materials
Article Lead-Bismuth Eutectic: Atomic and Micro-Scale Melt Evolution
Roberto Montanari 1,*, Alessandra Varone 1, Luca Gregoratti 2, Saulius Kaciulis 3 and Alessio Mezzi 3
1 Department of Industrial Engineering, University of Rome “Tor Vergata”, 00133 Roma, Italy; [email protected] 2 Elettra – Sincrotrone di Trieste, Area Science Park, 34149 Trieste, Italy; [email protected] 3 Institute for the Study of Nanostructured Materials, ISMN – CNR, P.O. Box 10, 00015 Montelibretti, Italy; [email protected] (S.K.); [email protected] (A.M.) * Correspondence: [email protected]; Tel.: +39-06-7259-7182
Received: 24 July 2019; Accepted: 25 September 2019; Published: 27 September 2019
Abstract: Element clustering and structural features of liquid lead-bismuth eutectic (LBE) alloy have been investigated up to 720 ◦C by means of high temperature X-ray diffraction (HT-XRD), X-ray Photoemission Spectroscopy (XPS) and Scanning Photoemission Microscopy (SPEM) at the Elettra synchrotron in Trieste. The short-range order in liquid metal after melting corresponds to the cuboctahedral atomic arrangement and progressively evolves towards the icosahedral one as temperature increases. Such process, that involve a negative expansion of the alloy, is mainly connected to the reduction of atom distance in Pb–Pb pairs which takes place from 350 ◦C to 520 ◦C. On an atomic scale, it is observed a change of the relative number of Bi–Bi, Pb–Pb, and Pb–Bi pairs. The Pb–Bi pairs are detected only at a temperature above ~350 ◦C, and its fraction progressively increases, giving rise to a more homogeneous distribution of the elements. SPEM results showed evidence that the process of chemical homogenization on an atomic scale is preceded and accompanied by homogenization on micro-scale. Clusters rich of Bi and Pb, which are observed after melting, progressively dissolve as temperature increases: Only a few residuals remain at 350 ◦C, and no more clusters are detected a 520 ◦C.
Keywords: liquid Pb–Bi eutectic alloy; chemical homogeneity; short range order; XPS; SPEM; HT-XRD
1. Introduction Many physical properties of liquid metals depend on their structure, thus, its knowledge is of fundamental importance. In the past, some attempts have been made to describe the liquids as disordered crystals or dense gases, but a simple structural description of liquids, such as “periodicity” for crystals or “sparsity” for gases represents a challenge in the science of condensed matter. The five-fold symmetry in liquid Pb was observed through measurements of the X-rays evanescent radiation [1]. In fact, this result demonstrated that a mono-atomic liquid is made up of icosahedral blocks, as theoretically conjectured by Frank [2] and Bernal [3] more than sixty years ago. Icosahedral clusters have been then studied through different approaches and techniques, of particular relevance are molecular dynamics simulations [4–6] and High Temperature X–ray Diffraction (HT-XRD) [7]. The experiment of Reichert et al. [1] represents an important step towards understanding the structure of liquids; however, much remains to be done. The following issues are of particular interest for scientific knowledge and metallurgical applications: (i) The structural correlations between solid and liquid during the solidification, (ii) the phase de-mixing in metal systems with a miscibility gap in the liquid state, (iii) the liquid–liquid phase transitions in pure metals and alloys.
Materials 2019, 12, 3158; doi:10.3390/ma12193158 www.mdpi.com/journal/materials Materials 2019, 12, 3158 2 of 16
(i) Structural Correlations between Solid and Liquid during the Solidification of Pure Metals The structural correlations between solid and liquid during the solidification of some pure metals (Zn [8] and In [9–11]) and alloys (In-10Sn and Sn-13Pb [12,13]) have been studied in recent years by one of the present authors through HT-XRD. Other papers have been published regarding the aforesaid binary systems (see for instance [14]) and the presence of clusters in melt correlated to the crystal structure of the solid is the main established result [12–15]. A number of metastable phases, whose nuclei pre-exist as clusters in the liquid, has also been revealed in the Sn-Pb system by quenching from liquid [16–18]. Two theoretical models, based on the statistical mechanics [19] and the nano-crystalline structure [20], have been developed to explain the presence of clusters in the liquid and their changes with temperature. Lianwen Wang [21] suggested that the energy state of liquids is reasonably approximated by the energy and volume of a vacancy.
(ii) Phase de-Mixing in Metal Systems with a Miscibility Gap in the Liquid State The concept of metastable micro-heterogeneity in molten alloys, which exhibit a monotectic reaction, has been pointed out in a recent review [22]. HT-XRD experiments showed that these alloys have liquid domains enriched in the two different kinds of atoms above the cupola identifying the miscibility gap. The characteristic scale of such domains was estimated to be in the range of 1–10 nm from sedimentation in a centrifuge or in natural gravity. A large number of examples confirms the importance of thermal treatment of liquid precursors in order to improve the structure and the physical properties of numerous alloys. Higher the cooling rate during the solidification, greater the influence of melt structure on the final solid structure. Likely heat treatments of melts will become in the future an integral part of specific technological processes as heat treatments of solid alloys are today. Important results have been obtained by investigating systems with a miscibility gap in the liquid state. Some relevant examples regard the possibility of obtaining bulk metal glasses in the systems, such as Nb–Y, where the two liquid phases can be frozen into a two-phase amorphous metallic alloy by rapid quenching [23] and the realization of Al alloys containing embedded Pb nano-dispersoids with enhanced wear behavior with respect to their coarse grained counterparts [24].
(iii) Liquid–Liquid Phase Transitions in Pure Metals and Alloys Metals in the solid-state may assume different crystalline structures depending on the temperature or pressure (polymorphic transformations). Recently, liquid–liquid phase transitions have been proved to occur in some one-component melts (e.g., Cs, Bi, Ga, Si, Ge and Se) [25–31] which undergo a discontinuous structure change. Discontinuous changes of the liquid structure have also been observed in some In-Sn, Pb–Bi, Pb-Sn, In-Bi binary alloys [32–35] depending on temperature change at constant pressure. The discontinuity occurs at hundreds of degrees above liquidus where there is no other defined phase line in the phase diagram. The phenomenon was revealed by HT-XRD, mechanical spectroscopy (MS) and differential scanning calorimetry (DSC). A recent paper of Zu [36] provides an overview of liquid–liquid phase transitions in metallic melts. Present work investigates the behavior of the liquid Pb–Bi eutectic (LBE) alloy, a good candidate as coolant and neutron spallation source in MYRRHA reactor [37]. For this application more information on atomic-scale interactions, structure and thermal physical properties, as a function of the temperature must be collected, because one of the main limitations of this reactor is the compatibility of structural materials with liquid LBE at high temperature, where corrosion and embrittlement take place. In previous work, MS tests showed a relevant change in the microstructure of liquid LBE [38]. In the same material, a damping maximum at ~550 ◦C has been recorded by Zu et al. [33] and ascribed to a structural change occurring when, above a critical temperature, the alloy, that still has minor residual crystals after melting, transforms into a configuration without crystalline conglomerates. Materials 2019, 12, 3158 3 of 16
Moreover, an anomaly of the electrical conductivity σ(T) curve, observed by Plevachuk et al. [39] and Li et al. [40], was explained by considering a melt structural inhomogeneity. This work presents the results of HT-XRD up to 720 ◦C, which describes the short-range order of the liquid alloy. XPS and scanning photoemission microscopy (SPEM) at the Elettra synchrotron (Trieste, Italy) with high lateral resolution [41,42] were used to investigate possible clustering of alloying elements.
2. Materials and Methods The examined material was the Pb–Bi alloy in eutectic composition (Pb 44.1-Bi 55.9 at %). The alloy was prepared from high purity metals, 99.999% Pb and 99.9999% Bi (Goodfellow Cambridge Ltd, Huntingdon, UK), in an alumina crucible under an atmosphere of Ar + 5% H2. HT-XRD experiments were done by using an ANTON PAAR HT–16 camera (Graz, Austria) with a sample-holder for liquid metals. The tests were made in an atmosphere of inert gas; the temperature, measured by a thermocouple in direct contact with the liquid metal, was kept constant ( 0.1 C). ± ◦ XRD patterns were collected at increasing temperatures with Mo-Kα radiation (λ = 0.07093 nm) in the 2Θ angular range 5–55◦ with steps of 0.05◦ and counting time of 5 s per step. Before each test run, liquid LBE alloy was thermally stabilized for 30 min. From each pattern, the radial distribution function (RDF) was determined with a procedure described in ref [12]. The samples used for XPS (manufacturer, city, country) and SPEM (manufacturer, city, country) measurements were prepared through rapid quenching of the liquid from different temperatures. The metal was preliminarily cast inside a thin-walled container of AISI 316L steel closed at an extremity, and a thermocouple was embedded into the metal. After solidification, the other extremity of the container has been sealed. A sketch of the sample holder and experimental set-up are displayed in Figure1a. To study the characteristics of the liquid alloy in an extended temperature range, the experiments were carried out from 125 ◦C (eutectic temperature) to 720 ◦C. In each experiment, the sample holder was suspended in a vertical tubular furnace (manufacturer, city, country), heated at the selected temperature, thermally stabilized for 30 min and finally quenched in water. The lower end of furnace is open, so quenching was realized by cutting the suspension wire allowing the sample holder to fall in a water tank allocated under the furnace. Finally, the solid metal was extracted from the container, and its surface was examined through XPS and SPEM techniques. Cooling curves of the liquid alloy were measured in different positions inside the sample holder. Of course, the cooling rate depends on the distance from the wall of the sample holder, where the 1 material experiences the fastest temperature change: It was ~520 ◦C s− at the centre of the sample and 1 ~3200 ◦C s− at the surface. In the conditions of present experiments, the free random walk W of Bi and Pb atoms at the surface of liquid LBE was calculated vs. the quenching temperature (Figure1b). W for the temperature T and time t is given by:
W = (6Dt)1/2, (1) where D is the diffusion coefficient. The diffusion coefficients of Pb and Bi atoms in liquid LBE were determined according to Yun Gao et al. [43]:
4 ! 4 1.4 10 D = 4.0 10− exp − × , (2) Pb/LBE × RT
4 ! 4 1.30 10 D = 4.0 10− exp − × , (3) Bi/LBE × RT where R is the gas constant. Each value of the random walk plotted in Figure1b has been calculated by integrating Equation (1) along the cooling curve in the range from the specific quenching temperature Materials 2019, 12, x FOR PEER REVIEW 4 of 16 Materials 2019, 12, 3158 4 of 16 where R is the gas constant. Each value of the random walk plotted in Figure 1b has been calculated by integrating Equation 1 along the cooling curve in the range from the specific quenching totemperature 125 ◦C where to solidification 125 °C where takes solidification place. Diff takesusion place. in the Diffusion solid-state in is the negligible solid-state with isrespect negligible to that with inrespect the liquid, to that therefore, in the liquid, it was nottherefore, considered. it was not considered. TheThe results results in in Figure Figure1b 1b show show that thatW Wis is equal equal to to 105 105 nm nm for for Bi Bi and and 80 80 nm nm for for Pb Pb at at the the highest highest temperaturetemperature examined examined here here (720 (720◦C); °C); its valueits value rapidly rapidly decreases decreases with temperature.with temperature. Therefore, Therefore, XPS and XPS SPEMand measurementsSPEM measurements carried out carried on the out free on surface the offree the surface quenched of samplesthe quenched describe samples a micro-chemical describe a distributionmicro-chemical close todistribution the original close one to of the liquidoriginal alloys one of at highthe liquid temperature. alloys at SPEM high temperature. is used in present SPEM workis used to describe in present elemental work to segregation describe elemental on a micro-scale, segregation with on thea micro-scale, experimental with limits the reportedexperimental in Figurelimits1 b,reported while the in heterogeneityFigure 1b, while on the an atomicheterogeneit scaley has on beenan atomic investigated scale has by been high investigated temperature by XRDhigh measurements. temperature XRD measurements.
(a) (b)
Figure 1. Sketch of the experimental set-up used for quenching liquid lead-bismuth eutectic (LBE) alloyFigure (a) and1. Sketch random of walkthe experimental of Bi and Pb atomsset-up inused liquid for LBEquenching vs. the quenchingliquid lead-bismuth temperature eutectic (b). (LBE) alloy (a) and random walk of Bi and Pb atoms in liquid LBE vs. the quenching temperature (b). The photoemission measurements were carried out in a spectrometer Escalab 250Xi (Thermo Fisher ScientificThe Ltd, photoemission East Grinstead, measurements UK) equipped were with carried the monochromatic out in a spectrometer X-ray source Escalab and 6-channeltron250Xi (Thermo detector.Fisher Scientific Before the Ltd, measurements, East Grinstead, all the UK) samples equipped were with cleaned the withmonochromatic pure ethanol. X-ray The surfacesource ofand the6-channeltron samples was detector. additionally Before cleaned the measurements, in ultra-high vacuum all the samples by Ar+ ion were sputtering cleaned atwith 2.0 pure keV energy.ethanol. ExperimentalThe surface dataof the were samples processed was additionally by the Avantage cleaned v.5 in software ultra-high (Thermo vacuum Fisher by Ar Scientific+ ion sputtering Ltd, East at Grinstead,2.0 keV energy. UK). Experimental data were processed by the Avantage v.5 software (Thermo Fisher ScientificXPS measurements Ltd, East Grinstead, with high UK). lateral resolution were performed by using the SPEM apparatus at the ESCAXPS measurements microscopy beamline with high of lateral Elettra resolution synchrotron were in Trieste,performed Italy. by Soft using X-rays the SPEM of synchrotron apparatus beamat the are ESCA focused microscopy to a diameter beamline of aroundof Elettra 150 synchrotron nm by Fresnel in Trieste, zone plateItaly. optics,Soft X-rays and theof synchrotron scanning isbeam performed are focused by raster to a movement diameter of of around the sample 150 nm under by X-raysFresnel nanoprobe.zone plate optics, Photoemission and the scanning signal is is collectedperformed by aby PHOIBOS raster move 100 hemisphericalment of the sample analyzer unde (SPECSr X-rays GmbH, nanoprobe. Berlin Germany) Photoemission and registered signal is bycollected a 48-channel by a detector.PHOIBOS This 100 systemhemispherical can be used analyzer in both (SPECS imaging GmbH, (chemical Berlin maps) Germany) and spectroscopyand registered (selectedby a 48-channel photoemission detector. regions) This modes, system which can were be carried used out in atboth 667 eVimaging photon energy(chemical with maps) an energy and resolutionspectroscopy of 0.2 eV.Acquired(selected photoemission chemical maps regions) were processed modes, which by Igor were v.6.3.2.3 carried and Matlab out at v.7.14667 eV software photon (MathWorks,energy with Cambridge, an energy resolution UK). More of details 0.2 eV. on Acquired this technique chemical have maps been were reported processed elsewhere by Igor [44 v.6.3.2.3]. and Matlab v.7.14 software (MathWorks, Cambridge, UK). More details on this technique have been reported elsewhere [44].
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3.Materials Results 2019 and, 12, x Discussion FOR PEER REVIEW 5 of 16
3.1.3. Results Structural and Characterization Discussion
3.1. StructuralThe XRD patternsCharacterization recorded at different temperatures were analyzed to determine the RDF curves. RDFs were calculated by using the following relationship: The XRD patterns recorded at different temperatures were analyzed to determine the RDF curves. RDFs were calculated by usingX the followingZ Qmax relationship: 2 α2Q2 RDF = 2πr ρe Z + Qi(Q)e− sin rQdQ, (4) j Qmax −α 22 = 2 2 ρπ UC +0 eQQiZrRDF Q sin)( rQdQ , e UC j 0 (4) where ρe is the mean electron density of the alloy, Q = 4π sinθ/λ, i(Q) the normalized diffracted intensity, where ρe is the mean electron density of the alloy, Q = 4π sinθ / λ, i(Q) the normalized diffracted Zj the atomic number of the atomic specie j (j = 1 Pb, j = 2 Bi), UC the composition unit. The G(r) curve intensity, Zj the atomic number of the atomic specie j ( j = 1 Pb, j = 2 Bi), UC the composition unit. The 2 P is obtained by subtracting the parabolic contribution 2 r Z from2 RDF. π ρe UC 2j ρπ Zr G(r) Figurecurve is2 obtainedshows G by(r) subtract curvesing at dithefferent parabolic temperatures. contribution All of theme UC exhibitj from twoRDF. peaks with positionsFigurer1 and 2 showsr2 (average G(r) radii curves of theat different first and second temperatures. atomic shellsAll of surrounding them exhibit a given two atom): peaks Thewith arrangement of atoms in the liquid metal can be identified from the ratio r2/r1. As clearly shown in Figure2, the variations of peak position are accompanied by changes in peak shape.
Figure 2.2. GG(r)(r) curves of liquid LBE atat didifferentfferent temperatures.temperatures.
TheThe halfhalf widthwidth ofof thethe firstfirst RDFRDF peakpeak atat 126126 ◦°CC isis aa littlelittle widerwider thanthan thatthat recordedrecorded atat aa closeclose temperaturetemperature (140(140 ◦°C)C) byby GudowskiGudowski etet al.al. [[45]45] throughthrough neutronneutron didiffraction.ffraction. SuchSuch discrepancydiscrepancy cancan bebe explainedexplained byby considering considering the the inherent inherent characteristics characteristics of neutron of neutron and X-rays and diX-raysffraction diffraction [46]: Neutrons [46]: exhibitNeutrons a greater exhibit resolutiona greater resolution in polyatomic in polyatomic systems because systemsthey because are scatteredthey are scattered by the nuclei; by the namely, nuclei; therenamely, is essentially there is essentially point scattering, point scattering, and the scattering and the scattering amplitudes amplitudes do not vary do withnot vary angle. with angle. FigureFigure3 3 displays displays the the distances distances rr11 and r2 determined from G(r)G(r) curves curves at at different different temperatures. TheThe valuevalue ofof rr11 is constant up to 350 ◦°C,C, decreases from 350 ◦°CC to 520 °C◦C and, and, finally finally is constant again. TheThe ratioratio rr22//rr11,, which which describes the short-range order in the liquidliquid metal,metal, isis alsoalso shownshown inin FigureFigure3 3.. TheThe trendtrend of of the the ratio ratior2 /r12 /vs. r1 temperaturevs. temperature shows shows that justthat after justmelting after meltingr2/r1 is ~1.41r2 / r1 andis ~ increases1.41 and tillincreases the value till the of ~1.61value at of 720 ~ 1.61◦C; at in 720 the °C; range in the from range ~350 from◦C to~350 560 °C◦C to the 560 ratio °C the exhibits ratio aexhibits plateau. a Thisplateau. result This indicates result thatindicates the short-range that the short-range order of liquid order LBE of gradually liquid LBE changes gradually from achanges cuboctahedral from a configuration (the ratio is √2 1.41) just after melting to an icosahedral one (the ratio corresponds cuboctahedral configuration (the ratio is 2 ≅ 1.41) just after melting to an icosahedral one (the ratio to the golden ratio φ = 1.61) at 720 ◦C. Figure4 displays the two structures of the liquid; in both corresponds to the golden ratio φ = 1.61) at 720 °C. Figure 4 displays the two structures of the liquid; configurations, the positions of 1st and 2nd nearest neighbors of a given atom in the position O in both configurations, the positions of 1st and 2nd nearest neighbors of a given atom in the position are shown. O are shown. From the r1 values in Figure4, the volumes of cuboctahedron at 125 ◦C and icosahedron at 720 ◦C From the r1 values in Figure 4, the volumes of cuboctahedron at 125 °C and icosahedron at 720 result to be 92 Å3 and 78 Å3, respectively. In both configurations each atom is surrounded by 12 next °C result to be 92 Å3 and 78 Å3, respectively. In both configurations each atom is surrounded by 12 next neighbors; thus, the lower volume of the icosahedral structure involves a negative expansion of the interatomic distances as temperature increases. This behavior is anomalous since materials Materials 2019, 12, 3158 6 of 16 neighbors; thus, the lower volume of the icosahedral structure involves a negative expansion of the interatomicMaterials distances 2019, 12, x FOR as temperaturePEER REVIEW increases. This behavior is anomalous since materials usually6 of 16 Materials 2019, 12, x FOR PEER REVIEW 6 of 16 dilate when heated; however, a similar phenomenon was recently observed also by Lou et al. [47] in usually dilate when heated; however, a similar phenomenon was recently observed also by Lou et al. some pure metals (Al, Zn, Sn, In, Cu, Ag, Au and Ni). usually[47] indilate some when pure heated metals; however, (Al, Zn, Sn, a similar In, Cu, phenomenon Ag, Au and Ni). was recently observed also by Lou et al. [47] in some pure metals (Al, Zn, Sn, In, Cu, Ag, Au and Ni).
Figure 3. Average distances r and r of 1st and 2nd nearest neighbors determined from G(r) at different Figure 3. Average distances1 r21 and r2 of 1st and 2nd nearest neighbors determined from G(r) at temperatureFigure 3. Average and their distances ratio r /rr1 .and The r2 scaleof 1st is and enlarged 2nd nearest in the ne lowerighbors part determined of the graph from to G evidence(r) at different temperature and2 their1 ratio r2 / r1. The scale is enlarged in the lower part of the graph to different temperature and their ratio r2 / r1. The scale is enlarged in the lower part of the graph to r2/r1 variations.evidence r2 / r1 variations. evidence r2 / r1 variations. r r G r The dataThe ofdata1 ofand r1 and2 determined r2 determined from from( G(r)) curves curves and and plotted plotted in in Figure Figure3 are3 are average average values values whichwhich doThe not data do account not of raccount1 and for ther2 fordetermined two the atomic two atomic from species, G(r) species, Bi curves and Bi Pb. andand In Pb.plotted fact, In both fact, in 1stFigureboth and 1st 3 2nd areand peaksaverage 2nd peaks are values the are sum the ofwhich threesum contributionsdo of not three account contributions coming for the fromtwo coming atomic Pb–Pb, from species, Bi–Bi Pb–Pb, andBi and Pb–BiBi–Bi Pb. pairsInand fact, Pb–Bi and bothG (pairs r1st) peaks and and 2nd areG(r) peaks the peaks overlaps are arethe the of thesesum contributionsoverlaps of three of contributions these which contributions have coming been which calculated from have Pb–Pb, been through Bi–Bi calculated the and following Pb–Bithrough pairs procedure.the followingand G(r) procedure.peaks are the overlaps of these contributions which have been calculated through the following procedure.
Figure 4. The structure of the liquid LBE alloy passes from the cuboctahedral configuration (a) to the Figure 4. The structure of the liquid LBE alloy passes from the cuboctahedral configuration (a) to the Figureicosahedral 4. The structure one (b) of as the temperature liquid LBE increasesalloy passes from from 125 the °C cuboctahedral to 720 °C. The configuration positions of (1sta) to and the 2nd icosahedral one (b) as temperature increases from 125 C to 720 C. The positions of 1st and 2nd nearest icosahedralnearest neighborsone (b) as of temperature a given atom increases in the position from 125 ◦O are °C shown.to ◦720 °C. The positions of 1st and 2nd neighborsnearest neighbors of a given of atom a given in theatom position in the position O are shown. O are shown.
Around a given atom there are shells of neighbour atoms designed by i; Nij is the mean number AroundAround a givena given atom atom there there are are shells shells of of neighbour neighbour atoms atoms designed designed by byi ;i;N Nijij isis thethe meanmean numbernumber of of atoms in the shell i at a distance rij from an atom of type j. The single contributions can be atomsof atoms in the in shell thei atshell a distance i at a distancerij from anrij from atom an of typeatomj. ofThe type single j. The contributions single contributions can be described can be by described by the pair functions Pij : thedescribed pair functions by the Ppairij: functions Pij :
Z Qmaxi Qmaxi f j fi −α 2Q2 , P (r) = fj fi 2e 2 sinQr sinQrdQ ij Qmax 02f f α2 2Q ij (5) Pij(r) = = i j gi e(Q−−α)Q sin Qrij sin QrdQ, , (5) Pij (r) 022 e sinQrij sinQrdQ (5) 0 gg ((QQ)) where fj and fi are the atomic scattering factors of the atoms forming the pair, α2Q2 is a factor of α2 2 whereconvergence fj and fi are introduced the atomic to scatteringavoid spurious factors oscillations of the atoms along forming with thethe pair,tails ofQ the is paira factor functions, of convergence introduced to avoid spurious oscillations along with the tails of the pair functions,
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2 2 where fj and fi are the atomic scattering factors of the atoms forming the pair, α Q is a factor of convergenceMaterials 2019 introduced, 12, x FOR PEER to avoidREVIEW spurious oscillations along with the tails of the pair functions,7 of while 16 1/g2(Q) is a sharpening factor. The function g(Q) decreases with increasing Q and has the value g(Q) = 1 while 1/g2(Q) is a sharpening factor. The function g(Q) decreases with increasing Q and has the value Q at g(Q)= 0. = The1 at Q function = 0. The function P UC fj g(Q) = P f, (6) UCZ j , g(Q) = UC j (6) UC Z j has been used by us, but other suitable functions can be used as well. hasThe been RDF used is expressedby us, but as:other suitable functions can be used as well. The RDF is expressed as: X X Nij RDF = Pij(r). (7) UC i Nrij = ij . RDF UC i Pij (r) (7) Equation (8), obtained by combining Equations (4)r andij (7), enables to analyze the RDF curves:
Equation 8, obtainedX X byN combining EquationX 4 and EquationZ Qmax 7, enables to analyze the RDF curves: ij 2 α2Q2 Pij(r) = 2π rρe Zj + Qi(Q)e− sin rQdQ. (8) UC i UC r N Qmax −α 2 2 . ij ij P (r) = 2π 2rρ Z + 0 Qi(Q)e Q sin rQdQ UC iij e UC j 0 (8) rij The pair functions Pij(r) have been determined for each of the rij, then used to find the Nij values which bringThe pair the left-handfunctions sidePij(r) ofhave Equation been determined (8) into the for best each fit of with the the rij, then right-hand used to side. find Anthe N exampleij valuesof fittingwhich of thebring first the RDF left-hand peak byside pair of Equation functions 8 Pintoij(r )th ise shownbest fit inwith Figure the right-hand5. side. An example of fittingFigure of6 the displays first RDF the peak distance by pair between functions Pb–Pb, Pij(r) is Bi–Bi shown and in Pb–BiFigure pairs5. vs. temperature. At the eutecticFigures temperature, 6 displays solid the LBE distance consists between of two phases,Pb–Pb, Bi–Bi Bi and and the Pb–Bi hexagonal pairs vs.β phase temperature. (cell parameters At the a =eutectic0.35058 temperature, nm, c = 0.57959 solid nm) LBE that consists has a Biof contenttwo phases, of 41.8 Bi at and %. Thethe distancehexagonal between β phase the (cell next neighborsparameters in the a =β 0.35058phase isnm, a ~0.35c = 0.57959 nm and nm) substantially that has a Bi corresponds content of 41.8 to thatat %. of The Pb–Pb distance pairs between just after the next neighbors in the β phase is a ~ 0.35 nm and substantially corresponds to that of Pb–Pb pairs melting. In fact, Pb is present only in the β phase, and the distance of Pb–Pb pairs in the melt is close just after melting. In fact, Pb is present only in the β phase, and the distance of Pb–Pb pairs in the to that of atoms in the solid. The Pb–Pb distance slightly decreases up to 350 C; then, a remarkable melt is close to that of atoms in the solid. The Pb–Pb distance slightly decreases◦ up to 350 °C; then, a drop is observed in the range 350–520 C, while above 520 C its value is nearly constant (~0.29 nm). remarkable drop is observed in the range◦ 350–520 °C, while◦ above 520 °C its value is nearly constant On the contrary, Pb–Bi and Bi–Bi distances substantially do not change with temperature. Therefore, (~ 0.29 nm). On the contrary, Pb–Bi and Bi–Bi distances substantially do not change with the variations of r displayed in Figure3 depends on the bonds between Pb atoms in the melt and on temperature. Therefore,1 the variations of r1 displayed in Figure 3 depends on the bonds between Pb theatoms change in ofthe the melt distance and on of the Pb–Pb change pairs. of the distance of Pb–Pb pairs.
Figure 5. Fitting of the first radial distribution function (RDF) peak at 126 C peak by means of the Figure 5. Fitting of the first radial distribution function (RDF) peak at 126 °C◦ peak by means of the pair functions. pair functions.
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MaterialsMaterials2019 2019, 12,, 315812, x FOR PEER REVIEW 8 of8 of16 16 3.6 Pb-Pb Bi-Bi 3.5 Pb-Bi 3.6 Pb-Pb 3.4 Bi-Bi 3.5 Pb-Bi 3.3 3.4 3.2 3.3 3.1 3.2 Pairdistance (Å) 3.0 3.1
2.9Pairdistance (Å) 3.0
2.8 1002.9 200 300 400 500 600 700
2.8 Temperature (°C) 100 200 300 400 500 600 700 Temperature (°C) Figure 6. Distance between Pb–Pb, Bi–Bi and Pb–Bi pairs vs. temperature. Figure 6. Distance between Pb–Pb, Bi–Bi and Pb–Bi pairs vs. temperature. From the fittingFigure of the 6. 1st Distance and 2nd between peaks Pb–Pb, of RDF Bi–Bi curves and Pb–Bi the ratios pairs vs.r2/r temperature.1 of Pb–Pb, Bi–Bi and Pb–Bi pairs Fromvs. temperature the fitting ofhave the 1stbeen and determined 2nd peaks (Figure of RDF curves7). The theratios ratios of Pb–Bir2/r1 of and Pb–Pb, Bi–Bi Bi–Bi pairs and slightly Pb–Bi From the fitting of the 1st and 2nd peaks of RDF curves the ratios r2/r1 of Pb–Pb, Bi–Bi and Pb–Bi increasepairs vs. with temperature temperature, have whereas, been determined that of Pb–P (Figureb pairs7). exhibits The ratios a more of Pb–Bi pronounced and Bi–Bi variation pairs slightly from pairs vs. temperature have been determined (Figure 7). The ratios of Pb–Bi and Bi–Bi pairs slightly ~increase 1,39 to with~ 1,62, temperature, two values whereas, very close that to of Pb–Pbthe ideal pairs cubooctahedral exhibits a more and pronounced icosahedral variation configurations, from ~1.39 increase with temperature, whereas, that of Pb–Pb pairs exhibits a more pronounced variation from respectively.to ~1.62, two values very close to the ideal cubooctahedral and icosahedral configurations, respectively. ~ 1,39 to ~ 1,62, two values very close to the ideal cubooctahedral and icosahedral configurations, respectively.
1.65
1.65 1.60 Pb-Bi ) 2
/r 1.60 Pb-Bi ) 1 2
1.55/r , (r 1 1.55 , (r Bi-Bi )
2 1.50 Bi-Bi /r ) 1
2 1.50 /r , (r 1.451 , (r 1.45 Pb-Pb
Pb-Pb Bi-Bi Pb-Pb ) 2 1.40Pb-Pb Pb-Bi Bi-Bi ) /r 2 1 1.40 Pb-Bi /r (r 1 1.35(r 1.35 100 200 300 400 500 600 700 800 100 200 300 400 500 600 700 800 Temperature (°C) Temperature (°C)
Figure 7. Ratios r2/r1 of Bi–Bi, Pb–Pb and Pb–Bi pairs vs. temperature. Figure 7. Ratios r2/r1 of Bi–Bi, Pb–Pb and Pb–Bi pairs vs. temperature. Figure 7. Ratios r2/r1 of Bi–Bi, Pb–Pb and Pb–Bi pairs vs. temperature. The relative amounts of Bi–Bi, Pb–Pb and Pb–Bi pairs vs. temperature are plotted in Figure8. The Therelative relative amounts amounts of Bi–Bi,of Bi–Bi, Pb–Pb Pb–Pb and and Pb–Bi Pb–Bi pa pairsirs vs. vs. temperature temperature are are plottedplotted in Figure 8.8.
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FigureFigure 8. 8.The The relative relative amount amount of of Bi–Bi, Bi–Bi, Pb–Bi Pb–B andi and Pb–Pb Pb–Pb pairs pairs vs. vs. temperature. temperature.
The Pb–Bi pairs are absent from the melting point to 350 C; then, their contribution becomes The Pb–Bi pairs are absent from the melting point to 350◦ °C; then, their contribution becomes increasingly important with temperature (Figure8). increasingly important with temperature (Figure 8). Since LBE consists of 44.1 at % of Pb and 55.9 at % of Bi the following relationships can be written Since LBE consists of 44.1 at % of Pb and 55.9 at % of Bi the following relationships can be for the fractions X of Pb–Pb, Bi–Bi and Pb–Bi pairs: written for the fractions X of Pb–Pb, Bi–Bi and Pb–Bi pairs: 1 X + +X1 == , Pb PbX − PbXBi − 0.441,0.441 (9)(9) − Pb Pb2 2 − Pb Bi 1 XBi Bi +1 XPb Bi = 0.559. (10) − + 2 − = . X Bi−Bi X Pb−Bi 0.559 (10) 2 1 Therefore, the increasing number ofXPb Pb + 2 XPb Bi = 0.441 Pb–Bi pairs above 350 ◦C involves − − a decreaseTherefore, of Bi–Bi the and increasing Pb–Pb pairs number and consequently of Pb–Bi pairs corresponds above 350 to °C a moreinvolves homogeneous a decrease distributionof Bi–Bi and ofPb–Pb the elements pairs and in the consequently alloy. It is noteworthy corresponds to to observe a more that homogeneous such distribution distribution of Bi and of Pb the atoms elements is not in fullythe randomalloy. It is (around noteworthy 0.19 for to Pb–Pb,observe 0.31 that for such Bi–Bi, distribution and 0.49 of for Bi Pb–Bi and /PbBi-Pb); atoms from is not the fully asymptotic random trends(around in Figure0.19 for8 the Pb–Pb, distribution 0.31 for is Bi–Bi, substantially and 0.49 stable for Pb–Bi/Bi-Pb); above ~450 ◦fromC, at leastthe asymptotic in the temperature trends in rangeFigure examined 8 the distribution here, and isis a ffsubstantiallyected by the stable tendency above of Pb~450 and °C, Bi atomsat least to in bond the withtemperature atoms of range the sameexamined type that here, hinders and is to affected reach a by completely the tendency random of Pb distribution. and Bi atoms to bond with atoms of the same typeThe that total hinders coordination to reach a number completely NT calculatedrandom distribution. from RDF curves vs. temperature is plotted in FigureThe9; the total value coordination is about 11, number and its N trendT calculated continuously from RDF decreases curves without vs. temperature abrupt variations is plotted as in temperatureFigure 9; the increases. value is Suchabout result 11, and is inits agreement trend continuously with the monotonical decreases without density abrupt decrease variations of liquid as LBEtemperature obtained fromincreases. experimental Such result measurements is in agreemen [48]t and with ab the initio monotonical molecular density dynamics decrease simulations of liquid of SongLBE etobtained al. [49] andfrom Han experimental et al. [50]. measurements [48] and ab initio molecular dynamics simulations of SongIn Figure et al.9 [49], the and partial Han coordination et al. [50]. numbers of Bi (N Bi) and Pb (NPb) are also reported. OwingIn Figure to its 9,interest the partial for nuclearcoordination applications, numbers the of characteristics Bi (NBi) and Pb of (N liquidPb) are LBE also have reported. been studied by manyOwing investigators to its interest and a lotfor ofnuclear data are applications, available in the literature.characteristics Its behavior of liquid is quiteLBE have puzzling been becausestudied some by many properties investigators exhibit and a continuous a lot of data trend are vs. available temperature, in the literature. such as density, Its behavior while is other quite propertiespuzzling showbecause a discontinuity. some properties Mechanical exhibit a Spectroscopy continuous trend tests madevs. temperature, by Zu et al. such [33] andas density, some of while the presentother authorsproperties [38 ]show showed a discontinuity. a damping maximum Mechanical accompanied Spectroscopy by a huge tests change made ofby dynamic Zu et al. modulus. [33] and Thesesome results, of the present clearly connectedauthors [38] to ashowed change a of damp the forcesing maximum between atoms,accompanied are in agreementby a huge withchange the of variationsdynamic ofmodulus. the relative These number results, of Pb–Pb,clearly Pb–Biconnected and Bi–Bito a change pairs described of the forces in this between work.On atoms, theother are in hand,agreement variations with of the the variations pair distribution of the relative modify number the electron of Pb–Pb, structure Pb–Bi of liquidand Bi–Bi LBE pairs and maydescribed lead to in thethis anomaly work. ofOn the the electrical other hand, conductivity variationsσ(T) of curve the pair observed distribution by some modify investigators the electron [39,40]. structure However, of σ theliquid redistribution LBE and may of chemical lead to elementsthe anomaly and of the the structural electrical change conductivity do not involve(T) curve an abruptobserved change by some of densityinvestigators because [39,40]. the trend However, of coordination the redistribution number vs. of temperaturechemical elements is continuously and the structural decreasing. change do not involve an abrupt change of density because the trend of coordination number vs. temperature is continuously decreasing.
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12 N T N Bi N Pb 11
6
5 Totaland partialcoordination numbers
100 200 300 400 500 600 700 800 Temperature (°C)
Figure 9. Total (N ) and partial coordination numbers of Bi (N ) and Pb (N ) vs. temperature. Figure 9. Total (NT) andT partial coordination numbers of Bi (NBi) andBi Pb (NPb) vs.Pb temperature. In a future work, advanced computational techniques (e.g., see Reference [51–53]) and topological In a future work, advanced computational techniques (e.g., see Reference [51–53]) and analysis, including Voronoi analysis or CNA (common neighbor analysis), will be adopted to analyze topological analysis, including Voronoi analysis or CNA (common neighbor analysis), will be the structural transformations in the liquid LBE. Such an approach will permit to get further information adopted to analyze the structural transformations in the liquid LBE. Such an approach will permit to to compare with present results. get further information to compare with present results. 3.2. Chemical Characterization 3.2. Chemical Characterization The surface chemical composition of LBE alloy quenched from different temperatures was The surface chemical composition of LBE alloy quenched from different temperatures was investigated by XPS. This analysis technique is surface sensitive; therefore, it is typically employed investigated by XPS. This analysis technique is surface sensitive; therefore, it is typically employed to investigate the chemical composition of the first layers (~4–5 nm) of materials in a solid-state. to investigate the chemical composition of the first layers (~ 4 - 5 nm) of materials in a solid-state. The The distribution of alloying elements on the surface, which experiences the highest cooling rate, is not distribution of alloying elements on the surface, which experiences the highest cooling rate, is not far far from that present in the original liquid; therefore, the results give information useful to understand from that present in the original liquid; therefore, the results give information useful to understand the chemical homogeneity of liquid LBE. In first approximation, it can be assumed that the liquid alloy the chemical homogeneity of liquid LBE. In first approximation, it can be assumed that the liquid is frozen in its original state. alloy is frozen in its original state. In all the samples, XPS results reveal the presence of Bi, C, Pb and O. Carbon is due to ambient In all the samples, XPS results reveal the presence of Bi, C, Pb and O. Carbon is due to ambient contamination and is removed after few cycles of ion sputtering (Ar+), whereas, the presence of O contamination and is removed after few cycles of ion sputtering (Ar+), whereas, the presence of O is is related to the formation of Bi and Pb oxides. The spectra of Bi 4f and Pb 4f were processed by related to the formation of Bi and Pb oxides. The spectra of Bi 4f and Pb 4f were processed by a a peak-fitting routine. This analysis revealed that Pb 4f signal is composed of two Pb 4f7/2 peaks with peak-fitting routine. This analysis revealed that Pb 4f signal is composed of two Pb 4f7/2 peaks with binding energy BE = 136.7 and 138.4 eV, which have been identified as metal and PbO2, respectively. binding energy BE = 136.7 and 138.4 eV, which have been identified as metal and PbO2, respectively. Similarly, the Bi 4f7/2 signal is composed of two peaks, localized at BE = 156.0 and 158.5 eV, which Similarly, the Bi 4f7/2 signal is composed of two peaks, localized at BE = 156.0 and 158.5 eV, which correspond to metal and Bi2O3, respectively. Since the presence of oxides can be misleading in the correspond to metal and Bi2O3, respectively. Since the presence of oxides can be misleading in the study of segregation phenomena in liquid LBE alloy, Ar+ ion sputtering was employed to remove the study of segregation phenomena in liquid LBE alloy, Ar+ ion sputtering was employed to remove the topmost oxidized layers. topmost oxidized layers. In all the examined samples, the XPS measurements made on the surface and on cross-section In all the examined samples, the XPS measurements made on the surface and on cross-section did not register the signals of Cr, Ni and Fe (i.e., the main elements of AISI 316L steel), therefore, the did not register the signals of Cr, Ni and Fe (i.e., the main elements of AISI 316L steel), therefore, the contamination of the melt by corrosion products coming from the container can be considered negligible. contamination of the melt by corrosion products coming from the container can be considered On the basis of XPS results, also the SPEM measurements were performed after the removal of negligible. 20 nm overlayer from the surface by ion sputtering. On the basis of XPS results, also the SPEM measurements were performed after the removal of SPEM is a very surface sensitive microscopy, which permits to observe the chemical distribution 20 nm overlayer from the surface by ion sputtering. of the elements at high lateral resolution (~100 nm). To study the micro-chemical distribution, SPEM is a very surface sensitive microscopy, which permits to observe the chemical SPEM measurements were performed by collecting maps of the surface area (100 µm 100 µm) on distribution of the elements at high lateral resolution (~100 nm). To study the micro-chemical× quenched samples. These maps (Figure 10) are composed of 128 128 or 256 256 pixels, where distribution, SPEM measurements were performed by collecting maps× of the surface× area (100 µm ×100 µm) on quenched samples. These maps (Figure 10) are composed of 128 × 128 or 256 × 256 pixels, where each pixel is the intensity of the selected photoemission signal (Pb 4f7/2 and Bi 4f7/2),
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Materials 2019, 12, x FOR PEER REVIEW 11 of 16 each pixel is the intensity of the selected photoemission signal (Pb 4f7/2 and Bi 4f7/2), mediated on 48-channelsmediated on [ 5448-channels]. Since the [54]. photoemission Since the photoemission signal depends signal on depends the sample on the height, sample i.e., height, the distance i.e., the betweendistance thebetween sample the and sample analyser and input analyser lens, input the chemical lens, the maps chemical of SPEM maps can of beSPEM influenced can be influenced by sample roughnessby sample [roughness54]. These [54]. topography These to epographyffects have effects been have eliminated been eliminated from the chemicalfrom the mapschemical by usingmaps (peak–background)by using (peak–background)/background / background routine of Igor routine software. of Igor The software. local concentration The local concentration of the elements of the in theelements maps isin describedthe maps byis described the colour by scale the oncolour the rightscale inon Figure the right 10. in Figure 10. ZonesZones enrichedenriched inin BiBi areare detecteddetected inin thethe samplessamples quenchedquenched fromfrom temperaturestemperatures inin thethe rangerange ofof 125–315125–315◦ C,°C, their their size size is ofis the of orderthe order of few of microns few microns at 125 ◦ Cat and 125 tends °C toand decrease tends withto decrease temperature. with At 400 C, some residual zones rich in Bi are still visible with size 5 µm, while at 520 C Pb and Bi are temperature.◦ At 400 °C, some residual zones rich in Bi are still visible≤ with size ≤ 5 µm,◦ while at 520 homogeneously°C Pb and Bi are distributed. homogeneously distributed. TheThe chemicalchemical mapmap acquiredacquired onon thethe cross-sectioncross-section ofof thethe samplesample quenchedquenched fromfrom 520520 ◦°CC isis quitequite didifferentfferent fromfrom thatthat recordedrecorded on on the the surface: surface: itit displaysdisplays largelarge clustersclusters richrich inin BiBi onon thethe innerinner partpart ofof thethe sample,sample, wherewhere thethe materialmaterial experiencesexperiences thethe lowerlower coolingcooling rate.rate. FigureFigure 11 11 displays displays the evolutionthe evolution of the of areas the rich areas in Bi. rich The in images Bi. The are obtainedimages fromare obtained corresponding from mapscorresponding of Figure 10maps by plottingof Figure in 10 red by colour plotting only in the red zones, colour where only Bithe content zones, iswhere in the Bi range content of 80–100 is in the at %.range It is of observed 80–100 thatat %. the It is aggregates observed richthat inthe Bi aggreg dissolveates as rich temperature in Bi dissolve increases: as temperature At 315 ◦C only increases: a few smallAt 315 areas °C only remain, a few and small the areas process remain, is substantially and the process completed is substantially at 520 ◦C. completed at 520 °C. WhenWhen thethe temperaturetemperature reachesreaches oror exceedsexceeds 315315 ◦°C,C, aa didiffusedffused interfaceinterface isis observedobserved betweenbetween thethe zoneszones withwith didifferentfferent compositioncomposition oror atat leastleast itit isis notnot possiblepossible toto identifyidentify specificspecific interfacesinterfaces withwith thethe laterallateral resolutionresolution of of the the images images in in Figure Figure 10 10,, where wher eache each pixel pixel represents represents the the mean mean elemental elemental content content of 0.8 0.8 or 0.4 0.4 µm2. In order to describe the process of homogenization, the relative areas of the of 0.8× × 0.8 or 0.4× × 0.4 µm2. In order to describe the process of homogenization, the relative areas of pixelsthe pixels with with Bi content Bi content in four in four diff erentdifferent ranges ranges (at %) (athave %) have been been plotted plotted vs. temperaturevs. temperature in Figure in Figure 12. The12. The ranges ranges of 80–100 of 80–100 and 30–50and 30–50 at % representat % represent the Bi-rich the Bi-rich zones, whichzones, progressivelywhich progressively dissolve, dissolve, and the areasand the with areas a composition with a composition tending totending the average to the one,average which one, is which about 70%is about at 520 70%◦C at 520 °C.
Figure 10. Cont.
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FigureFigure 10.10. ChemicalChemical mapsmaps ofof BiBi (left(left column)column) andand PbPb (right(right column)column) collectedcollected onon thethe samplesample surfacesurface afterafter quenchingquenching fromfrom increasingincreasing temperaturestemperatures (200,(200, 315,315, 400,400, 520520 ◦°C).C). TheThe lastlast twotwo micrographsmicrographs havehave beenbeen collected on the the cros cross-sections-section of of the the sample sample quenched quenched from from 520 520 °C.◦ C.All All images images show show an area an area 100 100µmµ ×m 100 100µm µexceptm except those those recorded recorded on the on thecross-se cross-sectionction (50 µm (50 µ×m 50 µm).50 µ mNumbers). Numbers on the on scale the scale axis × × axisindicate indicate the acquisition the acquisition channels. channels.
SPEMSPEM mapsmaps confirm confirm the the results results of HT-XRD of HT-XRD and provide and provide additional additional information information on the processes on the occurringprocesses inoccurring liquid LBE in liquid on an atomicLBE on and an micro-scale.atomic and micro-scale. From melting From point melting to 350 ◦pointC, the to atoms 350 °C, of thethe sameatoms species of the tendsame to species be bound tend together to be bound (Pb–Bi together pairs are (Pb–Bi not present) pairs andare not at the present) lowest and temperature at the lowest they formtemperature clusters, they which form progressively clusters, which dissolve progressivel as temperaturey dissolve increases as temperature and only a fewincreases residuals and remainonly a atfew 315 residuals◦C (Figures remain 11 andat 315 12 ).°C When (Figures the 11 temperature and 12). When exceeds the temperature 350 ◦C, a process exceeds of homogenization350 °C, a process alsoof homogenization starts on an atomic also starts scale: on The an fraction atomic scale: of Pb–Bi The pairs fraction increases of Pb–Bi at pairs the expense increases of at the the Bi–Bi expense and Pb–Pbof the onesBi–Bi andand thePb–Pb clusters ones break and the up andclusters completely break up disappear and completely at 520 ◦ C.disappear The behavior at 520 of °C. liquid The LBEbehavior suggests of liquid that homogenizationLBE suggests that on homogenization a micro-scale is theon a condition micro-scale for is a generalthe condition re-arrangement for a general on anre-arrangement atomic scale leading on an atomic to the formationscale leading of Pb–Bito the pairs.formation of Pb–Bi pairs.
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Figure 11. Evolution of the areas rich in Bi: The images are obtained by plotting in red colour only the zonesFigure where 11. Evolution Bi content of isthe in areas the range rich in of Bi: 80–100 The images at %. are obtained by plotting in red colour only the zones where Bi content is in the range of 80–100 at %. FigureFigure 11.11. Evolution ofof thethe areasareas richrich inin Bi:Bi: The images areare obtained byby plottingplotting inin redred colourcolour onlyonly thethe zoneszones wherewhere BiBi contentcontent isis inin thethe rangerangeof of80–100 80–100at at%. %. 80 80 0-30 at % Bi% 30-500-30 at at % % Bi% Bi% 80 50-8030-50 at %% Bi%Bi% 60 80-10050-80 at at % % Bi% Bi% 0-30 80-100 at %at %Bi% Bi% 60 30-50 at % Bi% 50-80 at % Bi% 60 80-100 at % Bi% 40 40
40Relative area (%)
Relative area (%) 20 20 Relative area (%) 20 0 1000 200 300 400 500 100 200 300 400 500 Temperature (°C)
0 FigureFigureFigure 12. 12.The 12. The The relative relative relative100 area area area of of theof thethe pixels200 pixelspixels with with Bi Bi 300 in in four four didifferentfferent 400 ranges ranges (at (at 500%) %) determined determined determined from from from the the the images in Figure 10. imagesimages in Figure in Figure 10. 10. Temperature (°C)
A schematicA schematic view view of of the the atomic atomic and and micro-scale micro-scale transformationstransformations occurring in in liquid liquid LBE LBE alloy alloy at at FigureA schematic12. The relative view ofarea the of atomic the pixels and micro-scalewith Bi in fo truransformations different ranges occurring (at %) determined in liquid LBE from alloy the at increasingincreasingincreasing temperature temperature temperature is displayed isis displayeddisplayed in Figure inin FigureFigure 13. The 13. figureThe figurefigure is just isis a just sketchjust aa sketch forsketch illustrating for for illustrating illustrating the chemical the the images in Figure 10. evolutionchemicalchemical of the evolutionevolution system of andof thethe does systemsystem not quantitatively andand does no accountt quantitativelyquantitatively for the local accountaccount atom for environment.for thethe locallocal atomatom environment.environment. A schematic view of the atomic and micro-scale transformations occurring in liquid LBE alloy at increasing temperature is displayed in Figure 13. The figure is just a sketch for illustrating the chemical evolution of the system and does not quantitatively account for the local atom environment.
FigureFigure 13. Schematic 13. Schematic view view of the of atomicthe atomic and and micro-scale micro-scal transformationse transformations occurring occurring in in liquid liquid LBE LBE alloy Figure 13. Schematic view of the atomic and micro-scale transformations occurring in liquid LBE at increasingalloy at increasing temperature. temperature. alloy at increasing temperature.
In conclusion, chemical heterogeneity in liquid LBE occurs on both micro- and atomic scale. The heterogeneity on an atomic scale has been studied by means of high temperature XRD, and the Figure 13. Schematic view of the atomic and micro-scale transformations occurring in liquid LBE alloy at increasing temperature.
Materials 2019, 12, 3158 14 of 16 results are summarized in Figure8 showing the distribution of Pb–Bi, Pb–Pb, and Bi–Bi pairs vs. temperature. Owing to insufficient spatial resolution SPEM and XPS are not able to evidence such type of heterogeneity; however, segregation takes place also on a micro-scale and SPEM has been used to realize chemical maps which describe the phenomenon. The comparison of the results obtained by XRD and SPEM leads to conclude that the homogenization at the micro-scale seems to be the condition for the occurrence of that on an atomic scale.
4. Conclusions The results of the present investigation carried out on liquid LBE from the eutectic temperature to 720 ◦C can be summarized as follows.
1. After melting, the short-range order in liquid metal corresponds to a cuboctahedral arrangement of atoms that progressively evolves towards an icosahedral one as temperature increases. This structural transformation involves a negative expansion of the interatomic distances. 2. This process is accompanied by variations of chemical distribution at the micro- and atomic scale, which take place in the temperature range of 350–520 ◦C. 3. A change of the relative number of Pb–Pb, Pb–Bi and Bi–Bi pairs is observed on an atomic scale. The Pb–Bi pairs are detected only at temperatures above ~350 ◦C and their fraction progressively increases, resulting in a more homogeneous distribution of the elements in the alloy. 4. The negative expansion of the interatomic distances in liquid LBE is mainly related to the atomic distance in Pb–Pb pairs, which drops from 350 to 520 ◦C, while Pb–Bi and Bi–Bi distances substantially do not change with temperature. 5. The SPEM elemental maps, collected on the alloy surface after quenching from different temperatures, confirm a process of chemical homogenization on a micro-scale. The clusters rich in Bi and Pb are observed after alloy melting. They progressively dissolve as the temperature increases: Only a few residuals remain at 315 ◦C, and no more clusters are detected a 520 ◦C. 6. Homogenization at the micro-scale seems to be the condition for the occurrence of that on an atomic scale.
Author Contributions: Conceptualization, R.M.; Data curation, A.V., S.K. and A.M.; Formal analysis, R.M. and S.K.; Investigation, R.M., A.V., L.G., S.K. and A.M.; Methodology, R.M.; Writing–original draft, R.M. and A.M.; Writing–Review and Editing, R.M., A.V., L.G., S.K. and A.M. Funding: This research received no external funding. Acknowledgments: The experimental work at the ESCA microscopy beamline was supported by Elettra synchrotron project n.20120196. The authors are grateful to Piero Plini and Benedetto Iacovone of Department of Industrial Engineering for the assistance in sample preparation. Conflicts of Interest: The authors declare no conflict of interest.
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