The overheating of lead crystals

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The overheating of lead crystals

J.J. Métois, J.C. Heyraud

To cite this version:

J.J. Métois, J.C. Heyraud. The overheating of lead crystals. Journal de Physique, 1989, 50 (21),

pp.3175-3179. �10.1051/jphys:0198900500210317500�. �jpa-00211135�

Short Communication

The overheating ^{of lead} crystals

J.J. Métois and J.C. Heyraud

Centre de Recherche des Mécanismes de la Croissance Cristalline (*), Campus ^de Luminy, ^Case 913,

13288 Marseille Cedex 9, ^France

(Reçu ^{le 28} juin ^1989, accepté ^sous forme définitive ^{le 7} septembre 1989)

Résumé. - Contrairement à la surfusion qui ^{est très} fréquemment observée, ^la surchauffe de cristaux

métalliques ^n’a que ^{rarement été} signalée. L’explication généralement ^{avancée est} que la surface des cristaux est recouverte d’un film liquide (préfusion ^de surface) ^{bien avant} que ^la température ^{de fusion} volumique ^ne soit atteinte. Le but de cette courte note est de montrer que ^la surchauffe est possible

et peut effectivement être observée (0394T ~ 3°C) lorsque les cristaux sont limités par ^{des faces non} mouillées (faces {111}) séparées par ^des parties ^{courbes de} très faible extension recouvertes de leur film liquide.

Abstract.

Overheating ^of crystals ^has scarcely ^been reported ^unlike undercooling which is fre-

quently ^observed. Admittedly ^the absence of overheating ^{is the} consequence ^{of the} crystal ^surface being ^covered by ^a liquid ^film (surface premelting) well under the bulk melting temperature. ^{In the} present ^{letter we show that} overheating ^is possible, ^{and is} actually ^observed (0394T ~ 3°C), ^when

the crystals ^are bounded by ^non wettable facets ({111} facets) separated by relatively small curved

regions ^covered by their melt.

Classification

Physics ^Abstracts

61. SOJ - 64.70D - 68.42

1. Introduction.

In the now accepted opinion, melting ^{of a solid starts at} the surface ^at temperature appre-

ciably lower than the bulk melting point This so-called surface premelting (already suggested long ago by Faraday [1] ^to explain ^the properties ^of ice) ^{has been confirmed and} studied in detail

using ^modern techniques ^of surface science. Premelting ^{was detected} (i) ^on physisorbed layers (Ar/graphite, CH4/MgO) by measuring their heat capacities [2] ^or by quasi-elastic neutron scat-

tering [3] ; (ii) ^on organic crystals (biphenyl) by ellipsometry [4] ^and (iii) ^{on metallic} crystals (Cu, Au, Pb, In) by optical emissivity [5], by ^ion scattering [6, 19] by ^Leed [7] ^and by observation of the

equilibrium shape of crystallites [8, 9].

In the case of lead crystals ^{it seems now} well established that the curved regions ^{are covered} by ^a liquid layer ^{below the} melting temperature whereas the {111} surface remain solide [19] ;

no equivalent ^{clear cut} situation exists for {100} (so far neither morphological ^studies [8] ^{nor ion} chanelling experiments [19] ^have definitely decided wether it is wetted).

(* ) Laboratoire Propre ^{du CNRS associé aux} Universités d’Aix-Marseille 2 et 3.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198900500210317500

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’Ib understand the continuous lowering ^{of the} melting point ^of crystallites ^whose size is less than roughly ³⁰⁰ Â, the existence of a quasi-liquid layer ⁱⁿ thermodynamic equilibrium ^{with the}

solid at a temperature lower than the melting point ^{has been} postulated ^{in the} past [10 - 14]. ^This

idea was introduced by ^{Reiss and} Wilson in 1948 [15] ^{and later} developped by Curzon in 1959 [16].

It has now been confirmed by ^the observation of surface premelting.

Another important consequence of surface premelting ^{is its} inhibiting role in the overheating of crystals (when overheating ^{occurs the} crystal remains in its solid state above the melting point).

In our present understanding ^of melting overheating is inhibited because the liquid layer ^thickens

when the temperature ^is raised, until the whole solid is molten (at ^{the bulk} melting point). ^{This is}

the currently explanation for the absence of overheating.

Th retain the solid state when the melting point has been crossed several methods can be

imagined : (i) eliminating the surface or (ii) growing crystals ^bounded exclusively by facets that do not premelt. ^Method (i) ^{was used} by Dages et aL [17] who covered a spherical Ag crystals by ^a continuous epitaxial layer of another metal (Au) ^{with a higher} melting point ^{than Ag and a} negligible interdiffusion coefficient. These authors were thus able to cancel surface premelting

and to observe an overheating ^{of 25 K for} Ag ^{on some of their} crystallites. However, ^this very

elegant experiment ^{is not} straight forwardly conclusive. Even though interdiffusion is small, ^{it can}

play ^an importan role in the melting ^{since the} Ag/Au interface is not stricly abrupt. ^{Moreover a}

small fraction only ^{of the} crystallites undergoes overheating, which is difficult to rationalize since all are submitted to the same treatment. Method (ii) ^{was used by} Spiller [14] who showed that tabular Pb crystallites, ^{assumed bounded} by {111} ^faces only, could sustain a 2 K overheating.

The experimental ^{result cannot} be doubted but its origin ^is questionable ^{since no evidence was} given for the existence of sharp edges ^on the tabular crystals.

Considering ^{the above} pieces of information we decided to investigate ^the overheating ^{of Pb} crystal ^on graphite experimentally.

2. Experiments.

Since the high temperature growth shapes of Pb seemed convenient for the type ^of experi-

ments planned, ^our goal ^was obtaining ^them with the smallest possible premelted regions.

We used a modified transmission and scanning microscope (Jeol 100C ^ASID 4D) ^{with ultra} high ^vacuum facilities in which in-sini growth experiments ^{can be made} [18].

Transmission and scanning microscope monocristalline graphite ^{was selected as} the substrate since a plane (00.1) ^{surface can be} easily ^obtained by ^air cleavage ^and subsequently cleaned in-situ

by heating ^{at 800°C} during 20 minutes under UHV In addition graphite ^{is an} unreactive material for Pb and has a satisfactory ^behaviour during ^thermal treatments.

As a deposit Pb has several advantages : ^{it has a f.c.c.} lattice, ^{a small} vapor pressure ^{and a} convenient melting point (MP : ^{327° C ; P - 10-9 Torr at} 327°C), ^which avoids unreasonable

evaporation. ^Its equilibrium shape, roughening transitions and surface premelting ^{domains are}

well known [8].

A typical experiment ^{is run in the} following way : ^the graphite is cleaned under UHV Pb is condensed at room temperature ^{until a} continuous layer is obtained about 3000 Â in thickness.

Then this layer ^{is annealed above the} melting point of Pb. These results in the layer fragmenting

and in spherical ^molten droplets being ^formed (diameter ^{0.1 -} 0.5 u). ^The droplets ^{are then} crys- tallized about 100° C below the melting point, ^{due to their} undercooling. ^A subsequent deposition

of Pb (3000 ^Â equivalent) is then made with the sample ^{at a constant} temperature ^{between 200° C}

and 326°C. A population ^of polyhedral crystallites is thus obtained. Most of them are cuboocta-

hedra ({111} ⁺ {100}) ^{while a} small fraction is composed ^of {111} octohedra and {111} ^tabular

crystals (Fig. 1).

Fig.1.- Typical population ^{of Pb} crystallites ^on graphite by ^{our double} condensation method (see text) ^be-

tween 2000C and 326°C.

The sample ^is subsequently ^{annealed at} increasing temperatures ^while it is observed by ^SEM.

Upon approaching ^the melting point step wise increments of temperature ^{are realized} every ¹

degree (15 minutes in duration) during ^{which the} temperature ^{is stable} within 0.5°.

3. Results.

As shown by figure ^{1 the} morphologies of the solid Pb crystals ^{fall into two classes :} (i) ^those (the biggest = 0 N 0.5 pm) ^{that have a} shape rather close to the equilibrium shape, display ( 1 1 1 ) and {100} facets connected by ^rounded regions ; (ii) ^those (about twice smaller than the former :

0 N 0.2 pm) ^{that are} polyhedra ^with sharp edges and bounded either by {111} and {100} ^facets

Fig. ^2.- Sharp-edged polyhedra ^observed by TEM. The actual rounded nature of the "edges" between the

{ 111 } ^{faces is} clearly ^visible.

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or by { 111 } only. ^For simplicity ^{in the} following ^{we call the} crystallites belonging ^{to this second}

class "sharp-edged polyhedra".

In the TEM mode 7 Â resolution of our microscope is much better than in the SEM mode.

By using ^{the TEM mode the} sharp-edged polyhedra ^{are seen to} have in fact rounded edges ^with fairly small radii of curvature (Fig. 2).

We judged ^{that the} melting point of bulk Pb was reached when the crystals belonging ^{to the}

first class (i.e. ^{with a} shape approaching ^the equilibrium shape) lose their {111} ^and {100} ^facets.

This is an actual signature ^of melting ^since undercooling ^{is then} always ^observed upon cooling ^the

substrate. These crystals crystallize ^{from the} Pb-graphite interface with the epitaxy relationship {111} Pb// {00.1} graphite ^and (110) Pb// (010) graphite ^{and a random} distribution of their

spatial orientations due to the rotational equivalence of directions in the graphite ^substrate plane (double positioning).

When the above defined bulk melting point is reached all crystallites ^melt simultaneously except for those that are sharp edged ^{and have} only {111} facets. In other words, among ^the

crystals belonging ^to the second class the sharp edged cubo-octahedra do not display overheating

whereas the sharp edged ^and {111} only polyhedra ^can be heated 2-4° above the bulk melting point. They ^{can be} maintained in this overheated state for several hours. No dependance ^{of this} phenomenon ^{on the} crystallite ^{size can} be detected. So,.neither ^the annealing ^{time nor the} crystal

size influences the overheating phenomenon.

Fig. ^{3.- A} population ^{of Pb} crystallites ^2° C above the bulk melting point. Note the random co-existence

of (overheated) sharp-edged {111} only polyhedra and of molten spheres of Pb ; a) ^and b) represent ^two different regions ^{of the} sample.

This is in disagreement ^with Spiller’s ^results [14]. ^{It was} checked that the electron beam had

a negligible ^influence by examining portions ^{of the} sample ^{that had} escaped prior exposition ^to

the beam. On these "virgin" regions only sharp-edged { 111 } polyhedra where observed under the

overheating conditions. Since a random overall distribution of overheated and molten crystals ^was

obtained no effect of a temperature gradient along ^the sample ^{can be} suspected.

4. Discussion and conclusion.

We summarize our experimental observations as follows.

1) By using ^{the SEM mode of our} microscope ^{one sees that} (i) ^the sharp-edged 111 1} ⁺ { 100 } polyhedra ^{melt at the same} temperature ^{as the} bigger crystallites ⁱⁿ pseudo equilibrium (i.e. ^with { 111 } ^and { 100} facets and well developed ^rounded regions inbetween), (ii) ^the sharp-edged { 111 } only polyhedra ^{can be} overheated. The overheating ^{domain is}

^3°C.

2) By using ^{the TEM mode the} sharp edges ^{of the} sharp-edged { 111 } only polyhedra ^{are seen}

to be in fact curved regions of very ^small extension and very high curvature. Since surface premelt- ing ^{has been} observed within a wide range ^of crystal ^sizes (from ^{1 mm} [19] ^{down to} 1 pm [8]) ^we extrapolate ^{and assume that the same} phenomena ^{also occurs for} crystals regions having ^curvature

radü in the nm range. Using this reasonable assumption, Spiller’s explanation ^of overheating (the

existence of a nucleation barrier for creating ^a liquid ^{nucleus on} { 111 } ^{does not seem valid.}

In contrast Nozières [20] recently proposed ^{a mechanism which allows an} explanation ^{of our}

observation to be given, ^{at least} qualitatively. The author considers the equilibrium ^{of two non}

wetted faces separated by ^a quasi molten rounded region. He shows that a premolten ^meniscus

can exist between the two faces at temperatures ^{lower than} Tf ^{and becomes a} biconvex molten lens above Tf. ^The stability ^{of this} system determines the temperature ^{domain of} overheating. ^The

width of this domain depends ^{on several} parameters ^either energetical (the specific ^free energies

of the various faces and interfaces) ^or geometrical (the angle between the facets, ^the wetting angle

of the facets and the rounded regions, the various radü of curvature).

In the Nozières’ picture ^{the lack of} overtheating ^{of the} sharp-edged { 111 } ⁺ { 100} polyhedra

means either that {100} itself is wetted (at ^{least at} Tf) ^{or that} the molten lens between f 11 1} ^and {100} is unstable at Tf.

Acknowledgments.

The authors wish to thank Pr. R Nozières and Pr. J.M. Bermond for helpful discussions.

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