The 14 Basic Bravais Lattices and more

Triclinic(1): a1 ≠ a2 ≠ a3; α ≠β ≠ γ Monoclinic(2): a1 ≠ a2 ≠ a3; α =β = 90°≠γ Orthorhombic(4): a1 ≠ a2 ≠ a3; α =β =γ = 90° Tetragonal(2): a1 = a2 ≠ a3; α =β =γ = 90° Cubic(3): a1 = a2 = a3; α =β =γ = 90° Trigonal(1): a1 = a2 = a3; α =β =γ<>1 = a2 ≠a3;α=β=90°; γ=120°

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The ZnS (or Diamond, or Sphalerite) Structure



zinc blende" lattice is face centered cubic (fcc) with two atoms in the base at (0,0,0) and (¼, ¼, ¼).
It is not only an important lattice for other ionic crystals like ZnS, which gave it its name, but also the typical lattice of covalently bonded group IV semiconductors (C (diamond form), Si, Ge) or III-V compounds semiconductors (GaAs, GaP, InSb, InP, ..)
The ZnS lattice is easily confused with the ZrO₂ lattice below.
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The CaF2 or ZrO2 Structure



The lattice is face centered cubic (fcc) with three atoms in the base, one kind (the cations) at (0,0,0), and the other two (anions of the same kind) at (¼, ¼, ¼), and (¼, ¾, ¼).
It is often just called the "fluorite structure".
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Perovskite



The lattice is essentially cubic primitive, but may be distorted to some extent and then becomes orthorhombic or worse. It is also known as the BaTiO3 or CaTiO3 lattice and has three different atoms in the base. In the example it would be Ba at (0,0,0), O at (½, ½, ,0) and Ti at (½, ½, ½).
A particular interesting perovskite (at high pressures) is MgSiO3. It is assumed to form the bulk of the mantle of the earth, so it is the most abundant stuff on this planet.
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CsCl structure



The lattice is cubic primitive with two atoms in the base at (0,0,0) and (½, ½, ½). It is a common error to mistake it for a bcc lattice.
Intermetallic compounds (not necessarily ionic crystals), but also common salts assume this structure; e.g.
CsCl, TlJ, ..., or AlNi, CuZn.
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NaCl (Rock Salt) structure



The lattice is face centered cubic (fcc), with two atoms in the base: one at (0, 0, 0), the other one at (½, 0, 0)
Many salts and oxides have this structure, e.g. KCl, AgBr, KBr, PbS, ... or MgO, FeO.
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Spinel Structure



The spinel structure (sometimes called garnet structure) is named after the mineral spinel (MgAl2O4); the general composition is AB2O4. It is essentially cubic, with the O - ions forming a fcc lattice. The cations (usually metals) occupy 1/8 of the tetrahedral sites and 1/2 of the octahedral sites and there are 32 O-ions in the unit cell.
There are two types of cubic building units inside a big fcc O-ion lattice, filling all 8 octants.
The spinel structure is very flexible with respect to the cations it can incorporate; there are over 100 known compounds. In particular, the A and B cations can mix! In other words, the composition with respect to one unit cell can be

* (A8) (B16)O32, or
* A8 (B8A8)O32 = A(AB)O4 in regular chemical spelling, or
* (A8/3B16/3) (A16/3B32/3)O32

and so on, with the atoms in the brackets occupying the respective site at random.
A few examples (in regular chemical symbols)

* Magnetite; Fe3+( Fe2+ Fe3+)O4
* Spinel; Mg2+( Al23+)O4
* Chromite; Fe3+(Cr23+)O4
* Jacobsite; Fe3+( Mn2+ Fe3+)O4

The spinel structure is also interesting because it may contain vacancies as regular part of the crystal. For example, if magnetite is slowly oxidized by lying around a couple of billion years, or when rocks cool, Fe2+ will turn into Fe3+ (oxidation, in chemical terms, means you take electrons away). Vacancies will be generated in order to balance the charges.
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Tetrahedral Sites


In a tetrahedral site the interstitial is in the center of a tetrahedra forms by four lattice atoms. Three atoms, touching each other, are in plane; the fourth atom sits in the symmetrical position
on top.
Again, the tetrahedral site has a defined geometry and offers space for an interstitial atom.
The configuration on top is the tetrahedral position in the fcc lattice. The black circles denote lattice points, the red circle marks one of the 8 the tetrahedral position.
The picture on the bottom shows the tetrahedral configuration for the bcc lattice. We have (6 · 4)/2 = 12 positions per unit cell.
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Octahedral Sites




An octahedral position for an (interstitial) atom is the space in the interstices between 6 regular atoms that form an octahedra.

Four regular atoms are positioned in a plane, the other two are in a symmetrical position just above or below. All spheres can be considered to be hard and touching each other.

The six spheres define a regular octahedra, in its interior there is a defined space for an interstitial atom, bordered by six spheres.

Octahedral sites exists in fcc and bcc crystals. The other prominent geometric environment for interstitials is the tetrahedral site.

The octahedral site in an fcc lattice bottom:
We have 12/4 +1 = 4 positions per unit cell.

Also we have octahedral sites in the bcc lattice. We have 12/4 + 6/2 =6 positions per unit cell.

Film Growth Modes

Growth modes

1. Layer by layer, or Frank-van der Merwe growth mode. It is because the atoms of the deposit material are more strongly attracted to the substrate than they are to themselves.
   For depositions of films on dissimilar substrates, full-monolayer nucleation will be promoted by strong film-substrate bonding (negative heat of mixing), low film surface energy and high substrate energy.
   
2. Island, or Volmer-Weber growth mode. It is because the deposit atomes are more strongly bound to each other than they are to the substrate.
   
3. Layer + island, or Stranski-Krastanov (SK) growth mode. It is an intermediate case and it is much more common than one might think. In this case, layers form first, but then for one reason or another the system gets tired of this, and switches to islands.
   

Basic Principles of Scanning Tunneling Microscopy

The scanning tunneling microscopy (STM) is based on the tunneling current between a metallic tip, which is sharpened to a single atom point and a conducting material.

A small bias voltage (mV to 3 V) is applied between an atomically sharp tip and the sample. There’s no current if the distance between the tip and the sample is large. When the tip is brought very close (<10Å) without physical contact, a tunneling current flows across the gap between the tip and the sample. It is because wavefunctions overlaps between the tip atom and the surface atom, electrons can tunnel through the vacuum barrier separating the tip and sample in the presence of a small bias voltage.

To produce images, the STM can be operated in two modes. One is constant current imaging and the other one is constant height imaging.