Lattice Definition and 437 Threads

Calculate the lattice constant of caesium chloride with ionic radii Cs+ 0.167nm and cl- is 0.181 nm I don't really get it, from all the structures i have seen the distance between one atom and the next is (a) or (a/2) but i don't think I am right.Any ideas. What is the difference between...

I'm answering a question where it becomes necessary to know the closest face of the BZ in a bcc structure. The answer is given as +/- (2*pi) / (sqrt(2)*a) where a is the cubic lattice parameter. I would have thought the Answer would have been sqrt(3)*a / 4. Where does the pi come from...

I wonder if somebody has ued it before. I have some probblems in compiling it to work in parallel and I hope that somebody can help in this!

Hey folks, Here's my problem: Knowing that for reciprocal lattice vectors K and real space lattice vectors R: and using the Kronecker delta: I need to prove b1, b1, b3 as shown http://www.doitpoms.ac.uk/tlplib/brillouin_zones/reciprocal.php" : I understand that for the...

vortex in superfluidity is well known in a continuum system, a vortex is well defined along a closed (continuous) path, the phase change is well defined. However, on a lattice, i don't think the phase change from site to site can be well defined. but people are talking about vortex...

Homework Statement Indicate the (111) and ([11]0) ([11] has an over line, so is negative, don't know how to do on forums!) planes in a cubic lattice in a diagram, then calculate the angle between them. The Attempt at a Solution I think I have drawn this right (see attatchment), but I am...

Homework Statement q: show that for an ideal hcp structure the c/a ratio is equal to (8/3)^(1/2) = 1.633 this question has come up before in the forum but still it has not fully answered: Kouros Khamoushi Dec30-05, 12:27 AM This is the mathematical calculation ^ means to the power of...

Homework Statement Hey guys. So, I got this question in the pic. First of all, I drew what I think to be a one-dimensional lattice (in the green box) but I'm not sure, is it right? Second of all, I don't really understand the question, I mean I know that a potential energy of charge q is...

1.Hey! I don't get the solution to the following question so I am hoping someone can explain! Ok so, the question is we have Silicon, which I have read has a DIAMOND LATTICE structure. Which basically seems to mean two face centered cubes come together. Now I need to calculate the VOLUME...

Homework Statement An element crystallises in a face-centered cubic lattice with a basis group of two atoms at [000] and [1/4 1/4 1/4]. The lattice constant is 3.55 x 10^-10 m (Q1) How many nearest and second-nearest neighbours does each atom have? (Q2) Calculate the average volume per...

K=\mathbb{Q}(\sqrt{2+\sqrt{2}}) is a Galois extension of \mathbb{Q} [I showed this]. Determine \text{Gal}(K/\mathbb{Q}) and describe the lattice of subfields \mathbb{Q} \subset F \subset K. I found that \text{Gal}(K/\mathbb{Q})=\mathbb{Z}_4. I do not know how to draw the lattice of subfields...

Homework Statement A metal fluoride crystallizes in a cubic structure such that the fluoride ions occupy lattice positions at the corners and on the faces while 4 metal atoms occupy positions within the body of the unit cells. The formula of the metal fluoride is? I don't know where...

Hi, I'm a college student in Singapore... Currently doing some research on carbon nanotubes, and so happened one of the honors student in the same lab said something about reciprocal lattice after seeing my experimental results. I went to search more about it, but i am totally clueless...

Homework Statement When x-rays are diffracted off NaCl, constructive interference is observed at an angle of 16.3 degrees. Determine the lattice constant of NaCl. Frequency of the X-ray is 1.948 x 10^18 hz Theta = 16.3 degrees Homework Equations (As far as what we're told to use and what's in...

Homework Statement The atomic mass number of copper is A = 64. Assume that atoms in solid copper form a cubic crystal lattice. To envision this, imagine that you place atoms at the centers of tiny sugar cubes, then stack the little sugar cubes to form a big cube. If you dissolve the sugar, the...

When setting up this derivation one assumes a chain of identical atoms. The interatomic interaction between atoms is short ranged and so only affects neighbouring atoms (see Hook and Hall, "Solid State Physics" chapter 2.3.1). The potential V(r) is expanded as a taylor series about r = a to...

Can anyone explain to me the difference between the bond length and the lattice constant? I'm thinking specifically about cubic crystal systems. Thanks. -Alan

packing fraction of body-centered cubic lattice -- solid state physics Homework Statement This is part of a series of short questions (i.e. prove everything in Kittel Ch. 1, Table 2): Prove that the packing fraction of a BCC (body-centered) cubic lattice is: 1/8 * pi * \sqrt{3}...

I've gone through undergrad courses of QFT, Solid State Physics and Quantum Statistical Physics but the first one didn't cross path with second and third so I only got taste in QFT applications in Solid State Physics through reading Zee's "QFT in a nutshell". My first impressions was WOW! Solid...

"empty lattice" energy bands (Kittel, problem 7.2) Homework Statement This is problem 2 of chapter 7 in Kittel's "Introduction to Solid State Physics". The student is required to sketch the free electron energy bands in the empty lattice approximation and in the reduced zone scheme, for...

In order for a dilute magnetic alloy to show the kondo effect (resistance minimum at low T), the magnetic impurites must be far apart and non-interacting. In the Kondo lattice, the magnetic impurities are much closer togeather (one impurity per unit cell), so why does this system show the...

How do you calculate lattice parameters c and a of Hexagonal ZnO ? if you are given the wavelength= 1.5406 nm, diffraction angle= 48 and the miller indexes (102)

Hi everyone- I am trying to run some MD simulations of martensitic iron. I am having a lot of trouble finding a lattice constant anywhere in the literature... I know the crystal structure is bct, so there will be some c/a ratio as well... any suggestions? Erin

Can anyone help me with few info abt carbon di oxide lattice

There is a lot of activity around the full identification of the light meson spectrum and the identification of glueballs. For these aims a lot of insight should come from lattice QCD. Presently, not all the resonances seen that appear on PDG review are obtained on lattice. What is the reason...

Homework Statement Barium metal crystallizes in a body-centred cubic lattice. The density of the metal is 3.50gcm^-3. Calculate the radius(in pm) of a barium atom. M(Ba)=137.3g/mol , NA = 6.022x10^23/mol The Attempt at a Solution For 1 unit cell: m=2x137.3/6.022x10^23...

Abstract: I propose a simple cellular lattice model with configuration space Aff(3)(Z^3). The model allows to obtain, in the continuous limit, all fermions of the SM, the gauge group of the SM, it's action on the fermionic sector, and an effective Lorentz metric. 1 a) Importance of a...

Wen's papers purport to show that given a 3D extended lattice spin model, the emergence of light, electrons, gravitons and others should work well. How similar is what he is doing with what LQG and SF have done? How hard would it be to construct a verion of LQG/SF that reproduces all of Wen's...

Hi, a few months ago, someone pointed me to an excellent primer on lattice calculations, available for free on arXiv. I was browsing and finding many results, so I was wondering if anybody had a good reference, including worked examples so one can readilly do such easy things as calculating...

Two approaches under one roof? Would it be too much to say that the following paper has made it possible for the double tetra to be imbeded into the cube? http://arxiv.org/abs/0803.4483 Numerical techniques for solving the quantum constraint equation of generic lattice-refined models in...

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...

Homework Statement Here's a problem I'm having: The primitive vectors of the hexagonal lattice are: a1 = ck a2 = (a/2)i + ([a√3]/2)j a3 = (-a/2)i + ([a√3]/2)j Find the primitive vectors of the reciprocal lattice, i.e. b1, b2, and b3. Homework Equations I do know that the...

[SOLVED] SHM: atom in a lattice [SIZE="3"]Homework Statement From Advanced Physics by Adams and Allday. Spread 3.34, Q 5. An atom of mass 5 \times 10^{-26} kg is in a cubic lattice with all bonds between adjacent pairs of atoms having a spring constant about 100 N/m. Estimate the natural...

If not, then what are the conditions for us to construct a periodic boundary condition(PBC)? If so, then please help me construct a PBC for the lattice shape in the attachments. I want to ask that what lattice site m's left neighbor is and what lattice site i's down neighbor is.From the...

Homework Statement Order the following compounds in order of increasing lattice energy: AlN, BaTe, KCl, Rb2Se Homework Equations The Attempt at a Solution Ok I know that as the distance between the two nuclei decreases and as the charge of the cation and anion increase the lattice energy...

Could anyone suggest a book for studying lattice models. Especially xy and Heisenberg models.

Calculate the lattice constant of a body-centered cubic iron crystal using the molar mass of iron, the density of iron and the Avogadro number.

First off, this is not a homework problem. I was reading Charles Kittel solid states book on Chapter 2, equation 3: electron number density, n(x), expanded in a Fourier series: n(x) = n_0 + \sum_{p} [C_p cos(\frac{2\pi p x}{a}) + S_p sin(\frac{2\pi p x}{a})] From this expansion, wouldn't...

Homework Statement Which one of the following ionic compounds has the largest lattice energy? NaCl CaO Li2O CaCl2 Homework Equations Ionic/Atomic size The smaller the ionic size, the larger the lattice energy. Size increases from right to left, increases top to bottom of...

It seems to me that the UV divergences in a quantum theory of gravity could be canceled by just requiring the distance between any two points be finite. I know loop quantum gravity basically addresses this through the quantization of area and volume, but you don't even need loop quantum gravity...

Will someone please give me a link that explains how to find the "lattice constant" of certain atoms. Or could someone please walk me through the process of how you find the lattice constants. Thanks in advance:smile:

Homework Statement "What does a reciprocal lattice vector represent in the real lattice?" The Attempt at a Solution The answer to that one is that the reciprocal lattice represent all possible k-values for the incoming radiation to be contained in the real lattice. Hence a...

I have been learning kittel's solid physics, But find it hard to have a firm grab of what a reciprocal lattice is like and can't understand it's relationship with e original lattice.. Is there a picture that draws a lattice n its reciprocal lattice into e same picture? so that i can visualize...

Let R be a convex region symmetrical about the origin with area greater than 4. Show that R must contain a lattice point different from the origin. This is the 2-D case of Minkowski's theorem, right ? How about the n-dimensional version ? The n-dimensional version is : Given a convex...

I am trying to understand 3D Si dispersion relations and reciprocal lattice vectors. My confusion is that when I look at dispersion relations the wave vector typically is normalized from 0 to 1 by a/2pi. I thought the edge of the first BZ was pi/a. Is this correct or is it 2pi/a for a diamond...

I'm having some problems with the calculations associated with this problem: Which compound in each of the following pairs of ionic substances has the most exothermic lattice energy? (a) LiF CsF I know I need to use Coulomb's law, but I don't know how to calculate r...

I am looking for informations about CoIr alloys. Who can tell me about crystal structure, lattice parameters of CoIr alloy? Please share me some references about this material. Thanks! :!)

Ok most questions (that I have come across) when dealing with the Born Haber Cycle give the Sublimation energy, the Dissociation energy, the Electron Affinity, the Ionization Energy, and the Formation Energy. I know that to get the Formation Energy it is: Hf= Hs+Hi.e.+1/2Hd+He.a.+U (Lattice...

Ok most questions (that I have come across) when dealing with the Born Haber Cycle give the Sublimation energy, the Dissociation energy, the Electron Affinity, the Ionization Energy, and the Formation Energy. I know that to get the Formation Energy it is: Hf= Hs+Hi.e.+1/2Hd+He.a.+U (Lattice...

My textbook treats lattice waves as if they are waves propagating through a mass-spring chain. Kind of like this: M -/\/\/- M -/\/\/- M -/\/\/- M The book talks about the motion of the nth atom. It says that the motion of the nth atom has been simplified by only considering the motion...