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Curvature is just a form of strain, and strain produces stress. Knowing the curvature, you can compute the strain field from which you can obtain the stress field using linear elasticity theory. In the case of fracturing, the stress causes cracks to propagate which results in fracturing. The wiki article on fracture mechanics is reasonably detailed.


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There are often several different methods of synthesizing materials, and in lots of cases they arrive at the same result. Sometimes the experiments you want to do will depend on your growth method, though: for instance, the polycrystalline samples you get from solid state reactions can be good for x-ray or neutron diffraction studies. If you want to ...


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The expression you obtained is almost correct (check the signs in your residue calculations more carefully). It is still true that $|G(r,t;r,t_0)|^2=G(r,t;r,t_0)^*G(r,t;r,t_0)=G_A(r,t_0;r,t)G(r,t;r,t_0)$ is the product of the advanced and retarded Green functions (it's just another perspective on the same math). In Fourier space, the product is transformed ...


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The presence of a ductile to brittle transition temperature implies there are insufficient (ductile) deformation modes at low temperatures to support plastic deformation and therefore fracture occurs to release energy/load. In FCC materials, dislocation slip of both edge and screw dislocations is relatively athermal and due to the number of active slip ...


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Both descriptions are correct; some people prefer the geometric description: the lattice of atoms is replace by a collection of planes, with different orientations. This corresponds to the Bragg model of partially reflective mirrors, and the K-vectors give the directions for the reflections which form the diffraction pattern. The description given by ...


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Well, $1/2\otimes1/2=0\oplus1$, so a system with two fermions has integer spin. But it is still a two fermion system, and therefore its wavefunction must be antisymmetric, as usual. This is not specific to Cooper pairs, but is basic Quantum Mechanics... [what is specific to Cooper pairs is that their size is $\gg a_0$, which means they are highly ...


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Too many words. Signal amplification is a fact. Negative power is an attempt to clarify a concept of stray reactances leading to a mathematical solution known as a "power factor" - not a fact. "P:ower" refers to the ability to perform work when force(pressure/voltage) is combined with the capacity to deliver "energy" (electrical current. or current of ...


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If I'm understanding your question correctly, then the answer is that you actually can't justify the connection of your equations along the quantized direction. In fact, the "bands" in the direction perpendicular to your slab are going to be completely flat, which corresponds to an infinite effective mass in that direction. (The infinity comes from the ...


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The question made me google "water nano structure" and sure enough: Water: Nanostructure and fluctuations S. D. Zakharov Recently a model of local organization of water was experimentally justified, in which tetrahedrally coordinated water clusters of 1–2 nanometers arise and disappear in liquid composed of H2O molecules with partially broken ...


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Scattering is phenomenon of deviation from its trajectory due to non-uniformities in medium through which it is passing. Eg. When a ball is deviated by tennis bat due to its motion. Flourescnce is consuming the photon, and emitting back lower energy photon.


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Things don't really have "colour". Colour is a perception that we have of light entering our eyes. We use our eyes to perceive the world, and in our eyes are a series of receptors (photoreceptors). These are the rod, and cone-shaped cells which exist in your retina. These cells send electrical signals to our brain, via the optic nerve, and it is a ...


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Every Element/atom has a different electron configuration. This gives the valence electrons unique energy levels and arrangements. When electrons absorb energy they are excited to certain and again unique energy levels. When The energy is released it gives a photon a certain frequency which we perceive as a certain color.


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A lot of things can affect the color of an object. As you've mentioned, absorption plays an important role in determining what part of the visible spectrum gets subtracted from the color your eyes perceive. Optical bandgap arising from the microstructure of materials determines what portion of the spectrum is absorbed. It is closely related to the electronic ...


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To my mind, the above explanation (and others commonly presented) is missing an important piece though. In the semi-classical intuition presented, there should never be a preference for spins to align. The reason is that Pauli exclusion slapped on top of a classical picture simply restricts the phase-space of the system, thus reducing entropy. Sure, the ...


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This is my favorite graphene reference. It's more concerned with the high magnetic field behavior of graphene (quantum Hall regime), but it's introduction is still very well done. A few points: -The wavefunction is the sum of two Bloch functions (one for each sublattice of graphene). The tight binding approximation assumes that the electronic wavefunction ...


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There is nothing wrong with looking for plane-wave like solutions of the form $A \exp (i (\omega t - k x) )$. Given the linearity of the equations, and as @ignacio pointed out the fact that the $\exp (i k x_n)$ form a basis of solutions, you can write a more general solution as a combination of these plane waves. This solution isn't necessarily periodic ...


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The answer to nearly everything is: yes :) your intuition about it is quite right, and your picture is good, too. You have two different kinds of points, and any pair with one point from each kind would be a suitable basis. You will of course take adjacent ones in practice. You could also take more than two points as primitive cell, but it will not be a good ...


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I have taught myself and several other people how to understand band diagrams properly and I find that universally (myself included) there is a certain need to "unlearn" things that you may have been mistaught in classes or misunderstood. Major problems occur if one has taken a solid-state physics course which only studied band structure in infinite ...


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The spin orbit coupling can be derived from the nonrelativistic limit of the dirac equation and is given by $$ H_{\text{s-p}} = \frac{\varepsilon_0}{2m_e^2c^2}\mathbf{\hat{s}}\cdot\left(\mathbf{E}\times\mathbf{\hat{p}} \right) $$ $\mathbf{E}$ is the total electric field acting on an electron, which consist of a microscopic electric field ...


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When we say that a lattice has a particular symmetry we mean that the lattice is mapped onto itself by the symmetry. So if I have a (2d) material which has inversion symmetry in the bulk and which has an atom at a point $(x,y)$ then inversion symmetry tells me that there is another, identical atom at $(-x, -y)$. At the surface, however, this is no longer ...


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In the thermodynamic limit (linear size of the system $L$ to infinity), boundary conditions don't really matter, and most physical observables will be the same for all boundary conditions. The use of periodic boundary conditions is mostly for practical reasons, in particular, translation symmetry is conserved, which really helps. One could in principle do ...


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Well, contrary to what Lemon said, internal energy is sum of ALL energy of constituting particles related to their DISORDERED motion only. To prove my statement, look out for the derivation of formula for internal energy for an IDEAL gas, and the derivation for value of C(molar heat capacity at constant volume) henceforth. Now coming to your question, since ...


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First of all, there are two general types of free energy: Gibbs and Helmholtz. Helmholtz free energy is $F=U-TS$, whereas the Gibbs free energy has an additional term that accounts for the work done on the environment by the system, $G=F+pV$. If you're modelling a system in a vacuum or a gas, say, then you'd typically use Helmholtz, whereas in a solution ...


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Exact mechanism varies with material, simple materials (non-organic) are easier to analyze. Simplest answer is if you bring them together they will join, provided size is small. For example in Cold Welding less than 10 nm wire is rejoined just by contact. The exact mechanics depends on what kind of Intermolecular force is in play. According to Grove Karl ...


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You should understand that the battery source is not a supplier of electrons. The electrons are inside the metal. The physics of semi-conductors and metal conductors are a little different. Let's start with conductors. A conductor is characterized by the availability of free electrons within the metal if you supply a little energy to liberate it. They have ...


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When the switch is closed the information is communicated to the whole circuit via electromagnetic waves at (less than) the speed of light. This means that an electric field, which the mobile charge carriers feel, is set up in the wires almost instantaneously. The movement of the mobile charge carriers is the electric current and that current exists in all ...


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A negative charged ion like Boron is towards P end of Junction. When it gains a photon , electron from $B^-$ is excited from valence band to conduction band. This creates a hole at lattice point where electron was formerly present. Free electron moves towards N doped side which is positively charged. ...


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Please keep in mind lemon's observation as to the correct nature of Block waves. This being said, the Hartree-Fock Hamiltonian is a general ansatz for localized orbitals, it applies equally well to periodic lattices and to non-periodic molecular systems. For a periodic lattice however, translation symmetry imposes that localized HF orbitals are (ideally) ...


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photoelectric effect can occur only in metals because in metals,electrons are freely moving. so when light fall on the surface of the metal, the electrons get sufficient energy to come out of the metal surface. But in non-metals,electrons are stationary and can't come out and no photoelectric effect is occured.


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Pressure is force per unit area. If you have 5N/m^2, it means that a force of 5N acts at every 1 m^2 area of the surface. Suppose you have a 100m^2 area. Then the total force distributed over the entire surface is 500N which corresponds to about 50Kg.


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If the pressure is uniform, there is no problem, because you just multiply the pressure by the total surface area of interest. However, if the pressure is varying on the surface, pressure should be regarded as a point function of location, and the contribution to the total force on the surface at a differential element of area on the surface dA is equal to ...


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The RKKY interaction is a generalization of the Kondo calculation in the case of two spins : it deals with finding the correct form of the interaction between two magnetic impurities via the Fermi sea. In this case you have a competition between two effects : the Kondo that describes the screening of each impurity bu the Fermi sea of electrons, and the RKKY ...


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It means 5 newtons acts on one meter square. Not exactly a point, any patch of any shape having 1 meter square area will have 5 newtons. If area is more then the force would be more if area is less force less. F=PxA



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