Lattice Definition and 511 Threads

Hi, I have a sphere that it contains many sub-spheres. I want to define these small spheres as volumetric source. But when I run MCNP, it doesn't work. MCNP error: the sampeling effeiciency is too low Maybe someone can help me. 100 0 10 200 1 -1 -10 fill=2 300 1 -1 -2 3 -4 5 -6 7...

Homework Statement Homework Equations I'm not sure. The Attempt at a Solution I started on (i) -- this is where I've gotten so far. I am asked to compute the Fourier transform of a periodic potential, ##V(x)=\beta \cos(\frac{2\pi x}{a})## such that...

Homework Statement ##\Omega = {nw_1+mw_2| m,n \in Z} ## ##z_1 ~ z_2 ## is defined by if ##z_1-z_2 \in \Omega ## My notes say ##z + \Omega## are the cosets/ equivalence classes , denoted by ##[z] = {z+mw_1+nw_2} ## Homework Equations above The Attempt at a Solution So equivalance classe...

Homework Statement Hi I am looking at the proof attached for the theorem attached that: If ##s \in R##, then ##\sum'_{w\in\Omega} |w|^-s ## converges iff ##s > 2## where ##\Omega \in C## is a lattice with basis ##{w_1,w_2}##. For any integer ##r \geq 0 ## : ##\Omega_r := {mw_1+nw_2|m,n \in...

I need details on this topic ,this is my assignment but my solid state physics is not so good,and don't know much about it but i have to do this assignment ,i have material on reciprocal lattice but for only including in assignment ,not for my understanding,so i directly need any material on...

From Courant's Differential and Integral Calculus p.13, In an ordinary system of rectangular co-ordinates, the points for which both co-ordinates are integers are called lattice points. Prove that a triangle whose vertices are lattice points cannot be equilateral. Proof: Let ##A=(0,0)...

This is schematic band structure for the dxz and dyz orbitals using a 2D square Fe lattice. What is the location in the Brillouin zone of the hole-like Fermi surface and the electron-like Fermi surface?

Hi everyone, I plan to do a simulation of a Boltzmann equation with experimentally known scattering between two particles. Initially I intend to incorporate the scattering into the collision integral and use Lattice Boltzmann Equation (LBE) afterwards. But I only see LGBK (DnQb) which requires...

Hamiltonian of tight binding model in second quantization is given as H = -t \sum_{<i,j>} a_i^{\dagger} a_j After changing basis it is H = \sum_{\vec{k}} E_{\vec{k}} a_{\vec{k}}^{\dagger} a_{\vec{k}} where E_{\vec{k}} = -t \sum_{\vec{b}} e^{i \vec{k} \cdot \vec{b}} where \vec{b} is a nearest...

Homework Statement 1. For a simple cubic lattice with a lattice constant of a, the energy band can be expressed as:E = Acos(kxa)cos(kya)cos(kza) + B. (a) Suppose the effective mass for the electron at conduction band is m* = -ħ2/2a2, find A. Homework EquationsThe Attempt at a Solution I...

Hi everyone, I've been given a problem where I have to index reflections from a cubic lattice, the procedure is simple enough but I'm getting a case where I get : h^2+k^2+l^2=7 I've taken to many books, but most either don't mention the topic or say they are simply 'forbidden' reflections. I...

1. Problem Statement: For the regular solution model, develop the equations for the compositions of the coexisting phases in a binary system and plot the phase boundary as a function of χ/RT.2. This question stems from Sandler's Introduction to Applied Statistical Thermodynamics. The Attempt...

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...

Can someone tell me that in bcc lattice why xrd 100 peak does not appear?

Hello everyone, I am not an expert in the topic so I apologize in advance if the question has an easy answer. I think it is well known that if we have a set of N vortices in a superfluid their mutual interaction is logarithmic. Meaning that if \vec x_n is the position of the n-th vortex, then...

How can i use F4 tally in hexagonal lattice geometry which composed of circular fuel assembly? For example one hexagonal lattice includes circle which is cell number 5 and another hexagonal lattice includes circle which is cell number 7 etc. I want to use all these cells in one f4 tally. Please...

HI, i´m trying to build a lattice in mcnp. Actually it works but there are still lots of red lines in the plot. Maybe someone can help me. The Lattice code looks like that : lattice 1 0 2 $ outer space 2 3 -0.00126 -2 #4 #39 #41 #42 #43 #44 #45 #46 #47 $ universe 4 2 -8.4 -1 $ ball to enable...

Hi there, I'm currently working on a relatively simple code to do some lattice simulations. I have access to a computing cluster at school and have been learning how to use OpenMP to parallelize my code (each node has 16 cores). I'm currently not planning to use MPI. My main question is...

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) >...

Homework Statement Silicon crystalises in a cubic structure whose lattice is face-centred, with a basis [000],[1/4,1/4,1/4]. How many optic/acoustic modes are to be found in the phonon dispersion diagram for silicon. How many distinct branches would you expect along the [100] direction...

Homework Statement Consider the network of spins shown below. The Hamiltonian is given by $$H = - \sum_{\langle i j k \rangle} [J \sigma_i \sigma_j \sigma_k + J_0]$$ with ##J,J_o \geq 0## and ##\langle i j k \rangle## denoting spin in the same triangle (the triangles under consideration are...

Homework Statement Consider a two dimensional triangular lattice, each point of which can either contain a particle of a gas or be empty. The Hamiltonian characterising the system is defined in terms of the particle occupation numbers ##\left\{n_i \right\}_{i=1,...,N}## which can either be 0 or...

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...

i have a simulation problem about a fuel assembly, after running this warring pop up:- " non-lattice cell in lattice universe "; and visual editor crash with one warning message " warning. 2 surfaces were deleted for being the same as others." So, what may be the problem with the input?

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 Given this image http://postimg.org/image/m9dyiqwy3/ find the lattice parametre of the reciprocal lattice and the coordinates of the point x. Homework Equations a*[/B]=2π(b×c)/(a⋅b×c) b*=2π(c×a)/(b⋅c×a) c*=2π(a×b)/(c⋅a×b) Which are the vectors of the reciprocal lattice a is...

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...