9 votes

Why are there exactly 5 types of two-dimensional lattices, and what distinguishes them?

First, about the black lines. I think they are helpful for the hexagonal and the rhombic lattice. For the hexagonal system, it shows you the hexagons. One hexagon contains exactly the same space as ...
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Do superoxide salts of heavier alkali metals contradict the principle that lattice energy depends inversely on cation-anion distance?

TL, DR: They do not contradict. Although larger ions decrease the lattice energy by increasing ion distance, it is compensated by another factor that increases the lattice energy. And like Nisarg ...
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7 votes
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Do we really have technology with the resolution to distinguish between layers of single atoms of materials?

X-rays do not allow you to look at the material just like an microscope. You get the spacing information from the diffraction pattern of only crystalline materials and a lot of mathematics. On the ...
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Stacking two square (2D) layers to make a 3D close packed structure

It's actually a sneakily disguised version of a lattice you already know. Read on ... . Let's try out the staggered square packing. The distance unit used here is the center to center distance ...
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6 votes

Stacking two square (2D) layers to make a 3D close packed structure

In the picture, the cubic face-centered packing is shown, with layers of identical atoms colored in red and blue for better contrast. The unit cell shown with thin lines is the conventional face-...
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Whats the difference between unit cell and motif?

Conceptually, the unit cell is the larger object, the (if relating to 3D crystals), the parallelepiped containing the crystallographic motif. It is the unit cell which, by mere translation along $\...
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6 votes

Converting fractional coordinates into cartesian coordinates for crystallography

You have to use a matrix to convert. This is derived in most textbooks on crystallography, such as McKie & McKie 'Essentials of Crystallography'. The matrix is $$ M=\begin{bmatrix} a & 0 & ...
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If a good choice of a unit cell should be the one of most symmetry ,then why keep body centered tetragonal if face centered cubic exists?

Body-centered tetragonal is face-centered cubic only if $c/a=\sqrt2$. If you try your transformation with a $c/a$ value greater/less than $\sqrt2$, your "cube" will have lateral edges that ...
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Does a unit cell have to contain a whole number of atoms?

Crystallographic background A unit cell cannot contain parts of atoms from a formula unit, otherwise it would not be a geometric unit of repeatability. The simplest condition arising from ...
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How many nearest neighbours does a corner atom have?

Let's just take a picture! For that I took the crystal structure data (CIF) of CsI from literature and changed the $1b$ position from iodide to another cesium, so all atoms are the same, like in your ...
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4 votes

Does a molecule need to be placed symmetrically in the unit cell?

Don't think of it so much as putting the center mass of an atom on a vertex but as matching the unit cell symmetry to the crystal symmetry. Take the definition from google below, I've bolded key parts:...
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4 votes

Why are there exactly 5 types of two-dimensional lattices, and what distinguishes them?

For the square, rectangular, and hexagonal lattices, the black lines show Wigner-Seitz primitive unit cells. They contain all points closer to a given lattice point than to any other lattice point. ...
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4 votes

Converting fractional coordinates into cartesian coordinates for crystallography

The answer by porphyrin is correct and arguably the proper way to perform the transformation. But there is another / simpler way to convert between fractional and cartesian coordinates that requires a ...
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4 votes

Hydrogen Bond Length and Lattice Density

Here is a sketch of a layer of ice: The hydrogen bonds are fairly short (177 pm, compared to a covalent O-H bond length of 100 pm), and the distance between hydrogen-bonded atoms is shorter than the ...
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Why are there only 14 types of Bravais lattices and not 28 when there are 7 types of unit cells and each can have four variations?

Essentially, certain combinations of the possible point-group symmetries (cubic, tetragonal, hexagonal, trigonal, orthorhombic, monoclinic, triclinic) and possible translational symmetries (simple, ...
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Why does density decrease when pressure is increased on an NaCl type lattice?

Two things to consider: Even though the sodium chloride crystal structure is face-centered cubic, it is not 12-coordinate. Face-centered cubic refers to the lattice formed by periodically equivalent ...
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4 votes

Why does density decrease when pressure is increased on an NaCl type lattice?

You've gotten a good answer from Oscar explaining the atomic details of what's actually happening. More broadly however, it is important to note that, irrespective of the atomic details, it's ...
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Interplanar distance given Miller indice of the planes

Your adjacent plane isn't. Worth a thousand words, they say.
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Is there a standard scholarly reference for lattice constants of crystals of the elements?

The CRC Handbook of Chemistry and Physics contains a dedicated compilation by H. W. King, titled «Crystal Structures and Lattice Parameters of Allotropes of the Elements». In case your research ...
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Radius ratio of octahedral interstitial site in BCC lithium

Actualluy it was a mistake. The impurities usually fall into the larger interstitial sites of crystal structures. According to this problem solving chapter, the interstitial sites in FCC and BCC ...
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Why sulfonate of detergent is less likely to bind to ions present in hard water than carboxylate?

Well. Solution of sodium alkylsulfonates are good detergents, because they produce calcium alkylsulfonates in hard water, and these calcium derivates are soluble in water. By contrast, usual soap ...
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3 votes

Why are there only 14 types of Bravais lattices and not 28 when there are 7 types of unit cells and each can have four variations?

Whether to use a centered cell or the smaller primitive cell is a question of convention. The conventions are guided by making life easy. You could take a primitive triclinic cell and redefine the ...
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2 votes
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How do the three Miller indices (hkl) denote planes orthogonal to the reciprocal lattice vector?

There are two equivalent ways to define the meaning of the Miller indices: via a point in the reciprocal lattice, or as the inverse intercepts along the lattice vectors. The reflecting plane are ...
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2 votes

Why don't ions form crystal lattices in water and other polar solvents?

They actually form: ions can be dissolved up till a certain concentration, and beyond that, they form ionic lattices just as you predict. The easiest way to describe the scenario as an equilibrium ...
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2 votes

Unit cell structure of ionic crystal

I looked and there are a lot of questions on the site about units cells, many of which are pertinent. However I couldn't find one that answers your question directly. First there is no reason to ...
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Sketching lattice points, primitive axes, primitive cell, and basis of atoms

I think the cell after EDIT is correct. Here I added a few neighboring cells: Admittedly, the atom in the right bottom corner is missing. Apparently the author didn't consider it important.
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  • 361
2 votes

Height of CCP Lattice

Face-centered cubic (FCC, or closest-packed cubic, CCP) and hexagonal close-packed spheres have the greatest (and equal) density of packed spheres, occupying 74.048% of the actual volume. Ref 1 ...
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2 votes

Conventional unit cell for a hexagonal crystal system

A crystal repeats contents of a unit cell in three dimensions. If you choose the unit cell to be a parallelepiped, the translation vectors are simply the edges of it. This is an easy way to describe a ...
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In calculating the radius ratio in a tetrahedral site in an FCC lattice, why do we take tetrahedral void in the middle of the body diagonal line?

That is not the center. The image shows 1/8 of the unit cell. It is unfortunate that they labelled the edge with $a$, conventionally used for the unit cell length. It does not matter for the result, ...
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1 vote

Conventional unit cell for a hexagonal crystal system

Interestingly enough, the reason why the cell in bold is the unit-cell for the crystal is actually because the hexagonal cell has this higher symmetry you mention. To understand why, we have to ...
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