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Contribuição do exchange na largura de linha de ressonância paramagnetica eletrônica do ion N POT. 2+ / Contribution of exchange in line width of the electron paramagnetic resonance ion \'N2 + I\'.Jose Carlos Sartorelli 24 June 1982 (has links)
Efetuamos medidas de RPE nos seguintes sais hexahidratados: fluorborato de níquel (Ni (BF IND. 4) IND. 2 6 H IND. 2 O) , perclorato de níquel (Ni(Cl O IND. 4) IND. 2 6 H IND. 2 O) e fluorsilicato de níquel (NiSi F IND. 6 6 H IND. 2 O). Os parâmetros da hamiltoniana de spin deste último sal foram redeterminados no intervalo de 100 K à 323 K. Os nossos resultados de RPE indicam a existência de anomalias no intervalo 153 K a 273 K que caracterizam uma transição de fase. Estudamos também as larguras de linha dos sais acima, separando as contribuições devido à interação spin- spin e a relaxação spin- rede. Os valores destas contribuições concordam perfeitamente com os calculados a partir de modelos teóricos. Desenvolvemos uma nova forma de linha que dá excelentes ajustes, por mínimos quadrados, das curvas experimentais. / We have performed EPR measurements in the following hexahidrated salts: nickel fluorborate (Ni(BF4)2 6H2O), nickel perchlorate (Ni(Cl04) 2 6H2O) and nickel fluorsilicate (NiSiF6 6 H20). The spin hamiltonian parameters of the last salt were determined once again in the range 100 - 323K. Our results of EPR indicate anomalies in the range 153 - 273K, which characterize a phase transition. Line widths of the above salts were also studied separating the contributions given by spin-spin interaction and spin-lattice relaxation. The values of these contributions agree with theoretical calculations. We have developped a new line form, which gives excellent fits, by least square fit, for the experimental data.
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Ressonância paramagnética eletrônica do fluorborato de zinco hexahidratado dopado com Mn2+ / Electron paramagnetic resonance of zinc fluoroborate hexahydrate doped with Mn2 +Eduardo di Mauro 04 April 1983 (has links)
Estudamos monocristais de Zn(BF4)26H2O dopados com Mn2+ no intervalo de temperatura de 94K à 353K empregando a técnica de Ressonância Paramagnética Eletrônica (RPE). Determinamos todos os parâmetros da Hamiltoniana de spin. Constatamos que o fator espectroscópico g = 2,000 ± 0,001 é constante com a temperatura. Calculamos o parâmetro D e através da curva de D versus T confirmamos a existência de uma transição de fase à 181K. Verificamos que este parâmetro D apresenta variação linear com a temperatura acima de 200K (D= (127 + 0,228T) Gauss), o que está de acordo com a previsão do modelo de Walsh. Com os espectros obtidos da variação angular do eixo c do cristal em relação ao campo magnético externo, constatamos que os resultados experimentais estão em excelente acordo com a teoria. Concluímos que o campo cristalino tem simetria trigonal em toda a faixa de temperatura pesquisada. / We have studied monocrystals of Zn(BF4)26H2O doped with Mn2+ in the range of the temperature of 94K to 353K employing the technics of Electron Paramagnetic Resonance (EPR). We have determined all the parameters of the spin Hamiltonian. We have verified that the temperature. We have calculated the parameter D and through the curve of D versus T confirmed the existence of a phase transition at 181K. We have verified that this parameter D shows linear variation with the temperature above 200K (D= (127 + 0,228T) Gauss), which agrees with the prevision of the Walshs model. With the spectra of the angular variation of the c axis of the crystal in relation to extern magnetic field, we have verified that the experimental results are in excellent agreement with the theory. We have concluded that the crystal field has trigonal symmetry in all range of temperature investigated.
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Dosimetria de elétrons em processos de irradiação com diodos resistentes a danos de radiação / Electron dosimetry in irradiation processing with rad-hard diodesThais Cavalheri dos Santos 28 September 2012 (has links)
Este trabalho teve como objetivo o desenvolvimento de sistemas dosimétricos baseados em diodos especiais de Si, resistentes a danos de radiação, para monitoração online de processos de irradiação com elétrons de 1,5 MeV de energia e para dosimetria relativa e escaneamento de feixe de elétrons clínicos dentro de uma faixa de energia de 6 a 21 MeV. Os diodos utilizados foram produzidos pelos métodos de fusão zonal padrão (FZ), Czochralski em presença de um campo magnético (MCz) e crescimento Epitaxial (EPI). Para utilizar os diodos como detectores, eles foram fixados em uma base de alumina permitindo a ligação dos eletrodos de polarização e de extração de sinais. Após a montagem na base, cada diodo foi fixado em uma sonda acrílica preta dotada de uma janela de Mylar® aluminizado e de conector do tipo LEMO®. Com os dispositivos operando em modo fotovoltaico, a integração dos sinais de corrente em função do tempo de irradiação permitiu obter a carga produzida no volume sensível de cada diodo irradiado. O acelerador de elétrons utilizado para as irradiações de doses altas foi o DC 1500/25/4 - JOB 188 de 1,5 MeV instalado no Centro de Tecnologia das Radiações do IPEN/CNEN-SP. Foram estudados o perfil da corrente em função do tempo de exposição, a repetibilidade de resposta, a sensibilidade em função da dose absorvida e a curva resposta de cada dispositivo. Foi observada uma queda na sensibilidade mais acentuada para o diodo MCz do que para o diodo FZ e uma boa repetibilidade nos dois casos. Ainda, o aumento da carga com a dose absorvida obedeceu a uma função polinomial de segunda ordem. Na caracterização do diodo EPI, ele exibiu melhor repetibilidade que a obtida por dosímetros CTA, rotineiramente aplicados em processamento por radiação. Os resultados acima descritos indicam a potencial utilização desses diodos de Si resistentes a danos de radiação em dosimetria online para aplicações envolvendo elevadas doses. Para as irradiações de doses baixas foram utilizados os Aceleradores Lineares KD2 e Primus, ambos fabricados pela Siemens e instalados no Hospital Sírio-Libanês. A resposta dos diodos foi avaliada para energias de 6 a 21 MeV. Foram estudados: a repetibilidade de resposta, a curva dose-resposta em função da dose absorvida, a sensibilidade em carga com a energia do feixe de elétrons, a porcentagem de dose profunda (PDP) e o perfil transversal de dose. Apesar da resposta dos diodos FZ, MCz e EPI serem levemente dependentes da energia do feixe de elétrons, a resposta dosimétrica, em todo o intervalo de energia de feixe estudado, mostrou-se linear. Ainda, em relação aos diodos epitaxiais, os dispositivos estudados mostraram excelente acordo com simulações de Monte Carlo e medições realizadas com MatriXX®, demonstrando que os dispositivos podem ser usados como dosímetros em elétrons radioterápicos para escaneamento de varredura de feixe, mapeamento de distribuições de dose de feixes, monitoramento rotineiro da constância do fator calibração e dosimetria relativa. / This work had the aim of the development of dosimetric systems based on Si special diodes, resistant to radiation damage to online monitoring of irradiation processing using 1.5 MeV electrons energy and for relative dosimetry and clinical electron beam scanning within an energy range of 6 MeV up to 21 MeV. The diodes used were produced by Float Zone standard (FZ), Magnetic Czochralski (MCz) and epitaxy growth (EPI) methods. In order to use the diodes as detectors, they were fixed on alumina base to allow the connection of the polarization electrodes and the signals extraction. After the diode assembly on the base, each one was housed in a black acrylic probe with aluminized Mylar® window and LEMO® connector. With the devices operating in photovoltaic mode, the integration of the current signals as a function of irradiation time allowed obtain the charge produced in the sensitive volume of each diode irradiated. The electron accelerator used for high doses irradiation was the DC 1500/25/4 JOB 188 of the 1.5 MeV installed at the Radiation Technology Center of the IPEN/CNEN-SP. The current profile as function of exposure time, the response repeatability, the sensitivity as function of absorbed dose and the dose response curve were studied for each device. In comparison to FZ diode, we observed a greater decrease in the sensitivity for MCz diode, and good repeatability in both cases. Also, the increasing of the charge with the absorbed dose was well fitted by a second order polynomial function. In the EPI diode characterization, this one exhibited repeatability better than CTA dosimeters applied routinely in radiation processing. The above results indicate the potential use of these radiation hardness Si diodes in online dosimetry to high doses applications. For low doses irradiation were used the linear accelerators KD2 and Primus, both manufactured by Siemens and located at Sirio-Libanês Hospital. The diodes responses were evaluated for electron beams within the energy range of 6 MeV up to 21 MeV. The following studies were carried out: the short-term repeatability, the dose-response curve as a function of absorbed dose, the charge sensitivity as function of electron beam energy, the percentage depth dose (PPD) and the dose transversal profile. Despite the response of the diodes FZ, MCz and EPI be slightly dependent on the electron beam energy, the dosimetric response was linear in all electron beam energy range studied. In addition to this, the EPI devices showed excellent agreement with simulation performed with Monte Carlo code and the measurements performed with MatriXX®, confirming that the devices can be used as dosimeters in radiotherapy for scanning purposes, dose distribution mapping, constancy monitoring of calibration factor and relative dosimetry.
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Low-dimensional electron transport and surface acoustic waves in GaAs and ZnO heterostructuresHou, Hangtian January 2019 (has links)
A surface acoustic wave (SAW) is a combination of a mechanical wave and a potential wave propagating on the surface of a piezoelectric substrate at the speed of sound. Such waves are widely applied in not only the communication industry, but also in quantum physics research, such as nanoelectronics, spintronics, quantum optics, and even quantum information processing. Here, I focus on low-dimensional electron transport and SAWs in GaAs and ZnO semiconductor heterostructures. The ability to pattern quantum nanostructures using gates has stimulated intense interest in research into mesoscopic physics. We have performed a series of simulations of gate structures, and having with the optimised boundary conditions and we find them to match experimental results, such as the pinch-off voltage of one-dimensional channels and SAW charge transport in induced n-i-n and n-i-p junctions. Using the improved boundary conditions, it is straightforward to model quantum devices quite accurately using standard software. With the calculated potential, we have modelled the process how a dynamic quantum dot is driven by a SAW and have analysed error mechanisms in SAW-driven quantisation (I=Nef, where N is the number of electrons in each SAW minimum, and f is the SAW resonant frequency). From energy spectroscopy measurements, we probe the electron energy inside a SAW-driven dynamic quantum dot and find that the small addition energy, which is around 3meV, is the main limitation for the SAW quantisation. To increase the confinement of SAW-driven quantum dots, we deposit a thin ZnO film, with a better piezoelectric coupling than GaAs, on a GaAs/AlGaAs heterostructure using high-target-utilisation sputtering (an Al2O3 buffer layer is deposited to protect the 2DEG during sputtering). With the ZnO, the SAW amplitude is greatly improved to 100 meV and the RF power required for pumping electrons using a SAW is greatly reduced. Finally, we have studied low-dimensional electron transport in a MgZnO/ZnO heterostructure. We have developed a technique for patterning gates using a parylene insulator, and used these to create one-dimensional quantum wires and observe electron ballistic transport with conductance quantised in units of 2e2/h The increasing electron effective mass as the 1D electron density decreases indicate that the electron-electron interaction in this MgZnO/ZnO heterostructure is strong. Because of these strong interactions, the 0.7 anomaly is observed just below each quantised plateau, and are much stronger than in GaAs quantum wires. Furthermore, we have also calculated the SAW-modulated spontaneous and piezoelectric polarisation in the ZnO heterostructure, and have observed a sign of this SAW-modulation in 2DEG density, which is different from the classical SAW-pumping mechanism. Our results show that a ZnO heterostructure should provide a good alternative to conventional III-V semiconductors for spintronics and quantum computing as they have less nuclear spins. This paves the way for the development of qubits benefiting from the low scattering of an undoped heterostructure together with potentially long spin lifetimes.
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Spin dynamics in organic semiconductorsSchott, Sam January 2019 (has links)
Organic semiconductors exhibit exceptionally long spin lifetimes, and recent observations of the inverse spin hall effect as well as micrometer spin diffusion lengths in conjugated polymers have spiked interest in employing such carbon-based materials in spintronics applications. The charge transport and photophysics of organic semiconductors have been intensely studied for optoelectronic applications, revealing subtle relationships between molecular geometry, morphology and physical properties. Similar structure-property relationships remain mostly unknown for spin dynamics, where the charge carrier spins couple to their environment through hyperfine (HFI) and spin-orbit interactions (SOC). HFIs provide a pathway for spin relaxation while SOC plays a dual role in such materials: it couples the spin to its angular momentum and therefore enables both spin-to-charge conversion and spin relaxation. Understanding the molecular SOC, and finding a means to tune its strength, therefore is fundamentally important for materials design and selection. However, quantifying SOC strengths indirectly through spin relaxation effects has proven difficult due to competing relaxation mechanisms. We initially present a systematic study of the g-tensor shift in molecular semiconductors and establish it as a probe for the SOC strength in a series of high mobility molecular semiconductors. The results demonstrate a rich variability of molecular g-shifts with the effective SOC, depending on subtle aspects of molecular composition and structure. We then correlate the above g-shifts to spin-lattice relaxation times over four orders of magnitude, from 200 µs to 0.15 µs, for isolated molecules in solution and relate our findings to the spin relaxation mechanisms that are likely to be relevant in solid state systems. Isolated molecules provide an ideal model system to investigate a spin's interactions with its environment but device applications commonly employ thin films. The second half of this thesis investigates polaron spin lifetimes in field effect transistors with high-mobility conjugated polymers as active layers. We use field-induced electron spin resonance measurements to demonstrate that spin relaxation is governed by the charges' hopping motion at low temperatures while Elliott-Yafet-like relaxation due to short-range, rapid spin density dynamics likely dominates high temperature spin lifetimes. Such a microscopic relaxation mechanism is highly sensitive to the local conformation of polymer backbones and we show its dependence on the degree of crystallinity in a polymer film.
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Feasibility of nuclear plasma interaction studies with the activation techniqueNogwanya, Thembalethu January 2018 (has links)
>Magister Scientiae - MSc / Electron-mediated nuclear plasma interactions (NPIs), such as Nuclear Excitation
by Electron Capture (NEEC) or Transition (NEET), can have a signi cant impact
on nuclear cross sections in High Energy Density Plasmas (HEDPs). HEDP
environments are found in nuclear weapons tests, National Ignition Facility (NIF)
shots and in the cosmos where nucleosynthesis takes place. This thesis explores
the impact of NPIs on highly excited nuclei. This impact is understood to be more
intense in highly-excited nuclei states in the quasi-contiuum which is populated
by nuclear reactions prior to their decay by spontaneous
-ray emission. Attempts
thus far have failed in measuring the NEEC process, while NEET process
has been observed experimentally. Direct observation of NPIs is hindered
by the lack of a clear signature of their e ect in HEDP environments. Hence this
should test a new signature for NPIs for highly-excited nuclei by investigating
isomeric to ground state feeding from the isomeric state. An experiment was performed
using the reactions 197Au(13C, 12C)198Au and 197Au(13C, 12C2n)196Au at
Lawrence Berkeley National Laboratory in inverse kinematics with an 197Au beam
of 8.5 MeV/u energy. Several measurements were performed with di erent target
con gurations. The activated foils were counted at the low-background counting
facility of Lawrence Livermore National Laboratory. From these data, the double
isomeric to ground state ratio (DIGS) were extracted with the assistance of the
decay equations that were included in the experiment. As the NPIs e ects are
rather small the lines for analysis had to be chosen carefully so that the extracted
ratios would not contain signi cant errors. The measured DIGS ratios were then
compared with the result of the theoretical DIGS ratios. The results showed that
the calculated DIGS ratios deviated substantially from unity although this was
with large uncertainties. Because of the large errors obtained, the DIGS ratios
were found to be inconclusive as a signature for detecting the e ects of NPIs such
as angular momentum distribution changes in HEDP environments.
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Establishment of a novel total internal reflection microscopy and its applications in colloidal research. / 新型全內反射顯微鏡的搭建及其在膠體研究中的應用 / Establishment of a novel total internal reflection microscopy and its applications in colloidal research. / Xin xing quan nei fan she xian wei jing de da jian ji qi zai jiao ti yan jiu zhong de ying yongJanuary 2008 (has links)
Gong, Xiangjun = 新型全內反射顯微鏡的搭建及其在膠體研究中的應用 / 龔湘君. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references. / Abstracts in English and Chinese. / Gong, Xiangjun = Xin xing quan nei fan she xian wei jing de da jian ji qi zai jiao ti yan jiu zhong de ying yong / Gong Xiangjun. / Abstract (Chinese) --- p.i / Abstract --- p.iii / Contents --- p.v / Acknowledgement --- p.vii / Chapter Chapter 1 --- Introduction to Total Internal Reflection Microscopy (TIRM) / Chapter 1.1 --- History of TIRM --- p.1 / Chapter 1.2 --- Instrumentation --- p.1 / Chapter 1.2.1 --- Apparatus --- p.1 / Chapter 1.2.2 --- Optical Tweezer --- p.3 / Chapter 1.3 --- The principle of the technique --- p.5 / Chapter 1.3.1 --- Total Internal Reflection --- p.5 / Chapter 1.3.2 --- Details on Scattering of the Evanescent Wave --- p.7 / Chapter 1.3.3 --- Data analysis --- p.14 / Chapter 1.3.4 --- A typical potential energy profile --- p.17 / Chapter 1.4 --- Noise Analysis and Removal Method --- p.19 / Chapter 1.4.1 --- Noise analysis --- p.19 / Chapter 1.4.2 --- Noise removal: low-pass filtering --- p.22 / Chapter 1.5 --- Other techniques on force measurement --- p.25 / Chapter 1.6 --- References --- p.27 / Chapter Chapter 2 --- Experiments on TIRM Calibration / Chapter 2.1 --- Introduction --- p.30 / Chapter 2.2 --- Pre-Experimental Section --- p.30 / Chapter 2.2.1 --- Glass Surface Preparation Methods --- p.30 / Chapter 2.2.2 --- Experimental Setup --- p.33 / Chapter 2.3 --- Calibration Results and Discussion --- p.36 / Chapter 2.4 --- Conclusions --- p.42 / Chapter 2.5 --- References --- p.43 / Chapter Chapter 3 --- TIRM investigation on polymer-induced collodial interactions / Chapter 3.1 --- Introduction to polymer-induced forces --- p.45 / Chapter 3.1.1 --- Non-absorbing case - depletion force --- p.46 / Chapter 3.1.2 --- Attached polymer layers --- p.49 / Chapter 3.2 --- Applications of TIRM in polymer-mediated colloidal interactions --- p.54 / Chapter 3.2.1 --- Measurements on depletion force --- p.54 / Chapter 3.2.2 --- Measurements on Steric Forces --- p.56 / Chapter 3.3 --- Direct measurement of thermosensitive Poly(N-isopropylacrylamide)-mediated colloidal interactions with TIRM --- p.56 / Chapter 3.3.1 --- Introduction --- p.56 / Chapter 3.3.2 --- Experimental Section --- p.57 / Chapter 3.3.3 --- Results and Discussion --- p.60 / Chapter 3.3.4 --- Conclusions --- p.73 / Chapter 3.4 --- References --- p.74 / Publication List --- p.77
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electron beam irradiation damage on ZnS nanostructures synthesized by hydrothermal and thermal evaporation methods. / 水熱法和熱蒸法製備硫化鋅納米结构的電子輻射損傷研究 / The electron beam irradiation damage on ZnS nanostructures synthesized by hydrothermal and thermal evaporation methods. / Shui re fa he re zheng fa zhi bei liu hua xin na mi jie gou de dian zi fu she sun shang yan jiuJanuary 2007 (has links)
Xu, Yeming = 水熱法和熱蒸法製備硫化鋅納米结构的電子輻射損傷研究 / 徐業明. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 61-63). / Text in English; abstracts in English and Chinese. / Xu, Yeming = Shui re fa he re zheng fa zhi bei liu hua xin na mi jie gou de dian zi fu she sun shang yan jiu / Xu Yeming. / Abstract --- p.i / 摘要 --- p.ii / Acknowledgment --- p.iii / List of Figures --- p.VII / Table of contents --- p.XI / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Background of electron beam irradiation --- p.4 / Chapter 2.1 --- Basic principles of electron beam irradiation --- p.4 / Chapter 2.1.1 --- Atomic displacement --- p.5 / Chapter 2.1.2 --- Electron beam sputtering --- p.7 / Chapter 2.1.3 --- Electron beam heating --- p.8 / Chapter 2.1.4 --- Radiolysis --- p.11 / Chapter Chapter 3 --- Instrumentation --- p.13 / Chapter 3.1 --- X-ray photoelectron spectroscopy (XPS) --- p.13 / Chapter 3.1.1 --- Basic principles --- p.13 / Chapter 3.1.2 --- Chemical shifts in x-ray photoelectron spectroscopy --- p.16 / Chapter 3.2 --- The principle of the Scanning Electron Microscopy (SEM) --- p.16 / Chapter 3. 3 --- Transmission Electron Microscope (TEM) --- p.19 / Chapter 3. 3.1 --- Principle of the TEM --- p.19 / Chapter 3.3.2 --- Electron specimen interaction in TEM --- p.21 / Chapter 3.3.3 --- Electron Diffraction --- p.22 / Chapter 3.3.4 --- Contrast --- p.22 / Chapter 3.4 --- Energy dispersive x-ray spectroscopy --- p.23 / Chapter 3.5 --- Elemental mapping using Electron Energy Loss Spectrometer (EELS) --- p.24 / Chapter Chapter 4 --- Structure Degradation of ZnS Nanomaterials Synthesized via Hydrothermal Method --- p.26 / Chapter 4.1 --- Experimental --- p.26 / Chapter 4.2 --- Structure degradation of ZnS nanotubes synthesized via hydrothermal method --- p.27 / Chapter 4.2.1 --- Chemical and structural characterization of the as-synthesized nanotubes --- p.27 / Chapter 4.2.2 --- Crystallinity and structural degradation of the nanosheet under the electron beam irradiation --- p.29 / Chapter 4.2.3 --- Nanotube structure degradation with different experimental parameters --- p.33 / Chapter 4.3 --- Structure degradation of ZnS nanosheets synthesized via hydrothermal method --- p.34 / Chapter 4.3.1 --- Chemical and morphological characteristics of the ZnS nanosheets --- p.34 / Chapter 4.3.2 --- Crystallinity and structural degradation of the nanosheet under the electron beam irradiation --- p.37 / Chapter 4.3.3 --- Nanosheet structure degradation with different experimental parameters --- p.41 / Chapter 4.3.4 --- Discussion on the damage mechanisms --- p.45 / Chapter Chapter 5 --- Structure Degradation of ZnS Nanobelts Synthesized via thermal evaporation Method --- p.48 / Chapter 5.1 --- Experimental --- p.48 / Chapter 5.2 --- Chemical and morphological characteristics of the ZnS nanobelts --- p.49 / Chapter 5.3 --- Crystallinity and structural degradation of the nanobelt under the electron beam irradiation --- p.50 / Chapter 5.4 --- Nanobelt structure degradation with different experimental parameters --- p.55 / Chapter 5.5 --- Discussion on the damage mechanisms --- p.56 / Chapter Chapter 6 --- Conclusion --- p.59 / References --- p.61
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Development of a single-particle tracking microrheometry method by incorporating magnetic tweezer to total internal reflection microscope. / 基於磁鑷和全反射顯微鏡的單粒子追踪微流變方法 / CUHK electronic theses & dissertations collection / Development of a single-particle tracking microrheometry method by incorporating magnetic tweezer to total internal reflection microscope. / Ji yu ci nie he quan fan she xian wei jing de dan li zi zhui zong wei liu bian fang faJanuary 2011 (has links)
Gong, Xiangjun = 基於磁鑷和全反射顯微鏡的單粒子追踪微流變方法 / 龔湘君. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Gong, Xiangjun = Ji yu ci nie he quan fan she xian wei jing de dan li zi zhui zong wei liu bian fang fa / Gong Xiangjun.
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Measuring Electron Gas Relaxation in Gold through Second Harmonic GenerationSanGiorgio, Paul 01 May 2001 (has links)
In a thermally equilibrated system, electron behavior in a metal is described by the Fermi-Dirac equation. With ultrafast lasers, electrons can be excited into temporary distributions which are not described by the Fermi-Dirac equation and are therefore not at a well-defined temperature. These nonthermal distributions quickly equilibrate through two primary processes: electron-electron scattering and electron-phonon scattering. In most situations, these effects are unnoticeable, since they are completed within 5 ps. A probabilistic numerical model for electron-electron scattering is presented. The model is robust, scaleable, and requires only one parameter. The success of the model suggests future work on a similar electron-phonon scattering model, which would provide a complete description of the elctron distribution during thermalization. Once complete, this model can be tested by measuring the amount of second harmonic light generated by an ultrafast laser in a pump-probe experiment.
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