science

Pearson symbol

Pearson symbol is a 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 Pearson symbol rather than just read about it. In short: The Pearson symbol, or Pearson notation, is used in crystallography as a means of describing a crystal structure. It was originated by William Burton Pearson and is used extensively in Pearson's handbook of crystallographic data for intermetallic phases.

Key takeaways

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

Reference excerpt

The Pearson symbol, or Pearson notation, is used in crystallography as a means of describing a crystal structure. It was originated by William Burton Pearson and is used extensively in Pearson's handbook of crystallographic data for intermetallic phases. The symbol is made up of two letters followed by a number. For example:

Diamond structure, cF8 Rutile structure, tP6

Construction The two letters in the Pearson symbol specify the Bravais lattice, and more specifically, the lower-case letter specifies the crystal family, while the upper-case letter the lattice type. The number at the end of the Pearson symbol gives the number of the atoms in the conventional unit cell (atoms which satisfy 1 > x , y , z ≥ 0 {\displaystyle 1>x,y,z\geq 0} for the atom's position ( x , y , z ) {\displaystyle (x,y,z)} in the unit cell). The following two tables give the six letters possible for the crystal family and the five letters possible for the lattice type:

The letters A, B and C were formerly used instead of S. When the centred face cuts the X axis, the Bravais lattice is called A-centred. In analogy, when the centred face cuts the Y or Z axis, we have B- or C-centring respectively. The fourteen possible Bravais lattices are identified by the first two letters:

Pearson symbol and space group The Pearson symbol does not uniquely identify the space group of a crystal structure. For example, both the NaCl structure (space group Fm3m) and diamond (space group Fd3m) have the same Pearson symbol cF8. Due to this constraint, the Pearson symbol should only be used to designate simple structures (elements, some binary compound) where the number of atoms per unit cell equals, ideally, the number of translationally equivalent points. Confusion also arises in the rhombohedral lattice, which is alternatively described in a centred hexagonal (a = b, c, α = β = 90°, γ = 120°) or primitive rhombohedral (a = b = c, α = β = γ) setting. The more commonly used hexagonal setting has 3 translationally equivalent points per unit cell. The Pearson symbol refers to the hexagonal setting in its letter code (hR), but the following figure gives the number of translationally equivalent points in the primitive rhombohedral setting. Examples: hR1 and hR2 are used to designate the Hg and Bi structures respectively. Because there are many possible structures that can correspond to one Pearson symbol, a prototypical compound may be useful to specify. Examples of how to write this would be hP12-MgZn 2 {\displaystyle _{2}} or cF8-C. Prototypical compounds for particular structures can be found on the Inorganic Crystal Structure Database (ICSD) or on the AFLOW Library of Crystallographic Prototypes.

See also Crystal structure Bravais lattice Strukturbericht designation

References

External links "Inorganic crystal structure database (ICSD)". Retrieved 13 December 2022. "AFLOW Library of Crystallographic Prototypes". Retrieved 13 December 2022.

Further reading United States Naval Research Laboratory - Pearson symbol (Examples and pictures)

Worked examples

Example 1 — a first encounter with Pearson symbol

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

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

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

Frequently asked questions

What is Pearson symbol in simple terms?

Why does Pearson symbol matter?

Because it connects several 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 Pearson symbol?

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 Pearson symbol.