The cycle starts with a clean positively polarized surface and returns to this state after multiple steps, thereby efficiently dissociating two NO molecules into N 2 and O 2. Atomic polarization in ferroelectrics can be furthermore manipulated to control electronic structure and local chemical reactivity, allowing for a novel approach to fabricating multicomponent, complex nanostructures Kalinin et al , Photoreduction on chemically patterned lithium niobate crystals is used to fabricate metallic nanostructures Sun and Nemanich , Carville et al Moreover, LiNbO 3 is employed as a photovoltaic substrate for massive parallel manipulation and patterning of nano-objects Carrascosa et al and for the photocatalytic nanoparticle deposition on LiNbO 3 nanodomain patterns via photovoltaic effect Liu et al An alternative way to produce surface nanoscale periodic structures in congruent lithium niobate is given by domain reversal patterning and following differential etching Grilli et al , which will be described in the next section.

Experiments with the adsorption of acetic acid Yun and Altman , NO Choso et al , Tabata et al , 2-propanol Yun et al a , dodecane Yun and Altman , water, methanol Garra et al and the anchoring of liquid crystal molecules Bharath et al indicate an influence of the LiNbO 3 surface polarization on the adsorption characteristics. Lithium niobate surface charges were found to enable the photo-assisted reduction of CO 2 , i.

The interactions of larger macro molecules with ferroelectric surfaces are interesting as well, from both the scientific and technological point of view. The integration of ferroelectric thin films with liquid environments is investigated in the context of lab-on-chip device designs, e. LiNbO 3 crystal surfaces have been employed to trap and pattern nano- and micro-meter particles using the evanescent light-induced photovoltaic fields in photovoltaic tweezers Villarroel et al High surface electric fields due to pyroelectricity were found to efficiently pole electro-optic polymers Huang et al and to lead to the reversible fragmentation and self-assembling of nematic liquid crystals Merola et al Exploiting the same principle, Habicht et al , achieved selective decoration of LiNbO 3 domains with polystyrene microspheres from an aqueous solution Habicht et al In order to achieve a good patterning for the described applications, a precise poling process is required.

Poling with different techniques, including UV assisted poling, or conventional electric field poling with an overpoling step that inverts all the material apart from a thin surface region directly below a patterned photoresist allows for the realization of multiform domain structures Busacca et al or periodic structures with homogeneous submicron gratings Valdivia et al Further improving the lithium niobate technology and applications requires a detailed understanding of the material's surfaces.

Therefore, several investigations have been dedicated to the characterization of the LiNbO 3 cuts, which will be described in the following section. X-ray' and ultraviolet photoelectron spectra showed only minor differences between the positively and negatively polarized surfaces, apart from a high binding energy feature on the oxygen 1 s core-level of the negative z -cut Yun et al b. UV-photoelectron emission microscopy on periodically poled LiNbO 3 samples revealed sizeable differences in the ionization energy of opposite domains.

While the photothreshold of the negative z -cut is 4. Different scattering spectroscopy methods have been applied to reveal the surface termination morphology and stoichiometry Kawanowa et al , Saito et al , however they did not yield a conclusive picture, due to the different cross sections of Nb, Li, and O to different ion beams. Agreement has been achieved about the fact that LiNbO 3 z -cuts can be rendered atomically smooth by annealing Lee , Saito et al However, a temperature treatment of the samples in vacuum leads ineluctably to the evaporation of several distinct Li and O gases depending on the annealing temperature, as pointed out with mass spectrometry, temperature programmed desorption measurements and Auger electron spectroscopy and Yun et al b , Lushkin et al These studies showed that the LiNbO 3 spontaneous polarization causes an asymmetry in the evaporating species from surfaces of opposite polarities Lushkin et al Time resolved Kelvin probe microscopy has revealed the activation of the surface ionic subsystem, with electric fields inducing the injection of surface charges Strelcov et al The surface temperature response and the thermally stimulated field emission of congruent and stoichiometric lithium niobate single crystals were also investigated by pyroelectric electron emission current measurements, current distribution collecting and proximity-imaging techniques Rosenblum et al , Bourim et al In spite of many intriguing applications, far less detailed information on the LiNbO 3 x - and y -cuts is available.

Lee has investigated coarse surfaces of commercial x -cut samples by atomic force microscopy, demonstrating that they can be made smooth at the atomic scale by a direct temperature treatment in air Lee Nagata has shown by Fourier transform IR spectrometry that the ion concentration of the hydroxyl groups, usually present in the wafers as unintentional dopant, varies alongside the z axis in x -cut samples Nagata et al , Nagata Bentini et al have studied x -cut single crystals of LiNbO 3 implanted with different ions by secondary ion mass spectrometry, x-ray diffraction, and Rutherford back-scattering spectroscopy.

They have shown that carbon implantation at low fluency does not produce substantial surface damage and does not lead to the formation of any new phase. Yet, the implantation causes a sizeable tensile strain at the surface and yields to a corresponding expansion of the crystal unit cell. In agreement with this behavior, Kalabin et al could not observe the formation of any new surface phase upon tempering and Ti indiffusion Kalabin et al Lithium niobate is an optical material with pronounced nonlinear coefficients for photon energies above 1.

The energy dependence of the bulk contribution to the four nonvanishing components of the second-order polarizability tensor as calculated from first principles by Riefer et al are presented in figure 4 and compared with experiments, represented by the dots, squares etc Boyd et al , Kleinman and Miller , Miller and Savage , Bjorkholm , Hagen and Magnante , Miller et al , Levine and Bethea , Choy and Byer , Shoji et al The comparison with the calculated spectra within the independent particle approximation IPA, red lines and within the independent quasiparticle approximation IQA, blue lines shows that the former overestimates the measured data, whereas, the IQA calculations, which include electronic self-energy effects, describe the optical nonlinearities better.

A further improvement of the agreement between theory and experiment is achieved considering the congruent composition dotted lines in figure 4. In non-centrosymmetric materials, second harmonic generation contributions from bulk and from the surface cannot be separated. Thus, employing a fundamental beam in the visible range, surface selectivity using reflection SHG can be realized. Coefficients of the second-order polarizability tensor for lithium niobate calculated within the independent particle approximation red lines and including quasiparticle effects blue lines , compared to experimental data represented by diamonds, squares, crosses, etc experimental references in the text.

Solid lines represent calculations for stoichiometric LiNbO 3 , while dotted lines represent calculations modeling the congruent composition. See Riefer et al for more details.

Due to the technological relevance of all the lithium niobate cuts, some information regarding growth techniques and post-growth treatments to improve the sample surface quality in particular to quench the very strong tendency towards faceting can be found in the literature Solanki et al However, the surface structure at the atomic scale of the LiNbO 3 surfaces has remained for a long time experimentally inaccessible. Indeed, charging effects prohibit the application of electron tunneling or diffraction techniques and unscreened surface charges hinder atomic force microscopy in lithium niobate.

A breakthrough was achieved by Rode et al performing the atomic force microscopy AFM measurement in liquid environment, in order to screen the AFM tip from the surface charges. This allowed for the first time true atomic resolution imaging of the z - and then of the x -cuts Sanna et al b.

No surface reconstruction was found in both cases for stoichiometric samples, however geometrical patterns not compatible with truncated bulk terminations were revealed on the x -cut. Successively, measurements on z -cut samples annealed at different temperatures showed a peculiar thermal behavior, which is discussed in section 1. Despite the successful employment of lithium niobate surfaces in a multitude of applications and the knowledge originating from the investigations described in the previous section, there are several aspects of these surfaces, which are far from being completely understood.

These include, among others, the impact of molecules and adsorbates and the temperature behavior. In the previous section we have provided several examples of molecular adsorption phenomena affected by the ferroelectric domain orientation and discussed potential applications. Vice versa, the impact of molecules on ferroelectric surfaces can be exploited to tune their chemical and physical properties, or even to alter the morphology or polarization. However, different aspects of this phenomena are still not clear or even puzzling. An extreme example in this sense is given by the chemical etching.

Due to this phenomenon, it is possible to visualize ferroelectric domains of, e. Even if this technique is routinely used Sones et al , Mailis et al , the reason for the different etching rate is still unknown Argiolas et al Reprinted from Barry et al , Copyright , with permission from Elsevier. Furthermore, the molecular adsorption as well as surface defects Gao et al b influences the ferroelectric phase transition, and therefore the polarization reversal properties of the substrate.

In a very recent experimental study Ramos-Moore et al a modification of ferroelectric hysteresis in Pb Nb,Zr,Ti O 3 thin films due to CO 2 adsorption was found and attributed to the existence of a depolarizing field induced by molecular adsorption at the surface. Also Yun and Altman have shown that the adsorption energy differences between positive and negative surfaces of ferroelectric oxides are large enough to switch the polarity of thin films. In the work of Sun et al , it was noted that the size of nano-scale ferroelectric domains on LiNbO 3 single crystals expands or shrinks with increases or decreases in the environmental humidity, i.

Thus, ferroelectric chemical sensors such as gas detectors can be envisioned, where adsorption switches the polarization of a thin ferroelectric gate of a field effect device. For broader samples instead, it has been proposed that the application of external electric fields will suffice to switch adsorption and catalytic properties; first successful experiments in this area have already made their appearance in the literature Giocondi and Rohrer This notwithstanding, both the mechanisms of the ferroelectric poling at the microscopic scale, as well as their modification by molecular adsorbates need further investigations.

The evolution of the LiNbO 3 z -cut with increasing temperature shows a rich variety of morphologies. More recently, an AFM investigation has shown a series of structural transformations on samples annealed at different temperatures Sanna et al Regular patterns of different form and size as shown in figure 6 are formed at determined temperatures.

A Fourier analysis demonstrated the occurrence of a surface reconstruction, stable only in a limited temperature range. The evolution of the surface structure with increasing temperature was discussed as the result of the interplay between several surface stabilization mechanisms. Reprinted figure with permission from Sanna et al , Copyright by the American Physical Society. The etching rate and the temperature behavior are not the only LiNbO 3 surface properties that are unusual and strongly polarization dependent.

The aim of this review is to summarize our knowledge of LiNbO 3 surfaces and interfaces, especially in the light of recent theoretical advances. These allowed for a comprehensive understanding of some of the fundamental properties of technologically relevant LiNbO 3 faces and their peculiar characteristics. Many experiments could be interpreted on the basis of the microscopic surface structure, and many of the unusual properties described above could be explained. The second section introduces the established crystallographic notations for ferroelectric LiNbO 3 and defines the different crystallographic directions, which, due to the highly anisotropic nature of LiNbO 3 crystals, are crucial to understand the material's surfaces.

The third section gives an overview of the first principles, atomistic calculations employed for the simulation of ferroelectric surfaces. Different aspects of this method, including the slab approach and the related issues with the boundary conditions are discussed. The thermodynamic framework underlying the investigation is described as well. Approximations and simplifications within the approach are explained in detail to give an estimate of the reliability level and predictive power of the models. Sections 4 — 6 deal with the technological relevant LiNbO 3 faces, usually referred to as lithium niobate x - y - and z -cut, respectively.

Most emphasis is given to the discussion of the z -cut, a polar surface that has been investigated in a multitude of experiments due to its huge potential for novel applications. After a short overview of further relevant LiNbO 3 surfaces in section 8 , the work is concluded with a short summary and a survey on future applications of ferroelectric surfaces. LiNbO 3 is a highly anisotropic material, and a consistent definition of the crystal axis is of fundamental importance to model and understand the inherent characteristics of the materials surfaces and interfaces.

As different representations of the crystal structure are currently employed, we briefly explain the notation we follow in this work. Ferroelectric LiNbO 3 is a trigonal crystal belonging to the space group R 3 c and point group 3 m.

It is characterized by the threefold rotational symmetry about the crystallographic z axis and by three mirror planes containing this axis. Crystals belonging to the trigonal group are typically described either by a hexagonal or by a rhombohedral primitive cell. Furthermore an orthorhombic cell is used for the specification of the LiNbO 3 properties described by a tensor, such as the electro-optic coefficients. Figure 7 illustrates the different cells used to model bulk lithium niobate. The smallest unit cell is the rhombohedral cell in figure 7 a and is made up of ten atoms, corresponding to two formula units.

The conventional hexagonal unit cell is larger, and contains 30 atoms or six formula units. The orthorhombic cell, with orthogonal translation vectors parallel to the x , y , and z Cartesian axis, is the largest unit cell, containing 60 atoms or 12 formula units.

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Most of the material properties exploited in technological applications dielectric constants, non-linear optical, elastic stiffness and piezoelectric strain coefficients as well as symmetries and surfaces are usually specified within the orthorhombic system. Rhombohedral a , hexagonal b , and orthorhombic unit cell of ferroelectric LiNbO 3. The ferroelectric axis is indicated in terms of the corresponding translation vectors , , and. For the sake of clarity the atomic basis is not shown.

The existence of different coordinate systems as well as some inconsistence in the application of the conventions used to define them causes a lot of confusion. We follow Weis and Gaylord and Sanna and Schmidt c to define the LiNbO 3 x , y , and z -cuts, which are shortly described in the following. The x axis is perpendicular to the z axis and is chosen as one of the hexagonal vectors or , representing equivalent directions of the LiNbO 3 crystal structure.

Applying the conventional transformation. After that the x and the z axis are defined, the y axis is chosen in order to form a right handed orthogonal coordinate system. The translational basis vectors of the hexagonal unit cell , and and the x and y directions of the orthorhombic system used to describe the LiNbO 3 tensor properties are indicated. The hexagonal unit cell is shown in gray.

Both t 1 and t 2 , as well as x and y are threefold degenerate due to the hexagonal symmetry. This results in two non-polar surfaces, which might however become charged upon compression. The above defined LiNbO 3 cuts are characterized by very different physical properties.

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## Surface Science: Foundations of Catalysis and Nanoscience, 3rd Edition

The unusually high spontaneous polarization of 0. This is due to the particular stacking of the atomic layers, which is, in the direction, Nb Li , Nb Li , Thus, y -cuts are nominally non-polar. However, the y -cut is characterized by a non vanishing surface charge as large as about Johann As the y axis lies in a plane of mirror symmetry, can be modified by compression along the y direction.

The y axis is therefore indicated as non ferroelectric but piezoelectric. This property can be exploited to determine the orientation of the y axis similarly to the procedure described for the z axis. By definition a negative excess charge is measured at the face upon compression Weis and Gaylord The situation at the x -cut is completely different. The x axis lies perpendicularly to a mirror symmetry plane, hence each charge displacement at one side of this symmetry plane is mirrored by the same charge displacement at the other side, resulting in no net surface charge.

One of the characteristic peculiarities of ferroelectric crystals is the temperature driven ferroelectric to paraelectric phase transition. In order to model the effects of the temperature, theoretical investigations of ferroelectric materials are traditionally performed within phenomenological approaches. Typical investigations start building up an effective Hamiltonian, with a simple form and a reduced number of parameters. The effective Hamiltonian is then employed to model the temperature behavior of ferroelectrics by means of classical Monte-Carlo Waghmare and Rabe , molecular dynamics Krakauer et al or quantum Monte-Carlo simulations Zhong and Vanderbilt , Akbarzadeh et al However, methods directly based on the fundamental laws of quantum mechanics and electrostatics i.

Due to steadily increasing computational power and to the development of efficient calculation algorithms, a multitude of materials properties has been determined from first principles, ranging from the microscopic structure to the macroscopic spontaneous polarization. The density functional theory DFT Hohenberg and Kohn , Kohn and Sham is one of the most successful first-principles approaches, and has become the most widely used atomistic method in the field of ferroelectrics.

It led to many breakthroughs in the understanding of the behavior of bulk crystals Vanderbilt , Veithen and Ghosez , Veithen et al , Rabe and Ghosez , Sanna et al c , Friedrich et al , Riefer et al , thin films, surfaces and nanostructures Sai et al , Ghosez and Rabe , Meyer and Vanderbilt , Neaton and Rabe Of particular value for the simulation of ferroelectrics is the implementation of the modern theory of polarization Vanderbilt and King-Smith , King-Smith and Vanderbilt , Resta , nowadays available in all major DFT software packages.

This theory represents the only proper quantum mechanical approach for the calculation of the electronic polarization in periodic solids, and allows for the calculation of key quantities such as such as the spontaneous polarization, the Born effective charges or the piezoelectric tensors. The DFT has also limitations. The number of atoms that can be handled in a first-principles calculation, is currently limited to a few hundred atoms, which imposes serious restrictions to the applicability of pure DFT calculations for the study of, e.

Furthermore, crystal structures and ferroelectric properties of many materials strongly depend on temperature. Quantitatively correct predictions that allow for a direct comparison with the experiment require therefore the estimation of the material properties at finite temperatures, which is in practice unaffordable within DFT. Indeed random thermal vibrations are not accurately described within the small simulation boxes which can be handled in today's calculations.

## surface-science-an-introduction

Despite these limitations, DFT is and remains the most successful tool for the investigation of ferroelectric surfaces, including the surfaces described in this review. Density functional theory is illustrated in detail in many dedicated reviews and will not be discussed in this work for reviews see Payne et al We limit ourselves to discuss some of the technical aspects concerning surface simulation of surfaces within the DFT.

These concern the choice of appropriate structural approach and the development of a consistent thermodynamic framework for the evaluation of the surface stability. Only the last method will be shortly outlined, as the vast majority of the investigations dedicated to LiNbO 3 surfaces were performed within the slab method. The Kohn—Sham equations for an infinite and periodic system are usually solved within the supercell approach. Within this approach, a limited number of primitive cells is employed to model the investigated material, and periodic boundary conditions are applied to mimic the continuum properties of the system Cohen et al This method is very favorable, e.

Unfortunately, surfaces represent a break in the crystal periodicity and are semi-infinite, no 3D-periodic anymore. Yet, it is possible to profit from periodic modeling by separating surfaces within the supercell by a vacuum region supercell slab. The new crystal hence describes a superlattice with an extended unit cell consisting of a slab and a more or less large vacuum region, which can be treated assuming periodic boundary conditions by electronic structure methods.

This approach accounts naturally for the lateral periodicity of surfaces. However, a sufficiently broad vacuum region has to be introduced to decouple the slabs, and a sufficient slab thickness has to be considered to mimic semi-infinite crystals. Most, but by no means all phenomena in surface science are relatively short-ranged normal to the surface, and the surface region can be usually restricted to a few atomic layers.

The number of atomic layers must be carefully tested, depending on the surface property that has to be modeled. Due to particular issues arising with ferroelectric surfaces, somewhat larger values are necessary for the simulation of polar LiNbO 3 surfaces. These will be discussed in the next section, though. In the slab method, two surfaces per unit cell on opposite sides are created see e. For centrosymmetric slabs, the two faces can be made equal. This is not possible, e. However, even in the case of equal, non-polar surface this method introduces some problems, as discussed, e.

In most cases it is preferable to consider the front end of a slab containing the polar surface of interest, and suitably passivate the back surface Shiraishi The passivation is carried out with hydrogen or pseudo-hydrogen atoms with appropriate valence charge. From Sanna et al After passivation, the back of the slab is a perfect, neutral semiconducting surface with corresponding electronic states well below the fundamental band gap. However, two problems remain.

At first, it is not possible to directly calculate the surface formation energy, as one calculates the formation energy of two different surfaces. This issue can be tackled by the energy density formalism Chetty and Martin A second problem is due to the fact that the two slab surfaces are not equivalent and electric fields remain both in the slab and in the vacuum region.

While this problem is a minor issue for non-polar surfaces modelled by thick slabs with large vacuum layers, it becomes crucial in the case of strongly polar surfaces. Possible solutions are discussed in the next section. In the particular case of LiNbO 3 , in which the chemical bonds are partially ionic and partially covalent, it is not easy to determine a proper passivation for the slab's back face. To circumvent this problem Levchenko and Rappe and Sanna and Schmidt c have employed lithium niobate slabs with two terminations and no passivation.

The drawback of this approach is that the two slab surfaces cannot be made equivalent because of lack of centrosymmetry. Thus, no surface free energy can be calculated. However, this approach allows an estimate of relative surface energies, i. The supercell slab is one of the most successful structural models employed in atomistic simulations to model atomic and electronic structures as well as thermodynamic and kinetic behavior of surfaces and interfaces.

Though, in presence of an electric polarization orthogonal to the surface, theoretical models have to deal with an additional problem, the problem of setting the correct electrical boundary conditions Fu et al , Meyer and Vanderbilt The polarization might be either due to an intrinsic bulk spontaneous polarization ferroelectrics or to the formation of a surface reconstruction with a strong dipole moment on a paraelectric bulk.

Periodic boundary conditions are usually applied both to geometries and to the electrostatic or Hartree potential V H to model bulk systems within the supercell approach. This results in a zero macroscopic internal field E , independently from the presence or from the exact value of a spontaneous bulk polarization P S of the modeled material. This situation is illustrated in figure 11 a. Planar averaged electrostatic Hartree potential of ferroelectric LiNbO 3. Any supercell modelling a termination with a non vanishing electrical dipole orthogonal to the surface will originate an electrostatic potential, as sketched in figure 11 b.

As previously discussed, the net dipole moment will be in general the sum of a share due to the bulk polarization and a share due to the surface: This situation corresponds to a surface in the artificial field originating from its neighboring periodic images. Due to the periodic boundary conditions, the electrostatic potential has thereby to be a continuous function, with a slope determined by the magnitude of the supercell.

Hence, neither the internal nor the external field have a direct physical meaning. Indeed, increasing the thickness of the slab or of the vacuum region the artificial fields become smaller, vanishing in the limit of infinitely large supercells with the bulk behavior as in figure 11 a as limiting case of infinite slabs. The error introduced by the artificial field in finite slabs can be accounted for by specifically developed dipole corrections Bengtsson , Neugebauer and Scheffler The correction consists in the application of an external electric dipole in the vacuum region of the supercell, and yields to the scenario sketched in figure 11 c , in which the external electric field E EXT vanishes.

The electrostatic potential is no more a continuous function. However, the discontinuity occurs far from the surface, in the vacuum region, where it is not expected to affect the model. The total macroscopic polarization gives rise to surface polarization charges. Meyer and Vanderbilt argued that the depolarization field E D originating from the surface charges might be large enough to render the ferroelectric configuration instable. This means that the structural relaxation of a ferroelectric slab within the periodic boundary conditions corresponding to zero external field will ineluctably lead to a paraelectric configuration.

In order to tackle this issue, they suggested employing periodic boundary conditions illustrated in figure 11 d , which mimic zero internal field. This boundary condition is equivalent to placing the slabs between the grounded plates of a capacitor short-circuit boundary conditions , and is adequate to model thin film structures, where ferroelectric and dielectric properties are largely dominated by surface effects Meyer and Vanderbilt It should be mentioned that none of the above illustrated periodic boundary conditions for the electrostatic potential is inherently correct and universally applicable.

Vanishing internal field boundaries represent the correct conditions far from the surface and are hence appropriate to model the 'bulk' of thin films. Vanishing external field conditions are the proper boundaries to model the surface itself, instead. Thus, the proper choice of the suitable boundary conditions as discussed above is related the system properties that have to be simulated. Different approaches have been used to model different properties presented in this work.

Surfaces geometries and surfaces charges are modelled within vanishing external field boundaries Sanna et al a. In this case, to prevent the slab to relax into the paraelectric configuration, the central region of the slabs corresponding to 18 atomic layers can be kept frozen into their ferroelectric positions, while the remaining 18 layers as well as the surface terminations are let free to relax see figure 23 and the discussion in section 6.

The surface charge as introduced by equation 1 can be evaluated for the positive and negative z -cut by integrating the planar averaged polarization charge, defined as. In this equation A is the surface unit cell area, and is the charge redistribution upon surface formation, which is calculated as the deviation from the bulk distribution. Hence, the slab is charge neutral and the integral over the whole supercell vanishes.

The definition of Bader atomic volumes and Bader charges Bader is employed to determine z cut as described in Sanna et al a. In order to model molecular adsorption in the physical external field created by the surface polarization charges, dipole corrections are switched off. The latter can be approximated as.

The grand potential is given by equation 5 only in approximate form. Indeed, the surface free energy , where U s is the temperature dependent internal energy should be used instead of the total energy as calculated by DFT. Yet, considering 1 that as for most solids, the direct influence of the pressure variation on the surface free energy is negligible, 2 that the surface formation entropy S s contributes to the surface energy at a certain temperature in similar magnitude for the terminations considered in equation 5 , and 3 that a large compensation of the lattice-dynamical contributions to F s can be assumed.

Accordingly, the free energy can be replaced in first approximation by the internal energy U s. Moreover, as a large compensation of the effects of the zero point vibrations on the internal energy and on the chemical potentials can be assumed, the internal energy U s is commonly substituted by its leading term, the DFT total energy , in actual calculations Bechstedt For the sake of simplicity, we employ as variables in our description of the thermodynamic framework the chemical potential variations.

The thermodynamically allowed range of these variables is limited by certain conditions, which will be discussed in the following. In order to determine the termination with the lowest restricted energy for certain preparation conditions represented by the chemical potentials , one has to compare the Landau potential of different surface models with varying morphology and stoichiometry. Using equation 4 , surface phase diagrams can be calculated, which show the most stable surface i.

Due to the approximations in equation 5 , phase diagrams are affected by not negligible errors. Furthermore, the stability of a given phase with a certain geometry and stoichiometry is not absolute. At finite temperatures, the surface phase with energy per unit cell is formed with a finite probability proportional to.

This probability is furthermore influenced by entropic effects, which affect the relative stability of a the different structures for a given temperature. The same theory that we have introduced to estimate the stability of surface terminations with different stoichiometry and geometry can be employed to estimate the stability of adsorbate structures depending on the preparation conditions.

We illustrate the corresponding formalism using water adsorption as an example. Water molecules are adsorbed at a LiNbO 3 surface in configurations which depend on the water availability. Hence, the thermodynamic Landau potential equation 8 has be used again to compare the relative stability of different surface water structures. Here, N is the number of adsorbed water molecules and is the total energy as calculated by DFT. This is a reasonable approximation of the free energy F , as different adsorption configurations are supposed to yield similar entropy contributions to the free energy.

The surface excess free energy of different water configurations as a function of the water chemical potential can be plotted in phase diagrams, in which the chemical potential represents the experimental conditions. Two representative values of , labeling water in the gas phase ideal gas, i. The availability grows continuously from to , while at each point is in equilibrium with the lithium niobate surface.

The chemical potentials can be then directly transformed in temperature and pressure. Considering , the difference between the water chemical potential and its value in the ice phase , the dependence of on temperature and pressure can be calculated in the approximation of a polyatomic ideal gas Landau and Lifshitz as:. In this equation T and p are the state variables temperature and pressure, respectively, while k B is the Boltzmann constant. In order to obtain the results presented in this work, the experimental values of the momenta of inertia I i and of the vibrational frequencies of the water molecule Laurie and Herschbach have been used.

H 2 O has the form of an equal-sided triangle, and. The chemical potentials in equation 5 are subject to different thermodynamic conditions, which we summarize here. The LiNbO 3 heat of formation is defined as. External organizations can pay for and organize their own high-level scientific and cultural events at ICTP. Travel fellowships for ICTP conferences and workshops are available. Sync your calendar Download records:. Suzie Radosic Organizer s: Luciano Bertocchi Cosponsor s: T17, Fermi Building, terrace level, open three days a week: Monday, Tuesday and Friday, Technology plays a big role in sustainable development in all of its aspects: The recent development of low cost technologies electronic boards, sensors, 3D printing, etc.

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### 1. Introduction

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There is no registration fee. Theory, Experiment and Evaluation smr Address: Petra Krizmancic Organizer s: Claudio Tuniz Cosponsor s: As part of the festivities, we are organizing a two-day workshop 17th and 19th of October which is aimed at reviving the African Physical Society with a focus on discussing about all the great science that is currently going on in the African continent, promoting networking amongst African scientists and setting out a roadmap for the future of science in general in Africa.

This activity will begin with a tribute to Prof. Francis Allotey who passed away last year. Because of citizens like you, we continue to grow each year. If you haven't already, join us to share ideas and engage with open data to address real-world problems, on Earth and in space. Work alone or with a team to solve challenges that could help change the world.

Don't let the name fool you Tackle a challenge using robotics, data visualization, hardware, design and many other specialties! Inspire each other while you learn and create using stories, code, design and, most of all, YOUR ideas. Show us your problem-solving skills and share your talents with the world! Find out more at https: The event starts Saturday morning at 8: Space-Apps Challenge smr Address: Erica Sarnataro Organizer s: Enrique Canessa, Carlo Fonda Cosponsor s: The African School series on Electronic Structure Methods and Applications is planned on a biennial basis from to The School will also cover basic and advanced topics and applications of these methods to the structural, mechanical and optical properties of materials.

The School will include hands-on tutorial sessions based on public license codes including, but not limited to, the Quantum Espresso package. During the second week, students will be asked to split up in teams and work on specific projects under the guidance of the lecturers and mentors. They can also be used to provide climate change information for impact and adaptation studies. With the aim of enlarging and strengthening the RegCM user community, the ICTP organizes a series of training workshops in different regions of the World.

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We never share your information and you can unsubscribe at any time. Recent years have witnessed tremendous progress in the theoretical treatment of surfaces and processes on surfaces. A variety of surface properties can now be described from first principles, i. In this book the theoretical concepts and computational tools necessary and relevant for a microscopic approach to the theoretical description of surface science is presented. Based on the fundamental theoretical entity, the Hamiltonian, a hierarchy of theoretical methods is introduced. Furthermore, a detailed discussion of surface phenomena is given and comparisons made to experimental results made, making the book suitable for both graduate students and for experimentalists seeking an overview of the theoretical concepts in surface science.

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