Appendix A

A.1 Structure Factor S.q/1 and High-Temperature/High-Pressure Neutron Diffraction

We consider a one-component fluid of monatomic particles interacting via cen-trosymmetric forces. The scattering law is formulated for coherently scatteredneutrons with scattering length b, but very analogous expressions apply for X-rayand electron scattering. The following assumptions are made: (1) Multiple scatter-ing shall be neglected. (2) The time a neutron needs to traverse a typical diffusionlength in the fluid is short in comparison with the characteristic diffusion time ofparticles (static scattering approximation). (3) Scattering is elastic, i.e. the incomingand scattered neutrons have the same energy, „!i D „!s or „ki D „ks, where k isthe wave vector. So, only the direction of the wave vector can be changed by elasticscattering by q with q D ki � ks and q D 4�=� sin ‚, where � is the wavelengthand 2‚ is the scattering angle; see also Fig A.1 for the scattering geometry.

Fig. A.1 Sketch of scattering experiment and scattering geometry

1 In the literature, both Q and q are used to describe the wave vector change.

W. Freyland, Coulombic Fluids, Springer Series in Solid-State Sciences 168,DOI 10.1007/978-3-642-17779-8, c� Springer-Verlag Berlin Heidelberg 2011

161

162 A Appendix

The amplitude of radiation scattered through the angle 2‚ by particles withposition vectors r i is given by

A.q/ D b=R

NX

i

exp.�iqr i /; (A.1)

where b is the scattering length, R is the distance of sample centre from detector,and q r i is the phase shift due to scattering. The intensity of scattered radiation thenis as follows:

I.q/ D hjA.q/j2i D b2=R2N

*1 C N �1

NX

i¤j

NXexp.�iqrij /

+; (A.2)

with r ij D r i � rj . The expression in the brackets h i is the structure factor S.q/,where the brackets indicate that a thermal or ensemble average has to be taken.This is calculated with the aid of the pair distribution function g.r ij/, which forcentrosymmetric interactions depends only on the magnitude of r ij D r . Thus, oneobtains for S.q/:

S.q/ D0

@1 C N �1

NX

i¤j

NXV �2

ZZg.r ij / exp.�iqr ij /

1

A dr i drj

D�

1 C N

V

�Z.g.r/ � 1/ exp.�iqr/dr C

Zexp.�iqr/dr

��(A.3)

where the following relation has been used:

ZZ: : : dr i drj D V

Z: : : dr: (A.4)

In the second equation of (A.3), the last term is zero for q ¤ 0. So it makesno contribution to the radiation scattered by the atoms of the fluid. Finally, forcentrosymmetric interactions S.q/ depends only on the magnitude q and withq r D q r cos ‚ and jdrj D sin ‚ d‚ d � r2 dr; S.q/ in (A.3) becomes

S.q/ D 1 C 4�N

V

Z 1

0

sin.qr/=.qr/.g.r/ � 1/r2dr: (A.5)

Taking the Fourier transform, the corresponding expression for g.r/ is as follows:

g.r/ D 1 C .2�2/�1 V

N

Z 1

0

sin.qr/=.qr/.S.q/ � 1/q2dq: (A.6)

A.1 Structure Factor S.q/ and High-Temperature/High-Pressure Neutron Diffraction 163

Fig. A.2 (a) High-pressure neutron diffraction autoclave: (1) Ti0:67Zr0:33 zero alloy neutron win-dow, (2) stainless steel cylinders, (3) high-pressure flanges, (4) water cooling, (5) Cd shields, (6)incoming neutron beam; (b) sample cell, heaters, and thermal insulation inside the autovlave: (1)W heater, (2) V heat shields, (3) additional Mo resistance heater, (4) ZrO2 thermal insulation, (5)measurement compartment of sample cell, (6) cell capillary dipping into liquid reservoir, and (7)thermocouples. See also [A.1]

High-temperature–high-pressure neutron scattering measurements of fluids requirespecial constructions of the sample cell and its surroundings. An arrangement, withwhich for the first time temperatures up to 2,000 K and pressures up to 300 bar havebeen achieved [A.1], is shown in Fig A.2. The central part of the high-pressure ves-sel consists of a cylinder with a thin wall of 5 mm thickness made from a Ti0:67Zr0:33

alloy. This material is a purely incoherent neutron scatterer. The neutron windowcan withstand a maximum internal pressure of 400 bar when properly cooled. Onboth sides of this window, high-pressure stainless steel cylinders are connected byappropriate seals and are closed at both ends by high-pressure flanges. These con-tain several electrical feedthroughs for thermocouples and resistance heaters and aconnection for a high-pressure Ar gas pipe. The sample cell together with the heat-ing elements and thermal insulations as mounted inside the high-pressure vessel isshown in Fig A.2b. The upper end of the sample cell – a thin wall Mo or a singlecrystal sapphire tubing closed at the top end – is surrounded by a cylindrical resis-tance heater made from a 50 �m W foil. The temperature profile along the samplevolume is controlled by additional heating elements wound directly on the capillaryunderneath of the measurement compartment. The advantage of the sapphire cell isthat it can be oriented in the neutron beam in such a way that the sapphire Bragg

164 A Appendix

reflections lie outside the scattering plane of the sample. In the height of the neutronbeam, thin foil vanadium heat shields reduce heat loss due to radiation and con-vection. So, in the case of the sapphire cell, only scattering of the thin wall W foilinterferes with scattering of the fluid sample. At the bottom end, the cell capillarydips into a liquid reservoir. In this way, the background scattering and absorption ofthe empty cell plus surroundings can be measured first and then – without changingthe alignment in the beam – the cell can be filled with the liquid sample by applying asmall argon pressure inside the autoclave and a sample scattering run can be started.

A.2 Optical and ESR Spectroscopy with In SituCoulometric Titration

In some spectroscopic investigations, small sample volumes of a few cubic milli-meters have to be handled, for instance in optical studies of ultrathin films or inESR spectroscopy. If, in addition, in situ variation of composition at high temper-ature is required, this is not an easy task. A solution of this problem is the use ofan electrochemical method for the in situ concentration variation and to combinethe respective sample cell with an electrochemical cell. However, at high temper-atures of the order of 1,000 K, which are necessary for the doping of molten saltsor liquid alloys, the choice of suitable electrochemical cells is rather limited. Here,we describe an EMF cell that has been successfully tested in optical, conductivity,and ESR studies up to 1,000 K and which enabled in situ variation of metal molefraction in molten salts in a range 10�5 � x � 10�1. The technique applied is basedon the Coulometric titration method [A.2, A.3].

The EMF cell is composed of a Ca0:1Sn0:9 reference and counter electrode, asingle crystal CaF2 solid electrolyte, and a working electrode consisting of a soliddouble salt CaF2–MF (e.g. M D Na, K, or Cs) and the MX melt in a separate com-partment of the optical or ESR cell. In order to ensure the stability of the referenceelectrode, the amount of the liquid Ca0:1Sn0:9 alloy should be relatively large so thatthe Ca activity of 10�7 at 1,000 K does not change during titration. Calcium fluorideabove �870 K undergoes a phase transition and becomes a fast F� ion conductor;at the same time, the high-temperature phase becomes relatively soft so that metalcups can be sealed against a CaF2 crystal plate by simple mechanical compression.Altogether the EMF cell can be written as follows:

Ca � Sn.1/ jCaF2.s/j CaF2 � MF.s/; M.v/; MxMX1�x.1/: (A.7)

If, at negative polarization of the working electrode, a current is passed throughthe cell, metal M is formed in the double salt and F� ions flow through the solidelectrolyte and react with Ca of the Ca–Sn alloy. Excess metal dissolved in the dou-ble salt equilibrates with metal in the vapour phase and thus, via the vapour phase,the molten salt MX in a separate compartment can be doped with excess metal.Measuring the charge passed through the cell, the amount of M in molten MX isobtained from the difference of the total charge and that part which corresponds

A.2 Optical and ESR Spectroscopy with In Situ Coulometric Titration 165

to M dissolved in CaF2–MF.s/. The latter can be determined in a calibrationmeasurement without MX (l). On the other hand, if the relation between metalactivity and metal mole fraction, aM.xM/, is known from thermodynamic data, thenxM can be determined directly from metal activity measurements according to theNernst equation:

aM D exp.F.E � E0/

RT; (A.8)

where F D Faraday constant and E0 D EMF at metal saturation. The E0 valuesfor the above EMF cell for different alkali metals are E0 D �133 mV at 1,073 Kfor Na–NaF [A.4, A.5], E0 D �233 mV at 1,073 K for K–KF–CaF2 [A.6], andE0 D �230 mV at 973 K for Cs–CsF–CaF2 [A.6].

The realization of a combined EMF–optical cell for high-temperature measure-ments is presented in Fig A.3 [3.82]. The optical cell consists of two polishedsapphire discs (20 mm diameter and 5 and 10 mm thickness, respectively), whichare sealed by squeezing a Ta ring (25, 50, or 100 �m Ta wire thickness, annealedunder UHV) inside a stainless steel–molybdenum frame. In this way, the optical filmthickness can be varied from �6 to �50 �m. The thicker sapphire contains a boringwhich connects the optical film with a spherically shaped and polished depressionon its circumference. At this depression, the optical cell is sealed and connected viaan iron capillary with a molybdenum plate that contains the working electrode com-partment. The capillary is made from high purity iron, which is soft enough for thissealing technique using another molybdenum frame. The high vacuum tightness ofthese seals has been checked with a He-leak detector. The EMF cell is mounted ontop of the bottom Mo plate, whereby a CaF2 single crystal (22 mm diameter and

Fig. A.3 Side view of theconstruction of a combinedEMF–optical cell forhigh-temperature absorptionspectroscopy with in situCoulometric titration. Seealso [A.6]

166 A Appendix

3 mm thickness) is pressed against the polished ends of the two Mo cups in a framewith Mo screws. On top of the reference electrode Mo cup is a stainless steel rodthat ensures that on heating the pressure on the CaF2 crystal is increased due tothe larger thermal expansion of steel relative to that of the Mo screws. With thistechnique, tight EMF cells have been achieved working up to 103 K. The finallyassembled combined EMF–optical cell was aligned inside a high vacuum furnacethat fitted into a Cary 17H spectrometer.

A similar construction of a combined ESR–EMF cell is shown in Fig A.4[3.84].The EMF part of this cell is essentially the same as that described above.

Fig. A.4 Schematic drawing of a high-temperature ESR cavity including a combined EMF–ESRsapphire cell heated by a CO2-laser from below; the different parts are (1) electrical feedthroughsof the vacuum jacket, (2) thermal Al2O3 insulation, (3) Mo heat shields, (4) Mo resistance heaters,(5) TE011 cavity, (6) Ca–Sn reference electrode, (7) CaF2 single crystal disc, (8) working electrodecompartment containing MF–CaF2 double salt, (9) Ta sealing cylinder, (10) sapphire capillary, (12)sealed quartz tubing, (13) pyrometer window, (14) bored and polished Mo mirror, (15) ZnSe lens,and (16) CO2–laser beam. See also [3.84] and [A.7]

A.3 Capillary Wave Spectroscopy at Elevated Temperatures 167

It is mounted on top of the ESR cavity and is surrounded by molybdenum resistanceheaters and heat shields. At the lower end of the EMF cell, a sapphire capillaryclosed one end is sealed to the molybdenum flange. This capillary with a boring of1 mm diameter is located in the centre of a TE011 cavity and contains about 2–3 mgof the MX salt. It is heated from below the cavity by a CO2 laser. For further details,see [3.84].

A.3 Capillary Wave Spectroscopy at Elevated Temperatures

On an atomic scale, the surface of a liquid is not plane and smooth, but rough.This is due to thermal motion of the molecules vertical to the interface. The verticaldisplacement, hz2i1=2, increases with temperature and with reducing the restoringforce, the surface tension � , i.e. hz2i1=2 / T=� . The surface displacement pro-files in space and time, z.r; t/, can be written as a sum of Fourier componentsthat define the surface modes or capillary waves. These have a characteristic fre-quency, !q , and a wave vector, q. Depending on the bulk viscosity �, capillarywaves either propagate as a damped oscillator or are completely damped. Their fre-quency is determined by the bulk and interfacial properties and is obtained fromsolving the linearized hydrodynamic equations with proper boundary conditions –see the review by Langevin [A.8]. In the case of a free liquid/vapour interface andfor low viscosities of the liquid, the solution is as follows:

!q D�

�q3

�

�1=2

and �1q D !q D

�2�q2

�

�; (A.9)

where � is the bulk density, q is the lifetime of the capillary wave, and !q isthe half width of the Lorentzian component of the spectrum of scattered light. Formore complex interfaces such as those of liquid crystals or with an adsorbed film,modifications of (A.9) must be considered; see [A.8].

In surface light scattering or capillary wave spectroscopy, the propagating sur-face modes act as a moving diffraction grating, where the scattered light is Dopplershifted by ˙!q . In general, only the intensities of the regularly reflected light.!0; k0/ and of the first order diffracted beam .!0 ˙ !q ; k1d/ are of interest andthose of higher orders are weaker. The wave vector q is given by the differenceof the projections of k0 and k1d in the surface plane, q D k0;s � k1d;s. Typically,the scattering angle ‚ of first-order scattering is of the order of a degree, so thatq D k0‚ lies in the range 100 � q=cm�1 � 1;000 for He–Ne laser light withk0 � 105 cm�1. The corresponding frequency for q D 500 cm�1; � D 1 g cm�3,and � D 102 mJ m�2 is !q � 105 Hz.

Capillary wave spectroscopy is a contactless method to measure the surfacefree energy and the viscoelastic properties not only of liquid/vapour, but also ofliquid/liquid – in transparent fluids – and liquid/thin film interfaces. Especially, forthese last applications it is a unique method. An experimental set-up developed for

168 A Appendix

measurements at elevated temperatures is schematically drawn in Fig A.5 see also[4.5]. In brief, laser light (10 mW He–Ne laser, TEM00 mode, and � D 632:8 nm)passes a lens and pinhole arrangement, is diffracted by a holographically etchedgrating, and is focused by a biconvex lens and prism on the liquid surface. Lightscattered at small angles by capillary waves is optically mixed at the photomultiplierwith a coherent reference beam of specific order generated by the diffraction grating(optical heterodyne detection). The amplified signal at specific q is recorded in thefrequency domain with a Fast Fourier Transform spectrum analyzer. All componentsincluding the vacuum chamber .�10�8 mbar/ are mounted on a vibration dampedtable. The surface of the liquid sample can be cleaned in situ under vacuum by Arion sputtering or with a heated W wire brush. The spectrum of scattered light is thepower spectrum of capillary waves that for large Y � 103 .Y D �=.4�2 �q/; � Dkinematic viscosity) can be approximated by a Lorentzian [A.8]. So, the powerspectra can be fitted by a convolution of a Lorentzian and a Gaussian – the latterrepresenting instrumental line broadening – and from these fits the peak frequency!q can be obtained with a typical precision of � 1%. For determination of the scat-tering angle ‚, the scattered and diffracted beams are imaged at two differentpositions of known distance (A and B in Fig A.5). In this way, q can be measuredwith an accuracy of �1%.

Fig. A.5 Experimental set-up for surface light scattering at fluid interfaces under UHV conditionsand elevated temperatures. The different components are (L1, L2) plane convex lenses, (PH1)80 �m pinhole, (DG) diffraction grating, (L3) biconvex lens, (P1, P2) prisms, (M1) Al mirror,(QW) quartz window, (PH2) pinhole with 0.9 mm diameter, (PMT) photomultiplier, Hamamatsu,(A) amplifier, (SA) FFT spectrum analyzer, Stanford, (UHV CH) ultra high vacuum chamber,(WS) wobble stick and Ar ion sputter gun, (MC) molybdenum crucible, (PE) Peltier element andMo resistance heater, (V1,V2) vacuum valves, (OP,TP,IP) oil, turbo, and ion pump. See also [A.5]

A.4 High-Temperature Ellipsometry 169

A.4 High-Temperature Ellipsometry

In ellipsometry, the change of the state of polarization of polarized light interactingwith an interface is recorded. It is generally assumed that this interaction is linearand energy conserving. If light is transmitted through the interface and the continu-ous change of polarization inside a medium is measured, this is called transmissionellipsometry. In reflection ellipsometry – for short-called ellipsometry in the fol-lowing – the abrupt change of the state of polarization at the interface betweentwo optically dissimilar media is recorded. This mode of ellipsometry is suitableto determine the complex optical constants – N D n C ik or " D "1 C i"2 withn being the refractive index, k the absorption coefficient, and " the dielectric func-tion – of highly absorbing media like metal alloys or metal–molten salt solutions;see Sect. 3.5. It can also be used to characterize thin interfacial films, their thickness,and optical properties; see Chap. 4.

The basic quantities in ellipsometry – for a comprehensive introduction, see thebook by Azzam and Bashara [A.9] – are the Fresnel complex amplitude reflectioncoefficients that describe the change of state of polarization on reflection:

rp � .Erp=Eip/ D ˇrp

ˇexp.i ırp/ and rs � .Ers=Eis/ D jrsj exp.i ırs/: (A.10)

Here, jrpj is the ratio of the amplitudes of the electric vectors of reflected (r) toincident (i) waves with the latter being polarized parallel (p) to the plane of inci-dence; ırp is the corresponding phase shift on reflection. The quantities jr sj and ırs

have analogous meanings but now for incident waves polarized perpendicular (s,senkrecht) to the plane of incidence. The ellipsometric angles ‰ and – these arethe central quantities determined experimentally – are defined by the ratio � of thecomplex Fresnel reflection coefficients:

� D rp = rs D tan ‰ exp.i/; (A.11)

withtan ‰ D ˇ

rp = rs

ˇand D ırp � ırs: (A.12)

For the determination of the corresponding optical characteristics of the interface,a model is needed. If the interface is solely defined by the contact of two isotropicand homogeneous phases with optical constants N0 and N1, respectively, then theso-called two-phase model can be applied. Here, the ratio N1=N0 is given by ananalytical expression that contains � and the angle of incidence ˆ; see [A.9]. Inthe case of a more complicated interface – e.g. a thin isotropic film of thickness d

and optical constant N2 between two bulk phases with N0 and N1 (three-phase orDrude slab model) – an analytical solution is not possible. Instead, the interestingparameters Ni and d must be determined from a numerical fit of the general expres-sion for � D �.Ni ; d; ˆ/; see also [A.10, A.11]. In this case, further experimentalinformation is needed, which can be obtained, for instance, from measurements atdifferent angles of incidence, �.ˆ/, or at variable frequency of the incident light,�.!/ (spectroscopic ellipsometry).

170 A Appendix

The principal arrangement of the optical components of a PSArotA ellipsometeris shown in Fig A.6 [3.87]. Collimated light passes a polarizer (P), which definesthe state of polarization of the incident light, and is reflected at an angle ˆ at thesample (S). The reflected light, which in general is elliptically polarized, passes ananalyser rotating at a frequency !.Arot/ and an analyser with fixed angle .A/ and isrecorded at a suitable detector (D). In this configuration, the detector signal I.t/ isgiven by a truncated Fourier series:

I.t/ D a0 C a2 cos.2!t/ C b2 sin.2!t/ C a4 cos.4!t/ C b4 sin.4!t/; (A.13)

where the Fourier coefficients ai and bi are functions of and ‰. These coef-ficients can be determined from the Fourier transform of the digitalized detectorsignal [3.87].

In the experiments on wetting films of K–KCl melts (Sect. 4.3), an ellipsometerwith PSArotA configuration has been employed. The ellipsometric angles ‰ and

have been determined at ˆ D 70ı and, in addition, the reflectivity at ˆ D 90ıhas been measured [A.11]. Because of the elevated vapour pressure of the dissolvedalkali metal, the fluid sample had to be sealed in an optical sapphire cell; see Fig A.7.

Fig. A.6 Schematic drawing of a PSArotA ellipsometer: P D polarizer; S D sample; Arot Drotating analyzer, A D analyser; the polarizations p and s denote light polarized parallel andperpendicular to the plane of incidence. See also [3.87]

Fig. A.7 (a) Optical sapphire cell for ellipsometric measurement at high temperatures: (S) sample,(RS) reservoir sapphire, (SP) sapphire prism, (Ta) Ta sealing wire, (MF) metal frame, (incomingupper beam) beam for ellipsometric measurement at ˆ D 70ı, (incoming lower beam) beam forbirefringence correction, and .R?/ reflectance measurement at ˆ D 90ı; (b) Arrangement of Tasealing wires (3) between prismatic and reservoir sapphire in (a) defining sample (1) and referencecompartment for birefringence corrections (2). See also [A.11]

A.5 Electrochemical Scanning Tunnelling Microscopy 171

This causes complications due to birefringence and stress birefringence of sapphire.The latter results from the sealing technique applied, whereby Ta sealing wires arecompressed between the two sapphire discs. These contributions can be correctedby in situ measurements at the sapphire/sample and sapphire/vacuum interfaces atthe same temperature and compression; see the two beams in Fig A.7.

A.5 Electrochemical Scanning Tunnelling Microscopy

The basic quantum mechanical equation and its consequences for tunnellingmicroscopy and spectroscopy have been introduced in Sect. 5.3. Here, this descrip-tion is completed by the energy level diagram involved in electron tunnelling and,on the basis of this, the difference between tunnelling in vacuum and electrolytesshall be illustrated. Finally, the schematic set-up of an electrochemical scanningtunnelling microscopy (EC-STM) experiment is briefly described.

Figure A.8a shows the energy diagrams of two solid metals, a tunnelling tip (T)and a substrate (S), which are separated by a vacuum gap of width d � 1 nm. Forsimplicity, conduction band s-states that have the well-known n.E/1 E1=2 energydependence of the density of states and are filled up to the Fermi energy EF areconsidered. The electron wave functions of both metals decay exponentially acrossthe gap, but for short enough values of d � 1 nm they have a small but finite prob-ability density at the respective opposite solid. The potential barrier the electronshave to tunnel through is essentially determined by the work functions ˆT and ˆS,respectively; in simplest approximation, the effective barrier height is given by theaverage ˆ D .ˆT C ˆS/=2. However, in realistic systems, image forces at the sur-faces lead to a rounding of the barrier as indicated by the parabolic curve in Fig A.8;see also [5.44]. A modification of the potential barrier can be induced by applying

Fig. A.8 Schematic drawing of the energy diagram for tunnelling in vacuum (a) and in electrolytes(b). For details see text

172 A Appendix

a bias voltage V . At thermal equilibrium of both solids – which can be establishede.g. by radiation – their respective Fermi energies are equal. However, if a bias volt-age V is applied to the substrate – the tip being grounded – the Fermi level, beingan electrochemical potential, is lowered by eV > 0. Now, tunnelling of an electronfrom an occupied state .˛/ of the tip into an empty state .ˇ/ of the substrate cantake place; see Fig A.8. The reverse process requires a negative bias voltage. Theseconsiderations illustrate how by varying the bias voltage different local density ofstates at the substrate surface can be probed, which leads to modifications in theSTM images.

Considering tunnelling through an electrolyte film in the gap, the main qualita-tive characteristics of vacuum tunnelling remain. The essential differences are thefollowing. The tunnelling barrier, in general, is strongly reduced. This is caused bydipolar adsorbate–substrate interactions of ions and solvent molecules adsorbed atthe tip/electrolyte and substrate/electrolyte interfaces. In the case of ionic liquids,measurements of the effective tunnelling barrier heights by tunnelling spectroscopyindicate a reduction of ˆ of Au, Ni, and Co by �4 eV [A.12]. Very similar resultshave been reported for aqueous electrolytes [A.13]. In the scheme depicted inFig A.8b, this decrease in ˆ has been taken into account. A second, not finallysolved problem concerns the tunnelling process itself in electrolytes. This, indeed,is a demanding problem if one takes into account the complex configuration ofoverlapping double layers of tip and substrate in the gap. Different models havebeen suggested; see e.g. [A.14]. In MD calculations, the tunnelling process has beentreated as scattering of electrons at the potential energy surface of the electrolyte.Another explanation considers resonant tunnelling where an intermediate state of asolvated electron is assumed. However, the lifetime of these states is relatively long(�10�12 s; see Sect. 3.5) in comparison with a typical tunnelling time across thegap .10�15 s/, so that this mechanism is not very likely. A probable solution to theproblem seems to be tunnelling through conduction band states of the electrolyte,which was suggested by Schmickler and Henderson [A.15].

A sketch of the principle components of an EC-STM experiment suitable formeasurements with ionic liquids is depicted in Fig A.9. The electrochemical cellconsists of a Teflon or glass cylinder, which is sealed by a silicon O-ring to the sub-strate or working electrode disc (WE). At the working electrode/ionic liquid (IL)interface, the atomic structure and a step edge at the surface are indicated by cir-cles. For in situ EMF measurements, counter (CE) and reference (RE) electrodesare needed. For STM measurements, an STM tip (T) from Pt–Ir or W, which isconnected with a piezo tubing (PT), is approached to the working electrode at adistance of �1 nm. Tungsten can be used in contact with ionic liquids as the inher-ent WOx oxides can be dissolved by applying a potential; this is not the case inaqueous electrolytes. For EC-STM experiments, it is necessary that that part of thetip, which dips into the electrolyte, is electrically insulated with exception of a tinyspot of �100 nm2 at the tip end. In this way, Faraday currents, which are orders ofmagnitude higher than the tunnelling currents, can be suppressed. To achieve such

A.5 Electrochemical Scanning Tunnelling Microscopy 173

Fig. A.9 Schematic drawing of electrochemical cell with periphery of an EC-STM experiment.For further description see text

a coating (IC), the tip is covered with an insulating film and then is heated upsidedown in a specially programmed furnace. In experiments near room temperature,epoxid coatings have proven effective; at elevated temperatures, the combinationof W tip and borsilicate glass coating with matched expansion coefficient is suc-cessful [A.16]. To achieve atomic resolution, good vibration (VI) and also acousticinsulation are important. In experiments using ionic liquid electrolytes, it is recom-mendable to house the electrochemical cell in a vacuum tight chamber that preventsadsorption of moisture and at the same time offers acoustic insulation. OtherwiseHCl or HF may form which not only attacks the electronics of the scanner. Thefinally assembled electrochemical cell – with ionic liquids, filling and assemblingshould be done in a glove box with low water content – is connected with a piezocontroller and a bipotentiostat. The latter ensures independent control of the tip biasvoltage V and the cell EMF. The piezo controller with suitable feedback enablesthe tip movement in the x-, y-, z-directions across the substrate/ionic liquid inter-face. With measurements in a constant tunnelling current .It/ mode, the z-movementof the tip is recorded during an x-, y-scan, which can be visualized on a screen.This information represents the local density of state profile of the substrate surface.A construction of an EC-STM cell for measurements at elevated temperatures isdescribed in [A.16]. It has been tested with a W(111) single crystal electrode in anAlCl3–NaCl melt at temperatures up to 500 K.

174 A Appendix

References

A.1. M. Edeling, W. Freyland, Ber. Bunsenges Phys. Chem. 85, 1049 (1981)A.2. C. Wagner, J. Chem. Phys. 21, 1819 (1953)A.3. J.J. Egan, W. Freyland, Ber. Bunsenges Phys. Chem. 89, 381 (1985)A.4. R. Alquasmi, J.J. Egan, Ber. Bunsenges Phys. Chem. 87, 815 (1983)A.5. J. Bernhard, PHD Thesis, University of Karlsruhe, Germany, 1994A.6. T.h. Rauch, PHD Thesis, University of Karlsruhe, Germany, 1992A.7. T.h. Schindelbeck, PHD Thesis, University of Karlsruhe, Germany, 1995A.8. D Langevin (ed.), Light Scattering by Liquid Surfaces and Complementary Techniques

(Marcel Dekker, New York, 1992)A.9. R.M.A. Azzam, N.M. Bashara, Ellipsometry and Polarized Light, 2nd edn. (North Holland,

Amsterdam, 1987)A.10. C.h. Buescher, PHD Thesis, University of Karlsruhe, Germany, 1997A.11. S. Staroske, PHD Thesis, University of Karlsruhe, Germany, 2000A.12. C.A. Zell, W. Freyland, Chem. Phys. Lett. 337, 293 (2001)A.13. J. Halbritter, G. Repphun, S. Vinzelberg, G. Staiko, W.J. Lorenz, Electrochimica Acta

40:1385 (1985)A.14. T.P. Moffat, Electroanal. Chem. 21, 211 (1999)A.15. W. Schmickler, W. Henderson, J. Electroanal. Chem. 290, 283 (1990)A.16. A. Shkurankov, F. Endres, W. Freyland, Rev. Sci. Instrum. 73, 102 (2002)

Index

Absolute thermoelectric power, S , of fluidcesium, 56

Adatom(s), 141Adatom superlattices, 118Adsorbed ion layers, 134Adsorption–desorption reaction, 137Ag monolayer, 138Alkali halides, 14Alkali metal alloys, 68Alloy adlayer, 145Aluminium alloys, 151Anderson model, 49Anion adsorption, 142Anodic dissolution, 141Anodic stripping, 146Anodic sweep, 139Antiferromagnetic, highly correlated electron

gas, 65Auger electron spectroscopy (AES), 122

Bipolaron binding energy, 86Bipolaron excitation, 86Bipolaronic structures, 85Bipotentiostat, 149Bix(BiCl3/1�x , 94Born–Mayer potential, 14Bulk phase behaviour, 22Bulk phase diagram of K–KCl, 113

Caesium gold alloys, 69Cahn–Hilliard diffusion equation, 142Cahn–Hilliard equation, 108Capillary wave spectroscopy, 102, 120Capillary wave spectroscopy at Elevated

Temperatures, 167Car–Parrinello MD simulations, 19Chloroaluminate(s), 17

Chloroaluminate melt, 150Chronoamperometry, 154Colour centre, 50Complete wetting films of fluid Hg on

sapphire, 116Complete wetting transitions, 102Computer simulation methods, 5Cottrell plot, 156Coulombic fluids, 3, 22Coulometric titration method, 75, 88, 164Covalently bonded Sb–Sb distance, 77Covalently bonded Sb�Sb� helical chains, 80Critical demixing of ionic liquid solutions, 26Critical exponent ˇ, 25Criticality in Coulombic fluids, 25Critical point wetting, 35Critical prewetting point, 35133Cs hyperfine-field correlation time in, 79133Cs nuclear resonance shift, 77Curie law, 62

limitations, 65paramagnetism, 88

Current transients, 155Cyclic voltammetry (CV), 136

Debye length, 132Density of states, n.E/, 9Desorption isotherms, 137Dewetting, 112Dielectric functions, 110Dielectric susceptibility enhancement, 91Differential capacitance Cd, 132Diffraction methods, 20Diffuse layer, 132Doped compound semiconductor, 75Droplet emulsion technique, 23Drude component, 86Dynamic structure factor, S.Q; !/, 58

175

176 Index

EC-STM experiment, 172Einstein relation, 30Einstein–Smoluchowski relation, 142Electrical double layer, 3Electrified interfaces of ionic fluids, 37Electrified ionic liquid/solid interfaces, 131Electrified metal/ionic liquid interface, 134Electrocapillarity, 39Electrochemical cell, 136Electrochemical dissolution, 143Electrochemical etching, 144Electrochemical interfaces, 131Electrochemical phase formation, 135Electrochemical scanning tunnelling

microscopy, 134, 171Electrocrystallization, 135

of Al on n-Si(111):H, 150of ZnxSb1�x , 158of compound semiconductors, 155

Electrodeposition, 134Electrodeposition of thin Ge films, 158Electromotive force, 136Electronic DC conductivity, �.0/, 28Electronic defect equilibria, 89Electronic mobility, 90Electronic structure in pure liquid alkali

halides, 81Electron localization, 2, 72Electron spin resonance (ESR), 83Electron transport in liquid metals, 27Electrowetting phenomena, 39Ellipsometric angles, 109EMF–optical cell, 165Emissivities, 109Emissivity of Bi, 110Enhancement of the spin susceptibility,

65ESR–EMF cell, 165ESR spectra of liquid KxKCl1�x , 88EXAFS investigations, 95Expanded fluid Cs, 24Expanded fluid metals, 2, 54Extrinsic semiconductor, 80

F-centre, 50band, 84dynamics, 84excitation, 114

F-centre-like states, 72Fe nanocrystals, 155Fermi–Dirac distribution function, 9Fermi energy, 9

First-order surface freezing transition,126

First-order surface phase transition, 119First-order wetting transition, 113Free electron (FE) model, 8Friedel oscillations, 11

Ga-based alloys, 101Gibbs adsorption equation, 32Gibbs adsorption isotherms, 103Glass forming ionic liquids, 93Glass transition, 24, 93Gouy–Chapmann–Stern model, 132Grazing incidence X-ray diffraction, 128

Hall coefficient, RH, 28Hall coefficient, RH, of liquid Cs, 55Hard-sphere model, 59Helmholtz layer, 132Herzfeld criterion, 91Hexatic phase, 117Highly doped semiconductors, 91High-temperature ellipsometry, 169High-Temperature: high-pressure neutron

diffraction, 161Hubbard model, 52Hydrodynamic continuum model, 147Hyperfine field, 73

Imidazolium-based ionic liquids, 18Imidazolium cation, 1, 13Impurity band, 95Independent surface phase, 125In situ STM imaging, 144Instantaneous nucleation, 155Interfacial excess, 33Interfacial free energy, 33Interfacial layering, 38, 128Interfacial oscillatory instabilities, 3Interfacial phase transitions, 2, 101Interfacial phase transitions of Coulombic

fluids, 31Interfacial phenomena, 31Interfacial structure of molten salts, 36Intervalence charge transfer, 29Ioffe–Regel limit, 67Ioffe–Regel rule, 45Ionic bonding in liquid CsAu, 70Ionic DC conductivity, 29Ionic liquids, 38It–V spectrum, 155

Index 177

Kinetics of the spinodal structures, 146Knight shift K , 63KTHNY theory, 117

Labyrinth structures, 143Landau diamagnetism, 63Layer-by-layer growth, 145Layering, 36Linear sweep voltammograms, 137Liquid–liquid miscibility, 113Liquid range of ionic liquids, 22Liquid semiconductors, 80Liquid/vacuum interfaces, 38Liquid–vapour critical region, 23Liquid/vapour interface of metals, 32Long wavelength limit S.0/, 60Low-density plasma model, 66

Madelung constant, 23Madelung potential(s), 70Madelung potential fluctuations, 82, 84, 91Magnetic properties of fluid alkali metals, 62Mean-field lattice-gas model, 132Mechanisms of electron localization, 49Melting in two dimensions, 117Melting of a monolayer of colloidal particles,

118Metal–molten salt solutions, 2Metal–nonmetal transition, 2Metal–nonmetal transition of the

Mott–Anderson type, 49Metastable binodal line, 125Metastable states, 142Microscopic segregation, 92Microscopic structure in CsxAu1�x , 70Miscibility gap, 108Mobility edges, 47, 49, 90Mobility gap, 78Mobility of ions, 30Molecular dynamics (MD), 15Mollwo–Ivey rule, 83Molten ZnCl2, 16Monoantimonides MSb, 74Monodisperse CdSe nanocrystals, 143Monte Carlo (MC) simulations, 15Mott–Anderson transition, 91Mott criterion, 48Mott–Hubbard transition, 53Mott’s minimum metallic conductivity �min,

57, 90, 95Mott transition, 48, 67

Nanocrystal self-assembly, 143Nanoscale electrodeposition, 3, 149Nanoscale systems, 117Nearly free electron (NFE) model, 10Nernst equilibrium potential E , 136Neutron diffraction autoclave, 163Ni nanocrystals, 154Normalized differential conductivity spectra,

158Nuclear magnetic resonance (NMR), 83Nucleation and growth mechanisms, 142

Onset temperatures of decomposition, 24Optical absorption, 82Optical conductivity, 91Optical gap Eg, 70, 71Optical sapphire cell for ellipsometric

measurement, 170Order–disorder transition, 117Oscillatory instabilities during phase

separation, 108Oscillatory phase separation, 107Oscillatory wetting instabilities, 106Overpotential �, 136

Pair correlation of Cs0:75 Sb0:25, 77Pair potential approximation, 7Partial molar Gibbs energy, 75Partial pair distribution functions, 14Partition function, 6Pauli exclusion principle, 9Pauli–Landau limit, 65Percolation threshold, 53, 92Percolation transition, 53Phase diagram

of the Bi–BiCl3 system, 93of the Cs–Sb alloy system, 74

Poisson–Boltzmann equation, 132Poisson’s equation, 10Polaron binding energy, 51Polaron formation, 51Prewetting critical temperature Tc;pw, 116Prewetting line, 115Prewetting transitions, 31, 35, 102, 113Progressive nucleation, 155Pseudoatom, 10Pseudogap model, 67, 78Pseudopotential, 10Pyridinium, 13

QMD calculations, 85

178 Index

Radial pair distribution function, 7Raman spectroscopy, 16Rapidly quenched M–MX melts, 93Rayleigh–Taylor instability, 112Redox couple, 144Relative interfacial entropy, 33

Scaling laws, 26Scanning tunnelling microscope (STM), 124Scanning tunnelling spectroscopy, 149Schottky defects, 50Schrodinger equation, 8Screened pseudopotential, 11Second harmonic generation (SHG), 109Self-diffusion coefficient of ion, 30Semiconductor electrocrystallizations from

ionic liquids, 150Solubility and solvation, 19Sommerfeld theory of metals, 10Spectroscopic ellipsometry, 83Spin–lattice relaxation rate, T �1

1 , 77Spinodal decomposition, 142Spinodal mechanism, 143Spinodal reactions, 142Spin susceptibility, 87Splat-cooling, 93Spreading coefficient, 35Static structure factor, S.Q/, 57Statistical thermodynamics, 5Stratification, 32Structural properties of ionic liquids, 17Structure factor S.q/, 8, 147Surface alloy, 141Surface alloying, 117, 146Surface charging, 115Surface excess entropy, 119Surface faceting, 128Surface freezing, 3, 117

in binary liquid alloys, 117in liquid Ga–Bi alloys, 119

Surface freezing film(s), 124Surface freezing film thickness, 127Surface freezing line, 121Surface-induced nucleation, 127Surface layering, 128Surface light scattering at fluid interfaces, 168Surface melting, 117Surface melting and freezing, 31Surface phase diagram, 102Surface spinodal reactions, 148Surface tension

of liquid metals, 33of molten salts and ionic liquids, 40

Tetra point wetting, 105, 115Thermodynamic defect models, 88Thermodynamic model calculations, 105, 122Thermoelectric power, S , 28Thickness induced metal–nonmetal transition,

157Thickness profiles of Bi-rich surface films, 123Thomas–Fermi approximation, 463D Ising model, 26Tight binding approximation, 49Topological disorder and potential fluctuations,

49Transmission electron microscopy, 128Tunnelling barrier, 149Tunnelling barrier height, 1522D electrochemical phase formation, 1382D melting, 1172D phase transitions, 134Two-phase spinodal structure, 143

Undercooling, 23Underpotential deposition (UPD), 136Unstable wetting film, 112

Vapour pressure curves of [C2 mim][NTf2] and[C2 mim][DCA], 25

Vogel–Tammann–Fulcher (VTF) relation, 30

Wagner polarization technique, 86Wetting film thickness, 104Wetting in dense mercury vapour, 116Wetting phenomena, 34Wetting temperature TW, 2, 35, 105Wetting transition, 35

at the liquid/solid Interface, 113at the liquid/vapour Interface, 101in metal-rich KxKCl1�x , 114

Wilson band model, 45

X-ray photoelectron (XPS), 122X-ray reflectivity, 128X-ray reflectivity measurements, 38

Young equation, 34Young–Lippmann equation, 39

Zincblende structure, 15Zn–Au surface alloy, 145