地球与地质Crystallization结晶，是指从过饱和溶液中凝结，或从气体凝华出具有一定的几何形状的固体（晶体）的过程。在自然环境下，气温的下降压力的作用，都会造成结晶。结晶的过程一般可分为两个阶段（包括成核和晶体生长期），时间也有所不同。 结晶亦是一种分离固态和液态物质的技术，其中溶质由溶液中转移至纯净的晶体里。不少自然过程都涉及结晶: 天然晶体的形成 （如矿物、宝石等） 雪花的形成 蜂蜜的结晶 如饱和溶液的气温下降速度慢，会形成一颗较大的晶体；如气温急剧下降，会形成粉状的小晶体。而小晶体可以放进饱和溶液充当大晶体的种子。 而重结晶或再结晶是重复结晶作用，用以准备纯度更高的结晶。
Crystallization is a process that leads to solids with a uniform pattern of atoms or molecules, i.e. a crystal. The uniform nature of a crystalline solid can be contrasted with amorphous solids in which atoms or molecules lack regular organization. Crystallization can occur by various routes including precipitation from solution, freezing of a liquid, or deposition from a gas. Attributes of the resulting crystal can depend largely on factors such as temperature, air pressure, cooling rate, or solute concentration. Crystallization occurs in two main phases. The first is nucleation, the appearance of a crystalline phase from either a supercooled liquid or a supersaturated solvent. The second step is known as crystal growth, which is the increase in the size of particles and leads to a crystal state. An important feature of this step is that loose particles form layers at the crystal's surface and lodge themselves into open inconsistencies such as pores, cracks, etc.
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查看内容许可 ↗晶体生长(英语：Crystal growth)是物质结晶过程中，继成核之后进行的一个重要阶段。宏观上，晶体生长过程是晶体——环境相(蒸气、溶液、熔体) 界面向环境相中不断推进的过程，即晶核超过临界大小之后，由包含组成晶体单元的母相从低有序相向高有序晶相的转变。晶体被定义为原子，分子或离子以有序的重复模式排列，晶格在所有三个空间维度上延伸。 因此，晶体生长不同于液滴生长，因为在生长过程中，分子或离子必须落入正确的晶格位置，以便有序的晶体生长。
Crystal growth is a major stage of a crystallization process, and consists of the addition of new atoms, ions, or polymer strings into the characteristic arrangement of the crystalline lattice. The growth typically follows an initial stage of either homogeneous or heterogeneous (surface catalyzed) nucleation, unless a "seed" crystal, purposely added to start the growth, was already present. The action of crystal growth yields a crystalline solid whose atoms or molecules are close packed, with fixed positions in space relative to each other. The crystalline state of matter is characterized by a distinct structural rigidity and very high resistance to deformation (i.e. changes of shape and/or volume). Most crystalline solids have high values both of Young's modulus and of the shear modulus of elasticity.
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查看内容许可 ↗断裂力学（Fracture mechanics）是研究含裂纹构件强度与寿命的一门固体力学的新分支，结构损伤容限设计的理论基础。可以分为线弹性断裂力学与弹塑性断裂力学两大类别，前者适用于裂纹尖端附近小范围屈服的情况；而后者适用于裂纹尖端附近大范围屈服的情况。就目前情况而言，弹塑性断裂力学发展很快，但是线弹性断裂力学在结构损伤容限设计中仍然占据重要地位。 在线弹性断裂力学中，最重要的力学参量是应力强度因子，它控制裂纹尖端场附近的应力场和位移场。
Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture. Theoretically, the stress ahead of a sharp crack tip becomes infinite and cannot be used to describe the state around a crack. Fracture mechanics is used to characterise the loads on a crack, typically using a single parameter to describe the complete loading state at the crack tip. A number of different parameters have been developed. When the plastic zone at the tip of the crack is small relative to the crack length the stress state at the crack tip is the result of elastic forces within the material and is termed linear elastic fracture mechanics (LEFM) and can be characterised using the stress intensity factor K {\displaystyle K} . Although the load on a crack can be arbitrary, in 1957 G.
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查看内容许可 ↗在材料科学中，断裂韧性是尖锐裂纹的临界应力强度因子，其中裂纹的扩展突然变得快速且无限。它是一种材料特性，可量化其在施加应力下抵抗裂纹扩展和失效的能力。部件的厚度会影响裂纹尖端的约束条件，薄部件具有平面应力条件，导致延性行为，厚部件具有平面应变条件，其中约束增加，导致脆性破坏。平面应变条件给出最低的断裂韧性值，这是一种材料特性。在平面应变条件下测得的 I 型加载应力强度因子的临界值称为平面应变断裂韧性，记为 K Ic {\displaystyle K_{\text{Ic}}} 。
In materials science, fracture toughness is the critical stress intensity factor of a sharp crack where propagation of the crack suddenly becomes rapid and unlimited. It is a material property that quantifies its ability to resist crack propagation and failure under applied stress. A component's thickness affects the constraint conditions at the tip of a crack with thin components having plane stress conditions, leading to ductile behavior and thick components having plane strain conditions, where the constraint increases, leading to brittle failure. Plane strain conditions give the lowest fracture toughness value which is a material property. The critical value of stress intensity factor in mode I loading measured under plane strain conditions is known as the plane strain fracture toughness, denoted K Ic {\displaystyle K_{\text{Ic}}} .
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。 本条中文为英文百科简介的机器辅助翻译，请结合英文原文核对专业术语。
查看内容许可 ↗在连续介质力学中，柯西应力张量（符号 σ {\displaystyle {\boldsymbol {\sigma }}} ，以 Augustin-Louis Cauchy 命名），也称为真应力张量或简称应力张量，完全定义了处于变形状态、放置或配置的材料内部一点的应力状态。
In continuum mechanics, the Cauchy stress tensor (symbol σ {\displaystyle {\boldsymbol {\sigma }}} , named after Augustin-Louis Cauchy), also called true stress tensor or simply stress tensor, completely defines the state of stress at a point inside a material in the deformed state, placement, or configuration.
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查看内容许可 ↗莫尔圆是柯西应力张量变换定律的二维图形表示。莫尔圆经常用于与机械工程的材料强度、岩土工程的土壤强度以及结构工程的建筑结构强度相关的计算。它还用于通过将许多平面中的应力简化为垂直和水平分量来计算应力。这些称为主平面，在其中计算主应力；莫尔圆还可用于在图形表示中查找主平面和主应力，并且是最简单的方法之一。对假设为连续体的材料体进行应力分析后，特定材料点处的柯西应力张量相对于坐标系的分量是已知的。
Mohr's circle is a two-dimensional graphical representation of the transformation law for the Cauchy stress tensor. Mohr's circle is often used in calculations relating to mechanical engineering for materials' strength, geotechnical engineering for strength of soils, and structural engineering for strength of built structures. It is also used for calculating stresses in many planes by reducing them to vertical and horizontal components. These are called principal planes in which principal stresses are calculated; Mohr's circle can also be used to find the principal planes and the principal stresses in a graphical representation, and is one of the easiest ways to do so. After performing a stress analysis on a material body assumed as a continuum, the components of the Cauchy stress tensor at a particular material point are known with respect to a coordinate system.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。 本条中文为英文百科简介的机器辅助翻译，请结合英文原文核对专业术语。
查看内容许可 ↗在材料科学和固体力学中，泊松比（符号：ν (nu)）是泊松效应的度量，即材料在垂直于特定载荷方向的方向上的变形（膨胀或收缩）。泊松比的值为横向应变与轴向应变之比的负值。对于这些变化较小的值，ν 是横向伸长量除以轴向压缩量。大多数材料的泊松比值在 0.0 到 0.5 之间。对于橡胶等软材料，其体积模量远高于剪切模量，泊松比接近 0.5。对于开孔聚合物泡沫，泊松比接近于零，因为孔在压缩时容易塌陷。许多典型固体的泊松比在 0.2 到 0.3 范围内。
In materials science and solid mechanics, Poisson's ratio (symbol: ν (nu)) is a measure of the Poisson effect, the deformation (expansion or contraction) of a material in directions perpendicular to the specific direction of loading. The value of Poisson's ratio is the negative of the ratio of transverse strain to axial strain. For small values of these changes, ν is the amount of transversal elongation divided by the amount of axial compression. Most materials have Poisson's ratio values ranging between 0.0 and 0.5. For soft materials, such as rubber, where the bulk modulus is much higher than the shear modulus, Poisson's ratio is near 0.5. For open-cell polymer foams, Poisson's ratio is near zero, since the cells tend to collapse in compression. Many typical solids have Poisson's ratios in the range of 0.2 to 0.3.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。 本条中文为英文百科简介的机器辅助翻译，请结合英文原文核对专业术语。
查看内容许可 ↗有限元法 (FEM) 是对工程和数学建模中出现的微分方程进行数值求解的常用方法。感兴趣的典型问题领域包括结构分析、传热、流体流动、质量传输和电磁势等传统领域。计算机通常用于执行所需的计算。借助高速超级计算机，可以实现更好的解决方案，并且通常需要解决最大、最复杂的问题。 FEM 是一种用于求解二空间或三空间变量中的偏微分方程（即某些边值问题）的通用数值方法。也有关于使用有限元法解决高维问题的研究。为了解决问题，FEM 将大型系统细分为更小、更简单的部分，称为有限元。
Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. Computers are usually used to perform the calculations required. With high-speed supercomputers, better solutions can be achieved and are often required to solve the largest and most complex problems. FEM is a general numerical method for solving partial differential equations in two- or three-space variables (i.e., some boundary value problems). There are also studies about using FEM to solve high-dimensional problems. To solve a problem, FEM subdivides a large system into smaller, simpler parts called finite elements.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。 本条中文为英文百科简介的机器辅助翻译，请结合英文原文核对专业术语。
查看内容许可 ↗在微分方程中，边值问题是一个微分方程和一组称之为边界条件的约束条件。边值问题的解通常是符合约束条件的微分方程的解。 物理学中经常遇到边值问题，例如波动方程等。许多重要的边值问题属于Sturm-Liouville问题。这类问题的分析会和微分算子的本征函数有关。 在实际应用中，边值问题应当是适定的（即：存在解，解唯一且解会随着初始值连续地变化）。许多偏微分方程领域的理论提出是为要证明科学及工程应用的许多边值问题都是适定问题。 最早研究的边值问题是狄利克雷问题，是要找出调和函数，也就是拉普拉斯方程的解，后来是用狄利克雷原理找到相关的解。
In the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics as any physical differential equation will have them. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. A large class of important boundary value problems are the Sturm–Liouville problems. The analysis of these problems, in the linear case, involves the eigenfunctions of a differential operator. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input.
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查看内容许可 ↗卡尔曼滤波（英语：Kalman filter）是一种高效率的递归滤波器（自回归滤波器），它能够从一系列的不完全及包含噪声的测量中，估计动态系统的状态。卡尔曼滤波会根据各测量量在不同时间下的值，考虑各时间下的联合分布，再产生对未知变量的估计，因此会比只以单一测量量为基础的估计方式要准。卡尔曼滤波得名自主要贡献者之一的鲁道夫·卡尔曼。 卡尔曼滤波在技术领域有许多的应用。常见的有飞机及太空船的导引、导航及控制。卡尔曼滤波也广为使用在时间序列的分析中，例如信号处理及计量经济学中。卡尔曼滤波也是机器人运动规划及控制的重要主题之一，有时也包括在轨迹优化。卡尔曼滤波也用在中轴神经系统运动控制的建模中。因为从给与运动命令到收到感觉神经的回授之间有时间差，使用卡尔曼滤波有助于建立符合实际的系统，估计运动系统的目前状态，并且更新命令。 卡尔曼滤波的算法是二步骤的程序。在估计步骤中，卡尔曼滤波会产生有关目前状态的估计，其中也包括不确定性。只要观察到下一个量测（其中一定含有某种程度的误差，包括随机噪声）。会通过加权平均来更新估计值，而确定性越高的量测加权比重也越高。算法是迭代的，可以在实时控制系统中执行，只需要目前的输入量测、以往的计算值以及其不确定性矩阵，不需要其他以往的信息。 使用卡尔曼滤波不用假设误差是正态分布，不过若所有的误差都是正态分布，卡尔曼滤波可以得到正确的条件概率估计。 也发展了一些扩展或是广义的卡尔曼滤波，例如运作在非线性系统的扩展卡尔曼滤波及无迹卡尔曼滤波（英语：unscented Kalman filter）。底层的模型类似隐马尔可夫模型，不过潜在变量的状态空间是连续的，而且所有潜在变量及可观测变量都是正态分布。
In statistics and control theory, Kalman filtering (also known as linear quadratic estimation) is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, to produce estimates of unknown variables that tend to be more accurate than those based on a single measurement, by estimating a joint probability distribution over the variables for each time-step. The filter is constructed as a mean squared error minimiser, but also relates to maximum likelihood statistics. The filter is named after Rudolf E. Kálmán. Kalman filtering has numerous technological applications. A common application is for guidance, navigation, and control of vehicles, particularly aircraft, spacecraft and ships positioned dynamically. Furthermore, Kalman filtering is much applied in time series analysis tasks such as signal processing and econometrics. Kalman filtering is also important for robotic motion planning and control, and can be used for trajectory optimization.
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查看内容许可 ↗在概率论与统计学中，协方差（英语：Covariance）用于衡量随机变量间的相关程度。
In probability theory and statistics, covariance is a measure of the joint variability of two random variables. The sign of the covariance shows the tendency in the linear relationship between the variables. Covariance is positive when variables tend to show similar behavior and negative when variables tend to show opposite behavior. The magnitude of the covariance is the geometric mean of the variances that are shared for the two random variables, where a larger magnitude means two variables more strongly depend on each other. Covariance has units of measurement, and the magnitude of the covariance is affected by said units. This means changing the units (e.g., from meters to millimeters) changes the covariance value proportionally, making it difficult to assess the strength of the relationship from the covariance alone.
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查看内容许可 ↗傅里叶变换 （法语：Transformation de Fourier，英语：Fourier transform，缩写：FT）是一种线性变换，通常定义为一种积分变换。其基本思想是一个函数可以用（可数或不可数，可数的情况对应于傅里叶级数）无穷多个周期函数的线性组合来逼近，从而这些组合系数在保有原函数的几乎全部信息的同时，还直接地反映了该函数的“频域特征”。因其基本思想首先由法国学者约瑟夫·傅里叶系统地提出，所以以其名字来命名以示纪念。在现代数学理论中，傅里叶积分变换可以得到各种推广，并在分析学中有广泛应用，构成了调和分析这一数学领域。 经过傅里叶变换生成的函数 f ^ {\displaystyle {\hat {f}}} 称作原函数 f {\displaystyle f} 的傅里叶变换，应用意义上称作频谱。在特定情况下，傅里叶变换是可逆的，即将 f ^ {\displaystyle {\hat {f}}} 通过逆变换可以得到其原函数 f {\displaystyle f} 。通常情况下， f {\displaystyle f} 是一个实函数，而 f ^ {\displaystyle {\hat {f}}} 则是一个复数值函数，其函数值作为复数可同时表示振幅和相位。
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex valued function of frequency. The term Fourier transform refers to both the mathematical operation and to this complex-valued function. When a distinction needs to be made, the output of the operation is sometimes called the frequency domain representation of the original function. The Fourier transform is analogous to decomposing the sound of a musical chord into the intensities of its constituent pitches. Functions that are localized in the time domain have Fourier transforms that are spread out across the frequency domain and vice versa, a phenomenon known as the uncertainty principle. The critical case for this principle is the Gaussian function, of substantial importance in probability theory and statistics as well as in the study of physical phenomena exhibiting normal distribution (e.g., diffusion).
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查看内容许可 ↗拉普拉斯变换（英语：Laplace transform）是应用数学中常用的一种积分变换，又名拉氏变换，其符号为 L { f ( t ) } {\displaystyle \displaystyle {\mathcal {L}}\left\{f(t)\right\}} 。拉氏变换是一个线性变换，可将一个有实数变量 t ( t ≥ 0 ) {\displaystyle t(t\geq 0)} 的函数变换为一个变量为复数 s {\displaystyle s} 的函数： F ( s ) = ∫ 0 ∞ f ( t ) e − s t d t .
In mathematics, the Laplace transform, named after Pierre-Simon Laplace (), is an integral transform that converts a function of a real variable (usually t {\displaystyle t} , in the time domain) to a function of a complex variable s {\displaystyle s} (in the complex-valued frequency domain, also known as s-domain or s-plane). The functions are often denoted using a lowercase symbol for the time-domain function and the corresponding uppercase symbol for the frequency-domain function, e.g. x ( t ) {\displaystyle x(t)} and X ( s ) {\displaystyle X(s)} . The transform is useful for converting differentiation and integration in the time domain into the algebraic operations multiplication and division in the Laplace domain (analogous to how logarithms are useful for simplifying multiplication and division into addition and subtraction).
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗差分，又名差分函数或差分运算，一般是指有限差分（英语：Finite difference），是数学中的一个概念，将原函数 f ( x ) {\displaystyle f(x)} 映射到 f ( x + a ) − f ( x + b ) {\displaystyle f(x+a)-f(x+b)} 。差分运算，相应于微分运算，是微积分中重要的一个概念。
A finite difference is a mathematical expression of the form f(x + b) − f(x + a). Finite differences (or the associated difference quotients) are often used as approximations of derivatives, such as in numerical differentiation. The difference operator, commonly denoted Δ {\displaystyle \Delta } (uppercase Delta), is the operator that maps a function f to the function Δ [ f ] {\displaystyle \Delta [f]} defined by Δ [ f ] ( x ) = f ( x + 1 ) − f ( x ) . {\displaystyle \Delta [f](x)=f(x+1)-f(x).} A difference equation is a functional equation that involves the finite difference operator in the same way as a differential equation involves derivatives. There are many similarities between difference equations and differential equations.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗在数值分析中，数值方法是一种旨在解决数值问题的数学工具。用编程语言实现具有适当收敛性检查的数值方法称为数值算法。
In numerical analysis, a numerical method is a mathematical tool designed to solve numerical problems. The implementation of a numerical method with an appropriate convergence check in a programming language is called a numerical algorithm.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。 本条中文为英文百科简介的机器辅助翻译，请结合英文原文核对专业术语。
查看内容许可 ↗佩克莱特数是流体力学中的无量纲数，指流体中对流和扩散质量、热量之比，计算式为： P e = R e P r = V L α {\displaystyle \mathrm {Pe} =\mathrm {Re} \mathrm {Pr} ={\frac {VL}{\alpha }}} 其中： R e {\displaystyle \mathrm {Re} } 为雷诺数 P r {\displaystyle \mathrm {Pr} } 为普朗特数 V {\displaystyle V} 为平均流速 L {\displaystyle L} 为特征长度 α {\displaystyle \alpha } 为扩散系数或热扩散率 佩克莱特数以Pe表示，是一个无因次参数，用来表示对流速率与扩散速率之比。若Pe >> 1，表示流速大，扩散十分缓慢，故当物质被带往下游时，扩散云团之尺度几乎不变，扩散云团可视为一凝结云团向下游平移，扩散对浓度的影响可予以忽略。反之，当Pe << 1时，表示扩散十分快速，而扩散主导浓度的变化。
In continuum mechanics, the Péclet number (Pe, after Jean Claude Eugène Péclet) is a class of dimensionless numbers relevant in the study of transport phenomena in a continuous environment. It is defined to be the ratio of the rate of advection of a physical quantity by the flow to the rate of diffusion of the same quantity driven by an appropriate gradient. In the context of species or mass transfer, the Péclet number is the product of the Reynolds number and the Schmidt number (Re × Sc). In the context of the thermal fluids, the thermal Péclet number is equivalent to the product of the Reynolds number and the Prandtl number (Re × Pr).
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗在流体力学中，雷诺数（英语：Reynolds number）是流体的惯性力 ρ v 2 L {\displaystyle {\frac {\rho v^{2}}{L}}} 与黏性力 μ v L 2 {\displaystyle {\frac {\mu v}{L^{2}}}} 的比值，它是一个无量纲量。 雷诺数较小时，黏滞力对流场的影响大于惯性力，流场中流速的扰动会因黏滞力而衰减，流体流动稳定，为层流；反之，若雷诺数较大时，惯性力对流场的影响大于黏滞力，流体流动较不稳定，流速的微小变化容易发展、增强，形成紊乱、不规则的紊流流场。
In fluid dynamics, the Reynolds number (Re) is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers, flows tend to be turbulent. The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow (eddy currents). These eddy currents begin to churn the flow, using up energy in the process, which for liquids increases the chances of cavitation. The Reynolds number has wide applications, ranging from liquid flow in a pipe to the passage of air over an aircraft wing. It is used to predict the transition from laminar to turbulent flow and is used in the scaling of similar but different-sized flow situations, such as between an aircraft model in a wind tunnel and the full-size version.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗菲克定律（英语：Fick's law）描述扩散作用，可以使用这条定律来求得扩散系数：D。定律由德国生理学家阿道夫·菲克于1855年推导出来。
Fick's laws of diffusion describe diffusion and were first posited by Adolf Fick in 1855 on the basis of largely experimental results. They can be used to solve for the diffusion coefficient, D {\displaystyle D} . Fick's first law can be used to derive his second law, which in turn is identical to the diffusion equation. Fick's first law: Movement of particles from high to low concentration (diffusive flux) is directly proportional to the particle's concentration gradient. Fick's second law: Prediction of change in concentration gradient with time due to diffusion. A diffusion process that obeys Fick's laws is called normal or Fickian diffusion; otherwise, it is called anomalous diffusion or non-Fickian diffusion.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗合金，就是两种或两种以上化学物质（至少有一组分为金属）混合而成具有金属特性的物质，一般由各组分熔合成均匀的液体，再经冷凝而得。 合金至少是以下三种中的一种：元素形成的单一相固态溶液，许多金属相形成的混合物，金属形成的金属互化物。固态溶液的合金其微观结构有单一相，部分为溶液的合金则是有二相或二相以上，其分布可能是均匀，也可能不均匀，依材料冷却过程的温度变化而定。金属互化物一般会有一种合金或纯金属包在另一种纯金属内。 由于合金一些特性比纯金属元素要好，因此会用在特定的应用中。合金的例子包括钢、焊料、黄铜、白镴、磷青铜及汞齐等。 合金的成分一般是以质量比例来计算。合金依其原子组成的方式，可以区分为替代合金或间质合金，又可以进一步区分为匀相（只有一相）、非匀相（不止一相）及金属互化物（两相之间没有明显的边界）。
An alloy is a mixture of chemical elements of which in most cases at least one is a metallic element, although the word is also sometimes used for mixtures of elements; herein only metallic alloys are described. Metallic alloys often have properties that differ from those of the pure elements from which they are made. The vast majority of metals used for commercial purposes are alloyed to improve their properties or behavior, such as increased strength, hardness or corrosion resistance. Metals may also be alloyed to reduce their overall cost, for instance alloys of gold and copper. In an alloy, the atoms are joined by metallic bonding rather than by covalent bonds typically found in chemical compounds. The alloy constituents are usually measured by mass percentage for practical applications, and in atomic fraction for basic science studies. Alloys are usually classified as substitutional or interstitial alloys, depending on the atomic arrangement that forms the alloy.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗晶粒边界（英语：grain boundary），简称晶界，指多晶材料中晶粒之间的接合区域。在结晶学中晶粒边界是一种二维的晶体缺陷。晶粒边界出现在结构相同方向不同的微晶区域里，通过化学腐蚀可以使之在晶体表面显现。晶粒边界有小角度晶界和大角度晶界之分。当两个微晶区域之间的角度差值大于15度时，我们称之为大角度晶界。大角度晶界阻碍了位错的形成，从而影响了相邻晶粒。因此大角度晶界对金属材料的机械特性影响显著。在大多数情况下，晶粒边界会导致强度的提高，也就是说细粒度晶体更加坚固，但是析出物（特别是在容易在晶粒边界聚集的氧化物）同时也会削弱晶体强度。
In materials science, a grain boundary is the interface between two differently oriented grains, or crystallites, of the same phase in a polycrystalline material. Grain boundaries are two-dimensional defects in the crystal structure, and tend to decrease the electrical and thermal conductivity of the material. Most grain boundaries are preferred sites for the onset of corrosion and for the precipitation of new phases from the solid. They are also important to many of the mechanisms of creep. On the other hand, grain boundaries disrupt the motion of dislocations through a material, so reducing crystallite size is a common way to improve mechanical strength, as described by the Hall–Petch relationship.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗位错（英语：dislocation），在材料科学中，指晶体材料的一种内部微观缺陷，即原子的局部不规则排列（晶体缺陷）。从几何角度看，位错属于一种线缺陷，可视为晶体中已滑移部分与未滑移部分的分界线，其存在对材料的物理性能，尤其是力学性能，具有极大的影响。“位错”这一概念最早由意大利数学家和物理学家维托·伏尔特拉于1905年提出。 理想位错主要有三种形式：刃位错（edge dislocation）和 螺旋位错（screw dislocation）及混合位错（mixed dislocation）兼有前面两者的特征。 数学上，位错属于一种拓扑缺陷，有时称为“孤立子”或“孤子”。这一理论可以解释实际晶体中位错的行为：可以在晶体中移动位置，但自身的种类和特征在移动中保持不变；方向（伯格斯矢量）相反的两个位错移动到同一点，则会双双消失，或称“湮灭”，若没有与其他位错发生作用或移到晶体表面，那么任何单个位错都不会自行“消失”（即伯格斯矢量始终保持守恒）。
In materials science, a dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allows atoms to slide over each other at low stress levels and is known as glide or slip. The crystalline order is restored on either side of a glide dislocation but the atoms on one side have moved by one position. The crystalline order is not fully restored with a partial dislocation. A dislocation defines the boundary between slipped and unslipped regions of material and as a result, must either form a complete loop, intersect other dislocations or defects, or extend to the edges of the crystal. A dislocation can be characterised by the distance and direction of movement it causes to atoms which is defined by the Burgers vector. Plastic deformation of a material occurs by the creation and movement of many dislocations. The number and arrangement of dislocations influences many of the properties of materials.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗成核（英语：Nucleation，也称形核、核化）是相变初始时的“孕育阶段”。天空中的云、雾、雨，燃烧生成的烟，冰的结晶，汽水、啤酒的冒出的泡等的形成，均为成核现象。 成核现象需要成核位点（nucleation site）才可发生。汽化时，液相分子聚集于固相物质上面，分子不断碰撞使得能量聚集，进而形成“汽化中心”；结晶时，若使局部的溶质浓度升高而导致晶体碰撞次数增加，则结晶的晶形构造加快，从而形成“结晶中心”。晶核（英语：crystal nucleus）为晶体的生长中心。晶核的成核有两种形式：初级成核（包括初级均相成核和初级非均相成核）及二次成核。在高于饱和度的情况下，溶液自发形成晶核的过程，称作初级均相成核；若晶核是在溶液外来物的诱导下生成，则称其为初级非均相成核；晶核如在含有溶质晶体的溶液中生成，则称为二次成核。
In thermodynamics, nucleation is the first step in the formation of either a new thermodynamic phase or structure via self-assembly or self-organisation within a substance or mixture. Nucleation is typically defined as the process that determines how long an observer must wait before a new phase or self-organised structure appears. For example, if a volume of water is cooled (at atmospheric pressure) significantly below 0 °C, it will tend to freeze into ice. Still, volumes of water cooled only a few degrees below 0 °C often stay completely free of ice for long periods (supercooling). Under these conditions, nucleation of ice is either slow or does not occur at all. However, at lower temperatures nucleation is fast, and ice crystals appear after little or no delay. Nucleation is a common mechanism which generates first-order phase transitions, and it is the start of the process of forming a new thermodynamic phase. In contrast, new phases at continuous phase transitions start to form immediately. Nucleation is often very sensitive to impurities in the system.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
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