首先根据课件展示的纳米颗粒形态，查找到如下图源论文对纳米颗粒的定义：
<aside> 🏆 Because of computing limitations, when studying the structural stability of NPs, the size range of Pt NPs is 2–20 nm, which contains approximately 400–400000 atoms. When researching the thermal stability of NPs, the size range of Pt NPs is 2–10 nm, which contains about 400–50000 atoms. The effects of size and shape on the structural and thermal stability of platinum nanoparticles .pdf
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得知计算物理研究的金属纳米颗粒是数百至数万个原子构成的原子团，尺寸为纳米量级。不妨认为原子团中原子仍按照晶格排列。
纳米颗粒的仿真过程于单相物质有什么区别呢？论文中选用等压等温系综（npt），升温过程是从0K逐步升温至熔化，升温速率为20K每40000步（40ps），并且每次升温后弛豫相同时间。文章中研究的是不同形状纳米颗粒熔化后的性质，故只提供了缓慢加热的过程。我们可以学到的是在仿真过程中考虑加入弛豫过程，可以选用npt或其他LAMMPS提供的系综进行仿真。
<aside> 📔 To study the effects of the size and shape on the thermal stability of Pt NPs, we calculated the structural evolution during the heating process and the melting point of Pt NPs using molecular dynamics simulation. Throughout the simulation process, the isothermal-isobaric ensemble (NPT), Nose-Hoover thermostat and Berendsen barostat were adopted, and the time step was 1 fs. Starting from 0 K, the system temperature was increased by 20 K within 40 ps, and then the system was equilibrated by 40 ps under a constant temperature. These heating and equilibrium processes were repeated until the NP completely melted. The output value of each physical quantity was obtained from the statistical average value in the last 20 ps of the equilibrium process.
The effects of size and shape on the structural and thermal stability of platinum nanoparticles .pdf
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建模应考虑如下因素
单质晶格
Cu fcc 面心立方 ，晶格常数$a=3.61$
lattice fcc 3.61
纳米颗粒尺寸
2~20nm,约400~5000个原子。
可以在一个region中建立这些原子。方形区域的指令格式如下：
block args = xlo xhi ylo yhi zlo zhi
xlo,xhi,ylo,yhi,zlo,zhi = bounds of block in all dimensions (distance units)
xlo,xhi,ylo,yhi,zlo,zhi can be a variable
region box block 0 8 0 8 0 8
边界条件
f f f
一种思路是将边界条件设为非周期边界条件。但是，这种思路无法使用特定系综计算，因为系综是定义在统计上的。周期性边界条件下LAMMPS可以利用虚拟在region之外的原子统计足够的原子；非周期边界条件region内不可能包含如此之多的原子（$N_A$量级）。故，如果不希望使用自定义时间积分，只能保持周期性边界条件。
系综
npt的p计算包括box中真空层，若$p\ne0$，则box返回为没有真空层的box，模型退化到单相铜的仿真。选用nvt系综升温降温。
#Cu melt
#基本参数
units metal
boundary p p p
atom_style atomic
timestep 0.001
neighbor 2.0 bin
neigh_modify every 1 delay 0
variable T0 equal 2.5
variable T1 equal 2000
variable N equal step
variable T equal temp
variable V equal vol
#模型
lattice fcc 3.61
region box block 0 20 0 20 0 20 units box
create_box 1 box
create_atoms 1 box
#热力学
thermo 100
thermo_style custom step temp vol pe ke
#势函数
pair_style eam
pair_coeff * * Cu_u3.eam
#温度初始化
velocity all create ${T0} 114514 dist gaussian
minimize 1e-4 1e-6 1000 1000
#melt output
dump 1 all custom 100 all.lammpstrj id type x y z
fix extra all print 100 "${N} ${T} ${V}" file data
# 计算msd
compute 5 all msd
fix msd all ave/time 10 100 1000 c_5[1] c_5[2] c_5[3] c_5[4] file msd5
# 平衡
fix nvt all nvt temp ${T0} ${T0} 0.01
run 10000
unfix nvt
# compute 1 all msd
# fix msd1 all ave/time 10 100 1000 c_1[1] c_1[2] c_1[3] c_1[4] file msd1
change_box all x scale 2.5 y scale 2.5 z scale 2.5
# 急剧升温
fix nvt all nvt temp ${T0} ${T1} 0.2
run 120000
unfix nvt
# compute 2 all msd
# fix msd2 all ave/time 10 100 1000 c_2[1] c_2[2] c_2[3] c_2[4] file msd2
change_box all x scale 2.5 y scale 2.5 z scale 2.5
# 平衡
fix nvt all nvt temp ${T1} ${T1} 0.01
run 120000
unfix nvt
# compute 3 all msd
# fix msd3 all ave/time 10 100 1000 c_3[1] c_3[2] c_3[3] c_3[4] file msd3
# 退火
fix nvt all nvt temp ${T1} ${T0} 0.05
run 480000
unfix nvt
# compute 4 all msd
# fix msd4 all ave/time 10 100 1000 c_4[1] c_4[2] c_4[3] c_4[4] file msd4
# 退火后平衡
fix nvt all nvt temp ${T0} ${T0} 0.01
run 10000
unfix nvt
write_restart rst.Cu
write_data rst.Cu.lmp
物理量表征
体积：颗粒的体积？（而非box的体积）
扩散系数 msd ：质心位移引起错误。
Lindemann index方法（非周期体系）：比msd更方便。
势能
文章的结论：纳米颗粒的熔点比体相铜的低。
初始晶格弛豫
晶体在力势作用下弛豫一段时间。
拆分出纳米颗粒，并快速升温
可以看到，纳米颗粒从较规则的体型到熔化后呈圆团状
