Structural defects of monolayer wet particles during melting under vertical vibration

The evolution of structural defects during phase transition is of great significance to the understanding of the mechanism of solid-liquid transition. However, the current research on topological defects still uses the pair-correlation function and the orientational order correlation function, so it is difficult to quantify the detailed changes of structural defects locally. In this paper, the local volume fraction is proposed as a key parameter to accurately quantify the variation of structural defects. The experimental results indicate that the evolution of structural defects in the particle system is caused by the decrease of local volume fraction, so the critical value of phase transition could be determined by the minimum local volume fraction ${\varphi }_{\min }$. Furthermore, according to the evolution law of structural defects, it can be deduced that the phase transition is continuous, which is consistent with the Kosterlitz-Thouless-Halperin-Nelson-Young theory. Therefore, the quantitative analysis of structural defects by using local volume fraction can help make the mechanism of solid-liquid phase transformation clearer.

Figure 1

Schematic of experimental setup. (a) A charge-coupled device is used to collect the data of the particles in the disk of the vertical vibrating table. (b) The camera captures the original images, in which each point of light is a particle.

Figure 2

Particle recognition and localization. (a) The original image; (b) the position of each particle obtained after image processing.

Figure 3

The collective behavior of wet particle system under different dimensionless accelerations. Topological structure of particle system changes at (a) $\mathrm{\Gamma }=7$, (b) $\mathrm{\Gamma }=14.4$, (c) $\mathrm{\Gamma }=20,$ and (d) $\mathrm{\Gamma }=40$. (e) Color coding for the local structure (free, line, square, or hexagonal) is identified by means of bond-orientational order parameters. Blue particles are free particles, yellow particles represent four bonds, and red particles represent hexagonal. In the particle system, the change in the particle structure is reflected as the phase change.

Figure 4

Pair-correlation function for (a) $\mathrm{\Gamma }=7$, (b) $\mathrm{\Gamma }=14.4$, (c) $\mathrm{\Gamma }=20,$ and (d) $\mathrm{\Gamma }=40$.

Figure 5

The formation and evolution of defects during melting. Red heptagon (sevenfold) and blue pentagon (fivefold) together indicate a defect (five- to sevenfold). The isolated fivefold/sevenfold represents the free disclinations. (g) The number fraction change curve of five- to sevenfold defect (circles), defect clusters (triangles), and free disclinations (rhombus) under different accelerations. We define the number fraction as the number of respective defects divided by the total number of particles.

Figure 6

The bar chart in (a) and (b) shows the local volume fraction of topologically defective particles in Figs. 5 and 5. The abscissa $n$ represents the $n\mathrm{th}$ defect pair in Figs. 5 and 5. The red column represents the local volume fraction of sevenfold particles, the blue column represents the local volume fraction of fivefold particles, and the black column represents the local volume fraction of hexagonal before the occurrence of defects.

Figure 7

The curve shows the variation trend of ${\varphi }_{\min }$ and ${\varphi }_{\mathrm{mean}}$ in the particle system is under different vibration accelerations when water content $W=2\%$ and $W=3\%$. The dashed lines represent the minimum local volume fraction of the particle system under different accelerations, and the full line represents the average local volume fraction of all the particles in the system. The critical local volume fraction is determined according to the phase transitions under different accelerations, and the phase transitions during the melting process are quantitatively studied.

Figure 8

Probability distribution of shape factor under different accelerations when water content $W=2\%$ and $W=3\%$. (a) The corresponding phase diagram is shown in Fig. 5.