Élie Bouttier
email: elie.bouttier@enseeiht.fr

Riadh Dhaou

Fabrice Arnal
email: fabrice.arnal@thalesaleniaspace.com

Cédric Baudoin
email: cedric.baudoin@thalesaleniaspace.com

Emmanuel Dubois
email: emmanuel.dubois@cnes.fr

André-Luc Beylot
email: beylot@enseeiht.fr

Improving content delivery with size-aware routing in hybrid satellite / terrestrial networks

As Internet usages expand quickly, access networks are modernized with new technologies like fiber-optic communications. However, upgrade costs are prohibitive in sparsely populated areas, the latter turning notably towards satellite connection. Indeed, this technology allows deploying a highthroughput Internet access quickly in these regions. Nevertheless, GEO satellites induce a long delay, not experienced on terrestrial infrastructures despite their low throughput.

In this paper, we consider a heterogeneous network with both a satellite and a terrestrial path. This kind of architecture is known to be difficult to operate because of the important differences between used technologies. The emerging Multipath TCP (MP-TCP) transport protocol, whose design enables to aggregate disparate paths properly, brought new hopes for heterogeneous networks. However, it does not take user Quality of Experience (QoE) into account as it focuses on maximizing the links occupancy.

This paper proposes an intelligent path selector using the content size to maximize users QoE in heterogeneous networks. Before detailing this method, we describe the architecture able to retrieve the size of delivered contents thanks to Content Delivery Network Interconnection (CDNI). Finally, we implement a testbed to evaluate the behavior of the proposed routing method. The results show a significant improvement of the delivery performance, outperforming MP-TCP.

I. INTRODUCTION

The massive increase of Internet usage leads to a rise of networks requirements. Legacy Asymmetric Digital Subscriber Line (ADSL) access networks are not able anymore to adequately satisfy users needs. Therefore, they are gradually upgraded mainly in favor of fiber-optic communications. However, for economic reasons, operators target densely populated areas while the countryside stays poorly served.

As a result, many users in these regions turn towards satellite Internet access which offers a high bandwidth broadband access without the need for very long and expensive works. However, the propagation delay to the geostationary orbit has a substantial negative impact on the user experience. Indeed, many services are highly sensitive to the delay, especially interactive services like VoIP or video games but also web browsing which requires numerous connections to retrieve a large number of contents. Moreover, HTTP relies on the Transmission Control Protocol (TCP) which is constrained by the delay, notably due to the initial handshake and the slowstart period. The common use of the Transport Layer Security (TLS) protocol adds another extra handshake.

From these observations, the short delay of long lines ADSL connections appears as a notorious advantage despite the limited throughput. Then, it becomes interesting to combine both networks with an intelligent routing to make use of the special benefit -capacity or short delay -of each network.

Multipath networks have been subject to numerous studies. However, heterogeneous systems, combining paths with different characteristics, bring some particular issues. Hybridization techniques mostly operate at layer 2 for local networks and layer 3 for global networks. But the widespread TCP protocol operates poorly in the presence of packet reordering, introduced by the difference of delay between the various disparate paths. Therefore, aggregation at these levels is excluded and load-balancing is limited to the flow decision scale.

Multiple load-balancing algorithms exist, such as classic Round-Robin (RR) or hash-based schedulers [START_REF] Qadir | Exploiting the power of multiplicity: A holistic survey of network-layer multipath[END_REF], and their implementation have been standardized through several protocols such as Link Aggregation Control Protocol (LACP), Shortest Path Bridging (SPB) or Enhanced Interior Gateway Routing Protocol (EIGRP). The new transport protocol MP-TCP [START_REF] Paasch | Multipath tcp in the linux kernel[END_REF] stands out and can aggregate heterogeneous paths by re-ordering the data at the receiver. The protocol knew significant improvement with the minRTT scheduler and the Opportunistic Linked-Increases Algorithm (OLIA) for congestion control which is inspired by [START_REF] Kelly | Stability of end-to-end algorithms for joint routing and rate control[END_REF] and brings pareto optimality. It is still evolving with new propositions such as the Blocking Estimation-based (BLEST) scheduler [START_REF] Ferlin | Blest: Blocking estimation-based mptcp scheduler for heterogeneous networks[END_REF] or Weighted Vegas (wVegas) [START_REF] Xu | Delay-based congestion control for mptcp[END_REF] and Balanced Linked Adaptation (BALIA) [START_REF] Walid | Balanced linked adaptation congestion control algorithm for mptcp[END_REF] congestion control algorithms.

However, neither routing algorithms nor MP-TCP takes into account application-level flow information as they focus on network metrics and resource utilization. Though, they can be used to improve the end-user experience significantly as proposed in the BATS Project [START_REF]D3.3.2 multi access networking architecture[END_REF] or sketch in [START_REF] Bouttier | Analysis of content size based routing schemes in hybrid satellite / terrestrial networks[END_REF] in a simplified unrealistic case using the UDP transport protocol.

In this paper, we propose a multipath routing algorithm, MinFCT, to enhance the performance of hybrid satellite / terrestrial networks. Thanks to CDNI, requested contents size can be retrieved. This information is then used by MinFCT to estimate the Flow Completion Time (FCT) and take the best possible routing decision, achieving an outstanding performance increase.

We start the paper by describing the proposed hybrid architecture. In part II, the MinFCT routing strategy and its Flow Completion Time estimation method are described. Afterward, we present our implemented experimental testbed and then the obtained results. Finally, we conclude on the large benefit of the MinFCT algorithm.

II. ARCHITECTURE

This section describes a multipath architecture enabling a home network to access the Internet through a terrestrial and a satellite path.

A. Hybrid architecture

In the hybrid architecture represented in figure 1, the enduser is not directly connected to any of terrestrial or satellite networks but instead is attached to a virtual Internet Service Provider (ISP) through a proxy called Intelligent User Gateway (IUG) reusing the terminology introduced in BATS [START_REF]D3.3.2 multi access networking architecture[END_REF]. The IUG is itself virtually connected through both access networks to its counterpart in virtual ISP networks, the Intelligent Network Gateway (ING).

By splitting the end-to-end connections, the IUG and ING can use any transport protocol on each path, such as TCP or SCTP [START_REF] Stewart | Stream control transmission protocol[END_REF]. Thus, the Intelligent Gateways operate in a transparent way for the end-user and the destination, while the data can be spread over the multiple underlying paths.

B. CDN Interconnection (CDNI)

We propose to retrieve content information, and especially content size, from Content Delivery Networks (CDNs). Indeed, CDNs know a lot of information about hosted contents such as file size but also content type, video bitrate, etc. On the other hand, more and more contents are subject to caching nowadays, increasing the scope of this approach. To retrieve CDNs have been introduced as a solution to solve new delivery issues due to the increase in bandwidth usage [START_REF] Peng | CDN: Content Distribution Network[END_REF]. They are composed of several cache servers called edge servers deployed in strategic places. Content requests from end-users are redirected to the closest edge server, reducing the experienced delay, the network usage, and the load of the origin content servers. Content providers delegate content delivery to CDN operators through service agreements.

Edge servers are usually located at the Points-of-Presence (POPs) on the Internet, allowing CDN operators to peer directly with ISPs avoiding transit delay and cost. However, POPs are still far away from end users. There is a trend to get edge servers closer to the user by placing them in access network. Sometimes, CDN operators provide cache servers to ISP to add them to their network. However, this approach is limited: these cache servers only enable to serve content from one CDN operator. Furthermore, they are still managed by CDN operators whereas ISPs have a better knowledge of their network and possible optimizations.

For these reasons, ISPs are interested in deploying their CDN inside their network (Telco CDN) to directly handle content requests from their users. These deployments are formalized through content delivery agreements between CDN operators and Telco CDNs. Thenceforth, content requests originating from the ISP are redirected by the CDN operator to the Telco CDN.

Such an agreement comes with the need to communicate several pieces of information between both CDNs: source IP address of content requests to redirect, redirection end-point, authentication, bandwidth limitations, . . . The CDNI Working Group at IETF is currently working on standardized interfaces to allow CDNs to communicate such information and encourage democratization of CDN interconnections. Four interfaces (using JSON over HTTP) have been defined including among others the Request Routing interface (RR) and the Metadata Interface (MI) [START_REF] Niven-Jenkins | Content delivery network interconnection (cdni) metadata[END_REF]. Thereby, the information that we need for routing can be easily recovered through the MI interface.

In our case, we assume the virtual ISP operates his Telco CDN interconnected with several upstream CDNs.

III. THE MINFCT ROUTING STRATEGY

The proposed routing strategy is called MinFCT which stands for Minimum Flow Completion Time. This strategy is in charge of the load balancing between the terrestrial and the satellite paths. It operates at the flow-level which means that all packets belonging to the same flow are sent on the same path. Indeed, aggregation of the same flow on different path turns out to be counterproductive, especially by increasing terrestrial congestion [START_REF] Bouttier | Heterogeneous multipath networks: Flow vs packet based routing in a size-aware context[END_REF]. Therefore, the routing decision is taken only once for each content.

The routing scheme aims to minimize the Flow Completion Time (FCT). Indeed, it is a homogeneous criterion to evaluate the performance of our multipath network, relevant for both delay sensitive flows and elastic traffic. For this purpose, the FCT is estimated on each path, the one that minimizes it being selected. The estimation method is based on the flow size and various path information: capacity, delay, loss rate and the number of flows sharing the path.

A. Estimation of path characteristics 1) Delay:

The path delay is merely estimated from TCP handshakes. This value could be temporally averaged and smoothed but our experiments did not show the need for it.

2) Capacity: On the satellite path, the capacity is supposed known. Indeed, satellite systems are very integrated, with a lot of interaction between different components. For instance, Performance-Enhancing Proxies (PEPs) could be coupled with resource allocators to obtain available capacity for the given user. We supposed this kind of cooperation with our proxy.

Of course, this method can not be implemented on the terrestrial path. A capacity estimation from TCP stack information has been considered, but this information turns to be highly unreliable. Indeed, as the traffic often presents a lot of short flows, the TCP congestion control is not reached or does not have time to converge.

Instead, the capacity is estimated from TCP acknowledgment (Ack) packets passively observed on the path near the gateway. Each TCP flow is tracked, the last acknowledged segment being recorded and updated when an Ack is observed. The distance between the previous and the new values indicates the number of bytes successfully received by the terminal. Finally, the total amount of acknowledged data is averaged on a sliding temporal window.

The estimated throughput is reasonably accurate but delayed by the path delay and recovery period after losses. Indeed, when a loss occurs, the following segments are acknowledged with the sequence number of the lost segment, no longer allowing estimating received data. The SACK option introduced in RFC 2018 [START_REF] Mathis | Tcp selective acknowledgment options[END_REF] adds thinner per-block acknowledgment and could be used to reduce the delay of the estimation introduced by losses.

3) Loss rate: The loss rate is estimated from duplicates TCP acknowledgment (DupAck) detected during the passive capacity estimation. When a DupAck is observed for a given flow, a loss is recorded, and the flow is marked in recovery. Subsequent DupAcks are ignored until a new segment is properly acknowledged, the recovery mark being removed. The loss rate is deducted from the recorded losses and the number of packets sent by the gateway to the terminal. As for capacity, the loss rate is averaged on a sliding temporal window.

This method somewhat underestimates the loss rate as multiple losses can occur in the same flows, but only one is recorded per recovery time. Precision could be improved by decoding the TCP SACK option field but at the cost of a substantial increase in the implementation complexity. Nonetheless, the estimated loss rate is quite accurate and completely sufficient for the operation of MinFCT.

4) Concurrent flows count:

In order to find out the individual available capacity for a given flow, the overall path capacity is divided by the number of flows competing for a given path. The proxy easily knows the number of flows affected to a given path, but it turns out to be an overestimation of active flows. Indeed, some flows are waiting for their initial handshake to complete and others, although having no more data to send, are still waiting for the acknowledgment of infly data. Therefore, only flows with a completed handshake and pending data, in applicative or TCP buffers, are taken into account. On congested links, defined here by a loss rate higher than 1%, flows with unacknowledged in-flight data are also taken into account as probably retransmitting.

B. Flow Completion Time (FCT) estimation

The literature proposing TCP performance models is based on an idea first published in [START_REF] Mathis | The macroscopic behavior of the tcp congestion avoidance algorithm[END_REF]. But they focus on the longterm behavior and rely on the loss rate which varies greatly and depends on the activity of several concurrent flows. Therefore, we propose our own FCT estimation method applicable to the MinFCT routing decision scheme.

The Flow Completion Time is estimated mainly from the content size, the path delay and the individual capacity available for the considered flow. It is computed as the sum of the times of the multiple steps of the TCP connection and other factors influencing the completion time:

• the initial handshake • the transmission time and the propagation time • the additional time due to the slow start • the additional time suffered by competing flows • the retransmission time due to losses These different times are computed as follow: 1) Initial handshake: naturally three times the path delay.

2) Transmission time: computed with the following formula:

e = ( + 1) ⋅ s (1)
with the number of competing flows on the path , the size of the content and the overall capacity of path .

3) Propagation time: once the path delay. 4) Slow start: Especially on paths with a large bandwidthdelay product, for instance satellite paths, the TCP connection can stay in the slow-start phase for a long time before reaching the congestion control. The slow-start phase is characterized by several round-trip times (RTTs) that increase the FCT by that much. To take the additional time into account, we compute the maximal congestion window (cwnd max) before entering the congestion control and estimate the number of required RTTs to reach it. The cwnd max, expressed in segments, is proportional to the per-flow bandwidth-delay product:

cwnd max = 2 mss ⋅ + 1 (2)
with usually a maximum segment size (MSS) of 1448 bytes per segment. The number of required RTTs is thus:

RTT (cwnd max ) = ceil { log 2 ( max ( 1, cwnd max initcwnd
))}

(3) with an initial congestion window (initcwnd) of 10 segments as defined in RFC 6928 [START_REF] Chu | Increasing tcp's initial window[END_REF]. However, the maximum cwnd is not necessarily reached for short flows. The maximum number of RTT regarding the flow length is:

RTT (end) = floor { log 2 ( 1 + /mss initcwnd )} (4)
Finally, the additional time introduced by the slow start is:

ss = 2 ⋅ ⋅ min { RTT (cwnd max ), RTT (end)} (5)

5) Additional time suffered by competing flows:

Assigning a new flow to a path results in a decrease of individual available capacity of competing flows, thus increasing their completion time. This additional time can be estimated with the following formula:

comp = ∑ =1 min( , ) (6)
with ranging all flows affected to the same path and being the remaining amount of data waiting to be sent for the flow .

6) Additional times due to losses: Each sent packet can be lost and must then be retransmitted, several times if necessary. The number of transmission of a packet has a expected value of 1 + + 2 + . . . = 1 1-= T with the loss rate of the considered path. Therefore, a flow of length will require on average to transmit ⋅ bytes before a successful reception. Thus, all sizes , or , present in formulas (1), ( 4) or ( 6) are multiplied by the quantity T.

Besides, retransmissions add extra round-trip times, equals on average to l = 2 ⋅ ⋅ T.

Finally, the selected path is the one which minimizes the estimated Flow Completion Time:

= argmin { 4 ⋅ + e + ss + comp + l } (7)

IV. TESTBED ARCHITECTURE

A. Architecture

The performance of MinFCT is compared to MP-TCP experimentally on a testbed schematized on figure 2. A test client requests contents from a content server through the Intelligent User Gateway using the SOCKS5 protocol. The gateways are interconnected with two links; the latency is emulated with the Network Emulator (netem) Traffic Control (tc) queueing discipline (qdisc) and the capacity with the Token Bucket Filter (tbf) qdisc.

B. Test client

The test client is composed of threads imitating the activity of users. Each thread follows a cycle of requesting an object, waiting for its reception, and finally waiting during a random period modeling the processing of the object.

C. Passive Throughput and Loss rate Reckoning (PTLR)

The throughput and loss rate estimations are done in the same tool. This standalone program runs multiple times, once per path, each instance estimating the parameters of its path.

Packets are captured with libpcap. Decoded events (data sending, data acknowledgment or losses) are timestamped and saved at the end of a circular resizable buffer. Periodically, e.g. every 100ms, path characteristics are recomputed and shared with the gateway proxy through shared memory. Before each recalculation, the beginning of the buffer is cleared from outdated values, older than the averaging window. For improved performance, the metrics are computed from aggregated values, like total recorded losses, which are refreshed on every buffer update.

D. Intelligent Gateways

Proxies are implemented in C with asynchronous programming using libevent2. The path RTT is obtained with the tcpi_rtt member of the Linux tcp_info structure which contains a lot of informations about the TCP stack internal state. The structure is retrieved with a simple getsockopt function call for the TCP_INFO option at the SOL_TCP level. The value is retrieved each new connection and smoothed like the SRTT in RFC 6298 [START_REF] Paxson | Computing tcp's retransmission timer[END_REF].

V. RESULTS

A. Experimental parameters

We consider, for our experiments, a terrestrial path characterized by a delay of 25 ms and a download capacity of 2 Mbps, and a satellite path characterized by a delay of 300 ms and a download capacity of 8 Mbps. We do not limit upload capacity as this direction is not part of our study. The tbf qdisc is configured with a peak rate set to 150% of the capacity, a buffer also known as burst, set to the amount of data transmitted during 10ms at the maximum capacity rate and a queueing capacity limit set to 40ms for the terrestrial path and 160ms for the satellite path.

Single-path experiments are conducted with TCP cubic between both gateways, the connections are not end-to-end and initiated by the terminal. The MP-TCP version used is 0.92.1 under Linux 4.4.83 with the OLIA congestion control algorithm (wVegas and BALIA give similar results) and the default "lowest RTT" scheduler. The fullmesh path manager is used, with two IP addresses on the gateway but only one locally visible on the terminal. MinFCT also relies on TCP; two connections are initialized in parallel, one on each path, the request being always sent by the IUG on the terrestrial path and the answer being sent on the path selected by ING with the MinFCT algorithm. Contents size is a multiple of the MSS (1448 bytes) and the number of packets follows a Zipf law with a parameter equal to 1.8 and shifted to a minimum of 8 packets. Between two requests, each user observes an exponential time with an average of 1 second.

B. Comparison of MinFCT with different strategies

1) Average Flow Completion Time: Figure 3 compares the average Flow Completion Time between MinFCT and MP-TCP hybridization methods, as well as standalone terrestrial and satellite paths using regular TCP, and this for different numbers of users in the system.

On the terrestrial path, we observe a very small average FCT for few users, thanks to the short path delay. However, there is a quick increase of the FCT as the number of users increases, the path being quickly saturated due to its small capacity. The gradient of the increasing FCT is related to the average flow length and the capacity of the path.

Oppositely, we observe an important average FCT for few users on the satellite path. Indeed, the FCT is bounded by the long path delay. Nonetheless, thanks to the high capacity, the satellite link can adequately fulfill users' requests for a relatively large amount of users. The link becomes saturated only when reaching 100 users. Also, the slope of the saturated portion of the curve is lesser than on the terrestrial path due to the higher path capacity.

The MP-TCP transport protocol shows its ability to improve the terrestrial path performance by aggregating the flows on the satellite path. However, only largest flows are concerned due to the "lowest RTT" MP-TCP scheduler. This scheduler sends a content on the path with the minimum Round-Trip Time, e.g. the terrestrial path. When the TCP buffer of the sub-flow is full, the scheduler starts sending the rest of the content on the satellite path. This operation has the major property of avoiding sending any parts of very short flows on the satellite path, which would have drastically increased the average FCT. Indeed, it would then be necessary to wait data flows in-flight on the satellite path. Nonetheless, MP-TCP performance deteriorates with the load increase, not so much, but similarly to the use of the single terrestrial path. Indeed, the terrestrial network is heavily congested as all flows try to use it. As a result, the terrestrial path becomes unreliable, increasing the time necessary for connections setup and due to retransmissions.In addition, MP-TCP has specific mechanisms (cookies, losses handling, fallback to regular TCP. . . ) which translates, with the congestion, into broken connections. Experiments with troubled connections are not represented as long flows are more likely to be subject to reset, distorting the results.

The MinFCT hybridization method dramatically outperforms all other schemes. For 30 users, the FCT is reduced by 32% compared to MP-TCP, 46% compared to the satellite network and 66% compared to the terrestrial network. This good performance is explained by several reasons. First, Min-FCT avoids sending short flows on the satellite path when the transmission time is lower than the satellite delay. Then, as the load balancing is achieved at the flow-level, the terrestrial path is fully dedicated to flows that are not subject to the satellite delay. This method also asserts a sustainable congestion level on the terrestrial path, preventing its counterproductive use. By sending smallest contents on the terrestrial path, MinFCT increases the number of flows that benefit from the short delay, which improves the average performance.

With only one user, terrestrial, MP-TCP and MinFCT results are very close. Although hardly observable, MinFCT slightly beat the terrestrial network by sending large flows on the satellite path, and is slightly beaten by MP-TCP which aggregate large flows. Under congestion, we observe an asymptotic improvement of MinFCT against the satellite network about 20%, corresponding to the ratio of path capacities.

2) Average flows size: Figure 4 shows the average flows size on the terrestrial and satellite path.

With a single user in the system, there is no congestion, and best routing decision is always taken. Therefore, short and medium flows are routed through the terrestrial path while only longest flows are routed through the satellite path. As the number of users increases, as the congestion on the terrestrial path, medium flows and even part of the short flows become routed through the satellite path. As a result, we observe a decrease of the average flows size on terrestrial and satellite paths.

When the number of users exceeds 140, the satellite path becomes also congested. Medium flows become partly routed through the terrestrial path again causing an small increase of the average flows size on the terrestrial path. As the satellite path is still used for many medium and short flows, overrepresented due to the Zipf law, we observe no visible increase of the average flows size on this path.

3) Paths occupancy rate: On figure 5, we observe the path occupancy ratio, defined as the average transmitted rates divided by the path capacity. We compare one path strategies with the MP-TCP and MinFCT strategies.

With the MinFCT scheme, the terrestrial path is congested from about 40 users whereas, when using the terrestrial path only, it is congested starting at 20 users. On the satellite path, we observe a reduced use of the available capacity, many short flows being sent on the terrestrial path. We with MP-TCP a consequent congestion of the terrestrial path while the satellite path is underused. This behavior has already been pointed out as the main reason for MP-TCP bad performance.

CONCLUSION

In this paper, we presented an architecture and a routing method allowing to take advantage of a heterogeneous network, composed of a terrestrial path and a satellite path. Contrary to other approaches, this method takes into account flows size to minimize the Flow Completion Time. For that, we presented an architecture able to retrieve flows size through Content Delivery Network Interconnection. We outlined a method to estimate the path delay, capacity and loss rate and finally an algorithm to reckon the Flow Completion Time considering the estimated path characteristics and the flow size. Finally, we have implemented a testbed and have evaluated our proposed routing method by comparing its performance to that of single path routing strategies and of the MP-TCP transport protocol.

Our results show the significant improvement brought by our size-aware routing compared to the MP-TCP approach. Though, many improvements are considered, in particular improving path metrics gathering, especially at low loads, or fine-tuning the estimation algorithm to take better decisions. The interconnection protocol of the Intelligent Gateways is subject to many enhancements, with the use of alternative transport protocols like SCTP or QUIC, the use of TCP Fast-Open or even the implementation of a reusable connection pool. Also, we plan to evaluate the performance of the method with different traffic laws and parameters, as well as different path characteristics. Finally, the method could be extended to non-CDN context with a different source of information for the size knowledge or its estimation.

Fig. 1 :

 1 Fig. 1: Hybrid architecture

Fig. 2 :

 2 Fig. 2: Experimental testbed architecture.

Fig. 3 :

 3 Fig. 3: Comparison of average Flow Completion Time with MinFCT, MP-TCP, TCP over the terrestrial path only and TCP over the satellite path only.

Fig. 4 :

 4 Fig. 4: Average flow size on each path with the MinFCT scheme.

Fig. 5 :

 5 Fig. 5: Occupancy rate for terrestrial and satellite path, considering routing through the terrestrial path only, satellite path only, with MP-TCP or with the MinFCT algorithm.


Leonie Gomell

Shyam Katnagallu

Abou Diack-Rasselio

Stefan Maier

Loic Perriere

Christina Scheu

Eric Alleno

Baptiste Gault
email: b.gault@mpie.de

Abou Diack

Loïc Perrière

Chemical segregation and precipitation at anti-phase boundaries in thermoelectric Heusler-Fe2VAl

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The necessity for generating low-carbon energy has led to extensive research in the field of thermoelectric (TE) materials in recent years. TE devices can directly transform waste heat into usable energy, are silent, scalable, and barely require any maintenance [1]. However, TE generators are still primarily used in niche applications, e.g. remote power supplies, such as in deep-space missions [2], where no other energy generation methods are available. Other possible applications such as automotive TE generators or solar thermal power generation are conceivable, but technological hurdles need to be overcome [3]. State-of-the-art TE materials such as Skutterudites [4], Bi2Te3 [5], Sb2Te3 [6], or TAGS [7] show good TE properties, but are expensive and toxic, hindering their wider applicability.

Alternative TE materials must be developed for a cost-effective, non-toxic, and scalable energy production. A promising material, which displays a good power factor (> 5 mW m -1 K -2 at 300K), is the Heusler compound Fe2VAl [8]. Fe2VAl is highly durable [9] and contains earth-abundant elements. It is a semimetal with a sharp pseudogap, which is favorable for TE applications [10,11].

Although the power factor is high, its high thermal conductivity (κ) is the major limiting factor in its TE performances [8]. Different routes to enhance phonon scattering and decrease κ have been investigated, such as doping [10,[12][13][14], off-stoichiometry [15,16], introduction of defects and exploiting disorder in the structure [17][18][19][20].

Another, not as widely studied way of introducing phonon scattering centers is to introduce interfaces, and in particular antiphase boundaries (APB). APBs can be generated inside the L21 Heusler phase by fast quenching from high temperatures, where Fe2VAl is stable in two variants: partly disordered B2 and fully disordered A2, as described by Maier et al. [19]. A method for achieving the necessary high cooling rates is melt spinning, where the melt is dropped onto a cooled, rotating metallic wheel and leading to rapidly quenched flakes of the material. A schematic of two antiphase domains (APD) in the L21 phase separated by an APB is visualized in the supplementary figure S1a. The APDs can be converted into each other by a {100}B2 translation, which exists in the disordered B2 structure but is missing in the ordered L21 structure [21]. Another possible interface (Fig. S1b) is a coherent order-disorder boundary. The ordered L21 phase and disordered B2 or A2 phase are coexisting without a change in the crystallographic orientation.

Here, we show evidence for segregation and precipitation in the bulk and at interfaces in melt spun Fe2VAl. We cannot differentiate specifically between different coherent interfaces, and for readability, boundaries observed and discussed herein will be referred to as APBs. Using scanning electron microscopy (SEM), atom probe tomography (APT) and field ion microscopy (FIM), we report on vanadium carbides and vanadium nitrides at APBs. These could act as phonon scattering centers and hence open opportunities for further microstructural adjustments for lowering the thermal conductivity. Stoichiometric Fe2VAl was synthesized by melt spinning. The pure elements Fe (Strem Chemicals, 99.95 %), V (Chempur, 99.9%), and Al (Alfa Aesar, 99.9965%) were melted together and subsequently ejected at 1490 °C onto a water-cooled, rotating CuCoBe wheel spinning at 24.5 m/s, ensuring a fast quenching rate. This process leads to approximately 20 µm thick flakes. Inductively Coupled Plasma Optical Emission Spectrometry determined the average chemical composition to be Fe50.54V24.81Al24.65 (at.%). X-ray diffraction (XRD) indicates the presents of the L21 ordered phase (Fig. S2). However, the co-existence of B2 and A2 phase cannot be excluded from the XRD pattern.

Microscale analyses of the microstructure were performed using scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDX) using a Zeiss 1540 XB SEM. The samples were analyzed as-cast without any polishing, and after hand grinding to observe the microstructure on the surface and inside the sample. The sample was initially prepared using SiC papers and final polishing was done using a colloidal silica suspension (0.25 µm) in a vibrating polishing machine (Buehler Vibromet 2).

Near-atomic scale investigations were performed using field ion microscopy (FIM) and atom probe tomography (APT). Needle-shaped specimens for APT and FIM were prepared using a dual-beam focused-ion-beam (FIB) instrument (FEI Helios Nanolab600i) with a Ga ion source or an FEI Helios Plasma-FIB with a Xe-plasma ion source by an in-situ lift-out method and a subsequent sharpening process [22]. For correlative FIM/APT analysis, a LEAP™ 5000 XS (Cameca Instruments) was used. APT was conducted in voltage pulsing mode using a pulse repetition rate of 125 kHz and a pulse fraction of 15%. For FIM, Ne was used as an imaging gas to image the sample surface at 50K. The Ne gas pressure while imaging was kept at 1•10 -7 mbar and, when possible, images were acquired at the best imaging voltage. APT measurements were also performed on a LEAP™ 5000 XR (Cameca Instruments) in laser-pulsing mode. The laser power was set to 25 pJ and the repetition rate was 250 kHz. For both APT measurements, the base temperature of the specimen was kept at 60 K and a target detection rate was set to 0.5%. The IVAS 3.8.4 software and MATLAB 2017a were used for data reconstruction and analysis. 2)). The SEM image used for the analysis of the mean grain sizes is shown in the supplemental data Fig. S3. Both layers are visible due to the interaction volume of the electron beam and the material, which is in the order of 1 µm for an acceleration voltage of 15 kV and therefore can penetrate the flake deeper than the mean thickness of the surface grains. Fig. 1b shows a polished surface, where only the regular grains are observed as the surface layer is polished away.

The small surface grains can also be seen in Fig. 1c on the edge of the flake (4), where they are observed from the surface (3) and the cross section (5). All SEM images show platelet-like precipitates, not only at the grain boundaries but also inside the grains. These precipitates are highlighted by white circles. The precipitates within one grain are oriented either parallel or perpendicular to each other (Fig 1a,c), but their orientation differs between grains (Fig 1a). This indicates that the orientation of the precipitates is dependent on the crystallographic orientation of the grains. The 90° angle between precipitates within one grain (Fig 1c) could indicate that the precipitates are on (100) planes. The average size of these precipitates is 120 × 40 nm 2 and they are separated by a mean distance of (140 ± 40) nm.

APT and FIM are used to confirm the presence of ordered phases and antiphase boundaries while analyzing the elemental distribution at the near-atomic scale. A field-ion micrograph is displayed in Fig. 2a. It shows two ordered domains separated bright-imaging feature and indicated by black arrows. The ordering of the right domain is revealed for instance by the relative contrast at the (111)-pole [23]. It consists of rings with alternating intensities, indicating planes with different atomic occupancies. This is true for the L21 phase, where a {111} plane, occupied by Fe atoms, sandwiches alternating Al and V planes, as visualized in Fig. 2b. The B2 phase consists of {111} planes occupied by Fe, followed by planes with a mixed occupancy of Al and V. Thus, only the A2 phase can be excluded from this FIM micrograph. The rings formed by {110} planes do not show any alternating intensity, as the planes are occupied with Fe, V, and Al, even in L21 ordering. The other domain on the left part of the micrograph shows the (100) pole. Ordering on that pole cannot be directly observed because of the small interplanar distance and associated limited resolution.

The two domains appear coherent, as evidenced by the pattern continuity at the (101) pole across the interface. The contrast of the interface indicates that it is decorated by high-evaporation field elements. This coherent boundary is likely a typical APB (Fig. S1a) or an interface between an ordered and a disorder region (Fig. S1b).

Fig. 2. a) FIM micrograph showing two domains separated by a coherent boundary. The boundary is marked by the arrows. The (111) pole shows rings with alternating intensities due to an ordering of the (111) lattice planes. (b)

Visualization of the {011} and {111} planes of the L21 phase. Fe, V, and Al are symbolized by blue, green, and orange spheres, respectively. The {011} plane shows a mixed coverage on parallel planes. On {111} planes, a plane occupied by Al is followed by a Fe-plane (half-transparent spheres), which is followed by a V-plane (green circles). The side view is rotated by 90° with regards to the top view, showing the crystallographic sequence of the corresponding planes, which are indicated by the black lines.

Correlative APT and FIM is shown in Fig. 3: FIM was performed before and after APT as indicated by the light blue and dark blue circles, respectively. During the APT measurement, approximately 56.7 million ions were detected and the analysis was stopped when a strong planar segregation appeared. The specimen fractured before FIM could be performed in the best imaging conditions, yet poles observed in both FIM micrographs are at the same positions, and can be indexed according to their Miller indices (Fig. 3a). The (111) pole, exhibiting a 3-fold symmetry, is observed near the center. The planar feature seen in APT appears as a brightly-imaging feature across the field-of-view in the second FIM image. The poles on either side of this feature seem to be at the same position, which indicates no change in the crystallographic orientation across this interface, which reinforces the likelihood that this is an APB. The crystallographic orientation of the APB can be observed in the AP reconstruction. A desorption map before and at the APB is shown next to the reconstruction (Fig. 3b). The different poles can be indexed similarly to the FIM micrographs.

Within the vicinity of the poles, the crystallographic planes can be indexed [START_REF] Gault | Atom Probe Microscopy[END_REF], which allows us to determine that this APB lies on the (010) planes.

The AP reconstruction of a small region across the boundary shows (011) planes on either side of the boundary (Fig. 3d). The angle between the APB, visualized by the iso-composition interface, and the planes is approximately 45°, which supports the (010)-orientation of the APB. The spatial distribution map, visualizing the distance of the planes on either side of the boundary is given in the supplemental figure Fig. S4. This further indicates that same sets of planes are imaged on either side of the APB as their separation is similar.

As shown in Fig. S1 an APB can exist without any change in the chemical composition. However, similar to grain boundaries, an energetically driving force for segregation exists at an APB and was analyzed theoretically for Fe3Al [21]. The APB appears to the segregated to a point where they can trigger precipitation of VCxNy. Here, we observe coherent precipitation of V, C, and N in the form of VCxNy, as evidenced by the iso-composition interface in the AP reconstruction (Fig. 3c). The iso-composition interface marks regions with a concentration of C, N, VC, and VN-ions of at least 3 at.%. Within the matrix, a smaller spherical VNy precipitate is found, which is also shown by the iso-composition interface. A closer look at an APB in another dataset is shown in Fig. 4. A set of iso-composition surfaces, with the same threshold as in Fig. 3, highlights two larger and a smaller platelet-shape precipitates (Fig. 4c). The density map on either side of the APB shows a continuity of the position of the (100) pole (Fig. 4a). Within a region-of-interest close to the pole, the planes and the APB appear parallel, as shown in Fig. 4b, confirming that the APB lies on the (100) planes. A composition profile was calculated along a 20 nm-diameter cylindrical region-of-interest with a step size of 0.3 nm (Fig. 4d). On either side of the APB, the composition is near-stoichiometric. In the vicinity of the APB, highlighted by the gray box, an enrichment of V, C, and N is observed, and its composition is (63.2 ± 1.7) at.% V, (13.5 ± 1.1) at.% N, (9.6 ± 0.9) at.% C, (8.2 ± 0.8) at.% Fe, and (5.3 ± 0.7) at.% Al.

These suggest precipitates with a stoichiometry close to (V,Fe,Al)3(C,N). Along the APB, outside of the precipitate, the concentration of C and N is small with (0.10 ± 0.02) at.% and (0.08 ± 0.01) at.%, respectively. Here, carbon and nitrogen were not intentionally added to the material. However, both elements are common impurities in commercial vanadium and iron pellets and may originate from the atmosphere during the processing. Due to the high affinity of vanadium to carbon, it can form carbides at temperatures of 800-1000 °C during the melt spinning process. It can also react with nitrogen at temperatures above 800 °C [25]. The tendency for segregation can be related to the relatively high APB energy of Fe2VAl is 0.27 ± 0.04 J/m² for a ( 𝑎 2 ) ⟨111⟩(011) APB [26], compared to e.g. 0.08 ± 0.025 J/m² for Fe3Al [27]. The high APB energy can act as a driving force for a segregation, as segregation to APB can reduce its energy [28,29]. It was shown, that Cr segregation to APBs in Fe3Al can either reduce or enhance the APB energy, depending on the position of the impurities within the matrix [27]. The locally higher composition in V, C, N can help trigger further precipitation [30]. For Fe3Al, Koizumi et al. [31] described a stabilization of APBs due to segregation of solute atoms and vacancies.

The high affinity of vanadium to form carbides and nitrides offers opportunities to intentionally add C and N and trigger additional precipitation. Carbides and nitrides might further increase phonon scattering and have interesting effects on the transport properties of the material. This combination of nanoprecipitates and APBs should reduce the thermal conductivity. To have a significant influence, the mean phonon free path needs to be longer than the mean distance of the precipitates. For Fe2VAl at room temperature, the mean free phonon path was estimated to be 2.4 µm. The mean distance ~140 nm of the platelet-shaped precipitates could be observed in the mesoscale SEM images and is smaller than the phonon mean free path. Additionally, the plateletshaped precipitates located at APBs, which give rise to another phonon scattering center. The experimental investigation and calculation of the thermoelectric properties of Fe2VAl, considering the APB and VCxNy precipitates, are presently beyond the scope of this paper. Nonetheless, they will be part of future work.

To summarize, we investigated the microstructure of Fe2VAl, synthesized via melt spinning. We performed microstructural observations using electron microscopy and investigated the composition of APBs and precipitates at the near-atomic level using atom probe tomography. This approach allows us to gain information on different hierarchical length scales. SEM observations were used to determine the statistical distribution of precipitates and their size on the microscale.

Platelet-shaped precipitates are found, separated on average by (140 ± 40) nm. APT reveals the chemistry of the platelet-shaped precipitates to be VCxNy. These precipitates appear at APBs oriented along the ⟨100⟩ direction, as indicated by APT and FIM measurements. APBs are stabilized in the L21 phase due to the fast quenching from the disordered B2 and A2 phase, in which Fe2VAl is stable at temperatures higher than 1080 °C and 1190 °C, respectively [19]. The APBs and corresponding precipitates may act as phonon scattering centers and lower the thermal conductivity, leading to an improvement of the thermoelectric properties.

Fig. 1

 1 Fig.1presents backscattered electron (BSE) and secondary electron (SE) micrographs of the unpolished and mechanically polished samples as well as a cross sectional image. Parallel to the surface (Fig.1a), the BSE image shows two layers of grains. The mean size of the small surface grains (Fig 1a, (1)) is (1.7 ± 0.1) µm whereas the regular grain size within the flake is (5.5 ± 0.4) µm (Fig 1a, (2)). The SEM image used for the analysis of the mean grain sizes is shown in the

Fig. 1 .

 1 Fig. 1. SEM images of melt spun Fe2VAl. The white circles indicate exemplary positions where platelet-shaped precipitates are observed. (a) BSE image of unpolished melt spun flakes (1) small surface grains (2) regular grains. (b) SE image of the polished sample, showing the regular grains and precipitates within the flake, (c) Cross section view along the edge of an unpolished sample. (3): surface grains observed from the surface of the flake, (4) edge of the sample, indicated by the dashed line, (5) surface grains layer observed from the cross section, (6) grain boundary of lower lying regular grains.

Fig. 3 .

 3 Fig. 3. Correlative APT and FIM study. a) FIM micrographs, conducted before and after the APT run, as indicated by the blue circles. The arrows mark the poles visible in both FIM images, which show no change in the crystallographic orientation on either side of the precipitate indicating an antiphase boundary. b) AP desorption maps, showing the same poles as the FIM micrographs. c) AP reconstruction showing the elemental distribution of Fe, V, and Al ions and an iso-composition interface with 3 at.% VCxNy as labeled next to the reconstructed data. The iso-composition interface shows a platelet-shaped VCxNy precipitate at the antiphase-boundary and a smaller VNy precipitate within the matrix. d) AP reconstruction of (011) planes around the APB. On either side of the APB, the parallel planes are observed.

Fig. 4 .

 4 Fig. 4. AP reconstruction of a second specimen. a) The desorption map shows the (100) pole before and after the APB. b) reconstruction of (100) planes around the APB. On either side of the APB, the parallel planes are observed. c) full reconstructed volume, showing the elemental distribution of Fe, V, and Al ions and an iso-composition interface with 3 at.% VCxNy as labeled next to the reconstructed data. A platelet-shaped precipitate is observed at an APB. d) elemental distribution, calculated in a cylindrical region of interest with a diameter of 20 nm and a step size of 3 nm and is shown as a concentration plot. An enrichment of V, N, C was found at the APB.

Supplementals

separated by an APB. The {100}B2 translation, which exists in the disordered B2 structure and which is missing in the ordered L21 structure, binds the two APDs [21] and is visualized by the arrow. b) orderdisorder boundary between an ordered L21 phase and the partly disordered B2 phase. The fully disordered A2 phase is not shown, but the kind of boundary is similar.

Fig S2. a) XRD pattern collected from the flakes without polishing. A D8 Advance A25-X1

diffractometer equipped with a cobalt x-ray source was used. X'Pert HighScore was used to determine the phase to be L21. The peaks are indexed according to their Miller indices. b) calculated powder pattern for the L21(ordered), B2 (partly disordered), and A2 (fully disordered) phases of Fe2VAl. The peaks, which only exist in the L21 phase are marked with blue dashed lines, peaks, which are visible in B2 and L21 are marked with the orange dotted line, and peaks, observed in all three pattern, are marked with a black line. The calculations of the powder pattern were made using Mercury [32]. The visibility of the peaks (111), ( 311), ( 331), (511) reveals the existence of the L21 phase. However, it cannot be excluded that B2 and A2 phases are coexisting, as the measured XRD pattern is not a powder pattern and, thus, a texture is observed due to the small amount of illuminated grains. Therefore, the intensity relation between the different peaks cannot be used for a calculation of the amount of different phases. This is easiest visible in the comparison of the intensity ratio of peaks (200)/(111) and ( 222)/(311). The high intensity of (200) compared to (111) could lead to the assumption that a significant amount of B2 phase is existing. In this case, however, the (222) peak would be more intense than the (311) peak, which is not observed.