By C. Lu, A.W. Czanderna
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Sleek desktop simulations make rigidity research effortless. As they proceed to switch classical mathematical equipment of research, those software program courses require clients to have an exceptional realizing of the basic rules on which they're established. strengthen Intuitive skill to spot and steer clear of bodily Meaningless Predictions utilized Mechanics of Solids is a robust instrument for realizing tips to reap the benefits of those progressive desktop advances within the box of reliable mechanics.
A conception of the equilibrium form of crystal assuming minimum floor unfastened strength was once formulated in the beginning of the century by means of Wulff. Assuming that the anisotropic interfacial loose strength (depending at the orientation of the interface with admire to the crystal axes) is understood, the Wulff building yields the form of crystal in equilibrium and permits one to appreciate its major good points.
Extra resources for Applications of Piezoelectric Quartz Crystal Microbalances
A simplified model of a quartz crystal microbalance. (a) At resonance, the wavelength is equal to half of the quartz plate thickness, (b) An increase in the q u a r t z plate thickness results in a decrease in the resonant frequency (an increase in the wavelength), (c) The mass of a deposited film is t r e a t e d as an equivalent amount of the quartz mass. The feasibility of using piezoelectric quartz resonators as quanti tative mass measuring devices was first explored by Sauerbrey [2,3] . The operating principle of a QCM, as postulated by Sauerbrey, can be described by the idealized physical model shown in Fig.
Thus, this curve, which holds for fluorides, does not necessarily hold for other groups of compounds such as oxides, carbides, or even other halides. The M versus F curve as defined by Eq. (47) is not highly sensitive to the value of Z (see Fig. 9), particularly in the region where M or F is relatively small (small mass load). Thus, the possible difference between the acoustic impedance of a material in the thin film form and that of the same material in bulk need not be overly empha sized. For all practical purposes, the use of acoustic impedances of the bulk material in Eq.
0 0 MHz A fq = 4 . 5 0 M H z D f q = 5 . 0 0 MHz o fq = 6 0 5 MHz THEORY Z = 0 381 (BULK Au) Z=l Fig. 10. A comparison between experimental d a t a and Eq. 381 for gold on quartz crystals with different resonant frequencies. The curve representing Eq. (47) with Z = 1 is also shown for comparison purposes. [f/Af - Pftf (48) Since M and F are both dimensionless parameters, for a specific material (or Z), crystals with different fq should obey the same M versus F curve; Fig. 05 MHz). The experimental data are in excellent agreement with the theoretical curve.
Applications of Piezoelectric Quartz Crystal Microbalances by C. Lu, A.W. Czanderna