2 SEM-EBSD R EBSD SEM-EBSD SEM-EBSD 法で測定される結晶方位 1. 鉱物の結晶軸と結晶軸の座標系 7 a, b, c 3 a b c c b c a a b x y z a b c z c K C x C, y

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1 SEM-EBSD R 3 1 SEM-EBSD 法の測定結果から結晶軸の方向を求める R 言語用関数金井拓人高木秀雄 Abstract The SEM-EBSD method is used to measure the crystallographic orientation of minerals, mainly in the field of structural geology. This method measure how many degrees the crystallographic orientation of the measurement spot rotated from the standard. By calculating rotation angle obtained from the SEM- EBSD measurement, it is possible to determine the direction of crystal axis in the thin section. We developed a function for R programming language to calculate the direction of the crystal axis from the measurement results of the crystallographic orientation by SEM-EBSD method. SEM-EBSD R はじめに CPO CPO 1996; Takeshita et al., 1998; Menegon et al., 2008; 2012 CPO SEM EBSD SEM-EBSD SEM- EBSD 2010MS 2012MS 2014 SEM-EBSD SEM-EBSD SEM-EBSD SEM-

By calculating rotation angle obtained from the SEM- EBSD measurement, it is possible to determine the direction of crystal axis in the thin section.

2 2 SEM-EBSD R EBSD SEM-EBSD SEM-EBSD 法で測定される結晶方位 1. 鉱物の結晶軸と結晶軸の座標系 7 a, b, c 3 a b c c b c a a b x y z a b c z c K C x C, y C, z C Fig y /2 Fig p l, m, n 2008 p l, m, n p l, m, n l, m, n,, l sin cos m cos cos n sin 1 2 3

y z a b c z c K C x C, y C, z C Fig. 1 3 2 2011 y 0 2 0 /2 Fig.

3 SEM-EBSD R 3 Fig. 1 Relationship between the coordinate axis and the crystalline axis. Gray thin lines and black bold lines express the coordinate axis and the crystalline axis, respectively. (a)cubic, (b)tetragonal, (c) orthorhombic, (d) hexagonal, (e) monoclinic, (f) triclinic. Fig. 2 Definition of trend ( ) and plunge ( ) in this report. K C V C l C, m C, n C Table 1

4 4 SEM-EBSD R Table 1 Vector notation of the crystalline axis direction. 2.SEM-EBSD 法 SEM Kikuchi, 1928 SEM-EBSD Hough SEM-EBSD Stojakovic 2012 SEM-EBSD 1,, K A x, y, z K B X, Y, Z 3 1. x, y, z z 1 x, y, z 2. x, y, z x x, y, z

5 SEM-EBSD R 5 3. x, y, z z 2 X, Y, Z 3 Bunge, 1985 cosφ 1 sinφ 1 0 z gφ 1 sinφ 1 cosφ g x z gφ cos sin 0 sin cos cosφ 2 sinφ 2 0 sinφ 2 cosφ g x g g g g z z φ1 φ2 cosφ 1 cosφ 2 sinφ 1 sinφ 2 cos sinφ 1 cosφ 2 cosφ 1 sinφ 2 cos sinφ 2 sin cosφ 1 sinφ 2 sinφ 1 cosφ 2 cos sinφ 1 sinφ 2 cosφ 1 cosφ 2 cos cosφ 2 sin sinφ 1 sin cosφ 1 sin cos 7 g orientation matrix SEM-EBSD K C x C, y C, z C K S x S, y S, z S Fig. 3 Fig. 3 Relationship between the direction of coordinate axes of the crystal of measurement point (x S, y S, z S ) and a standard (x C, y C, z C ).

0 0 0 1 5 6 g x g g g g z z φ1 φ2 cosφ 1 cosφ 2 sinφ 1 sinφ 2 cos sinφ 1 cosφ 2 cosφ 1 sinφ 2 cos sinφ 2 sin cosφ 1 sinφ 2 sinφ 1 cosφ 2 cos sinφ 1

6 6 SEM-EBSD R K S g K C 8 3. 結晶軸方向の算出方法 K C V C l C, m C, n C V S l S, m S, n S g V S g V C 9 V S V C V S V C V C V S V S 3 asinn 0 /2 n 0 9 n S V S V S n S R 言語用関数 ebsd 1. 統計環境 R について R 1 R Windows Mac OS X R R project web R 関数の使用方法 R ebsd Fig. 4 Windows R CSV 1 1,, 2 1

7 SEM-EBSD R 7 Fig. 4 Screenshot of the R interface, showing an example of output from the function ebsd. 2 R 3 ebsd.r > getwd > 4 R CSV mydata > mydata <- read.csv 5 ebsd > source ebsd.r R 6 ebsd mydata:

8 8 SEM-EBSD R vc: c vc c 0,0,1 mydata c 1,0,0 > ebsd mydata, vc=c 1,0,0 ebsd vc 3 vc 0 NA write.table > result <- ebsd mydata, vc=c 1,0,0 > write.table result,, sep =, write.table sep おわりに SEM-EBSD SEM-EBSD SEM-EBSD 謝辞 SEM-EBSD [ 文献 ] Bunge, H. J., 1985, Representation of preferred orientations. In Wenk, H. R., ed., Preferred orientation in deformed metals and rocks: An introduction to modern texture analysis, Academic Press, New York, The R Tips R15 P Kikuchi, S., 1928, Diffraction of cathode rays by mica. Jap. J. Phys., 5, Menegon, L., Pennacchioni G., Heilbronner, R. and Pittarello, L., 2008, Evolution of quartz microstructure and c-axis crystallographic preferred orientation within ductilely deformed granitoids (Arolla unit, Western Alps). Jour. Struct. Geol., 30, SEM-EBSP SEM-EBSD

$, 1928, Diffraction of cathode rays by mica. Jap. J. Phys., 5, 83 96. Menegon, L., Pennacchioni G., Heilbronner, R. and Pittarello, L.$

9 SEM-EBSD R Stojakovic, D., 2012, Electron backscatter diffraction in materials characterization. Processing and Application of Ceramics, 6, Takeshita, T., Nishikawa, O., Tagami, M. and Ando, J., 1998, Progress in the stdies of texture development in quartite: recent topics. Mem. Geol. Soc. Japan, 50,

Processing and Application of Ceramics, 6, 1 13. Takeshita, T., Nishikawa, O.

10 10 SEM-EBSD R 付録 (ebsd.r) # # ebsd ver. 1.0 # # August, 2014 # Developed by T. Kanai, H. Takagi # eul2g <- function(eul){ res <- c(cos(eul[1])*cos(eul[3])-sin(eul[1])*sin(eul[3])*cos(eul[2]),sin(eul[1])*cos(eul[3])+cos(eul[1])*sin(eul[3])*cos(eul[2]),sin(eul[3])*sin(eul[2]),-cos(eul[1])*sin(eul[3])-sin(eul[1])*cos(eul[3])*cos(eul[2]),-sin(eul[1])*sin(eul[3])+cos(eul[1])*cos(eul[3])*cos(eul[2]),cos(eul[3])*sin(eul[2]),sin(eul[1])*sin(eul[2]),-cos(eul[1])*sin(eul[2]),cos(eul[2])) return(res) vec2tp <- function(vec){ if(vec[3]>0){vec <- vec*(-1) pl <- -asin(vec[3]) l <- vec[1]/cos(pl) m <- vec[2]/cos(pl) tr <- acos(l) if (m < 0){tr <- 2*pi-tr tr <- (5/2*pi - tr (2*pi)) (2*pi) return(c(tr,pl)*180/pi) ebsd <- function(mydata, vc = c(0,0,1)){

11 SEM-EBSD R 11 if (length(vc)!= 3){ print ( Length of vc is not 3 ) return(na) if (sum(vc^2)== 0){ print ( Magnitude of vc is 0 ) return(na) vc <- vc/sqrt(sum(vc)^2) mydata <- as.matrix(mydata)/180*pi N <- nrow(mydata) res <- matrix(,n,2) colnames(res)<- c( trend, plunge ) for (i in 1:N){ res[i,] <- vec2tp(as.numeric(matrix(eul2g(c(mydata[i,])),3,3) * vc)) return(res) # EOF

01_辻

01_辻 20 EBSD 2008.11.28 scanning electron microscope: SEM EBSD electron back scattering diffraction [1-4] 10 EBSD anisotropy polycrystal orientation texture EBSD EBSD EBSD EBSD Table 1 EBSD Table 1-10 mmφ

2 SEM-EBSD R EBSD SEM-EBSD SEM-EBSD 法 で 測 定 される 結 晶 方 位 1. 鉱 物 の 結 晶 軸 と 結 晶 軸 の 座 標 系 7 a, b, c 3 a b c c b c a a b x y z a b c z c K C x C, y

2 SEM-EBSD R EBSD SEM-EBSD SEM-EBSD 法で測定される結晶方位 1. 鉱物の結晶軸と結晶軸の座標系 7 a, b, c 3 a b c c b c a a b x y z a b c z c K C x C, y