A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macroscopic single crystals are usually identifiable by their geometrical shape, consisting of flat faces with specific, characteristic orientations. The scientific study of crystals and crystal formation is known as crystallography. The process of crystal formation via mechanisms of crystal growth is called crystallization or solidification.
The word crystal derives from the Ancient Greek word κρύσταλλος (krustallos), meaning both "ice" and "rock crystal", from κρύος (kruos), "icy cold, frost".Examples of large crystals include snowflakes, diamonds, and table salt. Most inorganic solids are not crystals but polycrystals, i.e. many microscopic crystals fused together into a single solid. Examples of polycrystals include most metals, rocks, ceramics, and ice. A third category of solids is amorphous solids, where the atoms have no periodic structure whatsoever. Examples of amorphous solids include glass, wax, and many plastics.
Despite the name, lead crystal, crystal glass, and related products are not crystals, but rather types of glass, i.e. amorphous solids.
Crystals are often used in pseudoscientific practices such as crystal therapy, and, along with gemstones, are sometimes associated with spellwork in Wiccan beliefs and related religious movements.
Homework Statement
A two dimensional crystal process is modeled by an Avrami equation phi(t)= 1-exp(-k*t^2), where k>0. Experimental observation suggests that the inflection point of phi occurs at t=2 hours. Find the dimension and numerical value of k.
Homework Equations
I know how to...
Homework Statement
The scattering amplidtude, F, of a, by a crystal, diffracted beam is defined to be:
(1) F=\sum{_\vec{G}}\int n_{\vec{G}}e^{i(\vec{G}-\delta\vec{k})\cdot \vec{r}}\mathrm{d}V
The integral is over all the volumeelements, dV, of the crystal.
n_{\vec{G}} is the local...
Hi,
I have a question regarding the following picture of a lattice of ice:
Why does it form the shape that it does? Is it because of the repulsion of charges from the valence electrons?
Thanks,
The relative ordering of energy in the crystal field of d4 ions are arranged as 4A1g, 4T2g and 4T1g. How can I determine this? What is the rule for describe the relative energy of the terms for dn ions?
Crystal Oscillators -- accuracy versus temperature
I have done quite a lot of desk research and spoken to a few manufacturers, but I am still not clear about the specifications for crystal oscillators and I hope someone can help me out. It is a multi-part question.
1) The accuracy of an XO...
Hello all,
I am trying to make an FM transmitter that operates at only 1 frequency. I need the frequency tolerance to be very high, so I'd like to choose a crystal instead of an LC circuit.
This is the circuit I'm building: http://cappels.org/dproj/FMdist/fmdis.htm
If I were to replace...
Hello,
This is a multi-part question that stems from understanding how X-ray diffraction occurs in crystals (eg. protein crystals).
1. Diffraction occurs when Bragg's Law is satisfied, but I'm sure the waves aren't actually being reflected. The x-ray's are scattering. What type of...
Homework Statement
A certain crystal has a set of planes 0.33 nm apart. A beam of neutrons strikes the crystal at normal incidence and the first maximum of the diffraction pattern occurs at ∅= 38°. What is the de Broglie wavelength of the neutrons?
Homework Equations
nλ = Dsin∅ where D...
Hi, suppose I want to look up the crystal structure of a pure element (for example, the structure of pure Tellurium), is there an online database or reference to easily find this information?
Thanks.
For metals for instance, is the metallic bond that determines the crystal structure(i.e. FCC (face centered cubic), HCP (hexagonal close packed)) or is the crystal structure that determines the type of bond?
In other words, if someone were to ask me what kind of bond an element with an FCC...
I'm writing an essay on liquid crystal lasers and have written the intro to my paper. Can I just double check with you all that I haven't written anything that's wrong? Thanks. Please let me know if I should also post the source I used. It's the first time I've posted something qualitative so...
So, I read an article yesterday about a potential design for a spacetime crystal. The idea behind a spacetime crystal/4-dimensional crystal is pretty interesting and I'm curious to know what others think about them/this...
Bear with me (Two part question),
In the ideal case, an electron in a lattice under the influece of a static force will undergo bloch oscillations.
A simple hamiltonian for this system would be:
H=H° +Fx and V(x+d)=V(x)
If I used the kronig-Penney Model would I be able to derive...
I am currently building a circuit that produces a 200khz signal with a potential difference of 3 - 12 volts, depending on the force applied to a strain gauge. The input voltage is a 12V, 50hz source. With no force applied to the strain gauge, the output is to be 3V and 12V at breaking force...
Hi all,
I'm trying to solve a problem in Ashcroft - Mermin "Solid State Physics", Chapter 10: The Tight-Binding Method, and need your help.
Homework Statement
In problem 2(c) it says:
For a face-centered Bravais lattice with only nearest-neighbor \gamma_{ij} appreciable, show that the...
32 point group system "mmm" in Orthorhombic crystal
Hello,
I am trying to understand the mmm symmetry in a orthorhombic crystal. Looking from the diagram I know there are 5 diads which will give me 10 unique planes in the same form. But how do I know the exact planes that are in the form given...
Homework Statement
In an orthorhombic crystal the angle between (1 1 0) and (1 -1 0) is 38o and the angle between (001) and (201) is 65o. What is the angle between (211) and (2 -1 1) ?
Homework Equations
equation of direction cosines
The Attempt at a Solution
I found the b/a...
Hi, my name is Ofek and its my first post here. hope to be clear and if not I'll try to be more specific next time.
Link for the article: http://arxiv.org/pdf/cond-mat/9708043.pdf
Writen by N. S. Branco
The model H = J*ƩSiSj + ƩΔi(Si)^2 - first sum over nearest neighbors and second sum...
Homework Statement
Show that the direction [hkl] is perpendicular to the plane (hkl) in a cubic system.
Homework Equations
None, maybe cross product
The Attempt at a Solution
I've tried to define the crystal translation vectors(cubic means a=b=c):
\vec{a}_1 = a\hat{x}\\
\vec{a}_2...
Hello,
Does anyone know any (free) software for generating simple crystal structures like forms of SiO2 or TiO2? It must be a really common problem.
My current strategy is to search the web for hours until I get lucky. There are online databases which have really complicated structures from...
Homework Statement
Draw the position of the atoms in the two neighboring planes of the GaAs crystal perpendicular to vector [010].
Find the type of the lattice and the basis of 2D crystal which is made by singling out those two neighboring layers from 3D lattice.
Homework Equations...
As I know, electrical conductivity is a second rank tensor. So in a cubic structure, there is no orientation dependence of electrical conductivity (isotropic).
But how come Si has higher electron conducitivity along [001] and hole conductivity along [110]?
Homework Statement
Show that because a pure rotational displacement field u(r) has no effect, that the energy of a crystal only depends on the symmetric strain tensor epsilon_ij.
Homework Equations
As in Ashcroft & Mermin (22.72), the energy of a crystal as a function of displacement field...
Hello experts!
Q#1) Write down the family members of {110} plane in a cubic crystal.
Attempted Answer) According to my study the this family has 6 members. But what are they? Are these the members (110),(101),(011),(-1-10),(-10-1),(0-1-1)?
Q#2) Describe the method to construct the...
I need to create a 10 MHz square wave clock signal which gets terminated into a 50 ohm resistor for use by a waveform generator. The specifications for the waveform generator suggest a 12 to 14 dBm power level for the input clock. ie. a power level of ~16-25mW.
So I've been looking to...
To calculate the intensity of the scattered radiation from a crystal after irradiating with X-rays, one can add up all electromagnetic fields of the oscillating electrons (calculated using the Liénard–Wiechert potential). Taking the time-average of the norm of the Poynting vector of the...
I have been acquiring some nice molecular models of graphene, buckyballs, and things like the model below.
http://www.indigo.com/images/product/172.jpg
One thing I have not been able to find are crystal models with the different orientations like face-centered cubic, body-centered cubic...
Hi there,
I'm measuring the voltage on the output of an amplified photodiode circuit that is capturing light emitted by an Liquid Crystal Display (LCD) projector and there is a periodic voltage drop which I don't know the reason. The projector is projecting an all-white image.
I've been...
Homework Statement
A piezo-electric precision actuator is required that produces a displacement (length change) parallel to the crystal z axis of 1.0nm/V. If a commercial type 5H PZT material is available with d33 = 650. pC/N, what length (along the z axis) is needed for the crystal...
I'm trying to learn crystallography and I've had trouble with this concept since the very beginning of the course. It's been so long since it's been introduced that I'd be embarrassed to ask the prof. Right now, I seem to understand the principles of diffraction based on the Miller model; that...
Recently did an exercise calculating the theoretic heat capacity of a metal. In the solutions manual they put the degrees of freedom f=6. Why is that? I know that a rigid body has 6 degrees of freedom but does that apply to each atom in the crystal?
I need to derive the lattice parameter in terms of the Zn-S separation distance, l.
I looked up the value and I've found it to be
a = \frac{4}{\sqrt{3}}l
The way that I started my derivation was saying that each tetrahedron has a sulfide ion in the center, so then we can make a triangle from...
Homework Statement
I'm in grade 11 working on a science fair project I found on this site:
http://www.sciencebuddies.org/science-fair-projects/project_ideas/Elec_p014.shtml
Grade 11 physics doesn't cover much so I'm confused about why the radio is set up the
way it is...
I know that...
Hi there, I am reading some introduction of crystal and the book mention that we can use the x-ray to explore the structure of the crystal. I more or less understand the idea between that, it is kinda like scatter the incoming wave and observe the outgoing wave. But the mystery stated in the...
Hi there,
I am reading Kittel's Introduction to Solid State Physics and I am quite wondering how the Madelung constant was derived for ionic crystal as in the example. In the book, he consider the repulsive potential of the form \lambda \exp(-r/\rho) and the interaction energy can be written...
user meopemuk mentioned this:
In the case of a crystal model with periodic boundary conditions, basis translation vectors e1 and e2 are very large (presumably infinite), which means that basis vectors of the reciprocal lattice k1 and k2 are very small, so the distribution of k-points is very...
This is two questions really in crystal-field theory.
For tetrahedral crystal fields, why are the 't' and 'e' orbital sets switched in energy with the case in octahedral crystal fields?
For square planar crystal fields, why do we discard the ligands along the z-axis? Why not discard the...
What decides that which salt will take up which crystal lattice?
Some salts have cubic lattice , some have hexagonal , some have orthorhombic - but what factor decides which crystal system the salt will take over. Most of the examples i have seen consist of cubic lattice system. Is it becasue...
Homework Statement
A doped silicon ingot is to be grown by the Czochralski technique with a dopant concentration of 1016boron atoms/cm3. If k0 = 0.9 for boron/Si, what concentration of boron atoms should be in the melt?
Homework Equations
Cs/C0 = k0 (1 - m/m0) k0-1
k0 = Cs / Cl
The...
Hi, I'd be most grateful for any help regarding the following problem:
Consider a 1D crystal with 2 atoms in a primitive cell (let's call them atoms A and B). Each atom has only one valence orbital denoted as \left|\psi_A(n)\right> and \left|\psi_B(n)\right> respectively.
Show that the...
How do crystallographers go from a diffraction pattern to actually determining the structure of the crystal?
http://pwatlas.mt.umist.ac.uk/internetmicroscope/micrographs/microscopy/decr5a-a-big.jpg
Homework Statement
Be the vectors a, b, c such as:
| a | = | b | = | c | = 10.5 Angstron
The angles between these vectors are:
alpha = beta = gamma = 109.5 degree
These vectors represent the lattice vectors of a crystal.
Find out their components (a_1, a_2, a_3, b_1...
Homework Statement
We have that for a crystal the lattice parameters (in angstrom and degree) are:
a b c (in Angstrom)
10.5 10.5 10.5
\alpha β γ (in degree)
109.5 109.5 109.5...
Hi, this is my first post.
I have a problem to solve:
"Given the plane (1 1 1) of 3 lattice sc, bcc and fcc, says in which case there is diffraction"
I hope that someone helps me...
Thanks for helpers
Could someone give me a brief explanation of how to label crystal planes?
For example, labeling the back plane of a fcc crystal?
I know that you take the axial intercepts, take their inverse, and come up with the miller indices, but certain planes (like the back plane or the left side...