杨 春
论文题目：深过冷液态金属比热的分子动力学模拟及实验研究
作者简介：杨 春，女，1973年11月出生，1995年09月师从于清华大学过增元教授，于2001年01月获博士学位。
摘 要
深过冷快速凝固技术是利用空间条件制备优异性能金属材料的国际前沿技术。准确获得深过冷态（亚稳定状态）的液态金属热物理性质及其规律对于这一新技术具有决定性的意义。由于深过冷态是一种极易发生相变的亚稳态，因此通过实验获取深过冷液态金属的热物理性质有些是不可能的，有些则是非常困难且代价昂贵的。目前这方面的数据极少，只能采用将熔点以上的液态金属热物理性质外推以获得过冷液态物性。这种不得已的近似显然已远不能满足技术发展的要求。因此，对深过冷液态金属的热物性及其规律的研究是在科学技术发展过程中出现的材料科学和热科学的新交叉点，已成为一个国际前沿性课题。通过分子动力学模拟方法可获得范围很宽的深过冷液态金属的热物理性质及其变化规律，它具有可行性好，物理模型清晰，投资少等优点，对深过冷快速凝固技术的发展有着重要意义。
为完善并检验自行开发的分子动力学程序的实用性与可靠性，本文首先以简单流体为研究对象，采用了L-J双体势函数，对氩汽液界面的密度、压力以及温度分布进行了模拟，得到了与其他研究者研究结果一致的界面密度和压力分布，同时还发现了界面中的温度粒子动能分布呈非单调变化。模拟结果表明，分子动力学模拟方法是一种行之有效的研究手段，它能够从微观态出发对系统的性质进行分析，能够讨论和研究一些超常条件下的，实验难以做到的问题，并能从一定意义上揭示客观现象的物理本质。
在前期简单流体的分子动力学研究基础上，本文对有广泛应用背景的两种铜、银纯金属以及铜银、铁镍、铜镍三种二元合金的比热进行了计算和分析，并以铜镍合金为对象进行了比热的实验测量。
液态金属粒子之间的相互作用比较复杂，由于自由电子的影响，双体势能函数在描述金属粒子相互作用方面存在着较大的缺陷，对于应用广泛的过渡金属尤为不适合。本文则选用了适用于过渡态金属的嵌入能模型。对铜的模拟结果表明，在较大的温度范围内液态铜的比热基本不发生变化，在熔点以下的比热与在熔点附近的比热变化规律是一致的。而与此相反，银的比热随温度呈非单调变化，即在700-900 K的区域内，银的比热随着温度的升高而升高，在1000－2000 K 的范围内，比热随着温度的升高而下降。而且在1000 K 附近出现比热的突变峰值。通过分析1000 K 附近的银的结构因子，发现在1000 K 附近银的结构发生了从液态到玻璃态的转变。
为了阐明不同金属的比热变化规律，分析研究了金属其他物理性质对比热的影响。其中比较明显的影响因素有：金属离子的质量与比热的数值成反比，但是对比热随温度的变化规律没有大的影响；内聚功和剪切模量对比热随温度的变化趋势有较大影响，内聚功的增加或者剪切模量的减小都会使得比热随温度的变化变得平缓，反之则形成了比热随温度的非单调变化。而体模量对比热的影响则比较微弱。
对纯金属的成功模拟为研究应用更为广泛的二元合金提供了良好的基础。本文利用经过推广的嵌入势能模型对三种二元匀晶合金进行分析，得出了铜镍、铜银、以及铁镍合金的比热。这三种合金由于其良好的耐腐蚀性，或浸润性而被广泛地应用在国防、机械制造等工业领域。关于这三种合金深过冷液态下的比热数据尚未见到报道。在此之前，由于实验数据的缺乏，往往采用外推法或者利用理想溶液模型从纯金属的比热数据中推导得深过冷的比热数据。这样的方法无疑不够准确从而不能满足预测凝固过程的需要。本文通过模拟得出三种合金在液态以及深过冷液态下的比热变化规律：铜镍合金的比热随温度的变化是非单调的，其比热在1400 K 附近出现极大值，在1400 – 2000 K之间随温度的升高而下降，在800 – 1400 K 之间随温度的升高而升高。也就是说该合金的比热在熔点以上及熔点以下表现截然不同，因此不能使用外推法推算过冷液态下的比热。模拟结果还表明铜银合金与铁镍合金的比热表现与铜镍合金明显不同。这两种合金随温度变化很小——在相当大的温度范围内基本上保持为一个常数。这些结果表明液态金属比热的变化规律是多样的，很难用某一种趋势来概括所有的液态金属比热与温度的关系。
与分子动力学方法相对应，我们还采用熔融玻璃净化法研究了大块铜镍合金在过冷液态下的比热以及凝固组织与过冷度之间的关系。玻璃净化法的原理是采用一定种类的无机盐玻璃，同金属一起加热。这样，当金属样品融化时，熔融态的无机盐玻璃将样品包裹起来，或者说液态金属样品完全浸浮在熔融玻璃中，达到无容器处理的目的，从而避免了壁面形核的影响。由于所选择使用的玻璃具有较大的粘性，因此它可以将液态金属样品中的杂质及氧化物吸附，达到有效去除金属样品中异质形核的干扰作用，使得大块金属样品（直径为1cm）可以在慢速冷却条件下获得深过冷，并实现快速凝固。实验中获得的四种组分合金(Cu-25%Ni, Cu-33%Ni, Cu-50%Ni, Cu-75%Ni)的最大过冷度分别达到0.83
（0.26
）, 0.83
（0.25
）, 0.78
（0.28
）, 0.82
（0.26
），超过了经典形核理论所预言的均质形核临界过冷度0.2
。通过实验方法确定四种成分合金的超过冷临界温度以及结晶潜热，从而获得了铜镍系合金在过冷态下的平均比热。对比分子动力学，模拟得出的比热与实验得出的比热在数值上相差仅在10%以内。
使用一份醋酸、一份硝酸和两份丙酮配成的腐蚀剂对大块过冷合金的剖面进行腐蚀，金相显微镜下观察到的腐蚀表面呈现出合金的微观组织结构。实验发现随着过冷度的增加，合金的组织由粗大、发育良好的枝晶转变为晶粒细小的等轴晶。同时我们发现过冷度增加，组织细化使得铜镍合金的耐腐蚀性有了显著的提高。
利用超高真空落管模拟微重力环境，我们还对上述四种合金的结构变化进行了实验研究。超高真空落管一方面可以把样品分散成很多小液滴达到无容器处理状态并在液滴下落过程实现快速冷却和凝固，另一方面可以产生低重力加速度。观察实验结果，我们可知随着粒子直径的减小导致冷却速度的增加，在微重力条件下铜镍合金的结构会产生由粗大枝晶到枝晶熔断到等轴晶的变化。这一点与大块铜镍合金中的实验结果相一致。
本论文成果主要创新点为：
1、通过分子动力学模拟在较大温度范围内获得了铜和银两种纯金属以及三种二元合金，在深过冷液态下（亚稳态）的比热数据，这些数据在国内外均未见报导。本文所提供的较详细的数据填补了这方面的一些空白。
2、由于数据的缺乏，很长时间以来在不清楚液态金属比热随温度变化规律的情况下，人们普遍采用外推法获得过冷液态金属的比热。本文则揭示了某些金属（如银及铜银合金等）的比热随温度的变化是非单调的，因此外推法是不适用的。进一步的分析研究表明，发现内聚功以及剪切模量对比热有较大的影响，金属内聚功较低以及剪切模量较高是其比热随温度非单调变化的物理原因。
3、首次发现了在一定的条件下，银同样可以实现过冷液态到玻璃态的转变。它对应于深过冷液态金属比热的突变。这充分表明了，热物理性质的变化能反映结构的变化。
4、实现了大过冷度0.22
~0.26
条件下的铜镍合金比热的测量。该过冷度已经超越了经典形核理论所预测的极限过冷度0.2
。揭示了结晶平台的时间与过冷度之间近似线性的关系，从而准确地获得了四种组分的铜镍合金的过冷态平均比热
5、实验测得的深过冷铜镍合金的平均比热与分子动力学模拟所得的数据相互吻合较好（误差10％），表明所得数据的可靠性，同时也表明分子动力学模拟方法的可用性。
Molecular Dynamics Simulation and Experimental
Investigation
on Heat Capacities of Supercooled Liquid Metals
ABSTRACT
As an advanced processing technique for metallic materials, rapid
solidification of supercooled liquid metals offers a promising way for
preparing bulk amorphous metal, which is difficult of fulfilling by traditional
rapid quenching techniques. To control the solidification process of
supercooled liquid metal, specific heat capacity is of particular importance.
However, because of its metastable characteristic and inaccessibility for
direct-contact measurement, the specific heat capacity of supercooled metallic
liquids is difficult to be completely determined by experiment. Up to the present,
there are few existing data, and most of the time people have no alternative
but to extrapolate the existing normal properties to supercooled region. This
approximation can apparently not meet the demand of development of this
solidification technology. The shortage of thermophysical properties of
supercooled liquid metals has also emerged from the research crossover between
the material science and thermal science, and received worldwide attentions. Molecular
dynamics simulation provides an alternative to study the thermophysical
properties of supercooled liquid metals. The main advantage of this method is
the possibility of attaining detailed information of properties over a wide
range of thermodynamic conditions. This makes the molecular dynamic simulation
an important method of thermophysical property investigation in material
science and thermal science.
In order to investigate the reliability and feasibility of our
molecular dynamics method, we simulated the liquid-vapor interface properties
of density, pressure and temperature with Lennard-Johnes potential model. The
results are in good agreement with other reports available in literature.
Meanwhile, the simulation revealed that the kinetic energy distribution of
molecules across the interface was not identical.
Based on the previous simulation, investigations on specific heat
capacities of two pure metals and three series of binary alloys were
numerically and theoretically accomplished, and the specific heat capacity of
Cu-Ni alloy was experimentally measured.
The interatomic interaction between the particles of liquid metals
is more complicated than normal fluid. This makes the traditional two-body
potential model inapplicable to describe liquid metals, especially for
transition metals. In this work, potential models based on embedded-atom method
were used to describe the liquid metals’ particles. The simulation results showed
that the specific heat capacity of liquid copper decreases very slightly with
the temperature decreasing, and remained linear above and below the melting
point. In contrast, the simulated temperature dependence of specific heat
capacity of liquid silver behaves non-monotonously. Quantitatively, the
specific heat capacity of liquid silver increases with the temperature between
700-900K, while decreases with the temperature between 1000-2000K. There exists
an abnormity of specific heat capacity of liquid silver near 1000K. Detailed
analysis of structure factor showed that the liquid-to-glass transition took
place at this temperature.
A detailed analysis of the relationship between the specific heat
capacity of liquid metal and its atomic chemistry-physical properties was also
carried out. The analysis revealed that the specific heat capacity was in
inverse proportion to atomic mass, while the temperature dependence of specific
heat capacity did not show noticeable relationship with atomic mass. It also showed that cohesive energy and
share stress module of the metal affected the temperature dependence of
specific heat capacity. The increase of cohesive energy and the decrease of
share stress module weakened the temperature dependence of specific heat
capacity. In contrast, the decrease of cohesive energy and the increase of
share stress module strengthened the temperature dependence of specific heat
capacity. Bulk module showed very weak impact upon specific heat capacity.
The simulations of specific heat capacity were also
extended to three series of binary alloys, i. e. Cu-Ni alloy, Cu-Ag alloy and
Fe-Ni alloy. These series of alloys were selected because of their important
applications to mechanical machining and national defence, and the lack of
information of their specific heat capacities in supercooled region.
Simulations showed that the temperature dependence of specific heat capacity of
Cu-Ni alloy was not monotonic. It exhibits a slight decrease with increasing
temperature in the region from 1400K to 2000K, while increases with temperature
in the region from 800K to 1400K. It means the specific heat capacity of this alloy
in the supercooled region is remarkably different from that above the melting
point, and extrapolating of normal-state data into supercooled region is
inapplicable. Whereas the simulated specific heat capacity of Fe-Ni alloy
exhibits here approximately a constant value from the superheated condition to
supercooled condition. The behavior of the heat capacities in the supercooled
region depends on the species of the alloys.
The specific heat capacity, and
the relationship between the solidification structure and supercooling degree
were investigated with a series of supercooled Cu-Ni melts by using glass
fluxing technique. This technique is a special experimental process, which is
applied to restrain the nucleation in the melts and keep their containerless
condition. The maximum supercoolings of the Cu-25%Ni, Cu-33%Ni, Cu-50%Ni and
Cu-75%Ni alloys were 0.26
, 0.25
, 0.28
and 0.26
respectively, which exceed the critical supercooling of 0.2
in the classical nucleation theory. The experimentally
determined hypercooling points of the alloys were used to calculate the average
specific heat capacity. The experimental results were compared with current
molecular dynamics simulation results, and the deviation was less than 10%.
Microscopic investigation on the metallurgical phase in glass fluxing
experiment indicates that the solidification microstructure of the alloys
transformed from dendrite grain to equiaxed grain. Meanwhile, the refined
microstructure strengthens the etching resist ability.
In summary, the main innovations of the current work are:
1.
Specific
heat capacity of two pure liquid metals and three series binary alloys over a
wide rang of temperature were obtained by using molecular dynamics simulation.
Some of the data in the supercooled region are firstly reported in literature.
2.
Because
of the lack of detailed knowledge, people used to extrapolate the specific heat
capacity of normal state into supercooled region. Current study showed that at
least for some of the alloys, this extrapolate was inapplicable. Further
investigation revealed that the cohesive energy and the share stress module of
the liquid metal noticeably affected the temperature dependence of specific
heat capacity. The lower cohesive energy and higher share stress module are the
main reasons of non-monotonic temperature dependence of specific heat capacity.
3.
It
is the first time that the liquid-to-glass transition of silver is observed by
molecular dynamics simulation. The consistent behavior between the
liquid-to-glass transition and the specific heat capacity abnormity also
indicated the intrinsic relation between the structure transition and the
thermophysical property.
4.
The
experimental measurements of the specific heat capacities of supercooled liquid
alloys were accomplished. The reached supercoolings are larger than the critical supercooling of 0.2
in the classical nucleation theory. Meanwhile the average
specific heat capacities of a series of Cu-Ni alloys in the supercooled region
were determined.
5.
The measured specific heat capacities
of supercooled Cu-Ni alloys are in good agreement with those predicted by
molecular dynamics simulations. The deviation is approximately 10%. It approves
that the acquired data are reliable, and the molecular dynamics method is
practicable.
Keywords: Supercooled liquid metal,
Specific heat capacity, Molecular dynamics simulation, Glass fluxing technique
