of German wines: both "modest" Mosel from Wehlen, Bernkastel and Piesport, as well as Rhine wines from Rüdesheim, Bodenheim and even the very best Hochheim, from the vineyards of the Dean of Mainz Cathedral 24 . He also dealt in French and Spanish wines, which he 104 purchased from Rotterdam and Amsterdam wholesalers or at the brokers' auction in his home town 25 . Marshal's clientele was composed of dozens of customers in Dordrecht and other Dutch towns as distant as Leeuwarden and Groningen 26 . Most of them belonged to the local elite, others were military officers. They usually ordered a basket containing 45 bottles (one anker) of wine once or several times a year. Marshal also occasionally supplied fellow wine Pre-print Dans: Stéphanie Lachaud-Martin, Corinne Marache, Julie McIntyre, Mikaël Pierre ( Eds.), Wine, Networks and Scales. Intermediation in the Production, Distribution and Consumption of Wine, Bruxelles, Peter Lang, 2021, p. 95-114.

  Lachaud-Martin, Corinne Marache, Julie McIntyre, Mikaël Pierre ( Eds.), Wine, Networks and Scales. Intermediation in the Production, Distribution and Consumption of Wine, Bruxelles, Peter Lang, 2021, p. 95-114.

  Fig. 4. Advertisement for a sale at the Amsterdam brokers' auction of a batch of new Bergerac white wine, 1775

  der Poest and Clement. Stéphanie Lachaud-Martin, Corinne Marache, Julie McIntyre, Mikaël Pierre ( Eds.), Wine, Networks and Scales. Intermediation in the Production, Distribution and Consumption of Wine, Bruxelles, Peter Lang, 2021, p. 95-114.

	Pre-print
	Dans:

Table 1 . Wine brokers hired by Van der Poest and Clement, 1766-1793

 1 . They also supplied the local Chamber of the East India Company with wine. Outside of Middelburg, customers mostly belonged to the Zeeland and Holland urban elite. Just like Marshal, they also had clients in distant cities, such as Arnhem and Maastricht and in the Austrian Pre-print Dans: Stéphanie Lachaud-Martin, Corinne Marache, Julie McIntyre, Mikaël Pierre ( Eds.), Wine, Networks and Scales. Intermediation in the Production, Distribution and Consumption of Wine, Bruxelles, Peter Lang, 2021, p. 95-114. 110

	Name	Address
	Jan van Raalt	Rotterdam (at least) 1766-1770
	Gerard Verboom	Rotterdam 1771-1775
	Jacobus van Overzee Rotterdam 1775-1789 and 1793
	Jan Rademaker	Amsterdam 1768-1778
	ZA, 483 J.C. Clement, Letter copybooks, 81-85, 1766-1803.

  SR, 1 OSA, 2192, Dossier van het geschil tussen wijnkooplieden en makelaars, 1735. Stéphanie Lachaud-Martin, Corinne Marache, Julie McIntyre, Mikaël Pierre ( Eds.), Wine, Networks and Scales. Intermediation in the Production, Distribution and Consumption of Wine, Bruxelles, Peter Lang, 2021, p. 95-114.

	Pre-print
	Dans:
	In Amsterdam, in the year 1775.
	Barend de Harde, Lambert Olivier, Jan Rademaker and
	twenty other
	B R O K E R S,
	With permission of the honorable gentlemen mayors, as
	representatives their master, intend to sell to the highest
	bidder:
	A lot of excellent extraordinary
	WHITE BERGERAC
	PRIMEUR WINE
	including the renowned brands
	DFL. PL. P. and Toutifau.
	Displayed on barges at Heerengragt close to Oude
	Spiegelstraat in front of the house of the Widow P.
	Eyma son & Hugues.
	The sale will take place on Tuesday, 7 February 1775, at
	6 p.m. precisely, at the house of Jan Hendrik Voogt,
	publican at the Keizerskroon in Kalverstraat.
	Anyone who requires further information, should
	address the aforementioned brokers or Isaac Cordes,
	wine cooper.

Wholesalers were allowed to sell at least one cask of wine per transaction (about 900 liters); semi-retailers could sell quantities of at least 4 stoops at a time (approximately 9,6 liters) and only retailers were allowed to sell wine by the glass or by the can. Purchase was not bound by legal restrictions. This all applied to Amsterdam: the boundaries between wholesale, intermediate trade and retailing differed from one town to another.

Brennan T., The Wine Trade in Early Modern France, Baltimore/London, John Hopkins University Press, 1997; Musset B.,

Unless mentioned otherwise, this paragraph is based on: Wegener Sleeswijk A., Les vins français aux Provinces-Unies au XVIIIe siècle. Négoce, dynamiques institutionnelles et organisation du marché, Thèse de 3 ème cycle, Université d'Amsterdam and EHESS Paris, 2006.

Ricard J.P., Op. cit., 1722, p. 325. For an overview of total numbers of official brokers in Amsterdam in the early modern period: Stuart T., De Amsterdamsche makelaardij. Bijdrage tot de geschiedenis onzer handelswetgeving, Amsterdam, Spin en Zoon, 1879, p. 160.

Demont V. and Wegener Sleeswijk A., "Milieux du courtage à Amsterdam et à Hambourg (fin XVIIe-début XVIIIe siècle)", in Demont V., Scherman, M. and Wegener Sleeswijk A. (dir.), Op. cit., p. 185, 186.

Stadsarchief Rotterdam (from now on SR), 1 Oud Stads Archief (from now on OSA), 2192, Dossier van het geschil tussen wijnkooplieden en makelaars gebracht voor burgemeesteren, 1735.

The term "Vin du Haut-Pays" was used to refer to all wine from outside the city of Bordeaux jurisdiction. In Holland, this was mainly Bergerac, Cahors and Gaillac wine. RAD, 9 Gerecht van Dordrecht, 1390, Matthijs Marshal Letter copybook (from now on MML), Letter to Pieter van Overzee, Rotterdam,

Jan.1750.20 RAD, 3 Stadsarchieven, 3849, Auction sale of wine, 29 July 1700; 3850, Auction sales of brandy and wine, 16 Oct. 1700; 27 Dec. 1700; 12 and 17 May 1701.

RAD, 32 Collectie van eigendomspapieren van huizen en landerijen, 32, 15-1, Akte van transport, 18 april 1769, f. 31; RAD, 9 Gerecht van Dordrecht, 1663, transportakte 27 okt. 1761, f. 130; Frijhoff W., Geschiedenis van Dordrecht van 1572 tot 1813, Hilversum, Verloren, 1996, p.

 22 RAD, 3 Stadsarchieven, 3520, Lijst houdende een opgave van de toegelaten wijnkopers […] 1773.

RAD, 9 Gerecht van Dordrecht, 1390, Matthijs Marshal Letter copybook, 1745-1762.

RAD, 1390 MML, Letters to Jean Georg Voith, Mainz, 15 Oct. 1745 and 9 Nov 1745.

For instance: RAD, 3 Stadsarchieven, 3852, Brokers' wine auctions, 22 Aug. 1723 and 22 Aug. 1727.

RAD, 1390 MML, Letters to Jacoba Guerre, Leeuwarden, and Johannes Smith, Groningen, 20 Aug. 1746 and

June 1748.

The outgoing correspondence and excerpts from accounts have been preserved for this company for the period 1766-1803 including letters to brokers for 1766 to 1793.

networker asking him for instance to put him into contact with "a good house in Mannheim" [START_REF] Za | Letters to Jacobus van Overzee[END_REF] .

Until 1778, Jan Rademaker from Amsterdam was the broker with whom Van der Poest corresponded most. Rademaker was the son of a painter, but there had been several brokers in his family [START_REF] Sa | Civil deeds for Dirk Rademaker[END_REF] . By the time he dealt with the Middelburg firm, he had become one of Amsterdam's most active wine brokers. In the printed Directory of Brokers, he systematically indicated wine brokerage as his specialization [START_REF]Lyste der naamen en woonplaatsen van de makelaars[END_REF] . However, throughout his career, he was also involved in other trades and brokered for instance at auctions of ships and real estate 63 . While some successful wine brokers specialized, others on the contrary seem to have prospered thanks to diversification.

Van der Poest mainly ordered Spanish and rare French wines from Rademaker. This involved, for instance, Benicarlo used for adding color 112 and tannin to French wines, Rota "tint" imported from Cadix, fortified "sack" wines from Malaga and the Canary Islands, sweet white wines of the Pedro Ximénez grape variety and red Burgundy from Macon 64 . Spanish wines were seldom directly imported to the small harbor of Middelburg but were sought after by the Zealand Chamber of the VOC, for the Company's ship victuals and for the wine supplies of the trading posts in the East Indies 65 .

Just like Marshal's brokers, Rademaker performed diverse tasks, but he seems to have been more of a "connoisseur". On several occasions, he carried out wine assessments, as in 1777, when he expertized a batch of damaged Côteaux nantais Muscadet wines that had been recently unloaded from a ship involved in an accident at sea. Van der Poest needed the evaluation to decide whether he should sell the wine at auction in Amsterdam, or if it was worth having it shipped to Middelburg 66 .

The exchange of information about wine tastings, prices and other merchants' dealings played a central role in the correspondence with Rademaker. Letters were often detailed, mentioning producer brands and parishes for wine producing regions in France (Médoc, Graves, Bergerac, Béarn). The Middelburg merchants gathered most of their information at the local brokers' auction. In 1769, Van der Poest informed Rademaker for instance: "Yesterday evening the La Guere brand from Bordeaux was sold at the auction for 30 Flemish pounds. The wine was pretty good for this vintage. As for the Bordeaux red wines, the Médoc of the parish of St Estèphe satisfies me most 67 ". Van der Poest regularly tasted wines for sale at the auctions for other merchants, as wine brokers usually organized public tastings on the eve of the sale. On this occasion, he took notes, indicating types of wine, producer brands, names of sellers and buyers and quality appreciations.


Z K Low
email: zi.low@insa-lyon.fr

A Novikov

D De Sousa Meneses

D Baillis

Radiative behavior of low-porosity ceramics: II± Experimental and numerical study of porous alumina up to high temperatures

Keywords: Porous ceramics, Radiative properties, Infrared spectroscopy, Radiative transfer equation (RTE), High temperature

We compare two methods of characterizing the radiative behavior of 22% porous sintered alumina disks containing µm-sized pores on the 1 µm to 7 µm wavelength range up to very high temperatures. The first consists of direct spectroscopic measurements of the normal-hemispherical reflectance and transmittance at room temperature, as well as the normal emittance up to 1300 °C.

The second is a two-step multi-scale numerical approach: the volume radiative properties and surface reflectivity are first determined from physical optics computations on tomography-reconstructed microstructures, then applied to the resolution of the radiative transfer equation on an equivalent homogeneous medium to obtain the spectral reflectance, transmittance, and emittance. Uncertainties in the numerical results, mainly due to microstructural variability, are quantified through sensitivity studies. The good agreement between the experimental and numerical results confirm the ability of our proposed numerical approach to give accurate predictions of the high-temperature radiative behavior of porous ceramics.

Introduction

The knowledge of radiometric quantities such as the spectral reflectance, transmittance, or emittance of materials are of great interest notably for high-temperature applications [1±4], and a

Nomenclature

First-and second-order tensors (ªvectorsº and ªmatricesº) are written in bold face. wide array of experimental methods have been developed for their characterization [5±7]. In the case of semi-transparent materials such as metal oxide ceramics, these quantities depend not only on material composition, but also on extrinsic parameters such as sample thickness, surface roughness, and the morphology of pores and other heterogeneities [8±11]. To account for the influence of some of these parameters, inverse methods based on minimizing the differences between theoretical predictions and experimental radiometric measurements are often used to identify the intrinsic effective radiative properties [12±17]. Alternatively, numerical methods are increasingly used to predict the radiometric quantities of interest from tomography-reconstructed or digitally generated microstructures. These methods are more suitable for the study of microstructure-property relations compared to inverse methods, as a large number of microstructurally different samples may be characterized at a lower cost [START_REF] Rozenbaum | Determination of high-temperature radiative properties of porous silica by combined image analysis, infrared spectroscopy and numerical simulation[END_REF][START_REF] Rozenbaum | Texture and porosity effects on the thermal radiative behavior of alumina ceramics[END_REF].

Latin

In the so-called ªdiscrete-scaleº approach [START_REF] Petrasch | Discrete vs. continuum-scale simulation of radiative transfer in semitransparent two-phase media[END_REF], the quantities of interest are determined by simulating the radiation-matter interaction at the microstructural level. Direct Monte Carlo ray-tracing on 3D microstructures, usually assuming locally smooth interfaces that reflect and refract specularly [8, 16, 20±23], is a popular choice when heterogeneities are large and far apart compared to the wavelength. When this is not the case, numerical resolution of Maxwell's equations should be performed [START_REF] Chen | Microstructural effect on radiative scattering coefficient and asymmetry factor of anisotropic thermal barrier coatings[END_REF][START_REF] Liu | Spectral radiative properties of skeleton inner structure of ceramic foam based on ordered opal structure model[END_REF], though the high computational cost limits its application to very small geometries. On the other hand, a less computationally demanding ªcontinuum-scaleº approach treats the heterogeneous material as an equivalent homogeneous medium [START_REF] Dai | Optical characterization of multi-scale morphologically complex heterogeneous media ± application to snow with soot impurities[END_REF][START_REF] Yang | Radiative Properties of Ceramic Al2O3, AlN, and Si3N4ÐII: Modeling[END_REF], and solves for the radiometric quantities of interest using the radiative transfer equation (RTE) while usually assuming smooth boundaries [START_REF] Dombrovsky | Approximate analytical solution to normal emittance of semi-transparent layer of an absorbing, scattering, and refracting medium[END_REF]. Accurate microstructure-based determination of the effective radiative properties is the challenge in this case: most past work relied on analytical microstructure-property relations [START_REF] Li | Prediction of high-temperature radiative properties of copper, nickel, zirconia, and alumina foams[END_REF], ray-tracing simulations [25±27], or the independent scattering hypothesis coupled with Mie theory or electromagnetic scattering computations [START_REF] Dai | Optical characterization of multi-scale morphologically complex heterogeneous media ± application to snow with soot impurities[END_REF][START_REF] Lallich | Experimental Determination and Modeling of the Radiative Properties of Silica Nanoporous Matrices[END_REF].

This paper, which is the second of two papers on the infrared radiative behavior of low-porosity ceramics, presents two methods of characterizing the radiometric properties of thin samples of a 22% porous alumina ceramic with µm-sized pores up to very high temperatures. Infrared spectroscopy measurements of the room-temperature normal-hemispherical reflectance and transmittance as well as the normal emittance up to 1300 °C are first performed. These are then compared to numerical simulations of the same radiometric quantities at the same temperatures, obtained through a two-step multi-scale approach. The first step, described in detail in our first paper [START_REF] Low | 1± a physical optics approach to predict the radiative properties of semi-transparent porous ceramics[END_REF],

consists of performing physical optics computations on 3D tomography-reconstructed microstructures to determine the effective radiative properties of the porous alumina ceramic. This novel approach, developed for ceramics with a weakly absorbing solid matrix and requiring only knowledge of the (temperature-dependent) complex refractive indexes of the different phases present, takes into account wave effects and dependent scattering by heterogeneities close in size to the wavelengths of interest. Our first paper concluded with analytical relations linking the porosity to the volume radiative properties and non-specular surface reflectivity of the porous alumina.

These effective radiative properties are then applied to the second modeling step described in this paper, in which the reflectance, transmittance, and emittance are simulated via an RTE-based ªcontinuum-scaleº approach that considers non-specular boundaries of the equivalent homogeneous medium. Our present experimental and numerical studies aim to provide insights into the microstructural phenomena governing the high-temperature radiative behavior, and to validate the proposed multi-scale numerical method (notably the physical optics approach used to determine the effective radiative properties).

Section 2 describes the samples used in this study, and the experimental methods used for microstructural and radiometric characterization. Section 3 briefly summarizes the numerical method and key results of our first paper [START_REF] Low | 1± a physical optics approach to predict the radiative properties of semi-transparent porous ceramics[END_REF], then presents the RTE-based model used to predict the reflectance, transmittance, and emittance of the samples. Section 4 then presents and compares the experimental and numerical results, with the uncertainties in numerical results quantified through a sensitivity study.

Experimental procedure

Material and microstructure

The studied material is a high-purity porous alumina ceramic, fabricated as plane-parallel disk samples for the infrared spectroscopy measurements (presented in section 2.2). A raw powder mix composed of 99% α-alumina by mass, with a volume median grain diameter of 2.9 µm, was first dispersed in water to form a homogeneous slurry, then air-dried and ground back up into powder form. Uniaxial pressing at 10 MPa in a cylindrical mold followed by sintering at 1650 °C for 6 hours gave porous sintered alumina cylinders 33 mm in diameter. Finally, plane-parallel cuts perpendicular to the cylinder axis were made with a precision saw to obtain disks of thickness h = 2.0 ± 0.1 mm. The machined samples were heat-treated at 800 °C for 6 hours to remove all organic pollutants.

Scanning electron microscopy (Hitachi TM3030, 15 kV accelerating voltage, backscattered electrons mode) was performed at Saint-Gobain Research Provence (Cavaillon, France) on polished samples of the porous alumina ceramic (see Figure 1). The Fiji software [START_REF] Schindelin | Fiji: an open-source platform for biological-image analysis[END_REF] was then used to perform binarization, denoising, and microstructural analysis on the micrographs. Note that in our companion paper [START_REF] Low | 1± a physical optics approach to predict the radiative properties of semi-transparent porous ceramics[END_REF] we also presented the X-ray tomography and image processing protocol used to obtain the 3D microstructure. Physical measurements were also performed at Saint-Gobain Research Provence (Cavaillon, France) on the porous ceramic cylinders:

• A total porosity of f p = 0.22 ± 0.02 was measured on the cylinders by dividing their apparent density (caliper method) by the known density of the alumina powder mix. Open porosity measurements via the water immersion and saturation method [START_REF] Kuila | Total porosity measurement in gas shales by the water immersion porosimetry (wip) method[END_REF] gave almost identical results, showing that little to no closed porosity is negligible (note that the porosity was also estimated through void pixel counting on 15 electron micrographs giving f p = 0.20 ± 0.07, which is in good agreement with the physical measurement). We thus consider f p = 0.22 ± 0.02 as the nominal porosity for the remainder of this study.

• We also performed pore size measurements just to check that the different methods and samples agree: the mean pore chord length [START_REF] Maciver | Analysis of in situ microscopy images of flocculated sediment volumes[END_REF] is estimated at ⟨⟨ℓ p ⟩⟩ = 1.8 ± 0.3 µm from the electron micrographs (which is in good agreement with value found on the tomographic reconstruction [START_REF] Low | 1± a physical optics approach to predict the radiative properties of semi-transparent porous ceramics[END_REF]). It agrees with the value of ⟨⟨ℓ p ⟩⟩ ≈ 4f p /A V = 1.2 ± 0.2 µm measured using mercury intrusion porosimetry (A V is the specific surface area) [START_REF] De Kruijf | On the average chord length in reactor physics[END_REF][START_REF] Webb | An introduction to the physical characterization of materials by mercury intrusion porosimetry with emphasis on reduction and presentation of experimental data[END_REF]. The difference between the physical measurement and the image processing result may be attributed to the hypothesis of cylindrical pores in mercury intrusion porosimetry, which leads to underestimation when throats are present [START_REF] Webb | An introduction to the physical characterization of materials by mercury intrusion porosimetry with emphasis on reduction and presentation of experimental data[END_REF].

Infrared spectroscopy

The spectral radiometric quantities of interest (reflectance, transmittance, and/or emittance) are measured on the 2 mm thick disks of diameter 33 mm, for vacuum wavelengths λ 0 between 1 µm and 10 µm from room temperature up to 1300 °C using two setups developed at the CEMHTI laboratory (Orl eans, France), briefly described here.

At room temperature, the normal-hemispherical reflectance R h and transmittance T h are acquired using a 6-inch integrating sphere with infragold coating and a liquid-nitrogen-cooled mercury cadmium telluride detector, both coupled to a Fourier transform infrared spectrometer (Bruker Vertex 70) purged with dry air [START_REF] Dupleix | Mid-infrared absorption properties of green wood[END_REF]. Measurements were performed at least 4 times (both sides of two samples) and averaged to account for the influence of material variability, which incidentally is quite low in the present case. Other sources of uncertainty include imperfections in the integrating sphere [START_REF] Liu | Numerical investigation of measurement error of the integrating sphere based on the Monte-Carlo method[END_REF] and background parasite fluxes [START_REF] Dupleix | Mid-infrared absorption properties of green wood[END_REF]. Taking all these sources into account, the absolute uncertainty is estimated to lie between 0.01 and 0.02 in the general case. However, in the present case where transmission is low, the uncertainty in T h is estimated at 0.005 as some sources of uncertainty (e.g., those due the integrating sphere coating and opening) scale with magnitude of the measured signal. According to Kirchhoff's law [START_REF] Howell | Thermal Radiation Heat Transfer[END_REF], the room-temperature normal emittance E, equal to the absorbance, is then calculated from R h and T h as follows:

E = 1 ± R h ± T h (1)
At high temperatures, the normal emittance E of a sample maintained at a constant elevated temperature T is directly measured as the ratio of the spectral intensity emitted by the sample to that emitted by a blackbody at the same temperature [START_REF] Palmer | The measurement of transmission, absorption, emission and reflection[END_REF]. The apparatus, shown in Figure 2 and described in detail in reference [START_REF] Sousa Meneses | Apparatus for measuring the emittance of materials from far infrared to visible wavelengths in extreme conditions of temperature[END_REF], consists of a reference blackbody furnace and a sample heating system mounted on a computer-controlled turntable within a purged enclosure. Two Fourier transform spectrometers (Bruker Vertex 80v working under vacuum, and Bruker Vertex 70 purged with dry air) enable measurements from the far infrared to the visible range. The flux emitted by the sample in the normal direction within an aperture of diameter 1 mm is measured and compared to the reference blackbody flux, with supplementary measurements to quantify and correct for the parasite fluxes from the instruments. To minimize the axial temperature gradient within the sample, a 500 W CO 2 laser (Coherent K500) separated equally by a beam splitter is used to heat the sample on both faces. The temperature of the sample is determined by using the spectrometer as a pyrometer at the known Christiansen wavelength of alumina (≈ 10 µm) where it exhibits blackbody-like emissivity [START_REF] Brun | Infrared optical properties of alpha-alumina with the approach to melting: gamma-like tetrahedral structure and small polaron conduction[END_REF]. This methods allows the direct measurement of E with an absolute uncertainty of 0.02 at extreme temperatures up to 2500 K.

Interested readers are invited to consult references [START_REF] Dupleix | Mid-infrared absorption properties of green wood[END_REF] and [START_REF] Sousa Meneses | Apparatus for measuring the emittance of materials from far infrared to visible wavelengths in extreme conditions of temperature[END_REF] for more details on the apparatus used in this study.

Numerical method

The normal-hemispherical reflectance R h and transmittance T h of the porous alumina samples are simulated using a multi-scale approach presented in this section, then used to calculate the normal emittance E via equation [START_REF] Brewster | Thermal Radiative Transfer and Properties[END_REF]. In this approach, effective volume and surface radiative properties of the porous alumina material are first calculated using analytical relations, deduced from microstructure-based-simulation results of a novel physical optics model proposed in our companion paper [START_REF] Low | 1± a physical optics approach to predict the radiative properties of semi-transparent porous ceramics[END_REF]. We calculated effective radiative properties at selected temperatures from

Effective radiative properties modeling with a physical optics based approach

The effective radiative properties modeling approach proposed in our companion paper [START_REF] Low | 1± a physical optics approach to predict the radiative properties of semi-transparent porous ceramics[END_REF] has been developed for porous or multiphase materials with a homogeneous weakly absorbing dominant phase (henceforth referred to as the matrix, denoted with subscript m) having a much higher volume fraction compared to the other phases (pore or particle heterogeneities, denoted with subscript p). As the porous alumina samples in the present study contains 78% of highpurity α-alumina by volume, with grain sizes exceeding one-tenth of the wavelengths of interest allowing grain boundary effects to be neglected [START_REF] Harris | Refractive index of infrared-transparent polycrystalline alumina[END_REF], they fit the description. The model computes scattering and absorption in tomography-reconstructed volume elements of the material using the discrete dipole approximation (DDA) [START_REF] Draine | Discrete-Dipole Approximation For Scattering Calculations[END_REF][START_REF] Draine | Discrete-dipole approximation for periodic targets: theory and tests[END_REF], which takes into account physical optics effects and dependent scattering when heterogeneities are small and close to each other compared to the wavelength.

We determined the effective radiative properties of the porous alumina at temperatures T = 22 °C, 800 °C, 1000 °C, and 1300 °C for selected wavelengths between λ 0 = 1 µm and λ 0 = 7 µm.

For each investigated temperature, we provided the spectral complex refractive index n m +ik m of the sintered alumina matrix as input, obtained through directional averaging [START_REF] Pajdzik | Three-dimensional birefringence imaging with a microscope tilting-stage. I. Uniaxial crystals[END_REF] of the birefringent complex refractive indexes of α-alumina monocrystals [START_REF] Brun | Infrared optical properties of alpha-alumina with the approach to melting: gamma-like tetrahedral structure and small polaron conduction[END_REF]. Values are given in Table 1: DDA computations were performed on a large number of subvolumes of the reconstructed material (8 to 125 depending on wavelength and volume element size). This allowed us to extract analytical porosity-property relations for porosities ranging from a few percent up to f p ≈ 0.3, and also to quantify the uncertainty in the computed effective radiative properties as the root-meansquared (RMS) deviation between DDA results on all subvolumes and the analytical relation. Key conclusions from our companion paper [START_REF] Low | 1± a physical optics approach to predict the radiative properties of semi-transparent porous ceramics[END_REF] are summarized below:

λ 0 T = 22 °C T = 800 °C T = 1000 °C T = 1300 °C (µm) n m k m n m k m n m k m n m k m 1.0 1.
• DDA simulations confirmed that thanks to the low alumina absorptivity on the absorption coefficient κ eff may be calculated to 7% uncertainty on the wavelength range of interest with the analytical relation proposed by Dombrovsky et al. [START_REF] Dombrovsky | Use of Mie theory to analyze experimental data to identify infrared properties of fused quartz containing bubbles[END_REF] for porous ceramics with a weakly absorbing solid phase:

κ eff = 4πk m λ 0 f m (2)
Indeed, as pure alumina monocrystal data is used as input for the solid matrix, k m very low for the considered temperatures and wavelengths (≤ 6 × 10 ±3 ) and κ eff scales linearly with the matrix fraction f m . The values of κ eff at the nominal porosity f p = 0.22 = 1 ± f m of the porous alumina samples are plotted for the studied wavelengths and temperatures in Figure 3a. Note that as a logarithmic scale is used, the ±7% error bars are barely visible.

At room temperature, the extremely low κ eff (less than 1 m ±1 ) for wavelengths between 1 µm to 4 µm are not represented to improve legibility (practically no absorption occurs in the mm-sized samples at this temperature and wavelength range).

• Based on our discussion in the companion paper [START_REF] Low | 1± a physical optics approach to predict the radiative properties of semi-transparent porous ceramics[END_REF], we found that the porous alumina material, initially with scattering coefficient σ eff and anisotropic phase function φ eff , is appropriately modeled with a transport scattering coefficient σ tr associated with an isotropic phase function φ tr = (4π) ±1 instead [START_REF] Dombrovsky | The use of transport approximation and diffusion-based models in radiative transfer calculations[END_REF]:

σ tr = σ eff (1 ± g sca ) = σ eff 1 ± 4π φ eff ( û, û′ ) û • û′ dΩ ′ (3)
where û and û′ are the unit direction vectors of the incident and scattered light respectively, dΩ ′ is the elementary solid angle associated with û′ , and 4π is the solid angle of a sphere which represents the entire angular space. Note that in this work φ eff is normalized such that 4π φ eff ( û, û′ ) dΩ ′ = 1.

The values of σ tr simulated using the DDA were well described with a second-order polynomial function of the porosity:

σ tr = p 1 f p + p 2 f 2 p ( 4
)
with coefficients p 1 (λ 0 , T) and p 2 (λ 0 , T) identified from DDA results for every temperature and wavelength. The values of σ tr predicted with these correlations at the nominal porosity of f p = 0.22 are plotted in Figure 3b. Error bars indicate the uncertainty of ±20.8%, estimated by taking the RMS deviation between all DDA results and the analytical relation, and reflects the high microstructural variability.

• For the surface reflectivity, we assume that the surface of the studied porous alumina is smooth everywhere save where pores are present. DDA numerical results in our companion paper [START_REF] Low | 1± a physical optics approach to predict the radiative properties of semi-transparent porous ceramics[END_REF] for the case of normal illumination by light of wavelength λ = λ 0 = 2 µm were rather well described by a geometrical-optics-based analytical model that simply considers perfectly diffuse reflection for incident radiation incident on the pore phase, and perfectly specular reflection according to Fresnel's equations for the remaining radiation. The directional-hemispherical reflectivity ρ h and transmissivity τ h for incidence direction û are then modeled as follows [START_REF] Low | 1± a physical optics approach to predict the radiative properties of semi-transparent porous ceramics[END_REF]:

ρ h ( û) = f m ρ Fr ( û) ρ spec ( û) + f p ⟨ρ Fr ⟩ ρ diff (5a) τ h ( û) = f m (1 ± ρ Fr ( û)) τ spec ( û) + f p 1 ± ⟨ρ Fr ⟩ τ diff (5b)
ρ Fr ( û) is the specular reflectivity given by Fresnel's equations [START_REF] Brewster | Thermal Radiative Transfer and Properties[END_REF], here computed for light in vacuum incident on an alumina surface of refractive index n m . ⟨ρ Fr ⟩ is the diffuse reflectivity obtained by the following weighted average of ρ Fr [START_REF] Dombrovsky | The use of transport approximation and diffusion-based models in radiative transfer calculations[END_REF][START_REF] Siegel | Approximate solution methods for spectral radiative transfer in high refractive index layers[END_REF]:

⟨ρ Fr ⟩ ≡ û′ • n<0 2ρ Fr ( û′ ) û′ • n dΩ ′ ( 6
)
where n is the normal vector pointing outwards from the surface. For normally incident light on a surface with n m = 1.718 (corresponding to the sintered alumina phase at room temperature and λ 0 = 1 µm), equation (5a) gives ρ h = 0.0814. Uncertainties are estimated at 22.6% on ρ h and 27% on ρ spec , mainly due to neglected wave effects and microstructural variability.

These analytical relations are then used to determine the effective volume and surface radiative properties of the porous alumina ceramic studied in this paper, by setting f p = 0.22.

In the next section, the determined effective radiative properties are applied to the simulation of radiometric measurements on the 2 mm thick disks from room temperature to 1300 °C. While the uncertainties in some of the effective radiative properties are rather high, sensitivity studies presented in section 4.2 show that they have limited influence on the simulated radiometric properties.

Reflectance, transmittance, and emittance modeling

For all the considered temperatures, we first simulate the normal-reflectance R h and transmittance T h of the porous alumina disks by resolving the radiative transfer equation (RTE) on an equivalent homogeneous medium. With these two quantities, the normal emittance E is then calculated via Kirchhoff's law (equation ( 1)). The RTE-based model, which has the particularity of considering non-specular reflection and refraction at boundaries, is described here.

We consider a semi-infinite plane-parallel slab of thickness h placed in vacuum (n amb = 1), illuminated on one face by a collimated beam at incidence angle θ inc (= 0 in the present work).

The slab, at uniform temperature T, is composed of a homogeneous absorbing-scattering material prescribed the absorption (κ eff ) and transport scattering (σ tr ) in Figure 3. Per classic assumptions [START_REF] Dombrovsky | Near-infrared radiative properties of porous zirconia ceramics[END_REF][START_REF] Lallich | Experimental Determination and Modeling of the Radiative Properties of Silica Nanoporous Matrices[END_REF][START_REF] Kaemmerlen | Radiative properties of extruded polystyrene foams: Predictive model and experimental results[END_REF] of 1D radiative transfer, azimuthal symmetry, and negligible self-emission, the RTE simplifies to [START_REF] Howell | Thermal Radiation Heat Transfer[END_REF]:

µ ∂I * (x, µ) ∂x = ±(σ tr + κ eff )I * (x, µ) + σ tr 4π 4π I * (x, µ ′ ) dΩ ′ (7)
where x is the position along the thickness direction êx , and µ ≡ û • êx is the direction cosine for the unit direction vector û associated with the solid angle dΩ. Note we solve for the spectral basic radiance I * to account for the conservation of  etendue [START_REF] Chaves | Introduction to Nonimaging Optics[END_REF] when light refracts at the boundary between the surrounding vacuum medium and the slab:

I * = I n 2 ( 8
)
where I is the spectral radiance (radiance per unit vacuum wavelength) and n is the local refractive index: n = 1 in the surrounding vacuum (hence I * = I for x < 0 or x > h) and n > 1 within the slab (hence

I * I for 0 < x < h).
As the slab is under normal collimated illumination, the incident radiance I * inc is only non-zero at x = 0 ± , within a narrow solid angle ∆Ω about the normal direction µ = 1.

In section 3.1, we chose to model the directional-hemispherical reflectivity ρ h of the slab boundary under external illumination from the surrounding vacuum medium as the sum of a perfectly specular component ρ spec and a perfectly diffuse component ρ diff (equation (5a)). These terms are henceforth denoted with the superscript ªextº to distinguish them from their counterparts for radiation arriving at the boundary from within the material (internal illumination), denoted with the superscript ªintº. Based on microscopic reversibility principles [START_REF] Mahan | Microscopic reversibility and detailed balance. an analysis[END_REF], we assume that ρ int is also modeled in the same manner as ρ ext using equations (5a) and ( 6), with ρ int Fr = 1 for incident angles exceeding the critical angle for total internal reflection.

The boundary conditions are then expressed using the definitions in equations (5a) and (5b),

• For x = 0 + :

I * (µ > 0) = τ ext spec (µ)I * inc δ 1±µ + τ ext diff π ∆Ω I * inc dΩ ′ + ρ int spec (µ ′ R )I * (µ ′ R ) + ρ int diff π µ ′ <0 I * (µ ′ )µ ′ dΩ ′ (9a)
where δ represents the Kronecker delta, here defined as δ X = 1 if X = 0, and δ X = 0 otherwise;

• For x = h ± :

I * (µ < 0) = ρ int spec (µ ′ R )I * (µ ′ R ) + ρ int diff π µ ′ >0 I * (µ ′ )µ ′ dΩ ′ (9b)
where µ ′ R = ±µ represents the direction prior to a specular reflection event that reflected light towards the direction µ. These boundary conditions are illustrated in Figure 4. Equations ( 7) and ( 9) were resolved with the Monte Carlo method [START_REF] Howell | Thermal Radiation Heat Transfer[END_REF][START_REF] Cunsolo | Improved Monte Carlo methods for computational modelling of thermal radiation applied to porous cellular materials[END_REF]: converged results were obtained using 10 6 equal-energy packets. The reflected and transmitted radiance fields are 14 then calculated:

x = 0 e x n amb = 1 n p = 1 n m f p f m T x = h κ eff σ tr I * (û) θ inc I inc (û) ρ diff ρ ext ρ spec ρ ext τ spec τ ext τ diff τ ext τ spec τ int ρ spec ρ int ρ diff ρ int τ diff τ int
I * (x = 0 ± , µ < 0) = ρ ext spec (µ)I * inc δ 1+µ + ρ ext diff π ∆Ω I * inc dΩ ′ + τ int spec (µ ′ T )I * (x = 0 + , µ ′ T ) + τ int diff π µ ′ <0 I * (x = 0 + , µ ′ )µ ′ dΩ ′ (10a) I * (x = h + , µ > 0) = τ int spec (µ ′ T )I * (x = h ± , µ ′ T ) + τ int diff π µ ′ >0 I * (x = h ± , µ ′ )µ ′ dΩ ′ (10b)
where µ ′ T represents the direction prior to an outgoing specular refraction event that refracted light towards the direction µ, calculated using the Snell-Descartes law [START_REF] Chaves | Introduction to Nonimaging Optics[END_REF]:

n 2 m (1 ± µ ′ T 2 ) = n 2 amb (1 ± µ 2
). The normal-hemispherical reflectance R h and transmittance T h are then obtained as follows:

R h = µ<0 I * (x = 0 ± , µ)µ dΩ ∆Ω I * inc dΩ ′ (11a) T h = µ>0 I * (x = h + , µ)µ dΩ ∆Ω I * inc dΩ ′ (11b)
after which the normal emittance is simply calculated as E = 1 ± R h ± T h per equation (1).

Results and Discussion

Comparison of experimental and numerical results

Figure 5 compares the experimentally measured reflectance (R h ) and transmittance (T h ) at room temperature to the ones simulated at selected wavelengths using our new physical-optics-based approach. An excellent agreement is found between the two results at wavelengths smaller than 205 2.5 µm and greater than 5 µm, well within experimental uncertainties (±0.01), which is extremely encouraging for validation of our proposed numerical approach.

Note that the error bars represent numerical uncertainties denoted ∆Y for an observed quantity Y ∈ {R h , T h , E}, evaluated assuming that the input parameters X vary independently of one another: where (∆X/X 0 ) × 100% is the relative uncertainty in % on X, and S Y (X) is the sensitivity coefficient defined as the variation in Y per % increase in X, all other input parameters being constant:

(∆Y) 2 = X S Y (X) ∆X X 0 × 100% 2 (12)
S Y (X) = ∂Y ∂X X 0 X 0 100% (13)
Note that S Y (X) is studied later in section 4.2, with values given in Figure 7. Table 2 summarizes the input parameters X considered and their relative uncertainties. The computed uncertainties range from 0.01 to 0.07 depending on the radiometric quantity and wavelength.

∆ρ ext diff ρ ext diff,0 = ∆ρ int diff ρ int diff,0 ∆h h 0 7% 21% 26% 40% 5%
Table 2: Uncertainties in input parameters: effective absorption coefficient (κ eff ), transport scattering coefficient (σ tr ), specular (ρ spec ) and diffuse (ρ diff ) components of the surface reflectivity (for both external/internal illumination), and sample thickness (h).

Between 2.5 µm and 5 µm, a sharp dip is observed in the measured spectra for both R h and T h but is absent from the numerical results. This difference between numerical and experimental results at room temperature is expected: it is due to the characteristic absorption by hydroxyl (OH) groups and adsorbed water molecules, which are almost always present on the surface of alumina ceramics [START_REF] Nùrskov | The stability of the hydroxylated (0001) surface of α-Al2O3[END_REF] but are not taken into account in the input data for our numerical model. Recall that we worked with complex refractive indexes derived from measurements on impurity-free alumina monocrystals [START_REF] Brun | Infrared optical properties of alpha-alumina with the approach to melting: gamma-like tetrahedral structure and small polaron conduction[END_REF]. Precise determination of impurity content and its influence on radiometric quantities is generally challenging: Rozenbaum et al. [START_REF] Rozenbaum | Determination of high-temperature radiative properties of porous silica by combined image analysis, infrared spectroscopy and numerical simulation[END_REF] recently proposed an inverse method to identify the OH content in porous silica, which combines emittance measurements on dense and porous samples with discrete-scale ray-tracing simulations.

While this absorption peak is clearly seen on the room-temperature emittance curve in Figure 6, it is absent from the high-temperature emittance spectra since near-complete desorption of the OH groups occur at 800 °C and above [START_REF] Nùrskov | The stability of the hydroxylated (0001) surface of α-Al2O3[END_REF]. With the increase in temperature, the absorption front (sharp increase in emittance between λ 0 ≈ 3 µm and λ 0 ≈ 7 µm) shifts slightly towards shorter wavelengths under the influence of multiphonon processes [START_REF] Brun | Infrared optical properties of alpha-alumina with the approach to melting: gamma-like tetrahedral structure and small polaron conduction[END_REF]. The low emittance at wavelengths below 2.5 µm for all temperatures is a testament to the high purity of the alumina matrix. In the absence of OH absorption peaks, the high-temperature emittance spectra are extremely well reproduced by the numerical models. The numerical results appear to slightly overestimate the experimental results at all wavelengths, though the differences still remain within their re-spective confidence intervals. Notably, uncertainties in the temperature and reference blackbody flux determination during high-temperature emittance measurements give an estimated absolute uncertainty of ±0.02. These results validate our numerical modeling approach, notably the DDA-based method proposed in our companion paper [START_REF] Low | 1± a physical optics approach to predict the radiative properties of semi-transparent porous ceramics[END_REF] to compute the effective radiative properties, the use of alumina monocrystal data as input while neglecting grain boundary scattering.

Sensitivity study

Figure 7 shows the sensitivity coefficients S Y (X) defined in equation ( 13) as a function of wavelength X = σ tr , κ eff , ρ spec , ρ diff , h and Y = {R h , T h , E} at temperature T = 800 °C (note that similar trends are also observed at the other studied temperatures). The magnitude of S Y (X) indicates the sensitivity of Y to small changes in X, while its sign indicates whether a small increase in X leads to an increase (S Y > 0) or decrease (S Y < 0) in Y.

We observe that while S Y is generally quite low, it is always non-zero except when the observed quantity Y is null or very low. The non-zero value of S h shows the extrinsic nature of the radiometric quantities. Some interesting observations are summarized below:

• The signs of S Y (σ tr ) and S Y (κ eff ) are physically coherent: increasing σ tr increases R h , decreases T h and decreases E, while increasing κ eff decreases R h , decreases T h and increases E.

The similar trends in their magnitudes suggest that the influence of σ tr and κ eff are correlated. This is discussed further in section 4.3.

• The sensitivity coefficients for ρ spec and ρ diff are very similar, since R h , T h and E are quite insensitive to the exact angular distribution of radiative energy. Surprisingly, an increase in either of these parameters decrease R h while increasing T h and E. This is because a large part of the total reflected radiation is actually composed of radiation initially transmitted into the slab before exiting it from the illuminated face. When ρ spec or ρ diff is increased, the fraction of incident radiation transmitted into the slab decreases, and the probability of internal radiation exiting the slab also decreases. This ªtrappingº effect by the slab boundaries [START_REF] Cunsolo | Improved Monte Carlo methods for computational modelling of thermal radiation applied to porous cellular materials[END_REF] increases the emittance especially, and also the transmittance to a smaller extent. 13)) for the normal-hemispherical reflectance (left), normalhemispherical transmittance (center) and normal emittance (right) at 800 °C, with respect to five input parameters: transport scattering coefficient σ tr (•), absorption coefficient κ eff (△), diffuse reflectivity component ρ diff (□), specular reflectivity component ρ spec (⋄), and slab thickness h (⋆).

• While the thickness h is the most influential parameter on T h on the semi-transparent range (λ 0 < 5 µm), its effect on R h and E on this range appears limited. Indeed, when scattering dominates, the optical paths traveled by radiation within the material is generally tortuous with multiple internal reflections off the boundary, and are therefore insensitive to small changes in h. In the opaque range (λ 0 ≥ 5 µm), h has practically no influence on all radiometric properties since radiation-matter interaction is limited to a small region close to the incident surface.

Influence of porosity

Before concluding, we study the influence of porosity on the radiometric properties by comparing the room-temperature reflectance (R h ), transmittance (T h ) and emittance (E) of our 22% porous alumina disks to those of a dense sintered alumina. Literature data on dense sintered alumina are often obtained from experiments on fine-grained samples in which grain boundary scattering due to material birefringence, impurities, and residual pores is significant [START_REF] Yang | Radiative Properties of Ceramic Al2O3, AlN, and Si3N4ÐII: Modeling[END_REF][START_REF] Harris | Refractive index of infrared-transparent polycrystalline alumina[END_REF][START_REF] Cheng | Radiative Properties of Ceramic Al2O3, AlN, and Si3N4: I. Experiments[END_REF]. This makes it difficult to draw meaningful conclusions as to the role of porosity in the present material, in which grain boundary scattering is shown to be negligible by our experimental and numerical results. We therefore considered a hypothetical dense sample with no volume scattering, modeled with Fresnel's equations using the same complex refractive index n m + ik m used for the DDA computations (section 3.1. Figure 8 shows a remarkable increase in R h by more than 0.8 (and a corresponding decrease in T h ) due to the porosity of 22%. While the increase in reflectance and decrease in transmittance are natural when pores are present, the magnitude of these variations is much higher than past investigations on porous ceramics [START_REF] Rozenbaum | Determination of high-temperature radiative properties of porous silica by combined image analysis, infrared spectroscopy and numerical simulation[END_REF][START_REF] Rousseau | Modelling of the Thermal Radiative Properties of Oxide Ceramics[END_REF]. This shows the interest in being able to incorporate physical optics effects in radiative transfer modeling.

In addition, between the wavelengths of 4 µm to 8 µm on the emittance (=absorbance) plot, we see that the absorption front is significantly modified by the presence of pores, with higher emittance in the porous material between 4 µm to 6 µm and higher emittance in the dense material beyond 6 µm. In fact, when the porosity increases, two competing mechanisms are in play: on one hand, the increased volume scattering within the porous material prolongs the optical paths traveled by light and thus the probability of being absorbed [START_REF] Rousseau | Modelling of the Thermal Radiative Properties of Oxide Ceramics[END_REF]; on the other hand, the probability of being absorbed for the same optical path length is lower in the porous material than in the dense material due to the lower matrix fraction. The prevalence of one over another depends on the relative magnitudes of the absorbing and scattering coefficients and also on the shape of the phase function, which explains the correlation observed between the sensitivity coefficients taken with respect to σ tr and κ eff (see section 4.2). In the present case, it would appear that the first mechanism dominates for wavelengths below 6 µm, while for wavelengths beyond this threshold the second mechanism dominates.

Conclusion

The reflectance, transmittance and emittance of porous alumina disks are measured from room temperature up to 1300 °C are compared to numerical results obtained using a novel multi-scale approach: effective radiative properties are first determined from physical optics computations on 3D microstructures, then applied to the simulation of an equivalent homogeneous medium using the radiative transfer equation (RTE).

A sensitivity study using the RTE-based model was performed to quantify the uncertainties in numerical results, mainly arising from microstructural variability due to the small volume elements used in physical optics modeling. Uncertainties in the simulated radiometric quantities (reflectance, transmittance and emittance) are generally low, varying from 0.01 to 0.07 depending

  30µm

Figure 1 :

 1 Figure 1: Scanning electron micrograph of a polished section of the porous alumina ceramic, with pores in black.

Figure 2 :

 2 Figure 2: Apparatus at the CEMHTI laboratory (Orl eans, France) used to measure the high-temperature emittance [7].

  wavelength (µm) (b) Transport scattering coefficient.

Figure 3 :

 3 Figure 3: Spectral volume radiative properties of the porous alumina ceramic, evaluated at its nominal porosity f p = 0.22, for four different temperatures T.

Figure 4 :

 4 Figure 4: Diagram of the reflectance and transmittance model.

  200

  Normal-hemispherical reflectance.

  Normal-hemispherical transmittance.

Figure 5 :

 5 Figure 5: Measured (lines) and simulated (•) spectral normal-hemispherical reflectance and transmittance of the porous alumina disks at room temperature (T = 22 °C).

Figure 6 :

 6 Figure6: Measured (lines) and simulated (symols) spectral normal emittance of the porous alumina disks at different temperatures T: 22 °C (dotted lines vs. •), 800 °C (dashed lines vs. △), 1000 °C (dash-dotted lines vs. □), 1300 °C (continuous lines vs. ⋄). The inset shows the near-zero emittances at wavelengths between 1 µm and 3 µm.

Figure 7 :

 7 Figure 7: Spectral sensitivity coefficients (see equation (13)) for the normal-hemispherical reflectance (left), normalhemispherical transmittance (center) and normal emittance (right) at 800 °C, with respect to five input parameters: transport scattering coefficient σ tr (•), absorption coefficient κ eff (△), diffuse reflectivity component ρ diff (□), specular reflectivity component ρ spec (⋄), and slab thickness h (⋆).

Figure 8 :

 8 Figure8: Room-temperature normal-hemispherical reflectance (left), normal-hemispherical transmittance (center), and normal emittance (right): measurements and physical-optics-based simulations on porous alumina disks (dashed lines and • respectively) compared to calculations with Fresnel's equations for a hypothetical dense alumina (continuous lines).

Table 1 :

 1 Complex refractive index of sintered alumina at the studied temperatures.

		718 1.36 × 10 ±41 1.665 4.17 × 10 ±7 1.645 6.88 × 10 ±7 1.629 5.84 × 10 ±7
	1.5	1.712 8.12 × 10 ±21 1.659 5.93 × 10 ±7 1.640 9.86 × 10 ±7 1.624 8.38 × 10 ±7
	2.0	1.704 7.22 × 10 ±14 1.651 7.36 × 10 ±7 1.632 1.24 × 10 ±6 1.617 1.05 × 10 ±6
	3.0	1.680 4.25 × 10 ±9 1.628 9.31 × 10 ±7 1.611 1.61 × 10 ±6 1.595 1.40 × 10 ±6
	4.0	1.644 3.43 × 10 ±7 1.594 6.66 × 10 ±6 1.578 1.20 × 10 ±5 1.564 1.84 × 10 ±5
	5.0	1.594 2.78 × 10 ±5 1.547 1.42 × 10 ±4 1.534 2.02 × 10 ±4 1.521 2.77 × 10 ±4
	6.0	1.527 2.37 × 10 ±4 1.482 9.97 × 10 ±4 1.473 1.34 × 10 ±3 1.462 1.74 × 10 ±3
	7.0	1.435 1.94 × 10 ±3 1.390 6.03 × 10 ±3 1.392 6.91 × 10 ±3 1.385 7.06 × 10 ±3

on wavelength. The sensitivity coefficients also provided insight to the influence of different input parameters and the physical phenomena in play.

The excellent agreement between experimental and numerical results confirm the validity of the proposed multi-scale approach, in particular the microstructure-based modeling approach proposed in our companion paper [START_REF] Low | 1± a physical optics approach to predict the radiative properties of semi-transparent porous ceramics[END_REF] to determine the effective radiative properties. The extremely high reflectance and low transmittance in the present porous alumina samples for such a low porosity is never observed in the geometrical optics limit. It illustrates the strong influence of small heterogeneities on the macro-scale radiative properties, and highlights the need for more accurate physical-optics-based radiative transfer models.

Future work should focus on using the DDA numerical results to establish more accurate analytical modeling of microstructure-property relations, taking into account not just the porosity as we did, but also other parameters such pore size or pore shape. Application of the present DDA-RTE approach to the simulation and validation on other types of materials (e.g., multiple particle phases), or other types of radiometric quantities (e.g., bidirectional quantities) would also be of great interest to test the capabilities of the proposed approach.

Acknowledgments

This research was supported by Saint-Gobain Research (SGR) Provence and the French National Association for Research and Technology (ANRT) through the CIFRE grant number 2017/0775. The authors would like to express their gratitude to L. San Miguel (SGR Provence), L. Pierrot (SGR Provence) and J. Meulemans (SGR Paris) for their insight and discussions that greatly improved the research; to Y. Millot (SGR Provence) for sample preparation and physical microstructural characterization; to J. Adrien (MATEIS) and N. Naouar (LaMCoS) for assistance with X-ray tomography; and last but not least, to R. Coquard (EC2 Mod elisation) and S. Cunsolo (ex-LaMCoS) for helpful discussions on radiative transfer modeling.