材料科学基础(英)5
合集下载
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
10
11
Some rules
The following features are of interest in connection with compositional aspects of ternary systems. (1) If a straight line such as CD is drawn from one corner of the 等比例规则：沿成分三 triangle (i.e. from component C) to 角形的顶点 C引一条与对 intersect the opposite side (i.e. AB), 边相交的线段 then the ratio of CD the，在此 other two components (i.e. A and B) is 线段CD上的成分的合金 constant in两组元的质量分 alloys represented by 中A和B points lying on the line. Considering 数比值相等，但含 C的质 alloy compositions along CD, as the 量分数不同，距离 composition point C点越 becomes 远，C的含量越少。 progressively further away from C the percentage of C present in the alloys decreases, but the relative amounts of B and A remain the same.
Chapter 5 Ternary equilibrium diagrams （三元平衡相图）
5.1 The representing way of ternary phase diagrams There are 2 variables for
The differences between binary and ternary diagrams: 1) A entire ternary phase diagram is three-dimensional (a space model) but not planar. 2) Four-phase equilibrium transformation may occur in ternary systems. (Phase Rule) 3) Similar with single-phase and two-phase fields, threephase equilibrium regions take up certain space in a ternary diagram.
7
An alternative, but less convenient method of representing the composition on the equilateral triangle is to take the altitude of the triangle as 100%, in which case the percentages of the individual components in a ternary alloy are given by the heights of the respective perpendiculars from the composition point to the opposite sides of the triangle.
wM a1 wN a2 ( wM wN ) x wM x wN x wm x a2 wn a1 x wM wM x a2 x a2 NP wM N wM wN (a1 x) ( x a2 ) a1 a2 MN wN MP wM N MN
14
M（a1 b1 c1) N(a2 b2 c2) P（xyz）
wM a1 wN a2 wP x ( wM wN ) x wN wM x a1 a2 wM wN wM wN y z wN wM b1 b2 wM wN wM wN wN wM c1 c2 wM wN wM wN
Composition scales are commonly plotted in weight percentage. Then, the percentage by weight of each component in a ternary alloy (e.g. alloy x) is obtained by the following construction: a line mn is drawn parallel to side BC and the percentage of m A is B then givenn byC A % mB or the lengths nC. The percentage of AB B is given by AC the lengths of oA or pC, obtained by o A p C drawing side AC. B % line op parallel to Similarly, the AB percentage of C is BC obtained by drawing rs parallel to tA side AB and sB determining the C %rA lengths or sB.
15
Then, using weight percentages:
This is the so-called ' lever principle' or ' lever rule' which finds an important application in 'tie-lines' when an alloy decomposes into a two-phase mixture.
F+P=C+1
23Leabharlann Regarding the composition triangle the three corners represent the three components, points on the side represent binary alloys, and points within the triangle, ternary alloys. Generally, the length of each side of the triangle is considered as divided into 100 equal parts of which represents 1% on the composition scale in each of the binary systems. 通常考虑用成分三角形来表示三元合金的化学成 分，成分三角形的三个顶点代表三个纯组元，三 条边代表三个二元合金体系，三元合金体系的成 分点在此三角形内部。 成分三角形可以为任意三角形，但最常用的是等 4 边三角形。
BC
AC
5
Composition triangle
6
To facilitate the plotting of composition points, the equilateral triangle may be ruled with lines parallel to its sides. Consider the plotting of the composition point of an alloy y, containing 50% B and 30% C. Starting from point A, a length Ab corresponding to 50% B is marked out along AB, and then a length Ac corresponding to 30% C is marked out along AC. The composition point of the alloy then lies at the intersection of the appropriate ruled lines as shown.
9
A right-angled triangle is sometimes used to represent compositions. The percentage of A is obtained by subtracting the percentages of B+C from 100%. This method of representation is useful when interest in centred on alloys of metal A, containing relatively small amount of B and C, that is when the representation of the A-rich corner of the system is required, as is often the case in aluminum-base alloys.
等含量规则：在成分三 角形内做一条与边AB平 行的线段MN，则在MN 上任一点合金含有对顶 点C的质量分数相同。
C
M
N
A
13
B
(3) If two alloys (two phases) (e.g. d and e) are mixed together, the composition of the resulting mixture lies on a straight line joining the compositions of the two 共线规则（杠杆规则） alloys (co-linear principle). 如果两个相混合在一起， The total composition lies at 那么混合物的成分点必 the point dividing the line 然在两个原始相的成分 into segments inversely 点的连线上，并且符合 proportional to the ratio of 杠杆定律。 the quantities of the original alloys.
the component of ternary alloy. The temperature is plotted on the vertical axis, and the composition is represented on the base of the prism, which may be conveniently taken as an equilateral triangle. Thus, the vertical sides of the prism represent the three binary systems AB, BC, and AC that make up the ternary system ABC.
C
P
M
O
N
A
G
E
D F
H
B
等比例规则 背向规则
12
(2) A line drawn parallel to one side of the triangle is a line along which alloys contain a constant percentage of one component, i.e. along no the percentage of C remains the same.
杠杆规则
11
Some rules
The following features are of interest in connection with compositional aspects of ternary systems. (1) If a straight line such as CD is drawn from one corner of the 等比例规则：沿成分三 triangle (i.e. from component C) to 角形的顶点 C引一条与对 intersect the opposite side (i.e. AB), 边相交的线段 then the ratio of CD the，在此 other two components (i.e. A and B) is 线段CD上的成分的合金 constant in两组元的质量分 alloys represented by 中A和B points lying on the line. Considering 数比值相等，但含 C的质 alloy compositions along CD, as the 量分数不同，距离 composition point C点越 becomes 远，C的含量越少。 progressively further away from C the percentage of C present in the alloys decreases, but the relative amounts of B and A remain the same.
Chapter 5 Ternary equilibrium diagrams （三元平衡相图）
5.1 The representing way of ternary phase diagrams There are 2 variables for
The differences between binary and ternary diagrams: 1) A entire ternary phase diagram is three-dimensional (a space model) but not planar. 2) Four-phase equilibrium transformation may occur in ternary systems. (Phase Rule) 3) Similar with single-phase and two-phase fields, threephase equilibrium regions take up certain space in a ternary diagram.
7
An alternative, but less convenient method of representing the composition on the equilateral triangle is to take the altitude of the triangle as 100%, in which case the percentages of the individual components in a ternary alloy are given by the heights of the respective perpendiculars from the composition point to the opposite sides of the triangle.
wM a1 wN a2 ( wM wN ) x wM x wN x wm x a2 wn a1 x wM wM x a2 x a2 NP wM N wM wN (a1 x) ( x a2 ) a1 a2 MN wN MP wM N MN
14
M（a1 b1 c1) N(a2 b2 c2) P（xyz）
wM a1 wN a2 wP x ( wM wN ) x wN wM x a1 a2 wM wN wM wN y z wN wM b1 b2 wM wN wM wN wN wM c1 c2 wM wN wM wN
Composition scales are commonly plotted in weight percentage. Then, the percentage by weight of each component in a ternary alloy (e.g. alloy x) is obtained by the following construction: a line mn is drawn parallel to side BC and the percentage of m A is B then givenn byC A % mB or the lengths nC. The percentage of AB B is given by AC the lengths of oA or pC, obtained by o A p C drawing side AC. B % line op parallel to Similarly, the AB percentage of C is BC obtained by drawing rs parallel to tA side AB and sB determining the C %rA lengths or sB.
15
Then, using weight percentages:
This is the so-called ' lever principle' or ' lever rule' which finds an important application in 'tie-lines' when an alloy decomposes into a two-phase mixture.
F+P=C+1
23Leabharlann Regarding the composition triangle the three corners represent the three components, points on the side represent binary alloys, and points within the triangle, ternary alloys. Generally, the length of each side of the triangle is considered as divided into 100 equal parts of which represents 1% on the composition scale in each of the binary systems. 通常考虑用成分三角形来表示三元合金的化学成 分，成分三角形的三个顶点代表三个纯组元，三 条边代表三个二元合金体系，三元合金体系的成 分点在此三角形内部。 成分三角形可以为任意三角形，但最常用的是等 4 边三角形。
BC
AC
5
Composition triangle
6
To facilitate the plotting of composition points, the equilateral triangle may be ruled with lines parallel to its sides. Consider the plotting of the composition point of an alloy y, containing 50% B and 30% C. Starting from point A, a length Ab corresponding to 50% B is marked out along AB, and then a length Ac corresponding to 30% C is marked out along AC. The composition point of the alloy then lies at the intersection of the appropriate ruled lines as shown.
9
A right-angled triangle is sometimes used to represent compositions. The percentage of A is obtained by subtracting the percentages of B+C from 100%. This method of representation is useful when interest in centred on alloys of metal A, containing relatively small amount of B and C, that is when the representation of the A-rich corner of the system is required, as is often the case in aluminum-base alloys.
等含量规则：在成分三 角形内做一条与边AB平 行的线段MN，则在MN 上任一点合金含有对顶 点C的质量分数相同。
C
M
N
A
13
B
(3) If two alloys (two phases) (e.g. d and e) are mixed together, the composition of the resulting mixture lies on a straight line joining the compositions of the two 共线规则（杠杆规则） alloys (co-linear principle). 如果两个相混合在一起， The total composition lies at 那么混合物的成分点必 the point dividing the line 然在两个原始相的成分 into segments inversely 点的连线上，并且符合 proportional to the ratio of 杠杆定律。 the quantities of the original alloys.
the component of ternary alloy. The temperature is plotted on the vertical axis, and the composition is represented on the base of the prism, which may be conveniently taken as an equilateral triangle. Thus, the vertical sides of the prism represent the three binary systems AB, BC, and AC that make up the ternary system ABC.
C
P
M
O
N
A
G
E
D F
H
B
等比例规则 背向规则
12
(2) A line drawn parallel to one side of the triangle is a line along which alloys contain a constant percentage of one component, i.e. along no the percentage of C remains the same.
杠杆规则