|Michael Sullivan Online|
Density Functional Theory Studies of Fluorapatite under Pressure
Michael B. Sullivan and Ping Wu
Contribution from Institute of High Performance Computing, 1 Science Park Road, Singapore 117528 and Singapore-MIT Alliance, National University of Singapore, 4 Engineering Drive 3, Singapore 117576
Presented: 2005 Workshop on Fundamental Physics of Ferroelectrics, Williamsburg, VA, USA, February 6-9, 2005
Apatites are found in everything from natural sources like bone, shells and rocks to materials like fluorescent light bulbs and fuel cells as well as use in the treatment of industrial and nuclear waste. In many of these applications, the apatite is under stress or pressure. Apatites are an important class of mineral that are the most abundant form of phosphorus. Because of its geological significance, studying the way apatites respond to pressure is a useful endeavor. In addition to their geological importance, apatites are a major component of bone tissue and have been adapted to bone repair materials. Fluorapatite, specifically, is important in strengthening tooth enamel and has been studied extensively with respect to the use of fluoride in drinking water. In addition, apatites have been proposed as new ionic conductors.[1,2] The ion is thought to move along the c axis. Another related application is the potential use as a piezoelectric.
We used plane-wave density functional theory (DFT) to calculate the geometric and electron properties of fluorapatite at various pressures. Fluorapatite is a standard model for the apatite group and is widely studied due to its good crystallinity. Experimentally, it is hexagonal with a space group P63/m (176) and lattice parameters a = 9.375(2) and c (the hexagonal axis) = 6.887(1) ang with one formula unit consisting of Ca10(PO4)6F2 per unit cell.[3-5] Without any pressure, our fluorapatite has lattice constants of a=b=9.51 ang, c=6.89 ang, which agrees reasonably well with experiment. Our calculated structure is shown in Figure 1. There are two types of calcium. Ca(I) is in a channel between the phosphates and is coordinated to nine oxygens (six near and three far). The fluorine lies at the center of the Ca(II) triangles and at the edge of the unit cell. Each Ca(II) is coordinated to seven oxygens and the fluorine. In the phosphate, there are three kinds of oxygens.
When pressure is applied, the energy changes exponentially. Over the range of 100 GPa, the energy increases 40 eV. At low pressure, we measure a compressibility of 4.2 x 10-3 GPa-1 along the a and b axes and 2.0 x 10 -3 GPa-1 along the c axis.
The ion channel is thought to be along the c axis where the fluorine is the ion carrier. Thus a change in the a lattice parameter reflects a change in the size of the channel. Another way to look at this is through the Ca2-F bond, which changes more than most. This bond is a rough guide of the radius of the ion channel.
The P-O bond lengths do not change as much as the Ca-O bonds do. This is in line with previous experimental work. One of the unique features of this is that the bond lengths deviate less as seen in the standard deviation and this indicates that it is more tetrahedral. However at 20 GPa, the standard deviation increases again. The P-O1 and P-O2 bonds change faster than the two P-O3 bonds. At 20 GPa, the P-O3 bonds are close to the average and those are close to the P-O2 bond lengths. With a bit more pressure, the P-O2 bond compresses faster and becomes shorter than the P-O3 bonds.
The bond angles are a good measure of how tetrahedral a center is. The bond angles about the phosphorous were studied. As expected, the oxygens become more tetrahedral about the phosphorous as the pressure increases. The average bond angle goes to the ideal value of 109.5 and the standard deviation of the bond angles also decreases. As a potential piezoelectric material, we note that there is very little twisting of the phosphate group when pressure is applied. This is important as this type of movement can reduce the effectiveness of piezoelectric materials.
We have used computational methods to study fluorapatite. The a lattice constant changes more than the c lattice constant and this has to do with the Ca2-O1 bond length changing the most. The tetrahedron at the phosphorous as measured by the bond length of the P-O bonds is not clear since the two P-O3 bonds change slower than the other two bond lengths. The bond angles, though, move to the ideal tetrahedral angle of 109.5 with increasing pressure. We also look at the potential for this material as a new and unique piezoelectric.