Soumeya L Achour
email: soumeya.achour@hmn.ap-hop-paris.fr

MS, DVM Michel Dojat

PhD Claire Eng

Rieux

MD Philippe Bierling

PhD Eric Lepage

A UMLS-Based Knowledge Acquisition Tool for Rule-Based Clinical Decision Support Systems Construction

Keywords: Knowledge Engineering, Domain Ontology, Arden Syntax, and Blood Transfusion

Decision support systems in the medical field have to be easily modified by medical experts themselves. We have designed a knowledge acquisition tool to facilitate the creation and the maintenance of a knowledge base by the domain expert and its sharing and reuse by other institutions. The Unified Medical Language System (UMLS) constitutes the domain entities and relations repository from which the expert builds, through a specific browser, the explicit domain ontology. The expert is then guided in creating the knowledge base according to the preestablished domain ontology and condition-action rule templates that are well adapted to several clinical decision making processes. Corresponding Medical Logic Modules (MLMs) are eventually generated. The application of this knowledge acquisition tool to the construction of a decision support system in blood transfusion demonstrates the value of such a pragmatic methodology for the design of rule-based clinical systems that rely on highly progressive knowledge embedded in hospital information systems.

I. Introduction

Clinical decision support systems (CDSSs) have been shown to be very helpful to medical practitioners. Knowledge acquisition (KA) and modeling play leading roles in the development of such knowledge based systems. Unfortunately, two key factors limit the development of CDSSs and their integration in Hospital Information Systems (HIS): 1) the time and effort required by medical experts to create and maintain knowledge bases; and 2) the extreme difficulty of sharing and reusing the validated knowledge bases because of their idiosyncrasies and lack of clarity for users outside the originating institution. The latter factor is considered to be the main limitation to daily use of CDSSs [START_REF] Musen | Dimensions of knowledge sharing and reuse[END_REF] . The goal of our work is the design of a KA tool to facilitate the creation and maintenance of a knowledge base by the medical expert and its subsequent sharing and reuse by other medical institutions. There are several approaches to achieving reuse, notably through generic abstractions: Lexicons, ontologies and problem-solving methods are built up and then adapted to fit the specific needs of a typical medical domain application [START_REF] Chandrasekaran | Generic tasks in knowledge-based reasoning: High-level building blocks for expert system design[END_REF][START_REF] Steels | Components of expertise[END_REF][START_REF] Rector | The GRAIL concept modelling language for medical terminology[END_REF][START_REF] Shahar | A framework for knowledge-based temporal abstraction[END_REF] .

through the standardization of the knowledge representation: several standards have been proposed, such as KIF [START_REF] Genesereth | Knowledge Interchange Format[END_REF] , Ontolingua [START_REF] Farquhar | The Ontolingua Server: a Tool for Collaborative Ontology Construction[END_REF] and Arden Syntax 8 .

through specific models, such as GLIF [START_REF] Ohno-Machado | The guideline interchange format: a model for representing guidelines[END_REF] or PROforma [START_REF] Fox | Disseminating medical knowledge: the PROforma approach[END_REF] , to represent certain kinds of clinical guidelines and support their dissemination.

Our project relies on the first two approaches. Some KA environments have been proposed taking into consideration the specifics of the medical reasoning process and medical expertise. The research project GAMES [START_REF] Van Heijst | Foundations for a methodology for medical KBS development[END_REF] , views the KA process as the construction of two models: the epistemological model, entailing the knowledge required to perform a particular task, and the computational model, containing data structures and algorithms designed to allow the computerized execution of that task. The PROTÉGÉ environment allows developers to configure available problem-solving methods that are mapped to domain ontologies and generates task-specific knowledge acquisition tools. In parallel to architectures for KA, there is considerable work under way to create medical ontologies, a key component for building and reusing knowledge-based systems. For instance, the representation and integration language GRAIL, from the GALEN project, is especially designed to support models of medical terminology and achieve reuse of taxonomies 4, 13 . We consider that the

Unified Medical Language Sources (UMLS) constitutes a knowledge corpus useful for building knowledge bases. Our approach, less general than that of PROTÉGÉ, is designed for medical experts without specific training in medical informatics. It allows them to configure rule-based templates that are mapped to the UMLS-based domain specific lexicon they have formerly constructed. Medical logic modules (MLMs) written in Arden Syntax are eventually generated in order to facilitate reuse and sharing of this knowledge base.

MLMs have been used to generate clinical alerts, interpretations or diagnoses [START_REF] Hripcsak | The Arden Syntax for medical logic modules[END_REF][START_REF] Hripcsak | Design of a clinical event monitor[END_REF][START_REF] Gao | Pre-compiling medical logic modules into C++ in building medical decision support systems[END_REF][START_REF] Pryor | The use of medical logic modules at LDS hospital[END_REF][START_REF] Jenders | Medical decision support: experience with implementing the Arden Syntax at the Columbia-Presbyterian Medical Center[END_REF] . For several years there have been numerous attempts to facilitate the creation of MLMs with respect to the Arden syntax. Interesting clinical experiences with MLM editors have been reported [START_REF] Gao | Design and fuctions of medical knowledge editors for the Arden Syntax[END_REF][START_REF] Jenders | Assessment of a knowledge-acquisition tool for writing Medical Logic Modules in the Arden Syntax[END_REF][START_REF] Sailors | MLM Builder: an integrated suite for development and maintenance of Arden Syntax medical logic modules[END_REF] . Our project differs from previous work in that it integrates the generation of MLMs into the general process of KA (ontology and knowledge base). In this article we report on our KA methodology; on the use of this methodology to build a CDSS applied to blood transfusion; and on a preliminary test of our system. In blood transfusion, the evolution of both medical knowledge and government regulations imposes a continuous adaptation of the CDSS that wholly justifies the use of our approach. Several CDSS have been proposed in this field [START_REF] Spackman | A knowledge-based system for transfusion advice[END_REF][START_REF] Marconi | Quality assurance of clinical transfusion practice by implementation of the privilege of blood prescription and computerized prospective audit of blood requests[END_REF] . Similar to all classical rule-based systems, these systems were difficult to maintain and extend. No specific knowledge acquisition technique was used for their development. One application embedded in the HELP system, concerns a computerized monitor blood ordering system based on a critiquing approach [START_REF] Gardner | Computer-critiqued blood ordering using the HELP system[END_REF][START_REF] Lepage | Development of a computerized knowledge based system integrated to a medical workstation: Application to blood transfusion[END_REF][START_REF] Lepage | Improving blood transfusion practice: role of a computerized hospital information system[END_REF] . A set of knowledge tools is proposed to the expert for the definition and the maintenance of the knowledge base and a local data dictionary can be used. All these CDSS in blood transfusion turn essentially around the question of whether to transfuse or not. In addition to this issue, we studied, the choice of the qualifier (e.g. phenotyped or irradiated) of the product to be transfused. Our CDSS is currently being tested at the Henri Mondor Hospital (Créteil, France).

II. Methodology

Our methodology for knowledge acquisition and representation relies on two steps: first a domain ontology is developed: the expert selects the entities and relations present in UMLS that are relevant to constructing the domain ontology; and if needed, s/he introduces new terms and relations. Secondly, the domain knowledge is constructed: according to the pre-established domain ontology, the expert is guided in creating the knowledge base via condition-action rule templates. Corresponding MLMs are eventually generated automatically. Figure 1 represents our methodology.

Figure 1. Knowledge acquisition process and decision support system design. Block A: The domain ontology is built via the UMLS browser. Block B: The knowledge acquisition interface allows the instantiation of a general problem solving method using the domain ontology. MLMs are automatically created and organized thanks to the knowledge manager. Block C: An example of a decision support system architecture whose knowledge base is generated using our methodology. The arrival of new data (1) triggers the event procedure (2), and then the relevant MLMs (3), which represent the knowledge base, are executed by the inference engine (4). A results table containing a summary of the diagnosis and the order for blood products is provided (5). Initial data are sent automatically by the hospital information network or entered manually by a physician.

A. Construction of the Domain Ontology using UMLS

To facilitate sharing and reuse, we have chosen UMLS, elaborated to facilitate the integration of information from multiple biomedical sources, to constitute the repository of entities and relations from which the expert builds the domain ontology. Three components constitute the UMLS. The Metathesaurus contains a collection of biomedical concepts and their inter-relations. The Semantic Network, through its high level semantic types, provides a consistent categorization of all concepts represented in the Metathesaurus. The Specialist Lexicon is an English language lexicon with biomedical terms. The lexicon entries for each word or term records syntactic, morphological, and orthographic information. UMLS provides a shared source of terminology widely used in clinical applications [START_REF] Friedman | The UMLS coverage of clinical radiology[END_REF][START_REF] Cimino | Representation of clinical laboratory terminology in the Unified Medical Language System[END_REF][START_REF] Campbell | Representing Thoughts Words, and Things in the UMLS[END_REF][START_REF] Burgun | Knowledge acquisition from the UMLS sources: application to the description of surgical procedures[END_REF] . In order to navigate between concepts through the concept hierarchy and through the semantic network, we have designed a specific navigator [START_REF] Achour | The use of the UMLS Knowledge Sources for the Design of a Domain Specific Ontology : a Practical Experience in Blood Transfusion[END_REF] .

The UMLS Navigator

The conceptual model (Figure 2) of our navigator is based on two components of the UMLS: the Metathesaurus and the Semantic Network. We have adopted an object-oriented representation. Concept is the main class of our Metathesaurus model. It includes several attributes (for example ConceptDefinition, ConceptLinks,etc.). It reflects properties present in UMLS; each concept has a unique identifier. Different terms with the same meaning are linked to the same concept identifier. We have reified the link (LinkConceptToVariantes) between a concept and these terms (preferred term, synonyms, etc). The relation (ConceptLink) between two concepts has three parameters represented as classes: a ConceptRelation (parent, child, general, specific...), a ConceptRelationAttribut (isa, inverse_isa...) and an InformationSource (Mesh98...) that provides it. Our representation of the UMLS semantic network is then a reified graph whose edges are the semantic relations (SemanticLinks ) such as affected_by, occurs_in., and vertices are the semantic types (SemanticType) or semantic relations (SemanticRelation).

Figure. 2. Conceptual model of UMLS including Metathesaurus and Semantic Network (OMTdiagram 34 ).

The lines indicate relations between classes.

Domain Ontology Construction

The construction of the domain ontology requires four steps. First, the expert identifies the medical terms used in the specific domain. Using our specific browser (Figure 3), s/he looks in the UMLS metathesaurus for the corresponding concepts, selects any relevant concepts and adds them to create a list. To facilitate comprehension and to enrich her/his list s/he then identifies for each concept its ascending hierarchy (i.e. its parents). Depending on the source vocabulary within the Metathesaurus, a concept can be found at several levels within a specific ascending hierarchy. Figure 4 shows the different possible ascending hierarchies for hemolytic autoimmune anemia term. The expert selects the hierarchy that corresponds to the semantic meaning s/he associates with a specific concept, or constructs her/his hierarchy by choosing the concepts from the different sources. Because strong standardization is not always possible in medicine, a medical expert can insert new terms or extend the initial hierarchy corpus to take into account particular considerations [START_REF] Dojat | Effective domain-dependent reuse in medical knowledge bases[END_REF] .

For term insertion, two constraints must be respected: the new concept must be linked to a semantic type from the UMLS semantic network and must have a parent. If a specific classification is constructed, it is saved in the UMLS format (MRCXT table) with a specific tag (PERSO) in the raw source (SAB).

All the concepts extracted from the UMLS or created have a local identifier, and are stored in a local table. This local table allows the link with the clinical database of the hospital. When introducing new terms and classification, the expert has the responsibility, for checking their adequacy and their consistency with the set of information contained in PERSO. As semantic types are general, an intermediate layer, named categories, has been added to introduce more specific types. The categories correspond to the concepts located at the top of the hierarchy of the contextual list selected from those present in the Metathesaurus or created by the expert. For instance, Anemia Sickle Cell is initially linked to the Diseases or Syndrome semantic types. We have introduced the category Hematological Diseases as a subclass of Disease or Syndrome semantic type, to which Anemia Sickle Cell is linked (see Figure 5). In the fourth and final step, following the classification of the terms according to an ascending hierarchy, all possible relations among these terms are automatically determined. For this purpose, a query is performed on the UMLS semantic network, to extract relationships between semantic types and concepts useful to represent the expert's knowledge. Then, the expert selects the relevant relationships between concepts among those present in the Metathesaurus. Once again the expert may add new relationships to this contextual list (identified with the label «PERSO »). During the ontology design, a local identifier (CLI) is automatically created for each concept acquired. This CLI is stored in the slot data of the MLM during the knowledge acquisition process. A local table is then designed to link and translate these local identifiers to the clinical database identifiers (CDBI).

Medical Terms

Categories

A B

Semantic Types From the development of the domain ontology, three different structures are obtained: 1) the hierarchy of terms and concepts used in the domain. These terms have an ascending hierarchical context, connected by the relation "inverse_isa"; 2) the concepts located at the top of the hierarchy that have been selected will compose the list of categories that subsume the medical terms used; and 3) the UMLS semantic network excerpt covering the concepts selected for the domain, such that each of the terms has a semantic type and a category.

A 1 A 3 A 2
For the collection of terms present (n=120), in the blood transfusion domain, the medical expert found corresponding UMLS Metathesarus conceptsfor 88 (i.e., 73%). The blood transfusion domain used highly specialized terms such as "transfusion of red blood cell plasma depleted", " transfusion of red blood cells phenotyped ", " patient erythrocyte alloimmunised ", etc. which were not present in the version of the Metathesaurus used. The coverage of disease terms qualified by such adjectives as minor, severe, or chronic was uneven.

B. Domain Knowledge Construction

Starting from the predefined domain ontology, the expert creates the domain knowledge needed by the application. We have modeled the knowledge with production rule templates. Our knowledge acquisition tool guides the user through three steps of rule description: 1) documentation following the Arden syntax definitions; 2) specification of the condition part of each rule; and 3) specification of the action part of each rule. The entities that compose the conditions and action parts of the rules come from the domain ontology and are linked to the semantic types. To illustrate the process of rule specification, let us start with the rule template (see Figure 6

Generation of Medical Logic Modules

A MLM, equivalent to a single rule in a rule-based expert system, contains enough medical knowledge and data to make a single clinical decision [START_REF] Hripcsak | Rationale for the Arden Syntax[END_REF] . MLMs can be independent of one another but also can be linked by CALL statement. A MLM is an ASCII file composed of slots grouped into three categories: Maintenance, Library and Knowledge. The categories parts of the MLM are acquired via the KA-tool. The Figure 7 shows the interface for the construction of Rule 2.

In order to facilitate maintenance and avoid redundancy or inconsistency, MLMs are organized depending on the concepts they manipulate.

DISEASES OF THE IMMUNE SYSTEM

Primary immunodeficiency

FINDING

Hemathologic neoplasm

MLMs with the relation: "the action of ". This allows the expert to retrieve easily all MLMs that trigger a specific action. Finally, this knowledge is formalized according to the Arden syntax with MLMs linked to the domain ontology. One hundred and ten rules (translated in MLMs) entail the knowledge base. The indexing and the referencing of the terms that compose each MLM are used to identify possible redundancies and inconsistencies during the creation of a new MLM. In the current prototype, the checking for redundancy and inconsistency is performed manually. Inheritance property is not used during MLM construction.

III. Experience with a CDSS for Blood Transfusion

The transfusion of blood products is an inescapable therapy for certain pathologies that has the potential to induce undesirable immunological and infectious effects, like HIV or Hepatitis. The best guarantee for the patient's safety is strict adherence to transfusion guidelines. In addition, the transfusion of blood products is an expensive therapy that, in terms of public health, must be prescribed advisedly. A CDSS that assists the prescription of blood products seems to be an appropriate tool for enhancing patient safety and reducing heath care costs. However the expansion of medical knowledge about blood transfusion and changes in government regulations impose a requirement for frequent adaptations of decision rules for blood transfusion. At the Henri Mondor Hospital (Créteil, France), approximately 30,000 blood products per year are distributed to 5,000 patients. Such volume justifies the development of a CDSS integrated into the hospital information network to assist the clinician in blood product prescriptions. We constructed a CDSS for blood transfusion using the methodology previously described.

A. Architecture of the CDSS

Starting from blood data (essentially hemoglobin and platelet concentrations) and the patient's state (disease, current therapy, ect…), the system indicates whether transfusion is required and if so, which type and quantity of product to transfuse. It works according to the data-driven and application-driven principles of the MLM-controller 15, 16 that schedules the MLMs execution.

The CDSS is composed of three modules (see Figure 1): 1) The user interface to retrieve information from the patient database, 2) The knowledge base that contains expertise for blood transfusion in MLMs, 3)The inference engine that executes the relevant MLMs. Two modes are available: alert (data-driven) and consultation (application-driven). Alert: When biological data are automatically sent into the patient database (1), the event procedure is triggered (2). This activates (3) several MLMs executed by the inference engine (4).

Actions are performed and a table of results is generated (5). Depending on the seriousness of the diagnosis an alarm signal could be set on. These steps are shown in Figure 1.

Consultation:

The physician keys-in data about the patient as well as the prescription specifying the type and quantity of products to be transfused. Then, the system determines whether the transfusion is appropriate and the type, qualifier and quantity of the product to be transfused. Details of the system's decisions are displayed to the physician. If s/he disagrees, s/he can order other products and justify her/his choices in a brief report. A complete report including the system's and the physician's recommendations is sent to the blood bank.

B. Preliminary results

A first evaluation was performed in order to validate the coherence and the correctness of the CDSS. For that, thirty orders were studied, which demonstrated the reliability of transfusion order (98% for platelet and 97% for red cells transfusion). A discrepancy was observed between the system and the physicians in 18 of 30 cases (60%) for the qualifiers of the product to transfuse such as phenotyped and/or compatibilized. Analysis of these discrepancies revealed a need to add more information about the patient's status and to modify rules in the knowledge base. Twenty new orders were then evaluated using the modified CDSS. Some disagreements persisted between physician's order and CDSS's conclusions (40 %), but there was 100% agreement between the CDSS and the experts who reviewed the orders. This result was explained by the fact that physicians did not follow the current transfusion guidelines. A working committee was appointed to modify current practice, to adhere to new transfusion guidelines. The prototype is presently being evaluated at the Henri Mondor's Hospital.

IV. Discussion

We argue that our approach is a practical way to build CDSSs: it 1) avoids constructing the domain specific ontology from scratch, 2) limits the introduction of idiosyncratic terms and relations and 3) combines reuse and sharing with domain-specific lexicons familiar to clinicians. In our experiment, the UMLS provides a useful corpus of medical knowledge for designing a domain specific lexicon. Parallel to efforts to define a specific knowledge representation language for clinical concepts [START_REF] Rector | The GRAIL concept modelling language for medical terminology[END_REF] , UMLS constitutes a pragmatic way to facilitate knowledge sharing and reuse. There have been many projects to quantify the content coverage of the UMLS in several fields: clinical radiology [START_REF] Friedman | The UMLS coverage of clinical radiology[END_REF] , laboratory terminology [START_REF] Cimino | Representation of clinical laboratory terminology in the Unified Medical Language System[END_REF] , surgical procedures [START_REF] Burgun | Knowledge acquisition from the UMLS sources: application to the description of surgical procedures[END_REF] and in hypertension notes [START_REF] Campbell | The clinical utility of META: an analysis for hypertension[END_REF] . These projects showed limitations of Metathesaurus terms in specific areas, demonstrating the necessity to add new terms and relations for a particular use of UMLS. Nevertheless, like other investigations [START_REF] Campbell | The Unified Medical Language System: toward a collaborative approach for solving terminologic problems[END_REF] we consider that UMLS is a useful formal framework, easily available to medical institutions and continuously updated by NLM. The introduction of new terms besides those found in UMLS, reflects the specific needs of the expert and respects the philosophy of the UMLS, that concatenates several databases to gather the particularities of each of them.

We have designed a domain specific interface to allow the domain expert to input directly or modify existing knowledge in a CDSS using domain ontology. Our KA-tool uses rule templates appear well adapted to the decision-making process in the clinical applications we envisage. Our tool is designed for medical experts without specific training in medical informatics and allows their active participation during the process of CDSS construction. This can facilitate future integration of the CDSS into the hospital system. Domain knowledge is automatically transformed into MLMs in Arden syntax so that it can be reused and shared by other institutions.

Our KA-tool is not only a MLM editor. It allows the acquisition of knowledge through the predefined domain ontology. It is in the same vein that the work of Thurin et al. [START_REF] Thurin | Arden syntax and GALEN terminology support: a powerful combination to represent medical knowledge[END_REF] who proposed a tool for building MLMs from a GALEN based terminology. Arden syntax is mature enough to be used successfully in large working projects in clinical institutions. However, it does have drawbacks such as a style of rule representation that is not necessarily adapted to all clinical applications, low expressiveness of temporal primitives, and possible interactions between MLMs that can pose long-term maintenance problems.

In our system, the introduction of new terms, during domain ontology acquisition, can generate redundancies and conflicts with terms already present in the database. During domain knowledge acquisition, some conflicts may appear between rules. In the current implementation, the domain expert receives relatively little help from the system in solving redundancies and conflicts. Temporal aspects of the domain are currently not taken into account. Clearly, our tool should be extended to incorporate specific mechanisms to deal with these drawbacks.

To date we have used the prototype only in collaboration with two medical experts involved in this project in our hospital. Their involvement since the start of the project clearly biases their fully positive opinion. However, we believe that our tool will be accepted by end-users in those medical fields where decision support systems have to be easily modified by medical experts themselves. Creating domain ontologies that are reusable in new medical applications is a challenging task [START_REF] Van Heijst | A case study in ontology library construction[END_REF] . Our experiment provides a practical example of how large resources such as UMLS, can be used to design a domain ontology and how that ontology can be put to use.

Results reached in the area of blood transfusion demonstrate that UMLS provides a useful and manageable corpus of medical knowledge for domain ontology construction.

Figure. 3 .

 3 Figure. 3. Our UMLS Navigator GUI. The figure shows the exploration of the Metathesaurus for the anemia concept.

Figure. 4 .

 4 Figure. 4. General outline of the ontology. A: The semantic types in relation with categories. The expert also assigns the semantic types from the semantic network for any new concept added. B: 1) Categories that subsume the medical terms used, 2) Concepts in relation with medical terms according to a hierarchic classification, 3) Medical terms used, 4) some MLMs where b 1 , b 3 and b 7 are present in condition or action parts.

4 Figure 5 .

 45 Figure 5. Selection of the relevant hierarchy from different sources. A specific popup menu (not shown here) allows for the construction of our personal hierarchy (namely perso).

  ) (A 1 ) (A 3 ). After selecting, A1 for the condition part, the expert can choose between b α and b β . The selection of b α leads to three possible choices: b 1 , b 2 and b 3 , the expert chooses the concepts b 1 and b 3 for the condition part. A 3 then b δ and then b 7 is selected for the action part leading to rule 1: IF condition (b 1 ) present and condition (b 3 ) present THEN action (b 7 ) activated Rule1

Figure. 6 .

 6 Figure. 6. An excerpt of our domain ontology based on the UMLS. A: Semantic types, B: Categories, C: Terms used in the medical expertise. Rectangles with white background indicate entities used in rule 2 (see text).

Figure. 7 .

 7 Figure. 7. Knowledge acquisition interface. Three list boxes allow the selection of the corresponding entities that appear in condition or action parts of the rule. The rule under construction is shown at the bottom of the figure.

  The name of the MLM is stored in the slot filename of the category Maintenance and the concepts used in this MLM (e.g b 1 , b 3 , b 7 for Rule 1) are stored in the slot keywords of the category library. The concepts appearing in the condition part are linked, to the corresponding MLMs, by the relation "has as rule" to facilitate the retrieval of specific MLMs. The goal of each MLM, represented by its action, is stored in the slot purpose of the category library. The concepts appearing in the action part are linked to the corresponding

						THERAPEUTIC
	A	Disease or Syndrome				or PREVENTIVE PROCEDURES
	B	Hematologic Disesases	SIGNS and SYMPTOMS		Hematologic Tests	Transfusion and related procedures
		Anemia, Sickle Cell	FEVER	Platelet count	Hemoglobin	Erythrocyte Transfusion
	C	Multiple Organ Failure				Platelet Transfusion
		Rule 2
		IF (Sickle Cell Anemia)
		AND (Multiple Organ Failure)
		AND (Hemoglobin<10)
		THEN (ErythrociteTransfusion)


Iurii Dovgaliuk
email: iurii.dovgaliuk@mail.chimie.ens.fr

Vadim Dyadkin

Mathieu Vander Donckt

Yaroslav Filinchuk
email: yaroslav.filinchuk@uclouvain.be

Dmitry Chernyshov

Non-Isothermal Kinetics of Kr Adsorption by Nanoporous γ-Mg(BH 4 ) 2 from in situ Synchrotron Powder Diffraction

Keywords: porous frameworks, adsorption, thermodynamics, kinetics, crystal structure

Crystalline materials with pore dimensions comparable to the kinetic diameters of the guest molecules are attractive for their potential use in adsorption and separation applications. The nanoporous γ -Mg(BH4)2 features 1D channels matching this criterion for Kr uptake, which has been probed using synchrotron powder diffraction at various pressures and temperatures. It results in two co-existing crystalline phases with the limiting composition Mg(BH4)2•0.66Kr, expecting the highest Kr content (50.7 wt% in crystalline phase) reported for porous materials. Quasi-equilibrium isobars built from Rietveld refinements of Kr site occupancies were rationalized with a non-cooperative lattice gas model yielding the values of the thermodynamic parameters. The latter were independently confirmed from Kr fluorescence. We have also parameterized the pronounced kinetic hysteresis with a modified mean-field model adopted for the Arrhenius kinetics.

INTRODUCTION

The efficient sorption and separation of valuable noble gases, like krypton and xenon, with extremely low concentrations in air (1.14 and 0.089 ppmv, respectively) are of great interest. Indeed, their sorption properties are similar due to close kinetic diameters (3.6 and 4.1 Å respectively) and equally low chemical reactivity. [START_REF] Kerry | Industrial Gas Handbook Gas Separation[END_REF] New methods of selective capturing carry over to the need for trapping Kr and Xe radioactive products that are generated from nuclear fission. [START_REF] Chen | Separation of Rare Gases and Chiral Molecules by Selective Binding in Porous Organic Cages[END_REF][START_REF] Liu | Metal-Organic Frameworks for Removal of Xe and Kr from Nuclear Fuel Reprocessing Plants[END_REF] The most common way of noble gases adsorption from air or fission products requires energy consuming cryogenic distillation. [START_REF] Kerry | Industrial Gas Handbook Gas Separation[END_REF] Thus, alternative effective materials and methods are required for that purpose.

Metal-organic and other porous frameworks have been intensively studied as perspective materials for numerous applications in gas storage and separation, [START_REF] Furukawa | The Chemistry and Applications of Metal-Organic Frameworks[END_REF][START_REF] Adil | Gas/Vapour Separation Using Ultra-Microporous Metal-Organic Frameworks: Insights into the Structure/Separation Relationship[END_REF] sensing, 6 catalysis 7 and drug delivery. [START_REF] Horcajada | Metal Organic Frameworks in Biomedicine[END_REF] Recently, several promising metal-organic frameworks (MOFs) have been also proposed for Kr and Xe adsorption and separation. [START_REF] Banerjee | Xenon Gas Separation and Storage Using Metal-Organic Frameworks[END_REF][START_REF] Wang | The First Example of Commensurate Adsorption of Atomic Gas in a MOF and Effective Separation of Xenon from Other Noble Gases[END_REF][START_REF] Chen | Direct Observation of Xe and Kr Adsorption in a Xe-Selective Microporous Metal-Organic Framework[END_REF][START_REF] Banerjee | Metal-Organic Framework with Optimally Selective Xenon Adsorption and Separation[END_REF][START_REF] Mohamed | Hybrid Ultra-Microporous Materials for Selective Xenon Adsorption and Separation[END_REF] The main criteria for their practical applications are based on a maximal gravimetric uptake, an isosteric heat of adsorption and a Kr/Xe thermodynamic and kinetic selectivity. It was found that the optimal pore size of the framework channels defines the capture capability and kinetic separation of these molecules. The latter is achievable when the pore size is between one and two kinetic diameters of the molecules of interest, [START_REF] Perry | Gas Adsorption in Metal-Organic Frameworks Containing Open Metal Sites[END_REF][START_REF] Sikora | Thermodynamic Analysis of Xe/Kr Selectivity in over 137000 Hypothetical Metal-Organic Frameworks[END_REF][START_REF] Witman | The Influence of Intrinsic Framework Flexibility on Adsorption in Nanoporous Materials[END_REF] as available in nanoporous (ultra-microporous) frameworks. γ-Mg(BH4)2 attracted our attention as one of such perspective nanoporous materials, [START_REF] Filinchuk | Porous and Dense Magnesium Borohydride Frameworks: Synthesis, Stability, and Reversible Absorption of Guest Species[END_REF] due to its small pore size (≈ 7 Å) matching this criterion. Its 3D network of non-intersecting 1D channels contains small pores separated by even narrower apertures, and thus it is the good candidate to probe thermodynamic and the diffusion-controlled separation.

The characterization of volumetric and gravimetric gas uptake by γ-Mg(BH4)2 in bulk is complicated by the inherent presence of a dense amorphous phase, its weight fraction varies from one batch to other. [START_REF] Stadie | Supercritical Nitrogen Processing for the Purification of Reactive Porous Materials[END_REF][START_REF] Ban | Pressure-Collapsed Amorphous Mg(BH4)2: An Ultradense Complex Hydride Showing a Reversible Transition to the Porous Framework[END_REF] In situ synchrotron powder diffraction enables to estimate the capacity, thermodynamics and kinetics of Kr adsorption using temperature-and time-dependent crystallographic occupancies and fluorescence of Kr atoms exclusively from the crystalline porous γ-Mg(BH4)2, which is not biased by the presence of the amorphous phase. The low density of the host γ-Mg(BH4)2 structure in combination with a high X-ray contrast of heavy Kr atoms offer a unique opportunity to study its structural response in great detail. First, good quality data allow a full structural refinement revealing a microscopic picture of adsorption from isobaric variable-temperature experiments. Second, the macroscopic properties, such as adsorption isobars and heats of adsorption are accessed via refined Kr occupancies or by using another independent measure, the background signal. The latter in our case is dominated by the fluorescence from Kr, being proportional to the number of Kr atoms in the irradiated volume.

The thermodynamic parameters can be obtained using Clausius-Clapeyron relation applied to equilibrium isobars [START_REF] Filinchuk | Porous and Dense Magnesium Borohydride Frameworks: Synthesis, Stability, and Reversible Absorption of Guest Species[END_REF] or by using an isobaric equilibrium temperature dependences using a meanfield lattice gas model. [START_REF] Dovgaliuk | Cooperative Adsorption by Porous Frameworks: Diffraction Experiment and Phenomenological Theory[END_REF] These parameters characterize the equilibrium state of the guest molecules filling the pores. Here we show that in situ powder diffraction experiment with fixed temperature ramp rate may not necessary examine the equilibrium state. Non-equilibrium adsorption and desorption curves show ramp-dependent hysteresis that carry information on a non-isothermal kinetics. We parametrize various apparent "hysteresis" scenarios with a simple model adopted for the Arrhenius' kinetics.

RESULTS AND DISCUSSION

The data were collected at Kr pressures of 0.1 and 0.5 bar with two temperature regimes of a constant ramp rate of 6 K/min and of a constant step (ramp 6 K/min to a given temperature followed by waiting time of 2 min) modes; the initial aim was to detect non-isothermal kinetics effects, if any.

Powder diffraction isotherm at 298 K shows a progressive loading of Kr into the pores (Fig. S1): as expected, the uptake of Kr by γ-Mg(BH4)2 strongly affects the intensities of the diffraction peaks. Such change occurs due to high difference between scattering (form) factors of Kr (at 2θ = 0, it equals to the atomic number Z = 36) and light atoms of the host structure: Mg (Z = 12), B (Z = 4) and H (Z = 1). That is why Kr atoms can be easily localized close to the center of the pore by global optimization in direct space, [START_REF] Favre-Nicolin | Free Objects for Crystallography": A Modular Approach to Ab Initio Structure Determination from Powder Diffraction[END_REF] while the light atoms of B and H contribute little to the total scattering picture and were fixed in our refinements. Interestingly, the refined cell parameters decrease upon Kr loading (Fig. S1a). This cell contraction is due to gas adsorption and not due to the radiation damage, as the latter was reduced to the minimum by choosing the radiation dose and by doing the blank tests.

Close inspection of the data revealed diffraction peaks' asymmetries induced by adsorption.

They are hardly visible in the data collected in the ramp mode but are clearly seen for the powder patterns at high Kr loadings measured in the step mode, see Figs. S2-S4. The line shape asymmetry is very similar for all the lines, ruling out hkl-dependent microstructural effects.

Diffraction profiles can be very well modelled by two phases, one is similar to the empty framework, while the other has broader lines and smaller cell parameters, see Fig. S3c. No additional reflections or systematic absences have been observed for the broader diffraction component. We refined the two-phase model using Rietveld method [START_REF] Rodríguez-Carvajal | Recent Advances in Magnetic Structure Determination by Neutron Powder Diffraction[END_REF] to all the step mode data, while a single phase was fitted to the ramp mode data, see Figs. S2-S4 for more details.

Rietveld refinements of the powder patterns were done sequentially along the isobars, obtaining consistent results and good fits, see Fig. 1. The phase with larger cell parameter and sharper peaks, denoted as phase 1, is the majority phase at all temperatures. Its refined adsorption isobar shows a sigmoidal shape, with the saturation at one Kr atom per pore (16 atoms per cell or 2/3 Kr per Mg atom), see Fig. S5. Upon desorption, the phase 1 releases Kr with a small hysteresis. Phase 2 is the minor phase, containing smaller amounts of Kr than the phase 1 (at the same conditions), see its isobar on Fig. S5. The apparent Kr-rich composition of the phase 2 corresponds to ~0.84 Kr atom per pore (14 atoms per cell or 0.56 Kr per Mg atom). Surprisingly, the cell volume for the Kr-rich phase 1 is higher than for the Kr-poor phase 2, despite the cell contraction is observed upon Kr loading at 298 K (Fig. S1). This difference may be due to different crystal structures of the phases 1 and 2. Indeed, Rietveld refinement suggests a possible disorder of Kr around the center of the pore in the phase 1 (32e Wyckoff site), while the guest takes the center of the pore in the phase 2 (16b Wyckoff site), see Fig. 1 and Tables S1 andS2 with crystallographic data. In such case the shortest interatomic Kr-B distances will be comparable in both structures (4.13 and 4.07 Å for phase 1 and 2, respectively), while potential refinement of the Kr atomic coordinate in phase 2 is difficult due to its low fractional content (up to 30 wt%) and significant peak overlap. However, the disorder of guest atoms cannot be a sole reason for the volume difference at least at high temperatures where the Kr occupancies are nearly zero. This difference may be also related to a possible reorientation of the borohydride anions, not detectable by the X-ray powder diffraction. Importantly, the mixture of the two phases of slightly different compositions is thermodynamically stable, as the phase 2 appears only in the step mode, where the system is brought closer to an equilibrium. The phase 2 is thus forming slower than the phase 1 on loading and it transforms back to the phase 1 upon Kr unloading, as evidenced by the evolution of the weight fractions (Fig. S5). Analysis of crystal structure data in ICSD and CCDC databases, [START_REF] Belkly | New Developments in the Inorganic Crystal Structure Database (ICSD): Accessibility in Support of Materials Research and Design[END_REF][START_REF] Groom | The Cambridge Structural Database[END_REF] along with the literature on Kr adsorption [START_REF] Banerjee | Xenon Gas Separation and Storage Using Metal-Organic Frameworks[END_REF][START_REF] Wang | The First Example of Commensurate Adsorption of Atomic Gas in a MOF and Effective Separation of Xenon from Other Noble Gases[END_REF][START_REF] Chen | Direct Observation of Xe and Kr Adsorption in a Xe-Selective Microporous Metal-Organic Framework[END_REF][START_REF] Banerjee | Metal-Organic Framework with Optimally Selective Xenon Adsorption and Separation[END_REF][START_REF] Mohamed | Hybrid Ultra-Microporous Materials for Selective Xenon Adsorption and Separation[END_REF][START_REF] Perry | Gas Adsorption in Metal-Organic Frameworks Containing Open Metal Sites[END_REF][START_REF] Patil | A Highly Xe-Selective Nanoporous Organic Solid[END_REF][START_REF] Hulvey | Gas Adsorption in Copper Trimesate, HKUST-1: An Experimental and Computational Study[END_REF] allows us to state that the fully loaded crystalline phase 1, Mg(BH4)2•0.66Kr, has the highest encapsulated Kr content known to date for porous materials, namely 50.7 wt% as evaluated from the crystallographic Kr occupancy.

The microscopic picture of Kr adsorption, described above, allows to perfectly fit a relatively simple two-phase model to all the data collected over different pressures and temperatures, both on adsorption and desorption, providing adsorption isobars, see Fig. 2a,b,d The contributions from the phases 1 and 2 are shown in Fig. S5.

Kr content for 0.5 bar isobar shows a hysteresis for the ramp mode, that is almost suppressed for the step mode, compare Figs. 2a andb. On the other hand, the isobars at 0.1 bar are highly hysteretic for both temperature regimes, see Fig. 2d ande. These observations illustrate that the hysteresis is determined by the kinetics and not by cooperative effects (it was shown in Ref. 20 that γ-Mg(BH4)2 is a rather rigid porous framework and cooperative effects are expected to be weak if any). The data at 0.5 bar in the step mode can therefore be considered as the closest to the equilibrium, while the ramp mod e data have to be analyzed taking the kinetics of the gas uptake into account. Indeed, the low saturation limit at 0.1 bar, well below the maximum of 16 atoms per cell, is the result of the hindered adsorption kinetics, and the upturn in the desorption isobar is very indicative for the slowed down adsorption at low temperatures. [START_REF] Ravikovitch | Diffusion-Controlled Hysteresis[END_REF] While similar observations have been made using volumetric (picnometric) techniques, [START_REF] Ravikovitch | Diffusion-Controlled Hysteresis[END_REF] this is the first observation of this kind using powder diffraction. The present in situ diffraction studies provide simultaneously the micro-and macroscopic information on the crystalline phase in question. It is an efficient experimental approach that allows a phenomenological study of the phase and site-specific thermodynamics of adsorption in crystalline porous solids. [START_REF] Dovgaliuk | Cooperative Adsorption by Porous Frameworks: Diffraction Experiment and Phenomenological Theory[END_REF] The equilibrium fraction of filled guest sites for a cooperative adsorption is given in Ref. [START_REF] Dovgaliuk | Cooperative Adsorption by Porous Frameworks: Diffraction Experiment and Phenomenological Theory[END_REF] and it is based on a mean-field lattice gas model. For γ-Mg(BH4)2 we can neglect the cooperative interactions and use a simple van't Hoff dependence for the equilibrium fraction of Kr:

ln g 1-g ae è ç ö ø ÷ = - DH RT + DS R (1)
Here γ is a fraction of the adsorbed guest molecules from the maximally achievable at given gas pressure. Fitting this equation to the nearly equilibrium 0.5 bar step mode isobar yields the thermodynamic parameters of adsorption: ∆H of 21.2(1) and 21.9(4) kJ/mol for cooling and heating modes (21.6(4) kJ/mol in average), see Fig. 3a. The thermodynamic parameters extracted separately for the phases 1 and 2 are comparable (Fig. S7) and they suggest a slightly higher heat of Kr adsorption via the formation of the phase 2. The values of the adsorption enthalpies are in a good agreement with the previously reported benchmark materials for the Kr/Xe capture/separation (Qst, kJ/mol): 20.1-21.4 for Noria, [START_REF] Patil | A Highly Xe-Selective Nanoporous Organic Solid[END_REF] 18(1) for HKUST-1, [START_REF] Hulvey | Gas Adsorption in Copper Trimesate, HKUST-1: An Experimental and Computational Study[END_REF] The thermodynamics of the gas adsorption can be also parameterized to another independent observation: Kr fluorescence measured as a background signal. The latter originates from the Kr K-edge X-ray adsorption (14.3256 keV or 0.8655 Å), [START_REF] Bearden | Reevaluation of X-Ray Atomic Energy Levels[END_REF] achievable in our experimental conditions with higher energy. This information is directly contained in the experimental images without the need to resort to the localization of the guest molecules, Rietveld refinement etc.

Indeed, the temperature-dependent Kr fluorescent background behaves similar to the Kr occupancies, see Figs. S8 andS9, and gives ∆H = 22.8(4) kJ/mol (Fig. 3b), very close to the values extracted from the refined Kr occupancies. This method is a powerful tool to access the fluorescent probes, and to our knowledge is used for the first time to quantify the thermodynamics of gas adsorption. There is a difference in the nature of the fluorescent probe:

while the refined occupancies characterize the guest atoms inside the pores of the host lattice, the fluorescence accumulates both structurally coherent and non-coherent contributions from the surface, cracks, intergrain boundaries and other defects. Since both measures of the Kr content in the irradiated volume yield very similar results, we have evidence that the gas uptake is dominated by the Kr adsorption in the crystal pores.

Having characterized the quasi-equilibrium thermodynamics, we turn our attention to nonequilibrium isobars (Figs. 2b, d ande) containing information on adsorption kinetics. We apply an approach based on a first order reaction model. [START_REF] Taylor | International Reviews in Physical Chemistry Isothermal and Non-Isothermal Kinetics of Thermally Stimulated Reactions of Solids[END_REF][START_REF] Khawam | Solid-State Kinetic Models: Basics and Mathematical Fundamentals[END_REF] Assuming the Arrhenius kinetics, being a natural choice for an Ising-like lattice model, [START_REF] Klinduhov | Choice of Dynamics for Spin-Crossover Systems[END_REF] the temperature dependence of the apparent fraction of the occupied guest sites reads as:

(

) 2
Here γ0 is a starting value of the guest occupancy (e. g. 0 on adsorption or a maximal value if we consider the desorption), A is the Arrhenius prefactor, β is the temperature ramp rate, and an integral function in the exponent is:

(

) 3
where Ea is the Arrhenius activation energy and R is the gas constant.

Equation 2 models the fraction of the occupied sites as a function of temperature with finite kinetics characterized by A and Ea. The temperature is varied with the ramp rate β. The cooling (adsorption) branch is now below the equilibrium curve, the difference depends on the energy barrier and the cooling rate. The cooling may end up with a maximal value of the fraction α(Tmin)=γeq(Tmin)=1, that would correspond to the true limiting capacity, e.g. 16 Kr atoms per unit cell. In this case the heating (desorption) starts from γ0=1 and the entire desorption branch stays above the equilibrium curve. This is what has been observed for the step mode regime with p=0.5 bar (Fig. 2b). If the cooling ends up with an uncomplete adsorption, α(Tmin)<1, this value serves as γ0 for the heating branch. Depending on the kinetics, the heating may give rise to a continuous desorption or to an increase of the occupancy aiming at the equilibrium values. The latter case has been observed experimentally for p = 0.1 bar (Fig. 2e).

The results of the model calculations for the non-isothermal kinetics are shown at Figs. polymorphs. [START_REF] Soloninin | NMR Study of Reorientational Motion in Alkaline-Earth Borohydrides: β and γ Phases of Mg(BH4)2 and α and β Phases of Ca(BH4)2[END_REF] This hints for a possible correlation of Kr diffusion through pore apertures made of six borohydride groups with reorientational jumps of the [BH4] -tetrahedra, similar to Li ion diffusion in ht-LiBH4 and some other metal borohydrides. [START_REF] Skripov | Nuclear Magnetic Resonance Studies of Reorientational Motion and Li Diffusion in LiBH4-LiI Solid Solutions[END_REF][START_REF] Skripov | Nuclear Magnetic Resonance Studies of BH4 Reorientations and Li Diffusion in LiLa(BH4)3Cl[END_REF][START_REF] Corey | Atomic Motions in LiBH4 by NMR[END_REF][START_REF] Soloninin | Nuclear Magnetic Resonance Study of Li and H Diffusion in the High-Temperature Solid Phase of LiBH4[END_REF][START_REF] Shane | Exchange of Hydrogen Atoms between BH4 in LiBH4[END_REF][START_REF] Skripov | Nuclear Magnetic Resonance Study of the Rotational Motion and the Phase Transition in LiBH4[END_REF] This hypothesis needs verification by methods probing dynamics in the solid state. The in situ synchrotron powder diffraction data were collected at BM01 (SNBL/ESRF in Grenoble, France) using PILATUS@SNBL diffractometer. [START_REF] Dyadkin | A New Multipurpose Diffractometer PILATUS@SNBL[END_REF] The monochromatic beam (λ = 0.78290 Å for 298 K isotherm measurement; λ = 0.78487 and 0.69425 Å for 0.5 and 0.1 bar isobars, respectively) was calibrated using LaB6 powder with PyFAI. [START_REF] Ashiotis | The Fast Azimuthal Integration Python Library: PyFAI[END_REF] The obtained calibrations were used in Bubble [START_REF] Dyadkin | A New Multipurpose Diffractometer PILATUS@SNBL[END_REF] for azimuthal integration of the 2D images. The positions of Kr atoms were localized using FOX [START_REF] Favre-Nicolin | Free Objects for Crystallography": A Modular Approach to Ab Initio Structure Determination from Powder Diffraction[END_REF] and the resulting structures were refined in a sequential mode by Rietveld method in Fullprof. [START_REF] Rodríguez-Carvajal | Recent Advances in Magnetic Structure Determination by Neutron Powder Diffraction[END_REF]

ASSOCIATED CONTENT

The following files are available free of charge.

Supporting information with powder diffraction isotherms and all the refinement and calculation

Figure 1 .

 1 Figure 1. Rietveld refinement (synchrotron radiation with λ = 0.67522 and 0.78487 Å for step

  , where Kr content is taken over the two phases, see the corresponding structure models in supporting information and CCDC database: phase 1 (300 K -CCDC(1977686); 200 K -CCDC(1977685); 114 K -CCDC (977688)); phase 2 (300 K -CCDC(1977687); 200 K -CCDC(1977689); 115 K -CCDC(1977690)).

Figure 2 .

 2 Figure 2. Temperature-dependent Kr adsorption isobars by γ-Mg(BH4)2 extracted from powder

12 Figure 3 .

 123 Figure 3. The van't Hoff plots (p (Kr) = 0.5 bar) obtained from the refined Kr occupancies (a)

  2c and 2f. The model with a handful of parameters obviously mimics closely the observed scenarios, indicating that the hysteresis effects indeed may be related to finite kinetics. However, quantitative estimates of the activation energy and the elucidation of the kinetics model requires a dedicated isothermal time-dependent experiment, that is the subject of our next publication. Equation (2) applied to the non-equilibrium isobars allows only for an estimate of the activation energy at 10-20 kJ/mol of Kr and the Arrhenius constant A at 0.09-0.2 min -1 , thus expecting the initial adsorption rate of about 10-20 % per minute at room temperature. The equilibrium may therefore be reached within minutes and a diffraction experiment aiming to map such kinetics has to be relatively fast.Interestingly, the estimated activation barrier for Kr adsorption is of the same order as the activation energies for [BH4] -reorientations, namely 13.3 to 26.6 kJ/mol in βand γ-Mg(BH4)2

CONCLUSIONS

  We determined a microscopic picture of Kr adsorption in γ-Mg(BH4)2, featuring 1D channels with apertures comparable to the kinetic radius of Kr atoms. The fully loaded phase, Mg(BH4)2•0.66Kr, has higher crystallographic Kr content (50.7 wt%) than any other porous material. Synchrotron diffraction experiments allowed to build quasi-equilibrium adsorption isobars, the latter were rationalized with the non-cooperative lattice gas model yielding the values of the thermodynamic parameters for Kr adsorption. The latter can be independently determined from Kr fluorescence signal. This information is directly contained in the experimental images without the need to resort to the localization of the guest molecules.The fast-ramp diffraction data, especially taken at the lower pressure, uncovers the hysteresis of kinetic origin. The model of the first-order Arrhenius kinetics with two parameters mimics closely the observed scenarios, allowing to estimate the activation energy. Observed adsorption scenarios, in particular kinetic effects, make γ-Mg(BH4)2 an interesting candidate for separation of the Kr/Xe mixtures via selective adsorption.Many details of adsorption process in crystalline materials, its thermodynamic and kinetic characteristics are only possible to observe with in situ diffraction measurements like those presented in this work. Further investigations focused on the isothermal kinetic experiments with pure gases and their mixtures are the necessary next steps to determine the kinetic mechanisms and potential selectivity. Since diffraction probes the gas adsorption by the structural response of the porous crystalline phase only, it is expected to give an upper limit of the uptake. It would be also interesting to make a systematic comparison between microscopic structural and macroscopic bulk probes from gravimetric and volumetric methods, however this task is beyond the scope of the present letter.EXPERIMENTAL METHODSDetailed description of the experimental setup and structure refinement is given in the supporting information. γ-Mg(BH4)2 was prepared according to Ref. 17. The samples of γ-Mg(BH4)2 contain significant amounts of the amorphous Mg(BH4)2 phase, different from one sample to another. Therefore, the BET surface areas can not be compared to data extracted from diffraction, as the latter method is selective to the crystalline phase. The TGA/DSC data reported in the Ref.19 are reproducible on all our samples. The grinded powder was loaded into 0.5 mm glass capillaries in the argon-filled glove box. A capillary filled with γ-Mg(BH4)2 was transported in an closed Ar-filled flask prior the diffraction measurements. The capillaries were connected to a gas-loading manifold with much larger volume, equipped with the electronic manometer (working range of 0-100 bar with 0.01% full scale accuracy). The sample was activated at 350 K under dynamic vacuum (turbomolecular pump), right before Kr loading. Kr pressure was set to 0.1 and 0.5 bar for variable-temperature experiments. 298 K isotherm was measured between 0.050 and 5.600 bar with 60-120 min waiting time for each data point. The temperature was controlled using Oxford Cryostream 700+. Temperature varied from 300 to 115 K upon cooling followed by heating in the ramp mode (at 6 K/min rate) and in the step mode (waiting for 2 min at each temperature point).

This work was supported by FNRS (PDR T.0169.13, EQP U.N038.13, CdR J.0164.17). We thank the ESRF for beamtime allocation.

Notes

The authors declare no competing financial interests. ACKNOWLEDGMENT