In this dissertation the formation of precipitates in steel is studied.
In the first chapter some theoretical background is presented to the topic.
Then in the second chapter an analytical approximation to the classical nucleation and growth model is presented.
In the third chapter a reference-free modified embedded atom method (RF-MEAM) potential is constructed for Fe, suitable for ferrite and austenite.
In chapter four the formation of Nb-C and Ti-C clusters in ferrite is studied, here formation paths with a monotone decrease in Gibbs energy are found. Moreover, the resulting clusters remain stable up to 1100K.
In the fifth chapter other group IV and V transition metal-carbon systems in ferrite are studied in small cells using density functional theory. Showing similar energy patterns as previously found for Nb and Ti. Furthermore the transformation from a metal-carbon cluster to a carbide precipitate is studied, where the matrix strain is found to be the driving force behind the transformation.
in the sixth and last chapter some recommendations are presented.@en

Carbide nano-precipitates are commonly used to improve mechanical properties of steel. It has been experimentally observed that TiC, NbC, and VC carbide precipitates initially form as ‘plate-like’ particles oriented in the {1 0 0} planes of the ferrite lattice. These platelets share similarities with Guinier-Preston zones in Al-Cu alloys. The clustering of group IV and V transition metal atoms (M = Ti, Zr, Hf, V, Nb, Ta) in ferrite is studied using density functional theory. It is deduced that the transition metal carbides all form in a similar way. Furthermore, the transition from an initial M–C cluster to a NaCl-structured platelet to a NaCl-structured precipitate is examined through atomistic simulations using Modified Embedded Atom Method potentials. A route is established along which transition metal carbides form and transform into precipitates that possess the Baker-Nutting orientation relation with the ferrite matrix.

@en

In this study possible routes from dissolved M and C atoms to a M-C (M = Ti, Nb) cluster are studied. Using atomistic modelling to perform relaxation simulations and molecular dynamics (MD) simulations for the Fe-M-C ternary system, the formation of clusters is studied for M. Additionally the stability of M-C clusters is assessed. The clustering of M and C atoms as observed in experiments is also found in simulations. The initial clusters found in this work have a (Fe,M)C composition with a large Fe fraction. Moreover, structurally relaxed clusters reveal that there are growth pathways with a monotone decrease in Gibbs energy, suggesting that the highest energy barrier in the formation of M-C clusters is the diffusion barrier for the atoms forming the cluster. The development of M-C clusters as found in this study suggests a formation mechanism for nano-precipitation of carbides consisting of several steps; first a C cluster forms, then M atoms attach to the C cluster forming a (Fe,M)C cluster, and in the final step the (Fe,M)C cluster transforms to a NaCl-structured carbide.

@en

A reference-free modified embedded atom method (RF-MEAM) potential for iron has been constructed. The new potential is made to predict both bcc and fcc (α-Fe and γ-Fe) lattice properties, with a special interest in modelling in the 800-1300 K temperature range. This is the range in which transformations and key processes in steel occur. RF-MEAM potentials can be used directly in commonly used molecular dynamics simulation software (e.g. LAMMPS). The new potential is compared to several other (M)EAM potentials which are commonly used. It is demonstrated that the new potential combines good characteristics for point defect energies with free surface and stacking fault energies. Also the Nishiyama-Wassermann and Kurdjumov-Sachs orientation relation ratios and interface energies are reproduced, allowing for simulations of α-Fe and γ-Fe interphases.

@en

A new approximation to the equations describing Classical Nucleation and Growth Theories, is proposed providing quick, and intuitive insight. It gives a prediction of the mean precipitate radius and number density development under quasi-isothermal conditions. Current “mean-radius”, and “multi-class” approaches to modelling classical nucleation and growth theory for precipitation, require considerable computation times. An analytical approximation is proposed to solve the equations, and its results are compared to numerical simulations for quasi-isothermal precipitation. From the approximation a start and end time for the nucleation stage is predicted, as well as a time at which growth occurs and when the coarsening stage starts. Ultimately, these times, outline the numerical solution to the precipitation trajectory, providing key insight before performing numerical simulations. This insight can be used to more efficiently simulate precipitate development, as time scales at which the various stages in precipitate development occur can be predicted for individual precipitates. When these time scales are known a numerical simulation can be used for a specific goal, for instance to only simulate nucleation and growth, thus saving computational time. Moreover, for a first indication of the precipitate development in a composition under a particular heat treatment a numerical simulation is no longer necessary. This is also useful for process control as consequences of changes in treatment can be assessed on-line. Using these approximate analytical results an estimate can be made for the matrix concentration of precipitate forming elements. Additionally some dimensionless parameters are established to provide intuitive details to the precipitation trajectory.@en

We analyze quantum effects occurring in optomechanical systems where the coupling between an optical mode and a mechanical mode is quadratic in displacement (membrane-in-the-middle geometry). We show that it is possible to observe quantum effects in these systems without achieving the single-photon strong-coupling regime. We find that zero-point energy causes a mechanical frequency shift, and we propose an experimental way to measure it. Further, we show that it is possible to determine the phonon statistics from the cavity transmission, and propose a way to infer the resonator temperature based on this feature. For completeness, we revisit the case of an isolated system and show that different types of mechanical quantum states can be created, depending on the initial cavity state. In this situation, mechanical motion undergoes collapse and revival, and we compute the collapse and revival times, as well as the degree of squeezing.

@en