Lattice Definition and 437 Threads

I will soon start a Master thesis in Lattice QCD. There I will spends lots of time developing C++ code and running it on different supercomputers. After that I consider doing a PhD if the Master thesis runs well. For the experimentalists I can see a lot of almost-engineering jobs where they...

Hi all, I’m brushing up my skills on solid state physics and I have a few questions about crystal lattices: 1. What’s the spacing between allowed kx, ky, and kz states for a lattice of dimensions La x Lb x Lc? My attempt: The spacing is kx, ky, and kz: k_x = \frac{2\pi}{L_a}, \qquad k_y =...

To solve the full many-body electron problem one often uses the approximation that the dynamics of the electron system, is that of N interacting electrons living in a periodic lattice of positive ion cores. What justifies this approximation and does it have a particular name?

Hello! When computing the density of states of electrons in a lattice, a material with dimensions L_x, L_y, L_z can be considered. The allowed \mathbf{k} vectors will have components k_x = \displaystyle \frac{\pi}{L_x}p k_y = \displaystyle \frac{\pi}{L_y}q k_z = \displaystyle \frac{\pi}{L_z}r...

Homework Statement Nearly free electron model in a 2D lattice. Consider a divalent 2D metal with a square lattice and one atom per primitive lattice cell. The periodic potential has two Fourier components V10 and V11, corresponding to G = (1,0) and (1,1). Both are negative and mod(V10) >...

Is it correct that a crystall of simple lattice (lattice with primitive cells each having only one atom) cannot be antiferromagnetic? In other words, the antiparallelism must occur between atoms within each primitive cell. Thanks.

This is a continuation of a side issue from another thread.

I have the opportunity to pursue a research project in either lattice QCD or QED. In the case of QED, I'd be writing the code myself, will be able to understand the whole thing, et cetera. There shouldn't be any mystery in this. It almost seems like a long exercise, and there isn't anything I'd...

I need to generate a tree in a cubic lattice that, from any cell, visits every other cell in the lattice just once. This visit must be blind, that is, it is not allowed to mark the cell as visited. Thanks in advance for any solution or reference.

Hey could anyone please explain how you go about drawing a reciprocal lattice? For example a 2d rectangular lattice to it's reciprocal form? Also... I don't know if this is correct but if you have a 2d rectangular lattice with lattice vectors L=n1a1 + n2a2 would the reciprocal lattice vectors...

Hi. What are superconductor ions? Are they naturally occurring ions inside the lattice structure of a superconductor when it's manufactured or are they ions introduced artificially to a superconductor's lattice ? And do the ions have spin?

Hi. I'm wondering if anyone has any info on "quark seeding" like: Is it possible to dope the crystal lattice of a solid material by replacing electrons with quarks ?

If the Euclidean plane is partitioned into convex sets each of area A in such a way that each contains exactly one vertex of a unit square lattice and this vertex is in its interior, is it true that A must be at least 1/2? If not what is the greatest lower bound for A? The analogous greatest...

Homework Statement What is the area of the primitive cell for the lattice shown below? The nearest neighbor separation is "a." Homework Equations Here's the lattice we were given on our handout, and I have added the lines to indicate the square lattice (in red), the basis (in purple), and...

Homework Statement Analyze the specific heat of a one dimensional lattice of identical atoms: Show within Debye approximation that the specific heat at low temperatures ( ≪ Θ) is proportional to T/ΘD . Here ΘD=ℏD/ kB = ℏvs/KBa is the Debye temperature valid for 1D, kB the Boltzmann...

I understand that the lattice energy is the energy released when an solid ionic compound forms or it is the energy required to separate completely a mole of a solid ionic compound into its gaseous ions. So is second definition the same thing as vaporizing an ionic compound and so we can...

Hi! If I have points A and B in a lattice in the plane, and the closest path between them is n + m steps (for example 4 steps upwards and 5 steps to the right), there are C(9,(5-4)) = 9 combinations of paths between them. I have to choose the 4 ways upwards (or the 5 ways to the right) of the 9...

Peierls distortion states that for a 1 dimensional polymer (like polyacyteline) with lattice spacing a they should have a half-filled conduction band, why? And how does changing the lattice space to 2a cause it to form an energy gap? In my mind it should be the same as the first case...

Hello everybody, I have three quite mathematical questions in modern QFT. 1) Why it's supposed that N=2 SUSY Yang-Mills probably cannot be put on a lattice? 2) What is the recent status of lattice approach to conformal quantum field theories? This question is motivated by the following...

Homework Statement Consider a system of rotors, each of them placed at one node of a 3D cubic lattice. The system is known as a Heisenberg spin model. Each rotor is represented by a vector of unit length ##\mathbf S(\mathbf r)##, where ##\mathbf r## is its position on the lattice. The...

A Bloch wave has the following form.. ## \Psi_{nk}(r)=e^{ik\cdot r}u_{nk}(r)## The ##u_{nk}## part is said to be periodic in real space. But what about reciprocal space? I've had a hard time finding a direct answer to this question, but I seem to remember reading somewhere that the entire...

Hello guys! I just just wondering a general thing about calculations done in the field theory and those made in the lattice. In the field theory we have some results that in principle should match with the lattice ones in the thermodynamic limit. However, when we tried to solve the same problem...

Homework Statement Boron atoms at a concentration of 3.60E+16 atoms/cm3 are added to pure intrinsic silicon as a substitutional impurity. Assume that the boron atoms are distributed homogeneously through the silicon in a cubic array. Enter the fraction, by weight, accounted for by impurity...

Homework Statement the volume density of a body centered cubic lattice is 5.3*10^22 Calculate the lattice constant, effective radius of atom, surface density on 110 plane, and distance between two nearest parallel 110 planes. Homework Equations 4/a^3= volume density 2/sqrt2*a^2 The Attempt at...

Homework Statement A material contains two types of atoms (A and B) in a zincblende structure. Atom A is group V with a hard sphere radius of 2.5 Å. Atom B is group III with a hard sphere radius of 1.6 Å. (a) What is the lattice constant of this material assuming that nearest neighbour atoms...

Homework Statement a) A material is composed of two atoms, A with effecitve radius 2.00 angstroms and B with effective radius 3.10 angstroms. The lattice is a body-centred lattice. b)Enter the volume density of either the A or B atoms in atoms/cm3 Homework Equations .5*sqrt3=(r1+r2) surface...

Hi, I was wondering if there is code already available to draw group lattice diagrams if I already know what the subgroup structure of the group and its subgroups are. For example, it's easy to determine the subgroup lattice for cyclic groups simply using divisors via Lagrange's Theorem...

Homework Statement Use a computer to calculate numerically the potential energy, per ion, for an ifinite 2D square, ionic crystal with separation a; that is, a plane of equally spaced charges of magnitude e and alternating sign. Homework EquationsThe Attempt at a Solution The closest I can...

I'm reading M. Omar Ali's Elementary Solid State Physics and in it, in Subsection 1.4 The Fourteen Bravais Lattices and the Seven Crystal Systems he says that "..., but one cannot place many such pentagons side by side so that they fit tightly and cover the whole area. In fact, it can be...

Questions I have arrive from other forum by request. I asked: Why can't an infinite motionless lattice be stable or even possible? We set the stage with an infinite lattice and an exactly zero cosmo-constant ( which I gather results in infinite Minkowski space ) universe, what happens? Can't a...

In my course we are currently studyinh Bravis lattices. We were told that the reciprocal of the reciprocal lattice is the original lattice. This is very easy to prove when given an example of a SC/BCC/FCC lattice, however, is there a formal proof for this?

There are not found the WIMPs until now. Ma be the effect of Dark Matter is because of a defect in topology otherwise than time dilation in General Relativity. The lattice gauge theory formulated on a grid or lattice of points in space and time is successfully used in the quantum...

So I know that the basis vectors of an FCC in a symmetric form are: a = \frac{a}{2}(\hat{x} + \hat{y}) b = \frac{a}{2}(\hat{y} + \hat{z}) c = \frac{a}{2}(\hat{x} + \hat{z}) And that the reciprocal lattice vectors are the basis vectors of the BCC cells. I'm having a hard time doing the...

What is the "consensus" status of the existence of a lattice standard model? These two sets of notes don't seem to be in agreement. Wiese's 2009 notes http://www.itp.uni-hannover.de/saalburg/Lectures/wiese.pdf say "Thanks to a recent breakthrough in lattice gauge theory, the standard model is...

Does anyone have a good reference to a more modern introduction to lqcd? By modern I mean including unquenched, staggered quark, etc. Most intros I find are quite dated and I'm interested in learning about newer technology and methods/improved. Figured there may be some lattice theorists here...

Why are atoms taken to be spheres, and not of some other shape, in the calculation of the packing fraction of different crystal lattices? In other words, what experimental evidence and theoretical reasoning motivates this form of the atomic shape?

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...

Hi! I'm struggling in identifying the lattice points and atom basis. As I understand in a cube, there are 8 lattice points, on on each corner of a cube. But in 2d it is any square between 4 points which are the lattice points. Is this correct? So if the points on the corners are the lattice...

Dear Friends, I'm trying to bulid a non-ideal hcp lattice in order to use in MD simualtion. I have12 lattice basis. but 2 of them are negative values. Can anyone tell me how I can convert the negative values to positive? 0.66667 0.33333 -0.0416 0.66667 0.33333 -0.1668

In the following video,is he right at time at time 2:40 I don't think so .Because lattice energy of fe2o3 should be 36 times greater than Nacl (without considering radius factor)

Homework Statement A mixture of two substances exists on a cubic lattice of N sites, each of which is occupied by either an A molecule or a B molecule. The number of A molecules is NA and the number of B molecules is NB, such that NA + NB = N. The energy of interaction is k_BT\chi_{AA} between...

I stumbled across a paper which stated that the relation between statistical mechanics and field theory is exploited to recast lattice QCD in terms of a "microcanonical ensemble" of sorts. I was curious to know if this was still a commonly used technique. The paper in question...

in the solution for free electron we start with X(x) = A exp (ikx) + B exp (-ikx) then using boundary conditions we eliminate B if the wave is traveling in the positive direction and vice versa my questions are: 1. what is the boundary condition used? 2. is it X(-inf) = 0? because this would...

Homework Statement If there are a large number of ions oscillating in a straight line, we can pick the nth one oscillating about its equilibrium a*n. The potential of the entire lattice is then U = 0.5*K[u(an)-u([n+1]a)]^2 - summed over all n. How do I use Force = -dU/du(an) to derive that...

Hi. This is a very simple and stupid question: Why is the length of the reciprocal lattice vector ##G_{hkl}## equal to ##2 \pi / d_{hkl}##, where ##d_{hkl}## is the distance between the ##(hkl)## planes. Just like the length of the wave vector ##k## equals ##2 \pi / \lambda## I remember that...

The bulk modulus B = - V (∂P/∂V). At constant temperature the pressure is given by P= -∂U/∂V, where U is the total energy. We can write B in terms of the energy per particle u = U/N and volume per particle v = V/N : B = v...

Hi. A very quick question. Why is it impossible for a wave to travel on a linear one-atomic chain if its wavelength equals the lattice constant? I.e. the lattice points vibrate with a wavelength equal to the distance between them? Here's what I mean...

Hello every one, Can some one tell me about a reference (paper or book) that possible to find lattice constants of the transition metals. many thanks, Ave

Hello! I have some queries regarding Vortex Lattice Method. I want to design an airfoil using Vortex Lattice Method. For that, I need to find out the equation of airfoil first. So how exactly am I going to do that? Please refer the following link...

Hi all, Recently I am reading an introduction on using laser to create the so-called optical lattices and a periodic potential to trap the atoms or as a grating, some applications like to act on the cold atoms. I don't have much background on laser but there are few concepts I don't...