Computational modelling of boron nitride nanostructures based on density-functional tight-binding

Boorinitridin (BN) nanorakenteet ovat sekä rakenteellisesti että lujuusominaisuuksiensa puolesta hyvin samankaltaisia vastaavien hiilirakenteiden kanssa. Suurimpana erona on BN:n sähköinen eristävyys kun taas hiilirakenteet ovat johteita tai puolijohteita. BN onkin hyvin lupaava nanomateriaali ja si...

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Main Author: Nokelainen, Johannes
Other Authors: Matemaattis-luonnontieteellinen tiedekunta, Faculty of Sciences, Fysiikan laitos, Department of Physics, University of Jyväskylä, Jyväskylän yliopisto
Format: Master's thesis
Language:eng
Published: 2014
Subjects:
Online Access: https://jyx.jyu.fi/handle/123456789/44495
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author Nokelainen, Johannes
author2 Matemaattis-luonnontieteellinen tiedekunta Faculty of Sciences Fysiikan laitos Department of Physics University of Jyväskylä Jyväskylän yliopisto
author_facet Nokelainen, Johannes Matemaattis-luonnontieteellinen tiedekunta Faculty of Sciences Fysiikan laitos Department of Physics University of Jyväskylä Jyväskylän yliopisto Nokelainen, Johannes Matemaattis-luonnontieteellinen tiedekunta Faculty of Sciences Fysiikan laitos Department of Physics University of Jyväskylä Jyväskylän yliopisto
author_sort Nokelainen, Johannes
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description Boorinitridin (BN) nanorakenteet ovat sekä rakenteellisesti että lujuusominaisuuksiensa puolesta hyvin samankaltaisia vastaavien hiilirakenteiden kanssa. Suurimpana erona on BN:n sähköinen eristävyys kun taas hiilirakenteet ovat johteita tai puolijohteita. BN onkin hyvin lupaava nanomateriaali ja sille on odotettavissa sovelluksia muun muassa muiden nanorakenteiden suojaajana ja komposiittimateriaalien nanokudosaineena. BN:n nanorakenteiden ominaisuuksia tutkitaan laskennallisesti yleensä joko tiheysfunktionaaliteorialla (DFT) tai tiukan sidoksen (TB) malleilla. Ensin mainittu on tarkka mutta laskennallisesti vaativa, kun taas jälkimmäinen on laskennallisesti kevyt mutta epätarkka. Tässä työssä esittelen näiden teorioiden yhdistämisen tiukan sidoksen tiheysfunktionaaliteoriaksi (DFTB) ottaen huomioon myös tiheysfluktuaatioissa toista kertalukua olevan energiatermin. Seurauksena on huomattavasti DFT:tä nopeampi ja TB:tä laskennallisesti tarkempi teoria. Se kuitenkin vaatii ennalta määritettäviä parametreja. Ensinnäkin on laskettava tiukan sidoksen mallista periytyvät S- ja H-matriisielementit, jotka liittyvät systeemin atomiorbitaalien keskinäiseen limittäytyneisyyteen ja ominaisenergioihin. Lisäksi atomiydinten väliset repulsiopotentiaalit on määritettävä. Niiden kohdalla johtava ajatus on pyrkiä hienosäätämään ne sellaisiksi, että DFT:n ja DFTB:n tulokset vastaisivat toisiaan mahdollisimman hyvin mahdollisimman monessa relevantissa tilanteessa. Esittelen myös määrittämäni parametrisaation BN:lle ja sitä käyttäen laskemani tulokset sekä virheettömien että vaurioituneiden BN-tasojen ja -nano-putkien ominaisuuksille. BN-tasojen kohdalla tutkimani vauriot ovat B-, N- ja BN-vakansseja ja nanoputkien kohdalla Stone-Wales -virheitä. Saamani virheettömien rakenteiden elektronirakenteet ovat suhteellisen lähellä vastaavia DFT-tuloksia, samoin kuin vaurioituneiden rakenteiden muodostumisenergiat. Vaurioitumattomien rakenteiden kimmokertoimet ja kaikkien tutkittujen systeemien rakenteelliset ominaisuudet vastaavat viitetuloksia pääosin hyvin. Sen sijaan elastiset Poissonin suhteet eroavat merkittävästi DFT-viitearvoista. Kaiken kaikkiaan parametrisaationi on siis kykeneväinen suhteellisen hyviin tuloksiin. Parantamisen varaa kuitenkin on, sillä aikaisemman BN-parametrisoinnin tulokset ovat huomattavasti lähempänä DFT:n tuloksia ainakin nanoputkien tapauksessa. Minun olisi luultavasti erityisesti tullut käyttää useampia rakenteita, joissa varmistin DFTB:n ja DFT:n yhteensopivuuden. Boron nitride (BN) nanostructures are both structurally and elastically very similar to the corresponding carbon structures. The major difference is that BN is a wide bandgap insulator whereas carbon structures are either conductors or semiconductors. Therefore BN is a highly promising nanomaterial and it is expected to have applications in nanotechnology e.g. as encapsulating nanomaterials and nanofillers in composite materials. Properties of BN nanostructures are usually computationally researched either with the density-functional theory (DFT) or tight-binding (TB) models. The former is accurate but computationally demanding whereas the latter is computationally light but inaccurate. In this work I shall present combinination of these two theories into tight-binding density-functional theory (DFTB). I also take into account the energy term that is in the second order in density fluctuations. The resultant theory is significantly more accurate than TB and computationally faster than DFT. However, it includes parameters that have to be determined in advance. Firstly, it is needed to compute the TB-inherited S- and H-matrix elements related to overlaps and eigenenergies of atomic orbitals of the system. Secondly, the repulsion potentials between the nuclei must be determined. The idea behind them is to fine tune them in such a way that DFT and DFTB results are in correspondence in as many relevant situations as possible. I also shall present the BN parametrization determined by me and the computational results obtained with it for properties of both perfect and defected BN layers and nanotubes. In the case of BN layers the studied defects are B-, N- and BN-vacancies and in the case of nanotubes Stone-Wales defects. The obtained electron structures for undefected structures as well as the formation energies of defects are in relatively good accordance with the corresponding DFT results. The Young's moduli of perfect structures and agree well with the reference results. However, the elastic Poisson's ratios contradict strongly with the DFT references. All in all my parametrization is capable of producing sufficiently good results. However, there are room for improvement, as results of an earlier BN parametrization are notably closer to the DFT results at least in the case of nanotubes. I most likely should have used more reference structures where I ensured the consistence of DFTB and DFT.
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Suurimpana erona on BN:n s\u00e4hk\u00f6inen erist\u00e4vyys kun taas hiilirakenteet ovat johteita tai puolijohteita. BN onkin hyvin lupaava nanomateriaali ja sille on odotettavissa sovelluksia muun muassa muiden nanorakenteiden suojaajana ja komposiittimateriaalien nanokudosaineena.\n\nBN:n nanorakenteiden ominaisuuksia tutkitaan laskennallisesti yleens\u00e4 joko tiheysfunktionaaliteorialla (DFT) tai tiukan sidoksen (TB) malleilla. Ensin mainittu on tarkka mutta laskennallisesti vaativa, kun taas j\u00e4lkimm\u00e4inen on laskennallisesti kevyt mutta ep\u00e4tarkka. T\u00e4ss\u00e4 ty\u00f6ss\u00e4 esittelen n\u00e4iden teorioiden yhdist\u00e4misen tiukan sidoksen tiheysfunktionaaliteoriaksi (DFTB) ottaen huomioon my\u00f6s tiheysfluktuaatioissa toista kertalukua olevan energiatermin. Seurauksena on huomattavasti DFT:t\u00e4 nopeampi ja TB:t\u00e4 laskennallisesti tarkempi teoria. Se kuitenkin vaatii ennalta m\u00e4\u00e4ritett\u00e4vi\u00e4 parametreja. Ensinn\u00e4kin on laskettava tiukan sidoksen mallista periytyv\u00e4t S- ja H-matriisielementit, jotka liittyv\u00e4t systeemin atomiorbitaalien keskin\u00e4iseen limitt\u00e4ytyneisyyteen ja ominaisenergioihin. Lis\u00e4ksi atomiydinten v\u00e4liset repulsiopotentiaalit on m\u00e4\u00e4ritett\u00e4v\u00e4. Niiden kohdalla johtava ajatus on pyrki\u00e4 hienos\u00e4\u00e4t\u00e4m\u00e4\u00e4n ne sellaisiksi, ett\u00e4 DFT:n ja DFTB:n tulokset vastaisivat toisiaan mahdollisimman hyvin mahdollisimman monessa relevantissa tilanteessa.\n\nEsittelen my\u00f6s m\u00e4\u00e4ritt\u00e4m\u00e4ni parametrisaation BN:lle ja sit\u00e4 k\u00e4ytt\u00e4en laskemani tulokset sek\u00e4 virheett\u00f6mien ett\u00e4 vaurioituneiden BN-tasojen ja -nano-putkien ominaisuuksille. BN-tasojen kohdalla tutkimani vauriot ovat B-, N- ja BN-vakansseja ja nanoputkien kohdalla Stone-Wales -virheit\u00e4. 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Minun olisi luultavasti erityisesti tullut k\u00e4ytt\u00e4\u00e4 useampia rakenteita, joissa varmistin DFTB:n ja DFT:n yhteensopivuuden.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Boron nitride (BN) nanostructures are both structurally and elastically very similar to the corresponding carbon structures. The major difference is that BN is a wide bandgap insulator whereas carbon structures are either conductors or semiconductors. Therefore BN is a highly promising nanomaterial and it is expected to have applications in nanotechnology e.g. as encapsulating nanomaterials and nanofillers in composite materials.\n\nProperties of BN nanostructures are usually computationally researched either with the density-functional theory (DFT) or tight-binding (TB) models. The former is accurate but computationally demanding whereas the latter is computationally light but inaccurate. 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spellingShingle Nokelainen, Johannes Computational modelling of boron nitride nanostructures based on density-functional tight-binding boron nitride BN nanotubes density-functional tight-binding DFTB density-functional theory DFT Teoreettinen fysiikka Theoretical Physics 4024 nanorakenteet
title Computational modelling of boron nitride nanostructures based on density-functional tight-binding
title_full Computational modelling of boron nitride nanostructures based on density-functional tight-binding
title_fullStr Computational modelling of boron nitride nanostructures based on density-functional tight-binding Computational modelling of boron nitride nanostructures based on density-functional tight-binding
title_full_unstemmed Computational modelling of boron nitride nanostructures based on density-functional tight-binding Computational modelling of boron nitride nanostructures based on density-functional tight-binding
title_short Computational modelling of boron nitride nanostructures based on density-functional tight-binding
title_sort computational modelling of boron nitride nanostructures based on density functional tight binding
title_txtP Computational modelling of boron nitride nanostructures based on density-functional tight-binding
topic boron nitride BN nanotubes density-functional tight-binding DFTB density-functional theory DFT Teoreettinen fysiikka Theoretical Physics 4024 nanorakenteet
topic_facet 4024 BN DFT DFTB Teoreettinen fysiikka Theoretical Physics boron nitride density-functional theory density-functional tight-binding nanorakenteet nanotubes
url https://jyx.jyu.fi/handle/123456789/44495 http://www.urn.fi/URN:NBN:fi:jyu-201410283114
work_keys_str_mv AT nokelainenjohannes computationalmodellingofboronnitridenanostructuresbasedondensityfunctionaltig