science

Monoclinic crystal system

Monoclinic crystal system 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 Monoclinic crystal system rather than just read about it. In short: In crystallography, the monoclinic crystal system is one of the seven crystal systems. A crystal system is described by three vectors.

Key takeaways

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

Reference excerpt

In crystallography, the monoclinic crystal system is one of the seven crystal systems. A crystal system is described by three vectors. In the monoclinic system, the crystal is described by vectors of unequal lengths, as in the orthorhombic system. They form a parallelogram prism. Hence two pairs of vectors are perpendicular (meet at right angles), while the third pair makes an angle other than 90°.

Bravais lattices

Two monoclinic Bravais lattices exist: the primitive monoclinic and the base-centered monoclinic.

In the base-centered monoclinic lattice, the primitive cell has the shape of an oblique rhombic prism; it can be constructed because the two-dimensional centered rectangular base layer can also be described with primitive rhombic axes. The length a of the primitive cell below equals ⁠1/2⁠√(a2 + b2) of the conventional cell above.

Crystal classes

The table below organizes the space groups of the monoclinic crystal system by crystal class. It lists the International Tables for Crystallography space group numbers, followed by the crystal class name, its point group in Schoenflies notation, Hermann–Mauguin (international) notation, orbifold notation, and Coxeter notation, type descriptors, mineral examples, and the notation for the space groups.

Sphenoidal is also called monoclinic hemimorphic, domatic is also called monoclinic hemihedral, and prismatic is also called monoclinic normal. The three monoclinic hemimorphic space groups are as follows:

a prism with a wallpaper group p2 cross-section ditto with screw axes instead of axes ditto with screw axes as well as axes, parallel, in between; in this case an additional translation vector is one half of a translation vector in the base plane plus one half of a perpendicular vector between the base planes. The four monoclinic hemihedral space groups include

those with pure reflection at the base of the prism and halfway those with glide planes instead of pure reflection planes; the glide is one half of a translation vector in the base plane those with both in between each other; in this case an additional translation vector is this glide plus one half of a perpendicular vector between the base planes.

In two dimensions

The only monoclinic Bravais lattice in two dimensions is the oblique lattice.

See also Crystal structure Crystal system

References

Further reading Hurlbut, Cornelius S.; Klein, Cornels (1985). Manual of Mineralogy (20th ed.). pp. 69–73. ISBN 0-471-80580-7.

Illustrations

Worked examples

Example 1 — a first encounter with Monoclinic crystal system

Start with the simplest possible case. Write down what Monoclinic crystal system 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 Monoclinic crystal system 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 Monoclinic crystal system 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 Monoclinic crystal system

In research: Monoclinic crystal system 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 Monoclinic crystal system 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: Monoclinic crystal system is common in secondary-school and first-year university syllabi. It links to neighbouring topics Crystal systems, so understanding it makes those chapters shorter.
In everyday life: Look for Monoclinic crystal system 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 Monoclinic crystal system in 20 minutes

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

Frequently asked questions

What is Monoclinic crystal system in simple terms?

In crystallography, the monoclinic crystal system is one of the seven crystal systems. A crystal system is described by three vectors.

Why does Monoclinic crystal system 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 Monoclinic crystal system?

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 Monoclinic crystal system.