Lucie Jacquet

Nicolas Meyer

Maximilien Libert

Frédéric De Geuser

Muriel Braccini
email: muriel.braccini@simap.grenoble-inp.fr

Rafael Estevez

Marc Mantel

Study of cleavage fracture in ferritic stainless steels Part I: Development and characterization of model microstructures

Keywords: ferritic stainless steels, model microstructures, thermomechanical processing, precipitation, interstitial elements

A major drawback in ferritic steels production and usage is their mechanical brittleness at temperatures close to ambient temperature. Precipitation and grain size appear as two major parameters in such cleavage brittle behavior. This is why six model microstructures have been elaborated from the same base of chemical composition, but with different elements additions and thermal treatments. The base composition is 18% chromium and 2% molybdenum to ensure an entirely ferritic matrix at any temperature even with 0.015% of both carbon and nitrogen. The addition of titanium or niobium changed the nature, size and location of the carbides and nitrides, while carefully chosen heat treatments varied the size of the grains. Microstructure characterizations down to very fine scales (TEM, SANS) combined with thermodynamics and diffusion modeling allowed analyzing precipitates formation as well as remaining interstitial elements (carbon and nitrogen) in solution in the ferritic matrix. This multi-scale analysis of the microstructures is important to understand the mechanical behavior of the alloys, which will be presented in a companion paper.

Introduction

Four main families of grades make up the metallurgy of stainless steels: austenitic, martensitic, ferritic and duplex stainless steels. These families are distinguished by the nature of their major constituent phases. Austenitic stainless steels, enriched with chromium and nickel, are the most widely produced (around 75% of the world market [START_REF] Cunat | L'acier inoxydable, d'un siècle à l'autre[END_REF]), and are appreciated for their mechanical properties (high ductility and strain hardenability, high resilience at low temperature) and their resistance to corrosion [START_REF] Cunat | L'acier inoxydable, d'un siècle à l'autre[END_REF][START_REF] Baroux | Les aciers inoxydables ferritiques à 17%Cr[END_REF][START_REF] Durand-Charre | La microstructure des aciers et des fontes[END_REF]. Ferritic steels, whose chromium content varies from 11 to 30%, have lower alloying element contents than austenitic steels, and do not contain nickel or only a residual content. In addition to their generally low cost, these steels have the particularity of being ferromagnetic, a necessary asset for the design of solenoid valves, for example, used in the automotive and household appliance fields. Ferritic grades can be an alternative to austenitic ones, some of them with very good corrosion resistance: AISI 444 (EN 1.4521) ferritic grade has a PREN (Pitting Resistance Equivalent Number) equivalent to that of AISI 316 austenitic grade. The major drawback of ferritic steels is the strong dependence of their mechanical behavior on temperature which causes mechanical brittleness at low temperatures for mild steels, and at room temperature for ferritic stainless steels [START_REF] Tanguy | Modélisation de l'essai charpy par l'approche locale de la rupture : application au cas de l'acier 16MND5 dans le domaine de transition[END_REF][START_REF] Tioguem | Identification of ductile to brittle transition temperature by using plane strain specimen in tensile test and correlation with instrumented Charpy impact test : experimental and numerical study[END_REF][START_REF] Godin | Effects of cooling path and resulting microstructure on the impact toughness of a hot stamping martensitic stainless steel[END_REF][START_REF] Beremin | A local criterion for cleavage fracture of a nuclear pressure vessel steel[END_REF]. Their production and uses are then limited because of brittle fracture.

The objective of this work is to understand the mechanisms that govern cleavage brittle fracture in ferritic stainless steels and to quantify the role of two microstructural parameters of major importance: precipitation and grain size. To achieve this goal, we have elaborated different microstructures to establish relations between precipitation and grain size and fracture properties. Two consecutive articles bring together the results of this research work. This first article focuses on the characterization of these microstructures resulting from the same base of chemical composition, namely 18% chromium and 2% molybdenum to ensure an entirely ferritic matrix at any temperature. The chemical compositions will be systematically expressed as a weight percentage. The carbon and nitrogen content is set at C + N ≈ 0.030%, which is a content accessible via current processing means with an AOD (Argon Oxygen Decarburization) [START_REF] Saleil | La production des aciers inoxydables Histoire de son développement et des procédés de fabrication. Partie II. Évolutions de l'élaboration des aciers inoxydables au four électrique à arc[END_REF]. The addition of titanium or niobium changes the nature, size and location of the carbides and nitrides, while carefully chosen heat treatments will vary the size of the grains to obtain six distinct microstructures. The second article brings together the mechanical characterizations (impact tests, tensile tests with smooth and notched axisymmetric specimens) and the description of the mechanisms that govern cleavage brittle fracture of the six microstructures.

During cooling, precipitation of chromium carbides and nitrides in ferritic stainless steel is due to the drastic decrease of carbon and nitrogen solubility limit in ferrite [START_REF] De Cooman | Lectures on Stainless Steel[END_REF]. The second factor which inevitably leads to the precipitation of Cr2N nitrides and (Cr,Fe)23C6 carbides is the high diffusion rate of the interstitial elements in the ferritic structure. Thus, even during a hyperquenching, this precipitation cannot be avoided contrary to what is observed in austenitic stainless steels. These precipitates germinate intra or intergranularly depending on the cooling conditions: inside the grains for high cooling rates and at the grain boundaries for lower cooling rates [START_REF] Sarkari Khorrami | Study on microstructure and mechanical characteristics of low-carbon steel and ferritic stainless steel joints[END_REF]. This precipitation has an embrittlement effect [START_REF] Abo | The role of carbon and nitrogen on the toughness and intergranular corrosion of ferritic stainless steels[END_REF] and causes sensitization of grain boundaries to intergranular corrosion due to local chromium depletion on either side of the grain boundary. Ductility and corrosion resistance can be restored by an annealing heat treatment between 750 and 900 °C during which the carbides and nitrides coalesce and the chromium content is homogenized in the ferrite grains [START_REF] Sassoulas | Traitements thermiques des aciers inoxydables[END_REF]. The precipitation of chromium carbides and nitrides can also be avoided by adding a sufficient amount of stabilizing elements such as titanium and niobium, that have a greater affinity with carbon and nitrogen than chromium. The intragranular carbonitrides formed in this case, TiN, TiC, Nb(C,N), precipitate at a higher temperature than chromium carbides and nitrides [START_REF] Baroux | Les aciers inoxydables ferritiques à 17%Cr[END_REF][START_REF] Ostrowski | Precipitation of titanium carbonitrides in as-cast 17% chromium stainless steels[END_REF]. Stabilization tends to limit the brittleness of ferritic grades [START_REF] Redmond | Toughness of 18Cr-2Mo stainless steel[END_REF] but over-stabilization can be harmful due to the precipitation of intermetallic phases [START_REF] Mantel | Relation entre la microstructure et la résistance au fluage et à l'oxydation d'aciers à 17% de chrome stabilisés par du zirconium et du niobium[END_REF], 16]. During the production of these steels, deoxidation and desulphurization reactions take place to avoid inclusions of oxides and sulphides. However, very low contents of these elements remain (<0.010%) and inclusions of lime silicoaluminate oxides and manganese sulphides are observed in practice. Other phases can also form and lead to embrittlement, such as intermetallic phases of sigma, chi or alpha prime type [START_REF] Cunat | L'acier inoxydable, d'un siècle à l'autre[END_REF][START_REF] Sello | Laves phase embrittlement of the ferritic stainless steel type AISI 441[END_REF]. However, the kinetics of formation of these phases is relatively slow in ferritic steels and these intermetallic phases are not encountered following recrystallization heat treatments or even during welding operations. They will therefore not be studied in this work. The state of precipitation in steels stabilized with titanium and/or niobium is well described in the literature [START_REF] Chemelle | Mise en solution et précipitation des carbonitrures de Titane et de Niobium dans les aciers ferritiques stabilisés[END_REF] : as long as the quantity of stabilizers is sufficient, all the carbon and nitrogen precipitate in the form of carbonitrides of titanium and niobium. In unstabilized grades, the chemical composition and crystallography of chromium carbides and nitrides are clearly identified, but no study indicates whether carbon and nitrogen completely precipitate in the ferritic matrix following hyperquenching. Indeed, the quantitative characterization of this fine precipitation, the size of which can be nanometric, is complex and requires heavy means of investigation. In this first article, we explain our choices of chemical compositions and thermomechanical treatments to develop the six model microstructures for which only the precipitation and/or the size of the grains from laboratory ingots vary. We characterize the three microstructures stabilized with titanium or niobium and the three unstabilized microstructures using increasingly powerful tools to quantify grain size and study precipitation: optical microscopy (OM), scanning (SEM) and transmission (TEM) electron microscopies, small-angle neutron scattering (SANS). We will then discuss the presence or absence of carbon and nitrogen in solid solution, depending on the temperature and duration of the heat treatment and the rate of cooling of the ferrite in unstabilized grades.

Experimental methods

Development of the studied microstructures

To study the brittle fracture of stainless steels with a 100% ferritic matrix, the first step is to develop model materials. In order to vary only one element at a time to study its influence, we worked with laboratory casts. To ensure a ferritic structure from solidification and at any temperature, Figure 1 shows that 18% chromium is sufficient for a carbon content of 0.03%. 2% of molybdenum, an alpha-gene element, were also added to approach the chemical composition of AISI 444 industrial cast (18Cr-2Mo stabilized with Ti and Nb). Six microstructures were made from three different grades: one stabilized with titanium, one stabilized with niobium and the last one unstabilized. The carbon and nitrogen contents were kept constant for all the grades with a value of C + N ~ 0.030%. The Ugitech Research Center (CRU) is able to produce ingots of 25 kg of metal, with a square section of 10 x 10 cm², in a VIM (Vacuum Induction Melting) furnace. In order to produce enough metal for the study, five ingots were elaborated: Ti1 for the titanium stabilized grade, Nb1 and Nb2 for the niobium stabilized grades and Cr1 and Cr2 ingots for the unstabilized grades (Table 1). Since Nb1 and Nb2 ingots have very similar chemical compositions, they are considered as the same alloy, as well as for Cr1 and Cr2 ingots.

To obtain the six model microstructures, different ranges of thermomechanical treatments were performed on the alloys in order to vary and control precipitation and grain size. These ranges of thermomechanical treatments consist of forging ingots into bars, a heat treatment at 1050°C, a cold rolling step and then one or two final heat treatments; these steps are detailed below.

(i) The ingots were forged in 40 mm x 20 mm section bars in order to break the solidification structure and allow their cold rolling with a roller mill available at the CRU. Following forging, the bars were cut in half lengthwise before undergoing a first heat treatment at 1050°C for 15 minutes followed by water quenching. The purpose of this heat treatment is to reduce the structural differences between the edge and the core of the bar. Indeed, following forging, at the edge of the bar the grains are coarse and elongated while they are finer, recrystallized and equiaxed in the center. In addition, rapid cooling by water quenching limits the precipitation of chromium carbides and nitrides, dissolved back into solid solution when maintained at 1050°C for the unstabilized grade.

(ii) Following this first heat treatment, the bars were deformed by cold rolling. Between each rolling pass, the bars were a quarter turned to reduce the square section from 19x19 mm² to 12.5x12.5 mm². Obtaining a square section is necessary for machining the impact and tensile specimen. The cold deformation, at a reduction rate of approximately 50%, facilitates the recrystallization of the grains during the final heat treatments.

(iii) The final heat treatments depend on the microstructures.

-The Ti (Ti1 ingot), Nb (Nb1 ingot) and Cr (Cr1 ingot) microstructures were obtained via a recrystallization heat treatment at 1000°C for 5 minutes followed by water quenching. The thermomechanical treatment range illustrated in Figure 2(a) constitutes our reference range in order to obtain a recrystallized fine-grained microstructure. -The NbG microstructure (Nb2 ingot) was obtained following a heat treatment in several phases: holding at 1250°C for 30 minutes to recrystallize and then grow the grains, followed by a cooling at 1000°C in 3 hours, followed by a hold for 30 minutes at 1000°C before water quenching (Figure 2(b)). The aim of this heat treatment is to obtain a homogeneous grain growth, which necessitates the dissolution of niobium carbonitrides, and then to re-precipitate the Nb(C,N) in order to obtain the same precipitation as the one in the Nb microstructure. -The Cr0 microstructure was obtained following a final heat treatment at 1050°C for 10 minutes followed by water quenching (Figure 2(c)). As we will see later in this article, coarse chromium carbides and nitrides are present in the Cr microstructure.

Maintaining the final heat treatment of the Cr0 microstructure at 1050°C avoid these coarse precipitates thanks to the complete re-solution of the chromium carbides and nitrides. -Finally, the last microstructure, CrP, was obtained from the Cr microstructure with an additional treatment at 850°C for 2 hours followed by water quenching (Figure 2(d)). This latter heat treatment was chosen to completely precipitate carbon and nitrogen in the form of chromium carbides and nitrides. Equilibrium phase diagrams obtained with the ThermoCalc software indicate the expected phases, in addition to the ferrite, for each microstructure. In the Ti microstructure, the presence of nitrides, or even carbonitrides of titanium is expected. In the Nb and NbG microstructures, only the presence of niobium carbonitrides is expected in addition to the ferrite. For the CrP microstructure, maintaining at 850°C must lead to massive precipitation of chromium carbides and nitrides, while heat treatments at 1 000°C (Cr microstructure) and at 1050°C (Cr0 microstructure) should avoid this precipitation if water quenching is effective (Figure 3). The precipitation obtained in the six microstructures will be described in the next section of the article.

Tools for microstructural characterizations

Grain size was measured by image analysis method following the ASTM E112 standard after surface polishing and color etching of the samples. For this etching, the sample is immersed for 10 to 30 seconds in a solution heated to 70°C and containing 110 ml of water, 12 ml of sulfuric acid, 4 ml of hydrofluoric acid and 5 to 6 drops of nitric acid. This etching grows an oxide film on the surface, and generates different color under polarized light according to crystal orientation. Grains which have close orientations appear in similar colors. In addition, a homogeneous color in a grain is a sign that the grain is fully recrystallized. To observe the precipitation under optical and scanning electron microscopes, the surface was prepared with Vilella etching or simple polishing. Two scanning electron microscopes were used; the SEM JEOL 7000 AF from the CRU and the SEM FEG ZEISS GeminiSEM 500 from the Consortium of Common Technological Means (CMTC) of Grenoble INP. The qualitative observation of precipitation was supplemented by EDS (Energy Dispersive X-ray Spectroscopy) analyzes. A quantitative analysis of the precipitation of the stabilized microstructures was carried out at the CRU; a large number of images were analyzed using automation of image capture and processing. Figure 4 illustrates the steps in image processing: two threshold values were set for the Nb and NbG microstructures to separate the oxides from niobium carbonitrides and a single threshold value for the Ti microstructure (because oxides are at the center of titanium carbonitrides). The nature of the particles counted is verified thanks to an EDS point analysis at the center of mass of each of them. The conditions for acquiring the images and their processing are given in Two transmission electron microscopes were used to characterize the precipitation of unstabilized microstructures: FEG JEOL 2100F 200 keV TEM at CRU and at CMTC. Classically prepared replicas and thin sections were observed in addition to a thin section of the Cr0 microstructure prepared by FIB SEM. Finally, the finest objects of the studied microstructures were analyzed by small angle neutron scattering (SANS) on the D11 line of the Laue Langevin Institute (ILL). 3 mm thick wafers were prepared for this purpose. The reader may refer to the work of [START_REF] Perrard | A small-angle neutron scattering study of fine-scale NbC precipitation kinetics in the α-Fe-Nb-C system[END_REF] for more details on the sample preparation method and the SANS experiment. The wavelength of the neutron beam was set at 𝜆 = 5 Å ± 0.5 Å, above the Bragg cut-off, so as to avoid any parasitic (multiple)diffraction. Two detector-to-samples distances were used, 2.5 m and 20 m, so that the scattering vector 𝑞 ranged from 0.004 to 0.15 Å -1 .

A saturating magnetic field of about 1.2 T was applied by an electro-magnet, ensuring that the magnetic moment was fully aligned with the field. In these conditions, the SANS intensity collected is the sum of two components: magnetic and nuclear. Both contributions can be separated by a cos 2 fit of the signal along the azimuthal angle. Both the magnetic contrast signal and the nuclear contrast signal has been fitted to the same interpretation model given by the equation [START_REF] Baroux | Les aciers inoxydables ferritiques à 17%Cr[END_REF] in which the first term on the right hand side refers to a Porod behavior originating from any heterogeneity in the sample coarser than what is accessible by the qrange. The second term 𝐿 is a constant accounting for the incoherent contribution of the signal, which in the nuclear case is mainly due to the isotopic disorder. The third term is the contribution of the precipitates which are considered to be spherical with radius 𝑅 with a Schulz size distribution of width 𝑠 = 0.3. 𝑓 𝑣 is the volume fraction of particles and ∆𝜌 is the scattering length density contrast (magnetic or nuclear).

𝐼(𝑞) = ( 𝑘 𝑞 ) 4 + 𝐿 + 𝑓(𝑅, 𝑠, 𝑓 𝑣 , ∆𝜌) (2)
The volume fraction 𝑓 𝑣 and the scattering length density contrast Δ𝜌 cannot be extracted independently from the fit of the data. In fact, in the low volume fraction limit as it is the case here, only the product |Δ𝜌| 2 ⋅ 𝑓 𝑣 will result from the fit of the data. Estimation of the volume fraction will then necessitate assumptions on the composition of the precipitating phases to compute the scattering length density Δ𝜌 as will be discussed in section 4.2.

Results

Grain structure

The grains of the six model microstructures are recrystallized and equiaxed from the edge to the center of the bar (Figure 5). The grains of the Ti, Nb, Cr and CrP microstructures have roughly the same size, with an average diameter of 70 µm. The grains in the NbG microstructure are ten times larger than the grains in the Nb microstructure. Holding at 1250 °C for 30 minutes, followed by a slow drop in temperature to 1000 °C was effective in increasing the grain size. Note that the grains in the Cr0 microstructure are also relatively larger; their average diameter is about three times that of the grains in the Cr and CrP microstructures. Maintaining at 1050 °C for 10 minutes allowed the dissolution of the chromium carbides and nitrides, as it will be seen below, but had free the grain boundaries from their pinning.

Precipitation in the stabilized microstructures

In the Ti microstructure, particles visible at low magnification are homogeneously distributed in the ferrite grains. With SEM observation and EDS analysis, the chemical elements of these particles are identified: the nucleus is rich in Al and O while the envelope is enriched in Ti (Figure 6). Note that these particles have particular shapes, with salient angles. At higher magnification, Figure 7 reveals the outer envelope of the compounds, rich in Mo, and the presence of a fine precipitation rich in titanium distributed in the ferritic matrix. The compounds rich in Al and O are oxides that precipitate in the liquid metal and serve as nucleus sites for titanium nitrides TiN. TiN are then enveloped by titanium carbides (Ti, Mo)C that precipitated at lower temperatures. The two microstructures stabilized with niobium, Nb and NbG, present a distributed homogeneous intragranular precipitation, visible in the SEM images in Figure 8. An EDS analysis (see Figure 9) allowed to identify two types of particles: oxides, which appear darker than the matrix in the images in Figure 8, and niobium carbonitrides Nb(C, N) or (Nb,Mo)(C, N), enriched in molybdenum, brighter than the matrix. The uniformity of the silicon mapping and the absence of iron indicate that those precipitates are not Fe2Nb intermetallics but Nb(C, N), which is consistent with the low niobium overstabilization of the grades (ΔNb (Nb1) = 0.023% and ΔNb (Nb2) = 0.020%). The observed precipitation is consistent with the expected equilibrium precipitation of the phase diagram (Figure 3). It is noted that niobium carbonitrides appear to be thicker in the NbG microstructure, which will be verified in the following section. Thanks to quantitative SEM analysis, particles size distribution is obtained using their equivalent diameter. While niobium carbonitrides and oxides can be quantified separately in the Nb and NbG microstructures, titanium nitrides and oxides are counted as a unique inclusion due to the fact that the oxides are circled by the titanium carbonitrides in the Ti microstructure. The obtained equivalent diameter histograms are given in Figure 10. Only particles with an equivalent diameter greater than or equal to 1 μm are counted. Finally, in the two Nb-stabilized microstructures, we note that oxides are the largest particles present although much less numerous than the carbonitride precipitates. Indeed, the presence of oxygen between 50 and 100 ppm is inevitable in the castings despite deoxidation with aluminum and silicon. Our six model microstructures exhibit a similar population of oxides.

Precipitation in unstabilized microstructures

In this part, we focus on the precipitation of the three microstructures obtained from the unstabilized grade: CrP, Cr and Cr0. Optical micrographs in figure 11 allow a first comparison of the precipitation of these three microstructures. In the CrP and Cr microstructures, intra and intergranular precipitation is observed while, at this magnification, no precipitate is visible in the Cr0 microstructure (apart from the oxides inclusions). In view of the recrystallization heat treatment of the Cr microstructure (hold at 1000°C for 5 minutes followed by water quenching), the presence of micrometric carbides and nitrides of chromium is surprising and we explain it as follows: carbides and nitrides precipitated during the rise in temperature and could not be completely dissolved back into solid solution because the holding time was too short and/or the temperature too low. For the Cr0 microstructure, with a recrystallization treatment at 1050°C for 10 minutes followed by rapid cooling by water quenching, the chromium carbides and nitrides formed during the rise in temperature were dissolved. Finally, the CrP microstructure exhibits numerous micrometric particles thanks to the precipitation heat treatment at 850°C for 2 h. TEM observations confirm the presence of micrometric M23C6 carbides and Cr2X nitrides (being mostly Cr2N) in the CrP and Cr microstructures (Figures 12(a) and (b)). In addition, Cr2X of around twenty nm are agglomerated at the grain boundaries in the Cr microstructure (Figure 12(d)). For the Cr0 microstructure, agglomerates of Cr2X precipitates (30 nm in size) are also visible at grain boundaries (Figures 12(c) and (e)), while fine intragranular precipitates, of a few nm, were identified on a thin section (Figure 12(f)). Small-angle neutron scattering (SANS) experiment at ILL complements the study of precipitation in unstabilized microstructures. In the configuration used, SANS is sensitive to objects of size between few nm to hundreds of nm. In the CrP microstructure, no precipitation of this range of size has been detected, so that the signal consists only in the Porod and incoherent contributions. In the Cr and Cr0 microstructures, objects with a radius of around ten nm are present (Figure 13). For the Cr0 microstructure, the quantified precipitation could be the one observed with TEM on a thin intragranular section (Figure 12 (f)). The SANS data fit to equation (2) will be discussed in the next section.

Discussion

Two of the three unstabilized microstructures, Cr and Cr0 microstructures, have been water quenched from temperatures of 1000°C or above, temperature range where C and N are completely soluble in the ferrite (Figure 14). In this part, the presence of C and N in solid solution in ferrite in those microstructures is discussed by comparing the theoretical volume fractions of precipitates to the ones measured thanks to the different methods described previously (SEM, TEM and SANS). The difference between the theoretical and measured precipitates volume fractions will help to estimate the amount of C and N in solid solution. The Cr0 microstructure is chosen as an example in the following.

Theoretical volume fractions of precipitates

Since cooling by water quenching is particularly rapid, the thermodynamic equilibrium for which 𝑓 𝑣 𝑒𝑞 (𝐶𝑟 2 𝑋) = 0.2% et 𝑓 𝑣 𝑒𝑞 (𝑀 23 𝐶 6 ) = 0.24% is certainly not reached. Figure 15 groups together the changes in the volume fractions 𝑓 𝑣 𝑚𝑒𝑞 of the three types of precipitation observed as a function of temperature for the metastable equilibrium. Each volume fraction is calculated through the equilibrium between ferrite and one type of precipitate, excluding the other phases of the calculation. These fractions increase when the temperature decreases until they stabilize around 600°C, a temperature which seems to constitute an upper limit for the fraction of precipitates with:

𝑓 𝑣 𝑚𝑒𝑞 (𝐶𝑟 2 𝑋) = 0.34%, 𝑓 𝑣 𝑒𝑞 (𝑀 23 𝐶 6 ) = 0.24% and 𝑓 𝑣 𝑒𝑞 (𝑀𝑋) = 0.17%.

We will compare these theoretical volume fractions with experimentally measured fractions.

Volume fraction of intragranular precipitates quantified with SANS

Intra and intergranular precipitates have been identified in the Cr0 microstructure thanks to TEM observations. In addition, using SANS, a fine precipitation was quantified, but with an unknown nature and location. These may be intragranular precipitates like in Figure 12 (f), intergranular precipitates like in Figure 12 (c), or precipitates not identified by TEM. Since the intergranular precipitates are agglomerated, they would give rise to SANS signal at much lower angle than if they were isolated, and it is reasonable to assume that they would mainly contribute to the Porod contribution "baseline" so that the precipitates quantified by fitting the precipitates contribution to the SANS signal are most likely the intragranular precipitates. Therefore, we will assume that the precipitates quantified with SANS signal are the ones observed with TEM inside the grains. Then the total volume fraction of precipitates will be the addition of the volume fraction of intergranular precipitates measured on TEM images and the volume fraction of precipitates quantified with SANS. If our assumption is wrong, then the total volume fraction of precipitates will be underestimated.

As discussed above, to estimate the volume fraction from the SANS data, the scattering length density contrast must be determined: it depends on the composition of the phases and on the origin of the contrast (nuclear or magnetic). The magnetic scattering length density has a dependence with the composition which is non-trivial [START_REF] Tissot | Comparison between SANS and APT measurements in a thermally aged Fe-19 at.%Cr alloy[END_REF]. It was therefore chosen to estimate the volume fraction of the precipitates from the nuclear component of the signal, for which the composition dependence of the scattering length density is potentially more discriminant.

As discussed, what is extracted from the fit is the product |Δ𝜌| 2 ⋅ 𝑓 𝑣 . The scattering length density contrast Δ𝜌 𝑛𝑢𝑐 is given by the following expression:

∆𝜌 𝑛𝑢𝑐 =

Mean atomic volume of the precipitates or matrix

The nuclear diffusion length of the chemical elements of the metal is calculated from the equation 𝜎 𝑐𝑜ℎ = 4𝜋 𝑏². The coherent nuclear diffusion cross section 𝜎 𝑐𝑜ℎ of each chemical element is the sum of the cross sections of each of its isotopes weighted by their rate of presence. In practice, we will consider that 𝑉 𝑎𝑡 𝑚 ≈ 𝑉 𝑎𝑡 𝑝 because the precipitates and the matrix are constituted by the same atoms. The nominal composition of the matrix remains the same despite the precipitation of the particles. This assumption is valid for carbon and nitrogen because the nominal atomic composition of the matrix is already very low compared to that of the particles formed. If 𝑐 𝐶,𝑁 𝑚 tends to 0, the difference 𝑐 𝐶,𝑁 𝑝 -𝑐 𝐶,𝑁 𝑚 will be only slightly modified.

For the other chemical elements present in the precipitates, the volume fractions of precipitates will be low enough to consider that the chromium and the iron which leave the matrix to enrich these particles do not modify the average content of the matrix sufficiently to have a significant influence. The next step in the interpretation of the analysis of the data acquired with SANS requires assumptions on the composition, and therefore on the nature of the precipitation studied. The precipitates likely to be present in unstabilized ferritic grades are chromium carbides M23C6, chromium nitrides Cr2X or M2X and MX where M denotes iron, chromium, molybdenum, titanium and X carbon and nitrogen. Table 3 shows the volume fractions obtained from the SANS data fitting of the scattering length density for each potential phase in the Cr0 microstructure. The iron, chromium, molybdenum and titanium contents are those measured in TEM by EDS on the observed precipitates. Since the carbon and nitrogen contents were not quantified by EDS, we estimated that there is no nitrogen in the M23C6 and that the carbon represents between 0 and 50% of the share of light elements in Cr2X and between 0 and 25% in MX, the rest being nitrogen. The volume fractions in Table 3 give an estimate of the actual volume fraction of the quantified precipitation.

Volume fraction of intergranular precipitates measured from TEM images

The volume fraction of intergranular precipitates is estimated experimentally via TEM images before being reinforced by simulating the growth of a germ with DICTRA software. Fine precipitates agglomerated at grain boundaries are present in the Cr0 microstructure (Figures 12 (c) and (e)). The surface of these particles covers about 65% of the surface of the grain boundary. In order to estimate the volume fraction occupied by these particles the following assumptions are made: all the grain boundaries of the Cr0 microstructure are covered by this film of particles and, a single particle on average occupies the thickness of the intergranular film.

The volume fraction of particles at grain boundaries 𝑓 𝑣 𝑝𝐺𝐵 can then be estimated using the following equation:

𝑓 𝑣 𝑝𝐺𝐵 = 𝑉 𝑝𝐺𝐵 𝑉 𝑔𝑟𝑎𝑖𝑛 = 𝑆 𝑝𝐺𝐵 * 𝑒 * 𝑛 𝑉 𝑔𝑟𝑎𝑖𝑛 = 𝑆 𝑔𝑟𝑎𝑖𝑛 2 * 𝑓 𝑠 𝑝𝐺𝐵 * 𝑒 * 𝑛 𝑉 𝑔𝑟𝑎𝑖𝑛 (5)

Surface fraction of particles at grain boundaries

The volume fraction of particles at the grain boundaries 𝑓 𝑣 𝑝𝐺𝐵 is thus estimated at 0.02% for the Cr0 microstructure assuming the intergranular particles are cylinders.

In order to support those measurements from TEM images, thermodynamic calculations were carried out with the Thermo-Calc software and the DICTRA module (see Appendix A). First, the driving force of the two stable phases, M23C6 and Cr2X, that may form in the unstabilized microstructures (see section 2.1, "X" being mostly nitrogen) was calculated. Those calculations have shown that the Cr2X phase is the most prone to form during cooling. Second, simulating the growth of a 1 nm thick germ at the boundary of a spherical grain during quenching, it was shown that the size of a Cr2X precipitate at the grain boundary cannot exceed about twenty nm in thickness. Those numerical results are in agreement with our experimental observations: the precipitates mainly present in the Cr0 microstructure are Cr2X and the thickness of the particles in the grain boundaries is about thirty nanometers. Finally, the corresponding volume fraction obtained from such calculations is 0.02%, in agreement with what was measured here from TEM images and ten times lower that what is predicted from thermodynamic equilibrium calculations. Thus, we can conclude that, during water quenching, the proportion of nitrogen and carbon which precipitate at the grain boundaries represents only about 10% of their nominal content.

Carbon and nitrogen in solid solution

In order to determine if carbon and nitrogen remain in solid solution, Table 4 groups together the volume fractions estimated previously for the Cr0 microstructure from SANS measurements (section 4.2) as well as the intergranular precipitation volume fraction, for which the numerical calculation and the estimate from TEM image analysis gave the same value (section 4.3). Without concluding on the nature of the precipitation quantified with neutron scattering, we notice that the obtained total volume fraction is far less than the volume fraction of precipitates at metastable equilibrium, as calculated with ThermoCalc software in section 4.1.

Intergranular precipitation (TEM)

Precipitation quantified with the SANS Thus, for the Cr0 microstructure, assuming that the hypothesis made to estimate the volume fractions of particles are correct, either a precipitation containing carbon and nitrogen has not been quantified, or carbon and nitrogen remain in solid solution in supersaturation at room temperature. The difference between the expected volume fraction of precipitates and the one estimated here is at least 0.1%. Moreover, since we used increasingly sophisticated characterization tools, allowing the study of finer and finer precipitates, down to the nanometer, the precipitation of the Cr0 microstructure was particularly studied. So, we conclude that a significant amount of carbon and nitrogen remains in solid solution, from 30% to 80% of the initial amount, depending on the nature of the precipitation quantified with the neutron scattering. [START_REF] Van Zwieten | Some considerations on the toughness properties of ferritic stainless steels-A brief review[END_REF] and [START_REF] Abo | The role of carbon and nitrogen on the toughness and intergranular corrosion of ferritic stainless steels[END_REF] explained that with a heat treatment to re-dissolve the chromium carbides and nitrides followed by water quenching, the grain boundaries of ferritic stainless steels are free from precipitates. The deployment and improvement of characterization tools since the publication of their articles have enabled us to conclude the opposite by observing nanometric precipitation thanks to TEM and SANS.

For the Cr microstructure, the same approach is more complex to apply because many precipitates are present in the grains with micrometric sizes for which it is difficult to give an estimate of the volume fraction (Figure 11). In this case, the sum 𝑓 𝑣 𝑝𝐺𝑟𝑎𝑖𝑛 + 𝑓 𝑣 𝑝𝐺𝐵 + 𝑓 𝑣 𝑆𝐴𝑁𝑆 is of the same order of magnitude as the theoretical volume fraction determined using Thermo-Calc software with 𝑓 𝑣 𝑝𝐺𝑟𝑎𝑖𝑛 ∈ [0.13% ; 0.35%].

Nevertheless, in the CrP microstructure, the precipitates are more numerous and larger than in the Cr microstructure. Yet, the heat treatment at 850°C, which distinguishes the CrP microstructure from the Cr, allows the precipitation of carbon and nitrogen but without prior dissolution. The precipitates observed in the CrP microstructure certainly come from the reorganization of existing precipitates (coalescence) and also from new seeds formed with carbon and nitrogen still present in solid solution before the heat treatment at 850°C. In addition, tensile tests performed at room temperature reveal that the elastic limit of the Cr microstructure is 100 MPa greater than the one of the CrP microstructure (Table 5). This difference cannot be explained by grain size effect since grain have similar size in both microstructures (Figure 5); neither by precipitation effect since precipitates are more numerous in CrP. Thus, the presence of carbon and nitrogen in supersaturated solid solution certainly justifies these differences in microstructural and mechanical properties. Moreover, we notice from Table 5 that the elastic limit of Cr0 is even higher (200 MPa greater than the elastic limit of the CrP microstructure) certainly mostly due to the presence of C and N in solid solution.

Unstabilized microstructure Yield strength at 25 °C CrP 338 ± 1 MPa Cr 450 ± 10 MPa Cr0 539 ± 5 MPa

Conclusions

This first article devoted to the study of brittle fracture by cleavage in ferritic stainless steels with 18% Cr and 2% Mo focuses on the development and characterization of six model microstructures, for which the grain size, the nature and size of the precipitates and the presence of carbon and nitrogen in solid solution change.

Using two different stabilizing elements, Nb and Ti microstructures lead to comparable matrix and grain size (of about 70 µm) but with precipitates of different nature and size. In the Ti microstructure, Ti(N,C) precipitates with an angular shape and an equivalent diameter up to 4-5 µm are observed, while in the Nb microstructure Nb(C,N) precipitates are globular, smaller (equivalent diameter less than 2 µm) and more numerous. In the NbG microstructure, the precipitation is similar to the one in the Nb microstructure, even if the precipitates size is slightly larger. But the important differences between those two microstructures is the grain size, which is 10 times larger in the NbG microstructure. Thus the heat treatment consisting in a hold of 30 min at 1250°C followed by a slow cooling to 1000°C and a hold of 30 min was effective in changing the grain size while leading to a similar precipitation.

For the unstabilized microstructures, CrP and Cr microstructures have the same grain size (similar to the Nb and Ti microstructures) but the additional heat treatment at 850°C on CrP microstructure modifies the state of precipitation. While in both microstructures M23C6 precipitates inside the grains and Cr2X precipitates at the grain boundaries, the precipitates are more numerous and larger in the CrP microstructure. For the Cr0 microstructure, the dissolution heat treatment at 1050°C followed by water quenching cannot avoid chromium carbides and nitrides precipitation. However, a major part of carbon and nitrogen remain in solution in the ferrite at room temperature and harden the ferritic matrix. Such an effect is also observed in the Cr microstructure but with a lesser extent. Part II of this article will focus on the mechanical properties and brittle fracture by cleavage of these six microstructures. Finally, the chemical composition of the Cr1 ingot was simplified to the elements of primary importance in the Cr2X precipitation. Two calculations were conducted: one with a mother phase of uniform composition with 18% chromium, 2% of molybdenum, 0.017% nitrogen and the balance of iron (composition N); and one with a mother phase of composition 18% chromium, 2% molybdenum, 0.017% nitrogen, 0.012% carbon and the balance in iron (composition N+C). The obtained evolution of the germ during cooling is given in Figure A.4 as a plot of germ thickness versus temperature. It is noted that the growth begins only at 960°C, temperature from which the precipitation of the Cr2X phase becomes stable. From around 750°C, the thickness of the precipitates remains more or less constant because the precipitation is gradually limited by diffusion at lower temperatures. The calculation can therefore be stopped à 700°C. At grain boundary, the film thickness predicted by the diffusive growth model is 17 nm with composition N, and almost 20 nm with composition N + C, assuming that the film grows on either side of the grain boundaries. The addition of carbon only slightly modifies the thickness of the precipitation because the X of Cr2X mainly denotes nitrogen (there is about 4 times more nitrogen than carbon in Cr2X at 800°C based on the metastable equilibrium calculation). These dimensions are close to the mean diameter of 30 nm of the intergranular particles measured experimentally with TEM for the Cr0 microstructure. .5 shows the evolution of the volume fraction of Cr2N at the grain boundaries as a function of the temperature during water quenching. By comparison with the expected volume fraction if the thermodynamic equilibrium is respected, it is noted that the growth of an intergranular germ can only capture 10% of the nitrogen present in solid solution during the water quenching. A volume fraction hardly greater would be expected for the N + C composition. This result is in agreement with our experimental observations presented in section 4.3: Cr2X precipitates at the grain boundaries represent a volume fraction of 0.02% only, ten times lower than the one expected from thermodynamic equilibrium calculations.

CRediT authorship contribution statement

Figure 1 :

 1 Figure 1: Isopleth section of the Fe-xCr-0.3Si-0.3Mn-0.03C system calculated with ThermoCalc software and the TCFE6 database.

Figure 2 :

 2 Figure 2: Schematics of the thermomechanical treatments to obtain the six model microstructures: the Ti, Nb and Cr model microstructures (a), the NbG microstructure (b), the Cr0 microstructure (c), the CrP microstructure (d)

Figure 3 :

 3 Figure 3: Phase diagrams for unstabilized grades, with "X" of Cr2X being mostly N, obtained with the TCFE10 base from Thermo-Calc software.

Figure 4 :

 4 Figure 4: Example of the automatic processing of the SEM image in backscattered electrons mode (a) to quantify size of oxides, particles darker than the matrix (c) and niobium carbonitrides, particles brighter than the matrix (d) in the Nb microstructure in the long direction.

Figure 5 :

 5 Figure 5: Grains of the six model microstructures in transverse direction under a polarized light microscope (coloring attack).

Figure 6 :

 6 Figure 6: Backscattered electron (BSE) mode SEM image on Ti microstructure (magnification x1000, OPS finish) (a). EDS point analyses on the two phases which constitute the complex particles (b).

Figure 7 :

 7 Figure 7: Backscattered electron (BSE) mode SEM image on Ti microstructure in the long direction (a) and X ray mapping at 15 kV (simple polishing) (b). Note that the intensity scale of the spectrum corresponding to the Ti-Kα line is greatly expanded to reveal the presence of Ti in the fine particles.

Figure 8 :

 8 Figure 8: Nb microstructures (a) and NbG (b) using SEM, images in backscattered mode, magnification x1000 (simple polishing).

Figure 9 :

 9 Figure 9: Nb microstructure SEM image in backscattered mode and X ray mapping at 15 kV.

Figure 10 :

 10 Figure 10: Size distribution of the majority particles and of the oxides with an equivalent diameter greater than or equal to 1 µm for the Ti, Nb and NbG microstructures Precipitation is different in Nb and NbG microstructures: large particles are more numerous in the NbG microstructure. During the temperature rise to 1250°C, necessary to make the grains grow homogeneously, the Nb(C, N) dissolved back into solid solution but then re-precipitated during the cooling and holding at 1000°C. In the Ti microstructure, the precipitates are larger, their equivalent diameter reaching up to 4-5 μm, but they are less numerous than the niobium carbonitrides of the Nb and NbG microstructures.Finally, in the two Nb-stabilized microstructures, we note that oxides are the largest particles present although much less numerous than the carbonitride precipitates. Indeed, the presence of oxygen between 50 and 100 ppm is inevitable in the castings despite deoxidation with aluminum and silicon. Our six model microstructures exhibit a similar population of oxides.

Figure 11 :

 11 Figure 11: Secondary electron (SE) mode SEM image of CrP, Cr and Cr0 (magnification x1000, Vilella attack).

Figure 12 :

 12 Figure 12: TEM images on replica of CrP (a), Cr (b) and (d) and Cr0 (c) and (e). TEM image of Cr0 (f) microstructure on a thin section prepared with SEM-FIB.

Figure 13 :

 13 Figure 13: Analysis of SANS data acquired on CrP, Cr and Cr0 microstructures

Figure 14 :

 14 Figure 14: Solubility limits of carbon and nitrogen in ferrite as a function of temperature for the composition of the Cr1 ingot, calculated with Thermo-Calc TCFE10 software.

Figure 15 :

 15 Figure 15: Volume fraction of Cr2X, M23C6 or MX with temperature for metastable equilibrium for the composition of the Cr1 ingot with Thermo-Calc TCFE10 software.

L. Jacquet:

  Methodology, Experiments and Characterizations, SANS, Thermodynamic calculations, Writing-original draft. R. Estevez: Supervision, Writing-review&editing. M. Braccini: Supervision, Writing-review&editing. F. De Geuser : SANS M. Libert: Characterizations. N. Meyer: Methodology, Thermodynamic calculations, Funding Acquisition, Supervision. M. Mantel: Methodology, Supervision, Writing-review&editing, Project Administration, Funding Acquisition.

Figure A. 2 :

 2 Figure A.2: Diagram illustrating the germ from the DICTRA calculation, a film on the surface of the calculation box whose radius R is 125 µm

Figure A. 3 :

 3 Figure A.3: Continuous cooling curves depending on the size of the part during water quenching [20].

Figure A. 4 :

 4 Figure A.4: Thickness of the germ during cooling on either side of the grain boundary.

Table 1 : Composition of laboratory casts

 1

	Ferritic grades	Heat	Micro-structure	Si	Mn	Ni	Cr	Mo	S (ppm)	P (10 -3 )	Al (10 -3 )	O (ppm)	C (10 -3 )	N (10 -3 )	Ti	Nb
	Titanium stabilized	Ti1	Ti	0.42	0.47	0.01	17.9	2.01	16	2	13	61	13	17	0.19	X
	Niobium	Nb1	Nb	0.52	0.51	0.01	18.1	2.02	17	3	18	93	14	17	X	0.24
	stabilized	Nb2	NbG	0.51	0.51	0.01	18.0	2.02	18	3	22	104	16	16	X	0.24
		Cr1	Cr, Cr0	0.48	0.49	0.01	18.0	2.03	10	3	14	87	12	17	X	X
	Unstabilized
		Cr2	CrP	0.50	0.50	0.01	18.0	2.02	17	2	23	105	15	15	X	X
	The titanium and niobium contents were chosen to trap all the carbon and nitrogen, but without
	excess in order to avoid the presence of intermetallic compounds. The values of titanium and
	niobium weight percentages are given by equation (1) with 𝑀 the molar mass of the element

Table 2

 2

	Microstructure	Ti	Nb		NbG
	Direction	Transversal	Transversal	Rolling	Transversal
	Magnification	500	800	1000	500
	Number of fields	750	1800	2504	750
	Field size (px²)	1024 x 1024	1024 x 1024	1024 x 1024	1024 x 1024
	Analyzed area (mm²)	42.6	39.9	35.5	42.6
	Minimum area of a
	particule to be counted	15	20	50	15
	(px)
	Minimum area of a
	particule having an equivalent diameter ≥ 1µm	15	38	59	15
	(px)

. More than 10,000 particles were quantified for each stabilized microstructure.

Table 2 : Experimental conditions for quantitative automatic SEM analyzes

 2

Table 3 : Assumptions about the nature and composition of precipitation quantified by SANS and associated volume fractions, determined from nuclear contrast, in the microstructure Cr0.

 3

	Particules			Fe				Cr	Mo		Ti		C	N	fv Cr0 (%)
	𝑀 23 𝐶 6	23 29	x 31%	23 29	x 65%	23 29	x 4%		0%	6 29	x 100%	0%	0.032
	𝐶𝑟 23 𝐶 6			0%	23 29	x 100%	0%		0%	6 29	x 100%	0%	0.012
	𝑀 2 (𝐶, 𝑁)	2 3	x 13%	2 3	x 87%	0%		0%	1 3	x 50%	1 3	x 50%	0.028
	𝐶𝑟 2 (𝐶, 𝑁)			0%	2 3	x 100%	0%		0%	1 3	x 50%	1 3	x 50%	0.02
	𝐶𝑟 2 𝑁			0%	2 3	x 100%	0%		0%		0%	1 3	x 100%	0.027
	𝑀𝑋	1 2	x 6%	1 2	x 44%	0%	1 2	x 50%	1 2	x 25%	1 2	x 75%	0.05
	𝑀𝑁	1 2	x 6%	1 2	x 44%	0%	1 2	x 50%		0%	1 2	x 100%	0.072

Table 4 : Estimated or calculated volume fraction for microstructure Cr0

 4

Table 5 : Yield strength, determined by tensile tests at room temperature, for the three unstabilized microstructures

 5

Acknowledgements

The authors are grateful for the financial support of Ugitech and SIMaP Grenoble INP. Moreover, the authors would like to thanks all researchers and technicians of the SIMaP laboratory and the Ugitech' research center and in particular Pierre Chemelle for his help to characterize the microstructures. In addition, we would like to thanks Ralf Schweins and the rest of the staff of the ILL for their help during the SANS experiment (http://dx.doi.org/10.5291/ILL-DATA.1-01-177).

Data availability

The data can be made available upon request to the corresponding author.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Intergranular precipitation calculations

Thermodynamic precipitation calculations were carried out to support the measurement of intergranular precipitates volume fraction from TEM images. The Thermo-Calc software and the TCFE10 and MOBFE5 databases were used. Previous analysis of the thermodynamic equilibrium in the unstabilized microstructures reveals that Cr2X and M23C6 phases precipitate in the ferrite (Figure 3 in section 2.1). Then, the first step of our approach consists in calculating the driving force of each of these phases in order to determine which one has the higher probability to form. The Thermo-Calc calculation was carried out by considering three phases: ferrite, a solid solution of hexagonal structure which can describe the Cr2X phase (HCP_A3) and the M23C6 phase. The chemical composition was limited to the major elements, i.e. 18% chromium, 2% molybdenum, 0.017% nitrogen, 0.012% carbon, the balance being iron. It was also assumed that no segregation occurs in the grain boundaries. The results are plotted in figure A.1: the driving force obtained for Cr2X precipitation is twice the driving force for M23C6. The higher the driving force, the smaller the critical radius of the nucleus and so the greater the probability of forming such a nucleus. Thus, Cr2X phase is the most prone to form precipitates (as we have observed experimentally by TEM). The second step was to study the growth of a germ during the water quenching using the DICTRA module. Since Cr2X is the most likely phase to form, only the growth of this phase was considered. The DICTRA calculation were conducted with the following assumptions:

-One dimension calculations. The intergranular precipitation is described with a spherical geometry. The calculation box dimension corresponds to the mean radius of the grains and is composed of two regions: the ferritic matrix and a seed of Cr2X (phase HCP_A3#2) of thickness 1 nm which lines the sphere in order to simulate the intergranular growth of the Cr2X phase (the germ is shown in green on the diagram in


Travis West

Kalun Leung

early prototypes and artistic practice with the mubone

The mubone (lowercase "m") is a family of instruments descended from the trombone family, a conceptual design space for trombone augmentations, and a growing musical practice rooted in this design space and the artistic affordances that emerge from it.

We present the design of the mubone and discuss our initial implementations. We then reflect on the beginnings of an artistic practice: playing mubone, as well as exploring how the instrument adapts to diverse creative contexts. We discuss mappings, musical exercises, and the development of Garcia, a sound-and-movement composition for mubone.

introduction

The concept of "trombone" applies to a fuzzy group of instruments with uncertain borders. Although there is a clear central embodiment of this instrument, various other forms exist that can be made of brass or plastic, have a slide or set of valves, and even exist in the form of a digital app on a smartphone [START_REF] Wang | World Stage: A Crowdsourcing Paradigm for Social / Mobile Music[END_REF]. Similarly, the concept of "mubone" is meant to delineate a fuzzy group of instruments with shared properties and a distinct but flexible essence.

We are still exploring the boundaries of this design space, or perhaps instrumentfamily space, and in so doing discovering the essence of the mubone. The conceptual approach of developing an instrument family rather than an individual instrument has been an especially useful tool in this work. Rather than developing the mubone, we have allowed ourselves the opportunity to make many mubones. This has stimulated constant experimentation, and helped us avoid getting too attached to costly but ultimately unsuccessful developments, such as the yoke controllers presented later. It also sensitizes us to the exploratory nature of our work. In this presentation, we will share our insights so far, based on technical and artistic development since 2019.

related work

The trombone is a common platform for augmentation and electroacoustic exploration.

Prior work has variously appropriated the trombone as a speaker resonator and MIDI slider [START_REF] Collins | Low Brass: The Evolution of Trombone-Propelled Electronics[END_REF], self-actuating feedback instrument [START_REF] Snyder | The Feedback Trombone: Controlling Feedback in Brass Instruments[END_REF], and augmented instrument [START_REF] Lemouton | Using the Augmented Trombone in 'I Will Not Kiss Your f.Ing Flag[END_REF], [START_REF] Farwell | Adapting the Trombone: A Suite of Electro-Acoustic Interventions for the Piece Rouse[END_REF].

The mubone, as a form of augmented trombone, is most directly related to other trombone augmentations; trombone expertise is the foundation of performance with these instruments. Farwell [START_REF] Farwell | Adapting the Trombone: A Suite of Electro-Acoustic Interventions for the Piece Rouse[END_REF] developed an ultrasonic slide position sensor, actuator, and loudspeaker mute for the trombone. Lemouton and colleagues [START_REF] Lemouton | Using the Augmented Trombone in 'I Will Not Kiss Your f.Ing Flag[END_REF] use an infrared laser to measure slide position. In our work, although we have attempted to measure slide position, the main focus has been on using the orientation of the instrument rather than the position of the slide. We were also inspired by the handle of the sackbut (a predecessor of the trombone) and the double slide controller of Tomás Henriques [START_REF] Farwell | Adapting the Trombone: A Suite of Electro-Acoustic Interventions for the Piece Rouse[END_REF] in the design of our handheld controllers.

Our granular synthesis environment, described below, draws on the established techniques of granular synthesis [START_REF] Lemouton | Using the Augmented Trombone in 'I Will Not Kiss Your f.Ing Flag[END_REF], especially standout implementations such as GrainTrain [START_REF] Henriques | Double Slide Controller[END_REF], Borderlands [START_REF] Roads | Microsound[END_REF], and Nathan Weitzner's 3D granular program 1 .

Although we did not initially consider them in our literature review, we realized later that our granular environment is also closely related to concatenative corpus-based synthesis [START_REF] Çamcı | GrainTrain: A Hand-Drawn Multi-Touch Interface for Granular Synthesis[END_REF], gesture following [START_REF] Carlson | Borderlands: An Audiovisual Interface for Granular Synthesis[END_REF], and real-time adaptive approaches to mapping design [START_REF] Schwarz | Real-Time Corpus-Based Concatenative Synthesis with CataRT[END_REF]. The approach we have taken with the mubone is notable for the performative strategy used to build a corpus and "train" the synthesis environment about gesture and mapping. Sound, movement, and mapping are all recorded in real time as part of a performance.

mubone implementation (presented by Travis)

So far, we have made approximately four different mubones (depending on how you count). In this section, I (Travis, the first author and the main technical contributor to the project) will describe their common features, summarizing the traits we believe may be essential for an instrument to be considered a mubone.

orientation sensor

The first augmentation we added to the trombone was an orientation sensor, and this has proven to be the most enduring and vital feature of a mubone. Typically mounted on, near, or as part of the counterweight (near the fine-tuning slide), the orientation sensor measures the pose of the mubone with respect to a global coordinate system.

All implementations to date have used the MPU-9250 magnetic-inertial measurement unit (MIMU) from InvenSense. This part is now discontinued, but any similar 9-DOF MIMU should work. The data from the MIMU is read, calibrated, and fused by a microcontroller and streamed to a nearby laptop in OSC format. I have mainly employed the ESP8266 in this capacity. To date I have consistently used the sensor fusion algorithm described by Sebastian Madgwick [START_REF] Caramiaux | Mapping Through Listening[END_REF], based on the complementary filter introduced by Robert Mahoney [START_REF] Françoise | Gesture-Sound Mapping by Demonstration in Interactive Music Systems[END_REF], to derive the orientation of the instrument from the sensor's measurements. The sensors calibration constants have been estimated using the method described by Tedaldi and colleagues for the accelerometer and gyroscope [START_REF] Madgwick | AHRS Algorithms and Calibration Solutions to Facilitate New Applications Using Low-Cost MEMS[END_REF], and the method described by Li and Li for the magnetometer [START_REF] Mahony | Nonlinear Complementary Filters on the Special Orthogonal Group[END_REF].

The full details of the calibration and sensor fusion processes are outside the scope of this article.

In most of our developments so far, the orientation has been subsequently examined to derive a vector representing the direction in which the mubone is pointed. The rotation (i.e. orientation) of the instrument is given by the sensor fusion algorithm in terms of a unit quaternion: This is not a convenient representation, so the quaternion is converted into a rotation matrix :

The rotation matrix represents the way the basis vectors of the global coordinate space are changed by the rotation. The first column corresponds to the x-axis, the second to the y-axis, and the third to the z-axis. If there is no rotation, the matrix is an identity matrix, and each column corresponds to the unit basis vector for that axis. When there is a rotation, each column represents the unit vector where the basis vectors are [START_REF] Wang | World Stage: A Crowdsourcing Paradigm for Social / Mobile Music[END_REF] From the rotation matrix it is easy to determine the vector representing the direction in which the mubone is pointed. In our work we align the global coordinate axes so that positive x points to the right, positive y towards the audience, and positive z towards the sky. We consider the mubone to have zero rotation when held naturally, pointing towards the audience, with the slide parallel to the ground. This alignment implies that the y-axis of the mubone coordinate system is aligned with the slide, so the second column of the rotation matrix is a unit vector aligned with the slide, i.e. the direction the instrument is pointing.

q = a + bi + cj + dk with ||q|| = = a + b + c + d 2 2 2 2 1 where i = 2 j = 2 k = 2 ijk = -1 R (2) R = ⎣ ⎡ a + b -c -d 2 2 2 2 2bc + 2ad 2bd -2ac 2bc -2ad a -b + c -d 2 2 2 2 2cd + 2ab 2bd + 2ac 2cd -2ab a -b -c + d
We alternately represent the pointing direction of the instrument as a vector (the second column of the rotation matrix) or as a pair of angles derived from the vector (i.e. and ).

Latitude and longitude are appropriate since the direction vector is a unit vector, and can thus be considered to represent a unique location on the surface of a sphere.

Alternatively, latitude can be called altitude and longitude called azimuth, reflecting a horizontal coordinate system.

We have not yet explored using the angular rate or acceleration data directly in our mappings, but we consider this essential future work that we will eventually undertake.

handheld controller

We have employed five different versions of a handheld controller in our different mubone prototypes. In our earliest experiments, we used a controller from the Nintendo Wii gaming console, including 11 buttons on the top surface, one trigger button, and an accelerometer.

v = (x, y, z) = (R , R , R ) 1,2 2,2 3,2 latitude = atan2(y, x) longitude = arcsin(z)
In later experiments, I developed a rough prototype interface using three buttons and an orientation sensor connected to an ESP8266 (picture not available).

Next, I developed two much more elaborate controllers that we called "yokes'' in rough analogy with the flight yoke in an airplane cockpit. The yokes included a rigid attachment to the slide, potentiometers embedded to measure the rotation and deflection of the controller with respect to the slide, four thumb buttons, a thumb joystick, and in the latter version an analog trigger and three additional buttons on the grip. Both of these prototypes used Teensy 3.2 microcontrollers and streamed SLIPencoded OSC data over a USB serial port to the laptop.

Image 1

Wii remote attached to the slide.

Image 2

The first version of the yoke controller.

Image 3

The second version of the yoke controller. An analog trigger and 3 buttons on the grip are not pictured.

gaming console.

Although all of these versions of the handheld controller have included some form of orientation or movement sensing, we only briefly experimented with the orientation data from the first yoke controller in our mapping experiments. Instead, it's the discrete buttons that have been most productive.

Performance-ready reliability has been the most essential differentiator between these controllers. Our more elaborate yoke controllers never saw the light of the stage due to their more complicated design and DIY construction. Although it is more glamorous and exciting, and perhaps a better opportunity for novel research, to design a custom controller, the reliability and ease of replacement that comes with using an off the shelf controller is advantageous. Commercial products have also not noticeably slowed down the artistic and design research we have been conducting; on the contrary, there Image 4 Player holding a Joy-con while manipulating the slide. The orientation sensor assembly is also visible on the fine-tuning slide.

have been more delays to our schedule due to technical challenges in building the (now broken) custom controllers. This may reflect wider issues in the NIME community of longevity [START_REF] Tedaldi | A Robust and Easy to Implement Method for IMU Calibration without External Equipments[END_REF] and reliability [START_REF] Li | A New Calibration Method for Tri-Axial Field Sensors in Strap-down Navigation Systems[END_REF]. Commercial parts also allow for simpler research replication [19][20].

However, as noted by a reviewer, off the shelf parts are not without their drawbacks.

Much of the data from the Joy-Con is difficult to access on most platforms. As drivers are not provided by Nintendo, to our knowledge Linux is the only operating system that has robust drivers developed by the open source community. There is also the ever-looming threat of product discontinuation, which will eventually and inevitably require a new version of the handheld controller to be developed or appropriated.

The future may hold opportunities for more rigorous design and engineering of new elaborate yokes, but the use of off the shelf commercial products has so far proved more successful for us despite its shortcomings.

mugranular

Throughout our work with the mubone to date, we have used the same synthesizer as the sonic core of the instrument. A typical granulation-based synthesizer with a spatial twist, the mubone granular synthesizer (mugranular for short) uses the direction vector from the orientation sensor as an index into the granulation sound corpus rather than directly retrieving sound grains based on a time index, as in a typical granulator. The approach is very similar to corpus-based concatenative synthesis [START_REF] Çamcı | GrainTrain: A Hand-Drawn Multi-Touch Interface for Granular Synthesis[END_REF],

but using a gestural feature vector instead of audio features.

In a typical scenario, the player records sound 2 in real time, adding it to the corpus along with the concurrent direction vector. Later, previously recorded sounds are retrieved, in granulated form, by pointing the mubone in the same direction. The direction vector is relative to the global coordinate frame, and therefore does not account for the player's position in space, but as long as the player doesn't move around significantly from the position where they started recording, then the qualitative effect of mugranular's recording system is that sounds are recorded into and retrieved from the space around the performer. The actual sonic influence of a gesture is determined while playing; the result is a kind of mapping by demonstration [START_REF] Schwarz | Real-Time Corpus-Based Concatenative Synthesis with CataRT[END_REF], in real time, as part of a performance.

Internally, mugranular provides a certain number of grain clouds, each with a certain number of potentially concurrent grains. In our present implementation, one cloud always follows the current direction vector from the orientation sensor, and is used to retrieve sounds in real time. The eight remaining clouds can be placed in space; this sets the direction vector and granulation parameters so that the cloud will granulate sounds in that direction until picked up. This allows the player to build up layers of concurrent granulation and build enormous sonic environments in real time.

The last important feature of mugranular is its modular construction. Although the gestural control paradigm of mugranular is intensely spatial, to date the sound output has mostly been mono. We have recently implemented stereophonic spatialization based on randomly panning each grain. Further sound spatialization approaches remain as future work.

The main parameters of mugranular, referred to in the rest of the paper, are amplitude (alternately 0 to 1, or -127 to 0 in dB), grain rate (in Hz), grain duration (in ms), recording state and granulating state, and the spatial direction index used to look up grains in the corpus. Except for the last parameter, these all have the conventional meaning employed in granular synthesizers [START_REF] Lemouton | Using the Augmented Trombone in 'I Will Not Kiss Your f.Ing Flag[END_REF]. Development of mugranular can be followed in the git repository for the project, along with a detailed overview of the parameters of the synthesizer.

physical essence of a mubone

Based on these early explorations, we have developed a reasonably clear idea of what a mubone "is," although aspects of this essence/identity remain somewhat hypothetical. A mubone is an augmented trombone with an orientation sensor, a handheld controller, and perhaps a few other features. The orientation sensor must minimally allow the direction of the instrument to be derived and represented in terms of a vector or latitude/longitude pair. The hand controller must include at least three discrete on-off buttons.

In addition to these essential features, which have been present in all of our designs and experiments so far, we have also considered incorporating measures of the orientation of the handheld controller with respect to the body of the instrument, the angular rate, acceleration, and other kinetic measures of the body of the instrument and the handheld controller, additional continuous and discrete sensors on the handheld controller, and measures of the slide position (and/or its derivatives). These measures seem promising, but they have not yet figured into our exploration of the mubone. In the future, they may become essential components of the instrument's essence, as the family continues to evolve.

It is a matter of debate whether mugranular is an essential component of a mubone.

mubone practice (presented by Kalun)

We have been exploring the artistic affordances of the mubone for 3 years. In this section, I (Kalun, the second author and the main artistic contributor to the project) will recount the development of my interactions with the mubone, from initial

Image 5

Overview of our current implementation of a mubone. improvisations, to in depth ear training, to the development of Garcia, a sound-andmovement composition that was commissioned for the mubone.

mubone improvisation

The mubone was initially designed to be "improv spec," a modality that I adopted exclusively in the first year of practice. Improvisation was a process-oriented framework for exploration that was useful in discovering the affordances and limitations of the mubone. Rather than being goal-driven, this stage of development was more about free exploration and discovery than achieving a certain specific aim.

Choosing to improvise, or choosing to create an instrument with improvisation in mind, was a way to explore the sonic possibilities expansively. It is a fundamental part of my practice as a musician who both performs free improvisation and who uses improvisation to explore and workshop new material. It was advantageous to use improvisation as both the tool and the application, as I was familiar with this way of working as a musician in the creative music and free improvisation communities in New York City. This phase of the research illuminated certain features that I found to be unique to the mubone. Some of these qualities are summarized in appendix A below.

mapping for improvisation

The initial mapping from mubone to mugranular was simple and minimal. I focused my efforts on exploring the orientation feature of the mubone and kept the other parameters relatively fixed. It would be another two years before I was comfortable experimenting with different mappings as described in the lexicon building section below.

Granular synthesis parameters were set to a generic "freeze-like" preset-440Hz in frequency, 800ms in duration-which had the effect of sustaining any acoustic trombone and extended technique sounds. The direction vector from the orientation sensor was mapped one-to-one to the mugranular spatial index, causing sounds to be qualitatively placed onto the surface of a virtual sphere around me, or the effect of placing sounds at certain locations in a room. The other parameters of mugranular were exposed with a generic slider-oriented graphical interface.

Visit the web version of this article to view interactive content.

The only feature of note at this time was the mapping used to control recording and granulating state, which allowed a performer to alternately toggle the state with a brief press, or engage it actively by holding the associated button. Buttons were used to toggle recording and granulating state, and to place or pick up grain clouds. Any button on the hand controller could have been used.

For example, recording is initially not armed. On the leading edge of a button press, recording is turned on. If the following edge as the button is released occurs within 250ms of the leading edge, recording is left on. Otherwise, recording is immediately disarmed when the button is released. If recording is already armed, the leading edge of a button press is ignored and recording is disarmed when the button is released.

movement vocabulary

I had been developing a movement vocabulary with the mubone and trombone most notably with ECHOensemble, a New York City-based sound & movement company with 5 dancers and 5 musicians. We engaged as both sounders and movers and actively sought to find a balance between the two performing artforms.

The core building block for this practice is a singular sound-movement gesture which would evolve organically in relation to itself and with the other performers. The performances are not choreographed and are largely improvised around set structures. All of the gestures that I developed became the foundation for my movement language with the trombone and in turn the mubone. Many of these gestures were used in the choreography for Garcia such as dropping the slide on the floor, scraping the bell on the floor, and blowing air while extending the slide.

practice methodology

The mubone has the potential to operate at the intersection of several different artistic disciplines, some of which I have little formal training in such as movement and theater. I developed exercises to address these disparities in skill level. Doing so was fundamental in faithfully exploring the full expressive potential of mubone and mugranular; I gained a heightened awareness of space and movement as it related to The mubone's orientation (visualized with the aid of a flashlight), or it's direction vector, is mapped one-to-one to the mugranular spatial index. The player "places" sounds along a virtual path, i.e. the edges of the room, and retraces this path to "trigger" the recorded material using a "freeze-like" granular synthesis preset.

sound. I was also keen on achieving the same level of focus and rigor on mubone that I'm able to harness with the trombone. The exercises are described in appendix B.

lexicon building

Whereas the explorations in the initial improvisation phase emphasized developing taste and getting familiar with the spatial control paradigm of mugranular, the lexicon building phase focused on intensive ear training and systematic enumeration of the sonic affordances of the synthesizer.

With the orientation sensor disabled, I would record a sound (e.g. a wet flutter, a hiss, a single pop, or a pedal tone), and then systematically explore the way mugranular could react to that sound. I would set the frequency to a specific fixed value, then cycle through the duration parameter, noting points of interest. For some of these sounds, the input (e.g. wet flutter) would differ greatly from the processed sound. I also tried to refine my ear by determining blocks of ranges within the frequency and duration parameters that produced just-noticeable differences in the output sound. These ranges became essential building blocks when later developing a piece for the mubone.

It was a useful exercise to name or describe the new sound: high frequency crackle, babbling brook, and so on. Associating words to newfound sounds helped to further define the mubone vocabulary which proved to be convenient for non-musical collaborators. The result was a catalog of sounds and presets that were relatively discipline-agnostic.

mubone performance: Garcia

Garcia is a 10 minute movement-and-sound piece choreographed by Bettina Szabo and composed and performed by myself, Kalun Leung (the second author). The piece is the first of a series of works that were commissioned for the mubone and was developed in workshop

The workshop started with a brief period of familiarization for the choreographer. I improvised a few short pieces with the mubone and spent an hour or two going over how the instrument worked. We discussed the features and limitations of both the instrument and my abilities on it. The choreographer led me in a few guided movement exercises to observe my movement and gesture language.

One feature that we identified as relevant for mapping purposes was how "pixelated"

we wanted the corpus to be, as in the exercise described in appendix B called "spacesound relationship". We decided to set up the simplest number of zones, since this was a choreographed movement piece where I can't rely on my body movements to be super accurate when trying to recall a certain position. We determined three zones for use in Garcia: Head/sky, floor, and horizon.

We sketched out sections to work with (summarized in appendix C), and the choreographer recorded a version of her interpretation for me to reference. At this point, she handed off the work to me to begin building the sound composition. We had general sound ideas but nothing more concrete than a sentence long description.

composition/mapping considerations

After some refining of the choreography, I began designing sounds and treatments of sound that would be artistically suitable for my movements. I found it challenging and artistically interesting to compose to movement especially since it is often the other way around.

One area of feedback that I like to get from audiences is whether they can tell if I am placing and activating sounds in specific spatial (spherical) positions. The answer is usually no. Audiences do not pick up on the spatial control paradigm in improvised performances leaving me to question whether I should make the cause-and-effect obvious for Garcia. In honoring the memory uncovering concept of the piece, I determined that it would be important for audiences to know that space was an active ingredient in the piece.

The result was a mapping that untethered the altitude/azimuth angle pair and used them in isolation in order to maximize the saliency of height (altitude), as in how high or low the mubone was pointing. In performance, this mapping allowed me to anchor the mubone (trombone) on the ground and use it like a big joystick, and in another scene, point the mubone up in various degrees along the horizon, opening up possibilities to assign the angle of the mubone (altitude) to frequency or duration in a very salient way. As these gestures and positions are a large part of the source choreography, it made sense to amplify my movements with this mapping decision.

Based on these considerations, I experimented with three different direction vector mapping presets: latitude only, where it doesn't matter which direction I point and only the vertical height of the instrument is used to place sounds; longitude only, where only the azimuth is used; and the default mapping where the direction vector is used and sounds can be placed anywhere in the coordinate sphere. In the final version of the piece, only the first two modes were used, because of their more visible causeeffect relationship from an audience perspective, as described above. The mappings used in Garcia are summarized in appendix D.

mubone practice: summary

The approach thus far focuses on the mubone as a hybrid instrument that combines the acoustic trombone with a controller (orienter, handheld control, mapping) and sound synthesizer engine (mugranular). In other words, approaching the mubone as a sound creating tool can be thought of as categorically distinct from a compositional tool like a DAW or even a grid-based digital instrument with sampling and sequencing capabilities.

Garcia and the work leading up to it has only scratched the surface of the mubone as a sound creation tool, and furthermore, has provided a small glimpse of the compositional framework that space and movement has afforded. It would be interesting to focus future work on exploring the compositional capabilities of the mubone, particularly live composition, not unlike live painting where audiences can witness the creation of an artwork in real time.

Garcia was created to have elements of observer participation. Since a large part of the mubone identity is formed around the concept of live composing in space, it was important that the piece had the capability of demonstrating this concept to an audience member, especially being a premiere for the instrument. I wanted the observer to feel like they were discovering and exploring the sound-space with me and to witness the compositional process in performance. The feedback I received from audience members gave me a sense that this was what they felt, especially during the more childlike moments of the performance.

The project also proved the capacity for the mubone to be interdisciplinary both inherently as an instrument and as a tool for working across disciplines. It proved to an effective common ground for movement and sound and created a space for interdisciplinary artwork to be created. Future work will explore the possibilities of developing versions of the mubone adapted to different instrumentalists, the adaptability of the mubone in a variety of musical genres and artistic disciplines, and the usage of the instrument as a controller, interface, compositional tool, and the combinations within.

conclusion

In this paper we have reflected on the first three years of developing the mubone as an instrument family by designing and playing mubones. This has been a thoroughly collaborative process, not only because it draws on interdisciplinary collaboration with artists in various mediums, but because at its core it is a collaboration between a technically competent artist (Kalun) and an artistically competent technician (Travis).

This has proven to be a deeply satisfying and productive relationship, where both art and technology have been able to flourish and develop in exciting and novel directions.

It has also proven to be noticeably sustainable, with three years of development so far and no signs yet of slowing down. We note a similar collaborative relationship between, for example, Rebecca Fiebrink and Laetitia Sonami facilitating over 8 years of ongoing development of Wekinator and the Spring Spyre [START_REF] Zayas-Garin | DMI Apprenticeship: Sharing and Replicating Musical Artefacts[END_REF], or Joseph Malloch and Andrew Stewart's roles in the development and support of the T-Stick [START_REF] Calegario | Documentation and Replicability in the NIME Community[END_REF][23] and its growing community of practitioners [START_REF] Françoise | Gesture-Sound Mapping by Demonstration in Interactive Music Systems[END_REF]. Although there is no doubt that numerous other participants and contributors have played essential roles in these projects (the mubone included), this kind of central collaborative duo, with a technical artist and artistic technician, may still be a useful model for NIME research, providing a stable core that could improve the longevity and reliability of the instruments and technology developed compared to solo or large group research. We are admittedly still early in our development, and much remains to be seen, but the core-duo relationship has proven very effective so far.

Considering the second author's reflections above on the artistic development of the mubone, this account provides an important point of reference on learning, developing mappings, and exploring artistic goals and experiences with a DMI over a long term period. Future work may compare this account with prior research into the creative process working with DMIs, for instance the process of developing mappings [25][26].

Future work may also work to more rigorously assess the influence of specific creative choices on audience members' experiences of music for the mubone.

The potential design space for all musical instruments is effectively infinite. The potential design space for mubones initially began with this infinity, but we have been consistently narrowing the field of possibilities as we learn more about what a mubone feels like, what we still want to explore, and the immediate vicinity of the specific choices we have made along the way. We have learned that no matter how specific we get there always seems to be a hidden vastness of possibilities. We could spend the rest of our careers just exploring the musical affordances of mugranular with an orientation sensor and a few buttons. At the same time, we are drawn to the unfamiliar space around us. We look forward to continuing to explore the mubone, the depth of it's identity and the breadth of it.

acknowledgements

This work has been financially supported by the Canada Council for the Arts. Thanks to Alex Daigle, Ajin Tom, and Harish Venkatesan for early collaboration on the sensor fusion algorithm used by the orientation sensor.

ethics statement

We would like to acknowledge the traditional, ancestral, and unceded Indigenous lands where this project was developed. Tiohtià:ke/Montréal and the surrounding areas have historically been a meeting place for many First Nations. We strive to respect the history and culture of these diverse communities and to educate ourselves on the impact of our colonial past.

Whenever possible, the prototyping process made use of materials on hand in order to minimize waste. Reusing materials from other projects and previous prototypes continues to be a sustainability practice we strive to follow. Furthermore, procurement of certain components were motivated by cost savings in an effort to lower the financial barrier to entry for future contributors.

No research participants were engaged. Artistic collaborators and consultants who were engaged for the project were compensated at rates at or above market as determined by the relevant union representing their creative practice. Visit the web version of this article to view interactive content.

appendix A: mubone qualities

appendix C: Garcia choreographer's instructions

Table 3 space-sound relationship Ex. 3. Divide a wall in various ways with exercises that progress from "lower resolution" (4 quadrants) to "higher resolution" (4x4 grid).

Ex. 4. Height focus: divide the space into sky, horizon, ground. Assign sonic themes to each. Spatial awareness exercise: Using the edges of a wall and a flashlight as a training aid, the player layers chords at the corners and practices moving between them.

Section Instructions section 1

Mubone used as a joystick anchored to the ground.

Latitude only preset: The angle of the instrument (latitude) is mapped to grain rate.

Azimuth/longitude is disengaged.

When the instrument is vertical (perpendicular to the floor), frequency hovers near 0 Hz. The effect is a slow pulsing rhythm of recorded material. When the instrument is vertical, the frequency is 180 Hz. Duration is fixed at a range of between 400 to 600 ms, randomized between those values. Search angle is 60 degrees.

All recorded sound material is cleared after this section.

section 2

On the ground, mubone is mostly horizontal and searching, sweeping, sniping along the horizon (orbitally).

Longitude only preset: Longitude is not mapped to a sound treatment parameter (ms or hz), but is used as the spatial index to place and retrieve sounds. Frequency is fixed at 440 Hz, duration is fixed at 800 ms, (resembles sonic freeze effect), search radius is reduced to 15-30 degrees. Latitude "special" preset: same as previous but latitude is now mapped to duration. The higher I'm pointing, the more crispy and short the sound grains are.

coda

From standing and pointing straight up, go to bow, kneel and lie on belly.

Exit sequence is triggered, all mapping is disengaged and the hz and ms will gradually reach 0 over 2 minutes.

  author keywords mubone, augmented trombone, granular synthesis, mapping, interdisciplinary art, DMI design CCS concepts •Applied computing → Arts and Humanities → Sound and music computing •Human-centered computing → Interaction design → Interaction design process and methods

International

  Conference on New Interfaces for Musical Expression • NIME 2022 early prototypes and artistic practice with the mubone 3

  the rotation. Put another way, each column of the rotation matrix represents one of the basis vectors of the mubone's local coordinate space, as expressed in the global coordinate frame.

Finally

  , due to electrical and/or mechanical failure of both elaborate yokes, our most recent experiments have made use of the Joy-Con developed for the Nintendo Switch

  a residency-type setting in 2021. It was determined at an early stage that it was important for the mubone to not only exist, and thrive, as a solo instrument, but that it should be versatile in various types of performing arts settings. With the financial backing of the Canada Council for the Arts, we developed 3 new works with 3 different creators from various fields: movement and dance, composition and sound art, and new media art. In this section I describe the development of Garcia, the first of these new works, through workshops with the choreographer and my subsequent development of the sound and mapping.

Ex. 5 .

 5 Using a fixed search radius, plant a sound in a single location and scrub the edges of that sound. Listen for liminal space between sounding and silence. body and gestural awareness Ex. 6. Perform a sound-movement gesture and repeat the same gesture without the sound. music or dance specific focus Ex. 7. Choose a simple movement pathway (e.g. orbit clockwise). a) Play a melody in slow motion. Scrub back and forth to create a new synthesized melody. b) Moving very slowly along the pathway, stack pitches to form chords. Ex. 8. Saturate the entire spatial corpus with improvised sound. Then, activate the sound with movement only, using the synthesized sound as a movement guide.

  Playing at the sky and scanning in a more upand-down motion. Same as previous until section 3.b.

  The parameters of the synthesizer are set by sending OSC messages to the synthesis program (implemented in C++ using the JUCE framework). The synthesizer has no internal knowledge about the mubone, and the mapping from mubone gestural signals to sound parameters is implemented in a separate program (in our experiments, typically Max/MSP or Pure Data). This has proven to be an advantageous design, allowing for rapid experimentation in the mapping layer without having to edit or compile native

C++, which is used to implement the synthesizer. The design is functionally similar to implementing an external object in Max or Pure Data, but without tying the implementation to one or the other programming environment or having to individually support multiple environments. Both mugranular and the mapping program typically run on the same laptop computer, which receives sensor data from the orientation sensor and handheld controller.

Table 1 appendix B: spatial/movement exercises

 1

of Experienced Mid-Air Musicians." Digital Creativity 29[START_REF] Collins | Low Brass: The Evolution of Trombone-Propelled Electronics[END_REF][START_REF] Snyder | The Feedback Trombone: Controlling Feedback in Brass Instruments[END_REF].↩

appendix D: Garcia mappings

going back in time (walking backwards), drawing a spiral that brings you to the ground using the slide as a crutch.

The exploration for this section I think has to do more with sound than movement. But you need to rehearse "using " the crutch. Normally you would "lean" on it to move the "injured leg". I'll let you choose which one it is. Exploration on this theme.

section 4

Continue the journey backwards depicting Hong Kong's soundscape.

Once again the sound will be very important here. What I need to have is an exploration of movement where you "paint " your landscape.

Think of using the mubone as a brush, and as a pencil. Draw the landscape, the buildings. Think of wide standing positions that will let your torso move big.

section mapping (preset)