SimuLab 1: Nanoscale Structures at Phase Transition


You will be able to:

a) Observe the nonideal Gas behavior;

b)Observe condensation as the Gas is cooled down ;

c) Explore phase equilibrium between Gas and Liquid and study the surface tension;

d)Study supercooled Liquid;

e) Observe the formation of nanoscale structures during the homogeneous nucleation;

f) Observe polycrystalite growth;

g) Understand the nanoscale structure of polycrystalites.

Figure 2.2: The system crystallizes into 4 distinct crystallites with many defects. This solid is called polycristaline

Post-Lab In-Depth Discussions

As the surface of the crystalline nuclei increases, the rate of crystallization increases as well. Since we still taking away heat from the system the total energy decreases. The rate of cooling is proportional to the temperatures difference between the system and the heat bath. As temperature increases, the crystallization rate decreases and the heat exchange rate increases. At certain temperature these two rates equilibrate each other and the system reaches the steady state. At temperature T = 0.34, which is above the homogeneous nucleation temperature of 0.31, and thus the liquid and crystal phases are still far from equilibrium. The crystalline phase grows very fast. This means that the liquid at this temperature is metastable. It is called supercooled liquid. We were able to supercool liquid well below the equilibrium freezing point, when the crystal and the liquid are at equilibrium, i.e. neither liquid or crystal are growing. However when we cool the system to 0.31 the homogeneous crystallization happens (in water that happens at -40 0 C. This is the lowest possible temperature that one can achieve experimentally for a liquid.) .

Answers to the question

Simulab 1

A1.1: No, the temperature is about 2 C and the pressure 176 MPA 1750 Atm.

A1.2: P V = 2149 while kb N T = 2048. Thus the gas is not ideal, the deviation from ideal gas is 5%. Pressure is greater than one would expected from Ideal gas law by 5%.

A1.3: It is below liquid nitrogen. The temperature of liquid nitrogen is 60 K.

A1.4: The Total Energy goes down because as we put our system in the freezer the system gives away its heat to the freezer.

A1.5: The atoms attract each other and spend most of the time within the radius of attraction of each other. The potential energy of each pair is negative. As more and more atoms come within the radius of attraction, the potential energy decreases. The pressure goes down due to two factors. Firstly, the temperature goes down thus the particles collide with the walls with less speed. Secondly, the particles attract to each other, thus, an extra force towards the bulk of the container on the particles near the walls acts, thus reducing the pressure on the walls.

A1.6: No it does not old.

A1.7: No, it is 8 molecules, previously it was 12.

A1.8: It is due to the surface tension. Atoms at the surface of the liquid have few neighbors than in the bulk of the liquid and thus have a higher potential energy. At thermal equilibrium the system tries to minimize its free energy which at low temperature is almost equal to the potential energy. Thus it tries to minimize its surface. This phenomenon is called surface tension.

Table 1

Pressure Temperature Surface Tension
2.00 10-4 0.5
3.11 10-4 0.412
3.99 10-4 0.34  
6.04 10-4 0.318

A1.9: The surface tension is surface free energy (F = U -T S) per unit area. As we reduce the temperature the free energy decreases.

A1.10: 12

A1.11: -6

A1.12: 5

A1.13: The temperature goes up because the potential energy of interatomic  interaction decreases and is converted into kinetic energy of chaotic motion. The amount of energy released during the crystallization is called latent heat.

A1.14: At time 8500 the temperature reaches its maximum because at this point the crystalline surface is maximal, so is the crystallization rate (See "In-Depth Discussion"). As the amount of liquid phase decreases, the crystallization rate decreases and the temperature finally reaches the temperature of the thermal bath, when crystallization completely seizes.