engineering

Langbeinites

Langbeinites is a engineering 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 Langbeinites rather than just read about it. In short: Langbeinites are a family of crystalline substances based on the structure of langbeinite with general formula M2M'2(SO4)3, where M is a large univalent cation (such as potassium, rubidium, caesium, or ammonium), and M' is a small divalent cation (for example, magnesium, calcium, manganese, iron, cobalt, nickel, copper, zinc or cadmium). The sulfate group, SO2−4, can be substituted by other tetrahedral anions with a…

Key takeaways

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

Reference excerpt

Langbeinites are a family of crystalline substances based on the structure of langbeinite with general formula M2M'2(SO4)3, where M is a large univalent cation (such as potassium, rubidium, caesium, or ammonium), and M' is a small divalent cation (for example, magnesium, calcium, manganese, iron, cobalt, nickel, copper, zinc or cadmium). The sulfate group, SO2−4, can be substituted by other tetrahedral anions with a double negative charge such as tetrafluoroberyllate (BeF2−4), selenate (SeO2−4), chromate (CrO2−4), molybdate (MoO2−4), or tungstates. Although monofluorophosphates are predicted, they have not been described. By redistributing charges other anions with the same shape such as phosphate also form langbeinite structures. In these the M' atom must have a greater charge to balance the extra three negative charges. At higher temperatures the crystal structure is cubic P213. However, the crystal structure may change to lower symmetries at lower temperatures, for example, P21, P1, or P212121. Usually this temperature is well below room temperature, but in a few cases the substance must be heated to acquire the cubic structure.

Crystal structure The crystal structures of langbeinites consist of a network of oxygen vertex-connected tetrahedral polyanions (such as sulfate) and distorted metal ion-oxygen octahedra. The unit cell contains four formula units. In the cubic form the tetrahedral anions are slightly rotated from the main crystal axes. When cooled, this rotation disappears and the tetrahedra align, resulting in lower energy as well as lower crystal symmetry.

Examples Sulfates include dithallium dicadmium sulfate, dirubidium dicadmium sulfate, dipotassium dicadmium sulfate, dithallium manganese sulfate, and dirubidium dicalcium trisulfate. Dipotassium dinickel sulfate can also be synthesized. Selenates include diammonium dimanganese selenate. A diammonium dicadmium selenate langbeinite could not be crystallised from water, but a trihydrate exists. Chromate based langbeinites include dicaesium dimanganese chromate. Molybdates include Rb2Co2(MoO4)3. Potassium members are absent, as are zinc and copper containing solids, which all crystallize in different forms. Manganese, magnesium, cadmium and some nickel double molybdates exist as langbeinites. Double tungstates of the form A2B2(WO4)3 are predicted to exist in the langbeinite form. An examples with tetrafluroberyllate is dipotassium dimanganese tetrafluoroberyllate (K2Mn2(BeF4)3). Other tetrafluoroberyllates may include: Rb2Mg2(BeF4)3; Tl2Mg2(BeF4)3; Rb2Mn2(BeF4)3; Tl2Mn2(BeF4)3; Rb2Ni2(BeF4)3; Tl2Ni2(BeF4)3; Rb2Zn2(BeF4)3; Tl2Zn2(BeF4)3; Cs2Ca2(BeF4)3; Rb2Ca2(BeF4)3; RbCsMnCd(BeF4)3; Cs2MnCd(BeF4)3; RbCsCd2(BeF4)3; Cs2Cd2(BeF4)3; Tl2Cd2(BeF4)3; (NH4)2Cd2(BeF4)3; KRbMnCd(BeF4)3; K2MnCd(BeF4)3; Rb2MnCd(BeF4)3; Rb2Cd2(BeF4)3; RbCsCo2(BeF4)3; (NH4)2Co2(BeF4)3; K2Co2(BeF4)3; Rb2Co2(BeF4)3; Tl2Co2(BeF4)3; RbCsMn2(BeF4)3; Cs2Mn2(BeF4)3; RbCsZn2(BeF4)3; (NH4)2Mg2(BeF4)3; (NH4)2Mn2(BeF4)3; (NH4)2Ni2(BeF4)3; (NH4)2Zn2(BeF4)3;KRbMg2(BeF4)3; K2Mg2(BeF4)3; KRbMn2(BeF4)3; K2Ni2(BeF4)3; K2Zn2(BeF4)3. The phosphate containing langbeinites were found in 1972 with the discovery of KTi2(PO4)3, and since then a few more phosphates that also contain titanium have been found such as Na2FeTi(PO4)3 and Na2CrTi(PO4)3. By substituting metals in A2MTi(PO4)3, A from (K, Rb, Cs), and M from (Cr, Fe, V), other langbeinites are made. The NASICON-type structure competes for these kinds of phosphates, so not all possibilities are langbeinites. Other phosphate based substances include K2YTi(PO4)3, K2ErTi(PO4)3, K2YbTi(PO4)3, K2CrTi(PO4)3, K2AlSn(PO4)3, KRbYbTi(PO4)3. Sodium barium diiron tris-(phosphate) (NaBaFe2(PO4)3) is yet another variation with the same structure but differently charged ions. Most phosphates of this kind of formula do not form langbeinites, instead crystallise in the NASICON structure with archetype Na3Zr2(PO4)(SiO4)2. A langbeinite with arsenate is known to exist by way of K2ScSn(AsO4)3.

Properties

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Langbeinites

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

In research: Langbeinites appears in engineering 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 Langbeinites 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: Langbeinites is common in secondary-school and first-year university syllabi. It links to neighbouring topics Crystal structure types, Crystals, Double salts, so understanding it makes those chapters shorter.
In everyday life: Look for Langbeinites 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 Langbeinites in 20 minutes

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

Frequently asked questions

What is Langbeinites in simple terms?

Why does Langbeinites matter?

Because it connects several engineering 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 Langbeinites?

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 Langbeinites.