MD Dario Saracino

MSc Amandine Géraudie

MD, PhD Anne M Remes

Sophie Ferrieux

Marie Noguès-Lassiaille

MSc Simona Bottani

MD Lorenzo Cipriano

MSc Marion Houot

PhD Aurélie Funkiewiez

BSc Agnès Camuzat

PhD Daisy Rinaldi

MD, PhD Marc Teichmann

MD, PhD Jérémie Pariente

MD, PhD Philippe Couratier

MD, PhD Claire Boutoleau-Bretonnière

MD Sophie Auriacombe

MD, PhD Frédérique Etcharry-Bouyx

; The

MD, PhD Richard Levy

MD, PhD Raffaella Migliaccio

MD, PhD Eino Solje

MD, PhD Isabelle Le Ber
email: isabelle.leber@upmc.fr.

Affiliations

Hugo Bertin

Anne Bertrand

Olivier Colliot

Véronique Golfier

Didier Hannequin

Marie-Anne Mackowiak

Olivier Martinaud

Jacques Monteil

Christel Thauvin-Robinet

Primary progressive aphasias associated with C9orf72 expansions: Another side of the story

Keywords: 73, Figures: 2, Tables: 2, Supplementary Figures: 3, Supplementary tables: 3 Primary progressive aphasia, frontotemporal dementia, frontotemporal lobar degeneration, C9orf72, progranulin (GRN)

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

INTRODUCTION

Primary progressive aphasias (PPAs) are rare neurodegenerative diseases initially presenting with speech and language disorders [START_REF] Gorno-Tempini | Classification of primary progressive aphasia and its variants[END_REF]. The non-fluent/agrammatic variant (nfvPPA) is associated with effortful language production, agrammatism and apraxia of speech, related to involvement of inferior frontal gyrus of the dominant hemisphere. The semantic variant (svPPA) is dominated by conceptual knowledge and language comprehension deficits, associated with anterior temporal lobe atrophy. The logopenic variant (lvPPA) is characterized by phonological working memory impairment with single-word retrieval and sentence repetition deficits, and predominant temporal-parietal junction involvement in the hemisphere specialized into language. However, this classification may not be applied to all cases, some of them not meeting criteria for any of the abovementioned variants (unclassifiable PPA, uPPA), or fulfilling criteria for more than one variant (mixed PPA, mPPA) (Bergeron et al., 2018).

In some patients, PPA phenotypes are caused by mutations in genes responsible for autosomal dominant frontotemporal dementias (FTD). Gene-specific lesion tropism leads to the neuroanatomical profile of cortical atrophy and, hence, in some cases to the resulting predominant linguistic deficits. As such, PPAs are associated with GRN mutations in ~15-20% of carriers (Moore et al., 2020;[START_REF] Saracino | Primary Progressive Aphasia Associated With GRN Mutations: New Insights Into the Non-amyloid Logopenic Variant[END_REF] and their phenotypes are dominated by non-amyloid lvPPA and nfvPPA linguistic variants [START_REF] Ber | Phenotype variability in progranulin mutation carriers: a clinical, neuropsychological, imaging and genetic study[END_REF]Moore et al., 2020;[START_REF] Saracino | Primary Progressive Aphasia Associated With GRN Mutations: New Insights Into the Non-amyloid Logopenic Variant[END_REF]. Conversely, MAPT [START_REF] Henz | A Pair of Siblings with a rare R5H-Mutation in Exon 1 of the MAPT-Gene[END_REF], TARDBP [START_REF] Caroppo | Semantic and nonfluent aphasic variants, secondarily associated with amyotrophic lateral sclerosis, are predominant frontotemporal lobar degeneration phenotypes in TBK1 carriers[END_REF][START_REF] Gelpi | TARDBP mutation p.Ile383Val associated with semantic dementia and complex proteinopathy[END_REF][START_REF] González-Sánchez | TARDBP mutation associated with semantic variant primary progressive aphasia, case report and review of the literature[END_REF][START_REF] Mol | Distinctive pattern of temporal atrophy in patients with frontotemporal dementia and the I383V variant in TARDBP[END_REF], and TBK1 mutations [START_REF] Caroppo | Semantic and nonfluent aphasic variants, secondarily associated with amyotrophic lateral sclerosis, are predominant frontotemporal lobar degeneration phenotypes in TBK1 carriers[END_REF][START_REF] Pottier | Whole-genome sequencing reveals important role for TBK1 and OPTN mutations in frontotemporal lobar degeneration without motor neuron disease[END_REF][START_REF] Van Der Zee | TBK1 Mutation Spectrum in an Extended European Patient Cohort with Frontotemporal Dementia and Amyotrophic Lateral Sclerosis[END_REF][START_REF] Hirsch-Reinshagen | Clinicopathologic correlations in a family with a TBK1 mutation presenting as primary progressive aphasia and primary lateral sclerosis[END_REF][START_REF] Swift | Variable clinical phenotype in TBK1 mutations: case report of a novel mutation causing primary progressive aphasia and review of the literature[END_REF] much more rarely cause a PPA syndrome; in those rare instances, linguistic impairment usually meets criteria of svPPA, and less frequently nfvPPA.

C9orf72 repeat expansions are the most frequent genetic cause of FTD and amyotrophic lateral sclerosis (ALS). PPA variants are rather exceptional C9orf72-associated phenotypes [START_REF] Boeve | Characterization of frontotemporal dementia and/or amyotrophic lateral sclerosis associated with the GGGGCC repeat expansion in C9ORF72[END_REF][START_REF] Majounie | Frequency of the C9orf72 hexanucleotide repeat expansion in patients with amyotrophic lateral sclerosis and frontotemporal dementia: a cross-sectional study[END_REF]Moore et al., 2020). Therefore, their main linguistic deficits, and the underlying patterns of grey-matter atrophy are not well characterized. To fill this gap, we analyzed the linguistic and neuroanatomical profiles of a unique series of 16 PPA patients carrying C9orf72 expansions (PPA-C9orf72), including 11 patients coming from two independent French and Finnish study cohorts, and five additional patients with in-depth clinical descriptions identified in the literature.

MATERIALS AND METHODS

Study design and patients

The patients analyzed in the French cohort of this study were prospectively included in the context of a national clinical and research network on FTD and ALS between 1996 and 2020 (Research project RBM02-59), as well as PREV-DEMALS study (ClinicalTrials.gov Identifier: NCT02590276). All participating centers employed comparable diagnostic protocols and clinical evaluations (Le [START_REF] Ber | Demographic, neurological and behavioural characteristics and brain perfusion SPECT in frontal variant of frontotemporal dementia[END_REF][START_REF] Saracino | Primary Progressive Aphasia Associated With GRN Mutations: New Insights Into the Non-amyloid Logopenic Variant[END_REF]. Molecular analyses were performed in all patients to search for FTD diseasecausing mutations. The ethics committee of Paris-Necker Hospital approved the study. All patients provided written informed consent. No part of the study procedures and analyses was pre-registered prior to the research being conducted. We report how we determined our sample size, all data exclusions, all inclusion/exclusion criteria, whether inclusion/exclusion criteria were established prior to data analysis, all manipulations, and all measures in the study. During this time interval, 330 patients carrying C9orf72 expansions (at least >30 repeats) were included, 11 (3.3%) of whom received an initial diagnosis of PPA (PPA-C9orf72). Five were excluded because of severely compromised language/cognitive functions at first evaluation (n=3), or CSF biomarkers consistent with Alzheimer disease (AD) co-pathology (n=2, one with svPPA and one with lvPPA phenotype).

Here, we report the linguistic and clinical characteristics of the remaining six PPA-C9orf72 patients, among which CSF biomarkers were negative in four (not analyzed in two: #2 and #3). They did not carry mutations in all known FTD-causative genes, and had plasma progranulin levels within normal limits. The standardized speech/language evaluation protocol was carried out with the Boston Diagnostic Aphasia Examination-French version (BDAE/HDAE-F) [START_REF] Mazaux | HDAE (BDAE): Echelle d'évaluation de l'aphasie[END_REF] (n = 5) and/or the Montreal-Toulouse protocol for examination of aphasia (MT86) [START_REF] Nespolous | Protocole Montréal-Toulouse d'examen linguistique de l'aphasie MT-86[END_REF] (n= 3). Two patients were tested with both batteries. All underwent more extensive language evaluations also including oral confrontation naming [START_REF] Deloche | DO 80: Epreuve de dénomination orale d'image[END_REF], buccofacial praxis [START_REF] Teichmann | Deciphering logopenic primary progressive aphasia: a clinical, imaging and biomarker investigation[END_REF], phonological and semantic fluencies [START_REF] Godefroy | Fonctions exécutives et pathologies neurologiques et psychiatriques[END_REF], the Pyramid and Palm-Tree Test (PPTT) [START_REF] Howard | The pyramids and palm trees test: a test of semantic access from words and pictures[END_REF] or the BECS-GRECO semantic battery [START_REF] Merck | La batterie d'évaluation des connaissances sémantiques du GRECO (BECS-GRECO) : validation et données normatives[END_REF]. Other cognitive domains were evaluated with a semi-standardized battery [START_REF] Saracino | Primary Progressive Aphasia Associated With GRN Mutations: New Insights Into the Non-amyloid Logopenic Variant[END_REF].

Additionally, five patients belonging to a Finnish cohort, that have been partially described in a prior study [START_REF] Haapanen | C9orf72 Repeat Expansion Does Not Affect the Phenotype in Primary Progressive Aphasia[END_REF], were included for a more detailed linguistic analysis in the current work. They were diagnosed at the Kuopio University Hospital between 1996 and 2016. They were all of Finnish descent and were not tested for other FTD-causative mutations, which are, however, extremely rare in the Finnish population, likely due to genetic isolation [START_REF] Haapanen | C9orf72 Repeat Expansion Does Not Affect the Phenotype in Primary Progressive Aphasia[END_REF]. Their speech/language evaluation relied on the Western Aphasia Battery (WAB) [START_REF] Shewan | Reliability and Validity Characteristics of the Western Aphasia Battery (WAB)[END_REF], whereas the other cognitive domains were tested in neuropsychological assessment including the Consortium to Establish a Registry for Alzheimer's disease neuropsychological battery (CERAD-NB). Legal copyright restrictions prevent public archiving of the various assessment instruments and test batteries used in this study, which can be obtained from the copyright holders in the cited references.

The diagnosis of PPA variant was based on international criteria [START_REF] Gorno-Tempini | Classification of primary progressive aphasia and its variants[END_REF]. Patients were labelled as mPPA when criteria for more than one variant co-occurred in a relatively early disease stage (Bergeron et al., 2018), and as uPPA when their linguistic impairment did not meet the criteria for any of the variants.

After the first evaluation, patients were periodically evaluated for usual clinical care. The median disease duration at the last follow-up was 4.0 years [IQR: 2.6, 5.0]. Some patients secondarily developed additional neurological or cognitive symptoms leading to secondary diagnoses (Table 1).

Voxel-based morphometry (VBM) analysis

We performed VBM analyses to characterize the neuroanatomical features in two PPA-C9orf72 patients with the nfvPPA phenotype (nfvPPA-C9orf72), and in a third patient with the svPPA phenotype (svPPA-C9orf72). This latter individual was evaluated multiple times. Their 3D T1-weighted MRI scans were all performed ≤6 months before or after clinical evaluation. They were compared with 35 controls selected to match each patient based on their demographic characteristics.

We employed a VBM-based approach with the T1-volume pipeline of Clinica (http://www.clinica.run), a wrapper of the segmentation, run Dartel, and normalize to Montreal Neurological Institute (MNI) space routines implemented in Statistical Parametrical Mapping (SPM). After the unified segmentation procedure, a group template was created using Dartel, and the Dartel-to-MNI method was then applied, incorporating the native space images into the MNI space.

We used two-sample t-tests for the group analysis, applying the contrast PPA-C9orf72 vs controls, with age at MRI and gender as nuisance covariates. In order to capture the full extent of brain atrophy, we generated false discovery rate (FDR)-corrected maps at cluster level, because of the well-known limited statistical power of single-subject VBM. We used the AAL3.1 atlas to label cortical and subcortical regions harboring significant differences [START_REF] Rolls | Automated anatomical labelling atlas 3[END_REF].

Literature review

We performed an extensive literature review to get deeper insights in linguistic characteristics of previously reported PPA-C9orf72 patients (AG, DS). A PubMed search employed the following search terms: ((C9orf72) OR (chromosome 9 open reading frame 72) OR (c9)) AND ((primary progressive aphasia) OR (PPA)) OR frontotemporal* from 2011 (year of C9orf72 identification) to 2021. A total of 874 articles were found, 53 of which were initially selected for full-text review after a first screening of research studies on PPA and C9orf72 written in English. We subsequently reviewed the 31 more relevant papers specifically focusing on genetic screening in PPA cohorts, or on phenotypic characterization of C9orf72 cohorts or cases, to eventually focus only on those dealing with PPA-C9orf72 patients. We excluded the papers without detailed clinical/linguistic descriptions (n=26) or in which the causative role of C9orf72 expansion was not unequivocal (e.g., CSF biomarker profile in favor of AD pathology or presence of a second FTD or AD-disease causing mutation, n=2) (Supplementary Table 1). Finally, only five PPA-C9orf72 patients had in-depth linguistic evaluation and could be kept in the study [START_REF] Hsiung | Clinical and pathological features of familial frontotemporal dementia caused by C9ORF72 mutation on chromosome 9p[END_REF][START_REF] Snowden | Distinct clinical and pathological characteristics of frontotemporal dementia associated with C9ORF72 mutations[END_REF][START_REF] Cerami | Novel Evidence of Phenotypical Variability in the Hexanucleotide Repeat Expansion in Chromosome 9[END_REF].

RESULTS

Clinical phenotypes

Overall, 16 PPA-C9orf72 patients including our six novel French patients, five Finnish patients and five cases from the literature, were described and analyzed in this study. Their median age at onset was 63 (range: 39-78). Patients were at an early stage of the disease, as reflected by the short median disease duration (DD) (2.0 years; interquartile range, IQR: 1.5, 2.5). Their demographic, clinical and linguistic features are summarized in Table 1. In order to better illustrate the heterogeneity of clinical phenotypes, we described in detail the clinical histories and the linguistic characteristics of three paradigmatic cases, each presenting a different PPA variant. The conditions of our ethics approval do not permit public archiving of the individual patient clinical, behavioral and linguistic data supporting this study. Readers seeking access to the data should contact the corresponding author (Dr. Isabelle Le Ber). Data will be shared with named individuals following completion of a data sharing agreement and approval by the local ethics committee.

Patient #01: svPPA

At the age of 39, this right-handed patient with high-grade education (20 years of formal education) started to complain of insidious language difficulties. They mainly consisted of loss of word meaning, anomia, and difficulties in oral comprehension, especially with some idiomatic expressions. Notably, he had difficulties with his professional vocabulary (he worked as a veterinarian but could not define words such as "hippopotamus" or "chick"), mistook the names of his colleagues, and became unable to completely understand scientific articles. Speech/language evaluation (BDAE) at 3 years from onset showed fluent, moderately informative language, with anomia, semantic/verbal paraphasias, and circumlocutions. The severity of aphasia was rated 3/5. Naming was impaired (DO80: 52/80, below 2.5 SD), as well as single-word comprehension (56/72 for the BDAE subtest, normal value (n.v.) >68/72) and object knowledge (visual version of the PPTT: 33/52; n.v. >47/52). At the sentence level, comprehension was mildly affected in both the oral (14/15 for the BDAE commands subtest, n.v. >12/15) and written modalities (8/10 for the BDAE sentences and paragraphs comprehension subtest, n.v. >8/10). Surface dyslexia and dysgraphia were present.

Repetition, motor speech and syntactic skills were unaffected. The Mini-Mental State Examination (MMSE) was 27/30. There was no evidence of dysexecutive disorders, episodic memory impairment, or visuo-spatial or visuo-constructive dysfunction (forward and backward digit span: 7 and 7, Rey-Osterrieth Complex Figure copy and recall: 36/36 and 22.5/36). Brain MRI at age 43 showed left temporal pole atrophy (Figure 1A), with corresponding hypometabolism on cerebral 18 FDG-PET (Figure 1B). At 4.5 years from onset, the patient presented further deterioration of naming (DO80: 47/80) and semantic skills (PPTT: 25/52), along with increasing difficulties in reading and writing irregular words. Global cognitive efficiency remained stable and there was no evidence of additional cognitive deficits. After six years of follow-up (45 years), the patient manifested severe difficulties in understanding conversational speech, while his verbal output was almost not understandable due to word-finding difficulties and circumlocutions. He also displayed some repetitive, ritualistic-obsessive behaviors and behavioral disinhibition. Initial impairment in executive functions was noticed at cognitive testing (Frontal Assessment Battery, FAB: 15/18). Left temporal atrophy became more extensive in a follow-up brain MRI performed at age 46, along with subtle prefrontal atrophy (Figure 1C).

Comprehension difficulties became so severe as to no longer allow oral or written communication by the age of 47, eight years from onset. There was a family history of psychosis in one of the patient's cousins.

Patient #04: nfvPPA

Patient #04, a right-handed person with 9 years of formal education, complained of difficulties in speech production with articulatory troubles at age 57, progressively leading to reduction of speech output.

Moreover, he displayed mild personality changes with impulsiveness, reduced initiative and unawareness of risks. Speech/language evaluation (MT86) at age 58 revealed apraxia of speech, reduced fluency and loss of prosody, with moderately affected intelligibility (aphasia severity score 4/5). Syntactic difficulties were evident in speech production and perception, with impaired comprehension of complex sentences (30/38 for the syntactic MT86 subtest, n.v. >34/38). Morphosyntactic troubles were present also in sentence writing tasks (18/34 for the MT86 word and sentence writing subtest, n.v. >29/34). Phonological and semantic fluencies were reduced (13 words in 2 minutes for both: between 2.5 and 1.5 SD for phonological, and below 2.5 SD for semantic fluency). Repetition and semantic knowledge were unaffected. His MMSE was 27/30. Some elements of executive dysfunction were evident at neuropsychological testing (FAB 12/18; forward digit span: 5; backward digit span: 3). Episodic memory, praxis and visuospatial functions were unimpaired. Neurological examination did not reveal bulbar or pseudobulbar signs, and there was no dysphagia; muscle atrophy and fasciculations were absent, and there were no pyramidal signs. At age 58 brain MRI revealed bilateral cortico-subcortical fronto-temporal atrophy, prevailing in left peri-sylvian areas (Figure 2A). Bilateral prefrontal, left fronto-opercular and anterior temporal hypometabolism was found in 18 FDG-PET (Figure 2B). CSF biomarkers were not in favor of AD.

At 2.5 years from onset, a mild right-predominant akinetic-rigid syndrome was present at neurological examination; pyramidal or motor neuron signs did not appear during follow-up, and EMG testing was persistently negative. The family history was positive for dementia in the patient's mother, who deceased at 72 years.

Patient #06: mPPA

This right-handed patient with 11 years of education complained of initial difficulties in language production at age 68, with reduced fluency and troubles in word-finding, without comprehension impairment. His first speech/language evaluation at age 70, two years from onset, revealed non-fluent, slowed utterances with apraxia of speech (aphasia severity rating 3/5). Buccofacial apraxia was noticed too, with major impact on tongue movements. Aside from his articulatory disorder, he presented impairment in naming (DO80: 54/80, below 2.5 SD), due to a combination of semantic and phonemic paraphasias.

Occasional paragraphic errors (inversion or substitution of syllables) were noticed in writing tasks. His MMSE was 27/30 and Mattis Dementia Rating Scale (MDRS) 122/144, with prevailing deficit in the initiation subtask (23/37), which is a proxy of categorial verbal fluency. Executive impairment was present (FAB 14/18; TMT below 10 th percentile), whereas episodic memory was relatively spared. Brain MRI evidenced bilateral fronto-temporal atrophy, with slight predominance on the left perisylvian areas (Figure 2C). Cerebral 18 FDG-PET showed a discrete left-predominant temporal hypometabolism (Figure 2D).

Notably, EMG excluded motor neuron involvement. CSF biomarkers were not in favor of AD.

During disease evolution his communication skills further worsened, mainly because of increasing anomia.

Evaluation at 3 years from onset evidenced markedly impaired naming (Boston naming test: 9/34, <1 st percentile) and semantics skills (PPTT, verbal version: 36/52). His motor speech difficulties remained quite stable. The other cognitive domains did not get significantly worse, with except for initial ideo-motor apraxia for intransitive limb gestures. His motor testing was persistently normal. His mother was affected by ALS, one sibling had bvFTD and another had both FTD and ALS.

Characteristics of PPA-C9orf72 patients in this study and the literature

The most prevalent PPA variant among C9orf72 patients was nfvPPA in our series (5/11, 45%), and even more so when considering the overall dataset including this series and previously reported cases diagnosed as "PNFA" (9/16, 56%) (Table 1).

Notably, the defining feature was apraxia of speech in 80% of our nfvPPA cases, isolated agrammatism being present in only one patient. The other main features were slowed, hypofluent speech (4/5), impairment in naming (4/5), and difficulties in comprehension of (mainly complex) sentences (4/5); evidence of clear phonological disruption was seldom present (1/5). These characteristics were also common in PNFA cases from the literature, with the only remarkable exception of agrammatism prevailing over apraxia of speech among the core clinical features.

All reported svPPA patients (2/11 in our series, 18%; 3/16 in the overall dataset, 19%) had fluent, logorrheic speech, with massive impairment in naming and in comprehension in conversational speech.

The two svPPA we reported had the longest disease course (10 years at last follow-up in both cases).

Behavioral changes reminiscent of anterior temporal disruption (ritualistic, stereotyped or compulsive behaviors, loss of mental flexibility) appeared during disease course. Earlier and more severe frontal behavioral impairments were described in the previously reported svPPA patient [START_REF] Cerami | Novel Evidence of Phenotypical Variability in the Hexanucleotide Repeat Expansion in Chromosome 9[END_REF].

The two mixed PPA-C9orf72 patients (#05 and #06) showed a similar profile, with grammar-syntactical deficits and reduced fluency prevailing during the first year of the disease (apraxia of speech was clearly present in #06), associated with moderate verbal and visual semantic deficits at onset (comprehension and object-knowledge difficulties). The syndromic progression followed a similar time-course in both patients, semantic deficit becoming predominant after three years from onset.

Lastly, the linguistic profile of the two patients diagnosed as uPPA included word-finding difficulties and impairment in the comprehension of syntactically complex sentences, without frank agrammatism, motor speech disturbances, repetition impairment, phonological or semantic disruption. They showed discrete asymmetric, left-predominant frontotemporal atrophy, peaking in the perisylvian areas (Supplementary Figure 1). Both developed mutism relatively quickly after the diagnosis. Notably, no patients from our cohort showed a linguistic profile compatible with lvPPA.

Overall, the majority of PPA-C9orf72 patients eventually displayed at least a moderate degree of impairment in executive functions during follow-up (12/16, 75%), whereas clinically relevant behavioral troubles were reported in 6/16 cases (38%). In three patients (2 nfvPPA and 1 svPPA) the final diagnosis was PPA associated with bvFTD.

Concerning the intercurrent motor features, only one patient from the overall series (#03) developed (bulbar-onset) ALS, between 1 and 2 years from the onset of linguistic deficits. Atypical parkinsonism was more frequent during the disease course (6/16, 38%).

Grey matter atrophy profile in PPA-C9orf72 patients

VBM analysis in the svPPA-C9orf72 patient (#01) initially showed isolated left superior temporal pole atrophy at age 43, 4 years after disease onset. At 47 years, 7 years from disease onset, there was progression of left anterior temporal lobe atrophy, along with right temporo-polar and orbitofrontal involvement (Supplementary Figure 2, Supplementary Table 2).

VBM study in nfvPPA-C9orf72 patients compared with controls displayed a cluster of significant frontal atrophy in the left frontal lobe, peaking at the level of inferior and middle frontal gyri (Supplementary Figure 3, Supplementary Table 3).

DISCUSSION

A first contribution of the present study is the definition of a remarkably low frequency of PPA with C9orf72 expansions, representing only 3% of carriers. This frequency is fairly concordant with those estimated in the largest cohorts of C9orf72 carriers, PPA being the presenting phenotype in only 1-3% of C9orf72 carriers [START_REF] Majounie | Frequency of the C9orf72 hexanucleotide repeat expansion in patients with amyotrophic lateral sclerosis and frontotemporal dementia: a cross-sectional study[END_REF]Le Ber et al., 2013;Moore et al., 2020) (Table 2). On the other hand, the prevalence of C9orf72 repeat expansion in cohorts of PPA patients ranges from 1% to 8% (Table 2), with the remarkable exception of small Finnish cohorts where it reaches ~28% [START_REF] Kaivorinne | Clinical Characteristics of C9ORF72-Linked Frontotemporal Lobar Degeneration[END_REF][START_REF] Haapanen | C9orf72 Repeat Expansion Does Not Affect the Phenotype in Primary Progressive Aphasia[END_REF]. This finding, stemming from observations conducted on a limited number of PPA patients (<30 cases), is possibly related to the founder effect and high prevalence of C9orf72 repeat expansion in Finland, making it a very relevant genetic cause of FTD in this country [START_REF] Majounie | Frequency of the C9orf72 hexanucleotide repeat expansion in patients with amyotrophic lateral sclerosis and frontotemporal dementia: a cross-sectional study[END_REF][START_REF] Haapanen | C9orf72 Repeat Expansion Does Not Affect the Phenotype in Primary Progressive Aphasia[END_REF]. Aside from that, due to the rarity of PPA-C9orf72 patients, only single cases or small series have been described in detail [START_REF] Hsiung | Clinical and pathological features of familial frontotemporal dementia caused by C9ORF72 mutation on chromosome 9p[END_REF][START_REF] Snowden | Distinct clinical and pathological characteristics of frontotemporal dementia associated with C9ORF72 mutations[END_REF][START_REF] Cerami | Novel Evidence of Phenotypical Variability in the Hexanucleotide Repeat Expansion in Chromosome 9[END_REF], and comprehensive characterization of their linguistic and cognitive profiles is currently lacking.

Our study describes the linguistic features and the neuroimaging profiles of a series of 16 PPA-C9orf72 patients, including cases issued from French and Finnish cohorts, and five additional individuals described in detail in the literature.

In this cohort, 56% (9/16) of PPA-C9orf72 patients presented the nfvPPA phenotype, before svPPA (3/16, 19%), mPPA (2/16, 12.5%) and uPPA (2/16, 12.5%). Interestingly, the most prominent linguistic feature in the majority of nfvPPA-C9orf72 cases was apraxia of speech, whereas patients in our series less frequently presented with progressive agrammatic aphasia. Prior neuroimaging studies in nfvPPA patients supported the duality of its clinical presentation. Apraxia of speech is associated with bilateral, left-predominant superior frontal atrophy, including premotor and supplementary motor areas, while agrammatic PPA with more widespread prefrontal involvement, extending to middle and inferior frontal gyri, clearly lateralized on the left [START_REF] Botha | Classification and clinicoradiologic features of primary progressive aphasia (PPA) and apraxia of speech[END_REF][START_REF] Cordella | Quantification of motor speech impairment and its anatomic basis in primary progressive aphasia[END_REF][START_REF] Tetzloff | Progressive agrammatic aphasia without apraxia of speech as a distinct syndrome[END_REF]. These phenotypes are not unexpected in C9orf72 carriers, in which prefrontal atrophy has been reported long before symptom onset [START_REF] Rohrer | Presymptomatic cognitive and neuroanatomical changes in genetic frontotemporal dementia in the Genetic Frontotemporal dementia Initiative (GENFI) study: a cross-sectional analysis[END_REF][START_REF] Lee | Network degeneration and dysfunction in presymptomatic C9ORF72 expansion carriers[END_REF][START_REF] Bertrand | for the Predict to Prevent Frontotemporal Lobar Degeneration and Amyotrophic Lateral Sclerosis (PREV-DEMALS) Study Group[END_REF][START_REF] Blanc | Faster Cortical Thinning and Surface Area Loss in Presymptomatic and Symptomatic C9orf72 Repeat Expansion Adult Carriers[END_REF][START_REF] Swift | Variable clinical phenotype in TBK1 mutations: case report of a novel mutation causing primary progressive aphasia and review of the literature[END_REF]. A selective lesion tropism predominating on the left side, mainly centered on inferior frontal gyrus and/or fronto-opercular cortices may potentially drive the clinical presentation to nfvPPA in some patients, as observed in our cohort. From the neuropathological point of view, apraxia of speech and, more largely, nfvPPA are usually associated with tau protein deposition when occurring sporadically (Bergeron et al., 2018). The presence of the C9orf72 expansion thus qualifies as one of the causes of nfvPPA with underlying frontotemporal lobar degeneration (FTLD) with TAR DNA-binding protein of 43 kDa (FTLD-TDP) pathological substrate, as in the case of GRN mutations.

This study also highlights that svPPA could be a possible clinical phenotype in the C9orf72 expansion carriers, although with lesser frequency than nfvPPA. Interestingly, both the svPPA-C9orf72 patients from our series presented with an isolated, progressive disruption of the semantic system, and both showed a particularly long disease course, with 10 years of disease duration at last follow-up. Notably, slowly progressive FTD cases could be occasionally due to C9orf72 repeat expansions, and they reflect the major clinical heterogeneity associated with this genetic cause in terms of disease phenotype and progression [START_REF] Khan | Atypical, slowly progressive behavioural variant frontotemporal dementia associated with C9ORF72 hexanucleotide expansion[END_REF][START_REF] Suhonen | Slowly progressive frontotemporal lobar degeneration caused by the C9ORF72 repeat expansion: a 20-year follow-up study[END_REF]. These patients during their disease course exhibited behavioral changes which were mainly characterized by ritualistic, compulsive and stereotyped actions with loss of mental flexibility, rather than prevailing disinhibited or apathetic conducts, consistent with bilateral anterior temporal pathology. Accordingly, the progression of atrophy seen in one case study was greater in anterior temporal lobe, with later and less relevant involvement of orbitofrontal cortex.

Additional evidence for anterior temporal lobe disruption in the C9orf72 patients is provided by the two mPPA cases described in this study, in whom semantic disturbances took over the predominantly nonfluent/agrammatic disturbances shortly after disease onset. Similarly, semantic disturbances have been already reported in association with frontal behavioral disturbances in previous C9orf72 cases [START_REF] Snowden | Distinct clinical and pathological characteristics of frontotemporal dementia associated with C9ORF72 mutations[END_REF]. Furthermore, the relevance of anterior temporal lobe dysfunction in the C9orf72 expansion carriers has been recently highlighted in two patients presenting temporal-variant FTD (tv-FTD), with object recognition and language difficulties being part of the clinical picture during disease evolution [START_REF] Caso | Temporal variant of frontotemporal dementia in C9orf72 repeat expansion carriers: two case studies[END_REF]. Altogether, besides the svPPA phenotype, the C9orf72 expansion can trigger anterior temporal lobe degeneration, producing semantic deficits also in patients initially presenting with different linguistic variants or behavioral syndromes.

The linguistic spectrum of the C9orf72 repeat expansion appears in striking contrast with those observed in other FTD-causing mutations. The main presentations of PPA associated with GRN mutations (PPA-GRN) are logopenic variants, followed by nfvPPA syndrome in which agrammatism clearly predominates over apraxia of speech (Moore et al., 2020;[START_REF] Saracino | Primary Progressive Aphasia Associated With GRN Mutations: New Insights Into the Non-amyloid Logopenic Variant[END_REF]. Semantic deficits rarely occur in isolation, though they can add up to logopenic or agrammatic impairment in the mixed forms. Overall, sentence-level processing deficits, naming difficulties, and phonological disturbances are the main linguistic features of GRN-associated PPA (Rohrer et al., 2010a;[START_REF] Saracino | Primary Progressive Aphasia Associated With GRN Mutations: New Insights Into the Non-amyloid Logopenic Variant[END_REF]. On the other hand, lvPPA has been exceptionally if ever reported in the C9orf72 repeat expansion carriers (Moore et al., 2020). This phenotype requires the coexistence of word-finding difficulties and sentence repetition deficits to be diagnosed [START_REF] Gorno-Tempini | Classification of primary progressive aphasia and its variants[END_REF], and this latter impairment is remarkably rare in PPA-C9orf72 (Table 1). Therefore, it is not surprising that the atrophy pattern involves quite distinct, more posterior regions within the language network in PPA-GRN, namely posterior temporal lobe, temporo-parietal junction and posterior frontal areas (Rohrer et al., 2010b;[START_REF] Whitwell | Clinical and neuroimaging biomarkers of amyloid-negative logopenic primary progressive aphasia[END_REF][START_REF] Saracino | Primary Progressive Aphasia Associated With GRN Mutations: New Insights Into the Non-amyloid Logopenic Variant[END_REF]. Less common FTD/ALS genes may also produce PPA phenotypes, and the available information stems from the description of single cases or very small series. MAPT mutations may produce both nfvPPA and svPPA phenotypes, in association with underlying FTLD with tau pathology (FTLD-tau) (Moore et al., 2020). However, pure svPPA cases are rather rare, whereas bvFTD associated with anomia and profound semantic deficits is a more common occurrence [START_REF] Pickering-Brown | Inherited frontotemporal dementia in nine British families associated with intronic mutations in the tau gene[END_REF][START_REF] Henz | A Pair of Siblings with a rare R5H-Mutation in Exon 1 of the MAPT-Gene[END_REF][START_REF] Roncero | Multiple high dose tDCS sessions produces perceived improvement and stabilisation in a person with a MAPT gene, presenting clinically as semantic variant primary progressive aphasia with severe cognitive impairment[END_REF]. TARDBP carriers may also display important bilateral temporal atrophy, and the corresponding linguistic phenotype is more commonly svPPA [START_REF] Gelpi | TARDBP mutation p.Ile383Val associated with semantic dementia and complex proteinopathy[END_REF][START_REF] Caroppo | Defining the spectrum of frontotemporal dementias associated with TARDBP mutations[END_REF][START_REF] González-Sánchez | TARDBP mutation associated with semantic variant primary progressive aphasia, case report and review of the literature[END_REF][START_REF] Mol | Distinctive pattern of temporal atrophy in patients with frontotemporal dementia and the I383V variant in TARDBP[END_REF]. Somatic mutations of TARDBP in the lateral and medial temporal cortices of patients with sporadic svPPA also highlight the role of TARDBP in temporal lobe pathology [START_REF] Van Rooij | Somatic TARDBP variants as a cause of semantic dementia[END_REF]. Linguistic presentations associated with TBK1 mutations are more heterogeneous and almost equally represented by nfvPPA and svPPA [START_REF] Caroppo | Semantic and nonfluent aphasic variants, secondarily associated with amyotrophic lateral sclerosis, are predominant frontotemporal lobar degeneration phenotypes in TBK1 carriers[END_REF][START_REF] Pottier | Whole-genome sequencing reveals important role for TBK1 and OPTN mutations in frontotemporal lobar degeneration without motor neuron disease[END_REF][START_REF] Van Der Zee | TBK1 Mutation Spectrum in an Extended European Patient Cohort with Frontotemporal Dementia and Amyotrophic Lateral Sclerosis[END_REF][START_REF] Hirsch-Reinshagen | Clinicopathologic correlations in a family with a TBK1 mutation presenting as primary progressive aphasia and primary lateral sclerosis[END_REF][START_REF] Swift | Variable clinical phenotype in TBK1 mutations: case report of a novel mutation causing primary progressive aphasia and review of the literature[END_REF]. Overall, these findings suggest that the degenerative process resulting from distinct FTD gene mutations displays a differential lesional tropism in patients with PPA phenotypes. Involvement of frontal areas among the C9orf72 carriers is quite heterogeneous in terms of lateralization and peak of atrophy, thus giving rise to different nfvPPA sub-phenotypes. The temporo-polar cortex is predominantly involved in the context of C9orf72, as well as MAPT, TARDBP and TBK1 mutations, whereas it is rather atypical in the GRN carriers, who frequently display a quite distinct pattern involving the posterior language areas. Anyway, the rarity of PPA-C9orf72, and more largely of genetic PPA, may preclude the generalizability of our findings and the resulting genotype-phenotype correlations. Moreover, the speech/language batteries we used, though allowing a homogeneous description of patients observed across a wide time span, did not undergo validation studies in the PPA population and are not based on a cognitive approach to language dysfunction, thus lacking diagnostic accuracy to capture the most subtle linguistic deficits, especially for unclassifiable and mixed cases [START_REF] Ivanova | A tutorial on aphasia test development in any language: Key substantive and psychometric considerations[END_REF][START_REF] Macoir | Contribution of the Cognitive Approach to Language Assessment to the Differential Diagnosis of Primary Progressive Aphasia[END_REF]. A more exhaustive linguistic evaluation based on the most recently validated tests would represent an added value for future works in this field. Additionally, the limited number of patients available in our series (even if rather important for such a rare phenotype in a rare genetic form) may have led to statistically underpowered VBM studies. Nevertheless, cluster-level corrected VBM analyses have proven their usefulness in elucidating significant patterns of atrophy even in single subjects or small-sized groups [START_REF] Khan | Atypical, slowly progressive behavioural variant frontotemporal dementia associated with C9ORF72 hexanucleotide expansion[END_REF][START_REF] Josephs | Progranulin-associated PiB-negative logopenic primary progressive aphasia[END_REF]. Furthermore, our neuroimaging results are well concordant with the linguistic and clinical phenotypes, and closely mirror the profiles of cortical involvement seen in the native acquisitions (Supplementary Figures 2 and3).

In spite of the abovementioned limitations, this study offers an overview on the clinical progression of a relatively large series of PPA-C9orf72, cases. Interestingly, the frequency of patients developing ALS (6%, 1/16) was far below what it is expected in the C9orf72 carriers, approximately half of whom presenting motor neuron dysfunction during the disease course [START_REF] Majounie | Frequency of the C9orf72 hexanucleotide repeat expansion in patients with amyotrophic lateral sclerosis and frontotemporal dementia: a cross-sectional study[END_REF][START_REF] Snowden | Distinct clinical and pathological characteristics of frontotemporal dementia associated with C9ORF72 mutations[END_REF]Le Ber et al., 2013). Therefore, ALS seems a less common occurrence in patients initially displaying a PPA, rather than a bvFTD phenotype. Even if behavioral and executive disturbances were quite common during progression, the frequency of bvFTD as secondary diagnosis was indeed low, and specifically lower than what observed in a series of PPA-GRN recently reported [START_REF] Saracino | Primary Progressive Aphasia Associated With GRN Mutations: New Insights Into the Non-amyloid Logopenic Variant[END_REF].

In conclusion, the current findings provide some important information for genetic testing in clinical practice, showing that C9orf72 gene should be analyzed in PPA patients with nfvPPA phenotype, notably when manifesting with apraxia of speech, and in those with predominant semantic impairment, especially when family history is positive for FTD/ALS. Non-amyloid lvPPA variants are not associated with the C9orf72 expansion in our series, even if some exceptions may occur. Finally, this study comprehensively describes the linguistic spectrum in a large cohort of patients with PPA related to C9orf72 expansion, and to refine the indications for molecular analyses in PPA patients, according to their phenotypes, with major clinical impact as targeted disease-modifying therapies are upcoming.

ACKNOWLEDGMENTS

We are grateful to the DNA and cell bank of the ICM for the technical assistance (DNA and cell bank, ICM, Pitié-Salpêtrière hospital, Paris, France). We also thank Fabienne Clot for carrying out the genetic analyses. The study was partially conducted with the support of the Centre d'Investigation Clinique Neuroscience (CIC 1422), Pitié-Salpêtrière Hospital, Paris. This work is generated within the European Reference Network for Rare Neurological Diseases -Project ID No 739510.

COMPETITING INTERESTS

Disclosure of interests related to the present article:

The authors declare no conflicts of interest.

Table 1. Clinical and linguistic features of the 16 PPA-C9orf72 patients. + indicates presence, -absence, and (+) partial or mild difficulties. §: appeared during disease evolution; †: disease duration at death. AAO: age at onset; ALS: amyotrophic lateral sclerosis; AOS: apraxia of speech; BD: Behavioral disorders; bvFTD: behavioral variant of frontotemporal dementia; CS: complex sentences; DD: disease duration; FCSd: frontal cognitive syndrome; mPPA: mixed primary progressive aphasia; NA: not available; nfvPPA: non-fluent/agrammatic variant of PPA; Park: parkinsonism; PLD: parietal lobe dysfunction; PNFA: progressive non-fluent aphasia; PPA: primary progressive aphasia; SS: simple sentences; svPPA: semantic variant of PPA; uPPA: unclassifiable PPA; y: years. An overall description of the Finnish cohort without detail on individual phenotypes was provided in [START_REF] Haapanen | C9orf72 Repeat Expansion Does Not Affect the Phenotype in Primary Progressive Aphasia[END_REF].

Figure 1 .

 1 Figure 1. MRI and 18 FDG-PET studies in patient #01. A: cortical atrophy prevailing in the

Figure 2 .

 2 Figure 2. MRI and 18 FDG-PET studies in patients #04 and #06. A: bilateral fronto-

Table 2 . Summary of the most important revised papers contributing to determine the frequency of PPA in C9orf72 cohorts, and of C9orf72 expansion in PPA cohorts.

 2 The largest study cohorts, contributing to a better estimation of frequencies, are shown first. FTLD: frontotemporal lobar degeneration; lvPPA: logopenic variant of PPA; mPPA: mixed PPA; na: not available; nfvPPA: non-fluent/agrammatic variant of PPA; NOS: not otherwise specified; PPA: primary progressive aphasia; PNFA: progressive non-fluent aphasia; SD: semantic dementia; svPPA: semantic variant

	Duration at
	last follow-	10	10	2	2.5	4	5	4	4 †	1	3 †	5 †	4	4	NA	5	2
	up
	Other relevant impairments at follow-up	BD, FCSd	BD, FCSd, PLD	ALS	BD, FCSd, Park	FCSd	FCSd, (PLD)	FCSd, BD, Park	FCSd	FCSd, Park FCSd, Park	FCSd	FCSd, Park	-	FCSd, Park	BD	BD
	Diagnosis at last follow up	svPPA	svPPA	PPA/ALS	PPA/ bvFTD	mPPA	mPPA	uPPA	uPPA	nfvPPA	nfvPPA	nfvPPA	PNFA	PNFA	PNFA	svPPA/bvF TD	PNFA/bvF TD

FUNDING

The research leading to these results received funding from the "Investissements d'avenir" ANR-11-INBS-0011, the Academy of Finland (no315460), and the University of Oulu Scholarship Foundation. This work was partially funded by the PHRC FTLD-exome (to ILB, promotion by Assistance Publique -Hôpitaux de Paris), the ANR-PRTS PREV-DEMALS project (to ILB, grant number ANR-14-CE15-0016-07, promotion by Assistance Publique -Hôpitaux de Paris), the Finnish Brain Foundation (to ES), the Orion Research Foundation (to ES), the Instrumentarium Science Foundation (to ES), and the Sigrid Jusélius Foundation (to ES). The funding source had no role in study design, data analysis or interpretation, writing or decision to submit the report for publication.

Disclosure of interests unrelated to the present article: ILB served as a member of advisory boards for Prevail Therapeutic and Alector, and received research grants from ANR, DGOS, Vaincre Alzheimer Association, ARSla Association, Fondation Plan Alzheimer, JPND outside of the present work.

Verbal/sema ntic paraphasias


Xinyu He

Toan Tran

Assaad Zoughaib

Production planning for district heating networks: a sequential method to consider share of renewables in annual heat production

Keywords: district heating network, planning problem, optimization, MINLP

A district heating network has generally more than one production unit, and then there are different ways to fulfill the energy demand of the network. This paper deals with the planning problem which is a problem of optimization under constraints. The production units are modeled using MINLP (mixed integer non-linear programming), in particular the following technical aspects are considered: storage capacity (for municipal wastes and biomass), allowable operating range, allowable variation of power over time, partial load performances, minimum working time when a unit runs, and minimum waiting time when it is in stand-by mode. The environmental constraint is the annual share of renewable energies in the global energy mix (for example, at least 50 % over a year). The model aims to minimize the operating cost of the network. The problem cannot be solved by a one-shot optimization, so the paper proposes a sequential approach: first, a target of renewable share is calculated for each month of the year; secondly, the planning production is determined each day according to the calculated target. The results of a case study show that the planning strategy that only aims to minimize the operating cost violates the environmental constraint. Using the developed planning model raises a little bit the cost (4.5%) but fulfills the heat demand and environmental constraint at the same time. Considering a reduced VAT eligible in France when the constraint on renewable share is met, the proposed planning is even better in term of the total cost (10 % lower).

Introduction

District heating networks (DHN) play an important role in heating delivery in urban areas; it may provide heat at a lower cost and with lower environmental impacts compared to using individual heating systems [START_REF] Pirouti | Energy consumption and economic analyses of a district heating network[END_REF] [START_REF] Li | Economic and environmental optimization for distributed energy resource systems coupled with district energy networks[END_REF]. One of the common problems in monitoring is the planning problem. A network has generally more than one production system, and then there are different ways to fulfill the energy demand of the network.

The planning problem of DHN is not a new problem. [START_REF] Sameti | Optimization approaches in district heating and cooling thermal network[END_REF] have discussed different types of optimization, constraints and techniques as well as the optimization tools used in DHN. [START_REF] Stange | Operational optimization of energy systems, 25 years -established and promising use cases[END_REF] have combined the existing methods for operational optimization and the demand forecasting algorithm. [START_REF] Talebi | A Review of District Heating Systems: Modeling and Optimization[END_REF] have made a review of the different modeling approaches and the optimization methods to reduce the operating cost. [START_REF] Schweiger | Framework for dynamic optimization of district heating systems using Optimica Compiler Toolkit[END_REF] have provided a method based on dynamic optimization and the language Modelica.

Almost the available methods focus only on optimizing the cost, but do not take into account CO2 emission when setting up the operational planning. And yet, CO2 emission is playing a more and more important role nowadays, because it has impacts not only on the environmental aspect, but also on the economic one. For example, in France, there is a reduced VAT (value added taxes) for a district heating station once its renewable share in the global heat production is high enough (over 50% for a whole year). Considering CO2 emission when setting up the operational planning is not a trivial, because the horizon of the corresponding optimization problem is quite long (e.g. 1 year). In this context, the paper proposes a planning method which aims to optimize the operating cost while considering the constraint of renewable share. The method takes into account the main characters of the production units, such as storage capacity, allowable operating range, allowable variation of power over time, partial load performances, minimum working time when a production unit runs, and minimum waiting time when it is in stand-by mode.

Methodology

The method includes two models: prediction model and optimization model. The prediction model will predict the heat demand of the clients during a day depending on the weather forecast (temperature) and some other characters of the day (whether it is weekend or holiday). The optimization model aims to determine the planning (i.e. the production units to be used and their heating powers) which fulfills the heat demand while optimizing the cost and satisfying different operating constraints and renewable share criteria. In what follows these models will be described.

Heat demand prediction model

Regression model has been chosen considering its reasonable computing time and its appropriateness for daily use. More specifically, the ARMAX (AutoRegressive-Moving-Average model with eXogenous inputs) model is used, because it is well-known that the model gives an acceptable precision [START_REF] Fang | Evaluation of a multiple linear regression model and SARIMA model in forecasting heat demand for district heating system[END_REF]. Basically, an ARMAX model is made up of three parts: one auto-regressive part, one part depending on the exterior data, and the third part is the error:

1 1 1 p q t i t i j t j t i j y y x e ϕ η - -+ = = = + + ∑ ∑ (1)
where: t: time t y: heat demand x: vector of independent variables (e.g.: outdoor temperature, time...) e: error of the model ϕ, η: parameters of the model p, q: orders of the model

The heat demand at time t depends not only on the independent variables, but also on its values at t-1, t-2 ... For each pair of model orders (p, q), the parameters (ϕ, η) are determined using the least squares method with the historical data of the network, in other words the parameters are looked for to minimize the sum of the squares of the error e.

The performance of the model depends on the independent variables taken into consideration and on the orders (p, q). Four types of model are built up:

• Model «T»: only the outdoor temperature is considered as independent variable • Model «T72»: in addition of the outdoor temperature, 72 variables are used to represent the hours of a day:

24 variables for Sunday, 24 variables for Saturday and 24 variables for weekday (from Monday to Friday) • Model « T72w»: similar to the model « T72 » but Wednesday is considered as Sunday (in fact, schools are closed on Wednesday in some regions in France, so that the housing energy consumption on Wednesday is closed to the one on Sunday).

• Model « T72h»: similar to the model « T72 » with an additional variable to indicate if a day is in a holiday period.

For each of these types, 21 combinations of the order (p,q) are considered, where p's value is between 0 and 6 and q's value is between 0 and p-1.

In order to quantify the accuracy of the models, the average mean absolute percentage error is used:

1 1 1 1 N t t N t t t y y AMAPE N y N = = - = ∑ ∑ (2)
where: : real heat demand ŷ : heat demand calculated by the prediction model : time t : the number of time steps during the evaluation period

Optimization model

Because the renewable share must be calculated over a long period (1 year), it is not possible to solve the problem by a one-shoot optimization. For this reason, the method uses a sequential approach, so that the optimization model includes two sub-models, daily model and monthly model. While the monthly model determines a target of renewable share for each month of the year, the daily model aims to give the best planning solution during a day by following the determined targets. Both models use the MINLP (mixed integer nonlinear programming) and the multi-period approach. More specifically, continuous variables are used to represent the heating powers, binary variables to represent the status of the production units (on/off) and nonlinear equations to consider different constraints. For a given optimization horizon (e.g. 1 day), the problem is split into a number of periods with a step of time of 1 hour. The objective functions of both models are the operating cost calculated for the whole optimization horizon.

Monthly model

This model aims to determine the renewable share for each month of the year. The following constraints are considered:

• Lower limit and upper limit of the operating range of the production units • Partial load performances • Annual renewable share should be higher or equal than a threshold value (e.g. 50%)

To limit the calculation time, each month of the year is represented by one typical day of which the heat demand is known (using historical data of the network).

Daily model

The daily model aims to determine the daily planning. The following constraints are considered for all the production units:

• Lower limit and upper limit of the operating range of the production units • Upper limit of the variation of power over time • Minimum waiting time in the stand-by mode when a production unit is turned off;

• Minimum working time when a unit is turned on;

• Combustible storage capacity (for biomass and waste incinerators)

• Daily renewable share should be equal to the target fixed by the monthly model

The whole process of the method is shown in Fig. 1. On the first day of each month, the monthly model is run to identify a target of renewable share for that month. Note that the monthly model takes into account the actual energy production mix of the months prior to that day. Each day, the prediction model is run to calculate the heat demand, and then the daily model is used to determine the production planning.

The propose method aims to optimize the rate of heat production, and does not consider the supply temperature of DHN. In other words, the method is appropriate to be used when the network operating cost depends only on the heating powers provided by the production units, and not on the supply temperature (that is true for a number of production systems such as gas boiler, waste or biomass incinerators).

Case study

The presented method is implemented in Python, using Pyomo package [START_REF] Hart | Pyomo--optimization modeling in python[END_REF] for the optimization part. It is tested on a case study inspired from a real DHN in Paris.

Description of the case study

The DHN has four production units: two gas boilers, one Circulating Fluidized Bed (CFB) using biomass and one municipal waste incinerator. The gas boilers are considered as non-renewable source, while the CFB and incinerator as renewable energies. Each machine has different characteristics, which are given by the network operator and listed in Table 1. In the real life, the 2 gas boilers Gas1 and Gas2 are exactly the same, but a little difference for the cost for producing the heat is set, only to force to use only one gas boiler if its power is enough to satisfy the demand. That technique also allows to reduce the calculation time required by the solver. Indeed, if the 2 boilers have exactly the same cost, there are a number of equivalent planning solutions which have the same network operating cost and the solver may take time to differentiate them. For the incinerator machine, since it uses garbage as the source for producing heat, there is actually no cost for buying the combustible. As the capacity of the storage room is limited, garbage has to be sometimes burned even if it is not necessary to produce heat, because there is no place to stock the coming garbage. In that case, the total heat produced by the network will be higher than the demand required by the end-users, the difference is released to the atmosphere via a cooling tower. In order to avoid wasting the heat produced by the incinerator, a small cost is set for the machine. In this case study, the minimum renewable share of a whole year is set to 50%.

To quantify the performance of the proposed method of planning, 3 test scenarios are set up:

• Scenario 1: the full presented method is applied to plan the network • Scenario 2: the unique constraint on the renewable share (50%) is set for every day of the year. In this scenario, the monthly model is not used, only the daily one is. • Scenario 3: the constraint on the renewable share is not considered at all, and the model only aims to optimize the cost

Results

Performances of the prediction models

84 prediction models are tested (21 combinations of order for each of four types of model). It is found that for summer, the model « T72v » with the order (4,2) is the best one and for winter, the model « T72v » with the order (2,1) is the best. The value of AMAPE during the year is 0.048, in other words, there is a 4.8% difference between the real demand and the predicted demand. With the average annual heat demand equals to 30.6 MW, the annual average difference between the real and predicted demands is 1.46 MW. As example, Fig. 2 shows the performance of the selected prediction model during a day. The predicted demand follows the same trend with the real demand, even though there is sometime significant difference between these 2 quantities.

Performances of the optimization model

When simulating the HEN during a whole year, the planning determined by the optimization model is adjusted continuously in order to meet exactly the heat demand of the end-users. That is because there is always a difference between the real demand and the predicted one. When the real demand is higher than the predicted one, the planned heating powers are increased by preferring the cheapest production units first. On another side, when the real demand is lower than the predicted one, the planned heating powers are decreased by preferring the most expensive production units first. In both cases, the change of power is only allowable if it satisfies the technical constraints (i.e. operating range, limited variation of power over time, minimum working or waiting time). The planning is considered as failed when it is not possible to satisfy the technical constraints and fulfil the real demand at the same time.

Table 2 presents the results of the three tested scenarios. By definition, the failure rate is the time, in percentage, when the network fails to satisfy 100 % of the real heat demand. The results show that the demand is fulfilled in all the time in the scenario 2, the failure rates of the scenarios 1 and 3 are negligible (0.19 % and 0.27 %, respectively). Then, it can be concluded that all three scenarios ensure the thermal comfort of the clients.

In the scenario 3 where the model optimizes only the cost without considering the constraint of renewable share, the planning is unacceptable because the annual renewable share does not meet the criteria of 50 %. The scenario 2, that sets the target of renewable share to 50 % everyday, shows the highest cost. Note that the annual renewable share overpasses the target. Indeed, the renewable share of the periods of low demand exceeds what is required, because only the incinerator is enough to fulfil the heat demand. In the scenario 1 that corresponds to the proposed method of planning, the daily target varies month by month, and that allows the DHN to have an annual renewable share very close to the desired value (50 %). The corresponding cost is lower than the one of the scenario 2 (about 6.2 %), but higher than the scenario 3 (about 4.5 %). However, the expected gain thanks to the reduced TVA1 is 14.5 %, and that makes the scenario 1 the most attractive scenario in term of the cost (about 10 % less than the scenario 3). As example, Fig. 3 shows the heating powers of the four production units during 10 days (results from the scenario 1). The waste incinerator usually runs at its maximal power, because it is not only a renewable source but also the cheapest production unit. From time to time, its power is reduced when the demand is low, and that allows to store garbage for further use. The gas boiler 1 is used almost all the time because gas is the second cheapest combustible. The second gas boiler 2 is used only when the first one reaches its maximum power. The CFB is less used since it is the most expensive unit; it is used in order to satisfy the constraint on the renewable share.

Conclusion

This paper has built a model for planning the operation of a DHN composed of various production units. The model aims to minimize the operating cost, but the annual renewable share in the energy production mix has to satisfy a local regulation (at least 50 % in the case study). The model considers a number of technical constraints on the production units such as allowable operating range, allowable variation of heating power over time and minimum working (waiting) time. The proposed method of planning uses a sequential approach and is composed of two MINLP sub-models. The monthly model aims to determine the daily target of renewable share and the daily model identify the daily planning.

The case study is inspired from a DHN in Paris. The results show that the proposed method of planning allows to keep the annual renewable share to the desired value (50 %). The operating cost is higher than the case where only the cost is optimized without considering the constraint of renewable share. However, taking into account the reduced TVA, the planning provided by the method is in fact the most attractive one in term of the total cost (10 % lower). This result indicates a tax subsidy may really encourage the operators of DHN to use more and more renewable energies.

The corresponding cost is also 6.2 % lower than the case where a unique target of renewable share is set for everyday. Then, it can be concluded that using the monthly model to determine the target month by month helps optimizing the cost while maintaining the annual renewable share under control.

In the further work, the supply temperature of the network will be considered, allowing the method to be applied in the cases where the performance of the production units highly depends on the temperature, such as geothermal or heat pump.

Fig. 1 .

 1 Fig. 1. Proposed planning method

Fig. 2 .

 2 Fig. 2. Comparison between the predicted heat demand and the actual one

Fig. 3 .

 3 Fig. 3. Heating power (in MW): (a) gas boiler 1; (b) gas boiler 2; (c) CFB; (d) incinerator

Table 1 .

 1 Characteristics

	of the production units
	Gas1 Gas2 CFB Incinerator

Table 2 .

 2 Results of the planning model

	Scenario Annual cost (M€) Annual renewable share Failure rate
	1	16.10	50.1%	0.19 %
	2	17.16	56.6%	0
	3	15.40	45.9%	0.27 %

In France, the normal TVA is

%, while the reduced one is 5.5 %


H Jaballah

W Bouzidi

R Fersi

N Mliki

L Bessais

Structural, magnetic and magnetocaloric properties of (Pr,Sm) 2 Fe 17 compound at room temperature

Keywords: numbers: 75.50.Bb, 75.50.Tt, 76.80.+y Intermetallic rare-earth transition-metal compounds, Magnetic materials, Magnetocaloric Effect. 44

In the present work, we report on the structural, magnetic, and magnetocaloric properties of the (Pr, Sm)2Fe17 system prepared by arc melting under high pure argon and homogenized at 1073 K to minimize other possible impurity phases. X-ray diffraction (XRD) coupled with Rietveld analysis with FullProf computer code reveals the presence of a single-phase of (Pr, Sm)2Fe17. This compound crystallizes in the rhombohedral Th2Zn17 type structure. The lattice parameters decrease when Sm substitutes Pr. Hence, the temperature dependence of the magnetization is determined. The Curie temperature increases from 285 K to 299 K after the Pr substitution. This increase in TC is mainly due to the de Gennes factor. The Arrott plot around second-order magnetic transition, magnetic entropy changes ∆SM, the relative cooling power, and temperature-averaged entropy change (TEC) are reported. This compound is considered a magnetic refrigerant for use at a low magnetic field based on these results.

I. INTRODUCTION

The R-M intermetallic compounds combining a rare earth element (R) and a transition metal (M) have interesting properties due to their extremely varied potential applications. Among these applications, we may cite the high-density magnetic recording Sm 2 Co 17 -Cu [1], and TbFeCo [2], the hard magnetic materials SmCo, NdFeB, and PrCo [3][4][5][6], and the magnetic refrigeration [7].

Iron-rich R 2 Fe 17 intermetallic compounds are studied in several works for their: magnetic properties, as well as their thermodynamic properties, and the absence of thermal hysteresis [8][9][START_REF] Tishin | Institute of Physics[END_REF][START_REF] Mandal | [END_REF][12][13][START_REF] Dan | Ran-604 ganathan[END_REF][START_REF] Dan | Ran-606 ganathan[END_REF][16][START_REF] Dan | Ran-611 ganathan[END_REF][18][19]. Additionally, Kou et al. [20] have analyzed the magnetic anisotropy in several R 2 Fe 17 systems, where R = Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Lu, Y. Moreover, absorption and storage capacity of hydrogen were examined by Isnard et al. in R 2 Fe 17 (R = Ce, Pr, Nd, Gd) [21]. Their magnetostriction and thermal expansion properties were also studied by Mori et al. [22]. Sun et al. [23] have reviewed the magnetic properties, Fe-Fe and R-Fe exchange interactions for R 2 Fe 17 and their nitrides. Also, Long et al. [24] have as well investigated neutron and Mössbauer effect of Pr 2 Fe 17 and Pr 2 Fe 17 N 2. 6 . Further information about structural, magnetic, and microscopic physical properties of Sm 2 Fe 17 and Pr 2 Fe 17 and their nitrides have been provided by Zeng et al. [25].

On the other hand, for many years, human activities have led to a sharp increase in greenhouse gas emissions due to the need for refrigeration, air conditioning, and cryogenics. However, these systems mostly use refrigerants that contain volatile organic compounds such as hydrofluorocarbons. Such compounds are made up of carbon and hydrogen, which can easily be found in gaseous form in the atmosphere and cause climatic dam-ages. They can also have harmful effects on animals and Sm 2 Fe 17 is higher than room temperature. Several samples (Pr,Sm) 2 Fe 17 have been prepared with different compositions ( x=0. 24, x=0.3, x=0.36 and x=0.42), only the composition with the nominal composition x=0.36 one gives T C = 300 K. Here, we present the structural, magnetic, and magnetocaloric properties of (Pr, Sm) 2 Fe 17 with the nominal composition x=0.36.

II. EXPERIMENTAL METHODS

(Pr, Sm) 2 Fe 17 with the nominal composition x=0.36 has been prepared from high pure elements iron(Fe) 99.9%, praseodymium (Pr) 99.98% and samarium(Sm) 99.98% by arc-melting technique under a purified argon atmosphere. The elements are placed in a copper crucible cooled by cold water. After ingot formation, the compound is wrapped in tantalum foil and introduced into a silica tube sealed under secondary vacuum 2 × 10 -6 bar [50][51][START_REF] Khazzan | Djega-693 Mariadassou[END_REF]. The ingot has been heat-treated for seven days at 1073 K, and is finally water quenched [53][54][55].

Phase analysis has been performed by X-ray powder diffraction (XRD), using D8 Brucker diffractometer with Cu Kα radiation λ = 1.54178 Å. XRD data of the samples have been collected between 20 • and 80 • at room temperature with 0.015 step width.

XRD diagrams are analyzed with the Rietveld method [56,57] using the Fullprof program [58,59]. The peak shape function has been selected as Thompson-Cox-Hastings pseudo-Voigt type [START_REF] Bessais | and 709 NX[END_REF]. The goodness of fit indicators R B and χ 2 are calculated from the program output to measure the quality of refinement, and they are defined as:

R B = 100 K |I K (O) -I K (C)| K I K (O) and χ 2 = i w i |y i (O) -y i (C)| N -P
where I K (O) is the observed Bragg intensity and I K (C) is the calculated one. y i (O) is the intensity observed at the i th step in the step scanned powder diffraction pattern, y i (C) is that calculated, and w i is the weight of the observation. N is the total number of points used in the refinement, and P is the number of refined parameters.

The refined parameters are unit cell parameters, scale factors U, V, W, background points, and atomic positions [5,[61][62][63]. The atomic input parameters that have been used to determine the structure of our samples are from Ref. [9,64,[START_REF] Guetari | Bes-720 sais[END_REF] Magnetic properties are measured using a magneto/susceptometer Manics DSM8 operating on the same principle as a Faraday type balance between 300 and 124 900 K [66]. A Physical Properties Measurement System 125 (PPMS) magnetometer is used for magnetic measure- For Sm concentration 0 and 0.36, we note that all 165 angular positions shift to the right, in Fig. 3 reported in [START_REF] Guetari | Bes-720 sais[END_REF]72].

217

Table II. Interatomic distances (dFe-Fe( Å)) and coupling type for the rhombohedral R 3m structure type for Pr2-xSmxFe17, x = 0 and x = 0.36. NN is the number of near neighbor atom. T C in rare-earth transition-metal intermetallic com-

Sites x = 0 x = 0.
222 3k B T C = a FeFe + a RR + [(a FeFe -a RR ) 2 + 4a RFe a FeR ] 1/2
Where a α-β is the magnetic interaction energy between 223 α and β spin. where G is the de Gennes factor:

231 G = (g R -1) 2 J R (J R + 1)
J FeFe and J RFe are the exchange coupling constant be- according to the magnetic field. However, for tempera-300 tures higher than T C , the material is paramagnetic, the 301 magnetization increases slowly with the applied magnetic 302 field. We also note that for a given magnetic field, the 303 magnetization decreases when the temperature increases. Fig. 8 shows the magnetization as a function of the magnetic field applied at the temperature 200 K. To determine the value of the magnetization at saturation and the anisotropy constant we used the following saturation law: We plotted the Arrott plots M 2 = f (H/M ) deduced from isothermal magnetization M (H) curves (Fig. 9).

M = M s 1 - a H 2
From the shape and the slope of the curves, we can determine the type of the phase transition: If the slope is negative and the Arrott plots close to the Curie temperature have the S shape, the transition from the ferromagnetic state to the paramagnetic state is, therefore, a first-order transition. If the curves have a single inflexion point and a positive slope, the transition from the ferromagnetic state to the paramagnetic one is a second-order transition.

C. Study of the phase transition according to the

Landau model

We develop in this part the Landau model to confirm the nature of the phase transition. The order of the transition phase is determined by developing free magnetic energy as a function of temperature around the T C ,

Table IV. magnetic characterization of Pr2-xSmxFe17 and Pr2Fe17

Ms(Am neglecting the very high power terms of magnetization.

332

Free energy F as a function of total magnetization can 333 be developed in the form:

334 F = 1 2 a(T )M 2 + 1 4 b(T )M 4 + 1 6 c(T )M 6 -µ 0 M H
Applying the equilibrium condition for free energy 335 dF dM = 0 we obtain:

µ 0 H = a(T )M + b(T )M 3 + c(T )M 5
The coefficients a(T ), b(T ) and c(T ) are the Landau pa-

∂M ∂T H dH

Where M is the magnetization, T is the temperature,

353
and H is the applied magnetic field. Since, the isothermal 354 M (H) curves are measured by discrete field changes, the 355 following expression might be used [80]: Where M i and M i+1 are the initial magnetization at 399

356 |∆S M | = µ 0 i M i -M i+1 T i+1 -T i ∆H i 2
T EC = 1 ∆T H-C max        T mid + ∆T H-C 2 T mid - ∆T H-C 2 |∆S M (T )|dT       
Where ∆T H-C is defined as the temperature range for RCP because of their low working temperature range δT FWHM ∼ 10 K as opposed to materials with second order transition phase like the parent compound Pr 2 Fe 17 with δT FWHM ∼ 100 K [72].

For Pr 1.64 Sm 0.36 Fe 17 RCP is found to be around 159.4 J.kg -1 under a magnetic field change of 2 T which is around 75% of that observed in pure Gd and makes our compound a potential candidate for magnetic refrigeration around the room temperature [82].

From the point of view of magnetic refrigeration, the irreversibility of the magnetocaloric effect is a major disadvantage. Indeed, a minimal thermal hysteresis is a basic constraint for a practical refrigerant [91]. For example, the materials mentioned above like (Gd 5 (Ge,Si of rescaled temperature [94].

466 Θ = -(T -T C )/(T r1 -T C ), T ≤ T C 467 Θ = (T -T C )/(T r2 -T C ), T ≥ T C
Where Θ is the rescaled temperature, Tr1 and Tr2 are 468 the temperatures of the two reference points that have 469 been selected as those corresponding to -∆S M =-a× ∆S max (where 0 ≤ a ≤ 1) [95]. Some theoretical studies have proved that it is not necessary to use two reference point temperatures lower and higher than T C Tr1 and

Tr2, but only one Tr can be used for a material with a single magnetic phase. Nevertheless, in the case of an important demagnetization factor or the existence of multiple magnetic phases, it is required to use two reference temperature points [96].

The analysis of the universal scale demonstrates magnetic homogeneity. This approach should remove the dependency of the set of curves ∆S M (H, T) on both temperature and field so that all curves treated using the same scaling procedure will collapse on a common universal curve. A lack of success in achieving this universal collapse can be explained by a magnetic inhomogeneity in the material [96]. As described above, we use detailed statistical analysis to determine the magnetic homogeneity in the material and the order of magnetic transition.

After rescaling temperature and choosing a=0.5, Fig. 13 shows that the normalized entropy change for all applied magnetic fields collapses in a single universal curve. This suggests that Pr 1.64 Sm 0.36 Fe 17 is magnetically homogeneous undergoes a second-order magnetic transition phase around T C =299 K. where n=2/3 in the case of mean field model [97]. For real ferromagnetic material the previous relation was rectified by Lyubina et al [START_REF] Lyubina | Gschnei-799 dner[END_REF]. It was modified as follow:

∆S max M = A(µ 0 H + H 0 ) n -AH 2/3 0 + B(µ 0 H) 4/3
Where A and B are intrinsic parameters of the material

126Th 2

 2 ments at low temperatures between 200 and 340 K. Re-127 cently, it has been reported that the demagnetizing field 128 might have a notable influence on the result of magne-129 tocaloric effect [67]. To get the internal field H int =H ext -130 N Demag M(T, H ext ), where M is the measured magneti-131 zation, the external applied magnetic field H ext has been 132 corrected for the demagnetization effect. Demagnetiza-133 tion constant N Demag has been determined from M vs 134 H ext curve in a low field region following the method 135 given in Ref [68]. The corrected magnetic field H i has 136 been used for the present magnetic results. 137 III. RESULTS AND DISCUSSION 138 A. Structure analysis 139 XRD patterns of the Pr 2 Fe 17 and the Pr 1.64 Sm 0.36 Fe 17 140 compounds are presented with their Rietveld refinement 141 in Fig. 1(a) and Fig. 1(b), respectively. The pure Pr 2 Fe 17 142 compound crystallizes in a rhombohedral structure of the 143 Zn 17 type in the space group R 3m. In this structure, 144 Pr atoms occupy 6c sites, while Fe atoms occupy four 145 different crystallographic sites: 18f, 18h, 6c and 9d (in 146 Wyckoff notation). 147 Table I. a and c unit cell parameters, RB, χ 2 factors, and atomic positions from Rietveld refinement of Pr2-xSmxFe17. x = 0 x = 0.

  157

Figure 1 .

 1 Figure 1. The Rietveld refinement pattern of XRD data for (a) Pr2Fe17 and (b) Pr1.64Sm0.36Fe17 compounds. The black and red line presents respectively the calculated intensities and the experimental intensities. The green vertical bars correspond to (hkl) line positions (Positions of Bragg peaks). The blue line shows the difference between the calculated and experimental intensities.

2 F e 1 7 S m -c o n c e n t r a t i o n p e r f o r m u l a u n i t 1 Figure 2 .

 2712 Figure 2. Cell parameters versus Sm content x, Inset shows cell volume and c/a vs Sm content.

194Figure 4 . 204 Figure 5 .Fig. 4

 420454 Figure 4. Temperature dependence of magnetization of Pr1.64Sm0.36Fe17 under an applied magnetic field µ0H = 0.05 T. 203 204

218 pounds are governed by three kinds of exchange coupling 219 J

 219 RR , J T T and J RT . Therefore, T C can be given by the 220 following relation[73]: which allows us to discuss the 221 different parameters which influence the value of T C :

224 2 229 a

 2229 Neglecting the exchange interaction between two rare-225 earth atoms a RR is relatively weak compared to the other 226 terms of energy of magnetic interaction. So, it can be 227 written as follows: 228 3k B T C = a FeFe + [a 2 FeFe + 4a RFe a FeR ] 1/Where FeFe = Z FeFe J FeFe S Fe (S Fe + 1) 230 a RFe a FeR = Z 1 Z 2 S Fe (S Fe + 1)GJ 2 RFe

277

  the Fe-Fe distances in the 6c -6c site, which can de-278 crease the value of Curie temperature. So the increase 279 of T C cannot be explained by the variation of the Fe-Fe 280 distances. Ultimately, there is a competition between the 281 two contributions to T C : de Gennes factor and iron-iron 282 distance. In Sm 2 Fe 17 compound T C is equal to 400 K but 283 in Pr 2 Fe 17 T C is equal to 285 K, although the unit cell 284 volume and iron pairs distance for these two compounds 285 is very close (V P r2F e17 -V Sm2F e17 = 3 Å3 ) there is a rela-286 tively large difference in the value of T C . This difference 287 shows that rare-earth-transition metal magnetic energy 288 exchange is much stronger in Sm 2 Fe 17 than in Pr 2 Fe 17 . 289 In conclusion, the contribution of Sm de Gennes factor 290 in magnetic energy exchange can explain the increase of 291 T C after the partial substitution of Pr by Sm. Similar 292 behavior has been noted for other compounds such as 293 Pr 2-x Dy x Fe 17 [65].

  294

Figure 7 .

 7 Figure 7. magnetization M (µ0H, T ) curves of Pr1.64Sm0.36Fe17.

Fig. 7

 7 Fig. 7 presents isothermal magnetization M (µ 0 H, T ) 295

2 Where 1 )Figure 8 .

 218 Figure 8.Magnetization M (H) vs magnetic field of Pr1.64Sm0.36Fe17 measured at T = 200 K .

Figure 9 .

 9 Figure 9. The Arrott plots of Pr1.64Sm0.36Fe17 compound.

336 rameters determined from the equilibrium condition by 337 plotting µ 0 HFigure 10 .

 337010 Figure 10. Landau parameter a(T ) vs temperature around the TC for Pr1.64Sm0.36Fe17 sample.

Figure 11 .

 11 Figure 11. Landau parameter c(T ) vs temperature around the TC for Pr1.64Sm0.36Fe17 sample.

Figure 12 .

 12 Figure 12. Landau parameter b(T ) vs temperature around the TC for Pr1.64Sm0.36Fe17 sample.

Fig. 13 illustratesFigure 13 .

 1313 Fig. 13 illustrates the variation of the magnetic en-363

376

  The relative cooling power (RCP ) is an essential pa-377 rameter in the magnetocaloric application. It is related 378 with the maximum of entropy change by the following 379 relation [37]: 380 RCP = -∆S M δT FWHM Where δT FWHM is the full width at half-maximum 381 in the temperature dependence of the magnetic entropy 382 change, the maximum of -∆S M , the variation of the tem-383 perature ∆T and relative cooling power (RCP ) are given 384 in Table VI

  .

385

  Another important parameter to evaluate the magne-386 tocaloric effect is the refrigerant capacity (RC) Area , it is 387 the amount of heat that can be transferred in one thermo-388 dynamic cycle. The RC value represents the area under 389 -∆S M curve using the temperature of FWHM. It can be 390 calculated by integrating the following expression: 391 RC Area (H) = Tmax Tmin ∆S M (T, H)dT ; 392 T max -T min = δT F W HM In addition to RCP and RC area , temperature-averaged 393 entropy change (TEC) is another parameter that has 394 been used to check the applicability of materials for mag-395 netic refrigeration technologies. TEC was introduced by 396 L. D. Griffith et al. [90] as another figure of merit. TEC 397 can be calculated using magnetic entropy change data as 398 follows:

400

  the measuring device and represents the difference be-401 tween hot and cold heat exchangers. T mid represents 402 the temperature value in the middle of ∆T H-C that 403 maximises TEC. Fig. 14 shows the variation of TEC 404 with ∆T H-C under several magnetic field changes be-405 tween 1 T and 3 T. One can see that T EC decreases 406 slightly and monotonously with ∆T H-C , it is very close 407 to the maximum of entropy change value for low values 408 of ∆T H-C . It is easy to see that TEC increases mono-409 tonically with the applied magnetic field for a given tem-410 perature. The obtained TEC(∆T H-C =5 K, µ 0 H=3 T) 411 and TEC(∆T H-C =5 K, µ 0 H=1 T) for Pr 1.64 Sm 0.36 Fe 17 412 are 3.71 Jkg -1 .K -1 and 1.4 Jkg -1

Figure 14 .

 14 Figure 14. TEC vs ∆TH-C at several magnetic fields for Pr1.64Sm0.36Fe17.

) 4 ,- 1 Figure 15 .

 4115 Figure 15. Universal curve of entropy change VS reduced temperature Θ for Pr1.64Sm0.36Fe17 sample . 460 461

6 Figure 16 .

 616 Figure 16. Field dependence of magnetic entropy change at TC for Pr1.64Sm0.36Fe17 sample.

Fig. 13 clearly

 13 Fig. 13 clearly shows that magnetic entropy change of Pr 1.64 Sm 0.36 Fe 17 sample reach its maximum around Curie temperature. The maximum of magnetic entropy change depends strongly on the applied magnetic field. A nonlinear relation can be expected between ∆S max M and

504 and H 0 Fig. 16 Figure 17 .Pr 1 . 64 Th 2

 016171642 Fig.16shows ∆S max M vs µ 0 H and fit parameters. One

  569

  Fe 17 , Pr 2-x Sm x Fe 17 and

		{	P r 2 F e 1 7 ( 3 0 3 )	{	( 3 0 3 ) P r 1 . 6 4 S m 0 . 3 6 F e 1 7
		I n t e n s i t y ( a r b . u n i t )
		4 2 . 3 4 2 . 4 4 2 . 5 4 2 . 6 4 2 . 7
			2 θ
		Figure 3. (303) Bragg position for Pr2Fe17, Pr1.64Sm0.36Fe17
			.
		a A-B = a A (1 -x) + a B
	177	Where a A-B , a A , a B are lattice parameters of binary
	178	compound, pure A compound and pure B compound, re-
		spectively. From a value of Pr 2

179 Sm 2 Fe 17 the preceding equation gave x ∼ 0.35 which is 180 very close to the nominal composition within the exper-181 imental uncertainties. 182 B. Magnetic properties 183 Here, we present the magnetic properties of 184 Pr 1.64 Sm 0.36 Fe 17 compound. It is worthy to note that 185 this composition has been chosen for the following rea-186 son: It is well known that T C of Pr 2 Fe 17 and Sm 2 Fe 17 187 are equals to 285 and 386 K, respectively. To obtain a 188 compound with a Curie temperature around the room 189 temperature, we started by preparing Pr 2 Fe 17 as the ini-190 tial mixture, and we used the nearly linear variation of 191 reach T C ∼ 300 K. Therefore, for x = 0.36, this goal 193 is achieved.

  Fe and J R are the spin moment of the iron atom and In Pr 1.64 Sm 0.36 Fe 17 , each atom of Pr or Sm has an av-C in R 2 Fe 17 intermetallic materials. Among 249 these, we can mention de Gennes's factor. Indeed, T C is Another parameter is affecting T C in R 2 Fe 17 com-FeFe , when d FeFe is less than 2.45 Å J FeFe is FeFe is greater than 266 2.45 Å the exchange integral becomes positive, and the 267 iron pairs become ferromagnetically coupled. The pres-268 ence of Fe-Fe distances less than and greater than 2.45 Å 269 in Pr 2 Fe 17 and Pr 1.64 Sm 0.36 Fe 17 compounds results in a 270 competition between two types of ferromagnetic and an-271 tiferromagnetic couplings (Table II). The coexistence of 272 a negative and positive coupling is the origin of the rel-273 atively low temperature in the compounds Pr 2 Fe 17 and 274 Pr 1.64 Sm 0.36 Fe 17 . After the partial substitution of Pr by 275 Sm in Pr 2 Fe 17 the coupling nature of the different pairs 276 of Fe is not affected, but we notice a slight decrease in

	238
	239	erage of Z 1 = 19 iron near-neighbours; each an atom of
	240	iron has an average of Z 2 = 2 atoms of Pr or Sm and a
	241	number of Z FeFe = 10 iron neighbors. This relation shows
	242	that T C is governed by the 3d -3d exchange interactions
	243	between the transition metal atoms and the 3d -4f ex-
	244	change interactions between the rare-earth and the tran-
	245	sition metal. Consequently, T C is mainly controlled by
	246	the exchange interaction between the atoms of iron J FeFe
	247	and between the rare-earth atom and the iron atom J RFe
	248	[52, 74]. Many parameters can have an influence on the
		value of T 4f n 3 + ion G
		1	Ce 0.18
		2	Pr 0.80
		3	Nd 1.84
		5	Sm 4.46
		7	Gd 15.75
		8	Tb 10.5
		9	Dy 7.08
		10 Ho	4.5
		11	Er 2.55
		12 Tm 1.17
	261
		pounds which is the distances between the iron atoms. In

232

tween tow iron atoms and between iron atom and rare-233 earth atom, respectively. 234 g R is the Landé factor of rare-earth atom. 235 S 236 the total moment of rare-earth atom, respectively. 237 250 governed by the magnetic energies of exchange a F e-F e 251 and a R-F e , the strength of a R-F e is proportional to de 252 Gennes factor of rare-earth [75-77]. Ref [23] shows the 253 dependence of T C on the de Gennes factor in R 2 Fe 17 com-254 pounds (R = Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm). 255 A maximum of T C is shown for Gd with the highest de 256 Gennes factor, T C increases almost linearly when the de 257 Gennes factor increases with different slopes for light and 258 heavy rare-earth atom. Table III shows de Gennes factor 259 values tabulated by Kirchmayr and Poldy (1978)[78] 260 Figure 6. Curie temperature of R2Fe17 for different rare-earth atom Table III. de Gennes factor value of different rare earth 262 fact, the sign of the exchange integrals is determined by 263 the distances d 264 negative and the coupling between the pair of iron atoms 265 is antiferromagnetic [79]. Otherwise, d

Table VI .

 VI Magnetocaloric effect of Pr1.64Sm0.36Fe17. Pr 2 Fe 17 . |∆S M | remains almost constant after the substi-

		µ0∆H(T)	1	1.6	2	2.6	3
		|∆SM|(J/(kg.K)) 1.22 1.87 2.5 2.98 3.24
		δT FWHM (K)	51	58 63.76 69.4	78
		RCP (J/kg)	62.22 108.46 159.4 202.65 247.26
		RCArea(J/kg) 48.46 86.81 121.1 164 195.1
	371
	372	tution with Sm. Even though many research studies have
	373	reported materials with high ECM at low temperatures,
	374	there are few materials with high MCE and second-order
	375	transition phase from ferromagnetic state to paramag-
		netic state around to 300 K.

Table VII .

 VII Pr 1.64 Sm 0.36 Fe 17 Er 0.1 Sr 0.4 MnO 3 416 [86] and TmFe 0.7 Mn 0.3 O 3 [87], slightly higher than T EC Eu 0.1 Sr 0.4 MnO 3 [86], T EC ∆µ0H of TmFe 0.8 Mn 0.2 O 3 Pr 1.64 Sm 0.36 Fe 17 is around ∼ 250 J/kg for a TEC value of our sample and TEC values of other materials for comparison.

	Material	T mid ∆µ0H ∆TH-C	TEC	T EC ∆µ 0 H	Ref
		K	T	K	J(Kkg) -1 J(KkgT ) -1
	Pr1.64Sm0.36Fe17	300	3	5		3.71	1.24	This work
	Pr0.5Eu0.1Sr0.4MnO3 279.9	5	5		4.45	0.89	[86]
	Pr0.5Eu0.1Sr0.4MnO3 188.5	5	5		4.9	0.98	[86]
	TmFe0.7Mn0.3O3	11	7	5		7	1	[87]
	TmFe0.8Mn0.2O3	12	7	5		6.4	0.914	[87]
	La0.8Na0.2MnO3	330	5	5		4.6	0.92	[88]
	La0.8Ca0.05Na0.15MnO3 315	5	5		4.55	0.91	[88]
	Ho2CoMnO6	77	7	5		6.5	0.928	[89]
				415
				417	T EC ∆µ0H is comparable to T EC ∆µ0H of Pr 0.5 ∆µ0H
				of Pr 0.5 418
				419	[87], T EC ∆µ0H of La 0.8 Na 0.2 MnO 3 [88], and T EC ∆µ0H of
					Ho 2 CoMnO 6 [89].
				421
				422	magnetic field change equal to 3 T.
				423	There are several magnetocaloric materials that have
				424	been studied for magnetic refrigeration at room tempera-
					ture: Gd 5 (Ge,Si) 4 [27, 33-35], La(Fe,Co,Si) 13 (H,C) [36-

.K -1 , respectively. 413 Table VII shows TEC value of our sample and TEC val-414 ues of other materials for comparison.

420 RCP for 425 41], Fe 2 P [42-45], manganites R 1-x A x MnO 3 [46-49] and 426 related alloys and compounds. In these materials the 427 magnetic transition from the ferromagnetic state to the 428 paramagnetic state is a first order transition phase show a 429 large |∆S M | at operating temperature, but possess a low 430

ACKNOWLEDGMENTS

This work was supported by the National Center for 571 Scientific Research (CNRS), France, and by the Ministry

572