# What is bravais lattice: Definition and 12 Discussions

In geometry and crystallography, a Bravais lattice, named after Auguste Bravais (1850), is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by

R

=

n

1

a

1

+

n

2

a

2

+

n

3

a

3

,

{\displaystyle \mathbf {R} =n_{1}\mathbf {a} _{1}+n_{2}\mathbf {a} _{2}+n_{3}\mathbf {a} _{3},}
where the ni are any integers, and ai are primitive translation vectors, or primitive vectors, which lie in different directions (not necessarily mutually perpendicular) and span the lattice. The choice of primitive vectors for a given Bravais lattice is not unique. A fundamental aspect of any Bravais lattice is that, for any choice of direction, the lattice appears exactly the same from each of the discrete lattice points when looking in that chosen direction.
The Bravais lattice concept is used to formally define a crystalline arrangement and its (finite) frontiers. A crystal is made up of one or more atoms, called the basis or motif, at each lattice point. The basis may consist of atoms, molecules, or polymer strings of solid matter, and the lattice provides the locations of the basis.
Two Bravais lattices are often considered equivalent if they have isomorphic symmetry groups. In this sense, there are 5 possible Bravais lattices in 2-dimensional space and 14 possible Bravais lattices in 3-dimensional space. The 14 possible symmetry groups of Bravais lattices are 14 of the 230 space groups. In the context of the space group classification, the Bravais lattices are also called Bravais classes, Bravais arithmetic classes, or Bravais flocks.

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1. ### Equivalence between Bravais lattice definitions

Proof. To demonstrate that a Bravais lattice (Figure 1) can be considered as a set of points located by a linear combination of primitive vectors of the lattice with integer coefficients, a sequence of claims in increasing order of complexity can be adopted. First, what is shown for one octant...
2. ### I Can all possible periodic arrangements of lattices be arranged as a Bravais lattice just by taking a different motif?

or Are all naturally occurring crystals with periodic arrangement of lattices Bravais lattices? From two days, I have been trying to understand Bravais lattices and what it's importance is and after a lot of research, I came to know that they are a periodic arrangement of lattice points with...
3. ### I What is the Relationship Between Lattice Points and Basis Balls?

Hi, take a look at the picture from my textbook, specifically the bottom part: there are five lattice points, shouldn't that mean that there are also 5 "small basis balls"? Or can they be "shared"? If so, they are not all oriented in the same way - is that not important since there's no...
4. ### I Who can identify a Bravais Lattice?

I have a real hard time trying to imagine why a face centered cubic cell originates a Bravais lattice. Could you try to explain it? I have also been trying to figure out if a side-centered cell is a Bravais lattice as well. This cell is a simple cubic cell with additional point at the midpoints...
5. ### Figuring out Bravais lattice from primitive basis vectors

Homework Statement Given that the primitive basis vectors of a lattice are ##\mathbf{a} = \frac{a}{2}(\mathbf{i}+\mathbf{j})##, ##\mathbf{b} = \frac{a}{2}(\mathbf{j}+\mathbf{k})##, ##\mathbf{c} = \frac{a}{2}(\mathbf{k}+\mathbf{i})##, where ##\mathbf{i}##, ##\mathbf{j}##, and ##\mathbf{k}## are...
6. ### Seek help for space groups in 2 dimensions Bravais lattice

Dear experts, I'm not familiar with crystal structure theory. I'm seek expertise to figure out space groups in 2 dimensions Bravais lattice of the attached structures. In the figure, red and greens dots represent different atoms. I'll greatly appreciate your help. Struture 1...
7. ### Confusing on Bravais lattice and base vectors

Hi there, I know that primitive cell is not unique and there are more than one way to define the primitive vectors but my question is when we said "primitive vectors" do we have to construct the Bravais lattice with choosing a proper basis first? My reasoning is suppose the crystal consist of...
8. ### Bravais Lattice in Two Dimensions

In the book Applied Physics by P.K.Mittal, on page#25 under the heading of "Bravais lattice in two dimensions", a paragraph says, "The number of point groups in two dimensions is 10." My 1st question is, Then how many in three dimensions? Paragraph further says, "10 groups in two...
9. ### Can Bravais Lattices Be Expressed as a Combination of Primitive Vectors?

I have three primitive vectors a1,a2,a3 for the body-centered cubic (bcc) Bravais can be chosen as a1=ax a2=ay a3=(a/2)(x+y+z) or, for instance, as b1=(a/2)(y+z-x) b2=(a/2)(z+x-y) b3=(a/2)(x+y-z) where x,y,z are unit vectors. Now I should show that any vector of the form...
10. ### Analysis of Electron Orbits in Magnetic Fields: Bravais Lattice

Homework Statement IF we consider electrons in a crystal subject to a magnetic field. The electrons near the fermi energy wil obey open or closed orbits. Using semiclassical eqn of motion and band structure for a bravais lattice, discuss the behavour and derive all conserved quantities...
11. ### Proving Bravais Lattice Volume?

Proving Bravais Lattice Volume?!? Hi guys, So with a Bravais lattice, you have 3 basis vectors: a1, a2, and a3. I know that you would get the volume of the lattice as a scalar product of the three: V = a1 dot [a2 x a3]. How would you start going about PROVING this? A little direction...
12. ### Bravais Lattice of FeAl Crystal: What is It?

could some one please help me with this question, What is the bravais lattice of FeAl crystal I know Iron is bcc, and FeAl is bcc with the Al in the (1/2,1/2,1/2) position, but what is the bravais lattice for this crystal?? I would appreciate any pointers newo