In geometry, biology, mineralogy, and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. The geometry of the unit cell is defined as a parallelotope in n dimensions.
The concept is used particularly in describing crystal structure in two and three dimensions, though it makes sense in all dimensions. A lattice can be characterized by the geometry of its unit cell. The unit cell is a section of the tiling (a parallelogram or parallelepiped) that generates the whole tiling using only translations, and is as small as possible.
There are two special cases of the unit cell: the primitive cell and the conventional cell. The primitive cell is a unit cell corresponding to a single lattice point. In some cases, the full symmetry of a crystal structure is not obvious from the primitive cell, in which cases a conventional cell may be used. A conventional cell (which may or may not be primitive) is the smallest unit cell with the full symmetry of the lattice and may include more than one lattice point.
Questions regarding Primitive Unit Cell (and what I think the answer are, correct me if I am wrong)
1. Can there be more than one Primitive Unit cells for the same crystal?
yes, Wigner Seitz cell always will exist. There can be other primitive Unit cells along with Wigner Seitz too. But...
Hey guys,
I got an XRD data for my sample and want to determine its density. This requires finding lattice parameters. However, I'm not certain about the crystallographic system of my sample. How can I determine the type of the unit cell my sample has from XRD data (I can use GSAS II if...
First of all, I don't think the question was clear enough. Therefore, I had to assume they are referring to the volume of the unit cell.
V=a^3, side length a
aBCC=2R√2, aFCC=4√3/3R
%change=(VFCC-VBCC)/VBCC
I thought this was right until I checked with others who did this:
so the only...
I don't understand the ratio [ 1 g / 6.02*10^23 amu] in the following conversion factor:
[228.2 amu / 4.75*10^(-23) cm3] * [ 1 g / 6.02*10^23 amu] = 7.98 g/cm3
(This calculation is in a problem where you're finding the density of a unit cell in g/cm3 - though it has nothing to do with the...
I'm modelling the interiors of core-dominated (exo)planets. The EoS I use in my calculations are mostly either a Birch-Murnaghan formulation or a Mie-Grüneisen-Debye formulation. In either case, the ambient density ρ0 at ambient pressure and temperature are required for the implementation...
How do I get the wave dispersion for a 2D continuum unit cell subjected to a periodic boundary which is excited longitudinally? I'll be applying forces in ABAQUS with varying frequencies. I have come across Blochs theorem but I can't find any application of it in continuous systems. Every...
Hi guys , I want to construct a primitive unit cell for diamond, which is made of a fcc lattice and a basis of 2 carbons atoms. I know that a primitive unit cell isn't unique but the two variants I get are drastically different . As far as I can see they both include 2 whole atoms/points in the...
My textbook states that all the 14 bravais lattices have one of the 7 types of parallelepiped (7 crystal systems) that can be used as an unit cell. However in case of 3D HCP textbooks don't talk about this parallelepiped, rather they consider a hexagonal prism as the unit cell. Why is it so...
Dear All,
I've been recently reading the very clear text of Burns and Glazer entitled Space Groups for Solid State Scientists in the context of my thesis which requires understanding of symmetries of crystals, more specifically symmetries of (approximate triply periodic minimal surfaces)...
Long time no see, PhysicsForums. Nevertheless, I have gotten myself into a statistical mechanics class where the prof is pretty brutal and while I can usually manage, this problem finally has me stumped. I'd like to be nudged in the right direction, not outright given the answer if possible. I...
As you may know, below is the conversion process of square unit cell into circular shape in order to calculate the thermal utilization factor (f) for a lattice.
As far as I know, it is really difficult to make a simulation for which a lattice is constructed as a circular fuel and square...
hi, in perovskite crystal, such as BaTiO3, due to the off-centre of Ti ion, there exists a polarization moment in the unit cell (as shown in below link). my question is: does the disposition of Ti atom lead to separation of electron cloud from the nuclei of the Ti atom and so the Ti atom plays...
Experimentalists usually provide chemical unit cell information including full symmetry (space group) information of the crystal together with coordinates of independent atoms. But this cannot be directly used by ab initio packages, which requires either primitive cell or unit cell information...
Hi folks,
It is an elementary question for people expert in superconductivity.
I know there is a theory, the BCS theory, and the GIzburg Landau theory too that apparently explains superconductivity.
My question is, if I give you a unit cell would you be able to tell me the temperature at...
For inorganic chemistry, I am being asked to draw the solid state structure of polonium which i know how to do. However it asks what the symmetry of the unit cell is, and I don't know how to answer. I know what a unit cell is, I'm just not sure what the question means, or what it is looking for...
1) My teacher said that to analyze the properties of entire crystalline solid, we just need to analyze the properties of a unit cell, which is the smallest repeating unit of a crystalline solid.
2) But crystalline solids are known to be anisotropic, i.e. they have different properties in...
Homework Statement
So for my homework assignment in 'Materials Science and Engineering', We were given the following problem.
1. Li and Ra both are both BCC metals. For this problem assume they form a complete solid solution (even though the very large difference in their atomic size tell us...
I am trying to understand the concept of interatomic spacing. Below is a link to three pictures, and my questions is: why are they different? I thought atoms were packed together touching each other like in the first picture but the second and third imply otherwise. Any explanation or help is...
Homework Statement
[/B]
ZnS crystalizes in the B3 type structure with the space group is F¯43m. This structure is shown below and can be regarded as the bi-atomic form of the diamond lattice (F d¯3m). Upon applying a force along the [1,1,1] direction, the crystal might experience a change in...
Homework Statement
The fraction of volume unoccupied in the unit cell of the body centered cubics lattice is?
Homework EquationsThe Attempt at a Solution
I got the volume occupied by the atoms as (8/3)πr3. I am not sure if it is right. I just assumed that all the atoms were of same element.
I...
After specifying the primitive vectors of a structure namely (a,b,c) in Wien2k, one has to specify locations of atoms in unit cell.There are three components X,Y,Z which determine the atom location. I want to know whether "X,Y,Z components" are corresponding to vectors a,b,c or they are...
1. estimate the fermi energy for lithium... the crystal structure of lithium is a bcc with a unit cell size of 3.5*10^-10 m
[b]i need n, which equals N / V. if i divide by per atom, then i get (N/atom) / (V/atom) = valance / (V/atom). my question is how to get the volume per atom...
Hi all,
Im trying to think of a way of generating non-intersecting randomly oriented cylinders within a unit cell volume for micromechanical analysis.
Several research papers suggest a monte-carlo approach was used by displacing cylinders by vectors until the "condition was satisfied" -...
Hi all,
I read The unit cell is the smallest structure that repeats itself by translation through the crystal.
Some says premitive unit cells contains atoms only at the corners while a unit cell may contain extra atoms in between(like bcc or fcc).
At one place I found this:
For each...
I have some difficulty understanding how the volume per unit cell for the diamond structure is calculated.
I've seen in various websites that this volume is:
##v=a^3 = \left( \frac{8r}{\sqrt{3}} \right)^3##
Here ##r## is the radius of an atom. But how did they work out ##a## (the edge of the...
Homework Statement
The research notes from an x-ray diffraction experiment were damaged and information was lost. The wavelength of the x-rays used in the experiment, and measurements of the three smallest Bragg angles (θ) from the sample were all that remained: they were 0.71Å, 10.1°, 14.4°...
hello
i got to ask if the center of symmetry is specific to a unit cell or a pattern or system of specific unit cell? I mean is Cubic (Bravis Lattice) is Centro symmetric or the structures formed by it. As an example, Tetragonal unit cell appears centro-symmetric but forming structures like...
In statistical mechanics, nearly all the textbooks say that the volume of the smallest cell in the phase space of a N-particle system is h^{rN} where h is the Planck Constant, r is the degree of freedom.
Also these books say that this comes from the uncertainty principle. However, the...
Greetings everyone,
I am taking a course on elementary condensed matter physics and our textbook is "Introduction to Solid State Physics" by Charles Kittel. I have read the crystal structure from 4 books; however, I am still confused about the definitions such as unit cell, primitive vector and...
Hello Forum,
a lattice is a set of points. We can place a basis at each set of points.
The basis can be one atom or a group of atoms.
I thought that a translation of the basis would produce the whole crystal...
How is a basis different from the unit cell? Are they the same thing...
Knowing the atomic weights of Na+ and Cl- are 23 and 35.5, respectively, calculate the density (g/cm^3) of NaCl crystal. Hint: Avogadro’s number N = 6.02 x 10^23 is the number of atoms in one mole (weight of 1 mole = atomic weight in grams)
unit cell is Face centered
unit cell contains a...
So I usually use VESTA to make my figures, and though the new version is able to do many mad things with calculated electron density isostructures and whatnot, I can't seem to just be able to throw in some clover-leaf d or p orbitals like what was done in the image below (from this paper on...
Hi to all experts!
I know individually about primitive cell("It has lattice point at corners only") and unit cell("It has lattice point at corners as well as at center if bcc or at faces if fcc or at bases if it is base centered")
Are these right?
But I don't know what is Wigner-Seitz cell...
Homework Statement
Unit cell of a crystal lattice is a parallelepiped spanned by the vectors u, v, w vectors have lengths of 1, 2 resp3 (le). angles between the vectors is
[u, v] = pi / 4
[u, w] = pi / 3
[v, w] = pi / 6
Determine the volume of the unit cell.
Homework Equations
How do...
How is the distance between any two layers in a FCC unit cell equal to a/√3, where a is the edge length? I think it should be a/2 because the distance of a face centered atom from any 4 edges surrounding it is a/2. Can someone explain it geometrically?
Aluminum has a density of 2.699 g/cm3 , and the atoms are packed in a face-centered cubic crystal lattice. Find the mass of a unit cell.
-----I already know the answer is 1.792*10^-22g/unit cell
I have a question about how you get the answer:
I know you multiply 4.480*10^-23g * 4 atoms/1...
If I have the fractional coordinates of asymmetric unit and I know the space group of certain material, is there an easy way to generate the fractional coordinates of the atoms in the conventional unit cell?
Homework Statement
Calculate dhkl and vc for the (111) direction of germanium.
Homework Equations
dhkl=a/sqrt(h2+k2+l2)
vc=unit cell volume=a1dot(a2xa3)
or
vc=structure form factor/density
The Attempt at a Solution
dhkl=a/sqrt(3)
I know how to solve this, I've just...
Unit Cell -- Linear Density -- BCC&FCC
Homework Statement
Calculate the linear density for the most densely packed directions in BCC and FCC. Note the difference in linear density. Note the difference in linear density.
Homework Equations
LD = #of atoms/length
The Attempt at a...
Hello all,
I already have the answer to my question, but what I would like to know is why. My question is: why in the question below is the plane 111 used to find ao and not another plane?
An ordered compound of NiAl has a cubic structure with one formula unit/cell. One Al atom at...
Q.The unit cube length of LiCl (NaCl structure) is 5.14 amstrong . Assuming anion-anion contact, calculate the ionic radius for chloride ion.
How to assume anion-anion contact ? Can anyone help with a 3D figure?
What is the average radius for a unit cell, for example, for Na? Is it the average of the ionic radii for the different coordination numbers (weighting each coordination number the same)? Or would it be the covalent radii or something else?
Homework Statement
Q 2.
(a) For the HCP crystal structure, show that the ideal c/a ratio is 1.633. (10%)
(b) Hence, calculate the unit cell volume of cadmium with a HCP structure and atomic radius of
0.1490 nm. Assume that the lattice period is equal to two times of the atomic radius...
Homework Statement
The unit cell in a cubic crystal is 2.74Å. Determine the Bragg angle for reflections from the planes (200), (212) and (-112). [sorry i don't know how to put a bar on top of the numbers] if the x-ray wavelength used is 1.54Å
Homework Equations
Given Bragg's condition as 2d...
I am beginning study Crystal structure.
I am finding K-points of unit cell each lattice structure.
I have to simulation bandgap structure of all lattice structure.
Tell me please!
Thanks
sansab
Materials -- unit cell question
"In terms of the atomic radius, R, determine the distance between the centers of adjacent atoms for the BCC crystal structure along the [111] direction."
I got the answer 4R but it is wrong. I came up with this by assuming that atoms touch each other in the...
Homework Statement
Cobalt has an HCP (hexagonal close packed) crystal structure, an atomic radius of 0.1253 nm and a c/a ratio of 1.623. Compute the volume of the unit cell for cobalt.
Homework Equations
area of hexagon = apothem*perimeter/2
The Attempt at a Solution
calculate 1 of...
Hi All,
Let's consider a Copper bulk material. This one can be reproduce (ad infinitum) by using a cubic unit cell (fcc) of lattice constant a. Let's cut this bulk along the (110) plane and expose the Cu(110) surface to the vacuum. My question is: which are the x and y dimensions of a (1x1)...
Homework Statement
Calculate the maximum packing fraction of the unit cell volume that can be filled by hard spheres in the Hexagonal structure
Relevant eq: Volume of spheres is number of lattice points multiplied with the maximum volume of one sphere.
The Attempt at a Solution
I...
My attempts to derive the height as a function of radius of the spheres packing the unit cell have failed. The best attempt so far was to create a diagonal line from the top atom to one of the middle ones. With that distance I thought I could use trig to find the component parallel to the height...