Morgane Innocent
email: morgane.innocent@univ-brest.fr

Agnes Francois-Lecompte

Nolwenn Roudaut
email: nolwenn.roudaut@univ-ubs.fr

Comparison of human versus technological support to reduce domestic electricity consumption in France

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

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Comparison of human versus technological support to reduce domestic electricity consumption in France

In its "Framework for climate and energy", the European Union (EU) addresses a number of issues in relation to climate change. This Framework calls on EU member states to target a 27% decrease of their energy consumption in 2030 with respect to 1990 levels. This aim is not new and is not specific to Europe [START_REF] Svenfelt | Decreasing energy use in buildings by 50% by 2050 -A backcasting study using stakeholder groups[END_REF]. Many countries or institutions, such as the Conference of the Parties (COP), are trying to find a way to a more sustainable development including a decrease of primary energy consumption. The role of households is particularly important as they represent the largest consumer group, accounting for 35% of the total electricity consumption in France [START_REF] Rte | Bilan électrique[END_REF]. Reducing household electricity demand is thus one of the key challenges for public energy policies in Europe and most developed countries.

If the aim is to encourage households to reduce their use of electricity, it is important to examine the effectiveness of the different support systems that can be implemented for this purpose. After having identified the target behaviour (a decrease of electricity consumption by consumers), the next step is to identify and test the external interventions that are most likely to induce the desired change [START_REF] Geller | The challenge of increasing proenvironment behavior[END_REF][START_REF] Steg | Encouraging pro-environmental behaviour: An integrative review and research agenda[END_REF]. In that regard, it appears that many research projects and public programmes for mitigating climate change impact are based on a recourse to digital technologies [START_REF] Darby | Smart metering: what potential for householder engagement?[END_REF][START_REF] Hargreaves | Making energy visible: A qualitative field study of how householders interact with feedback from smart energy monitors[END_REF].

However, research also shows that it is far from simple to change consumer behaviours [START_REF] Bull | Moving beyond feedback: Energy behaviour and local engagement in the United Kingdom[END_REF]. The present article aims to test the impact of various systems for reducing domestic electricity consumption. In particular, we compare the efficiency of two alternative strategies to encourage consumers to engage in more ecologically sustainable behaviour, i.e. using a technological versus a human approach. The first approach is based on technological tools allowing consumers to consult detailed feedback information about their daily electricity consumption [START_REF] Marikyan | A systematic review of the smart home literature: A user perspective[END_REF]. This approach includes home-automation systems and innovations built upon smart-grids. The second approach relies on providing households with guidance on the topic of electricity, offering them the possibility of interaction as well as learning eco-friendly behaviour from other people's experience.

The research is based on an experiment conducted between December 2015 and June 2017 including 162 volunteer households in western France. The households were equipped with a smart-meter for monitoring the overall electricity consumption of each participant. The sample was divided into four groups, three of them being subject to different treatments and a control group without any particular treatment. Participants were not randomly assigned to a particular group and were free to choose one treatment or another. This choice could have been influenced by individual characteristics. Consequently, the analysis uses a treatmenteffect methodology [START_REF] Heckman | Characterizing selection bias using experimental data[END_REF] to compare households in terms of their response to the different programmes. In summary, our results suggest that providing detailed information on electricity consumption does not systematically lead to a change of consumers' daily practices. Similarly, without access to detailed information on electricity consumption, a change of consumption behaviour cannot be achieved [START_REF] Kendel | What do people 'learn by looking'at direct feedback on their energy consumption? Results of a field study in Southern France[END_REF]. The combined activation of human and technological leverages can trigger an effective decrease of electricity consumption in the short term. This study has important implications for both private and public actors involved in energy transition. It highlights the complementarity of human and technological solutions to induce more ecofriendly types of behaviour in the case of electricity consumption. In particular, we question the efficiency of purely technological approaches for the monitoring of electricity consumption, since consumers need to be assisted through human interaction.

Based on a literature review, the first part of this article presents the hypotheses tested in this research. We then develop the methodological aspects, with a presentation of the experimental design and the statistical procedure used to compare the different experimental treatments. Finally, the last part of the article provides the results and the ensuing conclusions.

Research background and theoretical framework

Research on electricity savings

Electricity savings (ES) behaviours involve all the choices and actions made by consumers that aim to minimize their home electricity consumption. These behaviours include everyday eco-gestures in various domains (e.g., heating, cooking, lighting and electrical appliances) and the choice of installations and devices (e.g., home appliances, insulation, heating system, use of renewable energy) [START_REF] Gardner | Environmental Problems and Human Behavior[END_REF][START_REF] Abrahamse | Energy conservation through behavioral change: Examining the effectiveness of a tailor-made approach[END_REF]Urban & Ŝčasnỳ, 2016).

Behaviours related to ES have been extensively studied in sociology and environmental psychology, in particular to identify their determining factors. These factors are usually classified according to two sets of antecedents: those related to the context or to psychological variables [START_REF] Wilson | Models of decision making and residential energy use[END_REF]Thøgersen & Gronhoj, 2010).

As far as the contextual determining factors are concerned, studies have shown the influence of the specific features of households as regards domestic appliances, heating and hot waterproducing devices [START_REF] Sardianou | Estimating energy conservation patterns of Greek households[END_REF][START_REF] Mills | Residential energy-efficient technology adoption, energy conservation, knowledge, and attitudes: An analysis of European countries[END_REF][START_REF] Ehrhardt-Martinez | Advanced metering initiatives and residential feedback programs: a meta-review for household electricity saving opportunities[END_REF][START_REF] Huebner | Understanding electricity consumption: A comparative contribution of building factors, socio-demographics, appliances, behaviours and attitudes[END_REF]. Similarly, studies have highlighted the role of sociodemographic factors such as age, gender, income, education level and housing tenure status [START_REF] Poortinga | Household preferences for energysaving measures: A conjoint analysis[END_REF][START_REF] Gram-Hanssen | Different everyday lives, different patterns of electricity use[END_REF][START_REF] Barr | The household energy gap: examining the divide between habitual-and purchase-related conservation behaviours[END_REF]Carlsson-Kanayama & Linden, 2007;[START_REF] Sardianou | Estimating energy conservation patterns of Greek households[END_REF][START_REF] Abrahamse | How do socio-demographic and psychological factors relate to households' direct and indirect energy use and savings[END_REF][START_REF] Ehrhardt-Martinez | Advanced metering initiatives and residential feedback programs: a meta-review for household electricity saving opportunities[END_REF][START_REF] Thøgersen | Electricity saving in households -A social cognitive approach[END_REF][START_REF] Stromback | The potential of smart meter enabled programs to increase energy and systems efficiency: a mass pilot comparison Short name: Empower Demand[END_REF][START_REF] Chen | A statistical analysis of a residential energy consumption survey study in Hangzhou, China[END_REF][START_REF] Jones | The socio-economic, dwelling and appliance related factors affecting electricity consumption in domestic buildings[END_REF].

Concerning the psychological antecedents of ES, two main groups have been identified. The first one relates to variables such as personality traits, values (Schwartz, 1977) and personal norms. These factors are relatively stable for different groups of the population, but do not really account for ES behaviours [START_REF] Abrahamse | Energy conservation through behavioral change: Examining the effectiveness of a tailor-made approach[END_REF]. The second antecedent is related more directly to ES behaviour. It includes ES drivers, deterrents, attitudes [START_REF] Gadenne | The influence of consumers' environmental beliefs and attitudes on energy saving behaviours[END_REF] and ES-related notions of self-efficacy [START_REF] Lindenberg | Normative, gain and hedonic goal frames guiding environmental behavior[END_REF][START_REF] Thøgersen | Electricity saving in households -A social cognitive approach[END_REF], linked to attitudes towards the effectiveness of daily-based actions [START_REF] Barr | The household energy gap: examining the divide between habitual-and purchase-related conservation behaviours[END_REF][START_REF] Botetzagias | Electricity curtailment behaviors in Greek households: Different behaviors, different predictors[END_REF]. Factors such as financial, comfort, and convenience issues and those related to knowledge have positive or negative effects upon people's behaviours [START_REF] Abrahamse | Energy conservation through behavioral change: Examining the effectiveness of a tailor-made approach[END_REF][START_REF] Abrahamse | How do socio-demographic and psychological factors relate to households' direct and indirect energy use and savings[END_REF]Ek & Soderholm, 2010;[START_REF] Sweeney | Energy saving behaviours: Development of a practice-based model[END_REF][START_REF] Ohler | Does environmental concern change the tragedy of the commons? Factors affecting energy saving behaviors and electricity usage[END_REF]. Another category involves multiple moral issues: preserving the environment, global warming, citizens' responsibility, or even hunting down waste [START_REF] Stern | Toward a coherent theory of environmentally significant behavior[END_REF][START_REF] Barr | The household energy gap: examining the divide between habitual-and purchase-related conservation behaviours[END_REF][START_REF] Sweeney | Energy saving behaviours: Development of a practice-based model[END_REF].

All these studies deal with the variables involved upstream of behaviours, but are insufficient to identify efficient programmes leading to behavioural change. The present study focuses on this specific topic and aims to analyse the effectiveness of different strategies to induce more efficient ES behaviours. In a general manner, strategies to induce pro-environmental behaviours either act on the information given to consumers or on the costs/benefits of the behaviour [START_REF] Steg | Encouraging pro-environmental behaviour: An integrative review and research agenda[END_REF].

In the field of electricity consumption, much research has concentrated on the first type of intervention, and more precisely the impact of providing more feedback to consumers [START_REF] Darby | Smart metering: what potential for householder engagement?[END_REF][START_REF] Hargreaves | Making energy visible: A qualitative field study of how householders interact with feedback from smart energy monitors[END_REF]. This feedback consists of giving people information about their electricity consumption, and has proven to be an effective way to promote proenvironment behaviours [START_REF] Abrahamse | Informational strategies to promote pro-environmental behaviour: changing knowledge, awareness and attitudes[END_REF]. The central assumption is that providing feedback on energy consumption makes electricity visible, thus raising awareness and thereby encouraging individuals to make a rational decision to reduce their consumption [START_REF] Hargreaves | Making energy visible: A qualitative field study of how householders interact with feedback from smart energy monitors[END_REF]. Feedback could also overcome several barriers to behavioral change such as perceived self-efficacy, knowledge of eco-gesture efficiency, or a rebound effect after the purchase of an energy-efficient appliance [START_REF] Gifford | The dragons of inaction: Psychological barriers that limit climate change mitigation and adaptation[END_REF]. Based on 36 studies carried out between 1995 and 2010, [START_REF] Ehrhardt-Martinez | Advanced metering initiatives and residential feedback programs: a meta-review for household electricity saving opportunities[END_REF] give an overview of the average household electricity savings by feedback type. They draw a distinction between "indirect feedback", provided, for example, by an enhanced billing statement or a weekly estimated consumption, and "direct feedback", which provides real-time information, ideally down to the appliance level. Electricity-savings can vary from 4% to 12% depending to the type of feedback. The "direct feedback" solution involves the implementation of technical solutions, such as electronic devices. In fact, these solutions provide a tool for customers to better control their consumption and ultimately save energy (Fischer, 2008). It has been shown to be effective in changing heating behaviours [START_REF] Jensen | Agent-based assessment framework for behavior-changing feedback devices: Spreading of devices and heating behavior[END_REF]. Based on a meta-analysis, [START_REF] Ehrhardt-Martinez | Advanced metering initiatives and residential feedback programs: a meta-review for household electricity saving opportunities[END_REF] conclude more generally that "Providing households with frequent, ongoing, and meaningful feedback regarding their energy consumption practices results in significant residential sector energy savings while engaging people to become part of the energy solution" [START_REF] Ehrhardt-Martinez | Advanced metering initiatives and residential feedback programs: a meta-review for household electricity saving opportunities[END_REF].

Another option to encourage households to reduce their energy use on a voluntary basis is to adopt a more tailored and human approach [START_REF] Abrahamse | Energy conservation through behavioral change: Examining the effectiveness of a tailor-made approach[END_REF]. Under that option, households are encouraged to change their behavior by means of interactions with experts on electricity savings aspects. This could take the form of collective workshops in which information about energy-saving measures is given through advice. These workshops address the "why" and "how" questions of participants about ES behaviors. Consequently, the aim of such workshops is to lead to higher levels of concern about climate change, to increased knowledge about energy conservation, and finally to enhance ES behaviors. These types of support are not only based on a "top down" communication of skills and knowledge but also use a lateral communication process based on human relationships, citizen friendliness and the sharing of experiences and ideas between participants [START_REF] Sweeney | Self-determination theory and word of mouth about energy-saving behaviors: an online experiment[END_REF]. The "Carbone Conversations" is a good example of this type of initiative even if these meetings address climate change in all its daily aspects (Buchs, Hinten & Smith, 2015). In a closely related idea, the coaching can be personalized. In such an approach, an expert comes into the home and can adapt his or her advice to each individual case. This solution is time consuming but an advantage of this approach is that participants receive relevant information only, rather than general information which may not always apply to a given household situation [START_REF] Abrahamse | A review of intervention studies aimed at household energy conservation[END_REF]. In France, several recent programmes have been based on home audits, such as the Trak O'Watts initiative (www.trakowatts.bzh).

Several studies have analysed the effectiveness of human approaches which mix awareness to climate change with teaching on how to act as an individual (see [START_REF] Abrahamse | Energy conservation through behavioral change: Examining the effectiveness of a tailor-made approach[END_REF] for a synthesis).

Hypotheses

Overall, except in the case of economic leverage, solutions for enhancing ES behaviors can be divided into two competing approaches, one based on a technological pillar allowing a detailed and real-time feedback on electricity consumption to consumers, and another based on a human pillar where consumers can interact with experts and benefit from a tailored support. The existing research literature offers a view on the way each solution operates on consumers. However, these studies suffer from two main limitations: firstly, they do not always measure the evolution of behaviors in time or under real conditions of use for consumers; secondly, they focus on a single solution that prevents a true comparison of the effectiveness of support systems.

Based on the above findings, the purpose of this study is to test and compare the effects of technological versus human support systems on consumer behaviour. The first support system is based on the transmission of information to consumers on their electricity consumption, whereas the second system is based on learning, awareness and know-how of eco-friendly gestures.

Based on the existing body of literature, it is hypothesized that: H1: Households who receive technological support providing detailed feedback on their electricity consumption show a greater reduction in their electricity consumption compared to individuals without any support system. H2: Households who receive human support by coaching show a greater reduction in their electricity consumption compared to individuals without any support system. Furthermore, following [START_REF] Abrahamse | Energy conservation through behavioral change: Examining the effectiveness of a tailor-made approach[END_REF], we posit that interventions work better when used in combination. Since these interventions operate on distinct drivers, it is then assumed that they act more efficiently compared to a single solution.

H3: Households who receive both human and technological support systems show a greater reduction in their electricity consumption compared to individuals receiving a single support system.

Methodological aspects

Presentation of the experiment

The study was conducted during the years 2015 and 2017 as part of an experimental electric Smart Grid in the Brittany Region. Electric smart grids are "smart" networks that rely on new technologies to promote better communication between consumers and electricity producers and better management of the electricity network. In France, their development is based on the "Linky" smart meters.

The project aimed to test, under real conditions, the impact of several support systems on electricity consumption on a sample of households. More precisely, the sample was divided into four distinct groups, each one corresponding to a particular experimental condition. The experimental design was based on the voluntary participation of individuals, even if the households had been recruited by means of a canvassing method. The participation of these individuals included answering several surveys1 throughout the duration of the project. All participants were also equipped with a "Linky" smart-meter for monitoring the overall electricity consumption in each household.

Experiment design

As mentioned, the sample is divided into four groups, three of them being subject to different treatments and a control group without any particular treatment.

The first group, called Home Automation System (HAS) (n= 18), was equipped with a home automation system for monitoring electricity consumption at a disaggregated level (heating, lighting, hot water, etc.). This was implemented by means of a home-based device and personal access to a dedicated web site. This group corresponds to a "purely technological" type of solution that allows consumers to measure their own electricity consumption in detail.

The second group, called Collective Coaching (CC) (n=27), was invited to participate in periodic collective workshops organized by the local energy agency which were focused on eco-friendly gestures with respect to electricity consumption. The purpose of these meetings was to create awareness among participants and to teach them how to reduce electricity consumption through daily gestures. This second group corresponds to a "purely human" type of approach, with no action to make detailed home energy monitoring available for consumers.

The third group, Individual Coaching (IC) (n=28) was offered personal coaching by the local energy agency; this included six home visits, measurement of the electricity consumption of appliances and personalized advice to reduce energy consumption. In that case, people could benefit from both a home-based device and personalized interaction with an expert. Then this third group represents the case of a "mixed approach" based on both human and technological support.

Finally, one group (n=89) without any treatment was integrated into the study to assess the possible effects of participation in the experiment on electricity consumption. The simple fact of being monitored for overall electricity consumption (by means of smart-meter) may induce a behavioural change, and may lead to a decrease in electricity consumption. This group received no incitation to save electricity and represents the Control Group (CG).

As summarized in Fig. 1, the four conditions can be divided into two electricity reduction support systems: a human approach versus a technological approach.

To test our hypotheses, five comparisons are made with the control group. Three of the comparisons involve tests between each treated group and the control group. The two other tests deal with composite groups, one corresponding to the human approach (Collective coaching + Individual coaching) and the other to the technological approach (Individual coaching + Home automation system). 1.

During the recruitment step, future participants were invited to choose between the four proposed treatments. As the data show, the distributions are not the same for the four groups.

For example, the HAS group is characterised by an over-representation of male participants, with around 80 % of the sample younger than 65, made up of owners having a family of three persons or more. The IC group is older, with a majority of two-person families.

Outcome variables

Two outcome variables are used to evaluate the impact of the different treatments.

The evolution of electricity consumption over time. Firstly, the electricity consumption of the households in the four groups was measured by smart-meters. Consumption is compared over two six-month periods: from January to June 2016 (P1), during which the different types of approach were progressively applied and a second period (P2), from January to June 2017, during which the treatments were continued. The total consumption for each period is measured in kilowatt-hours (kWh) and is called the "Electricity Index" (EI). To compensate for the effect of the consumption level of the households, the Evolution of the Electricity Index (EV EI) between the two periods P1 and P2 is calculated for each household:

= -

Evolution in the practice of eco-friendly gestures. In addition to this measurement, a survey was conducted on participants at the end of the first period (called T1) and at the end of the second period (called T2). These surveys included a measurement of the level of electricity eco-friendly gestures declared by the respondent. The measure of the intensity of Electricity savings Practice (EPI) used here is derived from the index developed by [START_REF] Thøgersen | Electricity saving in households -A social cognitive approach[END_REF], but is adapted to the French context. The original index comprised 17 items detailing simple and more technical eco-friendly gestures helping to reduce electricity consumption at home. After cleaning the data and adaptation to the French context, the final measure includes 13 items, which are listed in Fig. 2. Some items were deleted due to the low prevalence of equipment (tumble dryer, dishwasher) or certain cultural differences (like the use of vacuum flasks for coffee). Thus, the 13 items are a set of actions that can be performed in a French household to save electricity, regardless of the characteristics of the housing (size, mode of heating, etc.). The structure of the measure is similar to a Rasch model [START_REF] Thøgersen | Electricity saving in households -A social cognitive approach[END_REF][START_REF] Urban | Structure of Domestic Energy Saving: How Many Dimensions?[END_REF], in which the most common eco-friendly gestures are also the simplest. An individual with a basic eco-friendly practice will simply turn off the lights and television, while an individual with a more advanced practice will make use of low consumption bulbs and will be careful to not leave devices on standby mode. The similarity of the EPI index to a Rasch scale is reflected in a separation reliability coefficient of .67 very close to the standard of .70 [START_REF] Petrillo | Using classical test theory, item response theory, and Rasch measurement theory to evaluate patient-reported outcome measures: a comparison of worked examples[END_REF]. In line with Thøgersen and Grønhøj (2010), we operate this variable using the mean score of the responses to the 13 items on a 5-point scale. In addition, to assess the nomological validity of the measure, we use a regression to test the influence of a known determinant of EPI the Intended purpose to save electricity [START_REF] Thøgersen | Electricity saving in households -A social cognitive approach[END_REF], on EPI (in T1). The results show that the Intended purpose to save electricity explains 19.3% (F=38.279) of the index EPI, with an estimated parameter value of 0.44 (t=6.187).

Once the EPI scores for T1 and T2 are calculated, the evolution of Electricity savings Practice Intensity (EPI) between the two periods is determined for each household:

= -

Figure 2. Measure of the intensity of electricity saving practice (EPI)

How often do you … (Never/ Rarely/ Half the time/ Often / Always) 1_Switch off the light when you are the last person to leave a room? 2_Purchase energy-saving light bulbs such as compact fluorescent light bulbs (CFLs) or LED bulbs? 3_Start the washing machine when it is not full? (reversed item) 4_Swith the TV off when nobody's watching it? 5_Swith the computer off when nobody's using it? 6_ Switch off appliances in stand-by mode? 7_Thaw frozen foods in the refrigerator? 8_Put a lid on the pan when you are boiling food (e.g., pasta, vegetables, eggs)? 9_Switch the oven off a few minutes before the end of cooking time in order to take advantage of oven inertia?

How often do you … (Never/ Rarely/ Regularly/ Often/ Very often) 10_Control the temperature inside your refrigerator? 11_Control the temperature inside your freezer?

Do you pay attention to … (Not at all/ A little/ Moderately/ A lot/ Extremely) 12_The renewability of the electricity you use at home? 13_The information regarding the electricity consumption of the appliances you purchase, such as the information provided on the energy labels?

The treatment-effect measurement

The analysis uses a treatment-effect methodology [START_REF] Heckman | Characterizing selection bias using experimental data[END_REF] allowing us to compare the four groups in terms of their response to the different treatments by controlling and neutralizing the impact of effects other than those due to the treatments.

As households are self-selected into the four groups, there is no guarantee that the behavioural change depends solely on the treatment [START_REF] Hartman | Self-selection bias in the evolution of voluntary energy conservation programs[END_REF]. In our case, this means that comparing average variations of electric consumption or EPI between groups is inappropriate.

In fact, there are probably some individual characteristics that can affect the choice of a particular treatment as well as electricity consumption or electricity savings practice. For example, larger households, or those with children, could be more willing to reduce their electricity consumption [START_REF] Mills | Residential energy-efficient technology adoption, energy conservation, knowledge, and attitudes: An analysis of European countries[END_REF] and thus participate in programmes. In that case, electricity consumption is reduced not only because these households are treated but also because they are more likely to change their habits.

The advantage of a treatment-effect methodology is that it can identify and neutralize the contextual and psychological factors (called covariates), such as household characteristics, equipment or individual attitudinal factors that could impact the results, considered apart from the treatment. In other words, treatment participation has to be independent of the outcome variables conditionally on chosen covariates (Lechner, 2001).

For this study, we choose the procedure known as Propensity Score Matching [START_REF] Caliendo | Some practical guidance for the implementation of propensity score matching[END_REF] referred to here as PSM. In a general manner, this method can be presented in two steps: firstly, estimation of the probability to be treated and, secondly, based on this probability, evaluation of the effect of a specific treatment on outcomes. This procedure is performed by calculating an indicator called the Average Treatment Effect (ATE). For example, if, on average, treated individuals reduce their Electricity Index more that they would if they were not treated, then ATE will be significantly negative (and vice versa for the non-treated individuals). In this case, the conclusion is that the treatment helps to significantly reduce the Electricity Index. Then, the expected sign is negative for ATE related to the Electricity index and positive for ATE related to Practice intensity (the treatment helps to significantly enhance the Practice Intensity).

Estimating the probability of treatment

Firstly, the probability of a household to be treated is estimated, by calculating the propensity score. The aim is to create a "matching model" for each group of the experiment, and then select proper covariates for each group.

This selection has to comply with a number of rules [START_REF] Caliendo | Some practical guidance for the implementation of propensity score matching[END_REF]. Firstly, the potential covariates are selected from previous studies on the subject. That explains why the potential covariates have been selected from the contextual and psychological key factors set out in the first section. Secondly, the covariates have to be independent from the participation and from the anticipation of the treatment. For example, the psychological factors of the participants have to be measured before the start of the experiment.

The propensity score must explain, but not entirely, the participation of the households: if a group is entirely concentrated on one specific modality of a covariate, this covariate must be excluded from the matching model. In other words, individuals/households with the same characteristics must be present in treated and non-treated groups.

In our study, we faced an additional constraint due to the small number of observations. Thus, we use a parsimony criterion which means that only the significant covariates are included in the models [START_REF] Heckman | Characterizing selection bias using experimental data[END_REF][START_REF] Bryson | The use of propensity score matching in the evaluation of labour market policies[END_REF]. The list of covariates available for the study is presented in Annex 1.

Since we are estimating the probability of a household to be treated, logit or probit models (for an example see [START_REF] Caragliu | Smart innovative cities: The impact of Smart City policies on urban innovation[END_REF] are preferable options compared to linear probability models [START_REF] Caliendo | Some practical guidance for the implementation of propensity score matching[END_REF]. We chose a logit specification that is applied to the five treatment conditions.

Evaluating the effect of the treatment

Once the probability to be treated has been estimated, the PSM procedure uses this probability to match households and then goes on to estimate counterfactual outcomes.

The general idea is to compare "matching" outcomes of treated and non-treated households.

In other words, for a particular treated household, we compare its actual consumption with the one that the household would have had if it has not been treated. This fictitious consumption, called a counterfactual outcome, can be estimated using the consumption of households in the sample with almost the same characteristics. This corresponds to the matching step.

Different matching algorithms are available. They broadly differ regarding the definition of neighbourhood and the weights assigned to neighbours. In this study, we use the most straightforward matching estimator, i.e. nearest neighbour (NN) matching. The individual from the comparison group is chosen as a matching partner for a treated individual that is closest in terms of the propensity score [START_REF] Caliendo | Some practical guidance for the implementation of propensity score matching[END_REF].

Once satisfactory estimation models are drawn up, the treatment effect is evaluated in terms of the Average Treatment Effect (ATE), which is the mean of the difference between outcome variables (counterfactual and observed) of all households (treated and non-treated).

Results

This section is organized in two parts. Firstly, we present a set of descriptive statistics and secondly, an analysis of the results of the treatment-effect methodology.

Descriptive statistics

Table 2 summarizes the means of the outcome variables, EV EI and EV EPI, for the different treatment groups (the means and standard deviations of the variables used to define the outcomes variables are reported in annex 2). As expected, the statistics show that the experiment produces a decrease in the electricity consumption of the participants (-4.17%), but only a small increase in their declared electricity savings (+0.98 %). When we look at a disaggregated level, it appears that the four groups of participants lowered their electricity consumption, by 2% for the control group and 7.5% for the individual coaching group (Fig. 3). Regarding the declared eco-friendly gestures, the collective coaching group and the control group remain at a similar level for the two periods (Fig. 4). The individual coaching group again shows the highest increase, followed by the home-automation solution group.

Overall, the human support system approach is characterized by a decrease of 6.5% in electricity consumption and an increase of 3.2% in the declared electricity savings. For the technological support system, the mean values of EV EI and EV EPI are -7.4 % and 4.5% respectively.

Interestingly, these results reveal an effect of being part of the experiment, since the control group changed its behaviour. More precisely, the 89 households without treatment consumed 2% less electricity in the second period comparing to the first period. This shows the need to analyse the results in more detail though a methodology isolating the treatment effect.

Results of the treatment-effect measurement

The treatment-effect methodology was applied to both the electricity index and the declared electricity savings. Five comparison tests were performed for both indicators as shown in Table 3.

Estimating the probability to choose a treatment

Five logit models are estimated. This first step of the PSM procedure leads to the selection of covariates that explain in the best possible way the choice of a specific group by an individual. Originally, 16 covariates taken from the literature were included in the models (see Annex 1). Nine of these covariates prove to have an impact on the choice of treatment by the households, some of them after categorical transformation, and two of them show an additional quadratic effect. Ultimately, twelve covariates are used in the five models. The results are presented in Table 3, which reports the regression parameter and its significance (t test and P value) for each covariate.

These results show that different factors like individual characteristics (Energy culture, attitude towards the effectiveness of daily gestures, or the intended purpose to save energy),

or households characteristics (such as house size and the status of occupiers) and dwelling characteristics (surface area, date of construction, heating system and the number of electric appliances) can be identified as determinants of the willingness to participate or not in programmes. For example, members of IC and HAS groups (and consequently IC+CC and IC+HAS groups as well) show a lower perception of daily gestures effectiveness compared to the control group (regression parameters are significant and positive). This differs from the CC group for which this is not a significant covariate.

For the two continuous variables (Surface area of the housing and number of electric appliances), quadratic effects are observed.

While the choice of individual coaching and Home-automation support system are accurately explained by the models, the choice of Collective coaching appears to be more difficult to explain.

The aim of this first step of the PSM procedure is to predict the probability to be treated for each household. Then, at the matching step for a given treated household, we are looking for similar households that are not treated (similarity is based on the propensity scores calculated in the first step). These households give information about the level of outcome this particular household would have if it was not treated (counterfactual outcome). The ATE measure is obtained by performing this step for each household in the sample and calculating the average of the differences between observed and counterfactual outcomes.

Table 3.Results of the Logit regressions: determinants of participation in the experiment

(1) (2) (3) (4) (5)

Outcome of the PSM procedure: Average treatment effect

We estimate the impact of technological and human supports on electricity savings (EV EI), and Eco-friendly gestures practice intensity (EV EPI) by looking at the average treatment effects (respectively ATE1 and ATE2) for the different type of supports, i.e. Individual coaching, Home-automation system, Collective coaching, and more broadly with the subpanel involving both technological and human support. Results are reported in Table 4.

First, the significance level of ATE provides information about the effectiveness of the treatment. If ATE is not significantly different from zero, then this means that there are no significant differences between observed and counterfactual outcomes: being treated or not has the same impact on variations of the electricity index or variations of the practice intensity. For example, the Electricity index shows a decrease between P1 and P2 for each group (see Fig. 3), but this decrease is no greater for some treatment groups (Homeautomation system (ATE1=-.09) and Collective Coaching (ATE1=.03) compared with the control group.

Secondly, for the significant ATE, we find that ATE1 is negative and ATE2 is positive, which is as expected. More precisely, a significant decrease in electricity consumption (EI) and a significant increase of daily eco-friendly gestures (EPI) is only observed in the "mixed approach" group, i.e. the Individual coaching group (IC). The Collective coaching group (CC) increased its practice of daily eco-friendly gestures, but this did not give rise to significant electricity savings. There is no significant effect regarding the Home-automation system group (HAS).

Indeed, ATE1 estimation reflecting the rate of variation of the electricity index is not significant. Simultaneously, estimation of daily eco-friendly gestures based on ATE2 reveals no significant evolution of the effective behaviour. The results regarding HAS are discussed further below in the limitations section.

Finally, cross-group comparison tests show that technological support (HAS + IC) effectively helps households to decrease their electricity consumption, without effects on daily ecofriendly behaviour, while the Human support system (CC + IC) has a significant effect on daily behaviour and a moderate effect on electricity consumption.

Discussion and conclusions

It should be borne in mind that hypotheses H1 and H2 assume that technological (H1)/ human (H2) support leads to a reduction of the electricity consumption of the household. As table 4 shows, both the technological approach providing a detailed feedback (H1, validated by ATE1

(HAS + IC) significance), and the human approach by means of coaching (H2, validated by ATE1 (CC + IC) significance) help Households to reduce their electricity consumption.

Hypotheses H1 and H2 are thus validated.

Furthermore, the third hypothesis can also be confirmed since households having received both support systems (IC group) show a greater reduction in electricity consumption compared to those receiving a single support system (H3, validated by ATE1 (IC) value of 0.09***).

Nevertheless, our findings regarding H1 and H2 are more subtle than expected. It appears that the effect of human or technological support is significant only at the aggregate level, that is when bringing together IC and CG for the human approach, and IC and HAS for the technological approach. Two treatments, HAS and CG, show either mixed or no results when taken in isolation. A detailed analysis of the effects of the three treatments shows variations in the manner of operation of the different supports.

The human approach is shown to be effective on both outcome variables at the aggregate level. This implies, for example, the effectiveness of know-how transmission by demonstration. However, in the case of collective coaching (CC), there is an impact on frequency of daily eco-friendly gestures but not on electricity consumption. As the coaching only concerns individuals involved in the experiment, this approach does not necessarily lead to a decrease in the electricity consumption at the level of the household (ATE1 (CC) not significant). The participant might have some difficulties in triggering positive changes at the family scale. Additionally, without detailed information on his/her own consumption, it could be difficult to identify the most effective actions for electricity-savings.

Regarding the technological support, individual coaching leads to a decrease of the electricity consumption and an increase in daily eco-friendly gestures (AT1 and ATE2 (IC) are significant). But the Home-automation support alone does not induce an increase of daily ecofriendly gestures. Then, we can suppose that the drop in consumption would result from other factors, such as home insulation, or the buying of more efficient electrical appliances [START_REF] Gardner | Environmental Problems and Human Behavior[END_REF][START_REF] Abrahamse | Energy conservation through behavioral change: Examining the effectiveness of a tailor-made approach[END_REF]Urban & Ŝčasnỳ, 2016).

These results suggest that providing detailed information of electricity consumption does not systematically lead to a change of consumers' daily practices. Similarly, without access to detailed information on electricity consumption, a change of consumer behaviour leading to energy savings cannot occur [START_REF] Kendel | What do people 'learn by looking'at direct feedback on their energy consumption? Results of a field study in Southern France[END_REF]. In summary, only a combined activation of human and technological leverages can trigger a major change of electricity consumption in the short term.

Implications and recommendations

This study has important implications for both private and public actors involved in the energy transition. It highlights the complementarity of human and technological solutions to induce more eco-friendly types of behaviour as regards electricity consumption. In particular, we question the efficiency of purely technological approaches for the monitoring of electricity consumption, since consumers need to be assisted through human interaction.

As illustrated in this research, electric smart-grid solutions offer suitable tools for the monitoring household electricity consumption. As such, smart-grids are considered as key enablers for the implementation of the smart city paradigm [START_REF] Betis | Smart Cities [Scanning the Issue[END_REF]. This concept has rapidly risen to prominence within industry, especially in the context of policy programmes against climate change, and is well on its way to becoming the leading driver of urban sustainability (de Jong, Joss, Schraven, [START_REF] De Jong | Sustainable-Smart-Resilient-Low Carbon-Eco-Knowledge Cities; Making sense of a multitude of concepts promoting sustainable urbanization[END_REF].

Based on such perspectives and expectations, [START_REF] Martin | Smart and sustainable? Five tensions in the visions and practices of the smart-sustainable city in Europe and North America[END_REF] stress that digital technologies are envisaged as "solutions" to urban sustainability problems. These latter authors highlight several tensions between the smart city and the goals of sustainable development; some of these tensions are directly connected with the results of our study.

These authors also note that digital innovations have been designed based on the assumption that structural problems can be resolved through changes in the behaviour of individual citizens. This assumes a rational choice model that connects information provision with residential behaviour [START_REF] Karvonen | Towards systemic domestic retrofit: a social practices approach[END_REF][START_REF] Mcmeekin | Sustainability transitions and final consumption: practices and socio-technical systems[END_REF]. Smart-grids, in Smart cities, for example, will be able to empower citizens to make better decisions based upon the data created by smart infrastructure (Caragliu & Del Bo, 2012;[START_REF] Viitanen | Smart cities and green growth: outsourcing democratic and environmental resilience to the global technology sector[END_REF]. Our results show that, in the absence of Human support, the process of transformation from information into new behaviours does not systematically occur.

Our results outline a possible new vision on smart-grids and smart-cities, based not only on technology but also on its synergy with programmes fostering human relationships, citizen friendliness and the sharing of experiences and ideas. Taking this synergy into account could provide a new roadmap for local policies aiming to use digital technologies to empower citizens [START_REF] Martin | Smart and sustainable? Five tensions in the visions and practices of the smart-sustainable city in Europe and North America[END_REF]. At present, the main issue seems to place citizens/consumers at the heart of the action, and to make sure that they appropriate technological tools in their daily practices [START_REF] Innocent | The values of electricity saving for consumers[END_REF].

This clearly raises the problem of the cost of such ambitions. In the context of the experiment, a cost-benefit analysis of the different types of support shows that individual coaching is four times more expensive than collective coaching [START_REF] Lallouet | Évaluation socio-économique au périmètre de la collectivité et recommandations pour la mise en oeuvre d'une animation territoriale de la MDE[END_REF]. In the case of home automation support, the initial installation represented about half of the cost of individual coaching. Solutions to induce electricity savings at a large scale should then take into account the cost and feasibility of their implementation.

In a nutshell, this study leads to the conclusion that a balanced distribution of resources is necessary to accelerate the energy transition, which should be directed both towards the diffusion of new technologies and the appropriation of these tools by citizens through human support.

Limitations and future research

The main limitations of this study are the relatively small size of the sample and the short duration of the experiment -i.e. the comparison of results was obtained over only two time periods. The small size of the sub-panels, more specifically concerning the Home-automation support system, might reduce the validity of the results. Surprisingly, the 9% decrease of electricity consumption for the Home-automation support group is not statistically significant, which gives an illustration of this limitation. In addition, the short duration of the experiment prevents us from taking a potential rebound effect into account [START_REF] Sorrell | Empirical estimates of the direct rebound effect: A review[END_REF]. Nevertheless, it should be borne in mind that the experiment was conducted under real conditions, and that households were involved in the study over a long period of time.

A second limitation is that our methodology does not allow us to identify whether the efficiency of the different support systems is impacted by some socio-economic variables (socio-professional category, age, housing tenure etc.). This would involve measuring the influence of these variables, all other things being equal, within each studied group. Such tests would also require larger samples to isolate the impact of different socioeconomic variables. This could be an interesting extension of the present research, in order to define a more precise target for a particular approach.

In conclusion, it appears that the complementarity between technological versus human approach is a crucial issue of the energy transition. More research is expected on this aspect to ensure that more sustainable behaviours really occur.

Annex 1

Descriptive statistics of the 16 tested covariates

The nine selected covariates and modalities involved are in grey.

Figure 1 .

 1 Figure 1. Synthesis of the experiment design

Figure 3 .Figure 4 .

 34 Figure 3. Evolution of electricity consumption EI (in K-Watt-hour) between the two periods for the four groups

Table 1 .

 1 Descriptive statistics of the sample and the four groups

			Total	Control	CC	HAS	IC
	Indicators	Sample	Group	Group	Group	Group
			n=162	n=89	n=27	n=18	n=28
	Sex	Female Male	47% 53%	49% 51%	48% 52%	39% 61%	43% 57%
		25-39	9%	7%	15%	17%	4%
		40-54	20%	21%	19%	17%	18%
	Age	55-64	29%	24%	33%	39%	36%
		65 and over	38%	44%	30%	22%	39%
		undisclosed	4%	4%	4%	6%	4%
		1 person	22%	27%	26%	6%	14%
	House size	2 persons	49%	48%	44%	39%	61%
		3 persons or more	29%	25%	30%	56%	25%
	Housing tenure	Owner Tenant	81% 19%	76% 24%	81% 19%	94% 6%	86% 14%
		Collective	26%	27%	26%	17%	29%
	Type of Housing	individual	73%	72%	74%	83%	71%
		Other	1%	1%	0%	0%	0%

Table 2 .

 2 Means of the outcome variables of the experiment

		EV EI	EV EPI
	N	Mean	Mean

  Estimated parameters; t statistics in parentheses; * p < 0.10, ** p < 0.05, *** p < 0.01

		IC	HAS	CC	IC+CC	IC+HAS
	Surface area	-0.02 (-1.33)		-0.03 (-1.32)	-0.03 * (-1.75)	-0.05 ** (-2.45)
	(Surface area)²	1.12×10 -4* (1.79)		1.19×10 -4 1.19×10 -4** 1.9×10 -4*** (1.41) (2.01) (2.58)
	Electric Heating	-0.51 * (-1.71)			-0.16 (-0.65)	-0.27 (-0.98)
	Strong Intended purpose to save	-0.82 *			-0.17	-0.70 *
	electricity	(-1.86)			(-.62)	(-1.87)
	Low perception of daily gestures	0.70 **	0.66 **		0.42 *	0.73 ***
	effectiveness	(2.36)	(2.00)		(1.73)	(2.78)
	2-person household		0.54 (0.97)			0.81 * (1.93)
	3-person household		1.11 * (1.94)			1.09 ** (2.33)
	Owners		1.34 ** (1.99)			1.13 ** (2.53)
	Newer dwelling		0.76 *			0.43
	(built after 2004)		(1.82)			(1.27)
	Strong Energy culture			0.47 (1.47)	0.37 (1.32)
	Number of electric appliances			0.48 * (1.72)	0.25 (1.33)
	(Number of electric appliances) 2			-0.01 *	-0.01
				(-1.67)	(-1.18)
	Constant term	0.81	-3.32 ***	-3.76	-1.33	0.83
		(0.75)	(-3.86)	(-1.54)	(-0.82)	(0.77)
	N	116	107	115	143	134
	Pseudo R 2	0.15	0.20	0.05	0.06	0.19

Table 4 .

 4 Results of the treatment-effect methodology

		Electricity Index EV EI ATE1 t-stat	Practice intensity EV EPI ATE2 t-stat	Type of support	Effect
	Individual coaching (IC) versus CG	-.09 *** (-6.94)	.25 ***	(3.66)	Human + technological	Yes
	Home-automation system (HAS) versus CG	-.09	ns	-.21	ns	Technological	No
	Collective coaching (CC) versus CG	-.03	ns	.20 **	(2.04)	Human	Yes
	Human support systems (CC+IC) versus CG	-.06 ** (-2.52)	.20 ***	(2.64)	Human	Yes
	Technological support (HAS + IC) versus CG	-.11 *** (-4.23)	.12	ns	Technological	No
	t statistics in parentheses; * p < 0.10, ** p < 0.05, *** p < 0.01, ns: non-significant

  Modes of category indicator values are given in bold. Other numerical indicators: mean (standard deviation).a score based on six items for measuring knowledge of energy culture with correct and incorrect answers. Answers were recorded in terms of 1-0 (true-false) modalities.Means and standard deviations of variables used to build the outcome variables Mean St. Dev. Mean St. Dev. Mean St. Dev.

	Annex 2
				Total Electricity Index	Control Electricity Saving Practice Intensity CC HAS IC
					Sample (EI)	Group		Group	Group (EPI)	Group
	Indicators Sex		Modalities Female	EI P1 (kWh)	n=162 47% EI P2 (kWh) n=89 49%	n=27 48% EPI T1	n=18 39% EPI T2	n=28 43%
	Male 25-39 40-54 N Mean St. Dev. Total Age (at start of the 162 2841 2306 2697 2212 53% 51% 9% 7% 20% 21%	3.68	52% 15% 19% 0.47	61% 17% 17% 3.69	57% 4% 18% 0.50
	experiment) Control Group (CG)	55-64	29% 89 2643 2361 2527 2217 24%	3.66	33% 0.48	39% 3.63	36% 0.53
	65 and over Collective coaching (CC)	38% 27 2531 1760 2419 1783 44%	3.82	30% 0.43	22% 3.81	39% 0.45
	undisclosed 1 person Home Automation system (HAS) 18 3591 2508 3333 2398 4% 4% House size 22% 27% 2 persons 49% 48% Individual Coaching (IC) 28 3289 2289 3100 2307	3.54 3.67	4% 26% 0.54 44% 0.40	6% 6% 3.57 39% 3.87	4% 0.48 14% 61% 0.38
	3 persons or more Human Support (CC+IC) 55 2917 2081 2766 2095 29% 25%	3.74	30% 0.42	56% 3.84	25% 0.42
	Owner/tenant Technological support (HAS+IC) 46 3407 2382 3191 2346 Owner 81% 76%	3.62	81% 0.47	94% 3.76	86% 0.45
	Socio-professional	Craftsman, shopkeeper…	5%	4%		4%	6%	7%
	category		Farmer		1%	1%		0%	0%	0%
			Qualified working population	30%	30%		26%	39%	29%
			Technicians and inter. Prof.	27%	25%		33%	17%	32%
			Employees		27%	27%		26%	33%	25%
			Blue-collar workers	7%	10%		7%	6%	0%
			No formal profession	3%	2%		4%	0%	7%
	Education level		Graduate education	48%	45%		48%	67%	43%
			Bachelor's degree	21%	22%		22%	11%	21%
			Vocational qualification	21%	22%		22%	11%	21%
			Without degrees	10%	10%		7%	11%	14%
	Type of Housing	Collective		26%	27%		26%	17%	29%
			Individual		73%	72%		74%	83%	71%
			Other		1%	1%		0%	0%	0%
	Electric heating			30%	28%		22%	28%	43%
	Electric water heater			49%	47%		48%	61%	50%
	Construction	Before 1949		4%	8%		0%	0%	0%
	date	Between 1949 and 1974	30%	30%		33%	33%	25%
		between 1975 and 2004	50%	48%		52%	33%	64%
		Newer dwelling (built after 2004)	12%	10%		11%	28%	7%
		Not known		4	3		4	6	4
	Initial perception of		Strong	54%	61%		63%	33%	36%
	effectiveness of daily gestures (1 item)	Low	46%	39%		37%	67%	64%
	Initial Intended purpose to save	Strong	26%	30%		37%	11%	11%
	electricity(1 item)		Low	74%	70%		63%	89%	89%
	Initial Energy culture scoring (6	Strong	22%	18%		30%	33%	21%
	items) a			Low	78%	82%		70%	67%	79%
	Age			59.5 (12.4) 60.3 (12.5) 57.8 (11.4) 54.0 (13.0) 62.2 (12.4)
	Surface area				108 (37)	104 (33)	111 (39)	108 (31)	116 (50)
	Number of electric appliances		17.3 (4.3)	16.7 (4.3)	17.3 (3.3)	19.5 (4.5)	17.8 (4.7)

Surveys were conducted by a market research company using both on-line and phoning methods to maximize participants' response rate.

This study has received support from the French Environment and Energy Management Agency (ADEME) through the experimental smart-grid SOLENN (SOlidarity -Energy-INnovation) project.

1 corresponding author at all stages of the refereeing process


M Tillard

D Granier

C Reibel

L Daenens

P Armand

Structure, characterization, and properties of BaMoO 4 and BaKYb(MoO 4 ) 3 flux-grown single-crystals

Keywords: Molybdate, Crystal structure, Raman investigation; Magnetic susceptibility

), b = 12.1477(4), c = 5.2481(2) Å,  = 105.344(2)°. The Yb 3+ ions are surrounded by oxygen leading to YbO 8 coordination polyhedra while atomic disorder is observed for the cations Ba 2+ and K + , statistically sharing their positions inside 8-vertex coordination polyhedra. The Raman spectrum confirms the presence of distorted MoO 4 tetrahedra for the BaKYb(MoO 4 ) 3 molybdate. Investigation of its magnetic properties was undertaken in order to check whether a magnetic ordering occurs at low temperature.

Introduction

Simple molybdates with the general formula MeMoO 4 (Me 2+ = Ba, Sr, Ca, Pb) and the scheelitelike structure are potential stimulated Raman scattering (SRS) materials and promising hosts for the incorporation of optically active ions [START_REF] Basiev | Spontaneous Raman spectroscopy of tungstate and molybdate crystals for Raman lasers[END_REF][START_REF] Romanyuk | Low-temperature flux growth of sulfates, molybdates, and tungstates of Ca, Sr, and Ba and investigation of doping with Mn 6+[END_REF][3]. On the other hand, double molybdates of general formula ALnMoO 4 (A + = alkaline metals, Cu or Tl) have received considerable attention due to their amazing properties and their thermal and chemical stability [START_REF]Characteristic features of the crystal chemistry of lanthanide molybdates and tungstates V. A. Efremov Russ[END_REF][START_REF] Li | Mutual energy transfer luminescent properties in novel CsGd(MoO 4 ) 2 :Yb 3+ ,Er 3+ /Ho 3+ phosphors for solid-state lighting and solar cells[END_REF][START_REF] Cascales | The optical spectroscopy of lanthanides R 3+ in ABi(XO 4 ) 2 (A= Li, Na; X= Mo, X) and LiYb(MoO 4 ) 2 multifunctional single crystals: Relationship with the structural local disorder[END_REF][7][8][START_REF] Volokitina | Growth and spectroscopy of orthorhombic Yb:KY(MoO 4 ) 2 laser crystal with a layered structure[END_REF][START_REF] Zharikov | Double tungstate and molybdate crystals for laser and nonlinear optical applications E[END_REF]. They have a high potential application in various fields, such as lanthanide (Ln) luminescence [START_REF] Li | Mutual energy transfer luminescent properties in novel CsGd(MoO 4 ) 2 :Yb 3+ ,Er 3+ /Ho 3+ phosphors for solid-state lighting and solar cells[END_REF][START_REF] Cascales | The optical spectroscopy of lanthanides R 3+ in ABi(XO 4 ) 2 (A= Li, Na; X= Mo, X) and LiYb(MoO 4 ) 2 multifunctional single crystals: Relationship with the structural local disorder[END_REF], Li-ion or Naion batteries [7,8], and laser hosts activated by Ln 3+ ions [START_REF] Volokitina | Growth and spectroscopy of orthorhombic Yb:KY(MoO 4 ) 2 laser crystal with a layered structure[END_REF][START_REF] Zharikov | Double tungstate and molybdate crystals for laser and nonlinear optical applications E[END_REF]. Yb 3+ -doped solid state lasers with large ground state 2 F 7/2 splitting through strong crystal field effects (CF) are interesting alternatives to those based on Nd 3+ as large homogeneous spectral broadening and larger laser gain bandwidths could be reached [START_REF]Crystal Growth and Optical and Spectroscopic Characterization of the Ytterbium-Doped Laser Molybdate Yb-Li 3 Gd 3 Ba[END_REF]. Since CF effects are dependent on the structural characteristics of the lanthanide site in the crystal network, the search for new materials with a multisite Yb 3+ occupation and highly distorted coordination polyhedra around Yb 3+ has generated a lot of interest. The results presented in the current paper have been obtained in the course of a more general study aimed at the synthesis and structural evaluation of Yb-based magnetically-concentrated double molybdates more recently described [START_REF] Armand | Growth, single-crystal structure, and magnetic properties of the double molybdate KYb(MoO 4 ) 2 P[END_REF][START_REF] Armand | Structure, vibrational and magnetic characteristics of LiYbX 2 O 8 (X = W, Mo) single-crystals P[END_REF]. KYb(MoO 4 ) 2 crystallizes in the orthorhombic symmetry, space group Pbcn (No. 60), with a complete ordering of the Yb 3+ and Mo 6+ cations [START_REF] Armand | Growth, single-crystal structure, and magnetic properties of the double molybdate KYb(MoO 4 ) 2 P[END_REF]. The Yb 3+ ions are located in distorted YbO 8 antiprisms which form chains, by sharing edges, aligned along the c-axis. LiYbMo 2 O 8 displays the tetragonal symmetry and is described in the noncentrosymmetric I space group (No. 82) [START_REF] Armand | Structure, vibrational and magnetic characteristics of LiYbX 2 O 8 (X = W, Mo) single-crystals P[END_REF] with an atomic local disorder as Li + and Yb 3+ cations share their sites inside regular MO 8 dodecadeltahedra (M = Li/Yb).

The high-temperature synthesis of BaMoO 4 and BaKYb(MoO 4 ) 3 , grown from the solution as millimeter-sized single crystals, is described. Besides, the monoclinic structure of the new molybdate BaKYb(MoO 4 ) 3 is provided with also a structural determination from crystal diffraction of the tetragonal BaMoO 4 scheelite-like structure. The room temperature structural study is completed by vibrational characterizations via Raman spectroscopy. The magnetic properties of the ternary molybdate are presented with both the temperature-dependent susceptibility and the field-dependent magnetization recorded from 1.8 to 300 K.

Experimental

Materials preparation

The flux growth was carried out by the slow-cooling method with spontaneous nucleation. Ba 3 Yb 4 O 9 was chosen as the solute as we already synthesized this pure phase for previous works, and K 2 CO 3 (or Rb 2 CO 3 )-3MoO 3 mixtures as the fluxes (solvents). All the starting reagents are high purity Alfa Aesar commercial products, MoO 3 (99.95%), Yb 2 O 3 (99.9%), BaCO 3 (99%), K 2 CO 3 (99%), Rb 2 CO 3 (99%), and were used as received. Ba 3 Yb 4 O 9 was synthesized via a solid-state reaction from 3BaCO 3 and 2Yb 2 O 3 heated at 1400 °C during 12 hours in the air (see Supplementary Materials S.1). The K 2 CO 3 -3MoO 3 mixture (or Rb 2 CO 3 -3MoO 3 ) was heated in air at 520 °C for at least 8 days. This step allowed to get high quantities of K 2 Mo 3 O 10 or Rb 2 Mo 3 O 10 compounds in the powder form. We did not tried to use the self-flux method consisting to directly prepare the compound by heating a stoichiometric mixture of all the required oxides, as for example K 2 O-BaO-Yb 2 O 3 and MoO 3 .

The solute/flux powders, Ba 3 Yb 4 O 9 and K 2 CO 3 -3MoO 3 (or Rb 2 CO 3 -3MoO 3 ) were mixed in 10/90 weight proportions and an amount of 20 g of powder was loaded into a Pt crucible covered with a lid. This solute + flux mixture was heated in a resistance-heated furnace at 970 °C for 3 hours in the air to ensure a good dissolution of the solute. The complete dissolution of the solute in the flux has not been specially monitored or measured. After that, the sample was cooled by decreasing first the temperature to 600 °C at the rate of 0.9 °/h, and next to room temperature at 200 °/h.

Materials characterization

The materials obtained as individualized colorless crystals were characterized by classical analyses such as EDX, Raman spectroscopy, and X-ray diffraction. Their chemical composition was obtained by Energy Dispersive X-ray spectroscopy on a Quanta 200 FEG (FEI) scanning electron microscope equipped with an SDD diode detector (Oxford INCA). The spectra were recorded under a primary vacuum (around 10 -5 Torr) at a voltage of 15 kV. To control the quality/homogeneity of the crystals, at least three zones were probed for each sample.

X-ray diffraction

A stereo microscope equipped with a polarizing filter was used to select single colorless and faceted crystals suitable for X-ray diffraction data collection (Mo K radiation, room temperature) either using an Xcalibur CCD (Oxford diffraction) or a Bruker D8 Venture diffractometer. The appropriate software suites CrysAlis [START_REF]CrysAlis'Red software package[END_REF] or Apex [START_REF]APEX3. Version 2017[END_REF] were used for the treatment of data, the Lorentz-polarization, and absorption corrections. The structures were solved and refined using the SHELX programs [START_REF] Shelxl | Crystal structure refinement with[END_REF][START_REF]SHELXT -Integrated space-group and crystal-structure determination G. M. Sheldrick[END_REF] and anisotropic displacement parameters were considered for all atoms in full-matrix least-squares refinements on F 2 . The entire filling of the sites was checked by the free refinement of site occupation factors. Structural representations have been drawn using the program Diamond [START_REF] Putz | Diamond -Crystal and Molecular Structure Visualization Crystal Impact[END_REF].

Raman measurements

Unpolarized Raman spectra were recorded at room temperature on a LabRam Aramis spectrometer (Horiba Jobin-Yvon) at the He-Ne wavelength (λ = 632.8 nm). This device is equipped with a CCD detector cooled by the Peltier effect and a motorized stage. According to the instrumental error of 1 cm -1 on the measurement, the frequencies of Raman vibration modes in wavenumber, are given to within one unit.

Magnetic measurements

Magnetic measurements were carried out using a commercial Superconducting Quantum Interference Device (SQUID) MPMS-7XL magnetometer in DC mode, allowing to explore the temperature range of 1.8 -300 K with H external magnetic fields ranging from 0 to 5 Tesla with a sensitivity of the order of 10 -8 emu. A powdered sample of BaKYb(MoO 4 ) 3 of 63.6 mg was weighed and placed in a capsule introduced in a plastic straw. The negligible diamagnetic contribution of the straw has not been subtracted from our data.

Results and discussion

Growth of crystals

At the end of each high temperature flux growth experiment, the solidified mixture was dissolved in water, and numerous colorless and transparent crystals spontaneously grown (0.2-2 mm in size) were isolated. No post-growth annealing was applied.

In case of use of the K-based flux, two kinds of single-crystals were obtained with a growth yield of about 20%. Plate-like as-grown crystals with the KYb(MoO 4 ) 2 composition [START_REF] Armand | Growth, single-crystal structure, and magnetic properties of the double molybdate KYb(MoO 4 ) 2 P[END_REF], and bulky and well-faceted crystals with no inclusion visible to the eyes (Supporting information Figure S2). The EDX analyses have confirmed the formula BaKYb(MoO 4 ) 3 giving an atomic ratio Ba:K:Yb:Mo:O of 1.1(1):1.1(1):0.9(1):3:12(1) with no significant variation in chemical composition when scanning across the raw surface of the crystal. When using the Rb-based flux for the growth experiment, only one kind of single-crystals with under-millimeter size was obtained with a yield of about 5 %. The EDX analysis indicated that neither Rb nor Yb entered into the compound composition, leading to the barium molybdate BaMoO 4 .

Single-crystal structure of BaMoO 4

The single-crystal structure of BaMoO 4 refined in the tetragonal space group I4 1 /a to a final agreement factor R1 of 1.28% is in very good agreement with the previous works mentioned in the Pearson Crystal structure database [START_REF] Villars | Pearson's Crystal Data: Crystal Structure Database for Inorganic Compounds[END_REF] among which, only one, with R1 = 14%, refers to a single-crystal refinement [START_REF] Bylichkina | Crystal structures of Ba molybdate and Ba tungstate[END_REF]. It also closely matches the most recent and accurate structural determination undertaken on a nanosized polycrystalline sample using synchrotron data [START_REF] Rabuffetti | Structural Disorder in AMoO 4 (A = Ca, Sr, Ba) Scheelite Nanocrystals[END_REF].

Single-crystal structure of BaKYb(MoO 4 ) 3

The main structural parameters and the X-ray data collection parameters are reported in Table 1 for the two barium molybdates. Among the ten independent positions, a general site 8f and a special site 4e were attributed to the most electropositive elements, a site 8f and a site 4e to molybdenum atoms, and the six remaining 8f sites to oxygen atoms. As the same contents are expected for K, Ba, and Yb, an atomic mixing must be considered on the two sites assigned to electropositive elements, Table 2. Looking at the arrangement of polyhedra, the structure of BaKYb(MoO 4 ) 3 represented in Figure 2 bears a strong resemblance with that of BaMoO 4 , which can be otherwise formulated Ba 3 (MoO 4 ) 3 , given in Figure 1. They both contain discrete MoO 4 tetrahedra having no common O, but sharing their four O vertices with the neighboring XO 8 units (X = Ba, K, or Yb). Instead, the XO 8 units are involved in chains of polyhedra (Figures 1 and2) by sharing edges with neighboring analogs. However, the heterovalent substitution of two Ba in the Ba 3 (MoO 4 ) 3 formula by one K and one Yb changes the symmetry so that a lower-symmetry and larger monoclinic unit cell is needed to describe the compound BaKYb(MoO 4 ) 3 . Also, the cationic sites that were all equivalent in BaMoO 4 , Figure 4a, are now divided into two categories, those filled with a Ba/K mixture and those filled with Yb, each of which being involved in a building block , Figure 4c. Depending on the nature of the cation, this causes local distortions of the building blocks that can be visualized with the greater spaces between the tetrahedra placed in the same layers as Yb at a = 0, ½ (see also in Figure 2) than the separation between tetrahedra placed in the same layers as Ba/K cations. The interatomic distances inside the Ba/K and Yb cationic pairs are measured respectively at 4.020(1) and 3.839(1) Å. Interestingly, the same building blocks are found in the structure of LiYb(MoO 4 ) 2 (Figure 4b) where the statistical Li/Yb atom distribution on the cationic sites allows the tetragonal symmetry to be maintained (with only a shift in the origin of the cell) [START_REF] Armand | Structure, vibrational and magnetic characteristics of LiYbX 2 O 8 (X = W, Mo) single-crystals P[END_REF]. Note that the distance between the cationic sites is here shortened to 3.77 Å. [START_REF]Zwei Beispiele für partielle und totale Defekte im Ba Ln 2 Mo 4 O 16 -Typ: BaCu 0 . 41 Z 0[END_REF], and e-BaLi 1.5 Gd 1.4 Yb 0.1 (MoO 4 ) 4 [START_REF]Crystal Growth and Optical and Spectroscopic Characterization of the Ytterbium-Doped Laser Molybdate Yb-Li 3 Gd 3 Ba[END_REF]. Yellow balls for Ba/K, green for Li, black for Yb and red for O.

Common building blocks

Going further in the structural comparison reveals some similarities with the arrangement of polyhedra in the two barium molybdates BaYb 2 (MoO 4 ) 4 and BaLi 1.5 Gd 1.4 Yb 0.1 (MoO 4 ) 4 reported in the Pearson Crystal database [START_REF] Villars | Pearson's Crystal Data: Crystal Structure Database for Inorganic Compounds[END_REF]. These two monoclinic isostructural compounds are also formed with similar building blocks around the Yb cations, alternately tilted on the left or tilted on the right in the successive layers (Figure 4d and4e). or even in the more appropriate Shannon effective ionic radii (0.868 and 0.938 Å) , and the smaller ionic radii of Li + (0.76 Å) allows lithium to take place at insertion positions [START_REF]Revised Effective Ionic Radii and Systematic Studies of Interatomic Distances in Halides and Chalcogenides R. D. Shannon[END_REF]. On the contrary, the path from BaYb 2 (MoO 4 ) 4 to BaKYb(MoO 4 ) 3 needs to change Yb atoms for larger Ba or K elements, whether one considers their covalent (2.17 and 2.27 Å) or ionic (1.37 and 1.35 Å) radii, and this cannot be achieved without a structural reorganization.

Vibrational properties

The unpolarized Raman scattering spectra were recorded at room temperature on the as-grown crystalline samples, Figure 5. It should be mentioned that no Raman band is observed in the frequency range beyond 1000 cm -1 .

Compared to the T d symmetry of an isolated MoO 4 tetrahedron, the symmetry of [MoO 4 ] 2-units with strong covalent bonds Mo-O is reduced to S 4 (or ) point symmetry in the scheelite-type BaMoO 4 with tetragonal symmetry . This leads to a splitting of the degenerate vibrations due to the Crystal Field (CF) effect and Davydov Splitting (DS) [START_REF] Volokitina | Growth and spectroscopy of orthorhombic Yb:KY(MoO 4 ) 2 laser crystal with a layered structure[END_REF]. The MoO 4 internal modes are then identified as ν 1 (Ag), ν 3 (Bg and Eg) (stretching modes), ν 2 (Ag and Bg), and ν 4 (Bg and Eg) (bending modes) which are Raman-active vibration modes [START_REF] Basiev | Spontaneous Raman spectroscopy of tungstate and molybdate crystals for Raman lasers[END_REF][START_REF] Thongtem | Sonochemical synthesis of MMoO 4 (M = Ca, Sr and Ba) nanocrystals[END_REF]. The range of stretched vibrations of MoO 4 polyhedral is 700-1000 cm -1 . The narrowest and intensive line at 895 cm -1 is associated with antisymmetric Mo-O stretching vibrations into the MoO 4 tetrahedra, and attributed to the bond vibration line ν 1 (A g ) of BaMoO 4 crystal [START_REF] Basiev | Spontaneous Raman spectroscopy of tungstate and molybdate crystals for Raman lasers[END_REF][START_REF] Thongtem | Sonochemical synthesis of MMoO 4 (M = Ca, Sr and Ba) nanocrystals[END_REF]. The bands at 791 and 836 cm -1 are assigned to the ν 3 modes, and the frequencies of internal bending vibrations of MoO 4 tetrahedra are in the 300 -400 cm -1 range as already reported [START_REF] Basiev | Spontaneous Raman spectroscopy of tungstate and molybdate crystals for Raman lasers[END_REF][START_REF] Thongtem | Sonochemical synthesis of MMoO 4 (M = Ca, Sr and Ba) nanocrystals[END_REF] The Raman spectrum for the BaKYb(MoO 4 ) 3 material presents three main segment bands between 50 and 200 cm -1 , 250 -450 cm -1 , and 700 -1000 cm -1 , Figure 5b. The maximum phonon frequency is 942 cm -1 . Compared to BaMoO 4 , Figure 5a, the Raman spectrum of the ternary molybdate is composed of bands with larger width at half maximum in agreement with the existence of two independent crystallographic sites for Mo atoms in its disordered structure.

It is interesting to remark the strong resemblance of the Raman spectrum recorded in the current study for BaKYb(MoO 4 ) 3 with that reported for the yttrium homolog [START_REF] Li | Up-conversion luminescence and optical temperature sensing properties in novel KBaY(MoO 4 ) 3 :Yb 3+, Er 3+ materials for temperature sensors[END_REF]. This was expected given the presumed isotypy of their structures (same lattice and symmetry), despite some differences in the atomic coordinates reported for BaKY(MoO 4 ) 3 [START_REF]Assessment of structure and spectral characteristics of new laser crystal Nd 3+ :KBaY(MoO 4 )[END_REF]. However, no complete cif-file is available precluding further comparison with the Yb-based triple molybdate under study. We think that a transcription error in the atomic positions is at the origin of an erroneous description of this structure with two types of polyhedra, MoO 4 and MoO 6 . Our diagnosis is confirmed in the recent paper giving both the Raman spectra and the structure of the yttrium molybdate described with only oxygen tetrahedra around Mo atoms [START_REF] Kbаy | MoO 4 ) 3 :Er 3+ /Yb 3+ -an Erbium/Ytterbium-Codoped Upconversion Phosphor in the К 2 MoO 4 -BaMoO 4 -Y 2 (MoO 4 )[END_REF].

In the monoclinic structure of BaKYb(MoO 4 ) 3 , the Mo 6+ ions coordinate with oxygen in isolated tetrahedral (MoO 4 ) 2-polyhedra, which means that no Mo-O-Mo bridge is present in the structure. The complexity of the spectrum is well explained by the degeneracy removal of the stretching modes due to the symmetry lowering (Td  C 1 ) of the distorted MoO 4 tetrahedra since four lines can be present in the symmetric stretching domain and up to 12 in the asymmetric range [START_REF] Aleksandrovsky | Exploration of structural, vibrational and spectroscopic properties of self-activated orthorhombic double molybdate RbEu(MoO 4 ) 2 with isolated MoO 4 units V. V. Atuchin[END_REF]. The bands in the range 250 -450 cm -1 are assigned to the internal asymmetric and symmetric bending vibration (O-Mo-O) of the MoO 4 tetrahedra [START_REF] Armand | Growth, single-crystal structure, and magnetic properties of the double molybdate KYb(MoO 4 ) 2 P[END_REF][START_REF] Armand | Structure, vibrational and magnetic characteristics of LiYbX 2 O 8 (X = W, Mo) single-crystals P[END_REF][START_REF] Aleksandrovsky | Exploration of structural, vibrational and spectroscopic properties of self-activated orthorhombic double molybdate RbEu(MoO 4 ) 2 with isolated MoO 4 units V. V. Atuchin[END_REF].

Below 200 cm -1 , the bands are due to external vibrations that involve the rotational and translational modes of the (MoO 4 ) 2-anions and the translational modes of the cations [START_REF] Armand | Growth, single-crystal structure, and magnetic properties of the double molybdate KYb(MoO 4 ) 2 P[END_REF][START_REF] Armand | Structure, vibrational and magnetic characteristics of LiYbX 2 O 8 (X = W, Mo) single-crystals P[END_REF][START_REF] Aleksandrovsky | Exploration of structural, vibrational and spectroscopic properties of self-activated orthorhombic double molybdate RbEu(MoO 4 ) 2 with isolated MoO 4 units V. V. Atuchin[END_REF].

Magnetic properties

The magnetization of the triple molybdate BaKYb(MoO 4 ) 3 was measured for a powdered sample placed in a constant magnetic field H of 0.5 T at temperatures ranging from 1.8 to 300 K. The magnetic susceptibility  is defined as M/H. The electronic configuration of the paramagnetic Yb 3+ isolated ion is [Xe] 4f 13 and the effective magnetic moment μ eff of Yb 3+ is equal to 4.54 μ B .

The normalized Yb molar dc magnetic susceptibility is temperature-dependent, as shown in Figure 6.

No anomaly is visible on the curve in the entire temperature range studied. with the value expected for μ eff of the Yb 3+ free-cation (4f 13 , J = 7/2). The large negative value of  p (-33.8 K) suggests an antiferromagnetic exchange interaction between the Yb 3+ magnetic moments in the low temperature range.

In the 1.8-75 K temperature range and for H = 5000 Oe, the inverse susceptibility data no longer follow a strict linear behavior with temperature. Such a deviation of the data from the expected Curie-Weiss behavior for free ions would be rather assigned to the splitting of the J-multiplet ground state of the Yb 3+ Kramers ion under the influence of the CF effect than to a magnetic order (no Néel temperature).

Figure 6b shows the field-dependent M-H curves registered for BaKYb(MoO 4 ) 3 for temperatures ranging from 2 K up to 300 K. The temperature variation was found to significantly impact the shape of the curves. As already observed for Yb-based molybdates, different magnetic regimes are observed [START_REF] Armand | Growth, single-crystal structure, and magnetic properties of the double molybdate KYb(MoO 4 ) 2 P[END_REF][START_REF] Armand | Structure, vibrational and magnetic characteristics of LiYbX 2 O 8 (X = W, Mo) single-crystals P[END_REF]. At T = 300 K, the normalized magnetization M is a linear function of the external alternating magnetic field H in good accordance with a paramagnetic behavior. At T = 2 K, the magnetization displays a large field dependence with a saturation zone starting from H = 20 kOe up to the highest applied magnetic field H = 50 kOe.

The H strength is sufficient to magnetize the sample to saturation. This M-H curve shape could be attributed to an antiferromagnetic behavior between the Yb 3+ magnetic moments.

Conclusion

The new BaKYb(MoO 4 ) 3 triple molybdate was obtained as transparent and colorless single crystals, using a high-temperature solution technique. The flux-grown material crystallizes in the monoclinic symmetry with the Mo VI valence state and displays an ordered distribution of the Yb 3+ cations on a C 2 symmetry position while the K + and Ba 2+ are mixed at a general position.

The Raman analysis confirms that the symmetry lowering around the Mo 6+ position from BaMoO 4 to BaKYb(MoO 4 ) 3 leads to a degeneracy rise and thus to an increase of the number of bands assigned to the internal Mo-O vibrations of MoO 4 tetrahedra. Magnetic properties of BaKYb(MoO 4 ) 3 have been investigated from 1.8 to 300 K. The temperature-dependent magnetic susceptibility follows a Curie-Weiss law from 75 to 300 K, with a large negative paramagnetic constant θp of -33.8 K which may indicate an antiferromagnetic behavior between the Yb 3+ ions in the low temperature range. Therefore, an investigation of the magnetic interactions, and the magnetic unit cell, is needed to elucidate all interactions present.

  The structural model includes Mo at 4a, Ba at 4b and O at 16f positions. Regular MoO 4 tetrahedra ( symmetry) are characterized by 4 × Mo-O distances of 1.761(1) Å with 4 × 108.2(1) and 2 × 112.1(1) ° O-Mo-O angles that are close to those reported for a BaMoO 4 ceramic prepared by conventional solid-sintering method [22]. Eight oxygen atoms, 4 at 2.741(1) and 4 at 2.777(1) Å from Ba, are arranged at the vertices of BaO 8 coordination polyhedra with symmetry (Figure 1). The full CIF file is freely available with the CSD number 2112357 at the Cambridge Crystallographic Data Center [23].

Figure 1 .

 1 Figure 1. Representations of the scheelite-like BaMoO 4 structure with blue MoO 4 tetrahedra and green BaO 8 coordination polyhedra. The unit cell is drawn as brown lines. Yellow balls for Ba, red for O, and blue for Mo.

_________________________________________________________________________________________________________

  The reflections initially collected for a crystal selected as a single crystal indicated the Icentering for a monoclinic cell with a = 5.2, b = 12.1, c = 16.4 Å,  = 92 ° but slight dispersion was noted in the diffraction images suggests twinning. Since the monoclinic angle does not deviate too much from 90 °, a two-fold rotation around any of the axes would lead to an almost perfect lattice overlay. Yet, a reasonable structural solution could be found after transformation into a monoclinic C-cell with a = 17.4, b = 12.1, c = 5.2 Å,  = 105 ° by applying the transformation matrix [ 0 010100] to the data. The structure was finally confirmed by the full structural refinement to R1 = 1.52% using a new set of reflections collected later for a suitable single crystal, C2/c, a = 17.3517(5), b = 12.1477(4), c = 5.2481(2) Å,  = 105.344(2) °.

Figure 2 .

 2 Figure 2. Representation of the structure of BaKYb(MoO 4 ) 3 with blue MoO 4 tetrahedra The unit cell is drawn as brown lines, the 8-vertex coordination polyhedra around Ba/K in green, and around Yb in orange. Yellow balls for Ba/K, red for O, blue for Mo, and brown for Yb.

BaMoO 4 and

 4 BaKYb(MoO 4 ) 3 structures are composed with the same building blocks represented in Figure3involving four MoO 4 tetrahedra around two cationic positions (separated by 4.24 Å in BaMoO 4 ).

Figure 3 .

 3 Figure 3. The common building blocks in the Ba 3 (MoO 4 ) 3 and BaKYb(MoO 4 ) 3 structures. Blue MoO 4 tetrahedra and yellow balls for Ba/K, red for O.

Figure 4 .

 4 Figure 4. Respective arrangement of the 4×MoO 4 tetrahedra building blocks (highlighted with orange shapes) in some barium molybdates. Brown lines represent the unit cell limits. The representations were drawn from the structure data available in the literature. a-Ba(MoO 4 ) [this work], b-LiYb(MoO 4 ) 2 [13], c-BaKYb(MoO 4 ) 3 [this work], d-BaYb 2 (MoO 4 ) 4[START_REF]Zwei Beispiele für partielle und totale Defekte im Ba Ln 2 Mo 4 O 16 -Typ: BaCu 0 . 41 Z 0[END_REF], and e-

The barium ytterbium molybdate BaYb 2 (

 2 MoO 4 ) 4 can be viewed as deriving from BaMoO 4 (or Ba 4 (MoO 4 ) 4 ) by changing three Ba for two Yb and one vacancy and would be then formulated Ba□Yb 2 (MoO 4 ) 4 . From there, the substitution of Yb for Li and Gd is almost entirely achieved in the molybdate BaLi 1.5 Gd 1.4 Yb 0.1 (MoO 4 ) 4 with additional Li found on an "insertion" position. As the Li, Gd, and Yb atoms are statistically distributed in proportions 25:70:5 at two sites, this molybdate could be formulated BaLi(Li/Gd/Yb) 2 (MoO 4 ) 4 . The Yb to Yb distances within the Yb cationic pairs is 3.87 Å in these barium molybdates and the Li to Ba separation in the latter compound is 3.75 Å.

Figure 4

 4 Figure 4 illustrates the role played by the nature, size, and distribution of the cations between the

  . The external modes, called lattice phonon modes, correspond to the motion of the deltahedral [BaO 8 ] clusters and the rigid molecular unit and are present under 150 cm -1 [1, 29].

Figure 5 .

 5 Figure 5. The Raman spectra in 50 -1000 cm -1 range measured on the as-grown crystals of a) BaMoO 4 and b) BaKYb(MoO 4 ) 3 .

Figure 6 .

 6 Figure 6. (a) Magnetic and inverse susceptibility  of crushed BaKYb(MoO 4 ) 3 crystals in a constant H field as a function of the temperature, with a Curie-Weiss fit (red line) of the hightemperature data, (b) M-H curves recorded at different temperatures normalized by the mass.

Table 1 .

 1 Crystal data, structure refinement, and data collection details

	Formula	BaMoO 4	BaKYb(MoO 4 ) 3
	_________________________________________________________________________________________________________
		Lattice and symmetry
	Symmetry	tetragonal	monoclinic
	Space group	I4 1 /a (88)	C2/c (15)
	Lattice dimensions (Å, °)	a = b = 5.5723(4)	a = 17.3517(5)
		c = 12.7954(9)	b = 12.1477(4)
			c = 5.2481(2)
			 = 105.344(2)
	Lattice volume (Å 3 )	397.30(6)	1066.78(6)
	Z	4	4
	Calculated density	6.307	5.164
		Data collection at 298 K
	Radiation, wavelength (Å)	Mo Kα, 0.71073	Mo Kα, 0.71073
	θ range (°)	3.9-28.8	3.3-37.8
	Absorption coefficient (mm -1 )	13.03	16.19
		Full-matrix least-squares refinement on F 2
	Independent reflections	253 [R int = 0.025]	2596 [R int = 0.029]
	Final indices [I > 2σ(I)] R1, wR2	0.0128, 0.0361	0.0152, 0.0333
	R1, wR2 (all data)	0.0137, 0.0364	0.0154, 0.0334
	Density residuals (e.Å -3 )	0.60/-0.39	0.25/-1.15

Table 2 .

 2 Atomic coordinates (×10 site was found filled by ytterbium. Potassium and barium larger cations, with ionic radii of 1.42 and 1.51 Å, compared to 1.14 for Yb cation, are statistically mixed at the 8f position. Their fraction at this site freely refines, within the standard deviation limits, to equivalent amounts leading to the formula Ba 3.98 K 4.02 Yb 3.97 (MoO 4 ) 12 in which the charge balance is almost perfectly fulfilled without any constrain to the final formula is BaKYb(MoO 4 ) 3 . A bond valence sum analysis was performed using the most recently established parameters[START_REF] Gagne | Comprehensive derivation of bond-valence parameters for ion pairs involving oxygen[END_REF], available from IUCR resources[25]. This is an empirical way to estimate the oxidation state of a metal ion from its distances to surrounding ligands. It leads to valence numbers close to 6 for Mo and 3 for Yb and adds further weight to the complete ordering of the Yb atoms on the 4e site.

			4	) and equivalent isotropic displacement parameters (Å	2	×10 3	)
	Atom	site	x		y	z	U eq
	________________________________________________________________________
	Yb	4e	0		6154(1)	2500	7(1)
	Mo1	4e	0		1551(1)	2500	9(1)
	Mo2	8f	1552(1)	3928(1)	3976(1)	8(1)
	Ba/K	8f	3359(1)	3747(1)	752(1)	13(1)
	O1	8f	394(1)	2350(1)	266(2)	14(1)
	O2	8f	742(1)	4629(1)	1435(2)	11(1)
	O3	8f	2059(1)	3019(1)	2461(2)	15(1)
	O4	8f	786(1)	707(1)	4203(2)	19(1)
	O5	8f	2723(1)	285(1)	3807(2)	16(1)

The Mo-O distances are in range1.732-1.866 Å and more precisely the tetrahedra with symmetry 2 are built around Mo atom at 4e site with 2 × 1.751(1) and 2 × 1.792(1) Å distances while a greater distortion is found at the tetrahedra formed around Mo at the 8f site (symmetry 1, distances 1.732(1), 1.754(1), 1.780(1) and 1.866(1) Å). The Yb atoms are surrounded by eight oxygen at 2.313(1)-2.405(1) Å within YbO 8 units while the Ba/K atoms have eight oxygen neighbors located at longer distances from 2.702(1) to 2.866(1) Å. The full CIF file with the CSD number 2112359 can be freely obtained from the Cambridge Crystallographic Data Center [23].

Acknowledgments

The EDX experiments were conducted at the Plateau Technique Microscopie à Balayage at the IEM Institute in Montpellier, France. Raman and magnetic experiments were done at the Platform of Analysis and Characterization of the Pôle Chimie Balard in Montpellier, France. The single-crystal X-ray diffraction experiments were done using the technological resources of the X-ray and gamma-ray network of the University of Montpellier, France.

Funding information

Funding for this research was provided by the Ministry of Higher Education, Scientific Research and Innovation in France and the French National Center of Scientific Research (CNRS).