金属凝固原理作业

1. Al-Cu相图的主要参数为CE=33%Cu,Csm=5.65%Cu, Tm=660℃,TE=548℃.用Al-1%Cu 合金浇注一水平细长圆棒试样,使其自左至右单相凝固,冷却速度足以保持固-液界面为平界面。当固相无Cu的扩散，液相中Cu充分混合时，求：

①凝固10%时,固-液界面的CS* 和CL*；

②共晶体所占的比例；

③画出沿试棒长度方向Cu的分布曲线图，并标明各特征值。

2. 用Al-1%Cu合金浇注一水平细长试棒，使其自左向右单向凝固，并保持固-液界面为平界面。当固相无Cu的扩散，液相中Cu有扩散而达到稳定态凝固时，求：

（1）固-液界面的CS* 和CL*；

（2）固-液界面的温度Ti；

（3）固-液界面保持平界面的条件（DL=3×10-5cm2/s）；

（4）画出沿圆棒长度方向Cu的分布曲线。

3. 普通工业条件下，铸锭的冷却速度v=2.5×10-3cm/s；DL ≈10-5cm2/s；GL＜3~5℃/cm，|mL|＞1，令ρs=ρL，试分别求出某合金C0=10%、1% 、0.01 %（质量分数）以及k0=0.4与0.1时确保固-液界面平面生长所必须的GL值。根据计算结果能得出什么结论？

英文

2-1 A Ge-Ga ingot containing 10 ppm Ga is solidified（凝固）at R=8×10-3cm/s with negligible convection（忽略对流）, show schema t示意图: cally, the composition（成分）along the length of the fully solidified ingot, gaving the initial composition and lengths of the initial and final transients（瞬态）. Assume DL=5×10-5cm2/s,k=0.1

2-4 A Ge-Ga crystal is grown by normal freezing with forced convection so that δ=0.005cm.Initial composition is 10 ppm Ga .Assume DL=5×10-5cm2/s, k=0.1

(a)For a solidification rate of 8×10-3cm/s , what will be the composition of the solid forming when the crystal is 50 percent solidified.

(b)How much lower would the solidication rate need to be to make it reasonable to assume complete liquid diffusion?

(c)How much higher would the solidification rate need to be to obtion a crystal of essentially uniform composition?

2-5An alloy Al-1%Cu is normally solidified with K’=K.The phase diagram for this alloy is schematically as in Fig 2-3 with C E=33%Cu,C SM=5.65%Cu.T m=660℃and T E=548 ℃

(a)How much eutcetic will be present in the finally solidified bar assuming no solid diffusion?

2-10 A small Ge-Ga crystal is grown with a plane front by the Czochralski technique with force convection so that δ=0.005cm.Melt composition is Co=10ppm Ga .Assume D L=5×10-5cm2/s, k=0.1 plot the composition along the length of the crystal for (a) a very slow rate,(b) 8×10-3cm/s ,and (c) a very fast rate.

3-1A Ge-Ga crystal is grown by normal freezing. Initial melt composition is Co=10ppm Ga. Growth rate is 8×10-3cm/s. Assume k=0.1,m L=-4 ℃/%, D L=5×10-5cm2/s

(a)If convection is completely absent, What thermal gradient is required to maintain（保持）a plane front when the ingot is 50 percent solidified?

(b)If convection is sufficiently vigorous（充分的足够的）that k=k’, what thermal gradient（热梯度）is required to maintain a plane front when the ingot is 50 percent solidified?

(c)If δ=0.005.What thermal gradient is required to maintain a plane front when the ingot is 50 percent solidified?

3-2An Al-1%Cu alloy is grown by normal freezing at 3×10-4cm/s with convection complete suppressed（禁止）.The phase diagram for this alloy is as shown schematically in Fig,2-3 with C E=33%Cu,C SM=5.65%Cu.T m=660℃and T E=548 ℃,and constant k and m L; D L=3×10-5cm2/s

(a)What will be the temperature of the planar solid-liquid interface at steady state?

(b)What thermal gradient will be required to maintain the plane front according to the constitution supercooling criterion?

3-4 An Al-1%Cu ingot is solidified with no convection at 3×10-4cm/s ,with a thermal gradient of 300 ℃/cm. solidification is cellular,(see the data in prob.3-2)

(a)What is the approximate liquid composition at the cell tips?The solid composition?

(b)What is the temperature of the cell tips?

(c)What is the distance from the cell tips to the cell roots?

(d)How far does characteristic distance of the diffusion boundary layer extend in front of the cell tips?

3-5 What weight fraction eutectic will form in intercellular regions of the ingot of prob.3-4?