Molecular Dynamics Simulation of the Behavior of Beryllium Diffusion in Corundum

Abstract

Molecular dynamics (MD) simulations are highly useful for analyzing atomic behavior during diffusion, especially in systems that are difficult to investigate experimentally. The focus of the present study was the diffusion behavior of Be in corundum, which was analyzed by MD calculations. First, we derived new potential parameter sets for O, Al, and Be. This parameter set was verified to well reproduce the structures and properties of corundum, bromellite, and chrysoberyl. Based on MD simulations of corundum containing Be as interstitial atoms, where the simulations were performed using the newly derived potential parameters, the diffusion coefficient was estimated to be approximately 10⁻⁷ cm²/s at around 2100 K. This is consistent with previously published experimental results, which confirms the validity of the MD simulation. The present calculations also reveal the detailed atomic movement, where Be atoms jump between Al sites and/or interstitial sites, and that the activation energy of this process is approximately 1.1 × 10² kJ/mol.

Figures

Figure 1.

 Temperature dependence of cell parameter of corundum. MD calculated values are shown with solid circles, and experimental data (Fiquet et al. [9]) are open circles.

Figure 2.

 Atomic arrangement of corundum structure: projection along the c axis (top) and the stacking manner of Al and O layers (bottom). Interstitial sites are shown with dotted circles. These are illustrated after Hughes [2]. (Color online)

Figure 3.

 Relationship between the calculated diffusion coefficients and temperature.

Figure 4.

 (a)-(c) Schematic drawing of detailed atomic movement of Be diffusion in corundum. Be and Al ions move along solid and dotted arrows, respectively. (d) Trajectories of Be and Al atoms simulated with the calculations at 1900 K, are shown with purple and light blue lines, respectively. The position of atoms is the snapshot after the movement labeled as No. 2. It is shown that Be diffuses out of the area enclosed with yellow lines after the movement No. 3. (Color online)

Tables

Table 1. Newly derived parameter set for O, Al, and Be

Atom	Z[e]	A[Å]	B[Å]	C[kcal1/2 Å3 mol−1/2]
O	−1.500	1.755	0.160	20.000
Al	2.250	1.295	0.099	0.000
Be	1.500	0.955	0.080	0.000

Table 2. Calculated crystallographic data for corundum, bromellite and chrysoberyl

	Al2O3		BeO
	MD	Exp.a,b	MD	Expc
a [Å]	4.767	4.758	2.712	2.696
b [Å]
c [Å]	12.942	12.991	4.317	4.379
Density [g/cm3]	3.988	3.989	3.019	3.017
Bulk Modulus [GPa]	238	252	212	212
Melting point [K]	2350	2320
	BeAl2O4
	MD	Expd
a [Å]	4.439	4.424
b [Å]	9.415	9.369
c [Å]	5.520	5.471
Density [g/cm3]	3.656	3.75
Bulk Modulus [GPa]	169	242

a: Hughes, [2]

b: Singh et al. [6]

c: Hazen and Finger [7]

d: Hazen and Finger [8]

References

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