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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Sauerbrey equation ： ウィキペディア英語版 Sauerbrey equation The Sauerbrey equation was developed by G. Sauerbrey in 1959 as a method for correlating changes in the oscillation frequency of a piezoelectric crystal with the mass deposited on it. He simultaneously developed a method for measuring the characteristic frequency and its changes by using the crystal as the frequency determining component of an oscillator circuit. His method continues to be used as the primary tool in quartz crystal microbalance experiments for conversion of frequency to mass and is valid in nearly all applications. The equation is derived by treating the deposited mass as though it were an extension of the thickness of the underlying quartz. 〔QCM100 – Quartz Crystal Microbalance Theory and Calibration, Stanford Research Systems.〕 Because of this, the mass to frequency correlation (as determined by Sauerbrey’s equation) is largely independent of electrode geometry. This has the benefit of allowing mass determination without calibration, making the set-up desirable from a cost and time investment standpoint. The Sauerbrey equation is defined as: :$\backslash Delta\; f\; =\; -\backslash frac\backslash Delta\; m$. Equation 1 – Sauerbrey’s equation :$f\_0$ – Resonant frequency (Hz) :$\backslash Delta\; f$ – Frequency change (Hz) :$\backslash Delta\; m$ – Mass change (g) :$A$ – Piezoelectrically active crystal area (Area between electrodes, cm2) :$\backslash rho\_q$ – Density of quartz ($\backslash rho\_q$ = 2.648 g/cm3) :$\backslash mu\_q$ – Shear modulus of quartz for AT-cut crystal ($\backslash mu\_q$ = 2.947x1011 g·cm−1·s−2) Because the film is treated as an extension of thickness, Sauerbrey’s equation only applies to systems in which the following three conditions are met: the deposited mass must be rigid, the deposited mass must be distributed evenly and the frequency change $\backslash Delta\; f\; /f$ < 0.02.〔A. K. Srivastava and P. Sakthivel, J. Vac. Sci. Technol. A 19(1),97-100 Jan/Feb 2001〕 If the change in frequency is greater than 2%, that is, $\backslash Delta\; f\; /f$ > 0.02, the Z-match method must be used to determine the change in mass.〔 The formula for the Z-match method is:〔 :$\backslash frac\backslash \; =\; \backslash frac\backslash tan^\; \backslash left\; (Z\backslash tan\; \backslash left\; (\; \backslash pi\; \backslash frac\; \backslash right\; )\; \backslash right)$ Equation 2 – Z-match method :$f\_L$ – Frequency of loaded crystal (Hz) :$f\_U$ – Frequency of unloaded crystal, i.e. Resonant frequency (Hz) :$N\_q$ – Frequency constant for AT-cut quartz crystal (1.668x1013Hz.Å) :$\backslash Delta\; m$ – Mass change (g) :$A$ – Piezoelectrically active crystal area (Area between electrodes, cm2) :$\backslash rho\_q$ – Density of quartz ($\backslash rho\_q$ = 2.648 g/cm3) :$Z$ – $Z\; =\; \backslash sqrt\backslash \; \backslash right\; )\; \}$ :$\backslash rho\_f$ – Density of the film (Varies: units are g/cm3) :$\backslash mu\_q$ – Shear modulus of quartz ($\backslash mu\_q$ = 2.947x1011 g·cm−1·s−2) :$\backslash mu\_f$ – Shear modulus of film (Varies: units are g·cm−1·s−2) == Limitations == The Sauerbrey equation was developed for oscillation in air and only applies to rigid masses attached to the crystal. It has been shown that quartz crystal microbalance measurements can be performed in liquid, in which case a viscosity related decrease in the resonant frequency will be observed: :$\backslash Delta\; f\; =\; \}$ where $\backslash rho\_l$ is the density of the liquid and $\backslash eta\_l$ is the viscosity of the liquid (Kanazawa and Gordon 1985). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Sauerbrey equation」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.