physics

Pake doublet

Pake doublet is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Pake doublet rather than just read about it. In short: A Pake Doublet (or "Pake Pattern") is a characteristic line shape seen in solid-state nuclear magnetic resonance and electron paramagnetic resonance spectroscopy. It was first described by George Pake.

Key takeaways

Pake doublet belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Pake doublet to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Pake doublet from memory before moving on to harder problems.

Reference excerpt

A Pake Doublet (or "Pake Pattern") is a characteristic line shape seen in solid-state nuclear magnetic resonance and electron paramagnetic resonance spectroscopy. It was first described by George Pake. It arises from dipolar coupling between isolated two spin-1/2 nuclei, or from transitions in quadrupolar nuclei such as deuterium. It is the general shape obtained from an orientationally dependent doublet. The "horns" of the Pake doublet correspond to the situation when the principal axis of the coupling interaction (the internuclear vector in the case dipolar coupling and the principal component of the electric field gradient tensor for quadrupolar nuclei) is perpendicular to the magnetic field. This situation is the most probable and the intensity is much higher. The "feet" of the lineshape correspond to the situation when the principal axis of the coupling interaction is parallel to the magnetic field which is much less statistically relevant. Pake was the first to describe this lineshape and used it to extract the proton-proton distance from his experiments on a single crystal and powdered hydrates of gypsum (CaSO4.2H2O). This made it possible to experimentally determine the internuclear distance between the hydrogen atoms in water. In solids with vacant positions, dipole coupling is averaged partially due to water diffusion which proceeds according to the symmetry of the solids and the probability distribution of molecules between the vacancies. In the case the averaged lineshape is used to analyze crystal symmetry, phase transitions, and the degree of molecular disorder in crystalline hydrates, zeolites, clays and biological tissues.

References

Illustrations

Worked examples

Example 1 — a first encounter with Pake doublet

Start with the simplest possible case. Write down what Pake doublet claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Pake doublet before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Pake doublet ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Pake doublet

In research: Pake doublet appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Pake doublet in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Pake doublet is common in secondary-school and first-year university syllabi. It links to neighbouring topics Nuclear magnetic resonance, Nuclear magnetic resonance stubs, so understanding it makes those chapters shorter.
In everyday life: Look for Pake doublet outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Pake doublet in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Pake doublet means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Pake doublet out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Pake doublet in simple terms?

Why does Pake doublet matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Pake doublet?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Pake doublet.