earth science

Goldschmidt tolerance factor

Goldschmidt tolerance factor is a earth science 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 Goldschmidt tolerance factor rather than just read about it. In short: Goldschmidt's tolerance factor (from the German word Toleranzfaktor) is an indicator for the stability and distortion of crystal structures. It was originally only used to describe the perovskite ABO3 structure, but now tolerance factors are also used for ilmenite.

Key takeaways

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

Reference excerpt

Goldschmidt's tolerance factor (from the German word Toleranzfaktor) is an indicator for the stability and distortion of crystal structures. It was originally only used to describe the perovskite ABO3 structure, but now tolerance factors are also used for ilmenite. Alternatively the tolerance factor can be used to calculate the compatibility of an ion with a crystal structure. The first description of the tolerance factor for perovskite was made by Victor Moritz Goldschmidt in 1926.

Mathematical expression The Goldschmidt tolerance factor ( t {\displaystyle t} ) is a dimensionless number that is calculated from the ratio of the ionic radii:

In an ideal cubic perovskite structure, the lattice parameter (i.e., length) of the unit cell (a) can be calculated using the following equation:

Perovskite structure The perovskite structure has the following tolerance factors (t):

See also Goldschmidt classification Victor Goldschmidt

References

Illustrations

Worked examples

Example 1 — a first encounter with Goldschmidt tolerance factor

Start with the simplest possible case. Write down what Goldschmidt tolerance factor claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In earth science, 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 Goldschmidt tolerance factor 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 Goldschmidt tolerance factor 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 Goldschmidt tolerance factor

In research: Goldschmidt tolerance factor appears in earth science 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 Goldschmidt tolerance factor 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: Goldschmidt tolerance factor is common in secondary-school and first-year university syllabi. It links to neighbouring topics Crystallography, Mineralogy, so understanding it makes those chapters shorter.
In everyday life: Look for Goldschmidt tolerance factor 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 Goldschmidt tolerance factor in 20 minutes

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

Frequently asked questions

What is Goldschmidt tolerance factor in simple terms?

Why does Goldschmidt tolerance factor matter?

Because it connects several earth science 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 Goldschmidt tolerance factor?

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 Goldschmidt tolerance factor.