Premelting electrical conductivity and heat capacity in some alkali

Conductivity and Heat Capacity in Some Alkali Halides

The Journal of Physical Chemistty, Vol. 82, No. 11, 1978 1277

Premelting Electrical Conductivity and Heat Capacity in Some Alkali Halidest J.

L. Tallon,” W. H. Roblnson,

Physics and Engineering Laboratory, Depaltment of Scientific and Industrial Research, Lower Hun, New Zealand

and S. I. Smedley Chemistry Department, Vicforia University, Wellington, New Zealand (Received December 29, 1977)

The electrical conductivity and heat capacity of NaC1, KC1, NaBr, and LiF are investigated near their melting points and both properties show a rapid premelting rise commencing about 6 K below the bulk melting points. The changes in heat capacity are measured by differential thermometry at constant furnace heating rates while the conductance is measured using platinum wire electrodes which have been inserted in a crossed configuration by passing a current through the wires and allowing them to melt a path into the specimen. This new electrode geometry confines the conduction to the small region where the electrodes cross and nearly touch, and measurements are thus relatively unaffected by the specimen surfaces subliming or melting away. The use of guard electrodes reveals that the rapid rise in conductance occurs only on the surface, and within the crystal bulk there is no premelting to within at most 0.5 K and probably less. The rise in surface conductivity is strongly deformation dependent but is not attributable to the effects of impurities lowering the melting point at the surface. These results are interpreted in terms of intrinsic melting of the surfaces below the bulk melting point due to the excess surface free energy and a consequent rapid rise in vaporization rate. The ideas developed are used to explain the previous observation that vaporization of some alkali halides saturates below the melting point then rises rapidly at the melting point.

I. Introduction While melting is understood to be a discontinuous first-order transition between independent solid and liquid phases, in many instances it appears that the Gibbs function for the solid phase may curve toward the liquid phase Gibbs function below the melting points1 Associated with this are a number of premelting changes in elastic constants, heat capacity, thermal and electrical conductivity, and self-diffusivity.l There is as yet no generally applicable theory of melting, nor is the mechanism of melting well understood, although the cause of melting for a wide range of simple crystalline solids has been identified.2-4 This lack of understanding arises more from the complexity of t h e melt structure rather than of the solid structure. Our interest, then, in premelting effects is that processes possibly related to the mechanism of melting may be studied in the better understood solid state. In this paper we report studies on the premelting electrical conductivity and heat capacity of four alkali halides and present what we believe is a sensible interpretation of the data reported here and elsewhere. First, in order to facilitate later discussion we shall review some of the background material pertinant to our subject. Premelting. Of particular interest to the present work is a study by Allnatt and Sime on anomalous increases in electrical conductivity in NaCl and KC1 beginning about 4 K below their respective melting point^.^ In their experiments, in which care was taken not to deform the specimens and thus alter the geometrical factor during an mol experiment, a KC1 crystal was doped with 3.3 X % of SrC12and NaCl crystals were strained up to 5 % in simple compression. They observe that the anomalous rise is unaffected by the doping or the deformation and has an effective activation energy of -200 eV for NaCl and -400 eV for KC1. Discounting impurities as the cause of the effect, Allnatt and Sime are unable to present an explanation. Subsequently, Robinson6 has interpreted their results in terms of a dislocation theory of melting, ’Based in part on the Ph.D Thesis submitted by J.L.T. to Victoria University, Wellington, New Zealand. 0022-3654/78/2082-1277$01 .OO/O

the excess conductivity being attributable to “pipe diffusion” along thermally formed dislocation lines. Earlier observations of premelting conductivity have been made in sodium nitrate7 and cesium chlorideV8 These results are complemented by a number of measurements of elastic constants in alkali halides up to the melting point, T,. The first of these by Hunter and Siegel,g using NaCl single crystals in composite piezoelectric oscillators in the longitudinal and torsional modes, revealed up to 6% decreases in the shear moduli c44 and l/z(cll - c12)and the compressibility x, beginning about 5 K below T,. This means, surprisingly, that the lattice becomes “harder” near the melting point. A similar result obtains for KCI.1° SIagle and McKinstry,ll however, using a 20-MHz acoustic pulse technique found no deviations in c44 and 1/2(c11 - c12) and contrary to the above results an increase in isothermal compressibility near T,. To these results we may add that Robinson and co-workers using the piezoelectric composite oscillator technique have observed, near T,, rapidly increasing mechanical damping in single crystals of K C F 4and All6 and rapidly decreasing dislocation charge in KCl.13 There are some interesting pre- and post-melting effects observed in the vaporization kinetics of NaC1, KBr, and CsI.16 In each case up to moderately high temperatures the vaporization flux follows a simple Arrhenius behavior. Then from about 100 K below T , the flux begins to saturate until just below T , it is nearly independent of temperature. Above T, the flux rises quickly toward the extrapolated Arrhenius line. On the other hand, LiF and silver show no such irregularities, the vaporization flux increasing uniformly through the melting point. The anomalous behavior was tentatively ascribed to a change of the rate controlling step in a two step vaporization process. It is likely that these various electrical and mechanical changes near the melting point are related and it is possible that the climb in vaporization rate at T, is also connected to these effects. Theories of Melting. In the past 70 years a multitude of theories of melting have been advanced perhaps the best known of which is the vibrational instability theory of @ 1978 American Chemical Society

1278

The Journal of Physical Chemistry, Vol. 82, No. 11, 1978

Lindemann,l’ presented in 1910. This is what might be termed a homogeneous theory of melting in that it requires melting to occur uniformly and homogeneously throughout the extent of a crystalline lattice at its melting point. It is known, however, that melting commences heterogeneously a t certain preferred sites such as the crystal surfaces and this was recognized in another theory advanced in the same year by Tammann.18 We wish to discuss this theory here as it relates strongly to our experimental work. According to Tammann, melting commences on surfaces due to the excess Gibbs function there, then proceeds as a dissolution of the crystal in its own melt. This is the case only if the melt “wets” the crystal surface, i.e. ~

Y s 2 71 + Ysl (1) where ys, 71, and yd are, respectively, the specific surface free energies of the solid-vapor, the liquid-vapor, and the solid-liquid interfaces. If this inequality is satisfied the Gibbs function for the solid intersects that for the liquid at a temperature below the bulk melting point, T,, so that the surface melts prematurely and superheating is impossible. The latter is certainly borne out by general experience. Tammann’s ideas were consolidated by subsequent experiments by Volmer and Schmidtlg on Hg and Ga which showed that in fact not all surfaces were completely self-wettable and those which were not could be superheated. StranskizOdeveloped this viewpoint with the idea that it is the close packed surfaces which are least wettable, and which retain facets in the high temperature equilibrium shape of the crystal. Less densely packed surfaces tend to become rounded at high temperature and near the melting point a quasi-liquid layer should form across the surface, becoming increasingly thicker as T, is approached. Considerations of the solid-liquid (s-1) interfacial free energy have become important in the study of the depression of melting point of small spherical crystalsz1and in the homogeneous nucleation of crystallization of supercooled meltsz2and indeed the actual structure of the s-1 interface and of the crystal surface is important to an understanding of melting and the mechanism of melting. The s-1 interface and the crystal surface have been well studiedSz3Three types of crystal surface or interface obtain, namely, singular, which are atomically smooth or facetting, nonsingular which are atomically rough, and where a surface or interface is misoriented to a low index crystallographic plane and therefore consists of a sequence of singular terraces separated by steps, vicinal. The statistical thermodynamics of surface melting was first presented by Burton, Cabrera, and Frank26 as a classical two-dimensional co-operative problem. The picture that emerges is that at low temperatures low index faces are singular while above a transition temperature T, those faces become nonsingular, Le., they contain a high density of adatoms, holes, and kinks on ledges. In agreement with Stranski’s nonstructural view of surface melting they find that T, for close packed surfaces exceeds T, for the less densely packed surfaces. The structure of the s-1 interface was first worked out by Jacksonz6 and he expressed his results in terms of a parameter cy given by (2) where Lo is the change in internal energy between bulk solid and bulk liquid, q1is the number of nearest neighbors in the plane of the interface, and v is the total number of nearest neighbors in the crystal bulk. When (Y I 2 the interface is completely rough and interface movement may 0

=(771/~)(~O/W

J. L. Tallon,

W.H. Robinson, and S. I. Smedley

TABLE I: Values of a for Various Orientations of 5-1 Interfaces Calculated from Values of the Enthalpy of Melting in Ref 42 Orientation of interface Salt (100) (110) (111) LiF 1.94 0.97 0 LiCl

LiBr LiI NaF NaCl

NaBr NaI

KF

KCl KBr

KI RbF RbCl RbBr

RbI

1.80 1.72 1.58 2.11 2.10 2.05 2.03 1.93 2.03 2.03 2.02 1.82 2.06 1.82 1.56

0.90 0.86 0.79 1.05 1.05 1.03 1.02 0.96 2.02 1.02 1.01 0.91 1.03 0.91 0.78

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

readily take place at any point on its surface, while for a! > 2 the interface is singular so that it may progress only by two-dimensional nucleation and is therefore much slower moving and cannot move until a critical supercooling or superheating is reached. Table I lists values of cy calculated for the alkali halides at their melting points for the three lowest index planes and it appears that the sodium and potassium salts and possibly RbCl may facet on (100) near T, but certainly not on any higher index plane. This is indeed what is found in the case of KCI by depositing argon bubbles just under the s-1 interface, quenching, then examining the bubble surfaces by electron micro~copy.~’Only (100) faces grow from the melt as singular ones and these being poorly wetted by the melt may be completely stripped of the melt by the bubble. We thus have a process which may be very important in the study of premelting behavior. At a critical temperature T, below the melting temperature, surfaces will become disordered, i.e., they will melt, with resultant high diffusivity pathways around the exterior of the crystal. T, decreases the higher the index of the surface plane. These ideas are confirmed by a study by Pavlovska and NenowB on surface melting in diphenyl. They find that (201) faces melt 20-25 K below the melting temperature (342.7 K), (110) faces 10-15 K below T,, while for (001) faces T,1 Tm. We shall see that all of these effects discussed in this section have an important contribution to the premelting behavior of the alkali halides we have studied. 11. Experimental Section Our experimental measurements near the melting temperature were, in the main, of electrical conductivity and differential thermometry under various conditions of ambient gas, heating rates, and crystal type, orientation, and preparation. Other complementary information was obtained from optical and scanning electron microscopy. Specimens. Four alkali halides were studied LiF, NaC1, NaBr, and KC1. Each was investigated using differential thermometry, however, in only NaCl and KC1 was the electrical conductivity extensively examined. All specimens were cleaved or sawn from highest purity single crystal optical blanks procured from Harshaw Chemical Co. (Cleveland, Ohio). Wherever possible, specimens were fresh cleaved immediately prior to experimentation, however, to study the orientation dependence of surface conductivity we could not satisfactorily cleave faces of higher index than (100). (110) and (111) faces were

Conductivity and Heat Capacity in Some Alkali Halldes a

Figure 1. Various electrode systems used for measuring ionic conductance: (a)standard parallel plate capacitor with guard electrode: (b) crossed inserted wires with guard electrode and inserted thermocouple: (c)concentric rings of silver conducting paint for measuring surface conductance.

therefore prepared by sawing to the approximately correct orientation using a diamond wire (0.2 mm diameter) saw or by using orientations sawn by the suppliers. The faces were then microtomed and polished working down to 0.05-pm alumina grit in ethanediol. Microtoming tended to produce a fine mosaic of small pits on the surfaces due to cracking and these could be largely eliminated by moistening the blade with ethanediol. The concentration of divalent impurities in the specimens as determined from the position of the extrinsic/intrinsic “knee” in the conductivity curves was generally about 0.5 ppm. Specimen Electrodes. The electrical conductivity, 6,was measured using a number of electrode systems shown in Figure 1,the basic configuration being that of the standard parallel plate capacitor with and without guard rings. Specimens were fresh cleaved to typical dimensions of 10 mm X 10 mm X 3.5 mm. These were plated over the whole of their large surfaces by careful painting using GC silver conducting print No. 21-2 (Hydrometals, Rockford,’Ill.) and were attached to the electrode leads by platinum wires with a dab of silver paint. The guard electrode was painted as a fine line along the middle of the smaller faces as shown in Figure la. Corrections, reported e l s e ~ h e r efor , ~ field ~ fringing at the edges of specimens were included. Measurements of surface conduction alone were made using a silver print earth ring painted concentrically around a silver print disk electrode on the crystal surface as shown in Figure IC. Inserted Platinum Wire Electrodes. While accurate measurements of 6 may be effected using the parallel plate system, a number of problems became apparent when operating within a degree or so of T,: (i) differential thermal analysis required the thermocouple to be inserted in the specimen itself; (ii) evaporation and melting cause the geometrical factor to decrease with time; (iii) a more effective means of blocking surface conduction was required; and (iv) the conductance rose above the working limits of the conductance bridges. The most appropriate solution to these problems we were able to develop was to use platinum wire electrodes inserted at right angles into the crystals, with a guard electrode fixed around the specimen edges as shown in Figure lb. The 0.3-mm diameter electrodes were inserted into 10-mm cube specimens by passing a current through the wires and allowing them to sink slowly into the specimen by melting a very localized region. The wires needed to be supported 2-3 mm beyond the edges of the specimen

The Journal of Physical Chemistry, Vol. 82, No. 11, 1978 1279

-

and were held under 20 g weight tension so as to prevent slight buckling of the wire when heating. The whole procedure is carried out in an inert atmosphere of He. The thermocouple wires and junction may be inserted into the crystal using the same technique provided the junction bead is small, preferably no larger than the wire diameter. The result is that for NaC1, NaBr, and KC1 one can regularly insert wires which are bubble-free and have only a very thin sheath of crystal around the leading edge which has been melted and is therefore probably polycrystalline. Photographs obtained from the optical microscope suggest this sheath is less than 5 pm in thickness. After an experiment at high temperature near T,, the insertion track of the wire was no longer distinguishable on the side of the crystal suggesting that a substantial amount of grain growth had taken place in the polycrystalline region. Two platinum wires were thus inserted perpendicular to each other from opposite faces to a separation of 2.0-2.5 mm a little below the center of the crystal and the thermocouple was inserted above as shown in Figure Ib. In this way, the conduction was confined to the region near the center of the wires where they cross and was therefore unaffected by the presence of the thermocouple and by loss of crystal due to vaporization and melting. The absolute value of conductance was also lower than for the parallel plate system and the path for surface conduction was longer. In addition a silver print guard electrode was painted as shown in Figure l b on the four vertical edges and as a cross on the top and bottom sides so that the two electrodes were electrically isolated via the surface path. As a check that the inserted electrode technique gave valid results we prepared a specimen with parallel wires inserted 3 mm apart and painted silver print guard rings around each end of one wire. The electrostatics of this electrode system are readily solvable and it can be shownm that for wires with a finite length G = onA/ln { [(l + ( 2 D / X ) 2 ) ” 2 - 1]X2/Dd} (3) where u is the electrical conductivity of the specimen, X is the length of wire in the crystal, D is the separation of the two wires, d is their diameter, and G is the specimen conductance. Values of u thus obtained are compared in Figure 2 with values obtained by the conventional parallel plate system for a specimen annealed overnight at 975 K. On first heating, typical of all inserted electrode specimens, the conductivity of the parallel wire specimen at low temperatures has a negligible surface contribution which however increases markedly above the conductivity “knee” until it reaches and remains at an approximately constant multiple (- 2.3) of the bulk conductivity. The measured conductivity is less by a factor of 4.3 than the expected conductivity and is increased only a little by prolonged annealing at high temperature. It is not until the temperature is raised just into the anomalous premelting region that agreement is obtained and this remains after subsequent entries into the premelting region. The squares in Figure 2 show a cooling curve after the first entry and the agreement with the parallel plate bulk conductance fully justifies the use of inserted wires. The annealing in the premelting region is presumed to be due to the escape of bubbles from the electrode wires. Experimental Equipment. All specimens were mounted in a stainless steel rig which was baffled at intervals to reduce convective flow within the furnace and thus assist in eliminating temperature gradients. In an effort to reduce specimen vaporization, the specimen was enclosed in a fused quartz chamber and the furnace system was evacuated and filled with an inert gas. Leads to the

1280

The Journal of Physical Chemistty, Vol. 82, No. 1 I, 1978

T / “c 500

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Flgure 2. Arrhenius plot of the ionic conductivity of NaCl specimens: (0)well-annealed parallel plate specimen with guard ring and fringing correction; (solid line) first heating of a speclmen with parallel wlre electrodes and a guard ring. The upper solid line is allowlng surface conduction, the lower is suppresslng surface conductlon. On entering the premeltlng region and cooling the conductance (0) comes into agreement with that obtained wlth the standard system.

specimen were passed down eight alumina tubes into the specimen chamber, these leads comprising two platinum and one platinum-13% rhodium thermopure Johnson and Mathey thermocouple leads and five high-purity silver wires. This allowed the use of one absolute and one differential thermocouple and the silver leads provided for a number of simultaneous guarded conductance measurements. The thermocouples were calibrated against the melting points of NaCl and KCl agreeing to within 1.0 K of the values reported in NBS thermochemical tables.31 NBS thermocouple reference t a b l e ~ 3based ~ on the International Practical Temperature Scale of 1968 were used to calculate temperatures from the thermocouple voltages. The specimen platform was supported by a slender 1-mm diameter rod in order to ensure heat transfer to the specimen was radiative rather than conductive via the platform and its support. This was in fact demonstrated by the absence of preferential melting at the base of the crystal. The conductance rig was suspended down a furnace tube which had a working temperature range of 300-1250 K and may be pumped down to Pa using an oil diffusion pump or up to 3 X lo5 Pa (3 atm). The temperature gradient was adjusted to be a minimum in the region of the specimen at the appropriate melting point to be studied and under static conditions the gradient was measured to be usually less than 0.01 K/mm. Short-term temperature control was accurate to within 0.01 K. Electrical conductivity was measured using a Wayne-Kerr B331 autobalance conductance/capacitance bridge, although a bank of simple potential divider circuits was used for the simultaneous measurement of a number of con-

J. L. Tallon, W. H. Robinson, and

s. I.

Smedley

ductances on different specimen surfaces. The potential divider circuit comprised of an audiofrequency signal generator connected over a standard resistance and the specimen impedance in series. The source voltage and the “in-phase” and “out-of-phase” components of the specimen voltage were measured using ac voltmeters and a phase sensitive detector and from these voltages the specimen conductance and capacitance could be calculated. Where guarded measurements were required the specimen guard electrode was held at precisely the same voltage as the “live” electrode by using a voltage follower, power boosted to cope with the high specimen conductance close to T,. Most measurements were performed at a frequency of 1592 Hz. All voltages were continuously recorded on a Rikadenki KA-61 six-pen recorder and all channels could be “pipped” to mark temperature readings from the potentiometer. Experimental Procedure. The general procedure for an experimental run was to raise the temperature from room temperature at a rate of 100 K/h under a vacuum of 3 X Pa to 600 K then leave overnight under vacuum to remove all volatiles, particularly water and organic materials in the silver print. Then, to minimize sublimation at high temperature, a high-purity inert gas (usually He, although sometimes Ar or N2)was introduced to a pressure of 8 X lo4 Pa (0.8 atm) and the temperature was raised at a rate of 100 K/h to 50 K below the experimentation range and usually, although not always, held for an anneal of -6 h before experiments commenced. The premelting experiments were carried out by approaching the melting point a t a constant furnace heating rate of 50 K/h and measuring the specimen temperature and conductivity, alternately allowing surface conduction, then suppressing surface conduction. In the conductivity experiments, when the temperature was within 0.25 K of the melting point, the temperature was lowered rapidly back to -10 K below T,, then raised again and the process repeated. When differential thermometry alone was performed the specimen was heated right to T,. T, was measured as the temperature, when, at a constant furnace heating rate, the specimen temperature did not detectably increase in 2 min or more, i.e., the specimen temperature increased by less than 0.04 K, if at all, in an excess of 2 min. This temperature is the level of the heating curve plateau shown, e.g., in Figures 3 and 4.

111. Experimental Results Changes in Heat Capacity. The temperature increase with time is shown in Figure 3 for an NaCl crystal with an inserted thermocouple when the furnace temperature is raised at a constant rate of 50 K/h. Below 1065 K the temperature is quite linear with time but evidently beginning at 1068.7 K an increasing rate of heat absorption occurs which results in the specimen temperature lagging further and further behind the chamber temperature which is denoted by the straight line above the curve for 50 K/h. This means that the apparent specific heat in this region is rapidly increasing. The effect of increasing the heating rate is such that the premelting region appears to be narrowed and the height of the plateau slightly raised for faster heating rates. The melting temperature is 1073.96 K for heating rates of 100 and 50 K/h, while for 300 K/h it is 1074.06 K. This effect is not due to superheating of the specimen interior since the thermocouple wires would nucleate melting. Rather it is likely that some melting occurs around the thermocouple wires and the melt there rises a little above T , for the fast heating rates due to heat conduction along the wires.

The Journal of Physical Chemistty, Vol. 82, No. 11, 1978 1281


TABLE 11: Melting Points of Alkali Halides Obtained in This Work, as Reported in JANAF Thermochemical Tables: and as Reported Elsewhere Crvstal LiF NaCl NaBr KC1 3bsd T,/K Previously reported T,/K

a

Reference 31.

1118.3 i 0.1

1074.0 f 0.1

1121.3a (1120.5) 1118.2b

Reference 43.

1073.8a (1073.1)

Reference 44.

1074

1017.2k 0.1

1044.15 t 0.1

1020a (1019.5) 1013.5c

1044a (1043.4) 1044.4"

Reference 45.

Tn

800 1072 798

1070

Y

5,

7962

1068

794 1066

1036

792 0

200

600

400

11

762

800

t/s Flgure 3. Specimen temperature as a function of time for a constant furnace heating rate of 50 K/h for a 1 cm cube NaCl specimen. The straight solid line is the temperature of the specimen chamber.

760

m 2

0

In order to check that there was no substantial temperature gradient over the specimen such that the surface encountered the normal melting temperature before the interior we mounted a differential thermocouple in another specimen, with one junction in the middle of the interior and the other junction half protruding from a face. This revealed a temperature difference of only 0.08 K between surface and interior up to 0.1 K below T,. Thereafter the temperature differential rose rapidly. Since the premelting range is greater than 5 K the effect cannot arise from temperature gradients. The possible effect of specimen contamination by ambient gas and metal vapor from the specimen rig and furnace was investigated by raising a similar NaCl specimen under a vacuum of 2 X lo-' Pa from 970 to 1050 K at 300 K/h, then to the melting point at 100 K/h. The anomalous heat absorption was still present and although the data obtained were irregular, the smoothed curve was still very similar to that shown in Figure 3 for an ambient helium pressure of 8 X lo4Pa. Due to the heat absorption from the greater vaporization rate the temperature differential AT between the specimen and the chamber was larger (-10 K) under vacuum. The persistence of the premelting behavior in vacuo suggests that its cause is not the presence of ambient gas or metal vapor. In a number of experiments we heated the furnace at a rate of 300 K/h through the melting point until the entire specimen had melted. The heating curve for such a KC1 specimen is shown in Figure 4. Once the specimen temperature reached T,,, it remained constant (f0.04 K) during melting then, invariably, as the last portion of the specimen melted the temperature dropped by -0.18 K,

xx)

400

600

t /s Figure 4. Heating curve for KCI at 300 Klh. A drop of 0.18 K occurs as the last of the specimen melts.

even though the temperature of the specimen chamber was at that point about 24 K above that of the specimen. When melting was complete the temperature rose rapidly. The explanation of this effect appears to be in the small lowering of the melting point by the ambient gas. It is shown elsewhere33that the solubility of helium in NaCI. or KC1 melts is such that the depression of melting point i s up to 0.2 K. Consequently, while the melting point in the specimen interior adjacent to the thermocouple is unchanged due to isolation from the ambient gas, the melting point of the specimen exterior in contact with the gas will be lower by up to 0.2 K. In the course of melting this lower temperature region progresses closer to the thermocouple and eventually reaches it, resulting in the observed decrease in temperature of 0.18 K. Melting Temperatures. The heat absorption was studied in a number of crystals with a thermocouple, only, inserted. Lithium fluoride was a problem in that the melting point was just too high to successfully insert the thermocouple by the means described in section I1 and we eventually drilled a fine hole through a specimen to accommodate the thermocouple. The melting points for the four alkali halides studied, obtained from the levels of the plateau in the heating curves, are given in Table I1 and compared first with the values reported in the 1971 NBS Thermochemical Tables.31 The errors quoted are the random errors observed rather than absolute errors. Since the reported values were measured prior to the intro-

1282


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io3T-YK-' Flgure 5. Arrhenius plot of the conductance of the same specimen described in Figure 3: (0)first rise suppresslng surface conduction; (0)a typical subsequent rise suppressing surface conduction; (A)a typical subsequent rise allowing surface conduction. The rise in surface conduction coincides with the commencement of the heat absorption shown in Figure 3.

duction of the 1968 International Practical Temperature Scale (IPTS 68) they should be reduced by the appropriate amount to compare with our values. The corrected values are given in brackets. Underneath these are other measured values (corrected to the IPTS 68 scale) which show that our values are reasonable. Absolute errors are at least of the order of 1 K. Electrical Conductivity. We have, as yet, to explain the premelting excess heat absorption and an important clue is to be found in the measurement of electrical conductance. The conductance of the same specimen described in Figure 3 is shown in Figure 5 for a heating rate of 50 K/h. The bulk conductance for the first rise is denoted by circles and typical of many experiments is irregular and lower than on subsequent entries. This is presumably due to the presence of bubbles on the electrodes which disappeared with annealing in the premelting region. The triangles show the subsequent conduction when the voltage follower was disconnected from the guard electrode, that is, when surface conduction was permitted. Interestingly, the premelting rise in conductivity commenced at the same temperature as the excess heat absorption. On the other hand, the squares show a subsequent rise with the guard connected, that is, surface conduction was suppressed. In this case, no premelting was evident up to within half a degree of the melting point and the small rise which did occur there was largely attributable to our inability to completely suppress surface conduction. The premelting electrical conductivity is therefore due to a rapid rise in surface conductance. Moreover, it seems reasonable to suppose that since the excess heat absorption and the sudden rise in surface conductance appear simultaneously at the same temperature, that the heat absorption is also associated with the same phenomenon occurring at the surface, and that no premelting anomalies occur within the crystal bulk at least to within 0.5 K of T,.

J.

L. Tallon, W. H. Robinson, and S. I. Smedley

The substantial contribution of surface conductance to the apparent bulk conductance, even at temperatures below the premelting region, is often overlooked in measurements of the electrical conductivity of alkali halides and we discuss this elsewhere.29 In order to investigate the surface conductance alone the concentric ring electrode configuration sketched in Figure IC was used in a number of experiments specifically aimed at investigating the deformation and orientation dependence. The feature of this electrode configuration was that the premelting rise in conductivity tended to occur at temperatures sometimes up to 10 K lower than those usually resulting with the crossed wires configuration or the conventional electrodes. We presume this to be due to the fact that the ring electrodes have a much shorter surface path than have the other two electrode systems and consequently have a greater likelihood that there is a connecting path of surface defects such as scratches or cleavage steps between the two electrodes. This would inevitably result in the earlier occurrence of the premelting conductivity. Because of this feature one has to be more cautious in interpreting results obtained using the ring electrodes and certainly the region on which the electrodes were laid had to be carefully examined to ensure there were no visible defects there. Deformation Dependence. Allnatt and Sime6reported that there was no discernible effect on the premelting rise in conductivity due to a 5% compression of their specimens. However we note that for one deformed specimen the first rise was half as steep as the second rise which suggests there may in fact be a deformation effect but by the end of the first rise the dislocation arrays have annealed out. For this reason, simple compression is not an appropriate deformation to use and what is more suitable is to use a deformation which introduces stable arrays of dislocations which must remain present, even after annealing, to maintain the deformed geometry of the crystal. To do this we bent a 40 mm X 3 mm X 3 mm (100) NaCl single crystal very slowly at a temperature of 800 K in a three-point bending r i p so as to generate a single kink in the specimen with inner radius -15 mm and outer radius -19 mm. The excess of dislocations of one sign required to accommodate a bend of radius, r, has a density nd given by35 lld

= (br)-'

(4)

where b is the Burgers' vector of the dislocation, in this case a / d 2 where a is the cation-cation lattice parameter. This gives a dislocation density of 1.5 X 10" lines/m2. The straight ends of the specimen were cleaved off, leaving a specimen length 15 mm, and ring electrodes were placed at the kink on the convex surface and on the surface normal to the kink axis. The latter surface is the one cut by the dislocations which accommodate the bend. Another pair of ring electrodes was placed on a surface well away from the kink where there was no visible deformation. The three surface conductances, normalized at 1013 K, are shown in Figure 6 and these reveal a very definite deformation dependence. The surface cut by the dislocations shows a rise in surface conductivity at 1036 K, well below the melting point, the convex surface at 1044 K, and the deformation-free surface at 1054 K. In the last case, electrode contact was poor and the irregularity just before the premelting rise appeared intermittently at lower temperatures throughout the approach to melting. Orientation Dependence. The variation with surface orientation of the temperature, T,,, of the premelting rise in surface conductivity was examined for a number of KC1 specimens. Values of Tpmfor (100) and (111)surfaces in N

Condkmtvily and Heat Capacity In Some

T.

rhe Journal of mphr Chemistry, vol. 82. NO. I I. 1978 1203

Alkall Halides

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I d T Y K-’ m

aAnhr*rrplotof~auface~ofdlfaent~

of a bent NaCl single crystal: (0) suface normal to the axis of tlm bend: ( 0 )convex surface; (A)surtace In an undefwmedregbn.

Surface

760

Y 740

1 Fbum 0. Thermal facetting of an approximately (1 10) surface. The

bracket denotes

1 0

0

1

2

3

4

5

a d a c e Packing Densty x a2 Flpm 7.

Temperahwe of hammabus rlse h surface conductMty

fwaKCIspechenon(l00).(110),and(lll)svtaces: (0)vacuum Pa and (0) helium at 8 X lo‘ Pa. of 2 X

helium and under a vacuum of 2 X lo-* Pa are plotted in Figure 7 against the surface packing density. A definite order of Tpmis evident and this order is the same as is predicted for the surface melting temperature Tarn. However, as the (110) and (111)faces were cut and polished it is impossible to separate out the effect of the surface deformation, although much annealing of the surface will have taken place and many surface layers would have been stripped off by sublimation. Moreover, as we shall see in the next section all surfaces other than (100) tend to facet to (100) steps and ledges and the lower value of T,, on these surfaces may he due to premature melting along the edges of the steps. Surface Features. The physical appearance of the specimen surfaces was examined after experimentation by scanning electron microscopy and, as shown in Figure 8, the premelting surface features are distinct from those

20 p m .

which occur just below premelting and those which occur at T,. In the former case shown in Figure 8a there are many small, circular thermal etch pits due to preferential sublimation from dislocations cutting the surface, but apart from these and a few cleavage steps the surfaces are quite flat and featureless. The surface of an NaCl crystal which had briefly entered 0.5 K within the premelting region is shown in Figure 8b and here there are even more thermal etch pits evident, their rims are well rounded and the surface has a “puddled” appearance. On the other hand when the surface shown in Figure & encountered the bulk melting point, the etch pits disappear and the surface acquires long, smoothly rounded ledges and flow patterns. Clearly, then, the premelting su:face is distinct from the melting surface in that in the former, the single crystalline defects extend right to the surface, while when the surface has encountered the hulk melting point, crystalline defects such a~ dislocations become “buried” beneath the isotropic melt layer. The premelting surface features suggest that either melting has taken place on the surface to a depth in excess of 1 pm or excessive sublimation has occurred. A platinum wire placed on the surface caused two ridges to climb up round the base of the wire in capilliary fashion and again this suggests either the presence of surface melt, a high surface transport mobility, or a sublimation and redeposition process.

1284

The Journal of Physical Chemistry, Vol. 82, No. 1 I, 1978

Another important surface feature is the tendency of surfaces other than (100) to facet to (100) faces. Figure 9 shows a scanning electron micrograph of an approximately (110) surface of KCl which has been facetted to form an array of long (100) steps by sublimation at temperatures within -50 K of T,.

IV. Discussion We now attempt to explain the various experimental results we have presented. Our principal conclusion is that there is no bulk premelting rise in conductivity up to within at least 0.5 K of the melting point, and while we are unable to distinguish between bulk and surface heat absorption, it seems likely that the excess heat absorption also is at the Jurface only. We proceed therefore under the assumption that no premelting of any kind is occurring within the crystal bulk. Thus, no bulk theory of premelting finds application to the alkali halides we have studied. These include, for example, the possibility of a diffuse transition involving the disordering of the cation sublattice,33or Robinson’s6 analysis of the premelting conductivity reported by Allnatt and Sime in terms of pipe diffusion along thermally formed dislocations. Neither, it appears, can the results be accounted for in terms of the melting of substantial portions of the specimen surface at temperatures below the bulk intrinsic melting point. Surface melting due to the intrinsic excess free energy of a surface as proposed by Tammann and Stranski may be able to explain the observed sequence of melting of low index surfaces, but it does not explain the magnitude of the premelting electrical conductivity nor of the excess heat absorption. Since periodicity in the melt radial distribution function is fully damped at approximately four cation-anion spacings the surface layer of ions can have no influence on the s-1 interface if it is more than four layers below the surface. It might be expected, therefore, that the surface quasimelt immediately below the melting point occupies no more than four ion layers only, whereas the heat absorption occurring within the premelting region is consistent with surface melting to a depth of 1-100 pm. The same quantitative difficulty applies to the premature melting at the edges and corners of steps on the crystal and in the region where a dislocation cuts an external surface.33 For the calculated volume of crystal that would melt at approximately 0.5 K below T , in these highly strained regions is many orders of magnitude smaller than is consistent with our observations. The effect of the impurity content of the crystals and of the ambient gas is also too small to account for our results. The concentration of divalent impurities is approximately 0.5 ppm and typical analyses by the specimen suppliers suggest that other trace impurities are present in proportions of 20 ppm or less. Some metal vapor from the stainless steel may contaminate the specimen surfaces, however, Allnatt and Sime observe the same premelting conductivity behavior with a rig constructed solely from fused quartz and platinum. Moreover, the effect of metal vapor and ambient gas may be discounted on the basis of the following calculations. We shall see that at an ambient helium pressure of 8 X lo4 Pa our NaCl specimens have a sublimation flux just below the premelting region of 0.85 mg cmT2min-l which means that every second about 260 layers of crystal are stripped off while the equivalent of as much as 2.6 X lo8 layers of helium impinge on the crystal. However, the persistance of the premelting effect Pa appears to discount the under a vacuum of 2 X importance of the gas, for at this pressure the flux of helium is at most 64 layers per second and would in fact be less due to the helium in the specimen chamber being

J. L. Tallon, W. H. Robinson, and S.I. Smedley

displaced out by the specimen vapor. On the other hand, the flux from the specimen in vacuo has risen to 1200 layers per second so that under these conditions the specimen surface will be kept clean by the vaporization. Thus neither intrinsic nor extrinsic surface melting can explain our observed premelting effects and we deduce therefore that both surface melting and vaporization (rather than sublimation) combine to cause the effects. Facetting and Saturation of Sublimation. Sublimation and vaporization studies by Ewing and Stern16have been briefly referred to in the Introduction. They found that the sublimation of NaC1, KBr, and CsI began to saturate at about 100 K below T , and was nearly fully saturated just below T,. Sublimation is understood to be a two step mechanism: the first being an activation step from the crystal to an adsorbed surface state, the second a desorption step to the vapor. We suggest that the saturation of the flux arises from the facetting of the (100) faces. At lower temperatures the desorption step is rate controlling, however, at higher temperatures where the maximum flux is as large as 50 mg cm-2 m i d in vacuo,16 the activation step for singular surfaces will almost certainly become rate controlling and the flux will increase less with further temperature increase. The same applies to vaporization from vicinal surfaces and, in these, vaporization will be confined to the steps on ledges. Thus for singular and vicinal surfaces at high temperatures the vaporization sites are not formed fast enough to maintain the desorption rate and the flux is therefore less than what it might have been. However, when intrinsic surface melting commences near T,, the newly formed quasiliquid surface introduces a large number of further vaporization sites and a greater vaporization rate is possible. This disordering (which occurs particularly at corners, edges, and the points of exit of dislocations at surfaces) is very shallow but is sufficient to maintain the high vaporization flux and as more and more layers are stripped off the same depth of surface disorder is maintained and enhanced vaporization may continue until no further crystal remains. In this way the very substantial heat absorptions we have observed may be achieved via the enthalpy of vaporization. Use of the term “surface melting” suggests a first-order transition which would imply a discontinuous increase in vaporization flux associated with the instantaneous increase in vaporization sites. The fact that the heat absorption and hence the vaporization rate increases continuously from 6 K below T, is simply due to the “surface melting” being a higher order continuous transition as shown by Burton, Cabrera, and Frank.25 Our intepretation of Ewing and Stern’s data can be used to explain the excess heat absorption shown by our samples near T,. When the furnace temperature is increased at a constant rate below the premelting region, the vaporization flux is constant and the rate of heat absorption is also constant. This reveals itself (over a small temperature range of 10-20 K) as a constant temperature differential between the specimen chamber and the specimen as shown in Figure 3. When surface disordering commences the vaporization rate begins to climb and the specimen temperature lags increasingly further behind the chamber temperature. Surfaces which are nonsingular in the neighborhood of the melting point are so atomically rough that vaporization continues freely and thus in the case of silver, which is nonfacetting in vacuo, there is no anomalous vaporization.16 There is, of course, a problem with LiF in that no vaporization anomaly was observed by Ewing and Stern, yet we observed a distinct premelting effect. One likely ex-


planation arises. According to Table I LiF is borderline but may have nonsingular (100) surfaces. It may be that under vacuum (as in Ewing and Stern’s experiments) it is nonfacetting and in gas it is facetting. This is certainly so in the case of many metals36which thermally facet in the presence of absorbed gases but, in general, do not in the absence of an absorbate since for them CY < 2. On the other hand, MgO which has the same structure as the rock salt type alkali halides has been found to facet under vacuum on (100) planes3’ and this is because the value of CY at the facetting temperature of 1400 K is as large as 4.43. As a test of our hypothesis we had searched for a premelting heat absorption in a crystal with (1101, (1111, and (112) faces and with no (100) faces exposed. None of these faces according to Table I are facetting and consequently the crystal should evaporate freely and experience no premelting heat absorption. In fact it had been observed in our experiments on surface conductivity of higher index faces that these evaporated far more quickly than (100) faces. However, as we have noted the excess heat absorption for these crystals still occurs within 5-6 K of the melting point, and there is no trace of excess heat absorption at the surface melting transition which occurs up to 30 K below T, for these higher index surfaces. This, doubtless, arises from the fact that the (110), (lll),and (112) faces at high temperatures do not long remain such but quickly transform by vaporization to arrays of obliquely oriented (100) steps and ledges as shown in Figure 9, so that while the vaporization rate is higher than for a single cleaved (100) surface the facetting on the ledges causes the vaporization to remain saturated until the (100) surface melting temperature 6 K below T, is reached. A more critical test would be to look for premelting effects in LiBr, LiI, or RbI which according to Table I should have no facetting faces near T, and therefore, according to our hypothesis, no sublimation saturation and no premelting rise in vaporization rate. It is perhaps also significant to note here that, in the extremely careful demonstration of the lack of premelting phenomena in gallium by Wend and Mair,38gallium is characterized by a very high boiling point relative to its melting point (T, = 302.91 K, T b 1870 K) and consequently has a low vapor pressure at its melting point. Any changes in vaporization rate would therefore have an insignificant effect on its apparent heat capacity. Calculation of the Vaporization Flux. The vaporization flux may be calculated from the difference AT in temperature between the specimen and the specimen chamber for a constant heating rate. The heat balance between the radiant arrival of heat, heat capacity, and the heat of vaporization results in the following equation U e o , T3AT = mC,(dT/dt) + AAH,J (5) The term on the left-hand side is the Stefan-Boltzmann law, expanded to first order in AT, for the rate of arrival of radiant energy. A is the specimen surface area, e the emissivity, and BB the Stefan-Boltzmann constant. The right-hand side terms are first the heat absorption via the specific heat, C,, of the solid, where m is the specimen mass, and secondly via the vaporization. AHv is the enthalpy of vaporization and J the vaporization flux. We assume the emissivity to be unity, i.e., the specimen is a black body receptor, since any transmitted radiation will be reradiated by the walls of the chamber toward the specimen very many times. Using reported values of AHv and high temperature values of Cs,31measurement of AT and dT/dt from heating curves such as that shown in Figure 3 enables the vaporization flux, J , to be calculated. This is shown as an

-


IO.

7

.r

E Y E V

5.0

6

E

\ b

2.0

1.0

0.930

0.932

0.934

0.936

10~r-Y K-l Figure I O . Arrhenius plot of the calculated vaporization flux Jfor NaCl as determined from heat absorption near .T, The dashed line shows the gradient obtained by Ewing and Stern for free vaporization in vacuo: (0)50 Klh; (m) another specimen at 50 Klh; (A)at 100 K/h; (0)at 300 Klh; and (V)another specimen at 57 Klh under vacuum of 2 X IO-* Pa.

Arrhenius plot in Figure 10 for a number of NaCl specimens with different heating rates in helium at 8 X lo4Pa, Pa. and under vacuum of 2 X The vaporization flux of 0.85 mg cm-2 min-l just below the premelting region for a specimen in helium is sufficient to maintain the specimen 2.1 K below the temperature of the specimen chamber under static conditions, Le., when the temperature is not being increased. This contrasts with the value in 52 mg cm-2 m i d measured directly by Ewing and SternT6for NaCl in vacuo just below the melting point. The difference of course is due to the confined space about our specimen and the presence of ambient gas, both of which reduce J. The static value of AT for the NaCl specimen under vacuum of 2 X P a was about 10 K giving a higher static vaporization rate of 4.3 mg cm-2 rnin-l. The dashed line shows the slope of the vaporization curve above T, obtained by Ewing and Stern in vacuo and this matches the asymptotic slopes of our curves quite satisfactorily. This serves to illustrate that our estimated flux obtained over a narrow temperature range is not inconsistent with the relative changes in flux they observed at higher temperatures. Premelting Surface Features. The “puddling” shown in Figure 8b which occurs on the crystal surface when the crystal enters the premelting region, and the capilliary effect about the platinum wire placed on a specimen surface, both reveal a very high surface mobility. This is probably achieved by a process of sublimation and redeposition. When a surface is freely subliming there will be a diffuse region above the crystal in which the bond between molecule and crystal is tenuous and consequently a very high surface mobility is possible. This may allow sufficient mass transport for the surface effects described above. Indeed, in view of the presence of the quasimelt layer on the surface there is likely to be a continuous gradation at the surface from true solid to quasiliquid to vapor. Mobilities should be enhanced throughout this region and should increase in magnitude with the pro-

1286


gression outward. At the same time, mass density decreases with the progression so that, at some position intermediate between true solid and true vapor, there will be a region of maximum possible mass transfer. Premelting Electrical Conductivity. Similar arguments also apply to the apparent electrical conductivity. If the premelting rise in conductivity were due to conduction in a layer of surface melt covering the crystal then melt thicknesses of the order 1-100 pm are necessary to explain the magnitude of the surface conduction. However, with an intrinsic melt thickness of the order of 1.2 nm (4ionic spacings), mobilities of the order of lo3times those in bulk melt must be assumed to explain the premelting conductivity. In the diffuse surface region such mobilities may be possible. Indeed, if from the extrinsic/intrinsic “knee” in the conductivity curve up to T, surface conduction by highly mobile surface adatoms produces a significant contribution to the overall specimen conductance, then an even greater effect may be expected when the surface is disordered and rapidly vaporizing. With the progression from true solid through liquid to true vapor, as well as there being a decrease in mass density, the ions become increasingly bound as ion pairs and so are unable to contribute to electrical conduction. Consequently, again there will be some intermediate region between solid and vapor of maximum possible conductivity. Typical measurements of the electrical conductivity of ionic melts are performed in apparatus in which there is no free surface path between the electrodes, and therefore this high mobility effect would not be apparent. Elementary experimentation, however, could readily demonstrate the existence (or nonexistence) of this effect. Deformation Dependence. The effect of deformation on the surface melting temperature as shown in Figure 6 for a kinked specimen suggests that the large density of dislocation cores is sufficient to raise the free energy of the solid and cause premature melting. The energy per unit length of a dislocation comprises an elastic part, U,, and a core part, U,, given, for an edge dislocation, by3’

U = Ue t U, = {b2pu/4n(l- v)} In (Rc/ro)+ b2p(/4n(l - V) (6) where b = a/v’/2 is the Burgers vector of the dislocation, v is Poisson’s ratio, ro the radius of the core, R, the cutoff radius being half the average separation of dislocation cores, and is an experimental constant of the order of unity, which we show elsewhere33to have the value 4 = 0.75 for NaC1. The distributed energy density is therefore nd(Ue + U J , where nd is the dislocation density, and the shift in melting point is A m T = Tmnci(Ue

+

uc)/~sAHm

(7)

Using the estimated value of nd = 1.5 X loll lines/m2 and Hunter and Siegel’s elastic constants for NaCl at Tm9we obtain a very low value of A,T = 2 X lod K. Clearly then, any effect arising from the dislocations introduced by bending must occur at the cores rather than via the average distributed energy density. Two effects are possible at the cores: the cores may melt, even within the crystal bulk, or the region where the dislocation cuts the surface may melt causing a melt dimple much in the same way that a thermal etch pit forms at the exit of a dislocation. These questions are examined elsewhere33and it is shown that below T,, while the core does not melt, a broad shallow melt dimple does appear at the dislocation exit, the radius of which increases as (ArnT)lI2and the volume of which increases as (A,T)-4’3. The radius of this dimple is so small that if the dislocations

J. L. Tallon, W. H. Robinson, and

S.I. Smedley

accommodating the kink were uniformly distributed the dimples would never overlap except at temperatures less than 0.01 K below T,. However deformation usually results in the formation of subgrain boundaries due to dislocations multiplying and gliding along the same glide plane. These subgrain boundaries consist of a very close linear succession of dislocations the separation of which is determined by their elastic repulsion. Along these subgrain boundaries the successive melt dimples will overlap at substantially lower temperatures and thus provide high conductance pathways along the surface. This we believe is the origin of the earlier premelting rise in surface conductivity observed for deformed specimens, although it is beyond the scope of this paper to present a detailed quantitative discussion of this process. Premelting Changes in Elastic Constants. The rapid changes in elastic constants observed close to the melting point which were discussed in the Introduction could have been interpreted in terms of a bulk surface melting. For, depending on whether the resonant frequency of the specimen was greater or less than that of the total ultrasonic composite oscillator, so surface melting might increase or decrease the apparent elastic constant being measured. However, the depth of intrinsic surface melting is so small as to be negligible and we must suppose that the changes in elastic constants near T, are due to deformation. Indeed, these crystals are highly plastic near T,, the results of Hunter and Siegel, Enck, and Slagle and McKinstry are not consistent with each other near T, and the changes there are not reproducible but involve permanent displacement^,^ which strongly suggests the occurrence of plastic flow. L E E D Studies of Surface Melting. Goodman and Somorjai40have investigated the melting of lead, bismuth, and tin using low-energy electron diffraction (LEED) and find that there is no loss of diffraction features until the melting point is encountered thus demonstrating the absence of any premature surface melting. In the case of tin, loss of diffraction features did occur within 6-8 K of the melting point due to an effective surface melting arising from surface contamination (even at ultra-high vacuum pressures of 1.3 X lo+ Pa). This could be eliminated by cleaning the surface by ion bombardment. Surface contamination presumably is a difficulty in this case and not in the case of the alkali halides because tin has a very low vapor pressure near T, ( lo+ Pa) which means that there is little surface cleaning due to sublimation. The apparent absence of surface disordering in these metals presents a difficulty to the ideas we have developed here. However, we observe that Goodman and Somarjai do not detail how, or in fact whether at all, they distinguished between the bulk melting point and the surface melting point. The one case where it is obvious from their results that the former does not exceed the latter is with bismuth which on account of its volume contraction on melting may not exhibit intrinsic surface melting anyway. We have referred to a number of theories of surface melting or surface disordering, in particular the theories of Tarnmann,l8 Stranski,20Burton, Cabrera, and Frank,25 and Jackson.% Goodman and S ~ m o r j ahave i ~ ~ pointed out that premature melting of surfaces is also to be expected on account of the enhanced mean square vibrational displacements of surface atoms. Such enhanced displacements have now been demonstrated for a wide range of crystals and since the Debye temperature is inversely proportional to the root-mean-square displacements, simple application of Lindemann’s melting relationship predicts a reduced melting temperature for surface atoms. N

Conductivity and Heat Capacity in Some Alkali Halldes

A vacancy model discussed by Gurney41 also predicts surface melting below the bulk melting point. Unfortunately, none of these theories give good quantitative values for the surface melting temperatures. We have, elsewhere,33developed a dislocation theory of melting which incorporates premature surface melting and discusses the displacement of the s-1 interface from the surface into the crystal bulk. Many of the quantitative predictions of the theory agree well with the experimental data.

V. Conclusions (i) We have developed a technique for inserting heated platinum electrodes and thermocouples into single crystal alkali halide specimens by allowing the wire to melt a narrow pathway to the crystal interior. This avoids spurious temperature measurements when the specimen is absorbing heat more rapidly than its environment, and by inserting the electrodes at right angles to each other the electrical interaction may be confined to a small region in the crystal interior unaffected by changes in the external geometry of the specimen due to evaporation or melting on the surfaces. (ii) Melting temperatures obtained are as follows: LiF, 1118.3 K; NaC1, 1074.0 K; NaBr, 1017.2 K; and KC1, 1044.15 K. NBS thermocouple tables based on the International Practical Temperature Scale of 1968 were used to convert the thermal voltages to temperatures. These melting temperatures compare with the following values listed in NBS Thermochemical Tables: LiF, 1120.5 K; NaC1,1073.1 K; NaBr, 1019.5 K, and KC1,1043.4 K. Other reported values are listed in Table 11. (iii) Our experiments reveal that there is no premelting rise in the bulk electrical conductivity in LiF, NaC1, NaBr, and KC1 at least to within 0.5 K of the melting point and that previously reported premelting rises in conductivity are due to rapid increases in the surface conductivity. For (100) crystals this premelting rise occurs at -6 K below the melting point and is accompanied by a substantial heat absorption. Higher index surfaces become highly conducting on their surfaces at lower temperatures with (111) lowest, then (110), then (100). For these higher index surfaces the heat absorption does not accompany the rise in surface conductivity but always occurs -6 K below T,. Deformation causes the premelting rise in surface conduction to occur at a lower temperature. Ambient gas at 1atm pressure gives a calculated and observed depression of melting point of about 0.2 K. The surface features in the premelting region are distinct from both those below the premelting region and those at the melting point, and these suggest a very high surface mobility and a high vaporization rate. (iv) We interpret these results in terms of a premature melting of the crystal surfaces to a depth of a few ionic layers due to the intrinsic excess surface free energy. Melting below T, will also occur particularly at corners, edges, and at the points of exit of dislocations at surfaces. With the advent of surface melting the vaporization rate climbs rapidly and this produces a substantial absorption of heat. We suggest that at temperatures below the premelting region vaporization saturates due to facetting of (100) surfaces, then when the surface melts the appearance of many vaporization sites allows the vaporization flux to rise rapidly. The fact that the vaporization flux does not increase discontinuously suggests that the surface melting transition is higher than first order. The oc-


currence of the premelting surface conductivity at temperatures well below T, for deformed specimens appears to be due to surface melt dimples along subgrain boundaries overlapping and thus providing high conductance pathways over the surface.

Note Added in Proof. ‘Broughtonand Woodcock46have performed molecular dynamics computations on a (100) face of a Lennard-Jones crystal and have demonstrated that the outermost surface layers (3-4 layers) melt sequentially at temperatures below the bulk melting point resulting in greatly enhanced diffusivities within these layers. They also show that LEED may be insufficiently sensitive to detect this surface melting. This would explain the retention of LEED surface diffraction features in lead, bismuth, and tin right up to the bulk melting points as reported by Goodman and S ~ m o r j a i . ~ ~ References and Notes (1) A. R. Ubbelohde, “Meltlng and Crystal Structure”, Oxford University Press, Clarendon, 1965. (2) J. L. Tallon, W. H. Robinson, and S. I. Smediey, Nature (London), 288, 337 (1977). (3) J. L. Tallon, W. H. Robinson, and S. I. Smedley, Phil. Mag., 38, 741 (1977). (4) J. L. Tallon, Phil. Mag., to be publlshed. (5) A. R. Allnatt and S. J. Sime, Trans. Faraday Soc., 87, 674 (1971). (6) W. H. Robinson, J . Appl. Phys., 47, 5121 (1976). (7) M. Bizouard and P. Cerisier, C . R. Acad. Sci. Parls, 262, 1 (1966). (8) W. W. Harpur, R. L. Moss, and A. R. Ubbelohde, Proc. R. SOC. London, Ser. A , 232, 196 (1955). (9) L. Hunter and S. Siegei, Phys. Rev., 81, 84 (1942). (10) R. D. Enck, Phys. Rev., 119, 1873 (1960). (1 1) 0.D. Slagle and H. A. McKinstry, J. Appl. Phys., 38, 437 (1967). (12) W. H. Robinsonand H. K. Blrnbaum, J. Appl. Phys., 37,3754 (1966). (13) W. H. Robinson, J. L. Tallon, and P. H. Sutter, Phil. Mag., 38, 1405 (1977). (14) W. H. Robinson and H. K. Birnbaum, to be published. (15) A. Wolfenden and W. H. Robinson, private communlcatlon. (16) C. Ewing and K. Stern, J . Phys. Chem., 79, 2007 (1975). (17) F. A. Lindemann, Phys. Z . , 11, 609 (1910). (18) 0 . Tammann, Z . Phys. Chem., 88, 205 (1910). (19) M. Volmer and 0.Schmidt, Z . Phys. Chem., B , 35, 467 (1937). (20) I. N. Stranski, Naturwlssenschaffen, 28, 425 (1942). (21) C. R. M. Wronski, Brit. J . Appl. Phys., 18, 1731 (1967). (22) D. Turnbull, J . Appl. Phys., 21, 1022 (1950). (23) D. P. Woodruff, “The Solid-Liquid Interface”, Cambridge Unlverslty Press, London, 1973. (24) N. Cabrera, Trans. Faraday Soc., 55, 16 (1959). (25) W. K. Burton, N. Cabrera, and F. C. Frank, Phil. Trans. R . Soc., Ser. A , 243, 299 (1951). (26) K. A. Jackson, “Liquid Metals and Solidification”,ASM, Cleveland, 1958, p 174. (27) G. Grange, R. Landers, and B. Mutattschev, Surf. Sci., 54, 445 (1976). (28) A. Pavlovska and D. Nenow, Surf. Scl., 27, 211 (1971). (29) J. L. Talion, W. H. Robinson, and S. I. Smedley, J. Phys. C : Solid State, 10, L579 (1977). (30) E. Weber, “Electromagnetic Fields”, Vol. 1, Wiley, New York, N.Y., 1950, p 114. (31) D. R. Stull and H. Prophet, Nafl. Stand. Ref. Data Ser., Nafl. Bur. Stand., No. 37 (1971). (32) R. L. Powell et al., NBS Monogr., No. 125 (1974). (33) J. L. Talion, R.D. Thesis, 1976, Vlctorla University, Wellington, New Zealand. (34) L. R. Greenbank, W. H. Robinson, and P. H. Sutter, J . Phys. €3, 949 (1970). (35) J, F. Nye, Acta Met., 1, 153 (1953). (36) J. J. Lander, Prog. Solid State Chem., 1, 26 (1965). (37) V. E. Henrich, Surf. Sci., 57, 385 (1976). (38) H. Wenzi and G. Malr, 2. Phys. B, 21, 95 (1975). (39) J. P. Hirth and J. Lothe, “Theory of Dislocations”, McGraw-Hill, New York, N.Y., 1963, p 78. (40) R. M. W m a n and G. A. Somwjai, J. Chem. phys., 52, 6325 (1970). (41) R. W. Gurney, Proc. Phys. SOC.,02, 639 (1949). (42) R. C. Weast, Ed., “Handbook of Chemistry and Physics”, Chemical Rubber Co., Cleveland, Ohio, 1974. (43) H. Flood, V. Fykse, and S. Umes, Z . flektrochem., 59, 364 (1955). (44) M. Blanc, C. R . Acad. Sci., 248, 570 (1958). (45) J. W. Johnston and M. A. Bredig, J . Phys. Chem., 82, 604 (1958). (46) J. Q. Broughton and L. V. Woodcock, private communlcatlon.

Premelting electrical conductivity and heat capacity in some alkali

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