亚共晶Al-Si合金的组织主要由初生相α-Al和共晶Si组成，由于具有较佳性能而被广泛应用于汽车、航空航天等领域[1~4]。该合金的性能与凝固组织中Si的形态密切相关。常规凝固条件下，共晶Si沿<112>方向优先生长成为粗大的板片状，严重割裂基体，大大降低合金的力学性能。因此，对共晶Si进行变质处理，将其由粗大的板片状转变为细小的短棒状，显得尤为必要[5~7]。目前的工业生产中，通常通过向合金熔体中添加Na或Sr来变质共晶Si。虽然这2种元素对共晶Si的变质效果较好，但均存在一定问题，比如：Na的吸收率较低，在熔体中实际含量不易控制，而且有效变质期较短；相比Na，虽然Sr的吸收率较高、有效变质期较长，但添加Sr的合金气孔率明显增加，且Sr易与铝合金细化剂Al-Ti-B中的B反应，导致变质效果下降[8,9]。
研究[10]表明，添加适量稀土不仅能净化铝合金熔体，有效提高熔体质量、减少合金缺陷，而且也能变质和细化合金凝固组织，有效改善合金组织、提高合金的力学性能。自20世纪90年代以来，稀土元素，尤其是相对廉价的La元素等对Al-Si合金凝固组织影响的研究引起了人们的广泛关注。但以往的研究中，有关La用量说法不一，通常在0.1%~2% (质量分数，下同)间。近期的研究[11~15]表明，微量的La (0.01%)便能大幅细化基体，并与变质剂Na和Sr类似，通过诱发交错孪晶、增加孪晶密度来影响共晶Si的长大行为，将粗大的板片状共晶Si转变为细小的短棒状，从而有效提升合金力学性能。本工作将进一步深入探究微量La变质共晶Si的关键影响因素，并提出共晶Si变质元素选取原则。
1 理论模型
1.1 α-Al(S)/Al(L)界面处液相前沿溶质浓度分布
式中，
由
图1
图1
α-Al晶粒周围溶质M (La或Si)浓度分布示意图
Fig.1
Solute M (La or Si) concentration profile around an α-Al grain (
在α-Al(S)/Al(L)界面前沿熔体中，M的浓度
式中，z为距α-Al(S)/Al(L)界面处的距离。
式中，Z = 12为熔体中配位数，Na为Avogadro常数，Rg为气体常数，T为热力学温度，
式中，Ai/La和ALa/i 为Wilson参数，可由二元无限稀溶液活度系数
式中，aLai 为与合金组元熔点相关的参数；fLai 是表征合金形成热的参数；TmLa和Tmi 分别为La和i的熔点；
| Element | Tm / K | V 2/3 / (cm2·mol-2/3) | ϕ / V | (r / p) / V | u | |
|---|---|---|---|---|---|---|
| Al | 933 | 4.60 | 1.39 | 4.20 | 1.9 | 0.07 |
| Si | 1685 | 4.20 | 1.50 | 4.70 | 2.1 | 0.04 |
| La | 1193 | 7.98 | 1.18 | 3.17 | 0.7 | 0.07 |
键能体现的另一种形式是元素间化合物的形成热。键能越高，元素间化合物形成热越负，越容易析出。本工作采用密度泛函理论对Al m Si m La形成热
Al m Si m La化合物析出与否还与熔体和Al m Si m La间的界面能
式中，ΩAl-Si和ΩAl-La分别为Al-Si和Al-La熔体中Al和Si、Al和La原子间的相互作用参数；fb = 0.74是体堆垛系数；
1.2 共晶Si中La浓度
在亚共晶Al-Si合金的凝固组织中，La以3种形式存在：固溶在α-Al中、可能形成Al m Si m La三元化合物及在共晶Si中。其中只有后者对共晶Si的变质有作用。根据如下溶质守恒公式可求得共晶Si中La的浓度
式中，Xα-Al和XTe分别为α-Al和Al m Si m La化合物的摩尔分数，
由
2 结果与讨论
通过式(
图2
图2
La和i原子(Al或Si)间的相互作用参数ΩLa-i 随界面处熔体中La-i二元系中La浓度
Fig.2
Calculated results for the interaction parameters of La-i melt (ΩLa-i ) as a function of La concentration in the i-M system at α-Al/melt interface(
有关含Al、Si和La 3种元素化合物成分的研究报道很多，通常认为微量La在亚共晶Al-Si合金中会形成AlSiLa或Al2Si2La化合物[12,14,25~28]，但就三元化合物的具体成分，观点尚不统一。因此，本工作分别理论计算了这2种化合物的形成热及其与Al熔体间的界面能，结果如表2所示。可见，0 K下AlSiLa的形成热约为-66.1 kJ/mol，其绝对值远大于Al2Si2La的形成热(-40.3 kJ/mol)的绝对值；而850 K时AlSiLa与Al熔体的界面能极低(≈ 0)，小于Al2Si2La与Al熔体的界面能(0.021 J/m2)。形成热及界面能数据均表明微量La在Al-Si合金熔体中最易形成AlSiLa，这与前期的研究结果[12,14]一致。
表2
0 K下Al m Si m La的形成热(
Table 2
| m | ||
|---|---|---|
| 1 | -66.1 | 0 |
| 2 | -40.3 | 0.021 |
图3
图3
不同La添加量下Al-6Si合金中共晶Si内La的浓度(
Fig.3
Dependences of the La concentration in eutectic Si (
上述分析亦可用于判定其他微量元素对Si的变质效果。微量元素在α-Al中的最大固溶度及与Al、Si的相互作用参数共同决定变质效果。当微量元素与Al、Si的相互作用参数相近时，其在α-Al中的最大固溶度越小，变质效果越强；当微量元素在α-Al中的最大固溶度相近时，其与Al、Si的相互作用参数越小，越不易形成三元化合物，变质效果越强；当变质元素的添加量接近其在α-Al中最大固溶度时，变质效果最佳。
3 结论
(1) 当La的添加量低于其在α-Al中最大固溶度时，La分布在α-Al和共晶Si中，变质效果随着La添加量的增加而增加。
(2) 当La的添加量大于其在α-Al中最大固溶度时，由于La与Al、Si的相互作用参数较大且2者相近，会形成含Al、Si、La的三元化合物，在各种可能的Al、Si、La化合物中，AlSiLa的形成热较大，且与Al熔体间的界面能较低，最易在熔体中形成，此时，La分布在α-Al、AlSiLa和共晶Si中且其在α-Al和共晶Si中的浓度基本不随添加量的增加而变化，变质效果基本保持不变。
(3) 变质元素影响共晶Si变质效果的关键因素是共晶Si中变质元素的浓度，这主要取决于变质元素在α-Al中的最大固溶度、变质元素与Al、Si的相互作用参数及可能形成化合物的形成热、化合物与熔体间的界面能；当变质元素的添加量接近其在α-Al中的最大固溶度时，变质效果最佳。
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[J].利用DTA、OM、SEM、TEM、EPMA以及拉伸实验等方法研究了在添加α-Al晶粒细化剂Al-Ti-B中间合金和共晶Si变质剂Sr条件下，微合金化元素La对亚共晶Al-Si合金凝固组织与力学性能的影响。结果表明：添加微量稀土La能进一步细化α-Al，变质共晶Si，显著提高合金的塑性。分析表明：微量La能降低α-Al晶核与TiB<sub>2</sub>的润湿角，减小α-Al的形核过冷度，促进α-Al的进一步细化；La能诱发交错孪晶的形成，增大共晶Si的孪晶密度，改变Si相的长大行为，进一步改变共晶Si的形貌。当La的添加量达到0.10%时，LaAlSi金属间化合物在凝固过程的共晶反应阶段形成，该化合物的形成将降低合金的塑性。
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图1
表1
