Florence Kling-Eveillard
email: florence.kling@idele.fr

Clément Allain²
email: clement.allain@idele.fr

Xavier Boivin
email: xavier.boivin@inrae.fr

Valérie Courboulay
email: evalérie.courboulay@ifip.asso.fr

Pauline Créach
email: creach@itavi.asso.fr

Aurore Philibert
email: aurore.philibert@idele.fr

Yannick Ramonet
email: yannick.ramonet@bretagne.chambagri.fr

Nathalie Hostiou
email: nathalie.hostiou@inrae.fr

Farmers' representations of the effects of precision livestock farming on human-animal relationships Florence

Keywords: human-animal relationship, livestock farmer profession, precision livestock farming, robot, sensor, work

Precision livestock farming affects the nature and frequency of farmers' daily tasks, specifically in relation to animals. It consequently may modify how farmers consider their animals, the quality of the human-animal relationship and animal welfare. To better understand how new technologies impact human-animal relationships on the farm, a survey was carried out on 25 livestock farms in France. The farms raised dairy cows, gestating sows or broiler chickens using different equipment (sensors associated or not with robots). A qualitative thematic analysis to better identify farmers' views on the different topics, and secondly a statistical analysis to identify if farmer profiles exist and to better understand the diversity of views were conducted.

Most of the farmers expressed satisfaction about working with the new technology because their work becomes easier and allows more control over the management of the animals. Using PLF, the farmers describe a profession that has not fundamentally changed but which involves new tasks, new skills and daily schedules. Three farmers' profiles were identified. Profile A farmers consider that one cannot talk about a human-animal relationship on their farm, and do not enjoy either touching or talking to their animals. Profile B farmers associate a good human-animal relationship with the animals' welfare. Profile C is characterized by the central place occupied by animals and associate a good human-animal relationship with an absence of fear on the part of the animals. Farmers motivated by animals (profile C) find in precision livestock farming benefits related to animals, while the others (profiles A and B) find technical benefits detached from the animals. The farmers have room to manoeuvre in how they use the equipment; this can be seen for instance in the degree to which tasks are delegated to the equipment, which can be partial or total. Nevertheless, some farmers expressed concerns regarding the place of the new technologies on the farm, such as the risk of losing their own autonomy or their ability to observe animals and detect problems. Complementary studies could monitor these developments and contribute elements on the role of PLF in the sustainability of livestock farms.

1 Highlights :

 The human-animal relationship is not always degraded by the introduction of PLF  Farmers have room to maneuver when using a tool or equipment  Farmers choose to either completely or partially delegate a task to the equipment  With PLF farmers implement different new practices to familiarize animals  With PLF farmers fear the loss of observation skills and dependence on the tools

Introduction

The human-animal relationship, which is defined as the degree of closeness or distance between an animal and a person [START_REF] Waiblinger | Assessing the Human-animal Relationship in Farmed Species: A Critical Review[END_REF], develops over the course of daily interactions on a farm and expresses itself in their mutual behaviour. The relationship always exists, and may take different shapes, be pleasant or not for the animal, or for the livestock person. To study, to describe or to assess human relationship on farm, different aspects can be take into account and different disciplines used.

For the animal, the human-animal relationship is one criterion of animal welfare. In the Welfare Quality© protocols1 , the "Good human-animal relationship" criterion is linked to the "Appropriate behaviour" principle, alongside the criteria "Expression of social behaviour", "Expression of other behaviour" and "Positive emotional state" for all species. The relationship impacts an animal's health and performance. Positive interactions during physical or visual contact (touching, farmer can be seen by the animal, farmer speaking calmly...) help to build a relationship that animals perceive as positive, and instills confidence in the human. Negative interactions (painful treatments, blows, farmer shouting) build a relationship that animals experience as negative, and create fear and mistrust of the human [START_REF] Zulkifli | Fear and stress reactions, and the performance of commercial broiler chickens subjected to regular pleasant and unpleasant contacts with human being[END_REF][START_REF] Waiblinger | Assessing the Human-animal Relationship in Farmed Species: A Critical Review[END_REF] which expresses itself into a physical distance or closeness. When the relationship is poor, behavioural responses such as physical avoidance, fight or aggression are a result; when it is positive, there is a move toward and search for contact with the human i.e. physical closeness [START_REF] Boivin | Hommes et animaux d'élevage au travail : vers une approche pluridisciplinaire des pratiques relationnelles[END_REF][START_REF] De Boyer Des Roches | A prospective exploration of farm, farmer, and animal characteristics in human-animal relationships : An epidemiological survey[END_REF]. Approaches such as ethology, animal production and health science are used to understand the animal view on the human animal relationships on farm.

For the livestock farmer, this relationship is a factor determining his or her professional satisfaction, comfort and safety when working with animals as reported through sociological approaches focussing on the social representations of the farmer [START_REF] Bock | Farmers' relationship with different animals: the importance of getting close to the animals. Case studies of French, Swedish and Dutch cattle, pig and poultry farmers[END_REF][START_REF] Kling-Eveillard | Attitudes of farmers towards cattle dehorning[END_REF]. [START_REF] Dockès | Farmers' and advisers' representations of animals and animal welfare[END_REF] define four farmer profiles based on their closeness to their animals, which is assessed from the farmer's discourse. This closeness, or distance, is not physical, but relational. This typology brings to light differences between species and between productions regarding the closeness of the farmer to his or her animals.

Dairy cow farmers tend to be in the profiles where relational closeness to the animals is the most important, poultry farmers in the profiles most distant from the animals, and sow farmers are distributed among the different profiles. To understand and describe human animal relations from the livestock farmer view, ergonomic approach is used focusing on human work in interaction with the animals, observing the physical closeness or distance chosen or implemented by the farmer to interact with the animals. Other approaches are also developed, for instance psychology. We do not detail all possible approaches.

In this relationship, any improvement benefits both partners, impacting the farmer's daily work and the animal's welfare, and ultimately the livestock farm's economic performance [START_REF] Lensink | The relationship between farmers' attitude and behaviour towards calves, and productivity of veal units[END_REF][START_REF] Hemsworth | Human-Livestock interactions: the stockperson and the productivity and welfare of farmed animals[END_REF]. Likewise, any deterioration in the relationship will negatively impact both partners.

As reported by [START_REF] Kling-Eveillard | The effects of PLF (precision livestock farming) on human-animal relationships on farm[END_REF] in dairy production, the human-animal relationship is directly modified by any change in livestock farming conditions, particularly the arrival of sensors, automated machines and new technology, which is referred to as precision livestock farming (PLF). The impact on the farmer's work depends on whether the change involves an automated machine capable of replacing the human in the performance of a task, or a sensor which provides data on the parameters of the environment or the animal itself. Equipment combining sensors with automated machines reduce human-animal interactions the most [START_REF] Kling-Eveillard | The effects of PLF (precision livestock farming) on human-animal relationships on farm[END_REF].

With PLF, automated machines take over certain tasks that were previously done by farmers, and consequently directly influence farmers' interactions with their animals and thus the humananimal relationship [START_REF] Driessen | Cows desiring to be milked? Milking robots and the coevolution of ethics and technology on Dutch dairy farms[END_REF][START_REF] Schewe | Diversity in agricultural technology adoption: How are automatic milking systems used and to what end?[END_REF]. Moreover, the production of new, instant and readily accessible data on biological parameters and animal behaviour can influence how farmers perceive their animals and modify their direct observations of their animals, particularly by reducing their occurrence [START_REF] Kling-Eveillard | The effects of PLF (precision livestock farming) on human-animal relationships on farm[END_REF].

Farm size influences the reasons farmers to equip themselves. When herds are large or growing in size, becoming equipped with sensors and automated machines reflects a desire to increase productivity and save time [START_REF] Allain | Technical, economic and sociological impacts of an automated estrus detection system for dairy cows[END_REF][START_REF] Gargiulo | Dairy farmers with larger herd sizes adopt more precision dairy technologies[END_REF]. [START_REF] Cornou | Use of information from monitoring and decision support systems in pig production: Collection, applications and expected benefits[END_REF] have shown that the combination of new technologies and an increase in the size of a pig farm led to a change in how information is managed. The size of the herd also changes the daily interactions between a farmer and his or her animals [START_REF] Boivin | Hommes et animaux d'élevage au travail : vers une approche pluridisciplinaire des pratiques relationnelles[END_REF]. Furthermore, farmers do not all use the tools in the same way. [START_REF] Allain | Technical, economic and sociological impacts of an automated estrus detection system for dairy cows[END_REF] demonstrated that among dairy farmers equipped with heat sensors, some delegate the task entirely to the equipment and directly contact the inseminator as soon as an alert is sent on a cow, while others begin by first verifying the information, going to see if the cow signaled is actually behaving in a way characteristic of a cow in heat.

Lastly, the development of tasks linked on one side to computers and new technology and, on the other, to equipment and automated machines, can impact how farmers experience and think about their professions, and consequently their job satisfaction or dissatisfaction [START_REF] Cornou | Automation Systems for Farm Animals: Potential Impacts on the Human-Animal Relationship and on Animal Welfare[END_REF].

However, the new technology does not necessarily create greater distance between humans and animals. It can enable new relationships to develop, for example, when farmers with milking robots move frequently and calmly through their herd to maintain the machines and rub shoulders with their animals [START_REF] Lagneaux | De la traite robotisée au raid d'avatars. Incorporation et virtualisation[END_REF][START_REF] Wildridge | Transitioning from conventional to automatic milking: Effects on the human-animal relationship[END_REF]. Furthermore, several authors [START_REF] Butler | The impact of technological change in dairy farming: robotic milking systems and the changing role of the stockperson[END_REF][START_REF] Schewe | Diversity in agricultural technology adoption: How are automatic milking systems used and to what end?[END_REF] have shown a diversity between farmers with regard to the consequences of PLF on work organization and thus on the farmer's profession.

The present paper aims to present the results of a study conducted in 2016 using a sociological approach on the human-animal relationship on farm. This topic is rarely addressed through qualitative interviews which makes possible a better understanding of human animal relationship from the farmers' views. Most researches focus on the link between farmer practices and animal welfare or animal reactivity to humans. Some assess farmer's attitudes through a closed questionnaire, while our research is based on semi-directive interviews with open-ended questions which enable to collect a variety of viewpoints and thus to understand the different representations of the speakers on a given topic.

We studied the diversity of farmers' representations of their profession and the human-animal relationship in connection with PLF [START_REF] Kling-Eveillard | The effects of PLF (precision livestock farming) on human-animal relationships on farm[END_REF]. Interviews were conducted on farms in three animal sectors (dairy cattle, pigs and poultry). In this study, we chose not to examine the changes that have occurred with the arrival of PLF tools (to do so, we would have had to conduct interviews and observations before and after the equipment was installed).

Instead, we chose to explore the farmers' subjective vision and social representations of these impacts based on how they have experienced them. The aim is to understand how they currently were experiencing their work and their relationship with the animals while using these tools, and to listen to what they have to say about the changes that occurred before and after becoming equipped, and about how the arrival of the tools on the farm has taken place.

We relied in this work on the social representation concept, defined by [START_REF] Jodelet | Les représentations sociales[END_REF] as "a form of socially formulated and shared knowledge intended for a practical purpose". Other works have relied instead on the concept of attitude, such as has been used in the theory of reasoned action. In particular, [START_REF] Hemsworth | Human-animal interactions in livestock production[END_REF] uses it in his research on the attitudes of people who work with animals. The concept of social representations is broader than that of attitudes because it considers the social nature of the determinants of both attitudes and levers of change. Examples are how farmers influence each other, or the influence of parents if they themselves were farmers.

In the first part of the article, we present the methodological choices made in terms of the equipment and livestock farms studied. We then describe the results concerning the farmers' representations of the animal, their profession, and the human-animal relationship, and then on the satisfaction in and new practices stemming from PLF. These thematic results will be complemented by the presentation of the three profiles of farmers that emerged from the statistical analysis.

Material and methods

Sampling criteria

The aim of the sample of farms was to encompass diverse changes in the relationship between farmers and their animals resulting from the use of PLF tools. Farms were selected to cover a diversity of cases, and not to be representative of the French farmer population. We used the following criteria to select farms : i) animal species, ii) herd size, iii) adoption of PLF tools.

The animal species influence the human-animal relationship [START_REF] Dockès | Farmers' and advisers' representations of animals and animal welfare[END_REF]. For this, three species were studied : Prim'Holstein dairy cows (DC), gestating sows (GS), and broiler chickens (BR), all in conventional livestock farming systems. The Prim'Holstein being the most represented dairy cattle breed in France and especially in Brittany (around 10 000 Prim'Holsteins in each Breton department), it has become a sampling criterion for the dairy cattle farms to be studied.

The size of the livestock unit was a criteria used to select farms because PLF is often coupled with increased herd sizes. Surveys were therefore conducted for each species in two herd size classes, one above the Breton average and the other below, without including extremes in either class (Table 1).

We used the following criteria to choose the precision farming tools to study: i) tools widely used on farms, and ii) tools differing in terms of the impact they have on animals' living conditions, farmers' working conditions and human-animal interactions (Table 2). Two main types of equipment were selected according to whether they were composed exclusively of sensors or were associated with automated machines (Table 2). An automated machine combined with one or several sensors was chosen for each of the three sectors: milking robots for dairy cows, individual sow feeding (Electronic Sow Feeding (ESF) or free-access stalls) for gestating sows, barn electronic controllers and automatic weighing devices for broiler chickens.

The introduction of milking robots and automated feeding systems led to, or became associated with, a new way of managing animals. For dairy cows, this involved a transition from two milkings per day in a milking parlour to cows having direct access to a robot to be milked whenever the cows wished. For gestating sows, group housing required by European regulations replaced individual pens and access to feed was modified from one or two meals per day at the same time for all sows to open access all day long, one sow at a time. For broilers, electronic controllers have existed for some time. The new feature consists in being able to control barn atmosphere parameters from a distance (for example, remote control using a smartphone) without having to go to the building (for example, to open ventilation hatches). Sensors also were chosen that were not associated with an automated machine, namely heat detectors for dairy cows.

Identification of the farms to be surveyed

The surveys were conducted in Brittany, the leading livestock farming region in France in terms of numbers of farms. The farmers' contact information was provided by field experts. For dairy cows, the person conducting the survey contacted farmers on a private data base of 200 livestock farmers identified by their heat detection or milking robot equipment. For gestating sows and broilers, the snow ball sampling was used: the farmers surveyed themselves provided the names of other farmers [START_REF] Ghiglione | Les enquêtes sociologiques, théories et pratique[END_REF].

The sample was composed of 25 farms distributed between the three species (8 GS, 10 DC and 7 BR) and equipment presented in Table 1. The farms in the sample were slightly larger than the average French or Breton farm in terms of utilised agricultural area (115 ha for GS, 147 ha for DC, and 52 ha for BR), and herd size (263 gestating sows, 106 dairy cows, 2840 m 2 in broiler chickens farms) (Table 1). 21 farms combine different agricultural activities (livestock, crops), 4 farms (1 GS, 1 DC, 2 BR) are specialized. The average age of farmers was 45 years old. The farmers were slightly younger than the average French or Breton farmer. 8 farmers are between 30 and 40 years old and 10 farmers are between 50 and 60 years old. Pig farmers are on average younger (42 years old) than cow farmers (45 years old), and than chicken farmers (50 years old). The youngest farmer is a pig farmer, who is 23 years old, and a large majority of the chicken farmers interviewed are currently preparing for retirement. Of the 25 people surveyed, 7 were women and 18 men.

Survey method

We have given priority to semi-structured interviews, often used in sociology to study social representations of speakers like farmers. The interviews were recorded [START_REF] Ghiglione | Les enquêtes sociologiques, théories et pratique[END_REF]. The following topics were addressed: the profession of a livestock farmer; the introduction of PLF tools; the management of PLF; the human-animal relationship; PLF and the evolution of the profession (Table 3).

Once the qualitative interview was completed, a closed questionnaire was given to the farmers in which they could note the extent to which they agreed (6 levels possible, from "strongly disagree" to "strongly agree") to items involving their representations of animals, their profession, PLF, and what they appreciate about their profession. They were also asked to describe their relationships with their animals at the time of the interview and prior to introducing PLF using an ungraduated axis between "very poor relationship" to "very good relationship".

Analysis method

We carried out two types of analysis to get two kind of results : firstly a qualitative thematic analysis to better identify farmers' views on the different topics, and secondly a statistical analysis to identify if farmer profiles exist and to better understand the diversity of views. In our analysis a profile regroups farmers who have common characteristics compared to the other profiles. Doing so, we did not lose qualitative information, and both kind of results are complementary.

Thematic analysis

The notes taken during the interview were completed with the listening of the recording. A monograph for each farm was done for each interview gathering the interviewee comments, or the discourse, on the main topics addressed during the interview. The contents of the interviews and the answers to the closed questionnaires were analysed using an analysis grid crossing the different topics and the different interviews. The grid served as a support for an analysis of the thematic content concerning the representations of the profession, the animal and the humananimal relationship, and the satisfaction found in and the new practices used in PLF. The results of this qualitative analysis constitute the three first parts of the results presented below.

Statistical analysis

The statistical analysis had to answer to two questions : 1) Does it exist farmer profiles describing the diversity of attitudes and representations of the animals and of human-animal relationships among the interviewed farmers ?

To answer this question, the representations of the profession, of the animal and of the humananimal relationships were chosen to be the active variables to build the profiles.

2) Do these profiles show different views of precision livestock on the farm and of its impacts ?

To answer this question, the variables regarding the use of PLF were supplementary variables which add information on the profiles built from the active variables.

The thematic analysis of representations of the profession, the animal and the human-animal relationship then enabled the construction of a summary grid regrouping the most discriminating variables (Table 4).

A statistical analysis combining a multiple correspondence analysis (MCA) and an ascending hierarchical clustering (AHC) were carried out to identify the livestock farmer profiles. The 17 active variables selected concerned the representations of the profession, the animal and the human-animal relationship (Table 4). All these variables are qualitative. The AHC method cannot be used with qualitative variables, a step before using the MCA method is needed. This method is frequently used to analyze survey answers [START_REF] Saporta | Probabilités, analyse des données et statistique[END_REF]. The principle of the AHC method is to gather similar individuals in separate cluster, similar in sense that they have the same values for active variables. The method starts with each farmer in a separate cluster, then the farmers are grouped according to the values of their active variables. At the end, each farmer is assigned to one cluster. This ascending hierarchical building is represented in a dendrogram (figure 1). The best split of this dendrogram is selected by a statistical rule and create a given number of clusters. With MCA and AHC methods, three clusters were identified and are described as livestock farmer profiles. The 8 supplementary variables concerning representations and practices involved in PLF gave additional information regarding these profiles (Table 4). A chi-square test was used to compare the percentage of each modality of the variables in each cluster with its percentage in the population. Due to a low number of interviews, the level of significance was set at 10% for all the analysis. These analysis were made with R software version 3.6.0 and the FactoMineR package [START_REF] Le | FactoMineR: An R Package for Multivariate Analysis[END_REF].

Each profile is described in relation to the other two and to the survey population, highlighting the characteristics which are more common in the given profile than in the others. All farmers in a profile do not necessarily have all of these characteristics but they are broadly similar.

Results

We have chosen to first present the farmers' representations of the animals, their profession, and the human-animal relationship, and then to complement these with their representations of PLF on their livestock farms produced by an analysis of the thematic contents of the semi-structured interviews. In this part, as we have no quantitative objectives given our small sample size, we do not always indicate the number of farmers who expressed one view or another, and we highlight the diversity of the social representations identified. After these thematic results, we describe the three transversal profiles of farmers, applicable across the animal species (dairy cow, gestating sows and broiler chickens), produced by the statistical analysis.

Representations of the animal, the profession and the human-animal relationship

The satisfaction farmers say they find in their work and their definition of what makes a good farmer reflect how they view the place of the animal. What the farmers appreciate in livestock farming activities can be grouped around three features. Some emphasize the animal, the contact, and the work with animals. Others mention instead technical features, such as technical aspects of animal management, animal genetics, technical monitoring of production or technology at the service of farmers. Lastly, some note the characteristics of their profession, such as being independent, being their own boss, having a real profession, and pleasant working conditions. Diversity with regard to the place of the animal is also found in the farmers' definition of what makes a good farmer. Some farmers define a good farmer as one who takes good care of his or her animals. However, this can mean two different things: taking good care can mean being attentive to the animals' needs so that they are well, or it can mean ensuring that the animals are productive. Other notions are mentioned: a good farmer has strong technical skills, achieves good technical or economic results, or combines animal, technical and economic expertise.

With regard to the representation of the profession, some of the farmers interviewed demonstrated satisfaction with -or were even passionate about -their work, while others dwelled on the difficulties involved, and reflected a loss of motivation.

The farmers were questioned about what they thought the human-animal relationship encompassed. It was difficult for most of them to answer this question, both because they were unfamiliar with the term, and because the question involved a very personal dimension that is not usually discussed in livestock farming. Four farmers thus considered that they did not have a relationship with their animals on the farm (3 BR and 1 GS), this view meaning that they feel a relational distance with the animals. It was easier for the farmers to speak about their view of a good human-animal relationship. Most frequently, they mentioned the animal's welfare, and some (mainly dairy and pig farmers) spoke of the animal's absence of fear in relation to people, or even a mutual sense of confidence between the farmer and the animals. Good production levels are mostly considered as a reflection of a satisfying human-animal relationship. For the majority, a good human-animal relationship renders it possible to work more easily with the animals, regardless of the species. At the same time, they also mention farmer well-being, and good livestock farming conditions with equipment.

Satisfaction under PLF

For many farmers, setting up precision farming tools on their farms was an expression of their desire to work differently: to improve working conditions with robots (work comfort, reduced drudgery, free themselves from the constraint of milking, ...) or to improve their techniques and performance with sensors (better identify cows in heat, better adapt feed rations to animals' needs, ...). In addition to these motives, some farmers were encouraged to invest in new technologies by economic and regulatory incentives. The shift to group housing for sows required by European regulations accompanied the automation of feed distribution. On broiler farms, farmers receive a bonus if they provide an accurate estimation of the weight of the broilers in a batch. This has encouraged the installation of automatic weighing devices, as they can provide data on a greater number of chickens than if they are weighed manually.

Nearly all of the farmers surveyed expressed satisfaction about working with the new technology. They highlight that work is easier and the equipment allows them more control over the management of the animals, particularly with the provision of data. They furthermore consider that PLF will prove to be indispensable for farms in the future. Mastering new technologies appears to be a new job skill in a profession which has become more technical.

The modern image given to the profession deeply pleased many of the farmers surveyed, who felt less left behind in relation to other professions. Four farmers (sow or dairy with milking robot) describe a profession which is in closer contact with animals, and state feeling "more like a farmer" in livestock farming conditions where they and their animals are less restricted in their activities. According to the farmers interviewed, the improved working conditions and connectivity of the farming profession renders it more attractive to younger generations. Several farmers, however, expressed some reservations about the tools, which cannot do everything, and noted the importance of also trusting a farmer's eye and gut feelings. Four farmers appeared unenthusiastic about new technologies and either consider that they look for other satisfactions in their profession such as spending time in contact with their animals or do not like to use this kind of tools (computers, etc.), even in their private life.

New practices under PLF

Using PLF, the farmers describe a profession that has not fundamentally changed but which involves new tasks and daily schedules. They say they spend more time in front of the computer each day. In terms of time spent with their animals, some say that they now spend more time, while others say that they spend less. For many, "observing" animals includes both direct observations, for example by moving among a herd of cows in a shed, and looking at digital data about the animals on their computer. Furthermore, when questioned about what they thought of as a "good animal", some spoke of the "invisible animal" which does not trigger alerts because it poses no problems.

The morning routine illustrates the diversity of practices among farmers. Only five farmers (three dairy farmers and two pig farmers) say they start their day by first looking at the animals, while all of the others begin by looking at the computer and the daily alerts before going to see the animals. Of the five who start their day by going to see the animals, four are women. Three female pig farmers prefer to first go see their animals to get a feel of the atmosphere and identify the sows which will need attention. They explain that their associate starts his day by consulting the computer.

A range of practices also was identified with regard to delegating a task or a decision to the tool.

For the three species, delegation to equipment was not always complete, and some farmers verify the data provided by the sensors. For example, broiler chicken farmers weigh several birds manually in addition to using the automatic weighing device. Dairy cow farmers prefer to visually verify that a cow designated by a detector as being in heat is showing the associated signs before calling the inseminator. Regarding the detection of heat, the four farmers whose sows are equipped with electronic chips to record the visits of boars said that they check for the behavioral signs of heat when a sow is signaled by the computer. The other pig farmers delegate all responsibility to the equipment.

In certain situations, three farmers equipped with milking robots continue to manually carry out certain tasks, for example leading a heifer to the robot and attaching the teats in order to accustom the animal to the machine.

The equipment can induce new kinds of contacts with the animals when first set up or when new animals arrive. On dairy cow and gestating sow farms, the arrival of new animals appears to be a key period when opportunities exist for the famer to establish contact and implement habituation strategies (apple juice to tame gilts in quarantine for example).

Three profiles of farmers and their relation with PLF

Three farmer profiles emerge from the statistical analysis of variables involving the representation of the profession, the animal and the human-animal relationship (Figure 1). Profile A is characterized by a negative image of the profession, which is experienced as not very rewarding. Eighty per cent of individuals answered "rather disagree" to the item "The profession is rewarding", whereas 16% of the population answered that. The difference is significant because the p-value of this difference is less than 10% (80% vs 16%; <10%). The farmers consider that there is no human-animal relationship on their farm (80% vs 16%; <10%), and they do not enjoy either touching (60% vs 12%; <10%) or talking to their animals (60% vs 16%; <10%). They consult their computers first thing in the morning before going to see their animals (profile A 100% vs 76%). These five farmers are all men, working with all three species (2 GS, 2 DC, 1 BR).

Profile B is characterized by a rather positive image of the profession, which they consider rewarding (0% answered "rather disagree" to the item "The profession is rewarding"; <10%). Independence, a diversity of tasks and technical features are the characteristics which satisfy these farmers most. For them, a good human-animal relationship is associated with the animals' welfare (76,9% vs 44%; <10%). They consult their computers first thing in the morning before going to see their animals (profile B 76,9% vs 76%; ns). These 13 farmers (10 men and 3 women) are divided between the three species (3 GS, 4 DC, 6 BR), notably including nearly all of the broiler chicken farmers of the sample (6 out of 7).

Profile C is characterized by the central place occupied by animals. The animals are the main source of job satisfaction for these farmers (100% vs 48%; <10%). They associate a good human-animal relationship with the animals' absence of fear (100% vs 40%; <10%), revealing through this response their feelings for the animal. They enjoy touching (85,7% vs 28%; <10%) and observing the animals ( 71,4% vs 36%; <10%) and say that animals have a memory ( 71,4% vs 28%; <10%) more often than the farmers from the other two profiles. They implement strategies to familiarize the animals with humans and the equipment to facilitate their work (85,7% vs 40%; <10%). Among these seven farmers, there are three men and four women, and they are raising gestating sows and dairy cows (3 GS, 4 DC).

Farmer profiles in relation to the profession and the animal also differ with regard to PLF.

Profiles A and B farmers distinguish themselves from profile C farmers in their responses concerning PLF. In profile C farmers feel that they know their animals better since installing the equipment (milking robots for cows and automated feeders for sows housed in groups ; 100% vs 56%; <10%). They also say that the human-animal relationship is better (85,7% vs 52%; <10%).

In contrast, in profiles A and B farmers say less often that they know their animals better (profile B 30,8% vs 56%; <10% and profile A 60%; ns) and that the relationship is better (profile B 30,8% vs 52%; <10% and profile A 60%; ns). They tend to most often claim to appreciate working in a modern profession (profile A 80% vs 60%; ns and profile B 61,5%; ns).

Discussion

This exploratory study was conducted on a limited number of farmers per species and per equipment, but permitted farmers who were different from each other to be interviewed. This enabled the identification of three farmer profiles, determined by the farmers' proximity to their animals or their interest in management. In PLF, farmers motivated by animals find benefits related to animals (profile C), while those who are less motivated by their profession or animals find foremost technical benefits disconnected from the animals (profiles A and B). The profiles appear to be fairly generic due to their similarity with those identified in a previous study [START_REF] Dockès | Farmers' and advisers' representations of animals and animal welfare[END_REF] on closeness with animals. They illustrate the diversity which exists between farmers, and show that farmers have some flexibility in how they use equipment related to new technology.

The study showed that the farmers entertain a fairly positive image of PLF. They consider that their work has become easier with sensors and automated machines, and that they have greater control over the management of their animals. They describe a situation in which there are fewer constraints on both themselves and the animals. The farmers have some leeway in how they use the equipment; this can be seen particularly in the degree to which tasks are delegated to the equipment, which can be partial or total [START_REF] Allain | Technical, economic and sociological impacts of an automated estrus detection system for dairy cows[END_REF]. The improvements in the farmers' working conditions or in their experience at work are likely to positively influence their practices with the animals, moving towards a better human-animal relationship and improved animal welfare through the virtuous circle described by [START_REF] Boivin | Hommes et animaux d'élevage au travail : vers une approche pluridisciplinaire des pratiques relationnelles[END_REF]. In the same way, Hansen and Osteras (2019) have shown that high farmer occupational well-being and low level of stress are linked to a better animal welfare. As showed by some authors, the main motivation for farmers to invest in PLF is not economic but rather to improve their working conditions and their quality of life [START_REF] Vik | The political robot -The structural consequences of automated milking systems (AMS) in Norway[END_REF]. Introduction of PLF in farms modifies farmers' working conditions in terms of work duration, work flexibility and mental workload [START_REF] Kling-Eveillard | The effects of PLF (precision livestock farming) on human-animal relationships on farm[END_REF]Schewe and Stuart, 2005;[START_REF] Tse | Impact of automatic milking systems on dairy cattle producers' reports of milking labour management, milk production and milk quality[END_REF][START_REF] Vik | The political robot -The structural consequences of automated milking systems (AMS) in Norway[END_REF].

Most farmers are positive and say that PLF, sometimes associated with new farming conditions, has not degraded but has rather contributed to an improved relationship, as brought out by [START_REF] Wildridge | Transitioning from conventional to automatic milking: Effects on the human-animal relationship[END_REF]. These enhanced relationships appear through the implementation of new practices to familiarize animals with the new systems as well as to familiarize them with people. Getting the animals accustomed to the equipment facilitates its use over their entire life Some of the farmers surveyed mention that the human-animal relationship had deteriorated, such as has been cited in certain studies [START_REF] Boivin | Hommes et animaux d'élevage au travail : vers une approche pluridisciplinaire des pratiques relationnelles[END_REF][START_REF] Cornou | Automation Systems for Farm Animals: Potential Impacts on the Human-Animal Relationship and on Animal Welfare[END_REF]. The data provided by the new technologies indeed help to modify the way a farmer sees the animals, providing an individualized vision of the animals that is no longer at the herd scale. However, data management consumes time at the expense of other tasks. It also can prove difficult for the farmer to sort through the mass of data available. This change in the nature of the profession can lead to the acquisition of new skills, but it also can cause the loss of "traditional" skills and, for some farmers, result in a loss of interest in the profession and in the relationship with the animals [START_REF] Cornou | Automation Systems for Farm Animals: Potential Impacts on the Human-Animal Relationship and on Animal Welfare[END_REF]. This loss of certain skills raises questions regarding the long-term impacts of PLF [START_REF] Driessen | Cows desiring to be milked? Milking robots and the coevolution of ethics and technology on Dutch dairy farms[END_REF][START_REF] Marinoudi | Robotics and labour in agriculture. A context consideration[END_REF]. In this study, the technologies were installed on farms that previously had functioned without them for years. The farmers therefore analyse the contribution of this new information in the light of their previously developed knowledge and skills. What hindsight will be afforded to farmers and workers who directly start out on farms with PLF equipment? It could be interesting to survey the farmers who have practiced PLF for many years, or young farmers who are setting themselves up on farms that already are equipped with PLF tools. In order to better consider farmer discontent with PLF, studies could also be conducted with farmers who have stopped using the equipment or who have chosen not to equip themselves.

In this study, we focused on two types of equipment which are quite different: sensors alone, such as heat detectors, and sensors combined with automated equipment (milking robots, sow feeding systems). The sensors provide farmers data on their animals, and our results confirm that this changes how farmers view their animals and raises questions about the role of observation in their work. When the sensors are combined with automated machines, it is the daily tasks that may be changed, and in particular occasions for interaction between humans and animals. In addition to PLF, sometimes human-animal relationships are affected by changes in production and rearing conditions, such as the introduction of keeping gestating sows in groups.

In this case, the impacts thus result from this combination of new farming conditions and new equipment. The changes can vary greatly in nature and scope depending on the different situations.

Also of interest would be complementary studies on several parameters that could influence changes in farmer work in relation to animals and equipment like sensors and robots. These parameters can have an influence on both the work and the relationship with animals, and on interest in new technologies. Our study focussed on farmer representations considered as the farm manager. However the human-animal relationship is the result of interactions between animals and several people, as shown by de Boyer des Roches (2016). Studies should therefore better take into account how the farm workforce composition (including family and non-family workers) organises work with animals in farms that have adopted PFL. Moreover, our study showed that in our sample, there are proportionally more women in profile C, focused on the animals. The role of women changes with the introduction of PLF with an increasing involvement in animal husbandry and the use of new technologies [START_REF] Eastwood | Networks of practice for co-construction of agricultural decision support systems: Case studies of precision dairy farms in Australia[END_REF][START_REF] Hay | Technology adoption by rural women in Queensland, Australia: Women driving technology from the homestead for the paddock[END_REF]. Finally, PLF seems to be more adopted in larger farms [START_REF] Gargiulo | Dairy farmers with larger herd sizes adopt more precision dairy technologies[END_REF], which also has consequences on the human-animal relationship.

A comprehensive approach to the human-animal relationship should be multidisciplinary [START_REF] Boivin | Hommes et animaux d'élevage au travail : vers une approche pluridisciplinaire des pratiques relationnelles[END_REF]. It should involve complementing the sociological approach exploring farmer representations presented in this article with an ergonomic approach to farmers' activities and practices, observing farmers at work. Furthermore, it should take into account what animals "say" about the relationship and how this is reflected: these approaches are zootechnical (animal welfare and performance) and ethological (animals' responsiveness to people). Such an approach was not possible within this study but is planned for a new project (Courboulay et al, 2020).

Conclusion

Our study confirms that the human-animal relationship, and thus animal welfare, can be impacted by the introduction of PLF on a farm, just as it can be affected by any other changes in livestock farming conditions. As the farmers have described, the human-animal relationship is not always impacted in the same way, and it is notably not always degraded by PLF. The situations and farming conditions associated with PLF are diverse (for example, grouping or not grouping animals), as is the equipment (sensors, automated machines) and the farmer profiles.

The profiles illustrate the diversity of the farmers' experiences and choices, and confirm that they have room to maneuver when using a tool or equipment. Farmers thus can choose to either completely or only partially delegate a task or decision to the equipment. Others differentiate themselves by implementing (or not implementing) relational practices to maintain a sense of closeness with their animals; some start their day by observing their animals while others consult their computers.

In describing these profiles, three themes are linked: how farmers view their profession, how they define the human-animal relationship, and how they perceive the impacts of PLF. This convergence reinforces the idea of a link between animal welfare and farmer wellbeing, as expressed in the One Welfare concept. What enables farmers to better enjoy their profession and their work, with fewer constraints, contributes to a certain extent to a better human-animal relationship and to the welfare of the animals.

While the majority of the farmers interviewed demonstrated broad satisfaction with PLF as implemented on their farms, some reservations and questions were raised. They concern in particular dependence on the tools and the sustainability of animal observation skills over time with the development of new habits formed by the way the equipment functions. Some farmers were furthermore reticent about PLF. Complementary studies could monitor these developments and contribute elements on the role of PLF in the sustainability of livestock farms.

Lastly, the effects of the development of PLF on the general public's image of livestock farming was not addressed in this research but also merit being examined in detail as society's image of livestock farming is a decisive factor in the evolution of livestock farms and their sustainability. Table 4: The variables used in the statistical analysis

1) Active variables involved in the composition of profiles on representations of the profession, of the animal and of the human-animal relationships) :

-Variables resulting from the analysis of the discourse of the livestock farmer

  cycles. Familiarizing them with humans makes later human interventions easier. The shift from individual stalls to open buildings has provided an additional opportunity to work with animals differently.

Figure 1 :

 1 Figure 1 : Dendrogram from the hierarchical ascendant classification (HAC)

Table 2 :

 2 Characteristics of the equipment studied and consequences of human-

  Sources of satisfaction in the profession Motivations for becoming a livestock farmer To see the animals, the first task in the morning Visual observation of heat in addition to alerts by the equipment Task fully delegated to the machine Strategies for familiarizing heifers or gilts Definition of a good human-animal relationship Estimated score of the current human-animal relationship -Variables from closed questionnaire responses (degrees of agreement)Poultry / cows / sows have a memoryThere is a link between the welfare of the farmer and the well-being of the poultry

Table 1 :

 1 Number of surveys carried out by species and equipment type FAS : free access stall ; MR : milking robot ; HD : heat detector ; BEC : barn electronic controller ; AW : automatic weighing system

	Species	Gestating sows GS		Dairy cows DC			Broiler BR
	Number of animals	< 245	> 300	< 85	> 105		< 25000	> 40000
	System	ESF FAS ESF FAS MR	HD MR HD MR	BEC AW	AW + BEC
										+		+
										HD		BEC
	Number of farms per	3	2	2	1	2	2	4	1	1	2	1	4
	category
	Number of farms :		8 farms				10 farms				7 farms
	total
	Herd size (min/max)	263 gestating sows		106 dairy cows			2840 m 2
		(150 -430)			(50 -190)				(1000 -8100)
	Utilised agricultural		115					147				52
	area (ha)(min/max)		(0 -305)			(70 -305)				(0 -70)
	Average age		42					45				50
	ESF : electronic sow feeding ;

http://www.welfarequalitynetwork.net/en-us/reports/assessment-protocols/

Acknowledgements

The authors are very grateful to Emeline Ganis (student at AgroParisTech school, France) who conducted the study and interviewed the farmers. This study was co-funded by GIS Elevage Demain, RMT (mixed technology network) Travail en élevage and RMT Bien-être animal, supported by MAAF (French Agriculture Ministry).

Declarations of interest

None the call.

that everything is going well and to make occasional repairs.


Hervé Portalès
email: herve.portales@sorbonne-universite.fr

Nicolas Goubet
email: nicolas.goubet@sorbonne-universite.fr

Sandra Casale

Zhen Xiang

Mostapha Xu

Alain Ariane

Jeremie Mermet

Lucien Margueritat

Saviot

Xu

Mostapha Ariane

Alain Mermet

Jérémie Margueritat

Lucien Saviot
email: lucien.saviot@u-bourgogne.fr

Inelastic light scattering by long narrow gold nanocrystals: when size, shape, crystallinity and assembly matter

Keywords: gold nanocrystals, nanorods, nanobipyramids, plasmonic coupling, Raman scattering, eigenvibrations, anisotropy

teaching and research institutions in France or abroad, or from public or private research centers.

Gold nanocrystals have been studied extensively in the last few decades as they are promising candidates for a variety of applications in different fields including sensing, catalysis and biomedicine. [START_REF] Murphy | Anisotropic Metal Nanoparticles: Synthesis, Assembly, and Optical Applications[END_REF][START_REF] Mackey | The Most Effective Gold Nanorod Size for Plasmonic Photothermal Therapy: Theory and In Vitro Experiments[END_REF][START_REF] Amendola | Surface Plasmon Resonance in Gold Nanoparticles: A Review[END_REF] This is due to the tunability of their optical properties, plasmonic properties, when varying their composition, size, shape [START_REF] Lohse | The Quest for Shape Control: A History of Gold Nanorod Synthesis[END_REF] and environment. During the last twenty years the mechanical properties of gold nanocrystals, their vibrational properties, have been shown to also strongly depend on these parameters and to provide valuable information about the nanostructures themselves (size, shape, crystallinity) and their environment. [START_REF] Weitz | Anomalous Low-Frequency Raman Scattering from Rough Metal Surfaces and the Origin of Surface-Enhanced Raman Scattering[END_REF][START_REF] Montagna | Raman Scattering from Small Spherical Particles[END_REF][START_REF] Hodak | Observation of Acoustic Quantum Beats in Nanometer Sized Au Particles[END_REF][START_REF] Hamanaka | Ultrafast Electron Relaxation via Breathing Vibration of Gold Nanocrystals Embedded in a Dielectric Medium[END_REF][START_REF] Bachelier | Surface Plasmon Mediated Raman Scattering in Metal Nanoparticles[END_REF][START_REF] Mazurenko | Coherent Vibrations of Submicron Spherical Gold Shells in a Photonic Crystal[END_REF][START_REF] Portalès | Probing Atomic Ordering and Multiple Twinning in Metal Nanocrystals through their Vibrations[END_REF][START_REF] Pelton | Damping of Acoustic Vibrations in Gold Nanoparticles[END_REF][START_REF] Jais | Metal Nanoparticle Ensembles: Tunable Laser Pulses Distinguish Monomer from Dimer Vibrations[END_REF][START_REF] Fernandes | Acoustic Vibrations of Au Nano-Bipyramids and their Modification under Ag Deposition: A Perspective for the Development of Nanobalances[END_REF][START_REF] Yu | Damping of Acoustic Vibrations of Immobilized Single Gold Nanorods in Different Environments[END_REF][START_REF] Major | Damping of the Acoustic Vibrations of a Suspended Gold Nanowire in Air and Water Environments[END_REF][START_REF] Bayle | Vibrational and Electronic Excitations in Gold Nanocrystals[END_REF][START_REF] Kirschner | Size-Dependent Coherent-Phonon Plasmon Modulation and Deformation Characterization in Gold Bipyramids and Nanojavelins[END_REF][START_REF] Girard | Inelastic Light Scattering by Multiple Vibrational Modes in Individual Gold Nanodimers[END_REF][START_REF] Valley | Imaging Intra-and Interparticle Acousto-Plasmonic Vibrational Dynamics with Ultrafast Electron Microscopy[END_REF][START_REF] Kim | Ultrafast Electron Microscopy Visualizes Acoustic Vibrations of Plasmonic Nanorods at the Interfaces[END_REF] This correlated dependency of the optical and mechanical properties make gold nanoparticles the simplest opto-mechanical transducers where they act both as source and detector. [START_REF] Pelton | Viscoelastic Flows in Simple Liquids Generated by Vibrating Nanostructures[END_REF] Such optical and mechanical properties can be tuned by controlling their structural properties and environment. Moreover, recent works in this domain have shed a new light on the coupling between the optical and mechanical properties by showing that the inelastic light scattering process is governed by the variations of the electric field inside the nanoparticles even for very small nanospheres. [START_REF] Bachelier | Surface Plasmon Mediated Raman Scattering in Metal Nanoparticles[END_REF][START_REF] Girard | Mechanisms of Resonant Low Frequency Raman Scattering from Metallic Nanoparticle Lamb Modes[END_REF] By providing a way to probe these variations in particular under resonant excitation, inelastic light scattering may prove as valuable for the study of surface plasmons in metallic nanoparticles as resonant Raman scattering has been for the study of the electronic properties of other systems. [START_REF] Leite | Multiple-Phonon Resonant Raman Scattering in CdS[END_REF][START_REF] Dresselhaus | Raman Spectroscopy of Carbon Nanotubes[END_REF][START_REF] Ferrari | Spectrum of Graphene and Graphene Layers[END_REF] Analytical models exist to calculate the inelastic light scattering cross-sections 9,23 of metallic nanoparticles. They are restricted to systems having the spherical symmetry. They were developed thanks to numerous experimental results reported over the years for gold [START_REF] Weitz | Anomalous Low-Frequency Raman Scattering from Rough Metal Surfaces and the Origin of Surface-Enhanced Raman Scattering[END_REF][START_REF] Portalès | Probing Atomic Ordering and Multiple Twinning in Metal Nanocrystals through their Vibrations[END_REF] and also other metallic nanoparticles. [START_REF] Fujii | Low-Frequency Raman Scattering from Small Silver Particles Embedded in SiO 2 Thin Films[END_REF][START_REF] Fujii | Erratum: Low-Frequency Raman Scattering from Small Silver Particles Embedded in SiO 2 Thin Films[END_REF] One of the goals of the present paper is to provide measurements for non-spherical nanocrystals to help develop models for non-spherical shapes. Indeed, experimental inelastic light scattering measurements reported in the literature are scarce. Various authors have investigated the vibrational dynamics of long, narrow gold nanoparticles but mostly using time-resolved transient absorption with femtosecond pumpprobe measurements. [START_REF] Pelton | Damping of Acoustic Vibrations in Gold Nanoparticles[END_REF][START_REF] Fernandes | Acoustic Vibrations of Au Nano-Bipyramids and their Modification under Ag Deposition: A Perspective for the Development of Nanobalances[END_REF][START_REF] Yu | Damping of Acoustic Vibrations of Immobilized Single Gold Nanorods in Different Environments[END_REF][START_REF] Major | Damping of the Acoustic Vibrations of a Suspended Gold Nanowire in Air and Water Environments[END_REF][START_REF] Kirschner | Size-Dependent Coherent-Phonon Plasmon Modulation and Deformation Characterization in Gold Bipyramids and Nanojavelins[END_REF] This method is extremely powerful and even more so when it is used to investigate single particles. [START_REF] Beane | Ultrafast Measurements of the Dynamics of Single Nanostructures: A Review[END_REF] However, it also suffers from very restrictive selection rules. The observable vibrations are the totally symmetric ones because these are the only ones showing a variation of the volume of the particles during its oscillation. [START_REF] Ahmed | Understanding How Acoustic Vibrations Modulate the Optical Response of Plasmonic Metal Nanoparticles[END_REF] Inelastic light scattering (Raman/Brillouin) has less restrictive selection rules which make it possible to observe additional vibrations. In addition, the Raman selection rules are relaxed for large nanoparticles [START_REF] Montagna | Brillouin and Raman Scattering from the Acoustic Vibrations of Spherical Particles with a Size Comparable to the Wavelength of the Light[END_REF] and when interparticle plasmonic coupling exists. [START_REF] Girard | Inelastic Light Scattering by Multiple Vibrational Modes in Individual Gold Nanodimers[END_REF] The very low crosssections of the inelastic light scattering process prevent single-particle measurements in most cases. Still, ensemble measurements combined with narrow size dispersion have been used successfully in the past to investigate spherical nanoparticles and also in the case of transient absorption measurements when single-particle measurements remain difficult. [START_REF] Kirschner | Size-Dependent Coherent-Phonon Plasmon Modulation and Deformation Characterization in Gold Bipyramids and Nanojavelins[END_REF] In this work, we prepared narrow size dispersion elongated gold nanocrystals which are suitable for ensemble measurements without introducing a dramatic inhomogeneous broadening. We controlled their morphology and measured their size with electron microscopy and optical absorption. Then we measured their inelastic light scattering spectra. Previous works have generally focused on totally symmetric vibrations (the so-called extensional and breathing modes) [START_REF] Large | Acousto-Plasmonic Hot Spots in Metallic Nano-Objects[END_REF] even in the case of semiconducting nanoparticles. [START_REF] Miscuglio | Confined Acoustic Phonons in Colloidal Nanorod Heterostructures Investigated by Nonresonant Raman Spectroscopy and Finite Elements Simulations[END_REF] In that case, crystallinity only results in minor deviations compared to the case of elastically isotropic nanoparticles. For example, a coupling of the breathing vibration with m=5 vibrations for pentagonal structures has been reported [START_REF] Gan | Breathing Mode Vibrations and Elastic Properties of Single-Crystal and Penta-Twinned Gold Nanorods[END_REF] together with the necessity to take into account the right sound velocity corresponding to the lattice direction along the long axis for the extensional mode. [START_REF] Goupalov | Crystal Structure Anisotropy Explains Anomalous Elastic Properties of Nanorods[END_REF][START_REF] Goupalov | Correction to "Crystal Structure Anisotropy Explains Anomalous Elastic Properties of Nanorods[END_REF] However, for nanorods (NRs) additional vibrations can also significantly scatter light, 38 some of which are very sensitive to the crystallinity of the nanocrystals. [START_REF] Saviot | Vibrations of Single-Crystal Gold Nanorods and Nanowires[END_REF] Accordingly, we consider in this work only nanocrystals with a controlled lattice structure, i.e., monodomain NRs and twinned pentagonal nanobipyramids (NBP). In addition, a tandem Fabry-Pérot interferometer is used to measure the spectra. It enables measurements in a lower frequency range than conventional low-frequency Raman spectrometers (down to about 1 GHz). This enables to study larger nanoparticles for which deviations from the Raman scattering rules are expected.

Results and Discussion

Morphology

Colloidal solutions of Au NRs and NBPs were synthesized using the protocols described in the Methods section. In the various colloidal solutions, the size distribution of the NRs remains as narrow as a few percents. Such a low polydispersity allows for getting NR selfassembly after depositing them onto a Si substrate, as observed by high-resolution scanning electron microscopy (HRSEM) in Figure 1A. When looking at the high resolution transmission electron microscopy (HRTEM) image of one single NR in Figure 1B, the apparent profile is well described by a cylinder with half-sphere ends (Figure 1C). A similar profile is observed for most of the synthesized NRs. In the following we model them as half-sphere ended cylinders of total length L and diameter d. All of them are single domain with their long axis along [001].

Figure 1D shows the length versus diameter distributions of the six samples. The aspect 2C). Our observation matches the morphology reported in the literature. [START_REF] Liu | Mechanism of Silver(I)-Assisted Growth of Gold Nanorods and Bipyramids[END_REF] The average length, width at the center and aspect ratio are also given in Table 1.

-5000 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 5000

Frequency ! diagonal (m s ) Intensity (arbitrary units)

Raman spectra

Raman measurements were performed on NRs deposited onto a Si wafer after evaporation of the colloidal solution. No control of the orientation of the NRs is achieved, meaning that these latter are randomly oriented with respect to the polarization of the incident and scattered light. The low-frequency Raman spectra of samples NR#i are shown in Figure S8.

Each spectrum exhibits several bands in the 30-150 GHz frequency range. The peaks do not overlap significantly which demonstrates that the control of the size distributions of the NRs during the synthesis was good enough for this study. The bands shift towards higher frequencies for decreasing diameters. To highlight the dependence of the low-frequency Raman spectra on the NR diameter, we plotted them in Figure 1E as a function of νd, the product of the frequency ν by the diameter d. This scaling comes from the continuum elasticity approximation used in the calculations. The frequencies scale as the inverse of the dimensions provided the aspect ratio is kept constant. In a previous work, it was shown that the eigenmodes of NRs are governed mainly by either the length or the diameter. [START_REF] Saviot | Vibrations of Single-Crystal Gold Nanorods and Nanowires[END_REF] We take advantage of this scaling law in the following by considering the product of the frequency by the length and by the diameter of the NRs. They are expressed in m/s when multiplying frequencies in GHz by lengths in nm. Two bands at about νd =800 and 1200 m/s dominate the spectra. These bands hardly move from one spectrum to another, thus indicating that they originate from two vibrational modes with frequencies scaling as 1/d. In spite of a weaker signal/noise ratio of the spectra at higher frequency, one discerns other bands whose νd products remain also almost unchanged. At variance with the extensional modes detected by transient absorption measurements and whose frequency varies as 1/L, the frequency of most of the vibrational modes detected here scales approximately as 1/d. Therefore, the multiple features observed in the Raman spectra are probably due to radial modes of the NRs. Their assignment will be discussed in the following.

Three lengths are required to describe the shape of NBPs: the total length L and the width at the center w and at both ends t (see Figure 2C). For pentagonal cross-sections, the lateral dimension is chosen as the diagonal of the pentagon because this is the width which we expect to observe in HRTEM images when NBPs rest on one of their faces. We use the same representation as for the NRs and scale the frequencies by multiplying them by the diagonal of the bipyramids at the center (νw). This enables to easily compare peaks for samples having different sizes. The Raman spectra of the NBP#i samples are presented in Figure 2E. We note that they are as rich as in the case of NRs because they all contain 5 peaks or more. The lowest frequency peaks for NBP#1 and NBP#2 are at lower value of νw and may therefore correspond to modes related to the length of the NBPs. The case of NBP#3 is similar to the case of the NRs before with the peaks appearing at larger νw corresponding most probably to vibrations confined along the lateral dimension.

A 647 nm laser excitation was used to measure the inelastic light scattering spectra.

According to the UV-visible absorption spectra (Figures S14 andS15), the excitation is strongly resonant for the samples with the smallest aspect ratio. It falls in between the longitudinal and transverse surface plasmon resonances for the samples with the largest aspect ratio. However, these spectra were measured for the colloidal solution. The selfarrangement of the nanocrystals after deposition most probably alters this simple picture.

We chose the 647 nm laser excitation in the present work to favor a resonant excitation and facilitates the measurement of the spectra. Future works will have to look more closely at possible resonance effects which may enhance the scattering of some nanocrystals depending on their size or assembly.

The assignment of the experimental peaks is achieved by comparing their frequencies with calculated ones. There is never a perfect match in practice due to the size distributions and the approximations of the calculation method. Comparing frequencies works well for the lowest frequency vibrations where the different modes are well separated. The increase of the vibrational density of states with frequency renders this approach much less effective at higher frequencies. In the present case, the lowest frequency modes are the extensional ones. The features observed for the NRs are mainly diameter-dependent and are therefore not the lowest frequency modes. To assign the peaks, we use selection rules when possible to restrict the number of modes to consider.

Recent works have also shown that the plasmonic coupling between neighbor nanoparticles can break the usual Raman selection rules [START_REF] Girard | Inelastic Light Scattering by Multiple Vibrational Modes in Individual Gold Nanodimers[END_REF] resulting in a larger number of peaks in the spectra. In that case, the additional experimental features observed for spheres have been successfully assigned to the fundamental spheroidal vibrations with = 3, 4, . . . Such a coupling is possible in our samples because the nanocrystals tend to self-assemble as can be seen in the HRSEM images (Figures 1A and2A). Therefore, a similar assignment can be expected. To test this hypothesis, we focus in the following on describing how these spheroidal vibrations evolve when changing the shape from spheres to NRs and NBPs. Then we try to assign the spectral features with these vibrations. The same spheroidal vibrations with = 3, 4, . . . manifest also when the size of the nanoparticles is not small compared to the wavelength of light. [START_REF] Montagna | Brillouin and Raman Scattering from the Acoustic Vibrations of Spherical Particles with a Size Comparable to the Wavelength of the Light[END_REF] However, we do not anticipate that the same size effect manifests in our case. Indeed, vibrations with = 2 are not observed for gold nanospheres [START_REF] Girard | Inelastic Light Scattering by Multiple Vibrational Modes in Individual Gold Nanodimers[END_REF] having a diameter of about 100 nm which is close to the length of our elongated nanocrystals.

Monodomain NRs

We start from the well-known case of the isotropic nanosphere of diameter d, then change the shape to an isotropic circular cylinder and then to a cubic circular cylinder as an approximation for a monodomain NR.

The diameter-dependent modes of the cylinder corresponding to the fundamental spheroidal modes of the sphere with angular momentum > 0 are the ones with m = at the center of the Brillouin zone (q = 0). They are the lowest frequency E mu for odd m or E mg for even m > 0. [START_REF] Saviot | Vibrations of Single-Crystal Gold Nanorods and Nanowires[END_REF] The corresponding surface deformation for a cross-section of the isotropic gold cylinder is plotted in Figure 3A (top). For these q = 0 modes, the deformation is the same along the cylinder. The frequencies ν of these modes vary as the inverse diameter 1/d.

The diameter-independent values νd are given in Figure 3A and plotted in Figure 3B with squares as a function of m. For comparison, the spheroidal modes of the sphere are also plotted with circles as a function of . The frequencies are smaller for the cylinder but the variations with or m are very similar. Overtones of the spheroidal vibrations of the sphere are also interesting in this context. However, their scattering cross-sections are substantial only if they change the shape of the surface significantly. For spherical nanoparticles, the fundamental spheroidal mode with a given = 1 are such modes. [START_REF] Saviot | Longitudinal versus Transverse Spheroidal Vibrational Modes of an Elastic Sphere[END_REF] However, for ≥ 2, the next 2 or 3 overtones keep the shape of the nanosphere almost unchanged and their scattering cross-sections are small. [START_REF] Bachelier | Surface Plasmon Mediated Raman Scattering in Metal Nanoparticles[END_REF][START_REF] Girard | Mechanisms of Resonant Low Frequency Raman Scattering from Metallic Nanoparticle Lamb Modes[END_REF] We checked that a similar behavior still holds for cylinders.

For this reason, we will only consider the fundamental modes in the following.

The spheroidal-like modes of isotropic cylinders with even m = 2i > 0 have the E (2i)g irreducible representation. For single-crystal cylinders made of a cubic material, they split into B 1g and B 2g for odd i and A 1g +A 2g for even i. For odd m = 2i + 1, the isotropic spheroidal-like modes have the E (2i + 1)u irreducible representation. They do not split and transform into E u . [START_REF] Saviot | Vibrations of Single-Crystal Gold Nanorods and Nanowires[END_REF] For m = 0, the breathing mode of the sphere transforms into the radial breathing mode of the cylinder and the irreducible representation remains unchanged (A 1g ). The first few modes shapes and frequencies (m = 0, . . . 6) are illustrated in Figure 3A (middle). The deformations for the isotropic and cubic vibrations are almost identical for m = 2. They differ for modes at higher frequencies due to mixing with other modes having the same cubic irreducible representations and close frequencies. Such near frequency modes are more frequent at higher frequency due to the increasing vibrational density of states.

Only the cubic vibrations being the most similar to the isotropic ones are considered here.

As expected from previous works, [START_REF] Portalès | Probing Atomic Ordering and Multiple Twinning in Metal Nanocrystals through their Vibrations[END_REF] the significant splitting of the E 2g mode into B 1g and B 2g is a clear marker of the cubic lattice structure of gold in circular cylinders. The frequency shifts for the other modes are also significant. This demonstrates that taking into account this anisotropic structure is required.

Figure 3C was designed to help assign the peaks observed in the experimental spectra.

The axes correspond to νd and νL to help distinguish between diameter and length dependent Indeed, these vibrations do not significantly scatter light in the case of isotropic material because they do not change the shape of the surface. However, this is not true when the cubic lattice structure is present as can be seen in Figure 3A. Our experimental results do not allow us to explain the reason for the different behavior of sample NR#1 at this point. It could be related to a different arrangement of the NRs in the region illuminated by the laser.

Indeed, our assignment is based on identifying the vibrations which couple significantly with the surface plasmon resonance. However, the relative inelastic light scattering cross-sections of these modes are expected to depend significantly on the relative orientation of the NRs and the polarization of the laser but also on the position of the excitation wavelength with respect to the surface plasmon resonance.

The breaking of the Raman selection rules induced by plasmonic coupling and resulting in the scattering of light by vibrations with angular momentum larger than 2 was not observed in previous measurements on self-assembled nanoparticles. [START_REF] Portalès | Probing Atomic Ordering and Multiple Twinning in Metal Nanocrystals through their Vibrations[END_REF][START_REF] Margueritat | Crystallinity Dependence of the Plasmon Resonant Raman Scattering by Anisotropic Gold Nanocrystals[END_REF]43 The reason for this apparent contradiction is the different coupling regime achieved in the present work. An efficient coupling for gold nanorods requires separation distances shorter than the nanorod diameter. [START_REF] Vial | Plasmon Coupling in Layer-by-Layer Assembled Gold Nanorod Films[END_REF] A universal scaling behavior of the plasmonic coupling has been reported for dimers. [START_REF] Jain | On the Universal Scaling Behavior of the Distance Decay of Plasmon Coupling in Metal Nanoparticle Pairs: A Plasmon Ruler Equation[END_REF] We expect a similar law to exist for self-assembled nanoparticles, i.e., that the plasmonic coupling decreases quickly as a function of the ratio s/D where s is the separation distance between the nanoparticles and D their size. s/D 1 3 for samples prepared with pulsed laser deposition. [START_REF] Margueritat | Crystallinity Dependence of the Plasmon Resonant Raman Scattering by Anisotropic Gold Nanocrystals[END_REF] The separation distance was about 1 nm leading to s/d . This smaller value correspond to a stronger plasmonic coupling in agreement with the larger observed deviation from the usual Raman selection rules. The effect is even more pronounced if we consider the length of the NRs (s/L 1 50 ). The deviation from the Raman selection rules as the size of the nanoparticles increases is also observed in our spectra. We can safely compare samples NR#3 and NR#5 because they have almost the same aspect ratio. The NRs of sample NR#5 are about 30% larger than those of sample NR#3. More Raman peaks are observed for NR#5 than for NR#3 in Figure 1E which is again consistent with a stronger plasmonic coupling.

Finally, we note that the breaking down of the Raman selection rules which we report is quite dramatic. In the case of gold nanodimers, [START_REF] Girard | Inelastic Light Scattering by Multiple Vibrational Modes in Individual Gold Nanodimers[END_REF] the intensities of the additional peaks assigned to vibrations with > 2 was about one order of magnitude lower than the one for = 2. In the present work, the intensity of the peaks are about the same (see Figure 1). We note that each NR has several neighbor NRs in our deposited samples instead of a single one in nanodimers. Therefore, the plasmonic coupling occurs over a larger fraction of the surface of the NRs which may explain at least in part the larger intensities that we observed.

In addition, it is well-known that electric field is intense and varies strongly over short distances near the tips of NRs. This can also explain the large intensities for > 2 vibrations when the excitation wavelength is near the longitudinal surface plasmon resonance.

Pentagonal NBPs

The E (2i+1)u and E (2i)g modes at q = 0 of the isotropic circular cylinders split in pentagonal cylinders when the angular momentum m = 2i(+1) is a multiple of 5. The corresponding surface deformation and frequency×diagonal products are given in Figure 3A (bottom)for cubic twinned pentagonal cylinders. We used the lattice orientations given in reference 40.

Contrarily to the case of monodomain cylinders detailed above, taking into account the cubic elasticity plays only a minor role for twinned pentagonal cylinders. In a simple approach, we can consider that vibrations of actual bipyramids are intermediate between those of spheres (for L ∼ w) and pentagonal cylinders (L w). We checked this hypothesis for the lowest frequency E' 2 mode (quadrupolar-like) calculated using the finite element method and using the average dimensions given in Table 1. We obtained νw = 1095, 1100 and 1123 m/s for samples NBP#1,2 and 3 respectively. These values are close to the frequency of the sphere (νd = 1062 m/s) and about 10% larger than those of the cylinder.

Next we consider the well-known length-dependent extensional modes for the bipyramids.

Such vibrations have already been measured using femtosecond pump-probe experiments and their frequencies were also determined analytically. [START_REF] Pelton | Mechanical Damping of Longitudinal Acoustic Oscillations of Metal Nanoparticles in Solution[END_REF] Using the actual average sizes reported in Table 1, we calculated the extensional mode frequencies using this approximation and approximately the following values for odd "m" (νd = 1452, 2326, 3138 and 3928 m/s for m = 3, 5, 7 and 9). This assignment is only tentative at this point as it requires a thorough investigation of a larger set of the full parameter space (length and diagonals at the center and at the ends) which goes beyond the scope of the present work. Still, we would like to emphasize that it is consistent with the deviations from the Raman selection rules because of the plasmonic coupling as described above in the case of NRs. First, we note that the size of NBP#3 is almost twice that of NBP#1 and NBP#2. We can also assume that the distance s between neighbor NBPs is similar for each sample because it is governed by the length of the ligands. The s/D ratio is therefore much smaller in NBP#3 compared to NBP#1 and NBP#2 resulting in a significantly larger plasmonic coupling. This probably explains why the assignment of the peaks for NBP#1 and NBP#2 did not require considering m > 2 modes while such vibrations are involved for NBP#3. In addition, the SEM and TEM images show that NBPs do not self-assemble as easily as NRs. After deposition, their arrangement looks mostly random. However, we can point out that NRs tend to self-assemble so that their ends are aligned while neighbor NBPs are most often shifted so that the tip of one NBP is close to the center of an adjacent NBP. These differences probably result in a very different symmetry of the electric field inside NBPs compared to NRs which may be the reason for the unexpected odd "m" observation reported above.

Conclusion

Gold NRs and NBPs were synthesized. Their morphology was determined with electron microscopy and optical absorption. The nanocrystals are tens of nanometer large monodomain gold NRs and twinned pentagonal NBPs with narrow size distributions. Their vibrational dynamics was investigated experimentally by means of inelastic light scattering. Numerous peaks were observed. The vibrations were modeled in the framework of continuum elasticity.

Special care was taken to identify their symmetry and compare them to the vibrations of nanowires as the limiting case of very high aspect ratio NRs. We proposed a method to assign the experimental peaks following recent results for gold nanodimers. [START_REF] Girard | Inelastic Light Scattering by Multiple Vibrational Modes in Individual Gold Nanodimers[END_REF] For NRs, the frequencies of the peaks match those of the fundamental spheroidal vibrations which couple with the surface plasmon resonance by changing the shape of the surface. Deviations from the usual low-frequency Raman selection rules are observed because they are derived for small and isolated nanoparticles. [START_REF] Duval | Far-Infrared and Raman Vibrational Transitions of a Solid Sphere: Selection Rules[END_REF] Vibrations with angular momenta larger than 2 are involved more and more as the ratio of the interparticle separation to the diameter decreases.

The agreement between the experimental and calculated frequencies is good for NRs. The assignment is more complex for large NBPs for which different selection rules seem to be at work because of the different arrangement of the nanocrystals after deposition. However, the unusually large number of peaks observed for the largest NBPs, which occur at large values of the frequency×diagonal product, can not be explained without involving vibrations having larger angular momenta. These results show that inelastic light scattering in the GHz frequency range is a powerful probe of the plasmonic coupling in assemblies of nanocrystals.

The assignment obtained in this work is general but intensity variations can be expected when varying the experimental parameters. Future works will focus on carefully monitoring the assembly of the nanocrystals being probed as well as polarization effects, resonance conditions and developing new methods to calculate the inelastic scattering cross-sections for non-spherical shapes.

Methods Syntheses

Hydrogen tetrachloroaurate (Sigma-Aldrich, ≥99.9%), silver nitrate (Sigma-Aldrich, 99%), sodium borohydride (Sigma-Aldrich, ≥96%), sodium hydroxide (VWR, ≥98%), hydroquinone (Sigma-Aldrich, ≥99%), cetyltrimethylammonium bromide (Sigma-Aldrich, ≥98%), cetyltrimethylammonium chloride (Sigma-Aldrich, ≥99.5%), benzyldimethylhexadecylammonium chloride (Sigma-Aldrich). All chemicals were used as received. All solutions were fresh daily prepared.

All glassware were washed with aqua regia (HNO 3 /HCl 2:1 (v/v)) and rinced with ultrapure water (18.2 MW).

For gold NRs, the seed and growth solutions were prepared as follows.

Seed solution: under strong stirring, 460 µL of NaBH 4 (0.01 M) and NaOH (0.01 M)

solution was injected with one stroke in 10 mL of HAuCl 4 (0.5 mM) and CTAB (0.1 M) solution at room temperature. The color turned from yellow-orange to brown.

Growth solution: at 30 and under slow stirring, 160, 240, 320, 400, 480, 560, 640, 720, 800 or 880 µL of AgNO 3 (0.01 M) solution was added to 40 mL of HAuCl 4 (0.5 mM) and CTAB (0.1 M) solution. 2 mL of hydroquinone was mixed to the growth solution.

The color turned from yellow-orange to colorless. Finally, a volume of 640 mL of the seed solution was added and the growth solution was let undisturbed overnight.

Similarly, for gold NBPs, the seed and growth solutions were prepared as follows.

Material characterization

UV visible absorption spectra of the colloidal solutions were recorded using a Varian 50 scan spectrophotometer. For conventional TEM and HRTEM, we used a JEOL 1011, JEOL 2010 and 2010F, respectively. The samples were prepared by depositing a drop of colloidal solution onto a copper grid covered by an amorphous carbon film. The size distributions were determined using the NIH ImageJ software. HRSEM pictures were acquired with a HITACHI SU-70 instrument. The low-frequency Raman scattering measurements were performed using a tandem Fabry-Pérot interferometer. The scattered light was collected in the backscattering configuration. The excitation source was the 647.1 nm line of a Kr + laser.

For Raman measurements, either Au NRs or NBPs were deposited onto a silicon wafer by evaporation of the colloidal solution in a small beaker.

Calculation of the acoustic eigenmodes

The calculation of the eigenvibrations was performed using the Rayleigh-Ritz variational method as explained in a previous work by one of us. [START_REF] Saviot | Vibrations of Single-Crystal Gold Nanorods and Nanowires[END_REF] The point group for single-domain NRs having their main axis along [001] is D 4h and the one for the pentagonal bipyramids is D 5h . The intensity of inelastically scattered light is also calculated by considering a Brillouin mechanism, i.e., a constant electric field inside the nanocrystals. This approximation is poor [START_REF] Saviot | Vibrations of Single-Crystal Gold Nanorods and Nanowires[END_REF] but we use it as a rough guide since it is easy enough to calculate, and we are lacking a better model.

In the case of the NBPs, numerical issues resulted in a poor convergence using the previous approach. It was therefore replaced by finite element calculations (Abaqus/CAE 6.18). We used the cyclic analysis method which takes advantage of the 5-fold symmetry axis (C 5 )

and provides the nodal diameter for each eigenvibration. Additional characters (symmetry about the plane perpendicular to C 5 and one of the 5 planes containing C 5 ) were evaluated numerically to complete the determination of the irreducible representations.

Figure 2 :

 2 Figure 2: (A) HRSEM image of NBP#3 nanocrystals self-assembled on a Si wafer. (B) HRTEM image showing one typical pentagonal Au NBP. (C) Schematics depicting the relevant NBP dimensions. As a first approximation, each NBP can be modeled by a pentagonal biprysm of diagonal at the center w ended with two pyramids of diagonal t, with a total length L. (D) Length versus diagonal distributions of Au NBPs of samples NBP#1 (black), NBP#2 (green) and NBP#3 (red). (E) Stokes and anti-Stokes low-frequency Raman scattering spectra of Au NBPs with different sizes and aspect ratios as a function of the frequency shift multiplied by the average NBP diagonal at the center. The spectra of samples NBP#i (i=1-3) are plotted from bottom to top with the same colors as in D. The spectra are independently scaled and vertically shifted for clarity.

Figure 3 :

 3 Figure 3: (A) Surface deformation of isotropic gold cylinders deformed by the q = 0 radial vibrations with m = 0, . . . , 6 (top). The second degenerate isotropic mode is obtained by rotating by π 2m . The equivalent vibrations are also shown for cubic gold cylinders (middle) and for cubic twinned pentagonal gold cylinders (bottom). The irreducible representations and νd (frequency×diameter in m/s) or νw (frequency×diagonal of the pentagon in m/s) are indicated. (B) νd for the fundamental spheroidal modes of an isotropic gold sphere (circles) and cylinder (square) as a function of the angular momentum or m. (C) Color map of the intensity calculated using the Brillouin mechanism as a function of νL and νd for monodomain circular NRs with half sphere ends which are made of cubic gold. Experimental frequencies are plotted with full circles and the errorbars correspond to the FWHM of the diameter and length distributions. The frequencies of the "spheroidal-like" q = 0 diameterdependent modes of circular cylinders made of cubic gold are indicated with arrows together with their irreducible representations.

  works on small NCs (d ∼ 5 nm).[START_REF] Portalès | Probing Atomic Ordering and Multiple Twinning in Metal Nanocrystals through their Vibrations[END_REF]43 In the present work, s 2 nm leading to s/d 1 10

  Seed solution: under strong stirring, 100 µL of NaBH 4 (0.05 M) and NaOH (0.05 M) solution was injected with one stroke in 4 mL of HAuCl 4 (0.5 mM) and CTAC (95 mM) solution at room temperature. The color turned from yellow-orange to red. Ripening took place during one hour at 85.Growth solution: at 30 and under slow stirring, 0.8 mL of AgNO 3 (0.01 M) solution was added to 40 mL of HAuCl 4 (0.5 mM) and CTAB (0.1 M) solution. 2 mL of hydroquinone (0.1 M) was mixed to the growth solution. The color turned from yelloworange to colorless. Finally, 1500, 1300, 1100, 900, 700, 500, 300, 150, 100 or 50 µL of the seed solution was added and the growth solution was let undisturbed overnight.For the purification of the nanocrystals, 10 mL of solution was centrifuged during 15 min at 4500 rpm and 40. The precipitate was redipersed in 10 mL of CTAB solution (1 mM). Centrifugation was repeated one more time and the precipitated nanocrystals were redispersed in 3 mL of CTAB solution (1 mM). The nanocrystals were redispersed with BDAC solution (0.5 M) to a total concentration: [BDAC] = 651.52 -4.41L with L the nanocrystal length. After precipitation during 18 h, gold nanocrystals were redispersed in 3 mL of CTAB solution (1 mM). The solution was centrifuged during 5 min at 5000 rpm and 40. The precipitate was redipersed in 3 mL of CTAB solution (1 mM). Centrifugation was repeated one more time and the precipitated nanocrystals were redispersed in 3 mL of CTAB solution (1 mM).

Acknowledgement

The authors acknowledge IMPC (Institut des Matériaux de Paris Centre, FR2482) for providing access to the JEOL1011 and JEOL2010 microscopes. N.G. acknowledges the support of Nouraine Fadili for the synthesis of gold nanorods. This work has been supported by the EIPHI Graduate School (contract "ANR-17-EURE-0002"). Calculations were performed using HPC resources from DNUM CCUB (Centre de Calcul de l'Université de Bourgogne).

Comparing with the analytical calculations confirms that only the lowest frequency ones are "pure" extensional modes. At higher frequency, diameter-dependent modes having the same symmetry also manifest.

Using the calculated frequencies reported in Figure 3A and the ones calculated for the extensional vibrations, we propose the following assignment. NBP#1 peaks at νw = 611 and 1264 m/s and NBP#2 peaks at 660 and 1298 m/s are assigned to the first 2 extensional modes. NBP#1 peak at νw = 989 m/s and NBP#2 peak at νw = 1021 m/s are assigned to the "m = 2" mode at νw = 999 m/s. The broad feature observed at νw = 1670 m/s for NBP#2 is close to the "m = 3" mode at νw = 1601 m/s. An additional narrow feature is observed for NBP#1 at about νw = 775 m/s. It does not correspond to one of the vibrations described above. Its frequency is close to that of the E' 1 mode which is the first overtone of the bending mode as calculated with the finite element approach (νw = 747 m/s).

The peaks observed for NBP#3 have significantly larger values of νw. Most of the modes observed for NBP#1 and 2 are masked in the tail of the elastic peak for NBP#3.

To assign the peaks, we first look at the modes corresponding to larger values of "m" as

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