chemistry

Keating model

Keating model is a chemistry 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 Keating model rather than just read about it. In short: In physics, The Keating Model is a model that theoretical physicist Patrick N. Keating introduced in 1966 to describe forces induced on neighboring atoms when one atom moves in a solid.

Key takeaways

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

Reference excerpt

In physics, The Keating Model is a model that theoretical physicist Patrick N. Keating introduced in 1966 to describe forces induced on neighboring atoms when one atom moves in a solid. The term most often applies to the forces on first- and second-nearest neighboring atoms that arise when an atom is moved in tetrahedrally-bonded solids, such as diamond, silicon, germanium, and a number of other covalent crystals with the diamond or zinc blende structures. Crystalline solids generally consist of an ordered array of interconnected atoms, generated by repetition of a unit cell in three dimensions, and are of two extreme types—ionic crystals, and covalent crystals. Others are intermediate: partly ionic and partly covalent. Ionic crystals are made up of quite different ions, such as Na+ and Cl− in common salt, for example, while covalent crystals such as diamond are made up of atoms that share electrons in a covalent bond. In either case, attractive and repulsive forces resist moving an atom/ion or a set of them from their equilibrium positions, thus giving solids their rigidity against compressive, tensile, and shear stresses. The nature and strength of these forces is important for the scientific understanding of solids since they determine the way the solid responds to these stresses (elastic constants), the velocity of sound waves in it, its infra-red absorption, and many other properties.

Description The Keating model is the result of a general method proposed to ensure that the elastic strain energy satisfies the requirement that it is invariant under a simple rotation of the crystal, without deformation. It is a formalism for the way adjacent and close-by atoms respond when one or more atoms move in covalently bonded crystals. It is also a specific parameterization of this response for diamond, silicon, and germanium. (see the article listed under "Further Reading"). The general method is applicable for small atomic displacements to all crystal structures. It has been extended by P. N. Keating to include anharmonic effects (and calculate third-order elastic constants), and many other researchers have extended it to include forces between the covalent bonds, and augment it in other ways. The key paper that introduced the model was one of the 50 highest-impact papers over a century of Physical Review publications [1]). The model has been, and is, used by many research scientists for calculating elastic constants, lattice dynamics, band structure, dislocation strains, atomic configurations at surfaces and interfaces, and other purposes for a wide range of solids, including amorphous (i.e., non-crystalline) materials.

References

Further reading Keating, P. N. (1966-05-13). "Effect of Invariance Requirements on the Elastic Strain Energy of Crystals with Application to the Diamond Structure". Physical Review. 145 (2). American Physical Society (APS): 637–645. Bibcode:1966PhRv..145..637K. doi:10.1103/physrev.145.637. ISSN 0031-899X.

Worked examples

Example 1 — a first encounter with Keating model

Start with the simplest possible case. Write down what Keating model claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In chemistry, 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 Keating model 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 Keating model 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 Keating model

In research: Keating model appears in chemistry 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 Keating model 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: Keating model is common in secondary-school and first-year university syllabi. It links to neighbouring topics Chemical bonding, so understanding it makes those chapters shorter.
In everyday life: Look for Keating model 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 Keating model in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Keating model 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 Keating model out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Keating model in simple terms?

In physics, The Keating Model is a model that theoretical physicist Patrick N. Keating introduced in 1966 to describe forces induced on neighboring atoms when one atom moves in a solid.

Why does Keating model matter?

Because it connects several chemistry 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 Keating model?

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 Keating model.