Within the development of Generation IV Lead-cooled Fast Reactors, corrosion due to heavy liquid metal is still an open issue. In the last decades, great efforts were dedicated to get new insights on such topic. Experiments performed with steel in static and flowing lead with oxygen control highlighted the formation of a double oxide layers on steel surface with a consequently reduction of corrosion rate. In particular, experimental data showed the growth of an external layer of magnetite (Fe3O4) and an internal one of Fe-Cr spinel, however the structure and the composition of such protective oxide is not yet well understood. More recently, exploiting the advances in computational resources and the availability of software packages, some computational studies were reported in literature applying theoretical methods based on Density Functional Theory and Molecular Dynamics to study increasingly larger molecular systems and their properties. The present research work aims at developing a computational approach able to study the structure and composition of the oxide layer at the steel/lead interface, as well as to estimate some thermodynamic properties of the compounds involved. The DFT calculations have been performed with Vienna Ab initio Simulation Package (VASP) using the Projector Augmented Wave (PAW) method. Thermodynamic properties were estimated by means of equations of statistical thermodynamics. The approach was first validated by comparison among computed and experimental values on a set of compounds belonging to the spinel family and considering lattice parameter, enthalpy, entropy and heat capacity as figures of merit. The validation process highlighted the importance of the choice of the exchange-correlation approximation to improve the agreement of the results. As a matter of fact the errors have been reduced up to a range of 0.5-10 %. According to the experimental evidences available in literature and after an optimization of the computational details, the chemical composition of Fe-Cr spinel has been studied by substituting Fe atoms in Fe3O4 with Cr atoms until to obtain FeCr2O4. After geometrical optimization, the evaluation of formation enthalpy has allowed to identify Fe1.5Cr1.5O4 as the most thermodynamically probable compound present in the multi-layer. Furthermore, entropy and heat capacity of the compound of interest as a function of temperature were estimated. Analogous evaluations were attempted on plumboferrite (nPbO-mFe2O3), a more complex compound observed on steel surface in some literature works. Although the increased complexity of calculations, the approach succeeds in the description of crystallographic parameters. An explorative study has been also conducted to evaluate the possibility to computationally investigate diffusion phenomena of the elements in the investigated layers, through Molecular Dynamics. Although the method provides good results when applied to simple structures (iron bulk), the next step will be to extend the application on a more realistic systems with the help of new potential and force field. This thesis work provides still preliminary results since they were obtained under obliged approximations because of the lack of specific value of parameters or experimental data, however the research has well underlined the critical aspects in the computational approach and proposed how to overcome them, leading the way for future developments.
La corrosione da metallo liquido rappresenta ancora un punto critico per quanto riguarda lo sviluppo dei reattori veloci di quarta generazione raffreddati a piombo. Negli ultimi anni, sono stati dedicati molti sforzi per comprendere al meglio tale fenomeno. Numerosi esperimenti condotti in piombo stagnante e fluente hanno evidenziato la formazione di un doppio strato di ossido sulla superficie dell’acciaio con una conseguente riduzione del rateo di corrosione. Nello specifico, i dati sperimentali hanno mostrato la crescita di uno strato esterno di magnetite (Fe3O4) e di uno interno di spinello Fe-Cr, senza però spiegare appieno la struttura e la composizione dello stesso. Più recentemente, grazie alla disponibilità di calcolatori sempre più potenti e software di facile applicazione, sono stati sviluppati studi di tipo computazionale applicando la teoria del funzionale di densità (DFT) e la dinamica molecolare per analizzare fenomeni di corrosione in sistemi molecolari. Il presente lavoro di ricerca ha l’obiettivo di sviluppare un approccio computazionale capace di studiare la struttura e la composizione dello strato di ossido all’interfaccia acciaio/piombo e allo stesso tempo valutarne le proprietà termodinamiche. Le simulazioni DFT sono state condotte mediante il metodo Projector Augmented Wave (PAW) implementato nel codice Vienna Ab initio Simulation Package (VASP) e le proprietà termodinamiche sono state stimate utilizzando le equazioni della termodinamica statistica. L’approccio è stato validato mediante confronto tra dati calcolati e valori sperimentali considerando i composti più comuni appartenenti alla famiglia dello spinello e prendendo come figure di merito il parametro di reticolo, la capacità termica, l’entalpia e l’entropia. Il processo di validazione ha evidenziato l’importanza della scelta della corretta approssimazione della correlazione di scambio per ottenere un risultato in buon accordo col dato sperimentale, portando il range degli errori tra 0.5 % e il 10%. Dopo l’ottimizzazione dei dettagli computazionali, si è studiata la composizione chimica dello spinello Fe-Cr, sostituendo gli atomi di ferro nel composto Fe3O4 con atomi di cromo fino ad ottenere FeCr2O4. Dopo l’ottimizzazione geometrica, la valutazione dell’entalpia di formazione ha permesso di identificare Fe1.5Cr1.5O4 come il composto più probabile dal punto di vista termodinamico nella struttura a più strati. In seguito l’entropia e la capacità termica del composto di interesse sono state valutate in funzione della temperatura. Analoghe valutazioni sono in corso sulla plumboferrite (nPbO-mFe2O3), un composto più complesso che è stato osservato sulla superficie dell’acciaio. Nonostante l’elevata complessità di calcolo, l’approccio ha avuto successo nel descrivere i parametri cristallografici. Uno studio esplorativo è stato condotto inoltre per valutare la possibilità di studiare il fenomeno della diffusione degli elementi attraverso gli strati studiati, applicando la Dinamica Molecolare. Dalla letteratura, il metodo ha mostrato risultati promettenti nello studio di strati semplici, come la diffusione di Fe dovuta alla presenza del piombo attraverso un bulk di ferro. Il passo successivo sarà quello di estendere il metodo a strutture più vicine a quelle realistiche, come per esempio l’acciaio. In conclusione, i risultati del presente lavoro di tesi hanno ancora carattere preliminare, in quanto sono stati ottenuti introducendo approssimazioni a causa della mancanza di specifici valori per i parametri o di dati sperimentali. La ricerca svolta ha però sottolineato gli aspetti critici dell’approccio computazionale e prospettato possibili soluzioni, aprendo la strada a sviluppi futuri.
Computational study of steel corrosion by heavy liquid metal in lead-cooled fast reactors
CERVINO, STEFANO MATTEO
2015/2016
Abstract
Within the development of Generation IV Lead-cooled Fast Reactors, corrosion due to heavy liquid metal is still an open issue. In the last decades, great efforts were dedicated to get new insights on such topic. Experiments performed with steel in static and flowing lead with oxygen control highlighted the formation of a double oxide layers on steel surface with a consequently reduction of corrosion rate. In particular, experimental data showed the growth of an external layer of magnetite (Fe3O4) and an internal one of Fe-Cr spinel, however the structure and the composition of such protective oxide is not yet well understood. More recently, exploiting the advances in computational resources and the availability of software packages, some computational studies were reported in literature applying theoretical methods based on Density Functional Theory and Molecular Dynamics to study increasingly larger molecular systems and their properties. The present research work aims at developing a computational approach able to study the structure and composition of the oxide layer at the steel/lead interface, as well as to estimate some thermodynamic properties of the compounds involved. The DFT calculations have been performed with Vienna Ab initio Simulation Package (VASP) using the Projector Augmented Wave (PAW) method. Thermodynamic properties were estimated by means of equations of statistical thermodynamics. The approach was first validated by comparison among computed and experimental values on a set of compounds belonging to the spinel family and considering lattice parameter, enthalpy, entropy and heat capacity as figures of merit. The validation process highlighted the importance of the choice of the exchange-correlation approximation to improve the agreement of the results. As a matter of fact the errors have been reduced up to a range of 0.5-10 %. According to the experimental evidences available in literature and after an optimization of the computational details, the chemical composition of Fe-Cr spinel has been studied by substituting Fe atoms in Fe3O4 with Cr atoms until to obtain FeCr2O4. After geometrical optimization, the evaluation of formation enthalpy has allowed to identify Fe1.5Cr1.5O4 as the most thermodynamically probable compound present in the multi-layer. Furthermore, entropy and heat capacity of the compound of interest as a function of temperature were estimated. Analogous evaluations were attempted on plumboferrite (nPbO-mFe2O3), a more complex compound observed on steel surface in some literature works. Although the increased complexity of calculations, the approach succeeds in the description of crystallographic parameters. An explorative study has been also conducted to evaluate the possibility to computationally investigate diffusion phenomena of the elements in the investigated layers, through Molecular Dynamics. Although the method provides good results when applied to simple structures (iron bulk), the next step will be to extend the application on a more realistic systems with the help of new potential and force field. This thesis work provides still preliminary results since they were obtained under obliged approximations because of the lack of specific value of parameters or experimental data, however the research has well underlined the critical aspects in the computational approach and proposed how to overcome them, leading the way for future developments.| File | Dimensione | Formato | |
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https://hdl.handle.net/10589/134067