Andrzej Kochut
email: akochut@us.ibm.com

Alexei Karve
email: karve@us.ibm.com

Bogdan Nicolae
email: bogdan.nicolae@ie.ibm.com

Towards Efficient On-demand VM Provisioning: Study of VM Runtime I/O Access Patterns to Shared Image Content

IaaS clouds are becoming a standard way of providing elastic compute capacity at an affordable cost. To achieve that, VM provisioning system has to optimally allocate I/O and compute resources. One of the significant optimization opportunities is to leverage content similarity across VM images. While many studies have been devoted to de-duplication of VM images, this paper is to the best of our knowledge, the first one to comprehensively study the relationship between the VM image similarity structure and the runtime I/O access patterns. Our study focuses on block-level similarity and I/O access patterns, revealing correlations between common content of different images and application-level access semantics. Furthermore, it also zooms on several runtime I/O access pattern aspects, such as the similarity of the sequences in which common content is accessed. The results show a strong tendency for access pattern locality within common content clusters across VM images, regardless of the rest of the composition. Furthermore, it reveals a strong tendency for read accesses to refer to the same subsets of blocks within the common content clusters, while preserving the same ordering. These results provide important insights that can be used to optimize on-demand VM image content delivery under concurrency.

I. INTRODUCTION

One of the main features that has contributed to the growing popularity of Infrastructure clouds (Infrastructure-as-a-Service, or IaaS clouds) is the elastic on-demand provisioning of resources: users can bring up a whole virtual cluster made out of virtual machine instances and reconfigure it dynamically with a simple click of a button [START_REF]SoftLayer Bare Metal Servers[END_REF], [START_REF]Amazon Elastic Compute Cloud[END_REF]. However, behind the simplicity exposed to the users lie difficult challenges. On one hand, there is a need to minimize the provisioning time and guarantee scalability despite a growing number of VMs, otherwise users do not perceive IaaS as truly on-demand and lose interest. At the same time, cloud providers need to store and manipulate the VM images used to provision the VM instances with minimal resource utilization (storage space, I/O bandwidth), otherwise losing potential profit by not allocating these resources to actual user workloads.

In this context, techniques to provision VM instances saw two major developments. One way is to pre-copy the entire image from the image repository to the local file system of the target hypervisor before starting up a VM instance. Since disk images can quickly grow in the order of tens of GBs, a pre-broadcast can take in the order of tens of minutes or even hours [START_REF] Wartel | Image distribution mechanisms in large scale cloud providers[END_REF], not counting the time spent afterwards to actually boot and run the VM instance. Most of the time, this approach is sub-optimal because of two reasons: (1) not all content of the image is read; and (2) reads from the image need to wait for the whole pre-copy to finish. For this reason, on-demand techniques were developed that bring the content of the VM image as needed while the VM instance is running (e.g., locally derived copy-on-write images -such as QCOW2 -that use a remotely stored VM image template as a read-only backing file). However, despite fixing the issues of pre-copy, on-demand techniques are not without drawbacks: reading parts of the remote VM image is an expensive operation in terms of latency and I/O bandwidth consumption. Even if the performance overhead is not significant [START_REF] Chen | Empirical study of application runtime performance using on-demand streaming virtual disks in the cloud[END_REF] for single instances, at large scale where a large number of VM instances need to share and access the remote VM images concurrently, there is a high degree of I/O contention to the repository where the images are stored.

Under such circumstances, the I/O bandwidth can be quickly exhausted, which slows down not only the provisioning of the VM instances itself, but all other I/O to the repository as well (e.g. reads/writes of user datasets). This problem is further exacerbated by the fact that VM image repositories often apply redundancy elimination techniques based on deduplication to reduce the storage space and I/O bandwidth necessary to transfer the VM image content to VM instances. Several studies [START_REF] Jin | The effectiveness of deduplication on virtual machine disk images[END_REF], [START_REF] Jayaram | An empirical analysis of similarity in virtual machine images[END_REF] show a large degree of overlap of content between VM images, which can go as high as 94%. Thus, when storing only unique content on the repository, contention to the same pieces of data will rise even further.

In an attempt to alleviate the I/O pressure on the repository, peer-to-peer content delivery networks with the VM instances have been proposed [START_REF] Nicolae | Leveraging Collaborative Content Exchange for On-Demand VM Multi-Deployments in IaaS Clouds[END_REF]. Such approaches enable hypervisors to directly exchange the image content without involving the repository. Also, data redundancy across images have been exploited to optimize VM provisioning [START_REF] Kochut | Leveraging local image redundancy for efficient virtual machine provisioning[END_REF], which allows to reuse locally present content from another image instead of transferring it from the repository. In this context, the aspect of adapting to the read access pattern is critical. It is important to exchange only what data is needed and to do so as early as possible in order to mask I/O latency. However, despite extensive studies on how the content of VM images overlaps and what de-duplication potential can be achieved, there is little understanding in terms of how identical content (potentially belonging to different VM instances) behaves in relationship to the actual read access pattern issued by the VM instances during runtime. Such understanding could provide critical hints for the design of efficient on-demand provisioning techniques based on content delivery networks by introducing new optimization opportunities based on de-duplication. Thus, it is important to reveal questions like: what pieces of unique content are accessed in the first place? Which unique content is accessed more frequently and can lead to contention? Are there any orderings or temporal dependencies observable for the unique pieces accessed by the VM instances even if the original accesses refer to different images and different offsets?

This paper contributes with a comprehensive study that aims to answer the questions mentioned above. To the best of our knowledge, we are the first to explore such issues. Specifically, the key contributions of this paper are:

• Analysis of the content overlap structure (by computing 512-byte block digests and identifying matching blocks across VM images) for a set of representative combinations of OS versions and applications. The study covers several combinations of popular operating systems and middleware packages. The static analysis is augmented by the characterization of I/O access volumes to each of the content clusters during a typical execution.

• Correlation of runtime I/O access patterns with content similarity clusters revealed during the similarity analysis. In particular, we aim to understand: [START_REF] Abad | A storage-centric analysis of mapreduce workloads: File popularity, temporal locality and arrival patterns[END_REF] what blocks within a shared cluster are actually touched during runtime; (2) whether these blocks remain the same even when the images that share the cluster are different; and (3) whether their offsets within the images are the same.

• Analysis of temporal aspects exhibited by the runtime I/O access patterns in relationship to content similarity.

In particular, we aim to understand whether different pairs of VM instances (based on different images) access identical blocks in a similar order. This aspect is important in the design of on-demand run-time optimization for the purpose of prioritizing prefetching of blocks.

The remainder of this paper is organized as follows: Section II discusses related work, Section III describes static content overlap analysis. Section IV focuses on correlation of runtime I/O access patterns with content similarity clusters, analyzes I/O accesses within shared content clusters, and also examines temporal access patterns. Finally, Sections V and VI summarize our findings and outline future research directions.

II. RELATED WORK

On-demand instantiation of virtual machines based on images stored at a remote repository was shown to incur little runtime overhead [START_REF] Chen | Empirical study of application runtime performance using on-demand streaming virtual disks in the cloud[END_REF] and is already an industry-standard practice, thanks to image formats such as qcow2: the remote image is used as a read-only template, while all modifications are stored locally in a separate file. Using a centralized file server as a repository is still a popular choice [START_REF] Nicholas | Comparison of vm deployment methods for hpc education[END_REF]. Decentralized solutions see increasing adoption in form of parallel file systems [START_REF] Schmuck | Gpfs: A shared-disk file system for large computing clusters[END_REF] or dedicated repositories [START_REF] Nicolae | Going back and forth: Efficient multi-deployment and multisnapshotting on clouds[END_REF]. Content similarity detection is typically performed by means of de-duplication, which is broadly classified into static and content-defined. Static approaches split the input data into equally sized chunks, which are then compared among each other (either byte-by-byte or, for increased performance, based on their hash values) in order to identify and eliminate duplicates. While simple and fast, static approaches suffer from misalignment issues (i.e insertions or deletions lead to the impossibility to detect duplicates). To deal with such misalignment issues, content defined approaches [START_REF] Muthitacharoen | A lowbandwidth network file system[END_REF] were proposed. Essentially, they involve a sliding window over the data and that hashes the window content at each step using Rabin's fingerprinting method [START_REF] Michael Rabin | Fingerprinting by random polynomials[END_REF]. Many storage systems have adopted and refined de-duplication techniques [START_REF] Zhu | Avoiding the disk bottleneck in the data domain deduplication file system[END_REF], [START_REF] Dubnicki | Hydrastor: a scalable secondary storage[END_REF], [START_REF] Guo | Building a high-performance deduplication system[END_REF], [START_REF] Nicolae | Towards Scalable Checkpoint Restart: A Collective Inline Memory Contents Deduplication Proposal[END_REF].

Specifically in the context of IaaS clouds, de-duplication techniques have proven effective at reducing the amount of space and network bandwidth necessary to store and transfer VM images. Several studies report significant reductions that can reach up to 94% [START_REF] Jin | The effectiveness of deduplication on virtual machine disk images[END_REF], [START_REF] Jayaram | An empirical analysis of similarity in virtual machine images[END_REF]. This potential has been exploited in dedicated VM image repositories such as VMAR [START_REF] Shen | Vmar: Optimizing i/o performance and resource utilization in the cloud[END_REF] in order to store VM images in a de-duplicated fashion and redirect accesses for identical blocks to the same location before going through the OS. Utilizing content similarity in workloads from production storage systems is discussed in [START_REF] Koller | I/o deduplication: Utilizing content similarity to improve i/o performance[END_REF]. Several optimizations specifically targeting the performance of reading de-duplicated data during on-demand accesses have also been recently proposed [START_REF] Mao | Readperformance optimization for deduplication-based storage systems in the cloud[END_REF]. Furthermore, outside of storage, de-duplication has demonstrated important benefits in the area of live migration [START_REF] Deshpande | Live gang migration of virtual machines[END_REF], [START_REF] Al-Kiswany | Vmflock: Virtual machine co-migration for the cloud[END_REF].

Analysis of I/O access patterns has been performed in a variety of contexts and at various granularity. At block-level, several studies [START_REF] Li | Mining block correlations to improve storage performance[END_REF], [START_REF] Wang | Improving query i/o performance by permuting and refining block request sequences[END_REF], [START_REF] Marazakis | Optimization and bottleneck analysis of network block i/o in commodity storage systems[END_REF] aim to discover disk I/O bottlenecks and optimization opportunities related to caching, prefetching, data layout and disk scheduling. At file-level, areas of interest include: prefetching optimizations [START_REF] Xia | FARMER: A novel approach to file access correlation mining and evaluation reference model for optimizing peta-scale file system performance[END_REF], placement strategies to reduce energy consumption [START_REF] Iritani | Effects on performance and energy reduction by file relocation based on file-access correlations[END_REF], inter-file access patterns in the context of collective I/O [START_REF] Memik | Multicollective i/o: A technique for exploiting inter-file access patterns[END_REF], file-access patterns of data-intensive workflow applications [START_REF] Shibata | File-access patterns of data-intensive workflow applications and their implications to distributed filesystems[END_REF]. Furthermore, many studies focus on analysis of distributed storage systems as a whole: file popularity, temporal locality and arrival patterns for HDFS [START_REF] Abad | A storage-centric analysis of mapreduce workloads: File popularity, temporal locality and arrival patterns[END_REF], key-value stores [START_REF] Atikoglu | Workload analysis of a large-scale key-value store[END_REF], leadership class parallel file systems [START_REF] Kim | Workload characterization of a leadership class storage cluster[END_REF]. This contribution focuses a particular aspect: understanding correlations between the content similarity of VM images and the I/O access patterns generated during the lifetime of VM instances deployed from the VM images using on-demand techniques. To our best knowledge, we are the first to explore such correlations.

III. VM IMAGE COMPOSITION

The first step in our exploration is to understand how the VM images used to launch VM instances overlap in terms of content. To this end, we use a static de-duplication approach that splits each image in fixed sized blocks of 512 bytes (several studies [START_REF] Douglis | Redundancy elimination within large collections of files[END_REF], [START_REF] Karve | Redundancy aware virtual disk mobility for cloud computing[END_REF], [START_REF] Jayaram | An empirical analysis of similarity in virtual machine images[END_REF], [START_REF] Peng | Vdn: Virtual machine image distribution network for cloud data centers[END_REF] of VM image similarity have confirmed the effectiveness of fixed block de-duplication in the context of VM images). Then, all blocks from all images are compared with each other (based on SHA-1 digests) and all duplicates are eliminated. The remaining unique blocks are grouped together into clusters, with each cluster comprising blocks that appear in a different subset of images and each block is represented by its hash value.

We briefly detail the concept of clusters. For simplicity, consider four partially overlapping images numbered Image-0 through Image-3 composed out of blocks labeled by upper case letters as shown in Fig. 1. Each upper-case letter denotes a globally unique block with respect to content, i.e. the same block that occurs in multiple VM images will carry the same upper-case letter. Since the same block can occur multiple times in the same image, each such multiple occurrence is uniquely identified by the use of subscript.

Each cluster comprises the maximal set of unique blocks that occurs at the intersection of a given combination of VM images without occurring in any other combination. It is labeled with a four-bit signature: the least significant refers to Image0 while the most significant refers to Image3. The value of the bit indicates whether the image is considered in the intersection or not.

There are four singleton clusters, each containing blocks unique to their respective images: CL-0001 has block G present only in Image-0, CL-0010 has blocks B and P present only in Image-1, CL-0100 has block K present only in Image-2 and finally CL-1000 has block N present only in Image-3. Block G in singleton cluster CL-0001 occurs two times in Image-0, as indicated by the use of subscript and represents internal redundancy within the same image where a the same block occurs at different offsets. The rest of the clusters are shared between images. For example, cluster CL-0011 has blocks with hash values E and F, both these blocks are shared by two images Image-0 and Image-1. The block with the hash value C is shared between E and F in Image 0. Also, Block C occurs at three different locations in Image-0 while it occurs only once in Image-1. Thus, blocks identified in the cluster may be noncontiguous in any image and may occur a different number of times in different images. Also, note that CL-1101 is empty, i.e. there are no blocks in common between Image-0, Image-2 and Image-3.

In order to achieve this clustering, we start from an initial cluster corresponding to the first VM image. Then, we gradually from new clusters by adding new images oneby-one. More specifically, when a new image is added, we compute for each already existing clusters the intersection with the the new image to be added (in terms of unique SHA-1 fingerprints corresponding to blocks). Next, the label of the cluster is extended by one bit. If the intersection is empty, then the cluster is unchanged except for the additional bit in the label, which is set to 0. Otherwise, the cluster is split into two new clusters: one corresponding to the intersection (additional bit set to 1) and the other one corresponding to the content not present in the new image (additional bit set to 0). If any fingerprints are left over after checking against all existing clusters, an additional cluster corresponding to the unique content of the new image is created to hold them (additional bit set to 1, the rest set to 0). We use several optimizations to accelerate the cluster construction, including bloom filters and multi-threaded parallelism. A more detailed description of this process and its optimizations can be found in our previous work [START_REF] Karve | Redundancy aware virtual disk mobility for cloud computing[END_REF].

Using this approach, we analyze several variations of VM images that include two versions of the GNU/Linux operating system (Fedora Core 19 and 20), IBM DB2 version 10, two versions of Apache Tomcat application container (versions 7.0 and 8.0), as well as two versions of MySQL database engine (versions 5.1 and 5.5). From the numerous variations and combinations possible, these are relevant and representative of frequent VM image content (i.e. OS, web, database stack is very popular) and common access patterns (where an OS always needs to boot and a database, if needed, always needs to start). In practice, users upload a large number of VM images and spawn multiple instances from them, yet there is a limited number of popular choices for OS, DB engines, web stacks, etc. that are typically used to "cook" VM images. This introduces a high chance for similarity, which we argue offers a large potential for runtime optimization.

Table I summarizes the observed overlap structure, where only the non-empty clusters larger than 5 MB (a total of 24) are included. Each row corresponds to a cluster and each column corresponds to a VM image with a specific software stack. The values are sizes of the content (in MB) contained within a cluster. For example, cluster cl-05 is common for all VM images in the study and corresponds to the content present in both Fedora Core 19 and 20 (and thus representative of any image based on these operating systems). Cluster cl-11 contains content specific to MySQL version 5.5 but shared across both Fedora Core (FC) 19 and 20. On the contrary, cluster cl-10 contains content specific MySQL version 5.5 on Fedora Core 19. A comparative illustration of the similarity clusters grouped by the installed software stack is depicted in Figure 2.

The analysis of the overlap structure leads to an important observation that clusters formed by content analysis at block device level (which does not have any semantic information available at file system level within the VM guest) reflect very well the application content installed within VM images. The analysis allows to distill content fragments and relate it to software packages. For example, for MySQL there are two Another interesting observation is the filesystem's behavior while installing MySQL packages. Observe that the cluster cl-03 is shared among all images based on FC 19 except for the ones with MySQL installed. That is due to the fact that MySQL installation is done using yum package installer which, in addition to installing MySQL rpms, also downloads and upgrades several existing packages. As a result, it modifies data (17MB in that case) which becomes shared by only images with no MySQL.

IV. VM RUNTIME ACCESS PATTERNS

This section analyses the read access patterns generated during the runtime of VM instances in the context of the image content overlap structure described in Section III.

A. Experimental Configuration

In order to capture access patterns of the VM instances, we implemented a FUSE-based [START_REF]FUSE Filesystem[END_REF] filesystem that traces all read operations in terms of access time, the offset within the image and the number of blocks requested. To avoid the complexity of dealing with write operations and modifications to the image, all VM instances use derived qcow2 copy-on-write images as virtual disks, which in turn are based on the original images that are stored in the FUSE filesystem in the raw format.

The experiments were conducted on physical servers leased from SoftLayer [START_REF]SoftLayer Bare Metal Servers[END_REF] and involve booting a VM instance as described above, then optionally launching a specific workload while capturing the read accesses. We use the various configurations described in Section III as the base images. With respect to the workloads, we have chosen three representative use cases: (1) launching DB2, representative of large applications that occupy a large amount of space and exhibit a large initialization overhead; (2) launching Tomcat and going through the typical deployment cycle of a servlet (e.g., launch admin UI, browse documentation, issue requests, etc.), which is representative of web service management;

(3) launching OS tools and utilities (e.g. grep, awk, find) in various combinations, which is representative of scripting workloads (e.g. log analysis). After obtaining the traces for various combinations of images and workloads, we analyze these traces both individually and in selected pairs in order to identify correlations.

B. Runtime Read Rates

Virtual disk access patterns of VM instances are driven primarily by the workload executing in the guest. Usually, a relatively small set of applications from the installed content is actually launched and executed. Similarly, even when an application is launched, the read footprint may change significantly based on invoked functionality.

When observing the evolution of the read throughput during runtime, we see that on our test system it reaches up to 30MBps for well tuned VM instances. Figure 3 presents sample results for four scenarios. Figure 3a shows boot sequence for Fedora Core 19. It lasts under 30 seconds and generates between 2 and 30 MBps reads against the base disk (when averaged over 1 second intervals). The launch of applications is much shorter with the results for DB2 (Figure 3b) and two versions of Tomcat (Figures 3c and3d) indicating up to 6 second bursts and a similar range for the throughput. Figure 4a shows the read rate (averaged per second) during an execution representative of scripting workloads and Figure 4b shows activity for interaction with Tomcat 7.0 on FC 20, representative of web service management. Workload specifics are described in Section IV-A.

C. Semantic Locality to Cluster Boundaries

Next, we analyze the correlation between the read activities and content sharing structure (clusters) identified in Section III. We want to find out whether the activity for an application results in reads to the cluster related only to this application or also to other clusters. To do so, each 512-byte read operation captured at runtime was matched with the cluster that it belongs to. Based on the two cases above, it is worth noting that the accesses target both content specific to application being used as well as additional content from OS that is loaded as a result of usage of system libraries.

Next, let's consider start of IBM DB2 version 10 on FC 19. This scenario is depicted in Figure 7 that shows both fractions of clusters read in (a) and volumes read in (b). Only two clusters are being used, cl-1 and cl-2, both directly related to DB2. Note that cl-2 is shared across both FC 19 and FC 20. Also, only small fraction of DB2 content is used during launch (just under 5%), however it results in more than 100MB of reads.

Finally, let's consider the effects of using an OS or application in steady-state, i.e., using more OS programs or application features. This situation for FC 20 and Tomcat 7.0 is depicted in Figure 8.

Figure 8a shows content read during OS boot itself while 8b shows activity during launching OS tools and utilities (as described in Section IV-A). First, all reads were issued to the same clusters as during the boot, confirming semantic locality. Moreover, as expected, the fractions of clusters accessed has increased significantly. For cl-19 (which contains majority of FC 20 OS content) it more than doubled from 6.5% to 15%. For cl-18 the increase was even larger from 2% to 15%. Both clusters are shared across FC 20 instances (with exception of MySQL that was explained in Section III). Similar situation is observed for launching Tomcat and going through the typical deployment cycle of a servlet (e.g., launch admin UI, browse documentation, issue requests, etc.). Usage of shared clusters cl-13 and cl-14 grew significantly. The usage in case of cl-13 rose from 47% to almost 90% and in case of cl-14 rose from 15% to 70%. Also usage of cluster unique to Tomcat 7.0 on FC 20 (cl-23) rose from 6% to 10%.

D. Runtime Access Similarity

As shown in the previous section, the runtime read accesses are well localized within cluster boundaries that directly correspond to the semantic composition of the images (i.e. shared OS and application packages). However, one important aspect that is not revealed by the previous study is whether the accesses issued by different VM instances ultimately target the same blocks within a common cluster. Furthermore, when the instances are based on different images, the relative offsets of identical blocks of a common cluster may be different. Thus, it is important to understand not only how many common blocks were accessed from the same cluster, but also to what degree their offsets relative to the base image coincide, which ultimately reveals how the ordering of clusters inside an reflects on the access pattern. Figure 9a shows the results for launching DB2 on FC 19 FC 20 respectively. Cluster cl-2 captures most accesses (as show in Figure 7b). Furthermore, Figure 9a shows that almost 100% of the content read from this cluster is actually common between starting DB2 on FC 19 and 20. That confirms that in case of DB2 the accesses are not only localized to clusters, but also match the blocks almost exactly. Note, however, that most offsets in the image are shifted (only under 5% match), which stems from the fact that DB2 binaries ended up in different sections of virtual disk even though they were content-wise the same. This can be explained by the fact that the file system layout is affected by various factors, including previously installed and removed content, filesystem type, block allocation strategy, installed OS, etc.

Figure 9b shows comparison of launching Tomcat 7.0 and 8.0, both on FC [START_REF] Mao | Readperformance optimization for deduplication-based storage systems in the cloud[END_REF]. It shows that accesses on all three clusters match in terms of which blocks within a cluster are read (i.e., more than 90% matches). However, the offsets of the accessed blocks only matches for OS related clusters (cl-4 and cl-5 because both use the same base FC 19 OS image) and not for the Tomcat shared content cluster, since it is in different disk sections. Figures 9c and9d show corresponding results for Tomcat 7.0 and MySQL 5.1 started on both FC 19 and 20, respectively. The shared clusters again match almost exactly for content, but the offset does not. For Tomcat, the fraction common access between launching on FC 19 and 20 is only 70%, with the rest being unique to each launch. Similarly, the number for MySQL 5.1 is 82%.

E. Runtime Access Order within Clusters

The last aspect we study in our work is the degree of similarity between the access order of common blocks (as identified in prior sections) for the VM instances that share clusters. Such correlations are crucial in understanding how the temporal locality of read accesses of a VM instance relate to other instances.

In order to facilitate this understanding, we introduce a metric we call sequentiality match. Specifically, given two read traces of two VM instances TR-1 and TR-2 for a given cluster cl, we examine all 512-byte blocks from cl that are read in both TR-1 and TR-2 and keep only those blocks that share the same predecessor in both traces. The sequentiality match itself is the amount of the remaining blocks expressed as a fraction of the total number of common blocks accessed during the runtime.

Figure 10 shows the sequentiality match for several experiments. Figure 10a examines the case of DB2 starting on two different operating system versions. For cluster cl-2 that contains DB2 specific content shared across OSes, the content is accessed in almost identical order, with sequentiality match measure at 98%. The second cluster has a lower but still significant value of 78%. The conclusion is similar in case of Tomcat on two OS versions, which is depicted in Figure 10b. The clusters specific to Tomcat (cl-13 and cl-14) are accessed in almost identical order (metric value of above 95%), and the shared OS cluster cl-5 has a very high sequentiality match that amounts to 78%. Figure 10c shows results for two separate boots of the same FC 20 OS, which captures potential variations during separate boots. A similar trend is observable for the common cluster cl-5 in the case when FC 19 and FC 20 boot (Figure 10d), with the sequentiality match reaching close to 80%.

V. SUMMARY OF THE KEY FINDINGS

In summary, we have confirmed that there is a significant overlap across VM images due to commonality of OS and application base. That leads to forming of an interesting sharing structure, exemplified in Table I, which reflects potential for runtime sharing. The fact that large fraction of content is shared across images indicates significant optimization potential for VM instance runtime.

Moreover, the study shows a very strong relation between runtime read access patterns and the content commonality structure based on clusters. More specifically, the blocks accessed during the runtime of the VM instances for a given workload tend to stay within the boundaries of those common clusters that comprise the OS and application packages related to the workloads. Also, when two VM instances access a common block, the corresponding offsets in the base images generally do not coincide, with exceptions observable only in the case when the base images are both derived from a common image, which tends to preserve the offsets in the clustering itself. Furthermore, when two VM instances read from the same cluster, they generally tend to access the same blocks, with the proportion of common blocks read from the same cluster varying between 70%-99%.

The amount of content actually accessed in each cluster is workload specific: it relates to how much functionality of a particular application or set of applications that fall inside the same cluster is actually used. As expected, with increased utilization of the same OS or application, more reads are expected to the same clusters. At the same time, crosscorrelations between different clusters are observable as well: reads of blocks from some clusters trigger reads of blocks in other clusters, which can happen for example when certain applications invoke system packages (e.g. a Java application starts the Java Virtual Machine).

Finally, we observe that accesses tend to be sequenced in the same order independent of the software stack combination, with very high similarity of sequentiality observable (over 98%). Exceptions are mostly for OS content, where higher levels of access parallelism (e.g. daemons and tools launched in parallel) introduce more randomness. However, even for this situation the ordering of accesses is still quite similar, reaching 80%.

VI. CONCLUSIONS AND FUTURE WORK

With a growing need to deploy more VM instances based on increasingly larger virtual disk images, the problem of efficient provisioning becomes a key challenge in the context of IaaS clouds. Two important advances were made in this regard. First, due to the high content similarity exhibited by VM images, storage repositories have successfully employed de-duplication techniques in order to reduce the space necessary to store them. Second, based on the observation that VM instances access only a small fraction of the virtual image content during runtime, on-demand provisioning techniques that access the repository only when needed have seen increasingly wider adoption compared with pre-copy techniques.

Despite important progress in both directions, most advances are targeting either one direction or another, with little effort and understanding dedicated to the problem of how to co-optimize de-duplication techniques and on-demand provisioning techniques. As a first step in this direction, this study has shown that there is a strong link between the ondemand read access patterns issued by VM instances during runtime and the block-level content similarity identified at virtual disk level.

More specifically, most reads that involve a particular application are concentrated inside the same block-level content similarity clusters, regardless of the rest of the composition of the virtual disk. This cluster locality extends throughout the usage of the application, including launch and steady-state use of various functionalities. Furthermore, the read accesses refer to the same subsets of blocks within the clusters, while preserving the same ordering. Again, these properties hold regardless of the rest of the composition of the virtual disk images, including various combinations of OS and software stacks.

Based on these findings, we plan to explore in future work how to design novel on-demand provisioning techniques that leverage content and access pattern similarity in order to reduce the performance overhead and network traffic involved in the provisioning of a large number of VM instances at scale under concurrency. We envision peer-to-peer content delivery mechanisms that automatically adapt to the access pattern and minimize any dependency on the storage repository while emphasizing direct content exchange in a decentralized and scalable fashion, effectively overcoming I/O bottlenecks created by contention to the repository.

Fig. 1 .

 1 Fig. 1. Illustration of content clusters for four VM images. Upper case letters denote non-identical blocks. Identical blocks can appear more than once in the same image and are differentiated by the use of subscript

Fig. 2 .

 2 Fig. 2. Comparative illustration of the similarity clusters detailed in Table I grouped by installed software stack. Note the logscale on the X axis.

19 Fig. 3 .Fig. 4 .

 1934 Fig. 3. Read rates for launch activities on FC 19.

Figure 5 Fig. 5 .Fig. 6 .

 556 Figure 5 presents results for launching Tomcat 7.0 on FC 19 and FC 20. Figures 5a and 5c depict fractions of clusters that were read during the launch of Tomcat on FC 19 (a) and FC 20 (b). Figures 5b and 5d present related volumes of reads (in MB). The clusters accessed by starting Tomcat 7.0 are cl-4, cl-12 cl-13 and cl-14. Referring back to static overlap structure shown in TableIwe see that cl-12 contains content unique to Tomcat 7.0 on FC 19, cl-13 contains content unique to Tomcat 7.0 independent of OS version, and cl-14 contains content shared between Tomcat 7.0 and 8.0 also independent of OS version. Finally, cl-4 contains content common to FC 19 (OS blocks). Almost half of content in the shared cluster cl-13 is used. Overall volumes of reads are relatively small since the Tomcat installation footprint is small. Similar situation can be observed in case of Tomcat 8.0 starting on FC 19 (Figure6). There are two common Tomcat clusters, cl-14 and cl-16, related to content common across

19 Fig. 7 .

 197 Fig. 7. Fraction and volumes of base image reads while starting DB2 10 on FC 19.

Fig. 8 .

 8 Fig. 8. Comparison of fraction of clusters read from base images during launch and activities.

20 Fig. 9 .

 209 Fig. 9. Per-cluster fractional match across pairs of VM instances based on different images.

Figure 9

 9 Figure 9 examines both aspects. Each plot corresponds to one pair of runtime access traces for two VM instances that are based on two different images that share common clusters. Represented is the fraction of common blocks and common offsets accessed by both instances during runtime, broken down by cluster.

Fig. 10 .

 10 Fig. 10. Sequentiality match: fraction of common blocks accessed during the runtime of two VM instances that share the same predecessor.

TABLE I .

 I CONTENT OVERLAP STRUCTURE ACROSS 12 VIRTUAL MACHINE IMAGES USED IN THE ANALYSIS. COLUMNS CORRESPOND TO SPECIFIC SOFTWARE STACKS WHILE ROWS TO CLUSTERS SHARED ACROSS THE STACKS. SIZES IN MB.

	Cluster		Fedora Core 19				Fedora Core 20
	OS	DB2	MySQL	Tomcat	OS	DB2	MySQL	Tomcat
	only


Samir F Matar
email: samir.matar@icmcb.cnrs.fr

Jean Etourneau

Rainer Pöttgen

Pd, Ag, Pt, Au) with ZrNiAl type structure -A systematic view on electronic structure and chemical bonding

Keywords: A. functional alloys (magnetic, electrical, biomedical), B. Magnetic properties, B. Density functional theory, E. Ab initio calculations

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The equiatomic CeTX (T = electron-rich transition metal; X = element of the 3 rd , 4 th , or 5 th main group) phases [START_REF] Villars | Pearson's Crystal Data: Crystal Structure Database for Inorganic Compounds (release 2014/15[END_REF] are one of the broadest investigated families of intermetallic rare earth compounds due to their largely differing magnetic and electric properties.

Some outstanding examples are the heavy-fermion silicide CePtSi [START_REF] Lee | CePtSi: A New Heavy-Fermion Compound[END_REF], the 10 K ferromagnet CeAuGe [START_REF] Pöttgen | Ferromagnetic Ordering in CeAuGe[END_REF], the formation of an anisotropic energy gap in the valencefluctuating stannide CeNiSn [START_REF] Takabatake | Formation of an Anisotropic Energy Gap in the Valence-Fluctuating System CeNiSn[END_REF], the Kondo semiconductor CeRhSb [START_REF] Malik | Evidence of Pseudogap Formation in a New Valence-Fluctuating Compound: CeRhSb[END_REF][START_REF] Chevalier | Inducing Magnetism in the Kondo Semiconductor CeRhSb through Hydrogenation -Antiferromagnetic Behaviour of the New Hydride CeRhSbH0.2[END_REF], the non-Fermi liquid system CeRhSn [START_REF] Ślebarski | Low-Temperature Anomalies in Magnetic, Electric Transport and Thermal Properties of CeRhSn[END_REF], the valence modulations in CeRuSn [START_REF] Riecken | Trivalent-Intermediate Valent Cerium Ordering in CeRuSn -A Static Intermediate Valent Cerium Compound with a Superstructure of the CeCoAl Type[END_REF][START_REF] Feyerherm | Valence Modulations in CeRuSn[END_REF], or the heavy-fermion ( = 300 mJ/(mol K 2 )) antiferromagnet (TN = 0.9 K) CePtPb [START_REF] Movshovich | Magnetism in CePtPb[END_REF]. Several hundred manuscripts on CeTX intermetallics have been published. Most data are summarized in review articles [START_REF] Matar | Review on Cerium Intermetallic Compounds: A Bird's Eye Outlook through DFT[END_REF][START_REF] Gupta | Review on Magnetic and Related Properties of RTX Compounds[END_REF].

The peculiar bonding characteristics and magnetic ground states of the CeTX intermetallics are often a consequence of the Ce-T hybridization. Substitution of the X component or the formation of solid solutions on both the T and X sites leads to substantial influence on the cerium electronic situation and thus changes in the magnetic behavior, e. g. CePt1-xNixSn with a transition from an antiferromagnetic Kondo lattice to a mixed valence semiconductor [START_REF] Sakurai | Transition from Antiferromagnetic Kondo Metal to Mixed Valence semiconductor in Ce(Pt1-xNix)Sn[END_REF], CeNi1-xRhxSn with an interplay between spin-glass-like and non-Fermi-liquid behavior [START_REF] Ślebarski | Interplay Between Spin-Glass-Like and Non-Fermi Liquid Behavior in CeNi1-xRhxSn[END_REF] or CeRhSb1-xSnx with a quantum criticality at the border of Kondo insulator / non-Fermi liquid [START_REF] Ślebarski | Low-Temperature Anomalies in Magnetic, Electric Transport and Thermal Properties of CeRhSn[END_REF].

Other parameters that influence the magnetic behavior are temperature, highpressure or hydrogenation. Recent examples are the low-and high-temperature modifications of CePdZn [START_REF] Hermes | Structure and Properties of Dimorphic CePdZn[END_REF] with stronger Ce(4f)-Pd(4d) hybridization in -CePdZn, the temperature induced structural and cerium valence change in CeRhGe [START_REF] Svitlyk | Change of the Cerium Valence with Temperature -Structure and Chemical Bonding of HT-CeRhGe[END_REF] and the high-pressure modification of CePtSn [START_REF] Riecken | The High-Pressure Modification of CePtSn -Synthesis, Structure, and Magnetic Properties[END_REF]. Hydrogenation of CeZnSn to CeZnSnH1.5 increases the Curie temperature from 4.8 to 7.3 K [START_REF] Hermes | New Quaternary Hydride CeZnSnH1.5 -Structure, Magnetism, and Chemical Bonding[END_REF]. Modification of the magnetic properties is also possible through substitution of the transition metal by another p element, thus suppressing d-f hybridization. First investigations in such phase diagrams led to the magnetically ordering phases CeGaGe [START_REF] Dhar | CeGeGa -A Ferromagnetic Dense Kondo System[END_REF][START_REF] Grin | Physical Properties of Binary Cerium Gallides and Ternary Cerium-Germanium Gallides[END_REF], CeAlSi and CeAlGe [START_REF] Dhar | Magnetic and Thermal Behavior of CeAlX (X = Si and Ge) Compounds[END_REF] and CeGaSi [START_REF] Mori | An Electronically-Driven Volume Transition in CeSi2-xGax[END_REF][START_REF] Moshchalkov | The New Kondo Lattice Compounds: CeSi2-xGax[END_REF]. Systematic studies have been performed for the REMgX (X = Ga, In, Tl) phases [START_REF] Kraft | Magnetic and Electrical Behavior in CeMgGa[END_REF][START_REF] Kraft | Ternary Gallides REMgGa (RE = Y, La, Pr, Nd, Sm-Tm, Lu) -Synthesis and Crystal Chemistry[END_REF][START_REF] Kraft | Ternary Indides REMgIn (RE = Y, La-Nd, Sm, Gd-Tm, Lu) -Synthesis, Structure and Magnetic Properties[END_REF][START_REF] Kraft | Ternary Thallides REMgTl (RE = Y, La-Nd, Sm, Gd-Tm, Lu)[END_REF][START_REF] Singh | First Principle Study of Structural, Electronic and Thermodynamic Behavior of Ternary Intermetallic Compound: CeMgTl[END_REF] with ZrNiAl type structure, including the cerium intermetallics CeMgGa, CeMgIn, and CeMgTl of which CeMgGa orders antiferromagnetically at TN = 3.1 K. These phases can be considered as the p element analogues of the transition metal counterparts CeMgT (T = Pd, Ag, Pt, Au) [START_REF] Fickenscher | Synthesis and Crystal Structure of REAgMg (RE = La, Ce, Nd, Eu, Gd, Tb, Ho, Tm, and Yb)[END_REF][START_REF] Gibson | Synthesis, Structure, and Magnetic Properties of LaTMg and CeTMg (T = Pd, Pt, Au)[END_REF][START_REF] Johrendt | Magnetic and Electrical Properties, 151 Eu Mössbauer Spectroscopy and Chemical Bonding of REAgMg (RE = La, Ce, Eu, Yb) and EuAuMg[END_REF]. These substitutions offer an interesting situation for changes in chemical bonding while keeping the structure type. Herein we present a detailed study of the electronic structures and the chemical bonding situation of these two families of intermetallics.

Computational details

Within the framework of the density functional theory (DFT) [START_REF] Kohn | Self-Consistent Equations Including Exchange and Correlation Effects[END_REF][START_REF] Hohenberg | Inhomogeneous Electron Gas[END_REF] two computational methods were used in a complementary manner. For the purpose of firstly obtaining energy (total and cohesive) and charge transfer quantities, the Vienna ab initio simulation package (VASP) code [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF][START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmentedwave method[END_REF] was used with the projector augmented wave (PAW) method [START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmentedwave method[END_REF][START_REF] Blöchl | Projector augmented-wave method[END_REF]. DFT exchange and correlation effects were accounted for in the framework of the generalized gradient approximation (GGA) scheme following Perdew, Burke and Ernzerhof (PBE) [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF]. Atoms were relaxed and the conjugategradient algorithm [START_REF] Press | Numerical Recipes[END_REF] is used in this computational scheme. The tetrahedron method with Blöchl corrections [START_REF] Blöchl | Improved tetrahedron method for Brillouinzone integrations[END_REF] as well as Methfessel-Paxton [START_REF] Methfessel | High-precision sampling for Brillouin-zone integration in metals[END_REF] Brillouin-zone (BZ) integrals were approximated using the special k-point sampling of Monkhorst and Pack [START_REF] Monkhorst | Special points for Brillouin-zone integrations[END_REF]. A large number of 150 k-points was used in the irreducible wedges of the hexagonal Brillouin zone to perform total energy calculations. The optimization of the structural parameters was performed until the forces on the atoms were less than 0.02 eVÅ -1 and all stress components less than 0.003 eVÅ -3 .

Then the full investigation of the electronic and magnetic structures and the chemical bonding properties was performed using the full potential augmented spherical wave (ASW) method [START_REF] Williams | Cohesive properties of metallic compounds: Augmented-spherical-wave calculations[END_REF][START_REF] Eyert | Basic notions and applications of the augmented spherical wave method[END_REF] in a scalar relativistic implementation [START_REF] Eyert | The Augmented Spherical Wave Method[END_REF] with exchange-correlation effects accounted for within the generalized gradient approximation GGA [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF]. In the ASW method, the wave function is expanded in atom-centered augmented spherical waves, which are Hankel functions and numerical solutions of Schrödinger's equation, respectively, outside and inside the so-called augmentation spheres. In the minimal ASW basis set, we chose the outermost shells to represent the valence states and the matrix elements were constructed using partial waves up to lmax + 1 = 4 for La and Ce, lmax + 1 = 3 for Pd and, lmax + 1 = 2 for Mg and Ga. Self-consistency was achieved when charge transfers and energy changes between two successive cycles were such as: Q < 10 -8 and E < 10 -6 eV, respectively. The BZ integrations were performed using the linear tetrahedron method [START_REF] Blöchl | Improved tetrahedron method for Brillouinzone integrations[END_REF] within the irreducible hexagonal wedge.

The calculations were carried out assuming firstly spin degenerate, non spinpolarized (NSP), then spin polarized (SP) magnetic calculations for both ferromagnetic and antiferromagnetic long range orders for the cerium compounds. The relative magnitude of the chemical bonding is obtained based on the overlap population analysis: Sij, i and j being two chemical species. The crystal orbital overlap population (COOP) criterion is used [START_REF] Hoffmann | How Chemistry and Physics Meet in the Solid State[END_REF]. In the plots positive, negative and zero COOP magnitudes indicate bonding, anti-bonding and non-bonding interactions respectively.

Results and discussion

Structural chemistry

The CeMgX (X = Ga, In, Tl, Pd, Ag, Pt, Au) phases crystallize with the hexagonal ZrNiAl type structure [START_REF] Krypyakevich | Crystal Structures of the Compounds ZrNiAl, ZrCuGa and their Analogues[END_REF][START_REF] Dwight | Ternary Compounds with the Fe2P-Type Structure[END_REF][START_REF] Zumdick | The Intermetallic Zirconium Compounds ZrNiAl, ZrRhSn, and ZrPtGa -Structural Distortions and Metal-Metal Bonding in Fe2P Related Compounds[END_REF] The cell parameters of the CeMgX phases are listed in Table 1 along with their lanthanum counterparts. The latter have been used for additional calculations in order to avoid problems with the f states. For all pairs of compounds the cell volume of the cerium phase is smaller, a consequence of the lanthanide contraction. From comparison with the complete series [START_REF] Kraft | Ternary Gallides REMgGa (RE = Y, La, Pr, Nd, Sm-Tm, Lu) -Synthesis and Crystal Chemistry[END_REF][START_REF] Kraft | Ternary Indides REMgIn (RE = Y, La-Nd, Sm, Gd-Tm, Lu) -Synthesis, Structure and Magnetic Properties[END_REF][START_REF] Kraft | Ternary Thallides REMgTl (RE = Y, La-Nd, Sm, Gd-Tm, Lu)[END_REF][START_REF] Fickenscher | Synthesis and Crystal Structure of REAgMg (RE = La, Ce, Nd, Eu, Gd, Tb, Ho, Tm, and Yb)[END_REF], all cerium phases are trivalent, in agreement with the magnetic susceptibility data. An interesting situation occurs for the compounds with the heaviest X components. In the pairs CeMgPd/CeMgPt, CeMgAg/CeMgAu, and CeMgIn/CeMgTl, the platinum, gold, and thallium compound show the smaller cell volumes, a consequence of the relativistic contraction.

A drastic difference between the CeMgX phases with a p and a d element is the much larger c/a ratio for those with the p elements (Table 1). This behavior is directly related to the magnesium triangles forming the X2@Mg6 trigonal prisms around the origin of the unit cells. The Mg-Mg distances for CeMgIn (325.9 pm), CeMgTl (327.0 pm), CeMgAg (325.6 pm), and CeMgAu (323.1 pm) are all close to the average Mg-Mg distance of 320 pm in hcp magnesium [START_REF] Donohue | The Structures of the Elements[END_REF]. Thus, changes in Mg-X bonding are managed through increase or decrease of the height of the trigonal prism.

The shortest interatomic distances in the CeMgX structures occur for Mg-X. The average Mg-In (302 pm), Mg-Tl (301 pm), Mg-Ag (295 pm), and Mg-Au (291 pm) distances (Table 2) are all longer than the sums of the covalent radii [START_REF] Emsley | The Elements[END_REF] of 286, 291, 270, and 270 pm, respectively, indicating medium bond strength. It is evident from Table 2, that the cerium atoms have five indium, thallium, silver, or gold atoms as nearest neighbors. Thus, the electropositive cerium atoms bind to the more electronegative triel or transition metal atoms. Accordingly we can ascribe thallide and auride character to CeMgTl and CeMgAu. These features of chemical bonding are addressed in more detail in the following sections.

Electronic structure and chemical bonding

In view of the large CeMgX and LaMgX equiatomic family of X = triel and X= transition metal intermetallics, we have elected to show the results representative of X = Ga and X = Pd respectively.

Energies and derived quantities

The experimental crystal data (Table 1) were firstly used for carrying out unconstrained geometry optimization runs with VASP-PAW-GGA in order to get the minimum equilibrium energies and energy derived quantities as the bulk modulus B0 based on Birch energy-volume equation of state [START_REF] Birch | Finite strain isotherm and velocities for single-crystal and polycrystalline NaCl at high pressures and 300 K[END_REF] for the four selected compounds, as well as an analysis of trends of charge transfers. Table 3 provides the calculated parameters of total electronic energy, cohesive energy, volume and B0. According to the nature of X, the compounds are regrouped in close values of all four quantities with smaller magnitudes for X = Ga. The calculated volumes are found in relative good agreement with experiment with the trend of larger values due to the use of the GGA XC functional known to be under-binding. The cohesive energies obtained by subtracting the energies of the atomic constituents in their ground states from the total energies. The X =Pd compounds are found more cohesive than X = Ga ones and the cerium based compounds are found with larger cohesive energy than the lanthanum compounds Similar trends are found for the bulk modules which are found larger for X = Pd than for X = Ga with larger magnitudes for the Ce based ternaries. With one more electron brought in by Ce versus La and the presence of d states in Pd versus p Ga states, directional bonding should be at the origin of the observed differences. These aspects can be reflected in the analysis of the chemical bonding discussed in the next section. Lastly the B0 magnitudes are within the range of ternary equiatomic intermetallic compounds [START_REF] Matar | Review on Cerium Intermetallic Compounds: A Bird's Eye Outlook through DFT[END_REF].

We also discuss the trends of charge transfers obtained from the analysis of the charge density within the atoms in molecules AIM theory of Bader [START_REF] Bader | A quantum theory of molecular structure and its applications[END_REF]. Table 4 provides the charges on the respective atoms in the four studied compounds. The trend of negatively charged X is observed in all four compounds leading to assign the chemical labeling of gallides and palladides. Positively charged La, Ce and Mg are identified with larger electropositive values in the Pd based intermetallics likely due to the larger electronegativity: Pd > Ga (2.2 versus 1.81) while Ce and La have close  of 1.1. The difference in magnitudes between X1 and X2 arises from their respective crystal chemistry, i.e. with respect to X1@Ce6 prisms versus X2@Mg6 prisms.

Total-spins and spin-polarized magnetic calculations (NSP, SP)

With the experimental structure parameters (Table 1) the complete site and spin projected density of states (DOS) were computed in both non spin polarized (NSP) and spin polarized (SP) configurations using the full potential scalar relativistic ASW method. Table 5 provides the values of energy differences between the considered magnetic configurations and the spin only magnetic moment on Ce. For CeMgGa the energy difference between the two magnetic configurations is ESPF-NSP = -0.172 eV/cell. This value deceases down to -0.046 eV for X = Pd. The SPF configuration is stabilized with respect to NSP due to magnetic exchange which is then larger magnetic X = Ga case leading to larger magnitude of the Ce moment. Small moments are obtained for the other constituents resulting from some residual polarization due to the mixing of the valence states with those of magnetically polarized Ce. In view of the fact that both

CeMgX order antiferromagnetically at TN = 3.1 2.1 K respectively [START_REF] Gibson | Synthesis, Structure, and Magnetic Properties of LaTMg and CeTMg (T = Pd, Pt, Au)[END_REF], further SP antiferromagnetic (SPAF) calculations were carried out by doubling the cell along c so that the atoms belonging to the first half of the double cell are assigned SPIN UP magnetic subcell and the other half SPIN DOWN magnetic subcell. For CeMgGa the calculations lead to further stabilization ESPAF-SPF = -0.04 eV/cell whereas similar SPAF calculations carried on CeMgPd led to a vanishing of the magnetization. This can be assigned to its smaller TN value together with the lower magnitudes of the magnetization in the SPF configuration with respect to CeMgGa. This likely leads to instability of the heavier SPAF calculations with subsequent vanishing magnetic polarization on the atomic constituents, mainly Ce.

The SPF and SPAF results are further illustrated with the site and spin projected DOS shown in Fig. 4.

In the first two panels corresponding to SPF calculations, the majority spin (↑) are shifted to lower energy versus minority spin states (↓). This energy difference, related to magnetic exchange, leads to the onset of the magnetic moment which is, as described above, carried only by Ce. Within the valence bands of both compounds, very small intensity Ga, Pd d states and itinerant Mg and Ce states mix in a similar way as in the NSP state without any energy shift between the two spin channels (↑ and ↓). For Ce, it can be noted the larger energy shift in CeMgGa as with respect to CeMgPd, proportional to the magnitudes of the respective magnetic moments and total magnetizations (Table 5). The third panel of Fig. 4 shows the fully compensated magnetizations between the two magnetic subcells 'SPIN UP' and 'SPIN DOWN', signature of the SPAF configuration of CeMgGa.

Properties of chemical bonding (COOP)

Through exploring the energy quantities (Table 3) it was found out that the Pd based intermetallics were significantly more cohesive versus the Ga ones. This is also accompanied by larger hardness. These observations let suggest a role played by the chemical bonding accounting for pair interactions. Such properties can be qualitatively described based on the analysis of the overlap integrals Sij within the crystal orbital overlap population (COOP) introduced by Hoffmann in quantum chemical methods [START_REF] Hoffmann | How Chemistry and Physics Meet in the Solid State[END_REF] and implemented into the ASW method [START_REF] Eyert | The Augmented Spherical Wave Method[END_REF].

Figure 5 shows the COOP for X = Ga (top panels) and X = Pd (bottom panels). The calculations are for NSP configuration. Whereas in all panels the VB is of positive CO-OP intensities, i.e. of bonding nature, the antibonding states starts developing above EF within the CB. This comforts the cohesive nature of all compounds (Table 3).

Differences can be observed at two different levels, pertaining:

1) to the nature of X d which binds either with p states (Ga) in the close neighborhood of EF or with more intense and localized (directional) d states (Pd) at ~-4 eV below EF ; and

2) to the nature of the 4f element La or Ce whereby the latter has bonding sharp COOP at EF whereas La shows broader COOP arising mainly from d states, a character missing with the Ga itinerant states.

The major bonding contribution arising from (La,Ce)-Ga and (La,Ce)-Pd and the latter being more directional one may understand the larger bulk modulus of the Pd based compounds (Table 1).

Conclusions

In this work aiming at better rationalizing the properties of a rich family of Mg based

1 .

 1 , space group Pearson code hP9, and Wyckoff sequence gfda. A projection of the CeMgX structure onto the xy plane is presented in Fig. The striking structural motif is the trigonal prismatic coordination of the X atoms. The X1 atoms are coordinated by six cerium atoms and six of these X1@Ce6 prisms condense via common edges forming hexagonal rings. The latter are filled by the X2@Mg6 prisms. Both prismatic motifs are shifted with respect to each other by half the c lattice parameter, emphasized by thin and thick lines in Fig. 1. Condensation along the c axis proceeds through common triangular faces.

Figs. 2

 2 Figs. 2 and 3 regroup the NSP DOS for the two series. Along the x axis the energy reference is with respect to the Fermi level (EF) which is crossed by a large Ce(DOS) while a deep minimum is observed for LaMgGa and a small DOS magnitude can be seen for LaMgPd. The difference is due to the electron configuration of the rare earth elements Ce and La which differ by one 4f electron. This point is further stressed in the developments related with the magnetic instability.

  intermetallic compounds: LaMgX and CeMgX (X = triel or transition metal), DFT-built methods were applied to four representatives based on Ga and Pd. From charge transfer trends, the compounds are found as 'gallides' and 'palladides' with stronger cohesion and larger hardness characterizing the latter family. Magnetic polarization is found only in the Ce based compounds with a calculated antiferromagnetic ground state in agreement with experiment. Qualitative chemical bonding analysis shows different behaviors between the Ga and Pd families with a role played by Pd assigned to directional d states versus Ga broad s,p and subsequent stronger bonding for the former. This further illustrates the calculated cohesive energy and bulk module trends.

Fig. 1 .Fig. 2 .Fig. 3 .

 123 Fig.1. Projection of the CeMgX structure onto the xy plane. Cerium, magnesium, and X atoms are drawn as medium gray, black open, and filled circles, respectively. All atoms lie on mirror planes at z = 0 (thin lines) and z = 1/2 (thick lines). The trigonal prisms around the X atoms are emphasized. Fig.2. Triel intermetallics with X = Ga representatives in non magnetic total spin configuration (NSP). CeMgGa (top) and LaMgGa (bottom). Fig.3. Transition metal intermetallics with X = Pd representatives in non magnetic total spin configuration (NSP). CeMgPd (top) and LaMgPd (bottom).

Fig. 4 .

 4 Fig. 4. Site and spin projected density of states (DOS) in SPF configuration of CeMgGa (top) and CeMgPd (middle) and SPAF total DOS for SPAF CeMgGa (bottom).

Fig. 5 .

 5 Fig. 5. Chemical bonding for X = Ga (top) and X = Pd (bottom) in CeMgX and LaMgX.

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 5

 1235 Fig. 1.

Table 1

 1 Lattice parameters of equiatomic compounds LaMgX and CeMgX (X = Ga, In, Tl, Pd, Ag, Pt, Au) with hexagonal ZrNiAl type structure.

	Compound a / pm	c / pm	V / nm 3	c/a	Reference
	triel intermetallics
	LaMgGa	760.2(2)	459.6(1)	0.2300	0.605	[25]
	LaMgIn	782.6(2) 481.08(9)	0.2552	0.615	[26]
	LaMgTl	781.3(1) 477.84(8)	0.2526	0.612	[27]
	CeMgGa	752.7(2)	454.8(1)	0.2232	0.604	[25]
	CeMgIn	774.9(3)	477.7(2)	0.2484	0.616	[26]
	CeMgTl	774.1(1) 473.75(7)	0.2458	0.612	[27]
	transiton metal intermetallics
	LaMgPd	773.6(1) 413.79(4)	0.2145	0.535	[30]
	LaMgAg	788.8(3)	437.4(1)	0.2357	0.555	[29]
	LaMgPt	762.0(1) 417.48(5)	0.2099	0.548	[30]
	LaMgAu	781.0(1) 425.49(9)	0.2248	0.545	[30]
	CeMgPd	767.3(1) 410.37(4)	0.2092	0.535	[30]
	CeMgAg	782.5(3)	432.8(1)	0.2295	0.553	[29]
	CeMgPt	755.02(7) 413.82(4)	0.2043	0.548	[30]
	CeMgAu	774.1(3)	421.6(1)	0.2188	0.545	[30]

Table 3

 3 Calculated parameters of equiatomic compounds LaMgX and CeMgX (X = Ga, Pd): Total and cohesive energies per unit cell, volumes and bulk moduli are in eV, nm3 and GPa units respectively.Energies per atom of constituents: E(Ce) = -4.43 eV; E(La) = -4.92 eV; E(Ga) = -2.91 eV; E(Mg) = -1.39 eV; E(Pd) = -5.17 eV

	Compound	E total	E cohesive Vexp.(calc.)	B 0
	LaMgGa	-32.36	-1.56 0.230 (0.232)	49.8
	CeMgGa	-31.77	-1.86 0.223 (0.229)	51.4
	LaMgPd	-40.87	-2.13 0.214 (0.218)	60.5
	CeMgPd	-40.11	-2.38 0.209 (0.215)	62.3

Table 4

 4 Calculated parameters of equiatomic compounds LaMgX and CeMgX (X = Ga, Pd): Bader charges per atom in e units.

	Compound Q(La/Ce)	Q(Mg)	Q(X1)	Q(X2)
	LaMgGa	1.05	1.13	-2.53	-2.01
	CeMgGa	1.07	1.14	-2.03	-2.56
	LaMgPd	1.16	1.14	-2.86	-2.02
	CeMgPd	1.19	1.15	-2.87	-2.08

Table 5

 5 Calculated parameters of equiatomic CeMgGa and CeMgPd in ferromagnetic configurations (not ground state). Energies are in eV/cell and Ce magnetic moments (spin-only) in  B .

	CeMgX	ESPF-NSP	mCe	m Mg/X1/X2	M(cell)
	X = Ga	-0.176	0.841 0.04/0.004/0.01	2.674
	X = Pd	-0.046	0.595 0.02/0.019/0.02	1.922

Acknowledgment

This work was financially supported by the Deutsche Forschungsgemeinschaft. We acknowledge support from the Conseil Régional d'Aquitaine. Part of the computations were carried out on the MCIA supercomputers of the University of Bordeaux.