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Facts : The properties depending of the atomic mass are different. fact 1 : The melting point depend upon the atomic mass. There is no need of a new experiment to relate the hardness to the temperature distance to the melting point : ie heat helps to bend metals or makes other matters more brittle. fact 2 : Moreover, stress diffusion depends upon the ...


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One reason might be that the term is not "bucked" but it is "buckled". If you search for "buckled honeycomb lattice" you would find a lot of information. Basically, the difference between an ordinary and buckled honeycomb structure is that the ordinary honeycomb structure is flat, or planar. One good example would be to compare benzene molecule to ...


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The nuclear force is a contact force, with potential energy curve $$ V \propto \frac{e^{-r/r_0}}{r}. $$ The range parameter $r_0$ is roughly one femtometer. Nuclei in a solid are typically $10^5\rm\,fm$ apart, so the nuclear interaction between nuclei from different atoms is astoundingly suppressed. If you think of a solid as a lattice of atoms connected ...


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To construct a crystal you need a lattice and a basis. The lattice represents the translational symmetry of the system. Namely, graphene has a hexagonal lattice, meaning the two lattice vectors are 60 degress apart. Since the brillouin zone is constructed by inverting the lattice vectors, the brillouin zone is shaped based upon the lattice, but not the ...


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deriving the desired expression for $\boldsymbol k$ and figuring out what $\boldsymbol k$ really is we will begin with the definition of bloch's theorem. $$\psi_{\boldsymbol k}(\boldsymbol r + \boldsymbol t_n) = e^{i \boldsymbol k \cdot \boldsymbol t_n} \psi_{\boldsymbol k} (\boldsymbol r)$$ here $\boldsymbol k$ is a wave vector defined in the primitive ...


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deriving the desired equation for the density of states we are reminded that the surface which we are integrating over is a surface of constant energy in the reciprocal space which is denoted by $S(e)$, where $e$ is the 3-dimensional dispersion relation we know that the number of states between the surfaces $S(e)$ and $S(e + de)$ is given by the integral. ...


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Sputtering deposition is not normally preformed at ultra high vacuum pressures, thus the films tend to be polycrystalline while e-beam evaporated metal films could be done at much lower pressures resulting in a more uniform film, even single crystalline depending on other conditions like the substrate, lattice mismatch and so on. This is just one difference. ...


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Glass is a typical amorphous solid. Amorphous materials typically show no melting point but do have a Glass Transition Point ($T_g$). Below it, the material behaves like a solid, with a glass-like fracture surface when fractured. Typical amorphous materials include several types of elastomer (rubber) like natural rubber (NR), with a $T_g$ of around ...


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I fear your question is not very precise. Unfortunately my reputation is not high enough to allow me to comment instead of answer. What exactly do you mean by the term "exciton"? The way it is normaly understood, is a pair of one electron and one hole. So there are no multiple electrons whose spins could line up parallel oder antiparallel. In a biexciton ...


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$b_1, b_2$ and $b_3$ are reciprocal primitive vectors. $G$ is the set of all vectors that are in the reciprocal lattice and, as you said, is given by the linear combination of the reciprocal primitive vectors. The set of points, $G$, just define the lattice vectors or the locations of the origin of each Brillouin zone. Now we need to look within each ...


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There is one small effect that has not yet been covered in the other answers. When we solve Schrodinger's equation for the electron orbitals we use the so called reduced mass $$\mu=m_e m_n/(m_e+m_n)$$ so the solutions for the orbitals will be slightly different for the case where extra neutrons are added to the nucleus. The electron mass is so much smaller ...


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To delve more deeply into the origin of the various bands, you should go look at the literature where these bands are calculated. The classic reference for silicon and germanium is Energy-Band Structure of Germanium and Silicon: the k.p Method. Since this is still fairly early in band structure calculations, they do walk you through how the Hamiltonian is ...


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If you're looking for a strict derivation of the effective mass equation, check out S. Datta, Quantum phenomena. Reading, Mass.: Addison-Wesley, 1989. What he does is take the full Schrödinger equation with the periodic potential, and write it in the Bloch state basis. He then writes the effective mass equation in the plane wave basis. By comparing the ...


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When you have a great number of interacting particles (such as electrons in a solid), it becomes impossible to try to describe each electron individually. We introduce the concept of quasiparticle to describe whan can be the low-lying excitations of the ensemble of particles. For instance, If you take a metal at 0K, the ground state of the system is the ...


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The first case you mention where you just sandwich GaAs inside AlGaAs is worked out in page 66 of Semiconductor Nanostructures. By adding a doping layer you control the carrier density and with that the resistivity. Like you say, it's necessary to draw the electrons away from the doping layer using attraction to the smaller-gapped GaAs. This creates bound ...


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Regarding your question on sandwiching GaAs between two AlGaAs barriers: If you do this for a narrow quantum well (like you sketched above), the electron wavefunction protrudes into the barrier quite a bit. As the barrier material is a ternary alloy, the electrons are exposed to alloy scattering. This is simply due to the fact that Ga and Al atoms are ...


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It might help to just look at the vacuum level, and think of how the structure reaches equilibrium. In your first picture, electrons will start to flow from right to left, towards the lower fermi level. This will charge the left side negatively, and leave positive charge on the right side. Therefore the vacuum level will curve on both sides, with a U ...


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For a transition like electron-hole recombination, its probability is linear with time with some characteristic time scale that depends on the system: the probability of having a transition between $0$ and $dt$ is $\frac{dt}{\tau}$. So there is a non-vanishing transition probability at arbitrarily small times. In momentum space, the evolution of a ...



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