Dorian A H Hanaor
email: dorian.hanaor@sydney.edu.au

Matthias H H Kolb

Yixiang Gan

Marc Kamlah

Regina Knitter

Solution based synthesis of mixed-phase materials in the Li 2 TiO 3 -Li 4 SiO 4 system

Keywords: Breeder materials, Phase equilibrium, Li 2 TiO 3, Li 4 SiO 4, Organometallic synthesis

As candidate tritium breeder materials for use in the ITER helium cooled pebble bed, ceramic multiphasic compounds lying in the region of the quasi-binary lithium metatitanate-lithium orthosilicate system may exhibit mechanical and physical advantages relative to single phase materials. Here we present an organometallic solution-based synthesis procedure for the low-temperature fabrication of compounds in the Li 2 TiO 3 -Li 4 SiO 4 region and investigate phase stability and transformations through temperature varied X-ray diffraction and scanning calorimetry. Results demonstrate that the metatitanate and metasilicate phases Li 2 TiO 3 and Li 2 SiO 3 readily crystallise in nanocrystalline form at temperatures below 180°C. Lithium deficiency in the region of 5% results from Li sublimation from Li 4 SiO 4 and/or from excess Li incorporation in the metatitanate phase and brings about a stoichiometry shift and product compounds with mixed lithium orthosilicate/ metasilicate content towards the Si rich region and predominantly Li 2 TiO 3 content towards the Ti rich region. Above 1150°C the transformation of monoclinic to cubic γ-Li 2 TiO 3 disordered solid-solution occurs while the melting of silicate phases indicates a likely monotectic type system with a solidus line in the region 1050°-1100°C. Synthesis procedures involving a lithium chloride precursor are not likely to be a viable option for breeder pebble synthesis as this route was found to yield materials with a more significant Li-deficiency exhibiting the crystallisation of the Li 2 TiSiO 5 phase at intermediate compositions.

1.

Introduction:

A key component of the ITER thermonuclear demonstrator reactor is the helium cooled pebble bed (HCPB) breeding blanket that utilises Li bearing ceramic pebbles for tritium breeding purposes [1][2][3]. Numerous candidate oxide compounds have been studied towards this goal. Material requirements include adequate thermo-mechanical stability, low activation levels, and sufficiently high lithium density. In recent years lithium metatitanate (Li 2 TiO 3 ) and lithium orthosilicate (Li 4 SiO 4 ), in some cases with Li excess [4][5][6][7], have emerged as leading HCPB candidate materials, as these compounds are found to exhibit low activation relative to earlier studied compositions of Li 2 ZrO 3 and LiAlO 2 while maintaining favourable thermo-mechanical properties [1,[8][9][10]. The properties exhibited by candidate pebble bed materials are the subject of intensive investigation and review as these are critical to the viability and performance of the numerous solid breeder conceptual designs [START_REF] Billone | ITER solid breeder blanket materials database[END_REF]. Consequently increased versatility in the attainable properties of pebble material can be expected to yield meaningful benefits for breeder blanket design.

Research of breeder pebbles produced using melt-based processing methods involving the addition of TiO 2 to Li 4 SiO 4 melt has shown that materials comprised of biphasic mixtures of Li 4 SiO 4 and Li 2 TiO 3 exhibit improved mechanical properties relative to single phase materials, evident by increased crush stress [START_REF] Leys | [END_REF]13]. However, the stoichiometric and thermal limitations imposed by melt-processing restrict the range of compositions and microstructures attainable in the Li rich region of the ternary Li 2 O-SiO 2 -TiO 2 system. For this reason the wetchemical processes utilising precursor compounds in the form of salts and/or organometallic compounds to yield homogenous biphasic or triphasic oxide materials presents an attractive approach to breeder materials syntheses.

A number of recent studies have investigated methods for the fabrication of single phase Li 2 TiO 3 and Li 4 SiO 4 pebbles from powder-form precursor materials in dry and wet processes utilising binders and different spheroidisation techniques [14][START_REF] Mandal | Mechanical Properties and Performance of Engineering Ceramics and Composites VI: Ceramic Engineering and Science Proceedings[END_REF][START_REF] Knitter | [END_REF][17][18][19][20]. Such methods readily allow the fabrication of pebbles with well controlled geometry, density and consistency and reprocessing by melting and by wet chemical methods has further been the subject of various research efforts [21,22]. In parallel, multiple solution based syntheses for lithium metatitanate and orthosilicate have been reported to date [23][24][25][26][27][28]. Such processes generally utilise organometallic compounds and/or salts as Si, Ti and Li precursors for the synthesis of oxides of various stoichiometry. Relative to solid state processing, such syntheses have the advantage of better mixing and consequently shorter diffusion distances, imparting greater flexibility with respect to thermal processing, potentially allowing lower temperature synthesis of the desired oxide compounds, attainment of finer crystallite sizes and compositional versatility.

Li 2 TiO 3 is a congruently melting phase exhibiting high temperature polymorphism while Li 4 SiO 4 exists in a monoclinic structure up to temperatures of 1258°C at which this phase melts congruently, although earlier studies reported a peritectic decomposition at 1255°C [29][30][31][32]. The metasilicate phase is also studied for potential applications in breeder pebbles and melts congruently at 1209°C [30,33]. As both endpoints are congruently melting phases, the Li 2 TiO 3 -Li 4 SiO 4 composition range is considered to be a quasi-binary system. A summary of phase equilibria reported in the literature for the Li 2 O-TiO 2 -SiO 2 (LTS) ternary system is shown in Figure 1 [30][31][32][34][35][36][37]. In this figure the liquidus temperatures are taken from the most recent available references. Compositions 1-11 studied in the present work are further indicated in the diagram. Understanding of stability and equilibria in this system remains to date incomplete in the Li-rich ternary regime as tie-lines, liquidus surfaces and potential eutectic/eutectoid compositions have not been determined comprehensively in this region of the system. Reported results suggest a likely compatibility tie line between Li 4 SiO 4 and Li 2 TiO 3 as these two phases are found to coexist in melt-based products [START_REF] Leys | [END_REF]. A further compatibility tie line or potentially mutual solubility is likely to exist between the ortho-phases (66.67 mol% Li 2 O) in the system owing to these compounds exhibiting similar cation-oxygen bond lengths and the isostructural relationship between high temperature β-Li 4 TiO 4 (stable above 686 °C) and Li 4 SiO 4 [31,[38][39][40].

Consequently, in an effort to investigate the synthesis of breeder materials of new compositions, we seek to explore the wet-chemical synthesis of compounds in what is likely to be a binary Li 2 TiO 3 -Li 4 SiO 4 system.

Materials and Methods:

All sols fabricated in the presently reported work were ethanol based. LiOH monohydrate and LiCl (both Alfa Aesar, 99%) were examined for use as Li precursor compounds following similar methods for solution processing of metal oxides [23,27]. Prior to use, LiCl and LiOH•H 2 O were vacuum dried at 180°C yielding anhydrous products as confirmed by mass balance. Organometallic Ti and Si precursor compounds used were respectively titanium tetra-isopropoxide (TTIP, 97%, Sigma Aldrich), tetraethyl orthosilicate (TEOS, 99%, Sigma Aldrich).

11 Compositions were studied in the present work and these have been denoted according to their equivalent integer ratios of binary oxides as outlined in Chloride LT and L2S sols (those prepared using LiCl as a lithium precursor) were prepared by the gradual addition of LiCl, which had been pre-dissolved in ethanol, to clear ethanolic solutions of TTIP and TEOS under rapid stirring at room temperature. Subsequent to continued stirring for 4 hours, the respective sols were combined at appropriate ratios for compositions 2-10 (compositions 1 and 11 correspond respectively to the original LT and L2S precursor sols). While under stirring, HCl 1M was added to give an alkoxide hydrolysis ratio of R=4 (H 2 O:(TEOS+TTIP)) to ensure sufficient peptization and avoid the formation of large precipitates. The results were transparent/translucent sols with those containing greater LT content exhibiting higher levels of opacity.

Stirring was continued overnight resulting in stable gels which were then dried by evaporation of solvent in ambient air and subsequent heating at 180 °C in a vacuum oven. The resultant xerogel powders were observed to be strongly hygroscopic evident by the rapid appearance of adsorbed aqueous LiCl solution at the materials' surfaces. Subsequent to drying, 500 mg samples of powders were uniaxially pressed at ~293 MPa into 10 mm diameter pellets and calcined at 900°C using a heating rate of 2°/min. The firing temperature of 900°C represents typical operation parameters likely to be encountered in HCPB applications [41].

In subsequent fabrication processes LiOH precursor was employed for the fabrication of colloidal sols corresponding to LT and L2S compositions. This synthesis procedure utilised similar precursor compounds to those employed by Renoult et al. [23] In this synthesis procedure clear 200ml ethanolic solutions of TTIP and TEOS were prepared in separate flasks containing respectively 0.15 moles TTIP and 0.1 moles of TEOS. Hydrolysis of the TTIP solution was achieved by the addition of HNO 3 1M diluted in 50ml of ethanol, under moderate heating, to give a hydrolysis ration of R=2 (H 2 O:Ti). Acidic pH and heating were used to reduce particle size and prevent the onset of flocculation, dilution of HNO 3 in ethanol was undertaken in order to moderate and homogenize the rate of hydrolysis occurring in the solution. Hydrolysis of the ethanolic TEOS solution was achieved similarly using 0.2M HNO 3 at R=2. Subsequent to one hour of continued stirring, anhydrous LiOH was gradually added to the LT and L2S sols at respective ratios of Li:Ti=1 and Li:Si=2. Subsequent to approximately 2 hours of continued vigorous stirring, both precursors were in the form of stable colloidal suspensions exhibiting an opaque white appearance. These colloids were left to stir for a further 24 hours after which a distinct orange colouration was evident in both flasks. L2S and LT sols, which were adjusted to 300g by addition of ethanol, were then combined in individual containers following the ratios outlined in table 1. Subsequent to 1 hour of further homogenization by stirring, these were allowed to dry in ambient air, before being dehydrated under vacuum heating at 180°C. In similarity to chloride based materials, dried powders were used to fabricate uniaxially pressed 500 mg pellets which were then fired at 900 °C for 12h with a heating rate of 2°/min. As described in the following section, further analyses of powders fabricated from hydroxide sols were undertaken using temperature varied XRD, TG-DSC and ATR-FTIR.

Experimental

The phase composition of fired pelletised samples described above was determined by powder X-ray diffraction, XRD, of crushed samples that was carried out over the range 15-70° 2θ using a Bruker D5000 diffractometer with Cu-Kα emission in ambient air. In order to assess phenomena of crystallisation and phase stability in the synthesised materials fabricated using LiOH precursor, in situ Temperature varied XRD of dried powders was employed using a Bruker D8 Advance diffractometer equipped with an Anton Paar heating chamber. Scans were carried in air out over the range 10-80 °2θ and these were taken at temperature intervals of 50° during heating in the range 100-1200°C and at temperature intervals of 300° during cooling from 1200°C to room temperature. The powders were manually pressed in a platinum-rhodium sample holder to also allow for possible melting of the samples during XRD examination. This facilitated the acquisition of data relating to crystallisation, melting and phase retention in the 11 compositions fabricated. Phase identification was facilitated utilising the ICSD and ICDD PDF-2 databases.

To evaluate the possible formation of organo-lithium products through reaction of lithium hydroxide with solvents or alkoxide precursors, Attenuated Total Reflectance Fourier Transform Infrared spectroscopy (ATR-FTIR) of LT and L2S sols and precipitates was employed using a Bruker Tensor FT-IR spectrometer over the wavenumber range 600-4000 cm -1 .

To support high temperature XRD analysis, simultaneous thermogravimetry (TG) and differential scanning calorimetry (DSC) of dried powder samples, fabricated using a lithium hydroxide precursor, in the composition range LT-L2S was carried out using a Netzsch STA-449C Jupiter apparatus in ambient air. The reference and the samples were again kept in platinum-alloy crucibles during the experiments. Scans were carried out from room temperature up to 1350 °C with a heating rate of 5° min -1 and, subsequent to a dwell time of 1 hour, down to room temperature with a cooling rate of 20° min -1 .

Results

XRD

XRD spectra from samples fired at 900°C fabricated from chloride and hydroxide precursors for three compositions corresponding to lithium metatitanate (LT), the intermediate composition (L3TS) and lithium orthosilicate (L2S) are shown in Figure 2. It is evident that samples synthesised with the LiCl precursors showed a significant lithium deficiency relative to the target composition. This most likely is the result of the hygroscopic nature of the dried product and the consequent segregation of LiCl to material surfaces and Li loss during heating. Lithium loss through combined lithium rejection at growth interfaces and sublimation of lithium as either Li (g) , LiO (g) or Li 2 O (g) during firing, particularly above 800°C, is a commonly observed phenomena in Li bearing ceramics [42][43][44][45][46][47][48] and thus it is likely to be evident also in materials synthesised from a LiOH precursor, albeit to a notably lesser extent relative to chloride precursor derived samples.

Materials fabricated using lithium chloride exhibited the presence of lithium-poor phases observed by X-ray diffraction. In chloride LT samples the formation of a secondary cubic spinel of composition Li 1+x Ti [31,36].

The 1:1:1 ternary compound LTS (Li 2 TiSiO 5 ), was observed significantly in materials of compositions containing both Si and Ti fabricated using lithium chloride (compositions 2-10). This tetragonal ternary phase was first reported by Kim and Hummel in 1959 and has since been the subject of a small number of further studies [32,[53][54][55]. The presence of this phase is apparent in the presence of diffraction peaks at 20.2°, 24.5°, 27.7° and 34.5° 2θ corresponding to (001), ( 101), ( 200) and (201) planes [53]. At high Ti content, the existence of the LTS phase alongside some titanate spinel may indicate the existence of an as yet unreported compatibility tie-line between these two phases.

Although the synthesis of the tetragonal ternary LTS compound was not the objective of the present work, it should be noted that despite the lower lithium density of this phase (0.22 g cm -3 for LiTiSiO 5 compared with 0.37 g cm -3 for Li 2 TiO 3 , assuming isotopically homogenous 6 Li), a potentially improved mechanical strength (often observed for congruently melting ternary phases) may confer some advantages with respect to breeder pebble applications. For further specimen fabrication, LiCl based synthesis was ruled out owing to instability resulting from the hygroscopic nature of the chloride type material. Precipitated and dried compounds exhibit rapid decomposition and consequent phase segregation leading to deviation in stoichiometry. In similarity to other work involving chloride precursor compounds (TiCl) [27], the issue of chloride removal further discourages the use of this method for pebble fabrication.

In contrast to the chloride route, lithium loss is significantly less evident in materials synthesised using lithium hydroxide. LT samples fabricated by this method exhibit a single phase monoclinic β-Li 2 TiO 3 composition subsequent to firing at 900°C, while samples with increasing Si content exhibit some Li deficiency evident by the presence of a metasilicate secondary phase alongside the orthosilicate target phase. It should be noted that Li excess in Li 2 TiO 3 is a known phenomenon and thus some deviation from the projected LT-L2S tie-line is expected [29,31,36].

Spectroscopic analysis

During the synthesis of hydroxide-precursor derived material, subsequent to prolonged stirring under mild heating, sols of both L2S and LT compositions were found to exhibit a deep orange colour. This colouration was found to be stronger in L2S sols, suggesting possible formation of alkyl-lithium compounds, such as ethyllithium or methyllithium, the synthesis of which is favoured under strongly basic conditions. Consequently, ATR-FTIR spectroscopy was employed to ascertain the presence of organo-lithium compounds. Figure 2. Show FTIR scans from supernatant liquid and bulk. XRD of powders synthesised using lithium hydroxide show the formation of lithium carbonate and Li 2 TiO 3 subsequent to drying at 180° C. However, we cannot rule out the formation of lithium hydride upon drying /heating owing to the low X-ray scattering of this compound. The formation of carbonate is likely the result of a reaction with the retained organic content. A reaction with atmospheric carbon dioxide in the furnace is possible; however this is unlikely to feature prominently, particularly in materials towards the LT composition.

HTXRD

Temperature varied XRD (also known as High Temperature XRD, HTXRD) was employed across the range 25-1200 °C, with 50°C intervals. This was undertaken to ascertain the reaction and possible liquid formation sequence in the oxide materials. The use of eleven compositions for HTXRD analysis was carried out in order to determine the type of binary phase system exhibited over the LT-L2S range and ascertain whether any eutectic or eutectoid type behaviour is observable through the processing methods used.

For materials towards Ti rich side of the LT-L2S tie-line the dominance of Li 2 TiO 3 in its monoclinic phase with space group C2/c is apparent [29,61,62]. This phase is found alongside lithium carbonate after drying, as shown in Figure 4, and demonstrates stability up to 1150°C with increasing crystallite size, as indicated by higher and narrower diffraction peaks. Li 2 TiO 3 exhibits subsolidus polymorphism and above 1150°C, as predicted by reported phase equilibria studies in the Li 2 O-TiO 2 system [31,32,36,63], a displacive phase transformation is observed with cubic phase γ-Li2TiO3 solid solution, space group Fm-3m, emerging as the dominant phase at temperatures upwards of 1100°C. [51,64] This is evident by the increase in peak intensity of the (200) peak of the rock-salt type solid solution at ~44.5° 2θ while the (002) peak of the monoclinic phase diminishes. At or below 350°C some carbonate is evident from peaks at 21.5°, 30.5° and 31.5° 2θ. At lower temperatures, during heating and cooling, the presence of small quantities of spinel phase Li 4 Ti 5 O 12 cannot be ruled out, owing to weak diffraction signals at 79° 2θ which can be attributed to this phase and broadening of Li 2 TiO 3 peaks at ~35.9° and 43.6° 2θ which may indicate the overlap of ( 311) and (400) signals from the Ti rich phase [51]. At temperatures in the range 1000 -1150°C multiple peaks become apparent in the range 20.5 -25° 2θ corresponding to (111), (112), and (110) plane families in Li 2 TiO 3 (ICDD 04-009-2812, ICSD 162215) [62]. These peaks reappear prominently during cooling and are retained to room temperature suggesting possible thermally activated preferential grain growth along these planes.

Diffraction peaks exhibit a shift to higher 2θ angles, with this trend increasing with temperature. This suggests lattice distortion which may be the result of interstitial lithium in solid solution in Li 2 TiO 3 a phenomena which has been reported to occur up to the extent equivalent to ~44% TiO 2 [31]. For intermediate target compositions between LT and L2S, subsequent to drying the crystallisation of metasilicate and metatitanate phases is evident in powders, shown in Figure 5(a). With increasing lithium content diffraction peaks of carbonate material are more prominent and are present up to higher temperatures relative to compositions of lower Li content. Peaks from the orthosilicate phase are first observed in XRD patterns at 450°-500°C and this phase exhibits strong diffraction peaks in patterns obtained at temperatures at or above 550°C. At this temperature, the carbonate phase ceases to be observed in all compositions and peaks for metasilicate diminish relative to the stable metatitanate signal, suggesting a reaction between carbonate and metasilicate is involved in the formation of Li 4 SiO 4 . As temperature is increased, monoclinic Li 2 TiO 3 peaks exhibit increasingly high intensity while peaks from the orthosilicate and metasilicate phases exhibit a lesser increase in relative intensity, suggesting a coarsening process of metatitanate crystallites. Lithium orthosilicate and metasilicate phases are not observed in diffraction patterns above temperatures of 1050°C and 1100°C respectively, while the metatitanate phase remains present. Above 1150°C a conversion to the cubic phase solid solution γ-Li 2 TiO 3 is observed, while some peaks from the platinum crucible are evident as the result of liquid migration, as can be seen in Figure 5(b). With cooling down from 1200°C, the orthosilicate phase is not observed to recrystallise for specimens below 23.33 mole% SiO 2 (compositions 2-7) suggesting excess Li is retained in metatitanate and/or metasilicate solid solutions, thus impeding the recrystallization of the L2S phase. In particular The Li 4 SiO 4 (001) and (100) peaks around 16.7° and 17.2° 2θ [65] are not prominently observed for all Ti-containing specimens subsequent to cooling, suggesting a Ti-driven modification of the growth habit of this phase. For the sample corresponding to the L2S composition, the formation of lithium metasilicate in the as-dried material is evident by strong diffraction peaks present in as dried powder at room temperature. At temperatures below 550°C the metasilcate peaks are present alongside significant carbonate signals, as shown in Figure 6(a). This is likely owing to the unfavourable kinetics of formation of lithium orthosilicate at lower temperatures, relative to Li 2 TiO 3 and Li 2 SiO 3 . As with intermediate compositions, a reaction between carbonate and metasilicate leads to the formation of the monoclinic orthosilicate material at temperatures between 500° and 550°C, which is the predominant phase once formed. At temperatures, between 1000° and 1050°C, Li 2 SiO 3 peaks cease to be observed, in consistency with reported phase stability of compositions in the Li rich side of the Li 2 SiO 3 -Li 4 SiO 4 binary system which exhibits a eutectic decomposition at 1024°C [32]. The Li 4 SiO 4 phase exhibits strong peaks up to 1150°C. This is in contrast to Ti-bearing compositions where orthosilicate peaks diminished at lower temperatures than metasilicate. At 1200°C near complete melting of the material is evident, seen in the valley that is observed in the HTXRD stack shown in Figure 6. This occurs below the liquidus temperature (1258°C) reported in phase equilibria studies for single phase Li 4 SiO 4 [30]. As the actual melt temperature was in the range 1150°-1200°C, this suggests an actual Li 4 SiO 4 :Li 2 SiO 3 ratio in the region of 82:18 -78:22 by interpolation of the liquidus surface reported in the relevant region of the Li 2 O-SiO 2 phase diagram [32,34] and equates to a lithium loss of approximately 4.5-5.5 at% relative to the target composition. As with ternary compositions, at 1200°C, subsequent to the melting of silicate phases, signals at ~39.2° and 45.7° 2θ are evident which correspond to diffraction peaks from the platinum crucible, which is exposed in the x-ray illuminated region owing to significant melt formation and its migration away from the crucible centre. In contrast to intermediate compositions, upon cooling of composition 11 from 1200°C down to room temperature, the orthosilicate phase (corresponding to the target L2S ratio) recrystallises while the metasilicate phase remains notably less prominent, potentially owing to the formation of amorphous silicate phases. Peaks from the exposed platinum crucible remain during cooling. The lack of observed melting of Li 2 TiO 3 in compositions towards the orthosilicate side of the studied system suggests that the LT-L2S quasi-binary is a monotectic rather than a eutectic system, this is further shown in the behavioural diagram in Figure 8.

Thermogravimetry / DSC

Thermogravimetry (TG) and differential scanning calorimetry (DSC) were carried out in order to further examine the temperature and composition dependant transitions observed by XRD. Results for the endpoint and median compositions 1, 7 and 11 (LT, L3TS and L2S) are shown in Figure 7. These data confirm a significant loss of mass during heating up to 800°C, evident in the mass loss of approximately 17%, 19% and 26% in powders of LT, L3TS and L2S compositions respectively, as the result of the pyrolysis of residual organic content and Li 2 CO 3 in this temperature range. In L2S specimens a further ~2.5% mass loss occurs in the range 1150°-1350 °C and this is attributed to the near-complete melting observed in this composition and the accompanying further Li volatilisation.

Calorimetric data, plotted at different scales, show exothermic peaks in the region 300°-400°C with these peaks being more significant in titanate bearing compositions. The greater exothermic behaviour in compositions richer in Ti is likely the result of precursor chemistry leading to a greater organic content in these powders. It is worth noting that in Li 2 TiO 3 exothermic behaviour at ~400°C is also likely to be influenced by the transition from α-Li 2 TiO 3 to β-Li 2 TiO 3 which occurs around this temperature range [66]. The formation of a metastable cubic α-Li 2 TiO 3 at low temperatures which subsequently transforms to the stable monoclinic phase at 350°-400°C was recently reported by Laumann et al. in a series of publications [67][68][69], however this phase transformation is not readily observable in XRD scans as α-Li 2 TiO 3 diffraction peaks coincide with signals from the monoclinic βphase [68].

Regions of interest are numbered on the DSC scan data shown in figure 7.

Summary of phase transformation behaviour

The behavioural diagram shown in Figure 8 presents a summary of observed phase transformation behaviour during heating, compiled from the combination of XRD and DSC data for materials fabricated from hydroxide sol precursors. As temperatures above 1350°C were not investigated, higher temperature behaviour shown is an interpretive projection. The shown transformation of α-to β-Li 2 TiO 3 at 400°C is somewhat speculative as XRD results obtained in the present work cannot confirm or dispel the existence of this phase in synthesised materials reported.

Discussion

Synthesis route and Li deficiency

The use of chloride precursors is frequently reported in sol-gel processing of metal oxides and allows better pH control in sols relative to hydroxide precursors. In the present work the use of this compound was found to be unfavourable owing to a resulting stoichiometric imbalance. Additionally the use of chloride is problematic for HCPB materials as residual chloride is undesirable in breeder blankets [73].

The greater extent of Li loss in the chloride based materials may result from the hygroscopic nature of the precursor and consequent segregation of lithium towards the material surface during drying. This lithium deficiency manifested in the crystallisation of Li poor phases including Li 2 TiSiO 5 and Li 4 Ti 5 O 12 spinel. Alternative soluble Li precursors include LiNO 3 , Li 2 SO 4 and LiC 2 H 3 O 2 , while alternative Si and Ti precursors too are available and, subject to further investigation, may be employed to minimise Li loss to allow control of stoichiometry, morphology and crystallinity. Additionally processing procedures and parameters can be varied, facilitating the fabrication of compositions and microstructure different to those obtained in the present work.

In hydroxide synthesised materials, the presence of metasilicate alongside the target orthosilicate phase is a possible result of two main causes, the incorporation of excess lithium into Li 2 TiO 3 , as reported elsewhere, and/or the sublimation of lithium (as atomic lithium or gaseous lithia) from Li 4 SiO 4 leading to the formation of Li 2 SiO 3 as reported by Cruz et. al. [45] The phenomenon of lithium loss through volatilisation in analogous systems is well known [4,44]. The presence of lithium in glassy phases cannot be ruled out, however reported Li-Si glass systems are significantly richer in Si than the phases investigated in the present work, and hence their formation would not account for the lack of orthosilicate phase in compositions studied here relative to the target compositions [74,75], moreover one would expect rapid devitrification of these systems to result from the applied thermal treatments [76]. In materials fabricated using the present methods with a hydroxide precursor, from analysis of liquid formation temperature, at which the metasilicate phase is observed to melt, it can be inferred that the loss of lithium in the L2S composition was in the region of ~5% This implies that the use of excess lithium as employed by Hoshino et al. [1,4,77] can be used to correct for this occurrence and facilitate the attainment of biphasic metatitanate-orthosilicate mixtures. It should be noted that the precise loss of lithium and the excess lithium necessary to correct for this is dependent on specimen parameters and firing conditions.

Precursor sol-chemistry

The appearance of an aromatic orange compound in the LiOH based sols suggests a possible formation of organolithium compounds which merits further investigation. The decomposition of such compounds during drying is likely, resulting in possible hydride or carbonate formation.

Crystallisation

The formation of metasilicate and metatitanate phases occurs in nano-crystalline form subsequent to drying, as indicated by the wide diffraction peaks evident for these phases at low temperatures. The observed co-formation of carbonate can likely be avoided by use of alternative sol-gel processing using aqueous sols or otherwise removing organic content. While nanostructured material can be advantageous for tritium release characteristics, the expected application temperature in breeder blankets is in the region of 900°C, and thus nano-crystallinity is unlikely to be preserved in the absence of grain-growth limiting dopants, the use of which would be undesirable in breeder pebbles. DSC data indicates that the hydroxide route employed in the present work may result in the crystallisation of metastable cubic α-Li 2 TiO 3 in similarity to results obtained by hydrothermal processing by Laumann et. al. [67,68]. Ascertaining the formation of the metastable phase is attainable by synchrotron or neutron diffraction studies, however for breeder-pebble applications this phase is of little significance.

Phase stability

Observed compositions of Li 2 TiO 3 existing alongside a phase mixture of Li 4 SiO 4 and Li 2 SiO 3 are similar to 3phase compositions obtained by melt based breeder pebble processing [13] and are consistent with kinetic studies in the Li metasilicate-orthosilicate regime [45] and with studies into synthesis methods of lithium silicate powders [28,33]. The coexistence of lithium metatitanate with predominantly orthosilicate material infers compatibility between L2S and LT regions of the ternary system. The solidus temperature in this system appears to be in the range 1050°-1100°C while further studies are required to describe fully the liquidus surface in this regime. Based on the range of 11 compositions evaluated, the quasi binary system is likely to be of a monotectic type as no evidence of Li 2 TiO 3 melt existing alongside solid Li 4 SiO 4 was observed at any composition.

The absence of orthosilicate in compositions 2 and 3 during the heating stage of HTXRD analysis indicates a likely solid solution of excess lithium in the β-metatitanate phase. Such non-stoichiometry towards both Li and Ti rich compositions has frequently been reported in studies in the Li 2 O-TiO 2 system [31,36]. Additionally the recrystallization of orthosilicate was not clearly observed upon cooling from a composition of γ-Li 2 TiO 3 +liquid down to room temperature for intermediate compositions (samples 2-7). This may further indicate solid solution with excess Li incorporated into Li 2 TiO 3 and/or Li 2 SiO 3 although the evaporation of Li from the liquid phase is an additional contributing factor.

Conclusions

Biphasic mixtures in the quasi-binary Li 2 TiO 3 -Li 4 SiO 4 system offer the scope for improved properties, relative to single phase materials, for tritium breeding applications in fusion reactors. For this reason the solution based synthesis of materials in this system was studied using organometallic precursors with a focus on crystallisation and phase stability behaviour. Owing to deviation from target stoichiometries, the presently reported procedures did not result in purely biphasic Li 4 SiO 4 -Li 2 TiO 3 mixtures however it is likely that such two-phase compositions are attainable through solution based methods employing appropriate processing parameters including the addition of excess lithium. In addition, alternative fabrication methods warrant future investigation and in particular the use of inorganic precursor compounds merits further research in order to shed light on the lithium rich region of the ternary Li 2 O-SiO 2 -TiO 2 system, which remains poorly understood. In the synthesis procedures reported here we have identified several issues which require consideration for future solution-based syntheses of mixed phase materials.

 Lithium sublimation and its dependence on firing conditions and composition  Non-stoichimetry in Li 2 TiO 3 , particularly at high temperatures  Ubiquitous formation of metasilicate owing to favourable crystallisation kinetics of this phase  Potential formation of organolithium products in precursor sols, which may be controlled through parameters of time, temperature, pH and composition  Crystallisation of carbonate through reaction with retained organic content  The existence of a likely monotectic system with liquid formation at ~1050°C.

Figure 1 .

 1 Figure 1. Composite diagram of reported phase equilibria in the Li 2 O-TiO 2 -SiO 2 system [30-32, 34-37], indicating liquidus temperatures and the positions of compositions 1-11 targeted in the present work.

Figure 2 .

 2 Figure 2. XRD patterns for pellet samples subsequent to firing at 900°C prepared by chloride route (left) and hydroxide route (right). Compositions correspond to (a),(b) LT; (c),(d) L3TS; (e),(f) L2S. As shown in Figure 2(e), chloride based samples of L2S composition were predominantly of Li 2 SiO 3 phase with only trace signals of the orthosilicate phase observed in the form of low intensity peaks around 17°, 33.6° and 34.6° 2θ. Any coexistence of Li 4 SiO 4 alongside the 1:1:1 Li 2 TiSiO 5 phase cannot occur under conditions of equilibrium owing to these phases lying in separate compatibility triangles in the ternary phase equilibrium system.

Figure 3 shows

 3 Figure3shows FTIR spectra from sol and bulk dried precipitates of a 1:1 sol of L2S:LT. Lines indicate reported IR shifts of ethylithium[56][57][58]. The large stretching vibration mode observed around 3400 cm -1 is indicative of O-H bonds, present in solvent and precursor compounds. The lack of a significant H-O-H bending peak around 1630 cm -1 in the sol suggests the lack of residual or structural water in the product slurry while the presence of this peak in the dried precipitates may indicate surface adsorption of water vapour. At 1098 and 1050 cm -1 a possible C-Li stretching mode is observed. It should be noted that the formation of ethyl-lithium cannot be categorically concluded from these data, however the formation of an orange coloration may be indicative of reactions involving organolithium compounds which often degrade to form lithium hydride upon heating[59,60].

Figure 3 .

 3 Figure 3. FTIR spectra of combined lithium silicate and lithium titanate precursor sols (composition 7) and dried precipitates.

Figure 4 .

 4 Figure 4. (a) XRD pattern for hydroxide-route-synthesised material of LT composition subsequent to drying at 180°C. (b) Temperature varied XRD for hydroxide route synthesised LT material. From front towards back shows increasing temperature, up to 1200°C, followed by cooling. Reference patterns are superimposed on horizontal plane. (Interactive figure available online)

Figure 5 .

 5 Figure 5. (a) XRD pattern for hydroxide-route-synthesised material of L3TS composition subsequent to drying at 180°C. (b) Temperature varied XRD for hydroxide route synthesised L3TS material. From front towards back shows increasing temperature, up to 1200°C, followed by cooling. Reference patterns are superimposed on horizontal plane. (Interactive figure available online)

Figure 6 .

 6 Figure 6. (a) XRD pattern of L2S material fabricated by hydroxide route subsequent to drying at 180°C (b) Temperature varied XRD for hydroxide route synthesised LT material. From front towards back shows increasing temperature, up to 1200°C, followed by cooling. Reference patterns are superimposed on horizontal plane. (Interactive figure available online)

( 1 ) 2 ) 4 ) 5 ) 6 )

 12456 Endothermic removal at 100°-200°C of physisorbed moisture (Exothermic combustion at ~200°-400°C of residual organic groups (propoxide and ethoxide from TTIP and TEOS respectively) and α to β Li 2 TiO 3 phase transformation. (3) Endothermic reaction at composition dependant temperatures in the range 520°-580°C of Li 2 CO 3 to form Li 2 TiO 3 and, more significantly, Li 2 SiO 3 accompanied by mass loss through release of CO 2[70] (Endothermic behaviour with fluxed melting of residual Li 2 CO 3 (<724°C) accompanied by further silicate/titanate formation following reported reactions[70,71]. (Endothermic behaviour at temperatures above 900°C resulting from grain growth, phase transformation in Li 2 TiO 3 , and melting of orthosilicate. (Strongly exothermic crystallisation of Li 2 TiO 3 , Li 2 SiO 3 and Li 4 SiO 4 during cooling from 1350°C down to 600°C as well as the γ to β-Li 2 TiO 3 phase transformation (7) Exothermic behaviour accompanied by slight mass increase around 400°C during cooling of silicate containing compositions, potentially resulting from the reaction of Li 4 SiO 4 with atmospheric CO 2 , which is reported to occur most rapidly around this temperature regime[72].

Figure 7 .

 7 Figure 7. TG/DSC profiles for (a) LT material, (b) L3TS material and (c) L2S material.

Figure 8 .

 8 Figure 8. Behavioural phase transformation diagram from a summary of temperature varied XRD and DSC data of the 11 compositions studied in heating mode.

Table

Table 1 : Compositions of materials fabricated Sample Target Ratio Li 2 TiO 3 :Li 4 SiO 4 Ti:Si Primary oxide composition mol / wt % Li 2 O TiO 2 SiO 2

 1

	1	1 : 0	1:0	50.00 / 27.2	50 / 72.8	0 / 0
	2	9 : 1	27:2	51.67 / 28.9	45 / 67.3	3.33 / 3.8
	3	8 : 2	6:1	53.33 / 30.7	40 / 61.6	6.67 / 7.7
	4	7 : 3	21:8	55.00 / 32.6	35 / 55.5	10.00 / 11.9
	5	6 : 4	9:4	56.67 / 34.6	30 / 49.0	13.33 / 16.4
	6	1 : 1	3:2	58.33 / 36.8	25 / 42.1	16.67 / 21.1
	7	2 : 3	1:1	60.00 / 39.0	20 / 34.8	20.00 / 26.2
	8	3 : 7	9:14	61.67 / 41.5	15 / 27.0	23.33 / 31.5
	9	1 : 4	3:8	63.33 / 44.1	10 / 18.6	26.67 / 37.3
	10	1 : 9	1:6	65.00 / 46.9	5 / 9.6	30.00 / 43.5
	11	0 : 1	0:1	66.67 / 49.9	0 / 0	33.33 / 50.1

Acknowledgements

This work was supported by the Group of Eight -DAAD Joint Research Cooperation Scheme.


Chongpu Zhai

Dorian Hanaor

Gwénaëlle Proust

Laurence Brassart

Yixiang Gan
email: yixang.gan@sydney.edu.au

Interfacial electro-mechanical behaviour at rough surfaces

Keywords: Rough surfaces, contact stiffness, electrical contact resistance, electro-mechanical behaviour

published or not. The documents may come

Introduction

Interfacial electro-mechanical behaviour is fundamental to indicators of energy system performance such as electrical power loss, cycle life, and storage capacity in lithium-ion batteries [START_REF] Lee | Kinetics and fracture resistance of lithiated silicon nanostructure pairs controlled by their mechanical interaction[END_REF][START_REF] Bauer | Influence of dry mixing and distribution of conductive additives in cathodes for lithium ion batteries[END_REF], sodium-ion batteries [START_REF] Islam | Lithium and sodium battery cathode materials: computational insights into voltage, diffusion and nanostructural properties[END_REF], solid oxide fuel cells [START_REF] Abdeljawad | Connecting microstructural coarsening processes to electrochemical performance in solid oxide fuel cells: An integrated modeling approach[END_REF], photovoltaics [START_REF] De | Research on photovoltaics: review, trends and perspectives, Power Electronics Conference (COBEP)[END_REF] and thermoelectric systems [START_REF] Bell | Cooling, heating, generating power, and recovering waste heat with thermoelectric systems[END_REF]. determining how contacting solids interact with one another in a variety of processes including thermal swelling, electrical conduction, electrochemical reactions, friction, and adhesion [START_REF] Johnson | Contact mechanics[END_REF][START_REF] Holm | Electric contacts[END_REF][START_REF] Jin | Mechanics of axisymmetric adhesive contact of rough surfaces involving power-law graded materials[END_REF]. In energy storage and conversion applications the effective mechanical and electrical properties of granular electrode structures can be connected to microstructural characteristics [START_REF] Bauer | Influence of dry mixing and distribution of conductive additives in cathodes for lithium ion batteries[END_REF][START_REF] Ott | A micromechanical model for effective conductivity in granular electrode structures[END_REF]. However, the interfacial properties in the existing modelling approaches are usually simplified [START_REF] Xu | Mechanical interactions regulated kinetics and morphology of composite electrodes in Li-ion batteries[END_REF].

Surface morphology plays an essential role in

Energy losses at interfaces are usually associated with ohmic heating (also known as Joule heating) due to the passage of an electrical current through contacting surfaces. In the context of energy management, improved electrical contacts play a prominent role in mitigating energy losses in battery assemblies. The energy loss due to the electrical contact resistance (ECR) at interfaces between electrode layers and at contacts between electrodes and current-collectors can be as high as 20% of the total energy flow of the batteries under normal operating conditions [START_REF] Taheri | Investigating electrical contact resistance losses in lithium-ion battery assemblies for hybrid and electric vehicles[END_REF][START_REF] Kim | Effect of electrode configuration on the thermal behavior of a lithium-polymer battery[END_REF].

The effects of the mechanical properties and surface roughness of electrical contacts on the performance of electrical connectors are of great importance in terms of potential drop and heat accumulation in contact zones [START_REF] Kogut | Electrical conductivity and friction force estimation in compliant electrical connectors[END_REF][START_REF] Srinivasan | Analysis of electrochemical and thermal behavior of Li-ion cells[END_REF]. A significant increase in ECR can be caused by interfacial resistance due to the inevitable presence of resistive surface films, including corrosion deposits, fracture debris, oxide and hydrated layers at electrical contacts, resulting in excessive ohmic heating. In extreme cases, the heat can bring about system failure through sparks, fire and even melting of system components [START_REF] Taheri | Investigating electrical contact resistance losses in lithium-ion battery assemblies for hybrid and electric vehicles[END_REF][START_REF] Dorbolo | Effects of electromagnetic waves on the electrical properties of contacts between grains[END_REF][START_REF] Zhai | Stress-Dependent Electrical Contact Resistance at Fractal Rough Surfaces[END_REF].

The stress dependence of ECR at rough surfaces can be associated with the varying true interfacial contact area during system operation. However, the direct quantitative evaluation of real interfacial contact area between bodies through either experimental measurements or numerical simulations remains highly challenging due to the complex multi-scale morphologies exhibited by rough surface structures [START_REF] Pohrt | Normal contact stiffness of elastic solids with fractal rough surfaces[END_REF][START_REF] Carbone | Contact mechanics of rough surfaces: a comparison between theories[END_REF][START_REF] Hanaor | Contact mechanics of fractal surfaces by spline assisted discretisation[END_REF]. Significant difficulties remain in relating interfacial electro-mechanical properties to surface structure descriptors.

Employing

Theoretical background

Compared with the apparent or nominal contact area, the true area of contact at an interface is considerably smaller due to the existence of surface roughness. As shown in Fig. 1, when an electric current is conducted between two contacting solids, the restricted contact area, which depends on the size and spatial distribution of contacting asperities, causes additional constriction resistance (known as the electrical contact resistance, ECR) [START_REF] Greenwood | Constriction resistance and the real area of contact[END_REF]. In addition to the constriction resistance resulting from the limited areas of true contact at an interface, ECR is also affected by the existence of resistive surface films, such as oxide layers [START_REF] Holm | Electric contacts[END_REF]. Theories of ECR have since been further developed to include the effects of elastic-plastic deformation of the contacting asperities due to applied forces, multi-scale surface topography, size effects, and the contribution of insulating films between contacting bodies [START_REF] Pohrt | Normal contact stiffness of elastic solids with fractal rough surfaces[END_REF][START_REF] Barber | Bounds on the electrical resistance between contacting elastic rough bodies[END_REF][START_REF] Kogut | Electrical contact resistance theory for conductive rough surfaces separated by a thin insulating film[END_REF][START_REF] Mikrajuddin | Size-dependent electrical constriction resistance for contacts of arbitrary size: from Sharvin to Holm limits[END_REF][START_REF] Jackson | Rough surface electrical contact resistance considering scale dependent properties and quantum effects[END_REF]. The resistance of a contact with area, 𝑎, is given by [START_REF] Sharvin | On the possible method for studying fermi surfaces[END_REF]. where 𝜌 1 and 𝜌 2 are the specific resistivities of the contacting surfaces. On the other hand, when 𝑟 > λ, the electron transport through the contact can be treated classically (Holm contact). The resistance can be expressed in the following form [START_REF] Holm | Electric contacts[END_REF] :

𝑅 𝑆 = 𝜆(𝜌 1 + 𝜌 2 ) 2𝑎 , (1)
𝑅 𝐻 = √𝜋 (𝜌 1 + 𝜌 2 ) 4√𝑎 . (2)
The total electrical conductivity, 𝐺 𝑐 , of an interface is assumed to be the sum of individual conductivity 𝐺 𝑖 = 𝑅 𝑖 -1 at microcontacts, corresponding to the restriction resistances in parallel:

𝐺 𝑐 = ∑ 𝐺 𝑖 . (3)
In the case of rough surfaces with multiple contacting asperities, there is a distribution in the size of the contact area. The Sharvin and Holm expressions should therefore be considered as limiting cases.

In general, the area of contacts used in Eqs.

(1) and ( 2), and therefore the contact resistance, depends on the applied pressure.

Using theoretical and numerical approaches [START_REF] Pohrt | Normal contact stiffness of elastic solids with fractal rough surfaces[END_REF][START_REF] Barber | Bounds on the electrical resistance between contacting elastic rough bodies[END_REF][START_REF] Kogut | Electrical contact resistance theory for conductive rough surfaces[END_REF][START_REF] Paggi | Contact conductance of rough surfaces composed of modified RMD patches[END_REF], power-law type semiempirical correlations between the contact resistance and the normal pressure have been proposed for rough interfaces. In particular, previous theoretical studies found the contact conductance to be linearly proportional to the incremental stiffness [START_REF] Pohrt | Normal contact stiffness of elastic solids with fractal rough surfaces[END_REF][START_REF] Barber | Bounds on the electrical resistance between contacting elastic rough bodies[END_REF]. 1. These values are found to be comparable with descriptors of naturally occurring surfaces [START_REF] Persson | On the nature of surface roughness with application to contact mechanics, sealing, rubber friction and adhesion[END_REF]. Values of RMS roughness were calculated as the RMS average of the profile height from the scanning. In the digitised scanning, the slopes of triangular units formed by three adjacent pixels are used to calculate the RMS slope, which is commonly chosen as a higher order surface descriptor [START_REF] Majumdar | Role of fractal geometry in roughness characterization and contact mechanics of surfaces[END_REF][START_REF] Zhai | The Role of Surface Structure in Normal Contact Stiffness[END_REF]. The scaled triangulation method [START_REF] Zhai | The Role of Surface Structure in Normal Contact Stiffness[END_REF] was used for the calculation of tend to be dominated by finest scale surface characteristics [START_REF] Majumdar | Role of fractal geometry in roughness characterization and contact mechanics of surfaces[END_REF][START_REF] Zhai | The Role of Surface Structure in Normal Contact Stiffness[END_REF]. The unloading stiffness is here defined as the initial slope of the unloading curve, 𝑘 = d𝐹/d𝑆 , where 𝐹 designates the normal force and 𝑆 is the indentation depth. Subsequently, the reduced elastic modulus 𝐸 𝑟 was derived from the measured unloading stiffness as

It
𝑘 = 𝛽 2 √𝜋 𝐸 𝑟 √𝐴 , ( 4
)
where 𝐴 is the apparent contact area of the indenter tip and 𝛽 is a geometrical constant, taken as unity for a flat punch [START_REF] Oliver | Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology[END_REF]. Eq. ( 4) is a fundamental equation for assessing the The reduced modulus depends on the elastic properties of both the tested specimen and the indenter tip:

1 𝐸 𝑟 = 1 -𝜐 𝑐 2 𝐸 𝑐 + 1 -𝜐 𝑖 2 𝐸 𝑖 , (5)
where 𝜐 𝑖 and 𝜐 𝑐 represent the Poisson's ratios of the indenter tip material and the tested specimen respectively. For the diamond indenter tips used in this research, 𝐸 𝑖 and 𝜐 𝑖 are typically 1140 GPa and 0.07, respectively. Equations ( 4) and ( 5 We express here the power-law relation of the contact stiffness with the applied normal force

𝐸 𝑐 ∝ (𝐹) 𝛼 𝐸 , (6)
where 𝛼 𝐸 is the exponent of the power-law function [START_REF] Buzio | The contact mechanics of fractal surfaces[END_REF][START_REF] Jiang | A contact stiffness model of machined plane joint based on fractal theory[END_REF]. It should be noted that the fitting curves are achieved excluding the contributions from the measured stiffness under stress levels higher than 100 MPa, where the surface shows an apparent yield phenomenon. For all the three surface types, the value of the exponent 𝛼 𝐸 varies from 0.4626 to 0.6048 (in Table 1), changing as the fractal dimension increases.

In comparison, the typical value in cases of

Hertzian contact of two elastic spheres is 1/3, as shown in section 6. The power-law relationship found here experimentally is in good agreement with previous theoretical predictions on a quantitative basis [START_REF] Pohrt | Normal contact stiffness of elastic solids with fractal rough surfaces[END_REF][START_REF] Buzio | The contact mechanics of fractal surfaces[END_REF][START_REF] Jiang | A contact stiffness model of machined plane joint based on fractal theory[END_REF]. Full procedures and results have been previously published in greater detail [START_REF] Zhai | Stress-Dependent Electrical Contact Resistance at Fractal Rough Surfaces[END_REF].

The applied sweep current test consisted of two phases: a "loading" phase (P1) with current increasing logarithmically from 0.0001 A to 1.5 A, followed by an "unloading" phase (P2) with current decreasing logarithmically from 1.5A back to 0.0001A. Both phases were conducted under conditions of constant normal load.

During the sweeping loops, the voltage was recorded at a frequency of 2 kHz. The twophase sweeping process was completed within 0.2 seconds in order to avoid significant time dependant resistance degradation. in Table 1. Moreover, for all the three types of surfaces as shown in Fig. 6, the electrical conductance reaches a plateau under higher stresses, with the plateau value correlating to the RMS roughness. In the lower stress regime, the experimental data no longer seems to follow the power law.

Discussion

The key experimental results for contact stiffness and electrical conductance, measured for three types of rough surfaces, are summarised in Table 1. Both the contact stiffness and electrical conductance increase with the applied force, exhibiting power law behaviours with exponents 𝛼 𝐸 and 𝛼 𝐺 , respectively. These exponents vary with the surface roughness and increase with the fractal dimension. In contrast, no evident correlation between the RMS roughness value and the exponent was found. This suggests that the correlation between contact stiffness, electrical conductance and applied force is dominated by fine scale surface characteristics.

We rationalize the experimental findings by developing the following scaling arguments. Both the contact stiffness and conductance primarily depend on the true contact area 𝐴 𝑐 , which evolves during mechanical loading and cannot be determined in a direct way based on the considered measurement methods. As a workaround, we estimate the true contact area based on the following expression for the incremental stiffness:

𝑘 = 𝛽′ 2 √𝜋 𝐸 𝑟 ′ √𝐴 𝑐 , (8)
where 𝐸 𝑟 ′ is the (constant) reduced elastic modulus calculated for the bulk elastic properties of the tested material and indenter:

𝐸′ 𝑟 = ((1 -𝜐 * 2 )/𝐸 * + (1 - 𝜐 𝑖 2 )/𝐸 𝑖 ) -1
, and 𝛽′ is a geometric factor of the order of unity. By writing Eq. ( 8), we assume that the effect of surface roughness on the measured incremental stiffness can be described by considering the true contact area 𝐴 𝑐 (rather than the project contact area

𝑎 = 𝜋 ( 3𝑅𝐹 4𝐸′ 𝑟 ) 2/3 , (10)
where 𝑅 = (1/𝑅 1 + 1/𝑅 2 ) -1 is the equivalent radius of the two spheres, and the reduced modulus 𝐸 𝑟 ′ was introduced in Eq. [START_REF] Holm | Electric contacts[END_REF]. Eqs. ( 9) and [START_REF] Ott | A micromechanical model for effective conductivity in granular electrode structures[END_REF] indicate that the contact stiffness is a power function of the load, with an exponent 1/3. This simple scaling analysis is not consistent with our experimental findings for 𝛼 𝐸 , which takes significantly higher values. However, the scaling analysis based on the Hertzian contact theory does not consider the changing number of contact asperities, 𝑛, for the increasing load. Furthermore, at the rough interface, the contact areas are not uniformly distributed [START_REF] Mandelbrot | Fractal character of fracture surfaces of metals[END_REF], and interactions between asperities can exhibit complex deformation mechanisms, such as plastic deformation, adhesion, and friction.

On the other hand, introducing relation [START_REF] Ott | A micromechanical model for effective conductivity in granular electrode structures[END_REF] into Eqs. ( 1) and ( 2) for the Holm and Sharvin resistance at a single contact, one finds that:

𝐺 𝐻 = 4 𝜌 ̃(3𝑅𝐹 4𝐸′ 𝑟 ) 1/3 , 𝐺 𝑆 = 2𝜋 𝜆𝜌 ̃(3𝑅𝐹 4𝐸′ 𝑟 ) 2/3 , (11)
where 𝜌 ̃= (𝜌 1 + 𝜌 2 ). Combining ( 11) with (3), we find that the total conductance of the rough surface, 𝐺 𝑐 , approximately scales with the force following a power law with the exponent ranging from 1/3 (Holm) to 2/3 (Sharvin), depending on the dominant conduction mechanisms at individual contacts.

We further consider the contact model for a conical punch [START_REF] Sneddon | The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile[END_REF], where the contact area, 𝑎, is found to be linearly proportional to the applied force, 𝐹. With the same analysis as above, an exponent 𝛼 𝐸 = 0.5 can be derived for the contact stiffness, and an exponent 𝛼 𝐺 = 0.5~1 for the electrical conductance. This provides a better representation for the exponents of contact stiffness and electrical conductance as compared to the prediction by the Hertzian solution. Again, the exponents derived from this simple scaling analysis are lower than the experimental values of 𝛼 𝐺 . This may also be due to the fact that the scaling neglects the increase in number of contacting points under increasing compression.

Despite these discrepancies, it is interesting to consider the ratio of the exponents for

  interfaces with random multiscale morphologies. First, we conducted contact stiffness measurements using flat-tipped diamond nanoindentation tests on a set of rough surfaces. Then, we examined the evolution of electrical conduction with varying compressive loads. Based on these results, discussions are extended to the relationship between electrical contact conductance and contact stiffness. This study demonstrates the importance of a multi-physics understanding of the origins of the electromechanical behaviour at interfaces in order to improve the reliability and performance of electrical contacts in energy systems.

Fig. 1 .

 1 Fig. 1. Schematics of electrical conduction through a rough interface exhibiting multi-scale surface features.

  fractal dimension values. It was found that the smaller the particles used to modify the surfaces the larger the fractal dimension was. The fractal dimension, a cross-scale surface descriptor that incorporates localised and macroscopic surface information provides an effective means for modelling engineering surfaces with random self-affine multi-scale properties in the characterisation of surfaces and particles[START_REF] Almqvist | Fractal analysis of scanning probe microscopy images[END_REF]. The advantage of using surface fractality as a cross-scale surface descriptor stems in part from the tendency of first order descriptors (e.g., maximum height or mean roughness of the surface) to be dominated by highest scale features, while secondary descriptors (e.g., slope)

Fig. 2 . 4 .

 24 Fig. 2. SEM images and typical surface profiles of aluminium samples subjected to different surface treatments: (a) polished, S1; (b) sand blasted with 300 μm-sized glass beads, S2; (c) sand blasted with 50 μm-sized glass beads, S3.

Fig. 3 .

 3 Fig. 3. Typical loading-displacement curves of nanoindentation tests on three types of surfaces. Ten partial unloading tests were carried out to isolate elastic contributions to contact stiffness under different loading levels. The three flat indenter tips used in the experiments (FLT-D050, FLT-D100, FLT-D500) are also illustrated for comparison.

  Fig. 4 shows the evolution of the contact stiffness with the applied force for the different surfaces. Here, we normalised the contact elastic modulus 𝐸 𝑐 by the Young's modulus of aluminium alloy 5005, 𝐸 * =

Fig. 4 .

 4 Fig. 4. Curve fitting for the normalised stiffness, 𝐸 𝑐 /𝐸 * , and the normalised applied force, 𝐹/(𝐸 * 𝐴), for three tested surfaces, with 𝐸 * being the Young's modulus of the tested material, and 𝐴 the apparent contact area.

Fig. 5

 5 Fig. 5 shows the typical resistance-current characteristics for polished samples obtained from sweeping current tests. Each individual loop corresponds to a distinct load. The five loops shown demonstrate similar trends known as the Branly effect [30, 31], i.e., the measured resistance

Fig. 5 . 7 )

 57 Fig. 5. Typical measured results for polished samples using current sweep under various stresses (0.031 MPa, 0.061 MPa, 0.122 MPa, 0.245 MPa and 0.490 MPa, corresponding to loops 1-5, respectively) with solid lines representing the first phase (P1) and the dashed lines showing the second phase (P2).

Zhai,Fig. 6 .

 6 Fig. 6. Stress-dependent electrical conductance of different surfaces under various loading levels with a testing current of 10 mA, with 𝐸 * being the value of the Young's Modulus of the tested material, 𝐴 the projected area of the tested samples, and 𝐺 0 being set to 1 Ω -1 . The curve fitting were conducted for loading levels in a range of [0.031 MPa, 3.973 MPa].

Fig. 6 .

 6 Fig. 6. Therefore in this study the effect of the oxide layer is minimal and does not interfere with the findings. The observations made in this study can provide insights into the physical origin of the topological dependence of transport phenomena in energy materials applied in conversion, storage and generation systems. Parametric studies in to the performance of energy systems often yield unexpected behaviour arising from changes to the structure or processing of complex materials such as granular electrodes [2, 10]. The present work suggests that the structure and mechanics of interfaces in these systems may be in part a contributing factor to the observed processing dependence of performance.

Zhai, Chongpu, et al. "Interfacial electro-mechanical behaviour at rough surfaces." Extreme Mechanics Letters 9 (2016): 422-429.

Zhai, Chongpu, et al. "Interfacial electro-mechanical behaviour at rough surfaces." Extreme Mechanics Letters 9 (2016): 422-429. 3

3. Surface preparation and characterisation

		should be noted that many mechanisms of
		surface structure evolution have been
		observed during electrical conduction
		through rough interfaces, including
		dielectric breakdown of oxide layers,
		localised	current-induced	welding,
		chemical disorder arising with random
		composition and oxidation processes in
		corrosive environments, and surface
		diffusion [30, 31]. These phenomena are
		outside the scope of this paper.
		μm. The sand blasting process was
		conducted for one minute, a duration which
	Round disks, with a diameter of 25 mm,	was sufficient to yield homogeneously and
	made of aluminium alloy 5005 were used to	isotropically modified surface features.
	fabricate specimens for both the	The sample surfaces were fabricated in
	measurement of the interfacial contact	such a way that each set of surfaces
	stiffness and ECR. For each individual	exhibited a distinct combination of surface
	sample, both the top and bottom surfaces	roughness indicators, namely root mean
	were subjected to the same treatment using	squared (RMS) roughness and fractal
	standard polishing and sand blasting	dimension. Fig. 2 shows scanning electron
	procedures. The average diameters of the
	two selected groups of glass beads used in
	blasting treatments were 50 μm and 300

microscope (SEM) images and typical surface profiles of the different surface types used in this work. Based on the threedimensional digitised topographies obtained by optical surface profilometry (NanoMap 1000WLI), the mean values of RMS roughness, fractal dimension and RMS slope with standard deviations over ten scans on different samples were calculated, as shown in Table

Zhai, Chongpu, et al. "Interfacial electro-mechanical behaviour at rough surfaces." Extreme Mechanics Letters 9 (2016): 422-429.

elastic properties in nanoidentation tests.

Zhai, Chongpu, et al. "Interfacial electro-mechanical behaviour at rough surfaces." Extreme Mechanics Letters 9 (2016): 422-429.

	𝐴 ) and bulk material properties in the
	fundamental Eq (4). By comparing Eqs (4)
	and (8), and considering that 𝐸 𝑖 ≫ 𝐸 * >
	𝐸 𝑐 , we obtain the following scaling relation:
	𝐸 𝑐 /𝐸 * ∝ 𝛽′√𝐴 𝑐 /𝐴 .	(9)
	Next, we consider the true contact area to
	be the sum of 𝑛 individual contact areas,
	with average 𝑎 = 𝐴 𝑐 /𝑛 . Here, individual
	asperities are assumed not to interact with
	one another during deformation. In order to
	relate the evolution of 𝑎 to the applied
	force, we first rely on a classical result of
	Hertzian contact theory. Representing a
	single contact by two spheres with radii 𝑅 1
	and 𝑅 2 squeezed against each other, the
	contact area varies with the applied force
	according to

Zhai, Chongpu, et al. "Interfacial electro-mechanical behaviour at rough surfaces." Extreme Mechanics Letters 9 (2016): 422-429.

	contact	stiffness	and	electrical	decreasing from 2 to 1. Under sufficiently
	conductance, 𝛼 𝐺 /𝛼 𝐸 . This ratio	high forces, and hence high contact areas,
	characterizes the power law relation	the electric and mechanical properties
	between the conductance and contact	converge to those of the bulk material, as
	stiffness, with 𝐺 𝑐 ∝ (𝐸 𝑐 ) 𝛼 𝐺 /𝛼 𝐸 . According	expected.
	to the scaling analysis, this ratio ranges from 1 (Holm mechanism) to 2 (Sharvin	The ratio 𝛼 𝐺 /𝛼 𝐸 also tends to increase with the fractal dimension. A surface with a
	mechanism).	Experimentally,	an	higher fractal dimension demonstrates
	approximate value of 2 was found for loading levels in a range of 𝐹/(𝐸 * 𝐴) ∈ [5 × 10 -7 , 5 × 10 -5 ] . For sample 3,	Sharvin dominated conductance ( 𝛼 𝐺 / 𝛼 𝐸 ~2), while a less fractal surface presents combined Sharvin and Holm-type
	similar fitting in the low load region gives a higher value of 𝛼 𝐺 , and hence a higher	conductance (𝛼 𝐺 /𝛼 𝐸 between 1 and 2).
	value of the ratio 𝛼 𝐺 /𝛼 𝐸 , suggesting a	Note that in the contact stiffness
	larger proportion of Sharvin-type contacts at low loads. Similar observations seem to	measurements, the flat indenter tips can be considered as rigid flat surfaces (𝐸 𝑖 ≫ 𝐸 * ),
	hold as well for samples 1 and 2, but the	corresponding to a rough-to-flat contact
	transition takes place at even lower loads.	problem. In comparison, our interfacial
	As the load increases, new asperities come	electrical resistance experiments involve
	into contact, the contacting points enlarge	rough-to-rough contacts. However, a
	and small microcontacts merge forming	scaling analysis based on rough-to-flat
	large contacts, resulting in better	contact would yield identical exponents in
	conduction. The dominant conduction	the power law functions (10) and (11) [28,
	mechanism transitions from a Sharvin-type	33].
	to a Holm-type with the exponent ratio

Table 1 .

 1 Sample surface characteristics for different surface treatments

	Sample type	RMS roughness / μm	Fractal dimension, Df	RMS slope	Contact stiffness, 𝛼 𝐸	Electrical conductance, 𝛼 𝐺	Exponent ratio, 𝛼 𝐺 /𝛼 𝐸
	S1	0.057 ± 0.005	2.093 ± 0.062	0.009 ± 0.001	0.463 ± 0.022	0.816 ± 0.081	1.762 ± 0.194
	S2	4.179 ± 0.194	2.551 ± 0.022	0.224 ± 0.015	0.569 ± 0.029	1.026 ± 0.049	1.803 ± 0.126
	S3	2.970 ± 0.276	2.626 ± 0.017	0.202 ± 0.010	0.605 ± 0.022	1.494 ± 0.134	2.469 ± 0.239
	In the experiments, both contact stiffness	alloys ubiquitously exhibit thin passivated
	and conductance may be affected by oxide	hydrous and oxide layers arising from
	layers at the sample surfaces. Aluminium	reaction with atmospheric oxygen and
					water. This nanoscale layer exhibits locally

, et al. "Interfacial electro-mechanical behaviour at rough surfaces." Extreme Mechanics Letters 9 (2016): 422-429.

Acknowledgements

Financial support for this research from the Australian Research Council through grants DE130101639 is greatly appreciated. The authors acknowledge the facilities and the Zhai, Chongpu, et al. "Interfacial electro-mechanical behaviour at rough surfaces." Extreme Mechanics Letters 9 (2016): 422-429.


French influences in the works by Bacevičius

Jacques Amblard, LESA Abstract. During his stay in Paris, Lithuanian composer Vytautas Bacevičius was probably imbued, by a certain scientific (positivist?) atmosphere, which was important in all the arts at this time in the French Capital. This could have provided the "inspiration" for some of his future works, such as Electric poem (1932), Cosmic symphony (1960) or Graphic (1964). Paris would also have been the place to study certain aspects of French musical "impressionism". One can find harmonic procedures characteristic of Debussy or Ravel, for instance, in certain piano works of the French period (such as the Poem op. 10), procedures which don't appear before in his works. Several aspects of French neoclassicism also appear in his compositions. A certain taste for ostinato and polytonality may have come from Stravinsky (who was still living and creating his works in Paris at this time), but also Milhaud and Honegger, whose very pragmatic, "scientific", but also neoclassical Pacific 231 was famous in Paris for several years already. It is also possible that Varèse, who had just returned from the United States (and was about to stay in Paris for several years before flying back to America) served as some kind of model for Bacevičius, in connection with the scientific inspiration of the future works, of course, but also the positive evaluation of the New World (America), which Varèse was probably symbolising in Paris at this time period. There are few documents about the Parisian period of Bacevičius, between 1928 and1932. We can attempt to trace possible French influences of these three years by studying the evolution of the musical language.

First of all, let's start by examining a piano score of the beginning of the French period, the famous Poema Nr. 4 op. 10. It's the work of a young composer, and we will see that, as a work of youth, it shows a great ambition of being a « total work », of reaching every goal of modern art, of making the synthesis of many modern or previous musical tendencies. And the first influence that we can locate is not French, but German. Like many young composers of the 20 th century, Bacevičius obviously admires Wagner. We can find the chromatic shadow of a famous Wagnerian leitmotiv in the melodic line of the start of the Poema Nr 4: the leitmotiv that starts the opera Tristan and Isolde. In Wagner's leitmotiv, the strings begin with a jump of minor sixth and then gradually go down three steps on a chromatic scale. In the case of Bacevičius's Poema , the piano begins with a jump of fifth (thus, an interval close to the Wagnerian first sixth minor) and then, also climbs down a chromatic scale (three degrees again)1 .

Besides this Wagner-like melodic line, the young Bacevičius also uses the famous « Tristan chord », F, B, D#, G#, transposed one tone higher (as in its second occurrence in the work of Wagner itself), G, D b, F, B b. Already in the beginning of the Poema, the harmony seems to turn around this chord. Now, let's examine three bars in particular, further in the score (bars 26-28).

Poema Nr. 4, bars 26-28.

We can recognize the temptation of chromaticism (as often in this work and in Bacevičius's works in general) in the upper part of the right hand (bars 26-27), especially between the second note (G#) and the eighth note (F#). Chromaticism probably betrays Wagner's influence again. We can also find, this time precisely, an explicit quotation of the « Tristan » very specific chord (at the third beat of the first bar, left hand). In a way, Bacevičius seems as fascinated by Wagner as the young Viennese school can be (Schönberg, Berg and Webern). He quotes explicitly the « Tristan chord » like Alban Berg did it himself in the last movement (Largo desolato) of his Lyrical set (op. 15), composed three years before, in 1926. Bacevičius perhaps already knows this Viennese School, or perhaps follows a parallel way. Indeed, beyond this fascination for Wagner, like Schönberg, he also uses a kind of « anti-tonality ». For example at the very beginning of the bar 26, the E (at the left hand) and the D# are probably not constructing an empty major seventh, but perhaps more some kind of « anti-octave », avoiding octave to avoid tonal consonance, like we can find many examples in Schönberg's or Berg's music since the beginning of the century. Finally we can presume that the first inclination of Bacevičius, in his personal history, is Germanic, and lies towards Wagner and perhaps also his followers, who have made the Viennese modernity. We can find that kind of Germanic influence even stronger in the Poema Contemplation op. 5.

However, what is characteristic of this Poema Nr. 4 is that we can also recognize a new possible influence, something that mixes itself with the Germanic tendency. Let us study precisely the chord of the bar 28 of Poème Nr. 4. It enharmonically sounds like a chord of dominant (E b, G, B b, C#), with « added notes » however, as we say in the French harmonic system. Here, these added notes (the two highest notes as a matter of fact), are precisely the « blue note », F# (because E b-F# is enharmonically a minor third added upon the major third of the chord of dominant) and the « added tritone », A (E b-A is a tritone, i.e. an augmented fourth, "diabolus in musica"). These exact « added notes » (blue note and tone), precisely added to a dominant chord, before sounding « jazzy like », or like the second style of Scriabin, are first of all typical of the French style, what one calls « musical impressionism », developed by Debussy and Ravel. Debussy is already dead at this time but Ravel is still alive and composes, in 1928, his most famous work, Bolero, where he still uses that kind of harmonic system. Bacevičius has probably heard this immediately famous Bolero or has been studying the new French harmony a year before his arrival in Paris.

If the beginning of the Poema is German like, the end is definitely French like, with one of those Ravelian big notes added chord, C, E, G, B b, D, A b : a chord of dominant (C, E, G, B b, D), with an added minor sixth (A b).

Paris, the « City of lights », might also be, for the young composer, the theatre of a new bright and powerful orchestral music, especially in a time where orchestra becomes, in Paris, the symbol of savage energy, of implacable mechanicism, using great brass and percussion parts, notably in recent works of French neo-classicism, far from the ascetic Viennese taste for chamber music. It must not be forgotten that Stravinsky is still living in Paris at this time. If he as well already turned himself to chamber music, and to a more quiet style, his Parisian followers have very well understood his first message of youth and energy, the message of his Rite of the Spring, whose first performance took place precisely in Paris fifteen years before (1913). The new Parisian orchestral works, which people can hear during those « Années folles », try notably to reach the strongest sound ever heard, using a hypnotic rhythm, as in the famous Pacific 231 by Arthur Honegger, which had been composed five years earlier, and which all the cultivated Parisians certainly still remembered very well. 1928, the year of Bacevičius's arrival in Paris, is the year of composition of another powerful, strongly rhythmical and famous "symphonic movement" of Honegger, Rugby. Like Pacific 231, Honegger's Rugby immediately became famous and Bacevičius might have heard about it, and perhaps heard the work itself in a concert. However, 1928 is most of all the composition year of Bolero, as we mentioned before, the loudest orchestral work ever written by Ravel, a work which is a good symbol of these years, glorifying simple musical parameters like rhythm, percussions, brass, and choosing an efficient shortness of the duration (like Honegger's Rugby and Pacific 231), around 15 minutes only, Bolero which Bacevičius must have known about. The climax is attempted at the end of the work, with maximal power of the brass, particularly of the percussions with a noisy regular snare (generating a rhythmical fascination evoking military music) and notably with the triptych: bass drum on the first beat, cymbal on the second, orchestral tom-tom on the third. Above all, the whole work is a great ostinato. Indeed, since the Rite of spring of Stravinsky, the composers know well that, ostinato is a good way of simply repeating and thus multiplying the new power of the orchestra.

Two years after the Poema n°4, Bacevičius writes his first Piano Concerto. Before that, he had written his Symphonic poem (also in Paris), then his first opera, as if the concept of orchestra that would come to be defining for him had been born in Paris. Thus, it seems as if he had wished this orchestra to be as powerful as possible. We can also notice subtle new traces of ostinato in it. It is a fact that it is not a Stravinskian or a Ravelian powerful ostinato that comes in play here, but rather an ironic one, similar to what can be found, for example, in a work of Francis Poulenc written one year before (in 1928), and which Bacevičius had perhaps heard, the Country concert which uses amusing ostinato in different moments, evoking a childish idiotic but particularly jovial process. In his own Concerto, Bacevičius uses a similar ironic ostinato, which is new and even surprising, in comparison with the serious and abstract Poema op. 10.

If we consider bars 250-251 of the Piano concerto Nr. 1, we notice the strange and amusing use of castanets, in the same curious rhythm as the violins (quaver, two semiquavers), a rhythm which probably caricatures some kind of derisory cavalcade2 . This rhythm underlines the ostinato theme of the violins, in which we also notice the ironic scraping noises generated by the G# (violins 2) and the A played together. Thus, this rubbing noise is not employed here as a Viennese anti-tonal process but more as a form of French ironic "false music". We can find again this kind of rubbing noises ostinato in the part of the bassoons, bars 252-253 (B scraping against C and F# rubbing sharply against G), processes which Poulenc in particular employed at this time, a caricature of the more amusing side of Prokofiev's3 style, his first model.

Then, the end of this concerto seems to seek the greatest power of rhythm and intensity, as if Bacevičius were trying to emulate a Honegger-like or Ravel-like -a "Parisian"orchestra. Let us make a digression. Great orchestral chords might be too heavy to follow subtle rules, in this concerto. Those chords sometimes seem to be tempted by a new and simple harmonic process, parallelism. Thus, those -at least partial -parallelisms are probably originally French, because they are, first of all, fundamental processes of the Ravelian and Debussyst harmony. They have probably been studied by Bacevičius during his French period.

It needs to be pointed out at this stage that Mechanicism is the new philosophy of art at this time. Thus, harmonic parallelism perhaps becomes the way of harmony to become mechanical, systematic, breaking the old rules of counterpoint in a very simple and blind "industrial" way. Rhythmic ostinato has perhaps also become a mirror of the repetitive sounds of factories. The musicians adopt a new anti-sentimentalism. Even Ravel, composing Bolero, wanted to write -he said himself, a "non music", which justified the blind ostinato in it. If we go back to Honegger's Pacific 231, we notice that it's not only an orchestral demonstration. The title is an ode to industry and science, it quotes the name of a famous American train and the work describes the repetitive sound of it. The work testifies the new scientific, technical, industrial inspiration in arts. People still dream about recent theories of Einstein. Science has not yet been discredited by the Second World War and the atomic bomb. It is still unreservedly considered to be the future of humanity. The writer Paul Valéry uses a new dry and objective style in his poems and will write in 1935 that industry must take a part in the production of art4 . Almost twenty years before this, Busoni predicted the same phenomenon to the young Varèse5 . Later, Varèse seems satisfied to be able to claim: "music is the science-art6 ". Varèse, in 1928, has just returned to Paris from the United States (before soon flying back to America again) and begins the composition of Ionisation, a piece whose title is explicitly related to the scientific view of the world and notably physics. The French film director Jean Painlevé creates the concept of « scientific film » and produces in 1928 his film L'oursin (The sea urchin), precisely in homage to Edgar Varèse. Bacevičius might have known about the works of Varèse. Indeed, when he returns to Lithuania in 1932, he composes his famous Electric poem.

The title shows an obvious scientific influence, of course, and recalls the title of a future work by Varèse (Electronic poem).

Like Honegger's Pacific 231, the Electric poem of Bacevičius is a great orchestral ode to « science and technology ». Being at one with Paul Valéry on this point, Bacevičius wrote that, composing this work, he wanted to "reject sentimentality". Like in the Piano Concerto Nr. 1, we can also find traces of partial "parallelism" in it, serving powerful brasses.

If we consider bars 92-94 of Electric poem, for orchestra, we notice that the harmonic writing of the brass is not exactly parallel. However, Bacevičius chooses a particularly efficient homorhythmic process, with quite a fast tempo for the brass (around 100 bpm at this moment of the work). Finally, the audition will give an impression of powerful parallelism because of the trumpets. Indeed, the three trumpets move in a parallel way and especially, trumpets 1 and 3 draw parallel fifths: Bacevičius give us an impression of parallelism because of this old harmonic rule he breaks (parallel fifths are forbidden since the end of middle ages) and this in a quite noisy way if we consider that the trumpets take the higher (and then the most powerful) part of the brass.

In a future work, we could also search for traces of polytonality in the Electric poem (more than atonality). Those eventual traces of polytonality would also betray an influence of the Parisian musical world. Darius Milhaud, the French composer, uses polytonality very commonly, and also Stravinsky of course. Polytonality is notably a way of superposing, in different tonalities, several traditional themes, like Stravinsky did, for example, in his work Wedding. Thus, as in the First Piano Concerto, Bacevičius also uses traditional Lithuanian themes, according to the famous critic Vladas Yakoubenas, who recognized them during the first performance in Kaunas. This "national" folkloric position, so common at this time, is probably the legacy of his colleagues of the Ecole de Paris, or perhaps simply derives from being far away from his country during three years, and still feeling himself Lithuanian, as opposed to feeling in « exile », and thus capable of writing real national music. Bacevičius, like many composers before him, has perhaps used Debussy's harmonic style (whose influence has been useful for many « national composers ») to associate it with national themes, like Falla or Bartók did before him (both having lived in Paris during their youth).

In conclusion, we could compare Bacevičius, in the beginning of his life, with Bartók. Many points of comparison seem to be result from the first common point: the same trip to Paris when both composers where young. Like Bartók, Bacevičius was first fascinated by Germanic music, like Bartók he has probably been influenced by French harmony, notably parallelism (which one can find in a very simple way, for example, in Bartók's opera Blue beard), like Bartók he has tried to mix many different musical modern procedures, like Bartók he has used traditional themes, and like Bartók, he has finally flown to America, or perhaps he did it more like Varèse (not invited but aimlessly), to reach a New World filled with technical and scientific dreams, a perfect place to write his future works like Graphic or the Cosmic Symphony.

  Ce texte fut publié sous le titre « Possible French influences in the works by Bacevičius », dans Vytautas Bacevičius in context, Vilnius, Lithuanian composers Union, 2009, p. 70-77. En voici une version révisée (septembre 2019).

Even if one finds Bacevičius's melodic line quite different from a Wagnerian leitmotiv, the similitude will shine through during the audition (of the beginning of the Poema).

We can find this process again at bars 286-287. The flutes take the motif of the violins, once again underlined by the castanets.

Let us remind ourselves that Prokofiev was one of the first influences of Poulenc. Besides, Prokofiev was living in Paris during the 20's and found great success there. Bacevičius couldn't ignore this and probably studied Prokofiev's style himself.

Paul Valéry, Notion générale de l'art, § XIV, in OEuvres, tome I, Paris, Gallimard, 1957, p. 1411. (Collection de la Pléiade).

Odile Vivier, Varèse, Paris, Seuil, 1973, p. 20.

Fernand Ouellette, Varèse, Paris, Christian Bourgois, 1989, p. 37.