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The mechanism for increasing the thermal conductivity is phonon assisted hopping. For a disordered system, one which do not preserve the long range order, the electronic wave function becomes localized. The wave function extent is typically much smaller than the system size and is characterized by the localization length $\xi$, a parameter in theory. In this ...


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The higher the dimension, the more phase space you have for your fluctuations to spread. Imagine you make a small local disturbance in your system (caused by e.g. thermal fluctuations). In 1D this disturbance can freely propagate in the system without decaying : it destroys long-range order. In 3D, the disturbance also propagates but it quickly dies out ...


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But by combination of electrons with holes there will be increase in repulsion forces of electrons this will create more resistance. so currrent should not increase exponentially with voltage


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To briefly summarize the whole physics: P-n diode has excessive holes in one side of the junction and excess free electrones on the other but both sides are electrically neutral. Initially they diffuse to create an equilibrium of numbers of electron and hole , but in this way They create electric potential on the opposite side Off the flow. This Presents ...


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These two points of view are not so different in fact. To see that, let's work in the grand-canonical ensemble (which is the most natural to talk about the chemical potential in the Mott phase, since it is not well defined in the canonical ensemble). At a given (and small enough) $t/U$, there is a range of chemical potential $[\mu_-,\mu_+]$ where the ...


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If you are reasonably confident about the quality of the plate in question (uniform thickness, a well-defined square shape, etc.) you can measure the resistance of the copper square. This would be a non-destructive method for the arrangement in the OP. The specific resistivity of copper is (per google search) $1.68 \div 1.72 \times (10^{-8} \Omega\,m)$ ...


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I calculate that with 30u thickness we have 675mg mass. Use a microbalance and weight the sample.


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Do you have access to a precision balance? Then you could weigh the plate, and using the known dimensions of the plate and the density of copper, compute the thickness. For $5\,{\rm cm} \times 5\,{\rm cm} \times 30\,\mu{\rm m}$ the weight would be $0.672\,{\rm g}$ for example. The precision of that measurement depends on how accurately you can measure the ...


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In general your relation is $$ \vec{B}(\omega) = (1 + \chi_m(\omega))\vec{B}_0(\omega) $$ or in the time domain $$ \vec{B}(t) =\vec{B}_0(t) + \int\limits_{-\infty}^\infty \chi_m(t,t') \vec{B}_0(t') \;\rm{d}t' $$ Only in the case of instantanous material response, i.e. $\chi_m(t,t') = \chi_{m,0} \cdot \delta(t-t') $, your equation is correct. This already ...


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How can particles that exist where quantum mechanics "reigns supreme" be modeled successfully as classical particles? If the model is useful, it gets wide popularity and sticks in physics irrespective of which framework - classical, probabilistic or quantum - it seems closest to. The idea that the quantum theory is some kind of ultimate theory of ...


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The Drude model (1900) is based on statistical mechanics plus Maxwell's electrodynamics as updated by Lorentz to include the electron and atoms. It gives good results for some processes, such as conductivity/resistance of metals, but is way off on others, such heat capacity, and totally ignores important features such as band structure. The semi-classical ...


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For any crystal, the First Brillouin Zone is found using the Wigner-Seitz construction for the reciprocal lattice. The high-symmetry points are labeled by certain letters mainly as a convention--like you said Gamma for (0,0,0) etc. The important thing to realize as far as the group theory, is that the group of the wavevector at the Gamma point has the full ...


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The summation given in the OP includes all points within a single unit cell; in this case there are $N$ such points. This looks like the expression for the structure factor, but the weighting for each point is unity, which implies that the crystal is made up of a single type of atom. Lattice sum, as given here, means the sum over all lattice points in the ...


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$k$ is the incoming beam, $k'$ is the reflected beam, expressed as wave vectors in the reciprocal lattice, which makes $Q=k-k'$ represents a particular plane in reciprocal space. If you assume that the diffracting beam is essentially a plane wave when it elastically scatters off of multiple sites within the crystal, the kinematics of the Laue equation ...


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It is simply the thickness of the plate. From Landau's Theory of Elasticity, it is the $h$ in Fig. 11.2, which you can see to correspond to your $h_e$ in the second footnote on page 49.


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The Kondo effect is a phenomenon that occurs when we have a magnetic impurity located in one place of a non-magnetic metal. The magnetic impurity has an residual spin due your electronic configuration. The electrons of the conduction band would interact with this electron via exchange interaction. We can see in equation 10 of the wiki page that the ...


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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 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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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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