and expanded and focused beams are shown in fig4 a and 4 b respectively typical statistical results from each plot showed that the minimum frequency spread for samples of the same group was u02dc 10 and u02dc 6 7 around the mean for focused beam and expanded beam respectively similar results for other types of screws were obtained in the same manner and were also correlated with the mechanical hardness test results four samples of each type of screw were chosen for hardness case depth measurements using a conventional mechanical indentation method the samples were cut into halves encased in resin and the microhardness was measured from both edges toward the center typical results are shown in fig5 these results indicated that for nominally identically same hardness case depths the variation of the hardness profile is significant especially at large depths although surface hardness values converge to correct for the large baseline variations the effective case depth d eff was defined as the effective case depths calculated from fig5 a are shown in fig5 b from which the mean case depth and standard deviation were found to be lt d eff gt 401 6 u00b1 31 9 u03bcm representing a u02dc 8 10 uncertainty spread for the hexagonal head group of samples having measured the ptr phase minima and the mechanically tested hardness profiles for each type of screw the correlation between the effective case depth and the phase minima was then established typical results are shown in fig4 these results show these correlations in the form of calibration curves or calibration bands if the vertical and horizontal standard deviations are taken into account calibration curves.