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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
21

Structural, vibrational and morphological properties of La2CoMnO6 multiferroics films / Propriedades estruturais, vibracionais e morfolÃgicas de filmes multiferrÃicos de La2CoMnO6.

Antonio Vinnie dos Santos Silva 10 June 2016 (has links)
Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / FundaÃÃo Cearense de Apoio ao Desenvolvimento Cientifico e TecnolÃgico / FundaÃÃo de Amparo à Pesquisa e ao Desenvolvimento CientÃfico e TecnolÃgico do MaranhÃo / CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / Perovskitas duplas com fÃrmula na forma A2BBâO6 (A = La, Sr, Ca, B/Bâ = Co/Mn ou Fe/Mo) sÃo materiais multiferrÃicos de grande interesse na ciÃncia devido Ãs notÃveis propriedades, que permitem aplicaÃÃes em capacitores e em memÃrias, por exemplo. AlÃm disso, mudanÃas estruturais sÃo observadas entre a forma policristalina e o filme fino. Essas propriedades podem mudar de acordo com a rota utilizada para sintetizaÃÃo do material. No nosso trabalho estudamos filmes de La2CoMnO6 sintetizados pelo mÃtodo de Pechini Modificado (MPM), com trÃs deposiÃÃes e tratados em diferentes temperaturas: 700, 800 e 900 ÂC. Os filmes foram caracterizados por difraÃÃo de raios X, Microscopia EletrÃnica de Varredura (MEV), Microscopia de ForÃa AtÃmica e espectroscopia Raman à temperatura ambiente e tambÃm variando a temperatura. As tÃcnicas de MEV e AFM foram bastante eficientes na determinaÃÃo do diÃmetro mÃdio dos filmes, fornecendo resultados correspondentes. A tÃcnica de EDS trouxe dados qualitativos da composiÃÃo do material. A difraÃÃo de Raios X confirmou a fase do filme, alÃm de ter identificado a composiÃÃo do substrato: silÃcio e platina. A espectroscopia Raman em diversos pontos possibilitou identificar a regiÃo de melhor formaÃÃo do LCMO. O estudo da mudanÃa do fÃnon mais intenso com a temperatura mostrou diferentes temperaturas para a transiÃÃo de fase paramagnÃtica-ferromagnÃtica, possibilitando confirmar que a temperatura de calcinaÃÃo dos filmes determinou elevada desordem estrutural para os filmes de LCMO tratados a 700 e 900 ÂC. Discutimos nossos resultados com outros estudos na literatura, que mostram as medidas magnÃticas como um fator determinante para comprovar a temperatura do acoplamento spin-fÃnon.
22

Medidas de espectroscopia raman em cristais de dl-valina a altas pressÃes. / Raman spectroscopy measurements of DL-valine crystals at high pressures

Fellipe dos Santos Campelo Rego 28 January 2015 (has links)
Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Neste trabalho, apresentamos um estudo de espalhamento Raman em cristais de DL-valina (C5H11NO2) à temperatura ambiente e sob condiÃÃes de altas pressÃes hidrostÃticas, no intervalo espectral de 40 cm-1 a 3200 cm-1. Baseando-se em estudos anteriores sobre espectroscopia Raman em cristais de DL-valina e de outros aminoÃcidos, tais como, L-valina, L-isoleucina e L-asparagina, propusemos uma classificaÃÃo das bandas em diversos modos de vibraÃÃo. Os espectros obtidos, por espectroscopia Raman, em funÃÃo da pressÃo sugerem que a DL-valina sofreu duas transiÃÃes de fase estruturais atà 19,4 GPa. A primeira transiÃÃo de fase entre 1,4 GPa e 1,8 GPa onde foi observado o desaparecimento de trÃs modos, um modo de rede e dois modos internos classificados como rocking do NH3+, r(NH3+), e estiramento simÃtrico do CH3, vs (CH3). A segunda transiÃÃo de fase entre 7,8 GPa e 8,8 GPa, onde foi observado o desdobramento de um modo de rede, o desaparecimento de um modo interno associado a uma deformaÃÃo do esqueleto da molÃcula, d(esq) e a divisÃo de um modo designado como estiramento do CH2, v(CH2). / In this work, we present a study of the Raman scattering of DL-valine crystals (C5H11NO2) at room temperature under high hydrostatic pressures conditions using the spectral range of 40-3200 cm-1. Based on previous studies using Raman spectroscopy on crystals of DL-valine and other amino acids such as L-valine, L-isoleucine and L- asparagine, we proposed the classification of the bands in different vibration modes. The Raman spectrum obtained as function of pressure suggests that DL-valine suffered two structural phase transitions by 19,4 GPa. The first transition phase of between 1,4 GPa and 1,8 GPa where we observed the disappearance of three modes, one network mode and two internal modes classified as rocking of NH3+ and symmetric stretching of CH3, vs (CH3). The second phase transition of between 7,8 GPa and 8,8 GPa, where we observe the unfolding of a network mode, the disappearance of the internal mode associated with skeletal deformation, d(esk) and the splitting designated as CH2, v(CH2).
23

Síntese e caracterização de perovskitas complexas multiferróicas com estrutura dupla ordenada

Silva, Rosivaldo Xavier da 11 December 2015 (has links)
Made available in DSpace on 2016-08-18T18:44:20Z (GMT). No. of bitstreams: 1 Tese-RosivaldoXavierSilva.pdf: 12741226 bytes, checksum: 7bc7743bfa3e2f958b913f2d67969531 (MD5) Previous issue date: 2015-12-11 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The RE2CoMnO6 (RE = La e Y) and Gd(Co0.5Mn0.5)O3 samples were obtained via modified Pechini method (MPM). Raman spectroscopy (RS), Fourier transform infrared (FTIR) spectroscopy, X ray powder diffraction, X ray photoelectron spectroscopy (XPS), SQUID and scanning electron microscopy (SEM) were used to characterize the samples, investigate structural and microstructural evolution, as well as evaluate their vibrational, magnetic and intrinsic dielectric properties. The impact of synthesis conditions on the structural ordering was investigated. We obtained a good control of structural order depending on the annealing temperature for LCMO. We observed an increase in the saturation magnetization, lifetime of the phonons and dielectric constant while suppression of anti-site defects and reduction of dielectric loss. Our investigations on polar phonons by FTIR revealed the extrinsic character of CDC effect on LCMO and clarified the contributions of phonons for dielectric constant in these systems. The temperature dependence Raman spectra of GCMO was investigated between 40 and 300 K and revealed an intriguing spin-phonon coupling, characterized by an increase in the energy of the most intense stretching mode near the magnetic transítion. The correlation between the Raman data and the magnetization suggests that the structure influences the magnitude of the spin-phonon coupling. Correlated analysis of LCMO, GCMO and YCMO systems show that all samples have vibrational properties quite similar. The intrinsic dielectric constants were obtained from the polar phonons dispersive parameters ε intr ̴ 15.8, 17.9 and 16.0, making the contributions to this value explicit, as well as the quality factors, reciprocal of dielectric losses , 𝑄𝑢×𝑓 ≈ 124,74 e 83 THz, extrapolated to microwave region at 10 GHz, to LCMO, GCMO and YCMO, respectively. XPS measures showed that oxidation state for Co and Mn ions are similar each another, being mostly Co2 + and Mn4 + for all investigated systems, however to GCMO, the spin-phonon coupling behavior and losses relatively large indicate that this compound has a high level of structural disordering. / Amostras de RE2CoMnO6 (RE = La e Y) e Gd(Co0.5Mn0.5)O3 foram obtidas pelo método Pechini modificado (MPM). Espectroscopia Raman (RS), espectroscopia no infravermelho por transformada de Fourier (FTIR), difração de raios X (DRX), espectroscopia de fotoelétrons excitados por raios X (XPS), magnetometria e microscopia eletrônica de varredura (MEV) foram utilizados para caracterizar as amostras, investigar evolução estrutural e microestrutural bem como avaliar suas propriedades vibracionais, magnéticas e dielétricas intrínsecas. O efeito da temperatura de tratamento térmico sobre o ordenamento estrutural foi investigado. Um bom controle do ordenamento estrutural em função da temperatura de tratamento térmico para o La2CoMnO6 (LCMO) foi obtido. Observa-se um incremento da magnetização de saturação, aumento do tempo de vida dos fônons, supressão de defeitos de anti-sítio, redução de perdas dielétricas e incremento da constante dielétrica. A investigação dos fônons polares via FTIR revelaram o caráter extrínseco da constante dielétrica colossal (CDC) no LCMO e explicitou as contribuições dos fônons para a constante dielétrica nesses sistemas. A dependência dos espectros Raman com a temperatura do Gd(Co1/2Mn1/2)O3 (GCMO) foi investigada entre 40 e 300 K revelando um acoplamento spin-fônon, caracterizado pelo incremento na energia do modo de estiramento mais intenso próximo à transição magnética. A correlação entre os resultados obtidos pela espectroscopia Raman e a magnetização sugere que a ordem estrutural influencia a magnitude do acoplamento spin-fônon. Análise correlacionada dos sistemas LCMO, GCMO e YCMO, mostram que todas as amostras apresentam características vibracionais bastante semelhantes. A partir dos parâmetros de dispersão dos fônons polares foram obtidas as constantes dielétricas intrínsecas ε intr ̴ 15,8, 17,9 e 16,0, explicitando as contribuições dos fônons para esses valores, e o fator de qualidade, recíproco da perdas dielétricas, 𝑄𝑢×𝑓 ≈ 124,74 e 83 THz, extrapolado para a região de micro-ondas em 10 GHz, para o LCMO, GCMO e YCMO, respectivamente. Medidas de XPS mostraram que os estados de oxidação dos íons de Co e Mn são semelhantes entre si, e principalmente do tipo Co2+/ Mn4+ para todos os sistemas estudados, sendo que para o GCMO, o acoplamento spin-fônon e as perdas dielétricas relativamente maiores indicaram que esse sistema possui elevada desordem estrutural.
24

Etude de la dépendance en taille des propriétés physiques des composés à transition de spin / Study of the size dependence of the physical properties in spin crossover compounds

Mikolasek, Mirko 06 October 2016 (has links)
Sous l'influence de stimuli externes (température, irradiation lumineuse etc.), les matériaux à transition de spin peuvent commuter d'un état bas spin vers un état haut spin de manière réversible, entraînant une modification importante de leurs propriétés physiques (élastique, magnétique, optique etc.). De plus, dans les matériaux massifs, la transition de spin est souvent accompagnée d'un effet mémoire (cycle d'hystérésis). Toutes ces propriétés rendent ces matériaux moléculaires particulièrement attractifs pour des applications dans des dispositifs nanométriques. Cependant, ces propriétés sont généralement fortement dépendantes de la taille de l'objet. Cette dépendance peut mener à une perte du cycle d'hystérésis, une modification de la stabilité des phases et l'observation de transitions incomplètes. Ces phénomènes ont été étudiés à travers des approches de physique statistique et de thermodynamique mettant en exergue le rôle important des interfaces. Cette thèse se place dans la continuité de ces travaux et se focalise sur deux aspects. D'une part, une étude des surfaces et de leur relaxation à l'aide des modèles de type Ising et " spin-phonon " résolus numériquement (Monte Carlo, auto-convergence). Il est montré que les phénomènes de surface modifient en profondeur les propriétés du matériau, que le couplage entre surface et volume est d'autant plus important à l'approche de la transition et que ces inhomogénéités spatiales peuvent être à l'origine des transitions incomplètes observées. D'autre part, il est réalisé une étude expérimentale de la dynamique du réseau à l'aide de la diffusion nucléaire inélastique pour suivre l'évolution des propriétés élastiques et vibrationnelles avec la réduction de la taille à travers la densité d'états phononiques. Cette étude expérimentale est complétée par une étude théorique/numérique, à l'aide des techniques de la matrice dynamique et de la dynamique moléculaire. Les densités d'états vibrationnels de particules cubiques à motif octaédrique sont ainsi obtenues permettant d'appréhender les mécanismes de couplages des différents modes de vibration de l'octaèdre de coordination à l'état solide. Finalement, il est discuté des effets de confinement et de leurs conséquences sur les grandeurs liées à la dynamique du réseau telles que la vitesse du son. / Spin crossover compounds are able to reversibly switch from a low spin to a high spin state under the application of an external stimulus (temperature, light irradiation, etc.). This transition is associated with an important modification of the physical properties (elastic, magnetic, optical properties, etc.). In particular, in the solid state, a memory effect (hysteresis loop) can occur. All these features are particularly attractive for applications in nano-devices. However, these properties are largely dependent on the object size. This size dependence can lead to a loss of the hysteresis loop, a modification of the phase stability and to incomplete transition. These phenomena have been studied through statistical and thermodynamical approaches highlighting the important role of interfaces. This thesis is focused on two points. First, a study of the surfaces through the spatial relaxation is performed by numerically solving (Monte Carlo simulations and auto-convergence techniques) Ising-like and " spin-phonon " models. The analysis of the surface correlation length (surface thickness), revealed that the surface-volume coupling increases when getting closer to the transition temperature and that the spatial inhomogeneity can lead to incomplete transitions. On the other hand, an experimental study of the lattice dynamics is also performed. The density of phonon states is extracted from nuclear inelastic scattering in order to follow the size evolution of the vibrational and elastic properties. This experimental study is completed by the theoretical investigation (molecular dynamics simulations, dynamical matrix method) of the densities of vibrational states of cubic particles with an octahedral pattern allowing a better understanding of the coupling mechanisms of the different vibrational modes of the coordination octahedron in the solid state. Finally, the confinement effects and their consequences on the lattice dynamical parameters are discussed.
25

Structural, Electronic And Vibrational Properties Of n-layer Graphene With And Without Doping : A Theoretical Study

Saha, Srijan Kumar 04 1900 (has links) (PDF)
Graphene – a two-dimensional honeycomb lattice of sp2-bonded carbon atoms – has been attracting a great deal of research interest since its first experimental realization in 2004, due to its various novel properties and its potential for applications in futuristic nanodevices. Being the fundamental building block for carbon allotropes of other dimensionality, it can be stacked to form 3d graphite or rolled into 1d nanotube. Graphene is the thinnest known material in the universe, and one of the strongest materials ever measured in terms of its in-plane Young modulus and elastic stiffness. The charge carriers in graphene exhibit giant mobility as high as 20 m2/Vs, have almost zero effective mass, and can travel for micrometers without scattering even at ambient conditions. Graphene can sustain current densities six orders of magnitude higher than that of copper, shows record thermal conductivity and stiffness, is impermeable to gases, and renders easy accessibility to optical probes. Electron transport in graphene is described by a Dirac-type equation, which allows the investigation of “relativistic” quantum phenomena in a benchtop experiment. This results in the observation of a number of very peculiar electronic properties from an anomalous quantum Hall effect to Kien paradox and the absence of localization. All these enticing features make this material an excellent candidate for application in various electronic, photonic and optoelectronic devices. For instance, its ballistic ambipolar transport and high carrier mobility are the most useful traits for making ultrafast and low-power electronic devices. Its high surface area shouldmake it handy in manufacturing tough composite materials. The extreme thinness of graphene could also lead to more efficient field emitters that release electrons in the presence of strong electric fields. Its robustness and light weight are useful for micromechnical resonators. The tunability of its properties could make it possible to build so-called spin-valve transistors, as well as ultra-sensitive chemical detectors. Many of such applications of graphene require tuning of its properties, which can be achieved by varying the number of layers or/and by doping. There are several ways to dope graphene: (i)electrochemically gated doping, (ii)molecular charge-transfer doping, and (iii) substitutional doping by atoms like Boron or Nitrogen.Moreover, for graphene, a zero band gap semiconductor in its pristine form, to become a versatile electronic device material it is mandatory to find means to open up a band gap and tune the size of the band gap. Several strategies have been adopted to engineer such a band gap in graphene in a controlled way. Some of these are based on the ability to control the geometry of graphene layers, some use graphene-substrate interactions, while others are based on chemical reactions of atoms or molecules with the graphene layer. Motivated by these considerations, in this thesis we present a systematic and thorough study of the structural, electronic and vibrational properties of graphene and their dependence on the number of layers, and on doping achieved electrochemically, molecularly and substitutionally, using first principles density functional theory (DFT). In Chapter 1, we give an introduction to the hitherto beguiling world of graphene. Here, we briefly discuss the structure, novel properties and potential applications of graphene, and the motivation for this thesis. In Chapter 2, an overview of the DFT formalism adopted here is given. We clearly state the theorems of the formalism and the approximations used when performing calculations. We succinctly explain how the various quantities like total energies, forces, stresses etcetera are calculated within this formalism. We also discuss how phonon frequencies, eigenvectors, electron-phonon couplings are obtained by using density functional perturbation theory (DFPT), which calculates the full dynamical matrices through the linear response of electrons to static perturbations induced by ionic displacements. Calculations are done first using a fully ab-initio approach within the standard Born-Oppenheimer approximation, and then time-dependent perturbation theory is used to explore the effects of dynamic response. In Chapter 3, using such first-principles density-functional theory calculations, we determine the vibrational properties of ultra-thin n(1,2,...,7)-layer graphene films and present a detailed analysis of their zone-center phonons. We present the results (including structural relaxations, phonons, mode symmetries, optical activities) for bulk Graphite, single-layer graphene and ultrathin n-layer graphene films. and discuss the underlying physics of our main results together with a pictorial representation of the phonon modes. We demonstrate that a low-frequency (∼ 112 cm−1 ) optical phonon with out-of-plane displacements exhibits a particularly large sensitivity to the number of layers, although no discernible change in the interlayer spacing is found as n varies. Frequency shifts of the optical phonons in bilayer graphene are also calculated as a function of its interlayer separation and interpreted in terms of the inter-planar interaction. The surface vibrational properties of n-layer graphene films are presented in Chapter 4, which renders a detailed and thorough analysis of all the surface phonon modes by determining, classifying and identifying them accurately. The response of surface modes to the presence of adsorbed hydrogen molecules is determined. As an illustrative adsorbate, hydrogen is chosen here mainly because of its huge importance in fuel cell technology and as a molecular sensor. We demonstrate that a doubly degenerate surface phonon mode with low-frequency (~ 35cm−1)exhibits a particularly large sensitivity to the adsorption of hydrogen molecules, as compared to other surface modes. Futhermore, we show that a low-frequency (108.8 cm−1)bulk-like phonon with out-of-plane displacements is also very sensitive and gets upshifted by as much as 21 cm−1 due to this adsorption. In Chapter 5, we determine the adiabatic frequency shift of the and phonons in a monolayer graphene as a function of both electron and hole doping. The doping is simulated here to correspond to electrochemically gated graphene. Compared to the results for the E2g -Γ phonon (Raman G band), the results for the phonon are dramatically different, while those for the phonon are not so different. Furthermore, we calculate the frequency shifts, as a function of the charge doping, of the (K + ΔK) phonons responsible for the Raman 2D band –a key finger print of graphene, where [ΔK] is determined by the double resonance Raman process. Doping graphene with electron donating or accepting molecules is an interesting approach to introduce carriers into it, analogous to electrochemical doping accomplished in graphene when used in a field-effect transistor. In Chapter 6, we use first-principles density-functional theory to determine changes in the electronic structure and vibrational properties of graphene that arise from the adsorption of aromatic molecules such as aniline and nitrobenzene. Identifying the roles of various mechanisms of chemical interaction between graphene and the adsorbed molecules, we bring out the contrast between electrochemical and molecular doping of graphene. Our estimates of various contributions to shifts in the Raman active modes of graphene with molecular doping are fundamental to the possible use of Raman spectroscopy in (a)characterization of the nature and concentration of carriers in graphene arising from molecular doping, and (b) graphene-based chemical sensors. Graphene doped electrochemically or through charge-transfer with electron-donor and acceptor molecules, shows marked changes in electronic structure, with characteristic signatures in the Raman spectra. Substitutional doping, universally used in tuning properties of semiconductors, could also be a powerful tool to control the electronic properties of graphene. In Chapter 7, we present the structure and properties of boron and nitrogen doped graphenes, again using first-principles density functional theory. We demonstrate systematic changes in the carrier-concentration and electronic structure of graphenes with B/N-doping, accompanied by a stiffening of the G-band and change of the defect related D-band in the Raman spectra. Such n/p -type graphenes obtained without external fields or chemical agents should find device applications.
26

FIRST PRINCIPLES STUDY OF ELECTRONIC ANDVIBRATIONAL PROPERTIES OF WIDE BAND GAPOXIDE AND NITRIDE SEMICONDUCTORS

Ratnaparkhe, Amol 21 June 2021 (has links)
No description available.
27

Micro- and nano-optical spectroscopy investigation of 2D transition metal dichalcogenides (TMDCs)

Pan, Yang 01 December 2023 (has links)
Diese Dissertation konzentriert sich auf die Untersuchung der Schwingungs- und exzitonischen Eigenschaften von zweidimensionalen Übergangsmetall-Dichalkogeniden (TMDCs) unter Verwendung von mikro- und nanooptischer Spektroskopie. Im ersten Teil der Arbeit wird Mikro-Raman-Spektroskopie verwendet, um die Schwingungseigenschaften von 2D-TMDC-Homo- und Heterostrukturen zu untersuchen, mit dem Ziel, die Hochfrequenz-Raman-Signatur für die Wechselwirkung zwischen den Schichten und die Gitterdynamik zu erforschen. Basierend auf einer systematischen Raman-Studie, unterstützt durch Photolumineszenz- (PL) und Topographie-Untersuchungen an nicht gekoppelten und gekoppelten TMDC-Doppellagen, wird die aus der Ebene herausragende $B_{2g}$-Schwingungsmode experimentell als ein charakteristischer Raman-Fingerabdruck zur Einschätzung der Wechselwirkung zwischen den Schichten in 2D-TMDC-Systemen erklärt. Darüber hinaus wird anhand eines Beispiels mit verdrehter Doppellage (tB) von WSe$_2$ als typisches TMDC gezeigt, dass das Raman-Intensitätsverhältnis der beiden Peaks $I_{B_{2g}}/I_{{E_{2g}}/{A_{1g}}}$ mit der Entwicklung der Moiré-Periode korreliert. Mit einer Reihe temperaturabhängiger Raman- und Photolumineszenz-Messungen sowie \textit{ab initio}-Berechnungen wird das Intensitätsverhältnis $I_{B_{2g}}/I_{{E_{2g}}/{A_{1g}}}$ als Signatur der Gitterdynamik in tB-WSe$_2$-Moiré-Übergittern erklärt. Durch die weitere Untersuchung verschiedener Materialkombinationen von verdrehten Hetero-Doppellagen werden die Ergebnisse auf alle Arten von Mo- und W-basierten TMDCs erweitert. Im zweiten Teil der Dissertation wird die spitzenverstärkte Photolumineszenz-Spektroskopie (TEPL) eingesetzt, um die konventionelle optische Auflösungsgrenze zu überwinden und die konkurrierenden Mechanismen der lokalen Photolumineszenz-Dämpfung und -Verstärkung an 2D-TMDC/hBN/Plasmonik-Grenzflächen zu verstehen. Durch den Vergleich verschiedener Nahfeldemissions-Eigenschaften und TEPL-Spektren in Abhängigkeit von der Spitzen-Proben-Entfernung an einer komplexen Monolagen-MoSe$_2$/hBN/NT/SiO$_2$-Probe werden die lokalisierte Oberflächenplasmonenresonanz (LSPR), die Elektronen-Dotierung und der Tunneltransport sowie hochlokalisierte Belastung als dominierende Faktoren für die lokale PL-Dämpfung und -Verstärkung identifiziert.
28

Studying Atomic Vibrations by Transmission Electron Microscopy

Cardoch, Sebastian January 2016 (has links)
We employ the empirical potential function Airebo to computationally model free-standing Carbon-12 graphene in a classical setting. Our objective is to measure the mean square displacement (MSD) of atoms in the system for different average temperatures and Carbon-13 isotope concentrations. From results of the MSD we aim to develop a technique that employs Transmission Electron Microscopy (TEM), using high-angle annular dark filed (HAADF) detection, to obtain atomic-resolution images. From the thermally diffusive images, produced by the vibrations of atoms, we intent to resolve isotopes types in graphene. For this, we establish a relationship between the full width half maximum (FWHM) of real-space intensity images and MSD for temperature and isotope concentration changes. For the case of changes in the temperature of the system, simulation results show a linear relationship between the MSD as a function of increased temperature in the system, with a slope of 7.858×10-6 Å2/K. We also note a power dependency for the MSD in units of [Å2] with respect to the FWHM in units of [Å] given by FWHM(MSD)=0.20MSD0.53+0.67. For the case of increasing isotope concentration, no statistically significant changes to the MSD of 12C and 13C are noted for graphene systems with 2,000 atoms or more. We note that for the experimental replication of results, noticeable differences in the MSD for systems with approximately 320,000 atoms must be observable. For this, we conclude that isotopes in free-standing graphene cannot be distinguished using TEM.

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