# 物理代写|固体物理代写Solid-state physics代考|PHYSICS7544

## 物理代写|固体物理代写Solid-state physics代考|Normal and Umklapp Processes

The lattice thermal conductivity of a solid is determined by two contributions (a) specific heat and (b) mean free paths of the phonons. The phonons are major heat carriers in solids. In harmonic approximation, the phonons travel freely without attenuation. As a result, they have unlimited free path resulting in an infinite thermal conductivity. However, thermal equilibrium is attained in a solid as mean free path is restricted by (a) the anharmonic terms of Eq. (7.46) (b) imperfections and impurities in the crystals and (c) finite size of the lattice.

The anharmonicity results in scattering or collisions between phonons. Scattering from other phonons can be classified into (a) Normal process and (b) Umklapp process depending on the energies involved.
Normal Process
Consider a phonon of wave vector $\boldsymbol{k}_1$ which collides with another phonon of wave vector $\boldsymbol{k}_2$. As a result of this collision, a wave vector $\boldsymbol{k}_3$ is formed. The probability of such a collision is determined by the magnitude of the anharmonic terms. The property of the resulting phonon with wave vector $\boldsymbol{k}_3$ is determined by laws of momentum and energy conservation.
The energy conservation gives
$$\hbar \omega_1+\hbar \omega_2=\hbar \omega_3$$
Momentum conservation gives
$$k_1+k_2=k_3$$
Such a process is known as Normal process. This process is shown in Fig. 7.7 for two-dimensional square lattices. The square with dotted lines represents the first Brillouin zone in the reciprocal space.

The Brillouin zone contains all the possible independent values of vector. The vector $k$ with head towards the centre of Brillouin zone indicates that the phonon is absorbed in the scattering process while vector $k$ with arrow head away from the centre of Brillouin zone indicates that the phonon is emitted in the scattering process. In the scattering of two phonons with wave vector $k_1$ and wave vector $k_2$, another phonon having wave vector $\boldsymbol{k}_3$ is emitted. In the Normal process, the direction of energy flow is not changed. The Normal process does not make contribution towards the thermal resistance.

## 物理代写|固体物理代写Solid-state physics代考|Drude–Lorentz Model

P. Drude in 1900 proposed that physical properties of metals can be explained in terms of free electron model. According to this model, a metal consists of stationary ions and valence electrons. The valence electrons form the free electron gas. These electrons move in the volume of the metal. Drude applied kinetic theory of gases to the free electron gas. The basic assumption of Drude theory of metal is
(1) A metal consists of positive metal ions whose valence electrons are free to move between the ions as if they constituted an electron gas.
(2) The metal is held together by electrostatic force of attraction between the positively charged ions and negatively charged electron gas. The repulsion between the electrons is ignored, and the potential field due to positive ions is assumed to be uniform.
(3) The electrons are free to move about the whole volume of the metal like the molecules of a perfect gas in a container.
(4) In the absence of electric or magnetic field, each electron of free electron gas moves uniformly in a straight line, and in the presence of field, they move according to Newton law’s of motion.
(5) The electrons move from one place to another in the metal without any change in energy. During the movement, they occasionally collide elastically with the ions (which are fixed in the lattice) and other free electrons. Between collisions, the interactions of electrons with the others and with the ions are ignored. They have velocities determined at a constant temperature according to Maxwell-Boltzmann distribution law.

# 固体物理代写

## 物理代写|固体物理代写Solid-state physics代考|Normal and Umklapp Processes

$$\hbar \omega_1+\hbar \omega_2=\hbar \omega_3$$

$$k_1+k_2=k_3$$

## 物理代写|固体物理代写Solid-state physics代考|Drude–Lorentz Model

P. Drude在1900年提出金属的物理性质可以用自由电子模型来解释。根据这个模型，金属由固定离子和价电子组成。价电子形成自由电子气。这些电子在金属体内移动。德鲁德将气体动力学理论应用于自由电子气。德鲁德金属理论的基本假设是
(1) 金属由正金属离子组成，其价电子可以在离子之间自由移动，就好像它们构成了电子气。
(2) 带正电的离子和带负电的电子气之间的静电引力将金属结合在一起。忽略电子之间的排斥，假设正离子产生的势场是均匀的。
(3) 电子可以在金属的整个体积内自由移动，就像容器中理想气体的分子一样。
(4) 在没有电场或磁场的情况下，自由电子气中的每个电子作匀速直线运动，在有场的情况下，它们按牛顿运动定律运动。
(5) 电子在金属中从一处移动到另一处，能量没有任何变化。在运动过程中，它们偶尔会与离子（固定在晶格中）和其他自由电子发生弹性碰撞。在碰撞之间，电子与其他电子以及与离子的相互作用被忽略。它们具有根据麦克斯韦-玻尔兹曼分布定律在恒定温度下确定的速度。

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