How do you find the right quartz crystal?

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We reveal the six most important selection criteria

Choosing the right quartz crystal poses problems for both developers and buyers, because they often don't know the exact specifications and each quartz group has numerous subcategories. With a focus on six crucial factors, the right quartz crystal can be determined easily.

When faced with the task of buying a quartz oscillator or designing one into a new development at the right time, it makes sense to get to know with the characteristics of these frequency control components in advance. Six criteria have to be considered when you are looking for a reliable quotation.

Six selection criteria:

&#; Package form: A hermetically sealed and radially wound metal package is generally used with quartz crystals for conventional mounting (THT), including for clock crystals with a frequency of 32.768MHz. With this type, the packages are typically over 6mm long, and are therefore not suitable for space-saving applications. Quartz crystals in SMD packages offer considerably more compact constructions, measuring for example just 1.6x1.2x0.3mm.
Note: For technical reasons, a quartz oscillator cannot be reduced in size arbitrarily; i.e. not every quartz crystal is available in every mounting form.

&#; Frequency: The frequency of common quartz crystals lies between 32.768kHz and approx. 200MHz. Quartz crystals with higher frequencies are usually available in smaller mounting forms. Thus, an 8MHz quartz crystal measures around 7x5mm while a 20MHz quartz crystal just 2x1.6mm &#; crucial for circuit design.

&#; Operating temperature range: Quartzs demonstrate a certain level of temperature dependency. If the limit values of the datasheet are overstepped, this does mean that problems necessarily occur immediately, and, depending on the circumstances, operation can continue. However, this prevents the application from staying with the guaranteed tolerances.

&#; Frequency tolerance at 25°C: By specifying the frequency tolerance (= maximum expected total deviation from the rated frequency at an ambient air temperature of +25°C and operation within the permitted parameters), the manufacturer guarantees that the oscillating frequency of the quartz crystal will stay within the permissible range. By choosing a suitable frequency tolerance, the best possible solution in terms of economical operation and functional security can be achieved for the demands of the particular application.

&#; Frequency stability across operating temperature range: Manufacturers specify both frequency stability across the operating temperature range and frequency deviation in ppm per K change in temperature. Developers can therefore take temperature influences into account in advance and compensate if necessary.
Tip: For particularly high demands on frequency stability, it makes sense to look at using temperature-compensated crystal oscillators.

&#; Load capacitance: The right load capacitance (CL) of the oscillator circuit (= capacitance C, which the quartz oscillator recognises at its connections) is crucial when it comes to maintaining the frequency as precisely as possible. Manufacturers trim quartz crystals so that they operate within the promised range across the specified range of the load capacitance. Specific alterations in the load capacitance makes it possible to change the frequencies of the quartz crystals slightly, optimising them for particularly high frequency-precision requirements. Known as "pullability," this characteristic of quartz crystals, however, is limited &#; if you exceed the tolerance sensitivity, steady oscillation is no longer assured.

Implementation tip:

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If you have specified all six criteria, you can obtain a quotation tailored to exactly your requirements quickly and easily from your distributor. It should be noted at this point that type designations vary from manufacturer to manufacturer. A corresponding Ordering Guidance helps with classification.We are happy to advise and support you in selecting the right quartz crystals for your individual project.In the webshop we have for you the quartz crystals and quartz oscillators of the manufacturer Red Frequency.

Viewpoint

Toward a Complete Theory of Crystal Vibrations

Jan Berges
• U Bremen Excellence Chair, Bremen Center for Computational Materials Science, and MAPEX Center for Materials and Processes, University of Bremen, Bremen, Germany

A new set of equations captures the dynamical interplay of electrons and vibrations in crystals and forms a basis for computational studies.

J. Berges/University of Bremen

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Figure 1: To a first approximation, the vibrations of a crystal&#;such as the common mineral quartz, shown here&#;can be understood using a picture of springs stretched between the crystal&#;s atoms (background). But reality is much more complex, and a helpful tool to study such vibrations is the technique of Feynman diagrams, which graphically describe interaction processes (foreground). Here, each component of the system is represented by a symbol: an electron by an arrow, a vibration by a spring, an electron&#;vibration coupling by a square, and a Coulomb interaction by a wiggly line.

J. Berges/University of Bremen

Figure 1: To a first approximation, the vibrations of a crystal&#;such as the common mineral quartz, shown here&#;can be understood using a picture of springs stretched between the crystal&#;s atoms (background). But reality is much more complex, and a helpful tool to study such vibrations is the technique of Feynman diagrams, which graphically describe interaction processes (foreground). Here, each component of the system is represented by a symbol: an electron by an arrow, a vibration by a spring, an electron&#;vibration coupling by a square, and a Coulomb interaction by a wiggly line.×

Although a crystal is a highly ordered structure, it is never at rest: its atoms are constantly vibrating about their equilibrium positions&#;even down to zero temperature. Such vibrations are called phonons, and their interaction with the electrons that hold the crystal together is partly responsible for the crystal&#;s optical properties, its ability to conduct heat or electricity, and even its vanishing electrical resistance if it is superconducting. Predicting, or at least understanding, such properties requires an accurate description of the interplay of electrons and phonons. This task is formidable given that the electronic problem alone&#;assuming that the atomic nuclei stand still&#;is already challenging and lacks an exact solution. Now, based on a long series of earlier milestones, Gianluca Stefanucci of the Tor Vergata University of Rome and colleagues have made an important step toward a complete theory of electrons and phonons [1].

At a low level of theory, the electron&#;phonon problem is easily formulated. First, one considers an arrangement of massive point charges representing electrons and atomic nuclei. Second, one lets these charges evolve under Coulomb&#;s law and the Schrödinger equation, possibly introducing some perturbation from time to time. The mathematical representation of the energy of such a system, consisting of kinetic and interaction terms, is the system&#;s Hamiltonian. However, knowing the exact theory is not enough because the corresponding equations are only formally simple. In practice, they are far too complex&#;not least owing to the huge number of particles involved&#;so that approximations are needed. Hence, at a high level, a workable theory should provide the means to make reasonable approximations yielding equations that can be solved on today&#;s computers.

One way to reduce the complexity of the problem is to step back from the picture of individual particles in favor of one of effective quasiparticles specific to the system at hand. An early example of a quasiparticle in the literature is the phonon: instead of focusing on the atomic nuclei that could, in principle, be located anywhere in space, one considers their collective vibration about their positions in a predefined crystal structure. Scientists have studied such &#;elastic waves&#; for almost a century [2], often resorting to two famous approximations: the Born-Oppenheimer approximation, which assumes that the electrons respond instantaneously to displacements of the nuclei; and the harmonic approximation, which posits that this response results in restoring forces proportional to the displacements.

Stefanucci and colleagues&#; work builds on studies made in the middle of the last century that analyzed the interaction between quasiparticles by borrowing tools from quantum field theory. In , Gordon Baym published a corresponding theory of electrons and phonons, in which the phonon field assigns a displacement to points in space and time [3]. One of the aforementioned tools is the technique of Feynman diagrams, which represent interaction processes graphically (Fig. 1) and can be translated into mathematical formulas through simple rules. By combining such diagrams into sets of equations that recursively depend on each other, one can account for all possible processes occurring in physical reality. In , Lars Hedin presented examples of such equations, which completely describe systems of interacting electrons [4]. In a review, Feliciano Giustino merged these approaches and coined the term Hedin-Baym equations in the context of state-of-the-art materials simulations&#;answering many, but not all, open questions [5].

Stefanucci and colleagues have addressed several of the remaining issues [1]. First, they imposed requirements on the electron&#;phonon Hamiltonian, avoiding the mistake of trying to solve a problem not properly formulated in the first place. They emphasized that the equilibrium state around which the theory is built is not known in advance, making setting up and evaluating the Hamiltonian an iterative procedure. They also stressed that this Hamiltonian cannot generally be written in terms of physical phonons, contrary to what is often supposed. Second, the team generalized Giustino&#;s work [5] to systems driven out of equilibrium at any temperature&#;a key advance because this scenario reflects experimental and technological conditions. Mathematically, this generalization allows time to take on complex values. Third, the researchers carefully derived the corresponding rules for Feynman diagrams and provided the first complete set of diagrammatic Hedin-Baym equations. Such equations form the basis of systematic approximations, in which certain diagrams are neglected, and provide a criterion [3] for the resulting dynamics to respect fundamental conservation laws. Whereas the effects of electrons on phonons and vice versa are well studied separately [5], here it is crucial that both occur simultaneously.

Nowadays, parameter-free simulations of electrons and phonons rely heavily on so-called density-functional perturbation theory [6], which is based on the Born-Oppenheimer and harmonic approximations. By contrast, diagrammatic techniques are often&#;but not always [7]&#;used in combination with parameterized model Hamiltonians. Efforts to bring both approaches together have led to so-called downfolding methods, which already exist for the electron&#;phonon problem [8]. The insights gained by Stefanucci and colleagues will certainly help to further bridge the different strategies. Moreover, the advancements beyond thermal equilibrium will be of utmost importance because such an extension is needed to explain the latest time-resolved spectroscopy experiments and to design better photovoltaics. Finally, given that the team&#;s results apply to any fermion&#;boson system, such as an interacting light&#;matter system, many fields will benefit from this seminal work.

About the Author

Jan Berges is a postdoctoral researcher at the University of Bremen in Germany. He is working on electron&#;phonon interactions at the interface of first principles and model calculations, with a focus on computational implementation. Since the beginning of his doctoral studies, which he completed in , he has been interested in many-body instabilities&#;such as charge-density waves and superconductivity&#;especially in two-dimensional materials.

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