: α α α f B - 3: Barle 4: α, β, Θ, θ α β θ Θ

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1 : Bragg-Brenano x 1 Bragg-Brenano focal geomer 1 Bragg-Brenano α α 1 1 α < α < f B α 3 α α Barle 1. 4 α β θ 1

2 : α α α f B - 3: Barle 4: α, β, Θ, θ α β θ Θ

3 Θ θ θ Θ α, β θ Θ 5 a, a, a, b, b, b a a a b b b 5: a, a, a, b, b, b R a b R a R/ cos α 3 b R/ cos β 4 a R an α 5 b R an β 6 a b θ a b a b cos θ R cos θ cos α cos β 7 a b a a b b a b a b a b cos Θ a b R cos Θ an α an β 8 a b, b a, a b a b cos θ cos Θ an α an β 9 cos α cos β cos θ cos Θ cos α cos β sin α sin β 1 3

4 θ Θ α β.3 Θ θ Θ θ 1 Θ arccos cos θ an α an β θ 11 cos α cos β α β Talor α β α β 1 α α αβ 1 α β β β 1 α β, / α, / β, / α, / α β, / β α β cosθ cos Θ cos α cos β sin α sin β 13 cosθ cos Θ α sinθ cos Θ sin α cos β cos α sin β 16 α α β sin Θ 17 α / α 13 β sinθ cos Θ cos α sin β sin α cos β 18 β α β / β 4

5 16 α sinθ cosθ cos Θ cos α cos β sin α sin β 19 α α α β / α α sin Θ cos Θ / α co Θ 18 β / β co Θ 16 β α β sinθ cosθ cos Θ sin α sin β cos α cos β 1 α β α β / α / β sin Θ 1 α β / α β 1/ sin Θ α β Talor α β an Θ αβ sin Θ 3.4 w A z w A z δz f B αf B βdα dβ δ z α β an Θ αβ f B αf B βdα dβ 4 sin Θ x α β 4 an Θ 1 an Θ 1 an Θ an Θ 1 1 sin Θ 1 sin Θ cos Θ 1 cos Θ an Θ 1 α β an Θ αβ sin Θ α β 1 αβ1 4 α β α β

6 α x, β x x α β, α β x fα, βdαdβ fα, βdαdβ β α x β dα dx α x f x β, βdx dβ f x β, βdβ dx 9 x β x / dβ d/ β f f f x x, x d dx x, x d dx 4 9 w A z δ z α β an Θ αβ sin Θ δ z 1 x x, x dx d 3 f B αf B βdα dβ x x f B f B dx d Barle ϕ 1 1 ϕ < ϕ < f B ϕ 6 31 : x x : 31 w BB z 1 δ z x x x 1 1 dx d

7 x - - 6: Barle BB Barle w BB z δ z x x x 1 1 dx d 34 x x w BB z 4 δ z x 1 x x 1 dx d 35 1/ z z δ w BB z; w BB z; w BB z; 1/ 36 < 1 1 < < 1 35 z / x / u z / u x / x z u/ / x z u / xdx du dx du/x du/ z u x u z / z / / w BB z 4 z / ] / 1 1 z u z / 1 1 ] z u δ u du d 37 z u 7

8 δ- a < b b a fuδudu b a fuδ udu { f a < < b 37 z < < z < z < z u > z < z < 1 < z 1 < z / 4 z z - / 1/ - / z / 1/ Region V Region IV Region III z - / Region II - / Region I 7: 37, z z < / Region I < z Region V w BB z / z z 3 Region II, III, IV 8

9 .4.1 z < z < 7 Region IV 1 z < z z 1 ] z w BBz z z z 1 z d 1 ] ] 1 1 z ] z d z 1 z 1 z ] 1 d z 1 d z d z 44 x ± a dx 1 x x ± a ± a ln x ] x ± a dx ln x x ± a x ± a V 1 4 zd d 1 z d z 47 9

10 V 1 z z ln 1 z ] z ln z 1 4 z 1 z1 ln z 1 ] z 4 1 z1 ln z 48 V 4 w BBz V 1 V 49 u z 1 u u ln ] u ln ] 5 51 V 1 ] u u u 53 1 u 1 u u 1 u 54 V 1 1 u

11 < u V 1 u 56 4 w BB V 1 V 1 1 u 1 1 u 1 u 1 1 u 57 z1 1 u u u1 1 u1 u1 ] 1 1 u 1 1 u1 1 1 u ] < z < 1 < u < 1 1 < u1 < 1 < 1 u1 < 1 < 1 u1 < 1 1 u u 1 < 1 u1 < 1 < 1 1 u1 < 1 1 u u1 1 1 u ] 1 u u

12 ] u u u1 3 1 u1 1 1 u1 ] 3 1 u1 1 1 u1 1 u 3 1 u1 1 6 u1 1 u 3 1 u1 V 1 1 u1 V w BB V 1 V 1 u 3 1 u1 1 u1 1 1 u ln 1 u 1 1 u u u u u1 ln u 1 1 u1 65 u z u 1 4 w BB 1 1 ln

13 .4. / z 1 /4 / z 1 /4 8 7 Region II 1 z w BBz ] ] 1 1 z 1 1 z 1 1 ] z d z 1 z z 1 z ] 1 d z 1 1 z d z d 1 z 1 d z d z 68 xdx x ± a x ± a 69 V 1 4 z z ln z 1 z ] z ln z 1 4 z z z1 1 z ] ln z z1 ] ln z z 7 4 w BBz V 1 V 71 u z 7 13

14 V u u z u 74 u 75 V 1 1 u 76 1 u u1 1 < 1 1 u 1 1 u 1 1 u1 1 < u1 1 u u u 1 u 77 < 1 1 u u u u1 1 u1 3 1 { 1 1 u1 ]} 3 1 u1 1 u u1 3 1 u1 1 1 u

15 1 V 1 1 u 3 1 u1 1 1 u u1 1 4 w BBz V 1 V 1 u 3 1 u1 1 1 u u1 u 1 1 u 3 1 u1 1 1 u1 1 1 u 79 ln 1 1 u1 u1 8 z / u 1/ 1 / / 4 w BB / / ln 1 1 1/ 1 1/ ln 1 1/ 1 / /4 < z < < Region III, z u 15

16 3 3 z 1 u < < 1 < < 3 4 w BBz V 1 V 3 V 3 V 83 V 1 V V 3 V 3 3 u u u 1 u V u u ln u 1 84 ] u u V u u 1 1 u u u V u u 86 16

17 u 1 u V u 1 1 u u u u 3 1 u1 V 1 1 u u V 1 1 u 4 w BBz V 1 V 3 V 3 V 1 u 3 1 u1 1 u u 1 1 u1 1 u u u 1 1 u u u u 3 1 u1 1 u u1 u u u ln u 1 1 u

18 1 1 u 1 u 3 1 u1 1 u u1 u1 ln 1 1 u1 u u1 u z, an θ u z 89 u < 1 Region I: z / w BB z 9 Region II: / < z 1 /4 1 u 3 1 u1 4 w BBz 1 1 u u1 91 u1 Region III: 1 /4 < z < 1 u 3 1 u1 4 w BBz 1 u u1 u1 ln 1 1 u1 u u1 u1 Region IV: < z 1 u 3 1 u1 4 w BBz 1 u1 Region V: z 1 1 u 9 ln 1 1 u1 u1 93 w BB z 94 > 1 w BB z; w BB z; 1/ 18

(iii) 0 V, x V, x + 0 = x. 0. (iv) x V, y V, x + y = 0., y x, y = x. (v) 1x = x. (vii) (α + β)x = αx + βx. (viii) (αβ)x = α(βx)., V, C.,,., (1)

(iii) 0 V, x V, x + 0 = x. 0. (iv) x V, y V, x + y = 0., y x, y = x. (v) 1x = x. (vii) (α + β)x = αx + βx. (viii) (αβ)x = α(βx)., V, C.,,., (1) 1. 1.1...,. 1.1.1 V, V x, y, x y x + y x + y V,, V x α, αx αx V,, (i) (viii) : x, y, z V, α, β C, (i) x + y = y + x. (ii) (x + y) + z = x + (y + z). 1 (iii) 0 V, x V, x + 0 = x. 0. (iv) x V, y V, x + y

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