第三章固体材料中的扩散

第三章固体材料中的扩散

Chapter3 The Diffusion in Solid Materials

本章基本问题：

1. 菲克第一定律的含义和各参数的量纲。

2．能根据一些较简单的扩散问题中的初始条件和边界条件。运用菲克第二定律求解。3．柯肯达耳效应的起因，以及标记面漂移方向与扩散偶中两组元扩散系数大小的关系。4．互扩散系数的图解方法。

5．“下坡扩散”和“上坡扩散”的热力学因子判别条件。

6．扩散的几种机制，着重是间隙机制和空位机制。

7．间隙原子扩散比置换原子扩散容易的原因。

8．计算和求解扩散系数及扩散激活能的方法。

9．影响扩散的主要因素。

Questions for chapter 3

1. What is the the meaning of Fick’s first law?

2. How to solve the problems by Fick’s second law?

3. What is the the Kirkendall effect?

4. How to explain diffusion coefficient schematically?

5. What is the diffusion driving force;

6. What are diffusion mechanisms, expecially interstitial and vacancy mechanisms

7. What is the reason that interstitial diffusion is easier than substitutional diffusion?

8 What are the methods to compute diffusion coefficient and diffusion activation energy?

9. What are main factors affecting diffusion?

The field of diffusion studies in metals is of great practical, as well as theoretical importance. By diffusion one means the movements of atoms within a solution. In general, our interests lie in those atomic movements that occur in solid solutions. This chapter will be devoted in particular to the study of diffusion in substitutional solid solutions and atomic movements in interstitial solid solutions.

Diffusion is a process of mass transport that involoves the movement of one atomic species into another.

3-1扩散方程

Sec.3.1 Diffusion Equations

1 菲克第一定律Fick’s First Law

Diffusion can be modeled as the jumping of atoms from one plane to another.

（1）第一定律描述：单位时间内通过垂直于扩散方向的某一单位面积截面的扩散物质流量（扩散通量J flax or the rate of diffusion）与浓度梯度(concentration gradient)成正比。

The rate of diffusion is proportional to the concentration gradient.

（2）表达式：J=-D(dc/dx)。（C－溶质原子浓度；D-扩散系数Diffusivity or diffusion coefficient。）

（3）适用条件：稳态扩散，dc/dt=0。浓度及浓度梯度不随时间改变。

Fick’s first law assumes that the concentration gradient is independent of tim e.

2菲克第二定律Fick’s Second Law

一般：∂C/∂t=∂(D∂C/∂x)/ ∂x

二维：

（1）表达式特殊：∂C/∂t=D∂2C/∂x2

三维：∂C/∂t=D(∂2/∂x2+∂2/∂y2+∂2/∂z2)C

稳态扩散：∂C/∂t=0，∂J/∂x=0。

（2）适用条件：

非稳态扩散：∂C/∂t≠0，∂J/∂x≠0（∂C/∂t=－∂J/∂x）。

Assume that diffusivity, D is independent of C, the rate of change in concentration with time, ∂C/∂t is proportional to the rate at which the concentration gradient changes with distance in a given direction, ∂2C/∂x2

3扩散第二定律的应用

（1）误差函数解

适用条件：无限长棒和半无限长棒。

表达式：C=C1－(C1-C2)erf(x/2√Dt) (半无限长棒)。

在渗碳条件下：C:x,t处的浓度；C1:表面含碳量;C2:钢的原始含碳量。

（2）正弦解

C x=Cp-A0sin(πx/λ)

Cp:平均成分；A0：振幅Cmax- Cp；λ:枝晶间距的一半。

对于均匀化退火，若要求枝晶中心成分偏析振幅降低到1/100,则：

[C(λ/2,t)- Cp]/( Cmax- Cp)=exp(-π2Dt/λ2)=1/100。

Experimental work has shown that the atoms in face-centered cubic, body-centered cubic, and hexagonal metals move about in the crystal lattice as a result of vacancy motion. Let it now be assumed that the jumps are entirely random; that is, the probability of jumping is the same for all of the atoms surrounding a given vacancy. This statement implies that the jump rate does not depend on the concentration.