Max Planck Institutes for Intelligent Systems & Solid State Research Library

Phase diagrams are used in materials research and engineering to understand the interrelationship between composition, microstructure and process conditions. In complex systems, computational methods such as CALPHAD are employed to model thermodynamic properties for each phase and simulate multicomponent phase behavior. Written by recognized experts in the field, this is an introductory guide to the CALPHAD method, providing a theoretical and practical approach. Building on core thermodynamic principles, this 2007 book applies crystallography, first principles methods and experimental data to computational phase behavior modeling using the CALPHAD method. With a chapter dedicated to creating thermodynamic databases, the reader will be confident in assessing, optimizing and validating complex thermodynamic systems alongside database construction and manipulation. Several case studies put the methods into a practical context, making this suitable for use on advanced materials design and engineering courses and an invaluable reference to those using thermodynamic data in their research or simulations.

Proximity-induced superconductivity in single-walled carbon nanotubes below 1 kelvin, both in a single tube 1 nanometer in diameter and in crystalline ropes containing about 100 nanotubes, was observed. The samples were suspended between two superconducting electrodes, permitting structural study in a transmission electron microscope. When the resistance of the nanotube junction is sufficiently low, it becomes superconducting and can carry high supercurrents. The temperature and magnetic field dependence of the critical current of such junctions exhibits unusual features related to their strong one-dimensional character.

Tunneling of electrons traversing a few-electron quantum dot is strongly influenced by the Coulomb interaction leading to Coulomb blockade effects and single-electron tunneling. We present calculations which demonstrate that correlations between the electrons cause a strong suppression of most of the energetically allowed tunneling processes involving excited dot states. The excitation of center-of-mass modes, in contrast, is unaffected by the Coulomb interaction. Therefore, channels connected to these modes dominate the excitation spectra in transport measurements.

The use of cleaning instruments on titanium implants may cause undesired surface alterations. In a qualitative and quantitative assessment of these alterations, 5 titanium implant abutments were treated with a steel curet, a prototype pure titanium curet, an air abrasive polishing system, and an ultrasonic system. Custom-made polymer templates, used to secure the curet to a vertical guide bar and a spring scale to maintain a constant instrument pressure, guaranteed a standardized procedure and reproducible results. The ultrasonic and the air abrasive polishing method were also standardized. Evaluation by scanning electron microscopy (SEM) revealed surface alterations for all instruments and systems except the plastic curet, which did not roughen the surface at all. The confocal laser-scanning microscope allows a 3-dimensional reproduction of these surface alterations and their direct measurement. The profilometric tracing was not sensitive enough to register the minor effects caused by the titanium curet and the air abrasive polishing system. Dimensions of the resulting surface microstructure could be determined with the laser-scanning microscope. Since the influence of such surface defects on the peri-implant tissue reaction is unpredictable, the titanium curet and the air abrasive system can only be recommended with restrictions. The steel curet and the ultrasonic system proved to be totally unsuitable for cleaning titanium implants.

The far-infrared absorption of a two-dimensional electron gas with a square-lattice modulation in a perpendicular constant magnetic field is calculated self-consistently within the Hartree approximation. For strong modulation and short period we obtain intrasubband and intersubband magnetoplasmon modes reflecting the subbands of the Hofstadter butterfly in two or more Landau bands. The character of the absorption and the correlation of the peaks to the number of flux quanta through each unit cell of the periodic potential depends strongly on the location of the chemical potential with respect to the subbands, or equivalently, on the density of electrons in the system.

Starting the assessment In chapter 5, various models were described in order to understand how they can be fitted to the experimental features that were described in chapter 4. In the present chapter, we start from experimental evidence and search for the model best able to describe it. Therefore many topics of chapter 5 will be revisited here. An assessor working on a system will experience almost all the steps described and discussed here. Since a system is often reassessed many times, by the same researcher or by another, it is very important to keep records about the decisions made in order to make it easy to restart the work, for example, when new experimental evidence requires a new optimization. The process of assessing a system is made easier if an assessment logbook is kept. An important function of this logbook is that one should record all mistakes and failures so that one does not repeat them later. In the final paper only the sucessful modeling will be reported and there is no information about the difficulties encountered in obtaining it. The assessment methodology described here includes a critical assessment of the available literature in the way in which it is normally done, for example, in the Journal of Phase Equilibria and Diffusion . By combining this with thermodynamic models, an analytical description is created and the determination of adjustable model parameters is often done using the least-squares method to obtain a description that represents best the complete set of available consistent experimental data.

It is found that at a critical value of the magnetic field in which a system of composite fermions becomes completely spin-polarized, the temperature dependence of the electronic spin polarization is a linear function at low temperatures. It is shown that the slope of this dependence is determined by the Fermi energy of the composite fermions. This made it possible to measure the Fermi energy and the Zeeman splitting of the composite fermions. A large amplification of the spin splitting of composite fermions for complete spin polarization of the system is found. This makes it possible to measure the strength of the interaction between composite fermions.

We have for the first time measured the elastic properties (sound velocity and internal friction) of glasses below 1K in the audiofrequency range (∼ 1 KHz). The results obtained are discussed in the frame work of the tunneling model of glasses. The major assumption of the tunneling model regarding tunneling states with long relaxation times has been verified.

We show that within the extended pair approximation (EPA) the transition rate of Miller and Abrahams accounts better for the behaviour of σ (T, ω) et de σDC (T) than that given by Kivelson.

Digital imaging and analysis methods are applied to the quantitative study of microstructural changes which occur during hot‐pressing of yttria‐doped silicon nitride. Effects of processing changes upon the grain growth and microstructural anisotropy are described. Relationships between grain cross‐sectional area and mechanical properties are established. It was found that, over the range of processing conditions used, increases in grain size correlated strongly with an increase in fracture toughness. The grain size distribution broadened significantly with hot‐press time, resulting in reduced flexural strength. Although no significant change in the mean grain shape factor was observed, the variance in shape factor decreased as the hot‐press time was extended.

Starting from extensive simulations of photon emission by channeled electrons in tungsten crystals, a test experiment has been proposed. It concerns a 2 GeV electron beam impinging on a 1 mm tungsten crystal oriented along itsaxis. Radiation measurements are ensured by a preshower detector followed by a lead-plexiglas calorimeter. Channeling data are compared to those obtained for random incidence. They can be associated with simulations using shower codes (GEANT) for estimating performances of positron sources based on this principle.>

In this paper a short review of our results on the synthesis of nanosized CeO2, CaMnO3 and BaCeO3 solid solutions are presented. The nanopowders were prepared by two innovative methods: self propagating room temperature synthesis (SPRT) and modified glycine/nitrate procedure (MGNP). Different types of solid solutions with rare earth dopants in concentrations ranging from 0-0.25 mol% were synthesized. The reactions forming solid solutions were studied. In addition, the characteristics of prepared nanopowders, phenomena during sintering and the properties of sintered samples are discussed.

In the previous chapters it has been shown how to obtain the best possible agreement between thermodynamic models and experimental data using adjustable model parameters for binary and ternary systems. Even if each such assessment can be very important by itself, the main purpose of these assessments is to provide the building blocks of multicomponent thermodynamic databases. This objective must be considered when performing an assessment because it imposes some restrictions on the assessment of the individual system and on the possibilities of adjusting data and models to new experimental data. Such problems will be discussed in this chapter, together with the general concepts concerning thermodynamic databases. Experience has shown that thermodynamic databases based on a limited number of ternary assessments, all centered around a “base” element like Fe or Al, can give reliable extrapolations to multicomponent alloys based on that element. This means that the database can be used to calculate the amounts of phases, their compositions, and transformation temperatures and that the calculated values have an accuracy close to that of an experimental measurement. Such databases are a very valuable tool for planning new experimental work in alloy development, since detailed experimental investigations of multicomponent systems are very expensive to perform. It is important that the databases are based on ternary assessments, not just binaries, because the mutual solubilities in binary phases must be described, otherwise the extrapolations are not reliable.

In this chapter a number of models for the thermodynamic properties of various phases will be described. The integral Gibbs energy will be used as the modeled thermodynamic property. The reason to model the Gibbs energy rather than any other thermodynamic function is that most experiments are done at constant temperature and pressure. From the Gibbs energy all other important quantities can be obtained according to Eqs. (2.12). Using the Gibbs energy means that the modeling is limited to a “mean-field” approximation. Thermodynamic calculations using “Monte Carlo” methods or “molecular dynamics” are outside the scope of this presentation, but these techniques can provide important information about the type of mean-field model to be selected. A phase may sometimes have a particular physical or chemical feature that requires a special model in order for it to be described accurately. It is not uncommon that the mathematical expression for such a model may be identical to the expression derived to describe another physical feature. That simply means that the mathematical expression is more general than the physical model. Whenever such a generalized expression can be obtained, it will be called a formalism . A general formalism should be able to handle cases when various constituents added to a phase behave differently, for example some may dissolve interstitially or cause chemical ordering. Most of the models used in this book are special cases of the compound-energy formalism (CEF).

Promising cathode materials for fluoride-ion batteries (FIBs) are 3d transition metal containing oxides with Ruddlesden-Popper-type structure. So far, multi-elemental compositions were not investigated, but could alternate electrochemical performance similar to what had been found for cathode materials for lithium-ion batteries. Within this study, we investigate RP type La2Ni0.75Co0.25O4.08 as an intercalation-based active cathode material for all-solid-state FIBs. We determine the structural changes of La2Ni0.75Co0.25O4.08 during fluoride intercalation / de-intercalation by ex-situ X-ray diffraction, which showed that F- insertion leads to transformation of the parent phase to three different phases. Changes in Ni and Co oxidation states and coordination environment were examined by X-ray absorption spectroscopy and magnetic measurements in order to understand the complex reaction behaviour of the phases in detail, showing that the two transition metals behave differently in the charging and discharging process. Under optimized operating conditions, a cycle life of 120 cycles at a critical cut-off capacity of 40 mAh g-1 against Pb/PbF2 was obtained, which is one of the highest observed for intercalation electrode materials in FIBs so far. The average Coulombic efficiencies ranged from 85% to 90%. Thus, La2Ni0.75Co0.25O4.08 could be a promising candidate for cycling-stable high-energy cathode materials for all-solid-state FIBs

The Calphad technique has reached maturity. It started from a vision of combining data from thermodynamics, phase diagrams, and atomistic properties such as magnetism into a unified and consistent model. It is now a powerful method in a wide field of applications where modeled Gibbs energies and derivatives thereof are used to calculate properties and simulate transformations of real multicomponent materials. Chemical potentials and the thermodynamic factor (second derivatives of the Gibbs energy) are used in diffusion simulations. The driving forces of the phases are used to simulate the evolution of microstructures on the basis of the Landau theory. In solidification simulations the fractions of solid phases and the segregation of components, as well as energies of metastable states, which are experimentally observed by carrying out rapid solidification, are used. Whenever the thermodynamic description of a system is required, the Calphad technique can be applied. The successful use of Calphad in these applications relies on the development of multicomponent databases, which describe many different kinds of thermodynamic functions in a consistent way, all checked to be consistent with experimental data. The construction of these databases is still a very demanding task, requiring expertise and experience. There are many subjective factors involved in the decisions to be made when judging and selecting which among redundant experimental data are the most trustworthy. Even more subjective is the assessment of phases of which little or nothing is known, except perhaps in a narrow composition and temperature range.

Bilbao crystallographic server, http://www.cryst.ehu.es Crystal Lattice Structures website, http://cst-www.nrl.navy.mil/lattice International Union of Crystallography, http://www.iucr.org MICRESS phase field software, http://www.micress.de SGTE website, http://www.sgte.org Sluiter enthalpy database, http://www-lab.imr.edu/~marcel/enthalpy/enthlp.html Thermo-Calc Software AB, http://www.thermocalc.com Widom alloy database, http://alloy.phys.cmu.edu/

In this chapter, two of the most commonly used types of software for optimization, BINGSS and PARROT, are described. Common features Handling bad starting coefficients The definition of the “error” ( v i in Eq. (2.52)) is based on the “calculated value” ( F i ( C j , x ki )), which is often defined by an equilibrium calculation with two or more phases. The initial set of adjustable coefficients may result in improper Gibbs-energy functions, with which this equilibrium cannot be calculated. As an example, in Fig. 7.1 such a situation is shown for a two-phase equilibrium, liquid + bcc. There G bcc at all compositions is larger than G liquid and the construction of a common tangent is impossible, so also no equilibrium can be calculated numerically. The experimental information is either “at temperature T 1 there is a two-phase equilibrium, liquid + bcc, for which the composition of the bcc phase was measured as ( x bcc = x ′)” or “in a single-phase bcc sample of composition x ′ on heating the first liquid appears at temperature T 1 ” (see Fig. 4.4). In the least-squares calculation for Eq. (2.52) no “calculated value” ( F i ( C j , x ki )) can be provided as long as the starting values for the Gibbs-energy descriptions of liquid and bcc phases behave as in Fig. 7.1. To find better starting values by trial and error is not easy and is time-consuming. Therefore it is desirable to have a method whereby this problem is avoided and that can start even with a very bad initial set of adjustable coefficients.

There is a description since several decades ago those insects have evolved that an extra lift is obtained due to the rotational and translational mechanism especially during stroke reversals. Nonetheless, this issue is strongly depending on the consequences of the wing stroke kinematics prescribed. Another issue to be concerned is the inertial force created due to the rapid acceleration or deceleration by its own distributed mass. Most people found that the force exerted to the insect’s wing mostly comes from the inertial force but no one has been able to list down all the reacted forces including aerodynamic force, Magnus force and added mass effect. Subsequently, a simulation model will be made to integrate all the relevant forces in term of magnitude and direction to find a clean single force named as a resultant force. Several years ago, majority of the wing deformation analysis discussed are base on the certain forces and none of them analyze it by considering all the forces which possibly involved. Therefore, the deformation characteristics will be calculated based on the elemental stiffness data depends on the pattern of supporting three dimensional insect's wing architecture that will be subjected to all the forces which perhaps involved. The resultant force will be accurately dispersed in spanwise direction according to chord length and the wing mass distribution in order to obtain an accurate wing deformation characteristic depending on local wing’s flexural stiffness.

Abstract not Available.