bravais lattice Definition and 12 Threads

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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