while a Bruker CCD recorded the SAXS patterns. In order to record both the WAXS and SAXS patterns at each point, the MAR345 was laterally translated out of the beam direction to expose the CCD detector. A pressed ceria powder (CeO2, NIST SRM-674a) disc was used as a standard to calibrate the system. The second set of experiments, creep-load-unload, probed the changes in elastic properties with advancing creep time. Here, the samples were quickly loaded to -95MPa and the load was maintained for 1 hr. During the first hour, WAXS and SAXS measurements were taken every 3 min. The sample was then unloaded to zero stress and reloaded to -95 MPa in increments of -20 MPa. At each increment both a WAXS and SAXS pattern were obtained. The entire unloading and reloading process took approximately 1hr. Once reloaded, the cycle of creep, unloading and reloading was repeated twice. The longitudinal and transverse strains in the mineral and collagen phase are calculated as previously discussed in the literature [13, 18], but a summary is given here. Changes in d-spacing, between the lattice planes in the HAP were used to determine elastic strains in the ceramic material described here as HAP strains. The basic diffraction parameters were first obtained by analyzing the ceria diffraction patterns using Fit2D. The parameters determined from this program – beam center, detector tilt and specimen-detector distance – were then fed into a series of MATLAB programs developed at APS. These programs fit the diffraction rings, giving the center of each peak of interest, HAP(00.2) in our case, as a radial distance from the beam center at various azimuthal angles, R(η). The Cartesian plot for radial distance, R(Ș), versus azimuth, η, for all stress levels intersect at a single radius R* called the invariant radius. R* represents the strain-free point and is used to calculate the orientationdependent deviatoric strains using the equation: ( ( ) ) * * ( ) R R R− = η ε η . Azimuthal angles of 90 and 270 o give the longitudinal strain, along the loading direction, and 0 and 180 o give the transverse strain. In the case of the SAXS patterns, the well-defined peaks arise from the ~67 nm periodic gap spacing of the collagen matrix. In mineralized tissue like bone and dentin, the primary SAXS contrast associated with these peaks is between the relatively dense HAP particles, which are formed within the gaps, and the collagen matrix. Changes in the measured SAXS spacing with applied load therefore represent changes in the average HAP particle spacing, which in turn results from cooperative deformation between the collagen and HAP particles. Thus, the SAXS-derived strain will be described as the fibrillar strain. This fibrillar strain is measured in much the same way as the HAP strains using the third-order SAXS peak, except that a stress free point, R*, is not measured. Instead, the stress free point is taken to be the radial distance, R(Ș), of the rings when the sample is under zero load. Note that for the fibrils, transverse loads are difficult to determine due to low diffraction intensities at the 0o and 180o azimuths. With these strain values much information can be gathered about the samples and their mechanical behaviors. In the case of the creep experiments the obtained strains are plotted versus creep time. If linear, the slope of the plots can be defined as creep strain rate and provide an idea of how quickly a sample accumulates or sheds strain during constant loading. For the non-creep segments of creep-load-unload measurements the HAP and fibrillar strains are plotted as a function of applied stress. The slopes of these applied stress versus phase strain plots are defined as the apparent modulus (Eapp=ıapplied/İphase). This apparent modulus provides information about how load is transferred between the phases in the bulk material upon loading. The diffraction rings provide a wealth of information which can be extracted by further examining peak-broadening and peak intensity. Radial peak broadening (ǻRmeas) can be caused by a number of effects including strain distribution within or between HAP crystals in the sampled population, the small size of the HAP platelets, as well as instrumental effects. The instrumental contribution for the (00.2) peak was calculated using the ceria standard. Assuming the peaks had a Gaussian shape, the mineral peak width (ǻR) was converted to ǻ2 ڧ using ǻ2 ڧ =ǻR/z, where z is the sample to detector distance. From this, the crystallite size (t) and root mean square strain (İrms), also known as microstrain, was calculated according to Noyan and Cohen [19]. Now, the variation in intensity along the azimuthal direction of diffraction peaks is due to preferential alignments of the diffractors, or texture. In order to determine how the orientation of the HAP platelets might change with continuing creep, the normalized intensity of the HAP (00.2) peak was plotted as a function of azimuth creating intensity peaks in the angles of preferred orientation. Changes in the distribution of intensity with time during creep were determined by measuring the full-width-half-max (fwhm) of the high intensity peaks as a function of time. An increase in the intensity peak fwhm represents a tilting of the platelets away from the preferential orientation and vice-versa. 322
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