High Temperature Equilibrium and Growth Shape of Small Particles

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High Temperature Equilibrium and Growth Shape of Small Particles: The Case of Thallium Anastassia Pavlovska, Dobri Dobrev, and Ernst Bauer J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b07411 • Publication Date (Web): 28 Sep 2018 Downloaded from http://pubs.acs.org on October 6, 2018

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The Journal of Physical Chemistry

High Temperature Equilibrium and Growth Shape of Small Particles: the Case of Thallium Anastassia Pavlovska⃰, Dobri Dobrev and Ernst Bauer⃰ .

Department of Physics, Arizona State University, Tempe, Arizona 85287-1504, USA⁺

ABSTRACT The temperature dependence of the equilibrium shape and growth shape of small thallium particles is studied in situ by ultrahigh vacuum scanning electron microscopy. Pronounced anisotropic surface roughening and surface melting is observed and compared with earlier studies of four metals with different crystal structures illustrating significant differences in disordering behavior. A comparison with theoretical 0 K equilibrium shapes shows these do not allow in general to predict the equilibrium and growth shapes at high temperatures. INTRODUCTION Metal nanoparticles supported on oxides play an important role in catalysis. While very small clusters have shapes very different from that of the generalized Wulff construction, which takes into account the interaction with the substrate, larger nanoparticles are frequently assumed to have the shape expected from this construction. Room temperature high-resolution electron microscopy, for example Ref. 1, seems to confirm this. The Wulff construction, which gives the equilibrium shape of crystals, is generally based on surface energy values at 0 K, in recent years from advanced electronic structure calculations. These have been done for individual metals (Pb2, Ni3) and for all elemental crystals4,5. With the surface energy values from these calculations the Wulff construction6 shows that the surface is terminated by significantly more planes than predicted by earlier calculations such as the bondbreaking model (see for example Refs. 3-5, 7). Catalysis, however occurs in general at higher temperatures at which thermally-induced shape changes have to be taken into account. These have been studied intensively both experimentally and theoretically in the past, initially with light microscopy of organic crystals8, later with electron microscopy and scanning probe microscopy of metals (for reviews see Refs. 9-11). Two distinct thermally-induced surface modifications were found: surface roughening and surface melting. While high index surface planes disappear

from the surface already at relatively low temperatures resulting in a spherical form of the crystal, truncated by low index planes and the crystalsubstrate interface, low index planes remain stable to much higher temperatures and disappear or even grow over a finite temperature range below the melting point. In nanocrystals, with their reduced melting point, these transitions likely occur in the temperature range of some catalytic processes. Direct observation of these processes in nanocrystals used in catalysis with highresolution transmission electron microscopy is limited by the large fluctuations associated with them but extrapolation results obtained from microcrystal studies to nanocrystals should give information about the shape of nanocrystals at elevated temperatures. Here we report the temperature-dependent equilibrium and growth form of thallium microcrystals and discuss it in terms of surface roughening and surface melting, complementing earlier equilibrium shape results for Pb11,12, Sb13, Sn, In14and growth shape results for these crystals15,16. EXPERIMENTAL DETAILS Thallium (Tl) is a toxic metal with melting point Tm = 577 K (303.7⁰C). Its crystal structure has two enantiotropic modifications: the low temperature hexagonal α-structure and the high temperature bcc ү-structure with a polymorphic transition temperature Tp of 508.6 K (235.3⁰C).

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The experiments were performed in situ in a UHV scanning electron microscope (JEOL JAMP-30) which has a resolution limit of 10 nm and a base pressure after bakeout of 1.0 x10-10 Torr. The Tl particles were produced by depositing Tl in situ from a Knudsen cell on a cleaved 0.3 mm thick, 8 mm x 5 mm wide graphite single crystal, which was cleaned in situ by electron bombardment heating at 1500 K. 6 min deposition at 420 K at a maximum pressure of 5.0x10 -8 Torr followed by 6 min deposition at room temperature at about 1x10-9 Torr and subsequent melting and cooling produced crystals 2 to 40 µm in size. The temperature was measured with a PtPtRh thermocouple spotwelded on a Ta foil in contact with the graphite substrate. During the experiments the pressure was typically 2 x 10-10 Torr only during melting did it rise briefly. After 2 months of experiments the base pressure did not exceed 3.0x10-10. Between experiments the particles were cleaned by heating above the melting point at which the vapor pressure of Tl is about 10-8 Torr. This results in fresh surfaces because possible reaction products with residual gases such as CO, CO2, H2O are removed at this temperature: Tl2CO3 dissociates into Tl2O and CO2; Tl2O sublimates at 573 K. Tl2O3 formation is unlikely at the low pressure of oxidizing gases and H2 in the residual gas is expected to support the cleaning process. The following phenomena were investigated: the polymorphic transition; roughening transitions and surface melting via the disappearance of flat faces from the equilibrium and growth shapes. The equilibrium shape (ES) and growth shape (GS) of many crystals with sizes ranging from 2 to 44 microns in diameter were studied at different temperatures up to the melting point as follows: The ES was studied in two different ways: 1) directly by following 10 crystals at 11 temperatures from the melting point to 180 K below it. 2) by following 5 crystals while increasing and

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decreasing the temperature from Tm down to 170 K below Tm. The GS was investigated at 7 different temperatures at a constant deposition time of 4 min. Growing crystals of different sizes present a collection of different growth stages: the largest crystals show the initial growth, the smallest ones the final growth shape. In addition to these UHV studies crystals were studied also in the unbaked system to explore the influence of reactive gases in the particle shape. The contrast in the images is due to work function (φ) differences between rough (low φ) and smooth (high φ) surfaces: rough surfaces caused by surface roughening appear bright, smooth surfaces (flat faces or surface-melted regions) appear darker. The general brightness gradient results from the tilted take-off angle of the secondary electron detector. The data were recorded on still cameras and on 100 films and 8 videotapes and processed. RESULTS Polymorphy. The transition from the hexagonal low temperature form of Tl to the high temperature bcc form did not occur at 508.6 K but showed considerable hysteresis. With increasing temperature a transition temperature of 531 K (Tm-46 K), that is a hysteresis of 23 K was found, with decreasing temperature the transition occurred at 441 K (Tm-136 K). The much larger hysteresis (70 K) upon cooling is caused by the difficulty of nucleation similar to the undercooling in the crystallization from the melt in clean metals. The undercooled bcc phase is however metastable: during deposition at 80 K below Tm it converts into the hexagonal structure. As a consequence the GS of bcc crystals could be studied only down to Tm-70 K while ES studies of them were possible down to Tm-110 K. Undercooling during crystallization was 20-30 K depending of the size. The ES shape of hexagonal crystals at 2


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low temperature cannot be obtained directly because the surface mobility is too low. For the same reason also the GS shape is not accessible to experiment. The hexagonal crystals in our study were produced by cooling bcc crystals below the hysteresis temperature (Tm-135 K), usually down to Tm-185 K. Therefore, they do not have the ES but show the orientation relationship between the two phases. Figure 1 shows a crystal before and after cooling. Frequently, both phases were seen in the same particle after cooling.

Figure 1. Polymorphic transition from bcc into hexagonal structure. a) After 22 hours annealing at 458 K (bcc); b) after cooling to 391 K and annealing 36 hours (hexagonal). High temperature shapes of bcc particles. The study of these particles was possible despite surface diffusion limitations, in particular at the lower temperatures, by using long equilibration times for the ES and short growth times for the GS. At the lowest temperatures at which equilibrium could be achieved the ES shows only {110}, {211} and {100} faces while the rest of the crystal was rounded as seen in Figure 2. The corresponding stereographic projection illustrates the location of these faces.

Figure 2. a) Equilibrium shape of a bcc particle with {110}, {211} and {100} faces at 467 K; b) the corresponding stereographic projection. The {100} surfaces are barely visible at this temperature The transformation of a crystal face from flat to round is well accepted now as evidence of transition to a rough-crystalline or a surface-molten phase. Distinction between roughening and surface melting based on SEM contrast only is sometimes difficult. Whenever this is the case we use the term roughening/surface melting transition. The interpretation is easier when a face is surrounded by a bright ring. The ring corresponds to surface roughened region which has a lower work function than the flat surface inside the ring and the surface-molten region surrounding it. The roughening/surface melting transition of the {110} and {211} surfaces was studied both on the ES and on the GS, of the {100} surfaces only on the ES, because at the low temperatures at which this surface exists the bcc phase is metastable and deposition converts it into the hexagonal phase. On the {110} face no roughening/surface melting was observed up to the melting point. On the {211} face the roughening/surface melting transition occurred at TR = 547 K (Tm-28 K) and on the {100} face roughening/surface melting was determined to start at TR = 507 K (Tm-70 K). Figure 3 shows the temperature dependence of the equilibrium shape and the roughening/surface melting of the {100} and {211} faces. The {211} faces shrink with increasing temperature but their contour is still sharp (Figure 3 b). The contour is losing the sharpness when approaching the transition temperature (Figure 3 c). The {100} faces, barely visible in print, are no longer present at T = Tm-40 K (Figure 3 c). At T = Tm-30 K the {211} faces have also disappeared and the parti3



cle is rounded except for the {110} faces, whose sizes do not change. The rings initially surrounding the {211} faces are attributed to surface roughening, the darker regions around them to surface melting and the dark center to flat {211} planes.

Figure 3. Temperature dependence of the bcc equilibrium shape. Roughening/surface melting transition of the {211} and {100} faces with increasing temperature. a) 454 K (Tm-123 K) {110}, {211} and {100} present; b) 497 K (Tm80 K) {211} and {100} decreased in size. The arrow shows a {100} face; c) 537 K (Tm-40 K): the {100} faces have disappeared but the {211} faces are still present (see the arrow). d) 549 K (Tm-28 K): {211} is not visible anymore and only {110} remained. Note that the particle is rotating between b) and c). The roughening/surface melting transition of the {211} face was studied in more detail by recording the decrease of its size with increasing temperature on video tape for several particle sizes and fitting the radius r of the face, normalized to the particle radius R. The resulting fit is illustrated for a large particle with diameter 42.8 µm in Figure 4. The fit gives a power law dependence of about (Tm – T)/Tm -1.6. Smaller particles show

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the same r/R(T) dependence but are shifted to larger r/R values which increase with decreasing particle size. The difference of the face size at Tm-40 K between the particle 42.8 µm and particle 25.3 µm is about 20%. A similar size dependence was observed in our previous equilibrium shape studies of In and Sn (Ref. 14): smaller particles had slightly larger faces (about 15 %). Possible explanation could be an increase of the wetting temperature of a given face with decreasing particle size. To what extent this effect can be extrapolated to nanoparticles requires more measurements of smaller particles.

Figure 4. Face size ratio r/R of {211} faces (bcc structure) as a function of temperature (Tm-T). The last temperature at which the face could be measured was Tm-29.1 K. At Tm-27.7 K it was no longer visible. Thus the transition occurred at about Tm-28 K. Figure 5 shows the {100} face after annealing for 22 hours at Tm-80 K. 20 K higher it is absent. This leads to an estimated value of TR {100} of about Tm-70 K.

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Figure 5. The (100) face is still visible on the equilibrium shape (bcc) after annealing 22 hours at temperature Tm-80 K. The {110} face remains stable up to the very melting point of Tl, which is not surprising because it is the most densely packed face in the bcc lattice and least prone to thermal disordering. Its size does not change with increasing temperature over a wide temperature range but its surrounding is changing. On the 42.8 µm diameter particle, extensive measurements showed that the radius of the face is r/R = 0.19 +/- 0.02 from Tm80 K up to Tm-20 K. 20 K below the melting point a diffuse ring appeared around the face. At Tm-2 K the outer contour of this ring becomes increasingly sharper up to 0.3 K below Tm (Figure 6 a,b). During this transition its outer radius r0 was measured as ro/R = 0.23 +/- 0.02 at Tm. At Tm only a very sharp contour was visible but disappeared so rapidly that its diameter could not be measured with the video. The ring is reversible during cooling and heating. Figure 6 c,d shows the ES at a temperature very close to Tm. The ring, which is brighter than its surroundings and therefore attributed to surface roughening separates the surface melted regions from the flat {110} face up to the melting point. No roughening transition or surface melting of the {110} face of Tl was observed. This behavior is different from that of the {211} faces.

Figure 6. Equilibrium shape of two different bcc particles at temperature close to Tm. a) first particle Tm-13 K; b) first particle Tm-0.3 K; c) second particle: Tm-1.0 K; d) second particle Tm-0.22 K. The many GS studies with different particle sizes and at different temperatures support the conclusions drawn from the ES experiments. Figure 7 is an example of the GS shapes in the initial growth stage. Only {110} and {211} are growing as flat faces at 552 K (Tm-55 K) (a), at 573 K (Tm-4 K) only the {110} faces (b) on large crystals. The smaller crystals, which collect more atoms from the surroundings and are therefore in a later growth stage, show already at the lower temperatures only {110} faces.

Figure 7. Growth shape of bcc particles at different temperatures. a) 552 K (Tm-55 K) b) 573 K (Tm-4 K). Deposition time 4 min. Note the differences between large and small particles. All the images shown up to now are top views for easier analysis. The give no information on the 5



interaction of the particles with the substrate, which is important for their overall shape. Figure 8 demonstrates that the particles are not completely spherical but are nearly hemispherical. It also shows that many sizes are available for analysis.

Figure 8. Thallium bcc particles seen in profile at 60 degrees tilt. a) low temperature 502 K (Tm-75 K); b) high temperature 569 K (Tm-8 K). DISCUSSION Before comparing the results described in Sect. III with theoretical predictions of the equilibrium shape and with earlier experimental results for other metals a few comments should be made about recent related work. A study17 of the nearequilibrium shape of Ni microcrystals equilibrated at 1200 °C for 100 h under 10-4 Torr pressure showed large faces, which according the Wulff constructions based on recent calculations are expected to occur only in narrow regions between {111} and {100} faces.3,5 Based on the results obtained here and with other low melting point microparticles11-14 these faces should be absent because of surface roughening. Their existence is without doubt caused by adsorption, very likely oxygen. Crystal habit modification by facedependent adsorption is a well-known phenomenon and was recently demonstrated very nicely by high-resolution electron microscopy of nanosized Au: oxygen environment caused faceting, CO environment roughening.18 Preparing and

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studying the equilibrium and growth face in UHV as it was done in the studies of low melting point metals excludes or at least minimizes the influence of adsorption. A comparison of the results reported here with the surface energy calculations for 0 K5 shows that at low temperature in addition to the {110} and {211} faces other faces such as {332}, {331} have a low surface energy, but not {100} faces. In the high temperature equilibrium and growth shapes these non-low index faces are not observed because they have a high step density and are therefore prone to roughen already at relative low temperatures. The {100} face remains because of its close packing. Packing density arguments were also invoked earlier15 to explain differences between experimental observations and the surface energies expected based on the calculations available at that time, such as pairwise interaction and equivalent crystal theory19 models. Another reason for the difference between the observed equilibrium planes and theory may be surface reconstructions, which lead to a higher packing density, such as on the Au(100) surface.20,21 Reconstruction has been observed also on the In(100) surface.22 Nothing is known about reconstructions on Sn, Bi and Tl surfaces so that their possible presence, i.e. a higher packing density, may explain the difference between our present and earlier experiments13-15 and recent surface energy calculations.4,5 While the experimental results for Pb11,12 agree well with these calculations those for Tl reported here are in extreme disagreement: the theoretical equilibrium shape of Tl is bounded only by {211} planes,5 while the most stable planes found in experiment are the {110} planes, followed by the {211} planes and the much less stable {100} planes. CONCLUSIONS

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They study of the thermal disordering of Tl microcrystals and the comparison with similar studies of Pb, Sn and In microcrystals shows that with increasing temperature only the most densely packed surfaces persist while all other surfaces expected from their theoretical Wulff construction roughen and finally surface-melt. Close to the melting point only the most densely packed surface remains. An exception is Bi, which shows many surfaces up to the melting point, that is no surface roughening and surface melting. The differences between different materials in the surface roughening and surface melting process shows that there is no universality except the survival of the most densely packed surfaces. The disagreement between theory and experiment illustrates that 0 K surface energy calculations can in general not predict the equilibrium shape at elevated temperatures. This is determined by the sensitivity of surfaces to thermal excitations. Densely packed surfaces are least sensitive to these excitations and therefore survive at high temperatures, the most densely packed of them up to the melting point. For nanoparticles and clusters the conclusions concerning the growth shape and the validity of 0 K equlibrium shape at elevated temperature drawn here are valid in an even more pronounced manner.23 AUTHOR INFORMATION Corresponding Authors ⃰E-mail: [email protected] ⃰E-mail: [email protected] Notes ⁺ Work perfomed at the Technical University Clausthal, Germany. The authors declare no competing financial interest.

acknowledged. We wish to thank Andrea Locatelli for his support. REFERENCES (1) Akita, T., Maeda, Y., Kohyama, M. Lowtemperature CO oxidation properties and TEM/STEM observation of Au/c-Fe2O3 catalysts. J. Catal. 2015, 324, 127-132 (2) Yu, D., Bonzel, H. P., Scheffler, M. Orientation-dependent surface and step energies of Pb from first principles. Phys. Rev. B 2006, 74, 115408-1-7 (3) Zhang, W.B., Chen, Ch., Zhang, S-Y. Equilibrium Crystal Shape of Ni from First Principles. J. Phys. Chem. C 2013, 117, 21274−21280 (4) Tran, R, Xu, Z., Radhakrishnan, B., Winston, D., Sun, W., Persson, K. A., Ong, S. P. Data Descriptor: Surface energies of elemental crystals SCIENTIFIC DATA 2016, 3, 160080. DOI: 10.1038/sdata.2016.80 (5) Materials Virtual http://crystalium.materialsvirtuallab.org/ cessed June 2018)

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(6) NIST National Institute of Standards and Technology; Materials Science and Engineering Laboratory – CTCMS; Wulffman Working Group https://www.ctcms.nist.gov/wulffman/ (accessed June 2018) (7). Bonzel, H. P., Yu, D., Scheffler, M. The three-dimensional equilibrium crystal shape of Pb: Recent results of theory and experiment. Appl. Phys. A 2006, 87, 391–397 (8) Pavlovska, A., Nenow, D. Experimental investigation of the surface melting of equilibrium form faces of diphenyl. Surf. Sci. 1971, 27, 211217

ACKNOWLEDGEMENTS Support of this work by the Deutsche Forschungsgemeinschaft (DFG) is gratefully

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(10) Löwen, H. Melting, freezing and colloidal suspensions. Phys. Rep. 1994, 237, 249-324 (11) Bonzel, H. P. 3D equilibrium crystal shapes in the new light of STM and AFM. Phys. Rep. 2003, 385, 1–67 (12) Pavlovska, A., Faulian, F., Bauer, E. Surface roughening and surface melting in the high temperature equilibrium shape of small Pb crystals. Surf. Sci. 1989, 221, 233-243 (13) Pavlovska, A., Dobrev, D., Bauer, E. Surface melting versus surface non-melting: an equilibrium shape study. Surf. Sci. 1993, 286, 176181 (14) Pavlovska, A., Dobrev, D., Bauer, E. Orientation dependence of the quasi-liquid layer on tin and indium crystals. Surf. Sci. 1994, 314, 341352 (15) Pavlovska, A., Dobrev, D., Bauer, E. Roughening transition of tetragonal metals: an initial growth shape study. Surf. Sci. 1994, 314, 331-340 (16) Pavlovska, A., Dobrev, D., Bauer, E. Facet growth of spherical lead crystals. Surf. Sci. 1995, 326, 101-112

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17. Hong, J-S., Jo, W., Ko, K-J., Hwang, N. M., Kim, D.-Y. Equilibrium shape of nickel crystal, Phil. Mag. 2009, 89, 2989-2999. (18) Kamiuchi, N., Sun, K., Aso, R., Tane, M., Tamaoka, T., Yoshida, H., Takeda, S. Selfactivated surface dynamics in gold catalysts under reaction environments Nat. Commun. 2018, 9, 2060-1-6. DOI: 10.1038/s41467-018-04412-4 (19) Rodriquez, A. M., Bozzolo, G., Ferrante, J. Multilayer relaxation and surface energies of fcc and bcc metals using equivalent crystal theory. Surf. Sci. 1993, 289, 100-126. (20) F. Ercolessi, F., Tosatti, E., Parrinello, M. Au(100) surface reconstruction. Phys. Rev. Lett. 1986, 57, 719-722 and references therein (21) Havu, P., Blum, V., Havu, V., Rinke, P., Scheffler, M. Large-scale surface reconstruction energetics of Pt(100) and Au(100) by all-electron density functional theory. Phys. Rev. B 2010, 82, 161418-1-4 and references therein (22) Georgiev, N., Pavlovska, A., Bauer, E. Surface disordering without surface roughening. Phys. Rev. B 1995, 52, 2878-2887

(23) Baletto, F., Ferrando, F. Structural properties of nanoclusters: Energetic, thermodynamic, and kinetic effects. Rev. Mod. Phys. 2005, 77, 371-423

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Equilibrium shape of two bcc microcrystals at low temperature with {110}, {211} and {100} faces. 8 ACS Paragon Plus Environment

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High Temperature Equilibrium and Growth Shape of Small Particles

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