Volume Dependence in Handel's Model of Quartz Crystal Resonator Noise

International audienceAlthough criticized by many, Handel's quantum model for 1/f noise remains the only model giving a quantitative estimation of the level of intrinsic 1/f noise in quartz crystal resonators that is compatible with the best experimental results. In this paper, we reconsider the volume dependence in this model. We first argue that an acoustic volume, representing the volume in which the vibration energy is trapped, should be used instead of the geometrical volume between the electrodes. Then, we show that because there is an implicit dependence of the quality factor of the resonator with its thickness, the net effect of Handel's formula is not an increase of noise proportionally to the thickness of the resonator, as could be naïvely expected, but a net decrease when thickness increases. Finally, we show that a plot of Q4Sy versus the acoustic volume, instead of the usual Sy plot, could be useful to compare the quality of acoustic resonators having very different resonance frequencies

Growth and characterization of potassium cobalt nickel sulfate hexahydrate crystals : a new UV light filter.

Samples of the empirical formula K? 2 Ni2? x Co2? ?1 x? ?SO4? 2,6H2O were grown with a partial occupation of the cations Co and Ni. Mixed crystals with good optical quality were obtained by the slow evaporation growth method. In the decomposition process, these crystals suffer a mass loss of approximately 24%, equivalent to water molecules forming octahedral coordination ions of Ni and Co. The optical characteristics of the grown crystals were measured where transmittance reached more than 80% in the wavelength range of 190e390 nm. By Raman spectroscopy, the vibrational modes of SO2 4 , H2O and of the octahedral Ni(H2O)6 and Co(H2O)6 were identified

Contribution à l'étude des origines du bruit en 1/f dans les résonateurs à onde acoustique de vol

Since a few decades, frequency control technology has been at the heart of modern day electronics due to its huge areaof applications in communication systems, computers, navigation systems or military defense. Frequency controldevices provide high frequency stabilities and spectral purities in the short term domain. However, improvement of theperformance of these devices, in terms of frequency stability, remains a big challenge for researchers. Reducing noise inorder to increase the short term stability and avoid unwanted switching between channels is thus very desirable. It iscommonly admitted that the fundamental limitation to this short-term stability is due to flicker frequency noise in theresonators. In this manuscript, a first chapter recalls some basic facts about acoustic, crystallography and definitions oftime and frequency domain needed to explore ultra-stable resonators and oscillators. The second chapter is devoted to asummary of the literature on flicker frequency noise. Then, the third chapter concerns our studies on Handel’s quantum1/f noise model, which although criticized by many, is still the only one that provides an estimation of the flooramplitude of 1/f noise that is not invalidated by experimental data. In the fourth chapter, another approach, based on thefluctuation-dissipation theorem, is used in order to put numerical constraints on a model of 1/f noise caused by aninternal (or structural) dissipation proportional to the amplitude and not to the speed. The last chapter is devoted toexperimental results. An ultra-stable resonator used during this study is described. Phase noise measurements on severalbatches of resonators are given. Measurements of resonator parameters have been done at low temperature in order tocorrelate them with noise results. Another approach with a procedure that use transient pseudo periodic oscillations andput to their limits the capacities of presently available digital oscilloscopes, is presented, in order to assess rapidly thequality of various resonators. Finally, conclusions and perspectives are given.Depuis quelques décennies, la technologie de contrôle de la fréquence a été au coeur de l'électronique des tempsmodernes grâce à son vaste domaine d'applications dans les systèmes de communication, les ordinateurs, les systèmesde navigation ou de défense militaire. Les dispositifs temps-fréquence fournissent des stabilités de fréquence et despuretés spectrales élevées dans le domaine de la stabilité court-terme. L'amélioration de la performance de cesdispositifs reste un grand défi pour les chercheurs. La réduction du bruit afin d'augmenter cette stabilité court-terme etd'éviter les commutations non souhaitées entre les canaux est donc très souhaitable. Il est communément admis que lalimitation fondamentale à cette stabilité court-terme est due au bruit flicker de fréquence des résonateurs. Dans cemanuscrit, un premier chapitre rappelle quelques faits de base sur l’acoustique, la cristallographie et les définitions dudomaine temps-fréquence nécessaires à l’étude des résonateurs et oscillateurs ultra-stables. Le deuxième chapitre estconsacré à un résumé de la littérature sur le bruit de fréquence en 1/f. Ensuite, le troisième chapitre concerne nos étudessur le modèle quantique de bruit en 1/f du Pr. Handel, qui, bien que critiqué par beaucoup, est encore le seul qui fournitune estimation de l'amplitude de plancher de bruit en 1/f et qui n'est pas infirmé par les données expérimentales. Dans lequatrième chapitre, une autre approche, basée sur le théorème de fluctuation-dissipation, est utilisée afin de mettre descontraintes numériques sur un modèle de bruit en 1/f causé par une dissipation interne (ou de structure) proportionnelleà l'amplitude, et non à la vitesse. Le dernier chapitre est consacré aux résultats expérimentaux. Le design et lesparamètres du résonateur ultra-stable utilisé lors de cette étude sont décrits. Les mesures de bruit de phase sur plusieurslots de résonateurs sont données. Les mesures des paramètres de résonateur ont été effectuées à basse température afinde les corréler avec les résultats de bruit. Afin d'évaluer rapidement la qualité des différents résonateurs, une autreapproche dans le domaine temporel a été testée. Elle utilise des oscillations pseudo-périodiques transitoires mettant lesoscilloscopes numériques actuellement disponibles à leurs limites de capacité. Enfin, les conclusions et perspectivessont présentées

Study on the origin of 1/f noise in quartz resonators

International audienceIntrinsic frequency fluctuations with a $1/f$ power spectral density limit the short-term stability in quartz crystal ultra-stable oscillators. The physical origin of this $1/f$ noise remains not clearly explained. In this paper, a review of an experimental study on numerous ultra-stable quartz crystal resonators is presented. A comparison with past measurements is given. A theoretical approach, based on the fluctuation–dissipation theorem, is used in order to put numerical constraints on a model of $1/f$ noise caused by an internal (or structural) dissipation proportional to the amplitude and not to the speed, in the limit of low frequencies. The order of the magnitude of the noise is then discussed using a candidate physical process. Comparisons between theoretical and experimental results show that internal damping of thickness fluctuations by any internal friction force proportional to strain and independent of frequency may not be the dominant noise mechanism for the best SC-cut quartz resonators. Finally, we conclude on the work that could be done to solve the remaining open problems

Growth and characterization of ammonium nickel-cobalt sulfate Tutton’s salt for UV light applications.

We have obtained a set of sample crystals of the family of Tutton’s salt comprise in the isomorphic series with general chemical formula (NH4)2NixCo(1−x) (SO4)2·6H2O, by employing growth from solutions by slow evaporation technique. The samples crystals were characterized by ICP-AES, X-ray powder diffraction analysis, thermogravimetric analysis, UV–Vis-NIR, Raman and FTIR spectroscopy. This type of material has been studied because of its physical and chemical properties not yet understood and they have potential technological applications. Chemical analysis of the samples by ICP-AES method allowed us to investigate the efficiency of the method of growth used. Thermogravimetric analysis provides the information about the thermal stability of the obtained crystals for high temperature applications, and powder X-ray diffraction analysis at ambient and high temperature reveals the structural quality and structural change of the samples respectively. We have used Raman spectroscopy in the range 100–4000 cm−1 and FTIR spectroscopy in the range 400–4000 cm−1 to understand the internal vibrational mode of the octahedral complexes [Ni(H2O)6]2+ and [Co(H2O)6]2+, SO42− and NH4+ tetrahedra. The transmittance of our mixed ammonium nickel cobalt sulfate hexahydrate (ACNSH) crystals is 75% in the UV region, which indicates that they are ideal to use in UV light filters and UV sensors

Growth and structural analysis of ammonium nickel cobalt sulfate hexahydrate crystals.

We have obtained a set of crystals of the empirical formula (NH4)2NixCo(1?x)(SO4)2 ? 6H2O with the different concentrations of Ni and Co, by employing the growth from the solution technique. We have chosen the monocrystal (NH4)2Ni0.3Co0.7(SO4)2 ? 6H2O for the structural analysis. The structure was resolved by x-ray diffraction method and refined by the full-matrix least-squares method with the help of SHELXS software. This crystal belongs to a monoclinic space group P21/c with crystal parameters, a = 6.2455 (2) ?, b = 12.5065 (3) ?, c = 9.2303 (2) ?, ? = ? = 90?, ? = 106.995 (3)?, V = 689.49 (3) ?3, Z = 2. We have shown the configuration of the unit cell of the above monocrystal, along with that we have also reported the length, angles between the bonds and the geometry of the hydrogen bonds of the monocrystal

1/F Noise of Quartz Resonators: Measurements, Modelization and Comparison Studies

International audienceIn this paper, the description of the resonator realization and the topology of the resonator prototype is exposed. Phase noise measurements of a hundred of resonators are given. The noise results are discussed according to the position of the resonators inside the crystal block and physical analysis of the crystal (dislocation). The results are also compared according to their Q-factors measured at room temperature and at low temperature. Theoretically, the fluctuation-dissipation theorem is used in order to put numerical constraints on a model of 1/f noise caused by an internal (or structural) dissipation proportional to the amplitude and not to the speed. The order of magnitude of the noise is then discussed

Electron impact ionization and fragmentation of biofuels

We present in this article, a review of our recent experimental and theoretical studies published in the literature on electron impact ionization and fragmentation of the primary alcohols methanol, ethanol, 1-propanol and 1-butanol (C1–C4). We discuss the mass spectra (MS) of these alcohols, measured for the electron impact energy of 70 eV and also, total (TICS) and partial (PICS) ionization cross sections in the energy range from 10 to 100 eV, which revealed the probability of forming different cations, by either direct or dissociative ionization. These experimental TICS are summarized together with theoretical values, calculated using the Binary-encounter Bethe (BEB) and the independent atom model with the screening corrected additivity rule (IAM-SCAR) methods. Additionally, we compared data of appearance energies – AE and discussed the application of the extended Wannier theory to PICS in order to produce the ionization and ionic fragmentation thresholds for the electron impact of these alcohols