纳米材料的量子尺寸效应

Flywheel energy storage (FES) works by accelerating a rotor (flywheel) to a very high speed and maintaining the energy in the system as rotational kinetic energy. The energy stored is proportional to the square of the rotational speed. When energy is extracted, the flywheel's rotation slows down. The formula for stored energy is [latex]E = \frac{1}{2} I \omega^2[/latex], where I is the moment of inertia and ω is the angular velocity.

分子电子学探索利用单个分子或纳米级分子集合作为基本电子元件。该方法旨在构建微型化极限的电路，远远超越传统的硅基技术。关键元件包括分子线、开关和整流器，它们利用电子隧穿分子轨道等量子力学特性来实现功能。

失效物理学（PoF）是一种可靠性工程方法，它利用材料科学和物理学的知识来理解和模拟失效的根本原因机制。它并非仅仅依赖于以往失效的统计数据，而是通过分析导致性能退化和失效的物理过程（例如疲劳、腐蚀、蠕变）来预测失效。

The equilibrium vapor pressure of water over a liquid surface in moist air ([latex]p^*_{H_2O,a}[/latex]) is slightly greater than the equilibrium vapor pressure over a pure water surface ([latex]p^*_{H_2O}[/latex]). This difference is quantified by the water vapor enhancement factor, [latex]f_w[/latex], which depends on temperature and the pressure of the moist air. The relationship is [latex]p^*_{H_2O,a} = f_w(T, p_{ms}) \cdot p^*_{H_2O}[/latex].

稀土磁铁是由稀土元素合金制成的强力永磁体。稀土磁铁开发于20世纪70年代和80年代，最常见的类型是钕磁铁（NdFeB）和钐钴磁铁（SmCo）。它们是目前已知的最强永磁体，产生的磁场比铁氧体或铝镍钴磁铁强得多，从而能够实现许多技术的小型化和性能提升。注意：“稀土元素”一词是历史上的误称。这些元素在地壳中并非极其稀有。铈是含量最丰富的元素，与铜相似，是第25位最丰富的元素。即使是含量最少的稳定稀土元素镥，其常见程度也比黄金高出近200倍。“稀有”标签的出现是因为它们难以分离。

锂离子 (Li-ion) 电池是一种可充电电池，放电时锂离子从负极（阳极）经电解质移动到正极（阴极），充电时再返回。它采用嵌入锂的化合物作为正极材料，通常使用石墨作为负极材料。锂的高反应性使其具有高能量密度。

Superconducting Magnetic Energy Storage (SMES) systems store energy in the magnetic field created by the flow of direct current in a superconducting coil. The energy can be stored indefinitely as long as the coil is kept at superconducting temperatures, as there is virtually no energy loss due to electrical resistance. The stored energy is given by [latex]E = \frac{1}{2} L I^2[/latex].

The Ganz-Griesser whiteness index is a linear formula widely used, particularly in the textile industry. It is derived from CIE tristimulus values and is defined as [latex]W_{GG} = Y - Px - Qy + C[/latex], where P, Q, and C are constants specific to the illuminant and observer. For the D65/10° condition, the formula is [latex]W_{GG} = Y - 1868.322x - 3695.690y + 1809.441[/latex].

Lithium-ion batteries function via an intercalation mechanism, a reversible insertion of ions into a layered host material. During discharge, lithium ions ([latex]Li^+[/latex]) de-intercalate from a negative electrode (anode), typically graphite, and move through a non-aqueous electrolyte to intercalate into a positive electrode (cathode), typically a metal oxide. Electrons travel through the external circuit, creating current.

放电深度 (DoD) 表示电池容量已释放的百分比。它是充电状态 (SoC) 的倒数，其中 100% DoD 表示电池电量已耗尽。电池的循环寿命与其平均 DoD 高度相关；较低的 DoD 循环次数（例如，仅放电至容量的 80%）可显著增加电池的循环次数。

MEMS scaling laws describe how physical forces and properties change as device dimensions shrink to the microscale. Unlike the macroscopic world dominated by gravity and inertia, micro-domains are governed by surface forces like surface tension, viscosity, and electrostatic forces. For example, force due to gravity scales with volume ([latex]L^3[/latex]), while electrostatic force scales with area ([latex]L^2[/latex]), becoming relatively stronger at smaller sizes.

钕磁铁是目前市面上磁力最强的永磁体。它是钕、铁和硼的三元合金，化学计量式为Nd2Fe14B。其强大的磁力源于其四方晶体结构所赋予的高磁各向异性和饱和磁化强度。然而，钕磁铁易碎、易腐蚀，且居里温度较低。

单电子晶体管 (SET) 是一种利用受控电子隧穿效应来操控单个电子流动的开关器件。它由一个量子点（“岛”）组成，该量子点通过隧道结耦合到源极和漏极引线，并通过电容耦合到栅极。其工作原理依赖于库仑阻塞效应，从而实现极高的灵敏度和低功耗。