Zied Ben Houidi
email: zied.benhouidi@alcatel-lucent.com

Giuseppe Scavo
email: giuseppe.scavo@alcatel-lucent.com

Samir Ghamri-Doudane
email: samir.ghamri-doudane@alcatel-lucent.com

Alessandro Finamore
email: finamore@tlc.polito.it

Stefano Traverso
email: traverso@tlc.polito.it

Marco Mellia
email: mellia@tlc.polito.it

Gold mining in a River of Internet Content Traffic

With the advent of Over-The-Top content providers (OTTs), Internet Service Providers (ISPs) saw their portfolio of services shrink to the low margin role of data transporters. In order to counter this effect, some ISPs started to follow big OTTs like Facebook and Google in trying to turn their data into a valuable asset. In this paper, we explore the questions of what meaningful information can be extracted from network data, and what interesting insights it can provide. To this end, we tackle the first challenge of detecting "user-URLs", i.e., those links that were clicked by users as opposed to those objects automatically downloaded by browsers and applications. We devise algorithms to pinpoint such URLs, and validate them on manually collected ground truth traces. We then apply them on a three-day long traffic trace spanning more than 19,000 residential users that generated around 190 million HTTP transactions. We find that only 1.6% of these observed URLs were actually clicked by users. As a first application for our methods, we answer the question of which platforms participate most in promoting the Internet content. Surprisingly, we find that, despite its notoriety, only 11% of the user URL visits are coming from Google Search.

I. INTRODUCTION

The Internet ecosystem has been historically composed only by two actors: carriers (e.g., ISPs) offering telephony services and Internet connectivity, and end-users. Recently, a new class of actors progressively gained a prime role: Over-The-Top content and application providers (OTTs [START_REF] York | What is an over-the-top (ott) application or service?[END_REF]), i.e., third parties that are involved in the cross-domain distribution of content. Nowadays, this class of providers offers to end-users the same services that used to be offered by ISPs, plus a plethora of novel services. This is the case for instance of voice, texting and video services (e.g., Skype and Viber, WhatsApp and iMessage, or Netflix and YouTube).

In this context, ISPs are more and more assuming the low profitable role of "bits carriers". To counter this effect, ISPs have been trying to find new added-value services that go beyond the traditional network connectivity business, investing in platforms to offer content [START_REF]Telecom italia vod[END_REF] or cloud services [START_REF]At&t cloud service[END_REF], [START_REF]Telefonica cloud service[END_REF].

However, one of the possible assets of an operator is the information about its customer-base. Some major ISPs such as AT&T and Verizon have recently investigated how to translate this asset into profit [START_REF]At&t joins verizon, facebook in selling customer data[END_REF], [START_REF] Kleinman | Verizon selling customers' cell phone data: Report[END_REF], for instance by re-selling customers' data to advertisement agencies as already done by other big OTTs such as Facebook and Google. This work was supported by the European Commission under the FP7 IP Project "An Intelligent Measurement Plane for Future Network and Application Management" (mPlane).

Extending this concept further, ISPs are thinking of leveraging the information their networks carry. By looking at the traffic that naturally flows, they have access to a humongous river from which possibly gold mining valuable information. This information could be used for at least two use cases. First, for web analytics/marketing purposes. Second, it can serve as an input for novel recommendation systems based on network traffic observation. And, differently from most 1 OTTs, ISPs have a unique vantage point that offers a wide-angle perspective, where multiple services and customers' habits are possibly exposed. They can try to exploit this unique vantage point respecting end-users privacy and regulations, for example, avoiding targeting single users, but considering aggregate information only.

Putting ourselves in the same position of an ISP observing the traffic in its network, we first address the technical issues related to i) how to identify the "contents" that users access from the enormous set of "objects" the network carries, and ii) how to pinpoint "interesting content" that is worth recommending out of the previous set. Second, we contrast the information that ISPs could get against the one OTTs have. This is instrumental to quantify if the ISPs are really in a more rewarding vantage point compared to the OTT position.

In this work we focus on HTTP traffic, the standard protocol used to transport web objects 2 . We consider all URL requests that are passively observed on a link of an ISP network. Immediately, we realize that the very large fraction of these URLs consists of requests automatically generated by browsers to fetch objects that are part of a web page (images, CSS files, JavaScript code, etc.), or by applications to poll automatic services (e.g., software update, chat keep-alive, etc.). We refer to these as browser-URLs. We are instead interested in the small subset of URLs that were intentionally visited by users, which we call user-URLs. Lot of ingenuity has to be used to extract this second subset, and, to the best of our knowledge, little work has been conducted in the literature, with few methodologies that are either obsolete for nowadays scenarios [START_REF] Choi | A behavioral model of web traffic[END_REF], [START_REF] Barford | Generating representative web workloads for network and server performance evaluation[END_REF], or too complex for our needs [START_REF] Ihm | Towards understanding modern web traffic[END_REF], [START_REF] Xie | Resurf: Reconstructing web-surfing activity from network traffic[END_REF]. Our goal is to reach a good accuracy at identifying user-URLs using only HTTP requests, without the need to correlate them with corresponding responses.

Next, we address the problem of identifying interesting-URLs, i.e., those user-URLs that are possibly worth recommending in an eventual content promoting scenario. For instance, a popular news is worth being suggested, while the home-page of a home banking portal is less interesting.

To develop and validate our methodologies we use a set of ground truth traces collected by manually visiting the top 1,000 most popular web sites rated by Alexa and 1,000 news promoted by Google News. Then, we show the goodness of our methodologies with a three-day long HTTP traffic trace passively collected from a PoP of an European ISP.

Our major contributions are: • We present a first set of algorithms and filtering stages to extract user-URLs from passive HTTP traces. We tune and quantify the performance of the algorithms using the dataset for which we have the ground truth. Our results show that we successfully detect 96% of user-URLs with only 1% of false positive rate and 66% of precision. Besides, precision can be enhanced to 80% with a loss of only 6% of user-URLs. When applied to the ISP trace, we found that only 1.6% of the 190 million HTTP requests in the dataset corresponds to actual URLs intentionally visited by users.

• We propose two algorithms to detect which user-URLs should be promoted also as interesting-URLs. Both algorithms leverage the social network information that is typically present in popular and interesting web sites. We found that only 15% of user-URLs may be classified as interesting-URLs.

• We show how rich the perspective of an ISP can be. We observe users accessing videos hosted on 9 different platforms, and news coming from 80 different news portals. This indicates that the view most OTTs get is different from the wideangle picture an ISP could get. We further demonstrate this view by providing early web analytics results on the referral shares of well known content promotion platforms. We show that, surprisingly, only 11% of all user-URL views happened after (thanks to) a Google Search, and, in the best case, no more than 13% of them came from Facebook, Twitter or Google News.

The rest of this paper is organized as follows. First, Sec. II describes the background and resumes the related work of this paper. Second, Sec. III describes the datasets we use. Sec. IV describes our algorithms and presents their performance evaluation. Sec. IV applies our filtering methods on real data. Finally, Sec. VI presents the open problems of this work and concludes the paper.

II. BACKGROUND AND RELATED WORK

The structure of a web page has considerably grown in complexity in the last decade. Today, it often consists of a complicated tangle of HTML, JavaScript, multimedia objects, CSS, XML files, etc. As depicted in Fig. 1, when attempting to view a web page, the browser downloads each of these objects using separate HTTP requests. As a consequence, a simple user's click on a URL generates a cascade of several HTTP requests between the user terminal and an almost unpredictable number of servers and caches that store these objects. Besides, JavaScript, Ajax and Flash objects may generate extra HTTP traffic that was not intentionally requested by the user (e.g., the automatic fetching of a YouTube video). Furthermore, many non-web applications nowadays rely on HTTP to exchange their data (e.g., Dropbox and software updates). Therefore, even when a trace of HTTP transactions performed by a terminal is available, identifying which requests actually correspond to a human interaction is not a straightforward task.

To the best of our knowledge, only few methods have been proposed in the literature to detect URLs that were intentionally visited by users [START_REF] Barford | Generating representative web workloads for network and server performance evaluation[END_REF], [START_REF] Choi | A behavioral model of web traffic[END_REF], [START_REF] Ihm | Towards understanding modern web traffic[END_REF], [START_REF] Xie | Resurf: Reconstructing web-surfing activity from network traffic[END_REF].

The first method is time-based [START_REF] Barford | Generating representative web workloads for network and server performance evaluation[END_REF], it relies on the intuition that a cascade of browser-URLs follows the initial user-URL. Browser-URLs are tightly grouped in time after the user-URL request has been observed (see red dotted boxes in Fig. 1). As such, the first request after a given inactivity period can be considered as a new user-URL, while all the following HTTP requests happening before a time threshold are assumed to be browser-URLs. Unfortunately the estimation of the algorithm time thresholds is not a straightforward task, and many factors (e.g., latencies due to network conditions) may harm the performance of this method [START_REF] Ihm | Towards understanding modern web traffic[END_REF].

Another methodology, presented in [START_REF] Choi | A behavioral model of web traffic[END_REF], is type-based. It relies on the media information reported in the Content-Type field contained in the HTTP responses: the URLs associated to responses specifying text/HTML type are considered as main pages while the others are considered as browser-URLs. However, this approach has been shown to be unreliable [START_REF] Schneider | Pitfalls in http traffic measurements and analysis[END_REF].

To the best of our knowledge, the most recent methodologies to investigate the composition of modern web pages are StreamStructure [START_REF] Ihm | Towards understanding modern web traffic[END_REF] and ReSurf [START_REF] Xie | Resurf: Reconstructing web-surfing activity from network traffic[END_REF]. They both exploit the Referer 3 field to split HTTP transactions into multiple streams, thus reducing the temporal overlaps between clicks on different URLs (e.g., when a user keeps several tabs open in her browser, for the same time window the technique can identify different streams). StreamStructure processes each detected stream separately. On each of them, it first applies a type-based filter (based on Content-Type) to keep only HTML/text pages. It then applies a time-based filter to detect main pages. To set a proper time threshold, the method leverages the Google Analytics beacon: once the Google Analytics beacon is downloaded, the page is considered as loaded, so that there is no need to set a static time threshold. Despite the improvements, StreamStructure still suffer from some limitations. First, it leverages Google Analytics information, which is present in only 40% of web pages (according to [START_REF] Ihm | Towards understanding modern web traffic[END_REF], [START_REF] Xie | Resurf: Reconstructing web-surfing activity from network traffic[END_REF]). Furthermore, it relies on the HTTP Content-Type field which has two drawbacks: (1) it has been shown to be often unreliable [START_REF] Schneider | Pitfalls in http traffic measurements and analysis[END_REF] and (2) this needs to monitor both HTTP requests and corresponding responses, which increases the complexity of the traffic extraction phase . We target a solution that overcomes these drawbacks, and for which only outgoing network traffic is needed to be monitored, so that the traffic extraction and filtering are kept as simple as possible. More recently, ReSurf [START_REF] Xie | Resurf: Reconstructing web-surfing activity from network traffic[END_REF] has been proposed. Although it does a great job in overcoming the limitations of [START_REF] Ihm | Towards understanding modern web traffic[END_REF], it still rely on the Content-Type (as well as the Content-Size), which makes it inadequate for our needs.

III. DATASETS

While per-object information is sufficient to study caching (e.g., assess caching policies and gains) or filtering (e.g., blocking unwanted objects), further processing is needed to infer human-induced HTTP transactions. This is one of the challenges that we tackle in this paper. For this purpose, we rely on two types of traces. The first is collected in a controlled test-bed where the ground truth is known and used. The second corresponds to a real traffic trace on which we apply our algorithms to appreciate the type of information that is possible to extract.

For the preliminary evaluation of our methods, we collect two ground truth traces. First, similarly to [START_REF] Ihm | Towards understanding modern web traffic[END_REF], [START_REF] Xie | Resurf: Reconstructing web-surfing activity from network traffic[END_REF], we build a trace (HTTP-Alexa) by manually visiting the top 100 most popular web sites according to Alexa ranking. In each of these sites, we randomly visit up to 10 links contained in them. We manually collect all the clicked URLs as they were reported by the browser bar. In parallel, we capture and extract HTTP requests generated by the browser. This resulted in a total list of 905 user-URLs, corresponding to 39025 browser-URLs. Second, we build a similar trace (HTTP-GNews) by visiting around 900 news sites promoted on Google News.

For the real data, we use the open-source traffic monitoring tool Tstat [START_REF] Finamore | Experiences of Internet traffic monitoring with Tstat[END_REF] to rebuild HTTP conversations. Thanks to this tool, we obtained a three-day long HTTP traffic trace, HTTP-ISP, which we collected at a vantage point of a commercial ISP network. The dataset contains the HTTP requests generated by about 19,000 residential customers. In total we observed more than 190 millions of HTTP requests.

IV. CONTENT FILTERING ALGORITHMS

In this section, we introduce and evaluate our web object filtering algorithms. First, we aim at distinguishing between intentionally visited URLs, i.e., user-URLs, and automatically requested ones, i.e., browser-URLs.

A. Identification of user-URLs

As explained in Sec. II, we believe that new and simpler methods must be devised to identify user-URLs. As a design choice, we assume the ability to parse only HTTP requests to reduce the complexity at the probe capturing the traffic and the amount of data to process. To this end, we propose four filtering mechanisms and compare their performance as detailed below. 1) F-Referer: This method exploits the Referer field, not to separate requests in different streams as done in [START_REF] Ihm | Towards understanding modern web traffic[END_REF], [START_REF] Xie | Resurf: Reconstructing web-surfing activity from network traffic[END_REF], but to directly pinpoint user-URLs. As shown in Fig. 1, when the URL of a web page is clicked, a sequence of HTTP requests is generated by the browser to retrieve all the embedded objects, thus generating a cascade of browser-URLs. All these requests have as a referer the starting user-URL (see Fig. 1). Therefore, for each request, this filter ignores the URL and focuses on the referer field, so that we are sure of capturing all the original user-URLs. However, observe that this approach captures all web objects with a hierarchical structure (e.g., JavaScript and CSS files that embed themselves other files).

2) F-Children: The nowadays trend of web page design goes towards including lots of embedded objects, which we call children. By counting the number of URLs seen with a given referer, it is possible to know the number of children composing the corresponding parent URL. Thus, we can filter out those URLs with a low number of children, e.g., simple objects that contain few other objects (e.g., URL-3c in Fig. 1).

3) F-Type: Similar in spirit to [START_REF] Choi | A behavioral model of web traffic[END_REF], this filter acts on URLs based on their type. However, instead of relying on the Content-Type field which is exposed in HTTP responses, we inspect the extensions of the objects queried by the HTTP requests: we discard URLs pointing to .js, .css, .swf objects. 4) F-Ad: A large amount of advertisement is embedded in nowadays web pages through the mean of iframe HTML nodes. By design, an advertisement iframe may embed several other objects itself that has as referer the advertisement page. Thus, ads likely to pass all above filters. To counter this phenomenon, we blacklist URLs pointing to known advertisement platforms using the filter provided by AdBlock [START_REF]Adblock Plus[END_REF].

In addition to these methods, we also test a time-based filter (F-Time) as proposed in [START_REF] Barford | Generating representative web workloads for network and server performance evaluation[END_REF], [START_REF] Ihm | Towards understanding modern web traffic[END_REF], [START_REF] Xie | Resurf: Reconstructing web-surfing activity from network traffic[END_REF], using a static time threshold.

Performance on ground truth datasets: We first evaluate these methods on the HTTP-Alexa dataset, described in Sec. III. In Fig. 2 we graphically report the performance of filters F-Referer alone, F-Referer + F-Type and F-Referer + F-Type + F-Ad through a Venn diagram. We observe that the F-Referer method alone has a high "filtering capacity". In fact, it reduces the set of browser-URLs from the 39025 URLs in HTTP-Alexa to only 2616 candidate user-URLs. It has therefore a 4,4% of false positive rate (FPR) 4 . Besides, it has a high recall 5 (98,34%). Manually inspecting the few misses, we find that they either correspond to HTTPS visits which did not pass the referer field, or to Flash content for which no URL requests are issued for browsing. However, its precision6 is still low (34%), which means that there is still a considerable amount of false positives. To reduce the set of false positives, we combine the F-Referer filter with the other filters with different configurations, i.e., considering different thresholds. The results are summarized in Tab. I. Both F-Time and F-Children enhance the precision when we increase respectively the time threshold and the minimum number of children (they invalidate false positives). However, they come at the cost of decreasing the recall (invalidating valid user-URLs). On the other hand, the F-Type and the F-Ad filters let us enhance the precision, with almost no impact on the recall. In reality, the F-Ad filter removes 16 valid user-URLs (see the dark green slice that is cut by the introduction of F-Ad in Fig. 2), but these were unintentionally visited when we collected the trace 7 .

We acknowledge that there is a tradeoff between recall and precision. The best combination to apply depends therefore on whether we want to capture all user-URLs or to remove all false positives. As a start, we opt for now for a most conservative approach that favors recall over precision. For the rest of the paper, we retain the F-Type coupled with F-Ad filters applied after the F-Referer method (i.e., F-Referer + F-Type + F-Ad). This guarantees 96.57% of recall, with only 1.17% of false positive rate.

B. Pinpointing Interesting URLs via OSN metadata

With the goal of targeting a recommendation system, we are now interested in identifying interesting-URLs among the detected user-URLs. Indeed, manually looking we find that many of them do not correspond to URLs that might attract users' attention (e.g., the web portal of an online bank).

Therefore, an extra step in the filtering is needed to go from user-URLs to interesting-URLs.

Finding a measure of interest is challenging since it involves human subjects and tastes. We investigate on simple heuristics that leverages online social network meta-information. We assume that interesting URLs should be rich with "social" features (e.g., share buttons). The idea is that if a web page is meant to be shared, then it might interest other people. We thus develop two methods to understand which user-URLs are "social-networks enabled". In particular we considered two approaches: 1) Active: This method uses a web scraper to actively query the URL and parse the returned HTML code looking for the presence of the OpenGraph protocol8 [START_REF]Facebook OpenGraph[END_REF]. If the protocol is present, the user-URL is classified as interesting.

2) Passive: This approach aims at passively detecting if a web page contains any of the well known social networks buttons. Given a user-URL X, we inspect its children, i.e., URLs having X as referer, and match them against a list of URLs necessary to load such buttons 9 . Such list was built by following the web development guidelines of several different social networks.

Performance on ground truth datasets: To evaluate these methods, we test if they already work on platforms that are known to be "interesting". In particular, we test them against Google News. For this purpose, we visit 1000 URLs promoted by Google News. Applying the active and the passive methods on this trace, we find that they classify as interesting respectively 79% and 70.72% of Google News URLs. For the active method, this means that 79% of Google news URLs actually implement the OpenGraph protocol. To understand the passive method's false negatives, we manually inspect them. We find that they correspond to web sites that use custom methods to embed the social networks buttons and that our filter fails to identify. For instance, YouTube uses a non standard solution. However, since it is OpengGraph compliant, our active method correctly detects it. To estimate the capability of pinpointing interesting web objects, we first apply the filter chain F-Referer + F-Type + F-Ad on HTTP-Alexa trace to detect user-URLs; then we use our social-aware heuristics. Intuitively, the URLs Alexa ranking are less likely to be promoted than the Google News URLs, we expect them therefore to contain much less interesting URLs. This was confirmed by our both methods which gave similar results: 33% of the user-URLs were labeled as interesting-URLs using the active method, and 35% using the passive one.

These methods look promising, we use them in the rest of the paper and leave their enhancement for future work.

V. APPLYING THE FILTERING ON REAL DATA

In this section, we apply our filtering methods on the real data (HTTP-ISP) with two purposes in mind: first to rank and analyze user-URLs and interesting-URLs, and second to do some preliminary web analytics job.

A. Additional problems

When considering the real HTTP traffic for filtering, some additional sources of error have been detected and called for more ingenuity. In particular, we noticed two main problems, and we propose two simple mechanisms to factor them out.

i) URLs generated by non-browser applications: Most applications use HTTP to automatically download web objects. The queried URLs are clearly not relevant, and must be ignored. We identify those URLs by inspecting the User-Agent field, which informs about which client application generated the HTTP request, and white-listing well-known browsers only. This discards around 15% of URL requests in our dataset.

ii) Inflated popularity induced by some users: Sometimes browsers generate multiple HTTP requests for the same content, e.g., automatically reloading a page, or downloading videos in chunks. This phenomenon inflates the popularity of some URLs. We counter this effect by counting a URL only once for each user-id.

B. Ranking and Classifying URLs

We first apply the F-Referer + F-Type + F-Ad filters, and study the popularity of the resulting user-URLs. Fig. 3 shows the popularity of all-URLs, user-URLs and interesting-URLs. The x-axis reports the rank of URLs, while the yaxis reports the actual number of occurrences of each URL, i.e., its popularity. Both axes are log-scale. Observe that the distribution follows a typical Zipf law, and many URLs show a low popularity: only 10,000 out of millions URLs have a popularity larger than 1000.

As expected, the user-URLs represent a tiny fraction of all the URLs. Our method detects that among the 190 million URL requests, only 1,6% correspond to actual user-URLs requests. Among these user-URLs views, only around 15% were detected as potentially interesting.

We next analyze the interesting user-URLs. We manually classify the top 1000 URLs to build a set of rules to help us having a preliminary classification of the rest of the URLs. Among these top 1000 URLs, we find that 482 are news (or blogs), 336 are services (e.g., online shops, travel engines, etc.) and 91 were videos. Extending a similar classification on the rest of the interesting user-URLs, we find that (at least) 18% correspond to videos coming from 9 different platforms (YouTube alone 15%) and 22% correspond to news from around 80 different news web sites. This observation confirms that the ISP is probably the only entity that has such a rich cross-service and wide-angle vantage point on the Internet.

Open issues: We now report some of the limits observed with our filtering methods. First, for the user-URLs, although we drastically reduce the set of candidate URLs, our results still contain some false positives, which is not surprising given their relative high percentage. This is mainly due to the complex composition of web pages with a nested structure of objects. In the future, we plan to (1) test some of our other filtering methods that favor precision at the cost of recall (example the children method) as well as (2) work on enhancing our methods.

Another issue is that the returned list of the top most interesting-URLs contains popular and well-known web pages, e.g., the Google Search home page, or the most popular news portals. This confirms on the one hand the goodness of our algorithms; on the other hand, this opens the space for smarter algorithms to pinpoint interesting-but-not-obvious-URLs.

Finally, our algorithms outperform Resurf [START_REF] Xie | Resurf: Reconstructing web-surfing activity from network traffic[END_REF] in terms of processing speed. Applying F-Ref + F-Type + F-ad on one hour of HTTP-ISP (19,000 users) took us around 43 minutes. This is about the same time it took Resurf to process one hour traffic of only 1,000 users. However, our main bottleneck is the F-Ad due to the large size of its catalog; F-Ref + F-Type alone take only 3 minutes to complete. We plan to optimize it as part of our future work.

C. Early web analytics results

Web analytics is an important tool for business and market research. It helps companies to refine the target of their advertisement campaigns, eventually giving precious hints about where to place advertisement to collect more user clicks. Most of such tools today work on a per site basis: each site has a local view on where its visits came from (referring to it). Thus, a general view is missing, and it is not clear which web platforms drive most of today's user visits. Thanks to our filtering methods, ISPs overcome this limit, reaching a crossservice view, by simply inspecting the referers associated to the detected URLs.

As a preliminary step, we start by quantifying the referral share of Google, Facebook and Google News, i.e. how many visits are driven thanks to these promotion platforms. We report our results in Fig. 4 and Fig. 5, for user-URLs and interesting-URLs, respectively. The y-axis reports the referral share in percentage over all the views in the 3 days. In the x-axis, we apply the results on different populations of URLs depending on their popularity. The "No Referer" shares correspond to URLs which had no referer (e.g., due to direct browsing, bookmarks, email, etc.).

Interestingly, a considerable amount of visits came with no referer (around 13%). This goes up to 25% for the top 1000 interesting-URLs, meaning that direct browsing is common when browsing the web. As expected, the shares of visits driven by well-known platforms are larger for interesting-URLs compared to user-URLs. However, the share of requests coming from Google is more important for unpopular objects if compared to popular ones. This is again expected since users use search engines to look for unknown content rather than popular links. However, it is surprising that despite their notoriety, the referral shares of these platforms are relatively low: Only 11% of user URLs visits came from Google (and only 16% for interesting-URLs). Observe that the rest of the shares correspond to other platforms, such as news portals and blogs. We intend to rank them as part of our future work.

Open issues: One of the main issues that we figured out in this study is due to usage of HTTPS. In fact, when going from a page served over HTTPS to another served over HTTP, the standard imposes to not include the referer field [START_REF] Fielding | Hypertext transfer protocol-http/1.1[END_REF], so that users' privacy is preserved. However, because of its importance to marketers, many websites implement workarounds, either by using the meta referer or HTTP redirections, to still inform the landing page where the visit came from. This biases our results inflating the "No Referer" share with visits that came from HTTPS pages, and for which the referer was not passed. To get a hint on the consistency of our results concerning Google and Facebook (that both use HTTPS for browsing), we made experiments employing several popular web browsers and different operating systems. We visited URLs starting from Google Search and Facebook and check whether the referer was correctly passed. For Google, we found that the referer is always passed, but this does not always hold for Facebook, indeed we observed different behaviors depending on the browser and operating system. As a consequence, the Facebook referral shares are underestimated, but upper bounded by the "No Referer" share. We plan to investigate more this issue as part of our future work.

VI. CONCLUSIONS, OPEN PROBLEMS AND FUTURE WORK

Driven by the intuition that ISPs have a great deal of information at their disposal that can be extracted from passive observation of the traffic flowing in their networks, we propose in this paper a set of algorithms to extract popular URLs from real Internet traffic. In this study we analyzed the feasibility of the automatic extraction of useful/interesting URLs from the humongous amount of HTTP data that flows through an ISP-wide network. Other challenges must be clearly faced, and ingenuity must be used to find appropriate solutions: i) Users' privacy: tracking users' activity is (commonly) performed by OTT providers and it has been strongly criticized recently [START_REF] Akkus | Non-tracking web analytics[END_REF]. ISPs face similar issues. They are allowed to monitor traffic for troubleshooting or even marketing purposes. Data could even be stored if properly anonymized and/or aggregated, i.e., if user's identity is irreversibly hidden. Our algorithms monitor aggregated data by design, without the need to offend users' privacy. ii) Traffic encryption: Apart the issue discussed in Sec. V-C, traffic encryption deeply hampers whatever traffic mining operation. This is not a negligible aspect since today more than 20% of the HTTP traffic is encrypted [START_REF] Finamore | The need for an intelligent measurement plane: The example of time-variant cdn policies[END_REF]. Mining interesting URLs in presence of encrypted traffic is another interesting research direction. However, end-customers could be involved directly, e.g., offering them personalized services (such as media curation, or parental control filters) in exchange for installing some plugins that collect clicks. Our preliminary results suggest that the extraction of user-URLs from network traffic is a challenging task given the structure of nowadays web pages. However, "network gold mining" may represent a promising opportunity for ISPs to compete with OTTs in front of marketers and advertisers. Moreover, we believe information provided by our methodologies can be employed for a broad gamma of applications, ranging from new passive recommendation services to caching systems and parental control tools to name a few. In our ongoing efforts, we are developing each presented algorithm to run in a complete online extraction system, capable of working in a real ISP network scenario.

Fig. 1 .

 1 Fig. 1. Sequence of HTTP requests when accessing some standard web pages.

FFig. 2 .

 2 Fig. 2. Venn diagram reporting the effects of different filtering methods on our HTTP-Alexa dataset.

Fig. 3 .Fig. 4 .Fig. 5 .

 345 Fig. 3. Content items popularity before and after filtering (HTTP-ISP).

Google for instance observes a lot of visits thanks to its widespread Google analytics tool.

We ignore HTTPS for now. A discussion about how to deal with possible encryption is given in Sec. VI.

A field in the HTTP GET request that specifies from which previous page the URL has been referred.

Number of False Positives (here 1711) over the number of negatives (here 38120)

Number of URLs correctly labeled as user-URLs (true positives, here 890) over the number of user-URLs (ground truth, here 905).

Number of true positives over the number of items labeled as positive by the method (here 2616).

Although we acknowledge that some advertisements might interest people, we decide to skip them for now.

The OpenGraph protocol was developed by Facebook to help web pages getting integrated in "the social graph".

Available at http://www.retitlc.polito.it/finamore/plugins.txt.


Rémy Besson

Loïc Favergeon

Understanding the mechanisms of CaO carbonation: the role of point defects in CaCO 3 by atomic-scale simulations

Keywords: simulations, point defects, calcite, CO 2 storage

In order to improve our understanding of the mechanisms underlying the carbonation of CaO by CO 2 , a practically important reaction, we present a detailed atomic-scale study, by means of ab initio density functional calculations, of the point defect properties in calcite CaCO 3 . We perform a thorough investigation of the chemical potentials relevant in experimental conditions. Focusing on C and O defects closely related to CO 2 diffusion, we point out the absence of interstitial C, except possibly in complex form with other defects, whereas interstitial O is found stable. Whereas O and C vacancies are not significant in neutral form at low temperature, their role is clearly revealed when charged states are included. The formation energies of O and C vacancies, together with the profiles of chemical potentials across the growing calcite layer, are consistent with joint C and O diffusion by separate vacancy mechanisms of roughly equal amplitudes. As regards the possible influence of complex point defects, our results suggest that interstitial diffusion of CO 2 is unfavorable.

Conversely, the strong binding of the CO 2 vacancy may enhance CO 2 diffusion.

INTRODUCTION

Of high practical importance is the current issue of achieving a more efficient management of carbon dioxide. This requires a better understanding of the physical mechanisms underlying the capture and release of CO 2 by suitable substrates. Among these substrates, calcium oxide CaO offers several prominent advantages [START_REF] Boot-Handford | Carbon capture and storage updateEnergy and[END_REF], which turn it into a good candidate for the purpose of large numbers of capture-release cycles. The aim is to reach a better reversibility of the process, embodied in the CaO + CO 2 ↔ CaCO 3 carbonation reaction converting the oxide into carbonate (calcite). In the final stage of this carbonation reaction, the reaction rate is widely controlled by the diffusion of CO 2 through the carbonate layer [START_REF] Mess | Product layer diffusion during the reaction of calcium oxide with carbon dioxide[END_REF], possibly via bulk as well as grain boundary mechanisms. Nothing is known about the mechanisms of CO 2 diffusion within CaCO 3 , which may occur in molecular form, but also after appropriate dissociation towards O 2 or CO molecules, or even in elemental O or C species. Getting more information about CO 2 diffusion would certainly help building more realistic reaction mechanisms for the global carbonation reaction, of wide utility in macroscopic kinetic investigations [START_REF] Rouchon | New kinetic model for the rapid step of calcium oxide carbonation by carbon dioxide[END_REF].

On the route towards elucidating these complex questions are more basic issues connected with the point defect (PD) properties of CaCO 3 , since these properties most probably have a direct influence on the CO 2 behaviour in the compound. Recently, CaCO 3 calcite has formed the subject of several atomic-scale studies, using either semi-empirical force fields or ab initio Density Functional Theory (DFT) simulations, for the modelling of bulk or surface properties [START_REF] Fisler | A shell model for the simulation of rhombohedral carbonate minerals and their point defects[END_REF][START_REF] De Leeuw | Computer simulation of surfaces of metals and metal-oxide materials[END_REF][START_REF] Lardge | Ab initio simulations of the interaction between water and defects on the calcite (10ī4) surface[END_REF][START_REF] Rohl | Evidence from surface phonons for the (2x1) reconstruction of the (10ī4) surface of calcite from computer simulation[END_REF][START_REF] Akiyama | Atomic and electronic structures of CaCO 3 surfaces[END_REF] or for the investigation of nucleation from CaO [START_REF] Besson | Atomic-scale study of calcite nucleation in calcium oxide[END_REF]. As concerns PD properties, Fisler et al. [START_REF] Fisler | A shell model for the simulation of rhombohedral carbonate minerals and their point defects[END_REF] developed a semi-empirical shell model for CaCO 3 and applied this model to the study of PDs in this carbonate. The PDs investigated were the Ca(+2) and CO 3 (-2) vacancies, and the authors also considered the Schottky pair of such vacancies. The cases of antisite defects, interstitials and other (C, O, CO 2 ,...) vacancies were not studied. On the whole, the PD properties of CaCO 3 are still widely unknown, and elucidating this issue forms the subject of the present work. To this purpose, atomic-scale first-principles calculations will be employed, since the latter provide the most efficient way to probe nanoscale features hardly accessible via experiments. While CaCO 3 is a ternary compound, which makes its point defect structure rather complicated, the level of intricacy is raised further by the possibility of interstitials, and special care will therefore be given to these defects below. After describing the methodological background, the results will be presented, first in the context of neutral defects, which conveniently allows a global survey of PD properties, and then including more specifically the effect of PD charges. Our results on PDs in CaCO 3 will then be discussed in the context of CaO carbonation.

METHODS

First-principles calculations

The ab initio calculations were performed using the DFT approach, with the Vasp software [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF][START_REF] Kresse | Efficiency of ab initio total-energy calculations for metals and semiconductors using a plane-wave basis set[END_REF] in the projector-augmented wave (PAW) framework [START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmented-wave method[END_REF] and the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] form of the exchange-correlation functional. A Gaussian smearing was used, together with a 4x4x4 Monkhorst-Pack k-point mesh and a cutoff energy of 600 eV for the plane wave basis. All static T=0K calculations included relaxations of the atomic positions as well as optimizations of the system size and shape around the PDs. CaCO 3 calcite (Figure 1) is a rhombohedral compound (a = 0.637 nm, α = 46°) containing 3 sublattices (one for each chemical species), hence 9 types of point defects (6 types of antisites, 3 types of vacancies). In addition, the possibility of single interstitial species was investigated, as described below. In the present study of PDs in calcite, most T = 0 K relaxations and all molecular dynamics calculations were performed starting from a perfect 80-atom system (supercell) containing 2x2x2 Ca 2 C 2 O 6 unit cells. The effect on the PD properties of increasing the system size -up to a 270-atom supercell built on 3x3x3 Ca 2 C 2 O 6will also be discussed.

IPDA modeling of point defects

Point defect-related properties in ordered compounds around stoichiometry can be conveniently investigated by means of the independent-point-defect approximation (IPDA) [START_REF] Besson | Point defects in multicomponent ordered alloys: Methodological issues and working equations[END_REF]. Initially devised for selected systems, the IPDA framework has been recently applied to various compounds with increasingly sophisticated chemistries and crystallographies.

Whereas the IPDA has proved to be successful in metallic systems, including complex ordered compounds [START_REF] Kwon | Point defects and formation driving forces of complex metallic alloys: atomic-scale study of Al 4 Cu 9[END_REF], its efficiency has also been demonstrated by several works on nonmetallic systems involving charged defects [START_REF] Van De Walle | First-principles calculations for defects and impurities: Applications to III-nitrides[END_REF][START_REF] Erhart | Modeling the electrical conductivity in BaTiO 3 on the basis of firstprinciples calculations[END_REF][START_REF] Lany | Assessment of correction methods for the band-gap problem and for finite-size effects in supercell defect calculations: Case studies for ZnO and GaAs[END_REF][START_REF] Bjerg | Ab initio calculations of intrinsic point defects in ZnSb[END_REF][START_REF] Aberg | Contributions of point defects, chemical disorder, and thermal vibrations to electronic properties of Cd 1-x Zn x Te alloys[END_REF][START_REF] Jund | Lattice stability and formation energies of intrinsic defects in Mg 2 Si and Mg 2 Ge via first principles simulations[END_REF][START_REF] Zacherle | Ab initio calculations on the defect structure of β-Ga 2 O 3[END_REF]. These works were however mainly concerned with oxide semiconductors, and the case of carbonates such as calcite remains largely unexplored. The hypothesis underlying IPDA of independent PDs allows the energy of the system to be written as a simple linear function of the PD amounts. Minimization of this function with respect to the PD amounts at given composition is an efficient way to obtain an overall picture of the composition-dependent PD structure of a compound at low temperature (T = 0 K limit) [START_REF] Besson | Comprehensive ab initio themrodynamic treatment of impurities in ordered alloys: Application to boron in B2 Fe-Al[END_REF]. In the case of a ternary compound such as CaCO 3 , it conveniently allows to identify important composition domains characterized by two types of dominant PDs, the latter being required, even at low temperatures, to accommodate off-stoichiometry, and therefore named "constitutive" PDs. As illustrated below (section "Survey of neutral PDs"), these domains are separated by tie-lines, the crossing of which corresponds to sharp changes in the PD properties of the compound. The associated chemical potentials, which also undergo sharp changes, can be obtained easily in each domain, from the conditions of zero formation energies, in the low-T limit, for constitutive PDs together with the relations between formation energies and chemical potentials (Eq. (3) below). At higher temperatures, including various contributions to the entropy (configuration, phonons, etc.), the IPDA can be employed with either its NPT (constant particle numbers, pressure and temperature) or µVT (constant chemical potentials, volume and temperature) equivalent formulations [START_REF] Besson | Point defects in multicomponent ordered alloys: Methodological issues and working equations[END_REF], allowing to obtain the PD structure and related properties (free energy) as a function of composition and temperature, and its ability to multiple extensions towards more various fields, e.g. solution electrochemistry, has been pointed out recently [START_REF] Todorova | Extending the concept of defect chemistry from semiconductor physics to electrochemistry[END_REF]. The IPDA analysis relies on the determination of grand canonical (GC) energies defined, for a PD of type p and charge q, as: E GC (p,q) = E PD (p,q) -E perf [START_REF] Boot-Handford | Carbon capture and storage updateEnergy and[END_REF] where E PD and E perf are respectively the total energies of defected and perfect systems of same size. It allows easy determination of the PD amounts on their respective sublattices, namely given by:

x(p,q) = exp[-E f (p,q)/kT] (2)
where E f is the formation energy of the PD: E f (p,q) = E GC (p,q) + δµ(p) + qµ e [START_REF] Rouchon | New kinetic model for the rapid step of calcium oxide carbonation by carbon dioxide[END_REF] where µ e is the electronic chemical potential, controlling the global charge of the defected system. δµ(p) is a defect-dependent term involving the elemental chemical potentials: its value is respectively δµ(p) = +µ(A) for a vacancy (V A ) on an A sublattice, µ(A)-µ(B) for a B antisite atom (B A ) located on an A sublattice, and -µ(A) for an A atom (A int ) on an interstitial sublattice. Other specific temperature effects, for instance stemming from local defectinduced vibrations, can be included in relation [START_REF] Boot-Handford | Carbon capture and storage updateEnergy and[END_REF] [START_REF] Zacherle | Ab initio calculations on the defect structure of β-Ga 2 O 3[END_REF][START_REF] Tingaud | Point defects and diffusion in ordered alloys : an ab initio study of the effect of vibrations[END_REF], but in the case of CaCO 3 this will be left for future work. Finally, it should be noted that most previous works on charged PDs were concerned with semiconductors, i.e. interested in the point defect structure in systems with possibly non-zero global charges. This explains why these works investigated the influence of the electron chemical potential, since the latter quantity controls the global charge. Conversely, in our case, although various charge states of PDs were also investigated, we did not consider the possibility of non-zero global charge. Therefore, all other (i.e. Ca, C, O) chemical potentials being determined from solid/solid and solid/gas equilibria, the electron chemical potential was obtained via Eq. (1) from the global neutrality condition.

RESULTS

Choice of chemical potentials

Table 1 : Determination of chemical potentials in CaCO 3 : using local equilibria at the external (subscript "ext") calcite/gas and internal (subscript "int") calcite/oxide interfaces, relations used to obtain the elemental chemical potentials in O 2 + CO 2 conditions, via gaseous chemical potentials µ(O 2 ), µ(CO 2 ), and compound energies E(CaO), E(CaCO 3 ). Note that, in the present work, no attempt has been made to correlate "external" and "internal" interfaces with specific crystal planes. We simply use these words to distinguish between two different types of thermodynamic equilibria, implying different chemical potentials. external interface (calcite/gas) internal interface (calcite/oxide)

µ(O 2 ) = 2µ ext (O) µ(O 2 ) = 2µ int (O) µ(CO 2 ) = µ ext (C)+2µ ext (O) E(CaO) = µ int (Ca)+µ int (O) E(CaCO 3 ) = µ ext (Ca)+ µ ext (C)+ 3µ ext (O) E(CaCO 3 ) = µ int (Ca)+ µ int (C)+ 3µ int (O)
The PD structure of an ordered compound such as CaCO 3 is well-known to depend critically on the composition, or equivalently, on the elemental chemical potentials, µ(Ca), µ(C) and µ(O), which therefore have to be taken into account thoroughly. To this aim, it is reasonable to choose "O 2 + CO 2 " working conditions, namely characterized by a surrounding O 2 + CO 2 gas phase with controlled temperature and partial pressures, in order to fix µ(Ca), µ(C) and µ(O), via µ(O 2 ), µ(CO 2 ), E(CaO) and E(CaCO 3 ), according to the relations given in Table 1. In practical conditions for carbonation, a calcite layer is growing at the expense of the oxide, and the elemental chemical potentials are therefore deduced from the local equilibria existing at the external (calcite/gas) and internal (calcite/oxide) interfaces.

Moreover, whereas CO 2 is active only at the external interface, it is reasonable to suppose that O 2 with uniform gaseous chemical potential exists at the internal interface as well. Under these assumptions, while E(CaO) and E(CaCO 3 ) are directly obtained from ab initio calculations of solid compounds, the gaseous chemical potentials µ(Ο 2 ) and µ(CO 2 ) can be conveniently obtained from statistical thermodynamics descriptions of ideal gases, using ab initio estimations of energies for isolated O 2 and CO 2 molecules, together with rotation and vibration partition functions obtained using characteristic frequencies from experiments available in literature. Resorting to literature data for the vibration and rotation parts avoids performing ab initio calculations for these quantities, which is justified by previous studies [START_REF] Besson | CO 2 Adsorption on Calcium Oxide: An Atomic-Scale Simulation Study[END_REF] on CO 2 demonstrating the excellent agreement between DFT calculations and literature data. Moreover, it was previously found [START_REF] Rouchon | Analysis of the kinetic slowing down during carbonation of CaO by CO 2[END_REF] that efficient experimental conditions for the carbonation reaction correspond to CO 2 pressures ranging between 2 and 30 kPa, while the O 2

pressure is maintained at low values, typically 100 Pa. Using these conditions, the effect of temperature on the gaseous and elemental chemical potentials is displayed on Figure 2. These previous experiments [START_REF] Rouchon | Analysis of the kinetic slowing down during carbonation of CaO by CO 2[END_REF] suggested using 800 K as working temperature, and the latter will thus be considered in our work. At this temperature, while the pressure effect on µ(CO 2 ) appears rather low in the range of interest, the local equilibria imply that the C chemical potential is significantly lower (~1 eV) at the internal interface than at the external one. Finally, it is important to note that, while O 2 + CO 2 conditions were selected as most convenient for our theoretical study, they will have to be compared (see Discussion below) with available experimental results, obtained under H 2 O + CO 2 conditions often used in practice. Indeed, the oxygen residual pressure is often overlooked in experiments, contrary to P(H 2 O), which was shown to have a critical effect on the carbonation rate [START_REF] Nikulshina | Kinetic analysis of the carbonation reactions for the capture of CO 2 from air via the Ca(OH) 2 -CaCO 3 -CaO solar thermochemical cycle[END_REF].

Interstitial defects in CaCO 3

Due to the low symmetry of the CaCO 3 structure, finding the possible sites occupied by interstitials species is an intricate issue. To this purpose, ab initio molecular dynamics was employed to investigate the properties of interstitials inCaCO 3 . As a first step, using the three equivalent positions <1/2;0;0> (top part of Figure 3) as a reasonable starting point, systems containing each interstitial species on this position were initially relaxed to T = 0 K and zero pressure. In a second step, each system was then submitted to 2000 steps (1 fs) of molecular dynamics, using a 1000 K initial temperature and NVE conditions, namely with constant particle numbers, volume and energy. Figure 3 (bottom part) displays the final configuration for each species. As a main result, the interstitial behaviour appears to be strongly speciesdependent. Interstitial Ca undergoes an instability, which spontaneously converts it into a produces a three-site 2C int +V C complex (Figure 3b). Conversely, interstitial O is found to be stable (Figure 3c). On the whole, O will therefore be the only species considered as possibly occurring in simple interstitial form in CaCO 3 . We will briefly discuss the possible effect of complexes, such as the previous ones, including C int . Such complexes, however, should be hardly mobile, having thus no influence on the diffusion properties in calcite.

Survey of neutral PDs

Due to the complexity of the CaCO 3 structure, involving a priori 9 types of PDs as well as O interstitials, it is useful, in a first step, to confine our investigations to neutral defects and low temperature. The main advantage of this preliminary study is to provide an easy "at-a-glance" picture of the PD properties of the compound. On the other hand, including temperature and charges (next section) makes the analysis more cumbersome, which imposes to focus on selected working conditions (such as those described above) and fails in yielding a comprehensive idea of the PD properties of the compound. the PD formation energies defined by relation [START_REF] Boot-Handford | Carbon capture and storage updateEnergy and[END_REF] have to be positive, this provides conditions on the elemental chemical potentials, which implies that these quantities have to be confined to a restrictive domain. This is described on Figure 5, which displays this domain as a polygon, each corner of which corresponding to a composition domain (see Figure 6 below) characterized by a couple of structural PDs. Conversely, each polygon edge corresponds to a (infinitely at 0 K, see Figure 6) thin line of transition between a defect type and a neighbouring one. In this context, the working conditions deduced from Figure 2 are depicted as a blue square on Fig. 5, which indicates that, although these conditions are located on an edge of the positivity domain, µ(C) and µ(O) can be varied of a few eV within this domain.

However, a strong lowering of µ(O) should be compensated by an increase in µ(C), which will be illustrated below ("Discussion" part) when discussing H 2 O + CO 2 conditions. On the whole, Figure 5 confirms the ability of the selected PAW-PBE framework to describe the gaseous as well as the solid properties relevant for the CaO + CO 2 ↔ CaCO 3 reaction.

Following the IPDA framework, the E GC parameters straightforwardly provide a survey of the composition-dependent PD structure of CaCO 3 at low temperature. The T = 0 K limit allows to emphasize only the major "structural" defects, required to accommodate for departures from stoichiometry, while discarding other, thermally activated types of PDs. The results, displayed on Figure 6 in a form similar to representations of ternary phase diagrams, evidence seven domains delimited by various composition tie-lines (x Ca , x C and x O being the atomic fractions in the compound, x Ca + x C + x O = 1), namely a rather intricate PD structure for the CaCO 3 compound. Providing the composition-dependent counterpart of Figure 5 (associated with chemical potential-dependent properties), this demonstrates the sensitivity of CaCO 3 to the external conditions, such as the gaseous surrounding, and the influence of these conditions on the CaCO 3 composition and PD-based properties, especially diffusion. As main predicted properties for PDs in calcite, C vacancies and interstitial O are never found as major defects whatever the composition range. Conversely, various types of antisites do occur, and O or Ca vacancies may be favoured depending on the composition domain. Corresponding to these PDs, the analysis also yields the chemical potentials of the CaCO 3 ordered phase, constant in each composition domain in the low-temperature limit (Figure 6, also each polygon edge on Figure 5). Confronting these results with the chemical potentials deduced from the gas phase allows to connect the relevant PD domains with the composition range of the compound in working conditions. This range is embodied by the arrows represented on as such within the layer, a hypothesis to be examined further (see below). Moreover, our results suggest that the domains of variation of chemical potentials, when going from the external to the internal interface, may lead to the crossing of the x Ca =1/5 line, hence a possible change of the PD structure across the carbonate layer. This probably implies a change of the diffusion properties, especially for Ca, but this is not critical for carbonation, since this reaction is not submitted to Ca diffusion. according to the elemental chemical potentials deduced from Table 1 and Figure 2. While the previous study allowed to describe the main trends of PDs in CaCO 3 , it was restricted to neutral PDs, whereas the presence of charged defects may be possible in such carbonates. Investigating charged PDs requires the knowledge of the electronic densities of states (DOSs), primarily for the perfect, undefected system, since it directly influences the amounts of conduction electrons and valence holes, hence the global charge balance. In addition, the DOS for each type of charged PD is valuable as it may provide information about defect instabilities possibly occurring for specific charge levels. Although such instabilities have hitherto been reported in some semiconductors like Ga 2 O 3 [START_REF] Zacherle | Ab initio calculations on the defect structure of β-Ga 2 O 3[END_REF], similar features cannot a priori be discarded in carbonates. To clarify this issue for CaCO 3 , all charge levels in the range {-2 ; +2} were taken into account for all PDs, this range being possibly extended up to q = +/-4 for some defects, when this was required to localize the formation energy minimum according to relation [START_REF] Boot-Handford | Carbon capture and storage updateEnergy and[END_REF]. From inspection of all corresponding DOSs, the most remarkable result is obtained in the cases of Ca O for q < +2 (Figure 7a) and V O for q < 0 The GC energies of charged defects, displayed on Figure 8, show a globally increasing trend with charge decrease. This suggests that the dominant effect is due to the band energy, a more negative charge entailing the occupation of higher one-electron energy levels in the DFT framework. The other contributions to the total energy are not sufficient to modify this globally monotonic behaviour. For charges comprised between -2 and +2, the slope is quite identical for all PDs, except for Ca O and V O , namely both PDs pointed out in the previous DOS analysis. A similar behaviour is detected for V Ca and Ca C , though for more negative

Charged defects

C(Ca) O(Ca) V(Ca) Ca(C) O(C) V(C) Ca(O) C(O) V(O) O(int) GC energies (eV) charge C Ca O Ca V Ca Ca C O C V C Ca O C O V O O int
charges. These GC energies allow to investigate the formation energies of charged defects in O 2 + CO 2 working conditions (Figure 9). In these conditions, CaCO 3 is found to be exactly stoichiometric (to within 10 -4 ) and µ e = 1.432 eV for charge neutrality. Considering Ca defects, V Ca is found to be strongly stabilized by q = -2, whereas values = -2 and > +2 are

DISCUSSION

Our results on PDs in calcite can be compared with those of previous works, in particular the semi-empirical shell model for CaCO 3 proposed by Fisler et al. [START_REF] Fisler | A shell model for the simulation of rhombohedral carbonate minerals and their point defects[END_REF]. The only comparison with our work is possible for V Ca (+2) with a formation energy of ~ 20 eV, to be compared with ~ 7 eV in our work for the same charge level. Although the difference is quite large, both works agree to indicate that positively charged Ca vacancies are energetically unfavourable, and our work, considering other charge levels for this defects, indicates that a negative charge is more favourable. Moreover, both works differ in the chemical potentials selected in order to obtain the formation energies (Eq. ( 3) in our work), which may explain the numerical discrepancy for V Ca (+2). More systematic investigations would be required to compare the semi-empirical and ab initio energetics of CaCO 3 .

The previous results were obtained for PDs periodically repeated in 2x2x2 unit cells of Ca 2 C 2 O 6 , which raises the issue of possible interactions between defects. While Figure 4 indicates that such interactions can reasonably be neglected for neutral systems, the case of charged defects may require further investigation, due to the long-range nature of electrostatic energies. For larger systems consisting of 3x3x3 unit cells, each given (PD ; charge) involves ~ 270 atoms, which remains very demanding for current computational resources. Since the wide panel (~ 60) of PD types and charges in calcite leads to exceedingly long calculations, we therefore limited our study of these intricate convergence issues to several cases of PDs. In these cases, we checked that our PD analysis using 2x2x2 unit cells led to errors < 10 % in GC energies, which is reasonable in regard of the other possible sources of uncertainties inherent to the ab initio -IPDA approach, e.g. the validity of the PAW-PBE energy model.

We thus leave more accurate investigations for future works. Finally, the issue related to the alignement of local electrostatic potentials, also connected with the handling of charged systems [START_REF] Van De Walle | First-principles calculations for defects and impurities: Applications to III-nitrides[END_REF], was also examined for PDs in CaCO 3 , but the possible offsets (< 0.5 eV) were not found significant with respect to other sources of errors. suggest that, while interstitial diffusion of CO 2 is unfavourable, a strong binding of the CO 2 vacancy may enhance CO 2 diffusion.

Figure 1 :

 1 Figure 1 : Schematics of the rhombohedral unit cell (a 1 ,a 2 ,a 3 ) of CaCO 3 calcite: (a) top view,

Figure 2 :

 2 Figure 2 : From ab initio-based calculations, chemical potentials of gaseous O 2 and CO 2

Figure 3 (

 3 Figure 3 (color online) : Behaviour of interstitial defects in calcite viewed along the [111]

Figure 4 :

 4 Figure 4 : Grand canonical energies of neutral point defects in CaCO 3 , in 2x2x2 Ca 2 C 2 O 6 unit

Figure 5 :

 5 Figure 5 : Validity domain (area surrounded by bold line segments) of O and C chemical

Figure 6 ,

 6 Figure 6, suggesting the importance of the x Ca =1/5 tie-line, and to a secondary extent that of

Figure 6 :

 6 Figure 6 : Survey of composition-dependent structure of neutral point defects of CaCO 3 in

Figure 7 :

 7 Figure 7 : Electronic densities of states for charged defects in calcite: (a) Ca O (q=+1/+2) and

(

  Figure7b): whereas in most cases the Fermi level is located within, or closely above, the valence band, such charged defects correspond to additional peaks of occupied states just below the conduction band. As will be checked below by the detailed analysis of formation energies, this should entail a strong increase of energy cost for these charge levels, and the latter should thus be unstable. For all other PDs and charges, the DOSs (not shown for brevity) sometimes reveal the existence of intermediate peaks located in the gap, especially for C Ca , O C , C O and O int , but contrary to Ca O and V O , the analysis below will indicate no such charge-dependent changes of behaviour for these PDs.

Figure 8 :

 8 Figure 8 : GC energies of charged defects in calcite, from ab initio PAW-PBE calculations

  required for Ca C and Ca O respectively. With a formation energy of ~ 0.5 eV, the Ca vacancy remains by far the most stable PD in CaCO 3 , which is consistent with our previous results obtained from neutral defect analysis, pointing out V Ca as structural defect. This conclusion is not ruled out by charge effects. As for C defects, C Ca and C O have very similar behaviours, being more stable in neutral state, but their energies remain very high. Conversely, V C displays a much lower formation energy (~ 3 eV) and a moderate charge dependence, which should probably turn it into a favourable defect in various conditions. Finally, as regards O defects, V O remains neutral in its most favourable state (E f ~ 4 eV), while O C and O int have very close formation energies (~ 3 eV) and may adopt competing charge levels between -2 and 0, and O Ca requires q = -3 though maintaining a high formation energy (~ 5 eV). Finally, it is worth noting that V O , V C and O int have relatively low formation energies, which makes them good candidates for C and O diffusion in the context of CaO carbonation.

Figure 9 :

 9 Figure 9 : Formation energies of charged and neutral defects in CaCO 3 under "O 2 +CO 2 " (see text) working conditions: T = 800 K, µ(C) = -15 eV, µ(O) = -5 eV, from ab initio PAW-PBE

Further steps towards the

  elucidation of the carbonation mechanism would be related to thorough atomic-scale diffusion studies of the relevant defect species. The goal of these further works would be to reach a comparison of the efficiencies of several diffusion mechanisms for O and C within the carbonate layer. This comparison would allow to select the more efficient mechanism, which would be of direct utility in more macroscopic studies of CaO carbonation by CO 2 . in closer connection with practical issues.CONCLUSIONThe present work was devoted to a thorough atomic-scale study, by means of density functional calculations, of the point defect properties in CaCO 3 calcite. In addition to vacancies and antisite atoms, the stability of interstitials was explored by means of ab initio molecular dynamics, revealing that this possibility should be discarded for Ca and C, ,while interstitial O should be taken into account. The intrinsic complexity of this ternary compound giving rise to a wide panel of point defects, we first investigated neutral defects, which conveniently provided a survey of the influence of the overall compound composition on the point defect properties. This influence appeared as rather complex, with numerous composition domains limited by various tie-lines. This demonstrated the importance of determining the conditions of composition, or equivalently chemical potentials, undergone by CaCO 3 , especially during growth. In the practically important framework of improving our knowledge of CaCO 3 formation from calcium oxide and CO 2 gas, chemical potentials were therefore determined for experimental conditions. In addition, the role of charged defects, well known in semiconductors but far less documented in carbonates, was analysed. This pointed out O and C vacancies as thermally important defects, together with interstitial O. The latter conclusion has important consequences on CO 2 diffusion within CaCO 3 and CaCO 3 growth, since it is consistent with joint C and O diffusion via vacancy mechanisms of roughly equal amplitudes. As regards the possible influence of complex point defects, our results

  , which is the zone where carbonation occurs. The existence of such gradients for C will also be shown to be true in H 2 O + CO 2 conditions, see Table2. Although the same argument cannot be applied to O vacancies under our hypothesis of equal O chemical potential at both interfaces, a driving force for the ext.→ int. O flux may stem from a strong binding between C and O vacancies, as seen below. CO 2 working conditions performed in this section allows to focus on the role of x O = 3x C . Crossing this tie-line may imply deep changes in thermal defects within the calcite layer.In order to explore this possibility, we have checked that small changes of µ(C) entail no change of PD type across the calcite layer.While this work was mainly focused on simple PDs in calcite, our preliminary study of interstitials, stressing Ca and C instabilities, also reveals the formation of complex defects, namely 2C int +V C and Ca C +C int . In the context of CaO carbonation by carbon dioxide, it therefore seems reasonable to consider possible connections between complex PDs and CO 2 diffusion in calcite. Although a detailed investigation of complex defects in CaCO 3 is beyond the scope of this work, two complexes come to mind naturally in this framework, namely CO 2 (i) vacancy and (ii) interstitial. As for the latter case, our investigations suggest that interstitial C should be accompanied by C vacancies, rather than by interstitial O as required in the CO 2 molecule. Confirming this point would imply additional molecular dynamics investigations, in order to attempt to detect possible favourable sites for the CO 2 molecule within the calcite lattice. Leaving this highly exploratory task for future work, we here emphasize the role of the CO 2 vacancy located in a CO 3 plane of CaCO 3 , for which ab initio calculations indicate a strong binding energy ~11.6 eV in neutral form. Comparing this value with the formation energies of the isolated corresponding neutral defects (Figure9) leads to a CO 2 vacancy formation energy below 1 eV, a remarkably low value for such a complex PD, which should entail a strong enhancement of CO 2 diffusion via the complexation of O and C vacancies.

				C Ca	V C
				O Ca	Ca O
				V Ca	C O
				Ca C	V O
				O C	O int
	Table 2 : In H 2 O + CO 2 conditions (P(H 2 O) = 200 Pa, P(CO 2 ) = 2000 Pa) and for T = 800 K,
	influence of H 2 pressure (Pa) on the H 2 , O and C chemical potentials (eV) at the internal and
	external interfaces.
	H 2 pressure	µ(H 2 )	µ(O)(ext/int)	µ(C)(ext)	µ(C)(int)
	10 -3	-7.73	-7.35	-9.22	-9.88
	10 -1	-7.41	-7.67	-8.59	-9.24
	10	-7.09	-7.98	-7.95	-8.61
	While the previous low-T analysis suggested that both the x Ca = 1/5 and x O = 3x C tie-
	lines may be important in determining the PD properties of calcite, the more precise account
	of O 2 +

interfaceFurther insight into this issue would be gained from investigating the diffusion mechanisms in the calcite structure.

Table 3 :

 3 Comparison of PD formation energies (eV) in O 2 + CO 2 and H 2 O + CO 2 working As mentioned in the introduction, it is also useful to consider CO 2 + H 2 O working 2 ) at 800 K and (P(H 2 O) = 200 Pa, P(CO 2 ) = 2000 Pa). From these data, Table 3 then displays the comparison of PD formation energies in O 2 + CO 2 and H 2 O + CO 2 working conditions with µ(C) at the external interface. It shows that the choice of conditions has a strong influence on the PDs. In particular, while V Ca remains dominant in both cases, V C and V O are strongly affected by O 2 vs H 2 O control: whereas the former case corresponds to relatively equal amounts of these defects, the latter deeply breaks the balance in favour of V O while also raising the role of O int . The efficiency of purely vacancy mechanisms for joint O and C diffusion should thus be lowered in H 2 O + CO 2 conditions, the diffusion of O occurring then by interstitial mechanism. Moreover, the P(H 2 ) influence remains quite moderate, which suggests that our conclusions are reliable whatever the experimental conditions for which this parameter remains uncontrolled. Finally, it is useful to emphasize the connection between our work, providing clear-cut trends on point defect properties in CaCO 3 , and the more general context of CaO carbonation by carbon dioxide. The carbonation reaction, which occurs at the internal CaO/CaCO 3 interface, requires diffusion of O and C through the carbonate layer. Since diffusion is mediated by point defects, the present atomic-scale results on point defects in CaCO 3 provide a first, but necessary, step towards this connection. Our work gives hints on how to select those relevant species for diffusion: it indicates that such species could reasonably include O and C vacancies, as well as interstitial O (but not interstitial C) and CO 2 vacancies. As mentioned previously, the case of interstitial CO 2 would deserve separate investigations.

	conditions. The most stable charge level, indicated between parentheses, was selected for each
	defect (for µ(C) at external interface). Values relative to PD relevant for diffusion during
	carbonation are highlighted.
	defect	O 2 + CO 2	H 2 O + CO 2
			P(H 2 ) = 10 -3 Pa	P(H 2 ) = 10 Pa
	V Ca (-2)	0.57	1.0	1.2
	C Ca (0)	13.8	9.3	8.6
	O Ca (-3)	4.5	6.9	8.7

conditions, which correspond to carbonation performed under controlled water, rather than oxygen, pressure. These conditions are important in practice

[START_REF] Nikulshina | Kinetic analysis of the carbonation reactions for the capture of CO 2 from air via the Ca(OH) 2 -CaCO 3 -CaO solar thermochemical cycle[END_REF]

, previous works indicating gas pressures P(H 2 O) = 200 Pa and P(CO 2 ) = 2000 Pa as efficient for CaO carbonation. The O chemical potential µ(O) is determined via the dissociation equilibrium of H 2 O, which

however leaves the H chemical potential undetermined. In the present work, the latter was therefore considered as a parameter controlled by H 2 gas. To elucidate the influence of this parameter, we studied (Table

2

and thin lines on Figure

5

) the variation of µ(C) and µ(O) with µ(H