The thickness of molten surface layers on copper monocrystals

Surface Science @North-Holland

91 (1980) 655.-668 Publishing Company

THE THICKNESS OF MOLTEN SURFACE LAYERS ON COPPER MONOCRYSTALS

K.D. STOCK Institut B .fiir Physik der Trchnischen Universittit Braunschweig, Abteilung Grenzfl~cherlphysik, Postfach 3329, 3300 Braunschweig, Germa,z_y

Received

25 June 1979; accepted

for publication

21 .4ugust

ftir

1979

Spherical copper monocrystals solidify and melt at 1 X 10-a Pa in a gradient of temperature with a liquid-solid interface recognizable as a sharp bright-dark step in their light emission. Inferred from radiance observations the solid copper surface is covered by a wedge shaped layer of surface melt dependent on the surface temperature. Only circular areas round the (111) and (001) poles are free of the observed surface melt. On basis of the optical constants the observed melt layer at l-2 K below the bulk melting point was estimated to 2-7 monolayers of liquid copper in thickness and compared with theoretical values of Kristensen and Cotterill. The influences of impurity effects are discussed, they can be neglected. First AES observations on room temperature have shown only traces of sulphur beside copper.

I. Introduction

The existence of surface melting on solids has been discussed repeatedly; summaries are given in refs. [l-3]. Some experimental indications of surface melting shall be mentioned here: Rhead [4] inferred surface melting from the strong increase of the surface self-diffusion coefficient of copper in the vincinity of the melting point [S] ; the discussion is in continuation [6-91. Heyer, Nietruch and Stranski [IO] deduced surface melting on high-index planes of zinc from the growth form grown from the vapour. Zhdanov [ 1 l] concluded surface melting from the rotation of the smallest zinc crystals on carbon. Pavlovska and Nenow [ 121 inferred surface melting from the morphology change of vapour inclusions in tetrabrommethan crystals near their melting point. There are further indications in refs. [13-151. In contrast to these indirect indications direct observations of surface melting are possible on metals such as copper [ 16- 181. Because of the discontinuity of the optical constants at the copper melting point [ 191 an effortless discrimination between liquid and solid copper is possible. Molten surface layers of only a few monolayers are indicated in contrast to melt-free surfaces. Spherical monocrystals allow the observation of planes of each orientation with the identical preliminary 655

656

K.D. Stock / Thickness of molteM surface la)>ers on Cu monocrystals

treatment. Optical effective anisotropies (such as caused by molten surface layers) can directly be recognized on spherical monocrystals; the absence of surface melting on low-index planes was predicted by Burton, Frank and Cabrera [20]. If the experiments are performed in a gradient of temperature near the melting point T,,,. the visible liquid-solid interface marks the position of the isotherm of T,. Having measured the gradient of temperature it is possible to determine the surface temperatures by linear measurements. The visual observation of spherical copper monocrystals solidifying directly from a drop of melt in a gradient of temperature by a method of Menzel [21,22] give best presuppositions to detect an (anisotropic) cover with a molten surface layer. Some special observations arc already published in short notes: Below the melting point T,, on the copper surface the radiance reversibly reached the value of the liquid copper except the surroundings of the (1 11) and (001) poles [ 161. Here. Rhead [23] supposed nucleation of the liquid phase to be easier on the atomically rough surfaces. The movement of small particles of slag showed the existence of a molten layer outside the surroundings of the low-index poles [ 171. The main objects of this article are to discuss the basic phenomenon of the visible molten surface layer during growth and melting of copper crystals and the evaluation of the layer thickness based on optical data.

2. Apparatus and experimental

technics

In a UHV-system spherical copper crystals were prepared and simultaneously observed in their hot stage. Normally the coating of the window by condensing copper vapour complicates the observation. Therefore a standard UHV-pump-unit (PU 300 T, Leybold-Heraeus, Kiiln; base pressure less than 1 X 10m9 Pa) with a special experimental chamber was used. Here the growing or melting crystals were observed from above through a viewing window of 150 mm diameter. A suggestion of Menzel [2 1 ] was realized here in the UHV-system (fig. 1): In the experimental chamber a rotable quartz disk (100 mm diameter, 2 mm thickness; eccentric to the observation axis) is below the viewing window. Above a fixed shutter the quartz disk is rotated by a bevel gear and a rotary motion feedthrough. The shutter of stainless steel has a hole of about 7 mm (centric to the observation axis). The shutter keeps the quartr disk (and the viewing window. too) free of copper vapour except the field of 7 mm. This field is needed for observation. During the observation of the hot copper crystals this field will gradually be coated by copper. If it is coated too much the disk can be rotated a little bit and a new copper-free field of the quartz disk is available. The viewing window, the quartz disk, and the shutter are easily demountable for changing the crystals and cleaning the quartz disk. By a method of Menzel [21,22] spherical copper crystals of 2-~3 mm diameter were produced by normal freezing of a drop of melt in a gradient of temperature.

K.D. Stock / Thickness of molten surface layers on Cu monocrystals

viewing

quartz

disk

window

observation

657

axis

shuffer

with

wote;cooled

hole

current

Fig. 1. UHV experimental chamber for the observation of vapourizing materials after a suggestion of Menzel [ 211. The holding device with the special mounting support (spectral graphite) allows the preparation of spherical monocrystals in a gradient of temperature (the crystal diameter is exaggerated).

This gradient was generated by contact to an asymmetrically heated mounting support of spectral graphite (RW 0, Ringsdorff, Bad Godesberg). The mounting support itself was the filament resistance during the heating with high constant direct current. Ready crystals do not adhere to the graphite and the support could be used repeatedly. As we were only interested in the light emission of the copper crystals the light emission of the mounting support had to be as small as possible. So a special form of the support turned out to be favourable: here the crystal was centred in the observation axis by a ring of spectral graphite (outside diameter 4 mm, inside diameter 1.2 mm, 1.5 mm thick). This ring was positioned on the top of a 5 mm long stout (1.5 X 1.5 mm2 in section) which was clamped in one jaw of a holding device. The other jaw pressed another piece of spectral graphite against the ring. The holding device was mounted on massive watercooled current feedthroughs. Now direct current could flow from jaw to jaw through the mounting support (ring

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K.D. Stock / Thickness of molten surface layers ott Cu monocrystals

659

x

I xd

h

Fig. 2. (a) Slowly

solidifying

spherical

copper

mm/set; 1.8 X lob8 Pa). Black of solidification; LSI: liquid of the luminance I, as a function of the dis-

probe

(v = 0.005

(melt-free) areas round a (111) and a (001) pole. DS: direction solid interface (bulk). (b) Qualitative tance x from the LSI (X = 0). Sections

proceeding AB and El:

through black areas.

when the temperature T approached the melting point T, (considering the gradient of temperature dT/d_x in the copper surface). Lateron we see that this visible increase cannot be explained by a temperature factor of solid copper in the sense of Planck’s radiation law. However, the observations can be explained by assuming the appearance of a molten surface layer. Near the melting point T, the solid copper crystal is covered by a thin layer of copper melt. This molten layer is not present on the (1 11) and (001) poles predicted in refs. [20,24] and in addition not present on their vicinals described in ref. [ 171. The thickness D of the molten surface layer is a function of the temperature difference AT to T, and hence a function of the distance x from LSI in the copper

660

K.D. Stock / Thickness of molten surf&e laJ,ers on Cu monocrystals

surface. As the spectral emissivity E of liquid copper is higher than that of solid copper (Ed > ES), an increase in L with decreasing x can be observed (outside the black melt-free areas). Now we have tried to estimate the layer thickness on the basis of the distance xd (from LSI).

4. Emissivity contrast between liquid and solid copper Some thoughts to the distinction of solid and liquid copper at T,,, and to the effect of a red filter are needed. Here the application of the spectral emissivity e(h,T) is very useful. The function e(h,T) gives the ratio of the spectral radiance L,.,(h) to that of a Planck radiator at the same temperature. The function e(X,T) can be determined from Beer’s and Kirchhoffs law as:

Here, (n - ik) is the complex index of refraction. At the melting point T, there is a discontinuity of the optical constants from solid to liquid [ 191 and a discontinuity of E(X,T,), too. The discontinuity of the optical constants is also accompanied by a discontinuity of the electrical resistance 1251 at T,. Therefore we are able to distinguish solid (dark) and liquid (bright) copper by its light emission (Ed > es). The liquid-solid interface can be seen as a sharp bright-dark line of contrast. From Otter’s measured values [ 191 of the optical constants (k2 ~ n’)(X,T) and %k(X,T), the values of eL(h,Tm) and ~s(h,T,) have been calculated for the visible range of light by eq. (1) (fig. 3a). At the melting point T, we will define a spectral emissivity contrast C(h) between liquid and solid copper by:

(2) Fig. 3b shows a strong increase of C(X) with increasing wavelength h. This increase has been utilized for improving the distinction between liquid and solid copper: During visual observation the human eye integrates over an interval of wavelengths given by the spectral luminous efficiency V(h) (photopic vision) and a possible filter function 7(h) (eq. (3)). The effect of a red filter on the distinction between liquid and solid copper can be demonstrated by the effect on the so called effective wavelength h, [26]. For a more careful description of h, we have to refer to special literature [27]. The quantity h, is a wavelength in a sense of a “centre of gravity” in the used range of wavelengths. By a graphical procedure [27], X, was determined with and without the red filter RG 610. Without any filter h, approximately lays in the maximum of V(/‘(h)at X, = 560 nm. Here, fig. 3b shows C(560 nm) < 0.05. The red filter shifts X, to about 625 nm; here the liquid-solid contrast increases to C(625 nm) > 0.2. This a red filter considerably raises the contrast between liquid and solid. A further shifting of X, to larger wavelengths is no

K.D. Stock / Thickness of molten surface layers on Cu monocrystals

661

Fig. 3. (a) Spectral emissivity c(h) of liquid (L) and solid (S) copper at the melting point T, calculated from measured values of Otter [ 191; (0) from an extrapolated value. (b) Emissivity contrast C(h) between liquid and solid copper at T,; (0) from an extrapolated value.

because the absolute value of the luminance becomes too low. From measured values of Otter [ 191 the increase of C(h) with X is known up to 640 nm (fig. 3b). An infrared sensitive film should utilize a possible further increase of C in the near infrared region. The Kodak 2481 type has a sensitivity up to 900 nm [28]. Here the said filter shifts X,, too, and in addition protects the film against exposure in its high sensitive UV-range. There are no informations on the discontinuity of the optical constants at Tm in the near infrared range; therefore X, or C could not be calculated for the made photographs. The liquid-solid contrast obtained by use of the infrared film was neither attained with panchromatic films not with a Valvo XX 1050 image converter (sensitive up to about 800 nm). advantage

5. Thickness of the molten surface layer at xd On basis of the differences in the radiance of liquid and solid copper we come now to an estimation of the molten layer thickness D by the following model (fig. 4): The eye receives different luminances L,

L = Max

s

from the is (Kmax K ,,,V(X) Lek(X) the

three surface areas: liquid (L), solid (S), and surface melt covered (sm) a constant, v(‘(h) the spectral luminous efficiency (photopic vision), the spectral luminous efficacy of radiation, r(h) the filter function, and spectral radiance). L,, is composed by

L sm=LI

+Lz.

Le,(x> v(X) T(X)dX a

(3)

(4)

To simplify the problem we use the spectral radiance L,A(X) for the present. Leh,

662

K.D. Stock / Thickness of molten surface layers on Cu monocrystals

Fig. 4. Luminances L on a surface of liquid (L), solid (S), and surface D: thickness of the molten layer; LSI: liquid- solid interface (bulk).

melt (sm) covered

copper.

represents the part of the spectral radiance of the solid copper base weakened by the molten layer. Assuming the absorption coefficient K of liquid copper to be independent of the layer thickness D we find by Lambert’s absorption law: &hl (0) = LehS exp(-KD)

,

(9

where Lehl decreases with increasing D. The part Lehz of the spectral radiance of the molten layer itself is Lehz(D) = LehL [1 -

exp(-WI .

(6)

L + increases with increasing D. From the measured absorption coefficient K was calculated from K(X) = 4n k(X)/X

values of Otter

[ 191 the

(7)

(k(X)

in the complex index of refraction (n - ik)). During visual observation with the described red filter RG 6 10 the effective range of wavelengths is from 610 --640 nm; in this range K increases per about 4%~ only (K(625 nm) = 0.076 nm-‘). Neglecting this small variation we can write with the eqs. (3) and (4): L %rn

ZL

ehL ~ 6%~~

- LehS)

ew-W

L sm = LL - (LL - Ls) exp(-KD) ,

.

(83) @b)

So the layer thickness D is given by the ratios between the luminances L,, Ls and L sm. As we have already said the visual (and photographical) contrast between L,,, (dark area) and Ls (black area) was very low and decreased with increasing x (fig. 2). At the distance xd from the liquid-solid interface (LSI) this contrast reached the limit of the contrast perception of the eye. According to the Weber-Fechner law [48] the limit of perception of a step AL in the luminance (white light) lies at AL/L = 0.015. Analogeous to eq. (2) we can define a limit of visually perceptible

K.D. Stock / Thickness of molten surface layers on Cu monocrystals Table 1 Thickness L) copper

D of a molten surface layer visually distinguishable for values of C; (eq. (11)); C; limit of the contrast

G 0.0075 0.0150 0.0300

a

a Corresponds

Dsmp (nm)

&,IL

0.4 0.8 1.6

41 32 23

to Weber-Fechner

from solid (sm/S) and liquid perception of the eye

663

(sm/

(nm)

law [48].

contrast:

(for AL SL). Now for a given C: two limits of the thickness D of the molten surface layer can be determined; with the eqs. (9) and (10) we find:

D sm/s = - +ln D Smp_-iln(l

l(

2c: L,/Ls -~ 11 ’ _yiLJ

.

(1la)

(1lb)

The ratio LL/Ls = 1.5 was calculated with the spectral emissivities EL and ES (fig. 3a), the spectral radiance of a Planck radiator at T,, the spectral luminous efficiency V(h), and the filter function r(h) (RG 610, Schott data). D,,,s gives the lower limit of melt thickness D on solid copper (in the dark area) which is to be distinguished from a melt-free copper surface (black area). As already said in a gradient of temperature near LSI (outside the black areas) we suppose a molten surface layer of increasing thickness D with decreasing distance x to LSI or with decreasing temperature difference AT to T,. From visual observations at xd we can calculate D = D,,p with eq. (1 la). We found D,,,s to be in the order of 2-7 monolayers of liquid copper (see the table 1; monolayer thickness of liquid copper: 0.24 nm). Dsrn,~ we need in a later section.

6. Gradient of temperature

in the copper surface

For a comparison with theoretical values of the melt thickness D at xd (fig. 2) the temperature at xd was needed. Therefore an estimate of the surface temperature gradient dT/dx was necessary. A measurement with thermocouples was not practicable without strongly disturbing the temperature distribution in the copper surface. Therefore a contact-free method was used; the following pyrometrical method

664

K.D. Stock / Thickness of molten surface layers on Cu monocrystals

called for some idealizing assumptions: (i) The gradient of temperature dT/dx is constant in the investigated surface area and constant during small variations of the surface temperature T. (ii) The liquid-solid interface (LSI) and the visible bright-dark limit are identical to the isotherm of T,. (iii) T is a reproducible function of the heating power of the mounting support and of the control-resistance R. Starting from a given position of the LSI in the sphere surface T was raised by a small value dT. Now the LSI shifts in the direction of the temperature gradient by a value dx. Assuming (i) and (ii), dT and dx result in the needed gradient dT/dx. In contrast to dT the shift dx (about 0.5 mm) could be easily measured by the microscope equipped with a measuring eye-piece. However, dT was less than the resolving limit of the pyrometer being available (given limit: 1.5 K). Therefore we proceeded in three steps: (j) By assumption (iii) the surface temperature T and the position of the LSI, was a function of the control-resistance R. By potentiometers of high precision R was adjustable to &R/R = 5 X 10m6. A variation 6R shifts the LSI by dx; the measurable quotient was GRldx. (jj) The microscope was replaced by a micropyrometer, Pyrowerk Hannover. Near the melting point T,,, the temperature of the crystal surface was varied by varying the control-resistance R by dR. Here, dR was about 50 times greater than 6R; so the visual filament pyrometer could be used to measure the variation dT, of the radiation temperature T,. So the quotient dT,/dR was measured. Repeated variations of R showed T, to be a reproducible function of R in the investigated range of temperature. (jjj) With the described pyrometer Menzel and Stahlknecht [29] had measured T, on copper crystals. W-Re thermocouples had given the true temperature T of the crystals. These measured values now gave the quotient dT/dT, for the here investigated range of temperature. The needed gradient of temperature dT/d.x was now determined by: g=E dx

dx

dT, __- dT dR dT,’

(12)

The measured value of dT/dx was 2.5 + 0.5 K/mm. So defining the LSI to have the position of the isotherm T,,,, the copper surface had a difference of temperature AT to T, of about AT = l-2 K at xd = 0.3-0.8 mm (fig. 2). The described method is rather unwieldy but there were no other possibilities to measure dT/dx without disturbing the system. The increase of the luminance L with decreasing x (fig. 2, section CD) for 0
K.D. Stock / Thickness of molten surface layers on CM monocrystals

in radiance of this order would lie at the limit of perception; increase it would never be visually recognizable.

665

as a continuous

7. Comparison of experimentally estimated melt thickness with theoretical values Looking back at the results of the estimate of the molten layer thickness,D, we found D = DsmlS = 2-7 monolayers of liquid copper at xd, respectively at AT = 1-2 K. Only a few theoretical estimates of D are known. Lacmann and Stranski [30] qualitatively deduced D from a thermodynamical estimate of the free specific surface energy y; they could interpret growth and orientation of ice dendrites. The experimentally found value of D will now be compared with a theoretical estimate. Kristensen and Cotterill [2] found a quantitative thermodynamical estimate according to a method of Bolling [3 11. The thickness D of a molten surface layer on a solid which is in equilibrium with its own vapour is given as:

clcYs/v-Ys/L-

n = 0 [

W

-YL/v)

1l’(q+l)_

Tm

ar

1

(13)

(no: number of monolayers). The quantities ys/v, ys/L and ~L/v are the free specific surface energies of the solid/vapour, solid/liquid, and liquid/vapour interface. W is the latent heat per monolayer, q is a constant. Effects of anisotropy were not taken into account. For the evaluation of eq. (13) the following values were used: ys~ = 1570 erg/ cm*, “best value” after a summarizing sheet of Tyson [32] ; yLp = 1285 erg/cm2 [33] in good agreement with other authors; ys~L = 136 erg/cm2 [34] (the older value of Turnbull [35] of 177 erg/cm* would change no only a very little because of the root in eq. (13)); W=422 erg/cm2 [31]; T,,, = 1356K; AT= T, -T; the value 4 = 3 gave the best fit to experimental observations at grain boundaries in ref. [3 11. Now eq. (13) gives the equilibrium thickness no of the molten layer as a function of T; approximately no linearly increases with decreasing AT; in the immediate vincinity of T, (AT< 0.1 K), no increases very strongly. By the consideration of the gradient of temperature on the crystal surface this would mean an equivalent increase ofno with a decreasing distance x to the liquid-solid interface (LSI). Now we needed the value of tie expected for AT = l-2 K. Eq. (I 3) gives no(AT): no( 1 K) = 5.2 and rzo(2 K) = 4.2. So after Kristensen and Cotterill [2] we expect a molten layer thickness of about 4-5 monolayers at xd (fig. 2). This is in good agreement with the value of 2-7 monolayers estimated from optical data (section 5).

8. Effect of impurities Now we turn to the question whether impurities in the copper surface could be responsible for the observed surface melt. In principle it is conceivable that a segre-

666

K.D. Stock / Thickness of molten surface layers on Cu monocrystals

gation of solute impurities forms a surface alloy with a melting point lower than that of pure copper. There are several models discussing surface segregation (36.m 401. Here the driving forces of segregation are the minimization of elastic energy or of the surface energy. Common to all is an exponential factor containing l/T. That means that with increasing T the surface concentration of the first monolayer approaches the bulk concentration. Some models of segregation consider several layers near the surface [41-441 (multilayer model); generally the 3-4 outer monolayers are sufficient as verified by ref. [45], for example. Here the high temperature behaviour is important. Somorjai and Overbury [46] discussed [43] for high temperatures: increasing temperatures more and more caused an approximation of the multilayer model to the monolayer model verified in ref. [47]. Now we have to refer to the high temperature during the described experiments (T,, = 1356 K). For this high temperature we are encouraged to suppose a very low segregation and an essential segregation in the outermost monolayer only. The surface segregation of impurities in the used copper was estimated by the ideal dilute solution model [38] on basis of the metallic bulk impurities (specified by the originating firm). According to it calcium had the biggest concentration; as the element of high surface activity calcium was found to be of about 0.1% in the outermost monolayer. First surface investigations of our spherical copper crystals at room temperature by a 4-grid retarding field Auger analyzer (Vacuum Generators, Grinstead GB) in another apparatus exclusively showed traces of sulphur (beside copper). These results must be regarded as an upper limit of the concentration of surface impurities present at T,. At the copper melting temperature we have to expect an effect of surface segregation (out of the bulk) or adsorption (out of the residual gas, total pressure I X IO-* Pa) only in a layer thickness of one monolayer. The visible molten copper layer on solid copper had a thickness of about five monolayers minimum (sections 5 and 7). This thickness even increases approaching the LSI. The luminance of the area with surface melt (in contrast to the black areas round the low-index poles without surface melt) could be reversibly raised till the luminance of the massive liquid copper [ 161. That means that the thickness of the molten layer here had reversibly reached values of D sm,L (table I) of about 100 monolayers. These observations cannot be explained by impurity segregation.

9. Summary Visual observations of the light emission of solidifying and melting monocrystals of copper showed constant luminances on the surroundings of the (001) and (11 I) poles - so called black areas - and increasing luminances with decreasing distance to the liquid-solid interface outside the black areas. The observations were explained by the assumption of a molten surface layer outside the surroundings of

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(001) and (111) and a layer thickness dependent on the surface temperature (gradient of temperature in the copper surface). The gradient of the surface temperature was determined by a pyrometrical method: the measured value was 2.5 f 0.5 K/mm. At the distance xd from the liquid-solid interface the thickness D of the molten layer was estimated to 2-7 monolayers on basis of optical data. The distance xd corresponds to a temperature difference of AT = l-2 K below the melting point (T, = 1356 K). This result was compared with a thermodynamical estimate: according to Kristensen and Cotterill a thickness of 4-5 monolayers was expected for the said AT. Impurity effects were discussed: assisted by Auger investigations the observations cannot be explained by impurity segregation.

Acknowledgements The author wishes to thank Professor E. Menzel for helpful and interesting discussions and Dipl.-Phys. B. Grosser for the AES-investigations. This work was supported by the Deutsche Forschungsgemeinschaft.

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