This page contains a Flash digital edition of a book.
Homogeneity Testing


Table 1 : Results of the EPMA homogeneity studies of 36 fl uorapatite crystals ( N = 30 for each crystal). Crystal ID


Mean Ce


concentration (wt%)


s1.1 s1.2 s1.3 s1.4 s1.5 s1.6 s2.1 s2.2 s2.3 s2.4 s2.5 s2.6 s2.7 s2.8 s2.9 s3.1


s3.10 s3.2 s3.3 s3.4 s3.5 s3.6 s3.7 s3.8 s3.9 s6.1 s6.2 s6.3 s6.4 s6.5 s6.6 s7.1 s7.2 s7.3 s7.4 s7.5


*In these cases s2


0.347 0.336 0.216 0.242 0.320 0.216 0.244 0.410 0.210 0.211 0.214 0.205 0.207 0.205 0.220 0.218 0.218 0.210 0.215 0.204 0.423 0.210 0.208 0.221 0.217 0.217 0.210 0.215 0.203 0.208 0.440 0.323 0.239 0.219 0.363 0.378


Pois is larger than s2 s c (wt%)


0.0478 0.0320 0.0208 0.0172 0.0485 0.0177 0.0185 0.0308 0.0233 0.0305 0.0271 0.0236 0.0217 0.0228 0.0234 0.0247 0.0228 0.0204 0.0258 0.0171 0.0512 0.0208 0.0227 0.0221 0.0244 0.0195 0.0211 0.0195 0.0229 0.0195 0.0539 0.0611 0.0212 0.0224 0.0207 0.0380


s Pois (wt%)


0.0203 0.0201 0.0190 0.0193 0.0199 0.0191 0.0194 0.0207 0.0191 0.0190 0.0191 0.0190 0.0190 0.0191 0.0192 0.0192 0.0192 0.0192 0.0192 0.0190 0.0210 0.0193 0.0192 0.0192 0.0193 0.0191 0.0191 0.0190 0.0189 0.0190 0.0209 0.0200 0.0195 0.0193 0.0203 0.0206


s h (wt%)***


0.0433 0.0249 (0.0083) ---*


0.0442 ---* ---*


0.0228 0.0134 0.0239 0.0193 0.0139 (0.0105) (0.0125) 0.0133 0.0156 (0.0124) (0.0070) 0.0173 ---*


0.0467 (0.0076) (0.0123) (0.0109) 0.0149 (0.0039) (0.0089) (0.0043) (0.0129) (0.0041) 0.0497 0.0577 (0.0084) (0.0115) (0.0037) 0.0319


c due to statistical scatter, and the resulting s2


90.5 77.9


(39.9) ---*


91.1 ---* ---*


74.1 57.5 78.3 71.1 59.1


(48.4) (54.6) 56.8 63.0


(54.3) (34.3) 66.9 ---*


91.2


(36.7) (53.9 (49.3) 61.3


(20.1) (42.4) (22.2) (56.2) (20.8) 92.2 94.5


(39.4) (51.2) (17.7) 84.0


2.36 1.59 1.09 0.89 2.43 0.93 0.96 1.49 1.22 1.61 1.42 1.24 1.14 1.19 1.22 1.29 1.19 1.06 1.35 0.90 2.44 1.08 1.19 1.15 1.27 1.02 1.10 1.03 1.21 1.02 2.58 3.06 1.09 1.16 1.02 1.84


s h,rel (%)*** Homogeneity index H


Heterogeneity detected?**


yes yes no no


yes no no


yes yes yes yes yes no no


yes yes no no


yes no


yes no no no


yes no no no no no


yes yes no no no


yes h is negative (and the homogeneity index smaller than unity). **At N = 30


the critical homogeneity index is 1.21; a measured homogeneity index larger than this indicates detected heterogeneity. ***Values in parentheses are below the detection limit of heterogeneity of s h,rel = 56.4% (calculated from the critical homogeneity index at N = 30) and should not be stated because they are statistically not signifi cant. Instead the upper limit of heterogeneity (i.e. “<56.4%”) and the corresponding value of s h (i.e. “<56.4% of s c ”) should be stated. They are shown here to illustrate the principle.


2017 January • www.microscopy-today.com 31


Page 1  |  Page 2  |  Page 3  |  Page 4  |  Page 5  |  Page 6  |  Page 7  |  Page 8  |  Page 9  |  Page 10  |  Page 11  |  Page 12  |  Page 13  |  Page 14  |  Page 15  |  Page 16  |  Page 17  |  Page 18  |  Page 19  |  Page 20  |  Page 21  |  Page 22  |  Page 23  |  Page 24  |  Page 25  |  Page 26  |  Page 27  |  Page 28  |  Page 29  |  Page 30  |  Page 31  |  Page 32  |  Page 33  |  Page 34  |  Page 35  |  Page 36  |  Page 37  |  Page 38  |  Page 39  |  Page 40  |  Page 41  |  Page 42  |  Page 43  |  Page 44  |  Page 45  |  Page 46  |  Page 47  |  Page 48  |  Page 49  |  Page 50  |  Page 51  |  Page 52  |  Page 53  |  Page 54  |  Page 55  |  Page 56  |  Page 57  |  Page 58  |  Page 59  |  Page 60  |  Page 61  |  Page 62  |  Page 63  |  Page 64  |  Page 65  |  Page 66  |  Page 67  |  Page 68