In Situ Observation of Antisite Defect Formation during Crystal Growth

In situ x-ray diffraction (XRD) coupled with molecular dynamics (MD) simulations have been used to quantify antisite defect trapping during crystallization. Rietveld refinement of the XRD data revealed a marked lattice distortion which involves an $a$ axis expansion and a $c$ axis contraction of the stable $C11b$ phase. The observed lattice response is proportional in magnitude to the growth rate, suggesting that the behavior is associated with the kinetic trapping of lattice defects. MD simulations demonstrate that this lattice response is due to incorporation of 1% to 2% antisite defects during growth.

Figure 1

Unit cell volume (a) and lattice parameters $a$ axis (b) and $c$ axis (c) as function of temperature for the heating rate of $5\mathrm{K}/\min$. The unit cell volume and the $a$ axis both exhibit a jump in their thermal expansion during rapid growth while the $c$ axis shows a decrease. The stages of crystallization for the heating rate $5\mathrm{K}/\min$ are described in the text. The insets show the temperature dependences of the lattice parameters for the heating rate of $20\mathrm{K}/\min$. At 775 K the trends in lattice expansion for the $a$ and $c$ axes reverse.

Figure 2

The change in the $a$ and $c$ axes lattice parameters (a) as a function of the fraction crystallized ($f$) for the $5\mathrm{K}/\min$ data set. The anisotropic changes in lattice as a function of the maximum in the growth rate (b) estimated for the $5\mathrm{K}/\min$ (open symbols) and $20\mathrm{K}/\min$ (closed symbols) data sets.

Figure 3

Calculated changes in the lattice parameters as a function of site defects concentration using MD simulation. Open symbols are for interstitial and closed symbols for antisite defects. Diamonds are for the $B2$ (cubic) phase and circles for $C11b$. Inset is an illustration of the $B2$ and $C11b$ structures showing the double Zr layer in between the Cu layers along the $c$ axis. Swapping the smaller Cu for the larger Zr atoms is responsible for the contraction of the $c$ axis and expansion of the $a$ axis.