4.6. Reflection Conditions (Systematic Absences) and Space Groups

　diffractionとは、crystalに対して特定の条件(Bragg condition)で波を入射したとき散乱波が強め合う現象のことです。where、Bragg conditionを満たしたからと言って、必ずdiffractionが起きるわけではありません。crystalが複合格子並進、らせん、映進などのsymmetry operationを有している場合は、たとえBragg conditionを満たしても、特定のMiller indicesのdiffraction波の強度は消滅¹します。このページでは、diffractionが観測されたcrystalMiller indicesのリストからspace groupを絞り込むための方法を提供します。

　belowに示す表は、diffractionによって出現するMiller indicesとspace groupの関係一覧を示します。消滅するMiller indicesでないことにご注意ください。

reflection conditions(Reflection conditions)はMiller indicesのタイプによって分類されており、たとえば上段に (h0l) とある場合は「(h) と (l) は任意だが (k) が (0) であるcrystal面」が条件の対象となります。 (hkl) と書かれていたらすべてのcrystal面が対象となりますし、(hhl) と書かれていたら(h=k) であるようなcrystal面が対象です。
条件中の (h, k, l, h+k) などはその値が偶数のときに出現することを意味しています。(h,l) などカンマで区切られている場合は「 (h) と (l) がともに偶数」が出現条件であることを意味します。偶数以外の出現条件は (=3n,,, =4n,,, =6n) などと明記されています。空欄の場合は、そのMiller indicesタイプに対して出現規則がないことを意味します。
space groupの表記は、標準表記でないものもありますのでご注意ください。space group表記に続くカッコ内の数値はInternational Tables for Crystallography, Vol A. に記載されているspace group番号を示しています。

Triclinic triclinic crystal system

Reflection conditions	Extinction symbol	Point group
None	(P – )	(P1, _{(1)})	(Pbar{1}, _{(2)})

Monoclinic monoclinic crystal system

Unique axis b

Reflection conditions			Extinction symbol	Laue class (1 2/m 1)
Reflection conditions				Point group
(hkl, 0kl, hk0)	(h0l, h00, 00l)	(0k0)		(2)	(m)	(2/m)
			(P1 – 1)	(P121, _{(3)})	(P1m1, _{(6)})	(P1 2/m 1, _{(10)})
		(k)	(P12_11)	(P12_11, _{(4)})		(P1 2_1/m 1, _{(11)})
	(h)		(P1a1)		(P1a1, _{(7)})	(P1 2/a 1, _{(13)})
	(h)	(k)	(P1 2_1/a 1)			(P1 2_1/a 1, _{(14)})
	(l)		(P1c1)		(P1c1, _{(7)})	(P1 2/c 1, _{(13)})
	(l)	(k)	(P1 2_1/c 1)			(P1 2_1/c 1, _{(14)})
	(h + l)		(P1n1)		(P1n1, _{(7)})	(P1 2/n 1, _{(13)})
	(h + l)	(k)	(P1 2_1/n 1)			(P1 2_1/n 1, _{(14)})
(h + k)	(h)	(k)	(C1 – 1)	(C121, _{(5)})	(C1m1, _{(8)})	(C1 2/m 1, _{(12)})
(h + k)	(h, l)	(k)	(C1c1)		(C1c1, _{(9)})	(C1 2/c 1, _{(15)})
(h + l)	(l)	(k)	(A1 – 1)	(A121, _{(5)})	(A1m1, _{(8)})	(A1 2/m 1, _{(12)})
(h + l)	(h, l)	(k)	(A1n1)		(A1n1, _{(9)})	(A1 2/n 1, _{(15)})
(h + k + l)	(h + l)	(k)	(I1 – 1)	(I121, _{(5)})	(I1m1, _{(8)})	(I1 2/m 1, _{(12)})
(h + k + l)	(h, l)	(k)	(I1a1)		(I1a1, _{(9)})	(I1 2/a 1, _{(15)})

Unique axis c

Reflection conditions			Extinction symbol	Laue class (1 1 2/m)
Reflection conditions				Point group
(hkl, 0kl, h0l)	(hk0, h00, 0k0)	(00l)		(2)	(m)	(2/m)
			(P11 – )	(P112, _{(3)})	(P11 m, _{(6)})	(P11 2/m, _{(10)})
		(l)	(P12_11)	(P112_1, _{(4)})		(P112_1/m, _{(11)})
	(h)		(P11a)		(P11a, _{(7)})	(P11 2/a, _{(13)})
	(h)	(l)	(P11 2_1/a)			(P11 2_1/a, _{(14)})
	(k)		(P11b)		(P11b, _{(7)})	(P11 2/b, _{(13)})
	(k)	(l)	(P11 2_1/b)			(P11 2_1/b, _{(14)})
	(h + k)		(P11n)		(P11n, _{(7)})	(P11 2/n, _{(13)})
	(h + k)	(l)	(P11 2_1/n)			(P1 1 2_1/n, _{(14)})
(h + l)	(h)	(l)	(B11 – )	(C112, _{(5)})	(C11m, _{(8)})	(C11 2/m, _{(12)})
(h + l)	(h, k)	(l)	(B11n)		(C11c, _{(9)})	(C11 2/c, _{(15)})
(k + l)	(k)	(l)	(A11 – )	(A112, _{(5)})	(A11m, _{(8)})	(A11 2/m, _{(12)})
(k + l)	(h, k)	(l)	(A11a)		(A11n, _{(9)})	(A11 2/n, _{(15)})
(h + k + l)	(h + k)	(l)	(I11 – )	(I112, _{(5)})	(I11m, _{(8)})	(I11 2/m, _{(12)})
(h + k + l)	(h, k)	(l)	(I11b)		(I11b, _{(9)})	(I11 2/b, _{(15)})

Unique axis a

Reflection conditions			Extinction symbol	Laue class (2/m 1 1)
Reflection conditions				Point group
(hkl, h0l, hk0)	(0kl, 0k0, 00l)	(h00)		(2)	(m)	(2/m)
			(P – 11)	(P211, _{(3)})	(Pm11, _{(6)})	(P2/m 11, _{(10)})
		(h)	(P2_111)	(P2_111, _{(4)})		(P2_1/m 11, _{(11)})
	(k)		(Pb11)		(P a 11, _{(7)})	(P2/b 11, _{(13)})
	(k)	(h)	(P2_1/b 11)			(P2_1/b 11, _{(14)})
	(l)		(Pc11)		(Pc11, _{(7)})	(P2/c 11, _{(13)})
	(l)	(h)	(P2_1/c 11)			(P2_1/c 11, _{(14)})
	(k + l)		(Pn11)		(Pn11, _{(7)})	(P2/n 11, _{(13)})
	(k + l)	(h)	(P2_1/n 11)			(P2_1/n 11, _{(14)})
(h + k)	(k)	(h)	(C – 11)	(C211, _{(5)})	(Cm11, _{(8)})	(C2/m 11, _{(12)})
(h + k)	(k, l)	(h)	(Cn11)		(Cn11, _{(9)})	(C2/n 11, _{(15)})
(h + l)	(l)	(h)	(B – 11)	(B211, _{(5)})	(Bm11, _{(8)})	(B2/m 11, _{(12)})
(h + l)	(k, l)	(h)	(Bb11)		(Bb11, _{(9)})	(B2/b 11, _{(15)})
(h + k + l)	(k + l)	(h)	(I – 11)	(I211, _{(5)})	(Im11, _{(8)})	(I2/m 11, _{(12)})
(h + k + l)	(k, l)	(h)	(Ic11)		(Ic11, _{(9)})	(I2/c 11, _{(15)})

Orthorhombic 直方晶系

Reflection conditions							Extinction symbol	Laue class (mmm (2/m, 2/m, 2/m))
Reflection conditions								Point group
(hkl)	(0kl)	(h0l)	(hk0)	(h00)	(0k0)	(00l)		(222)	(mm2), (m2m), (2mm)	(mmm)
							(P – – – )	(P222, _{(16)})	(Pmm2, _{(25)}) (Pm2m, _{(25)}) (P2mm, _{(25)})	(Pmmm, _{(47)})
						(l)	(P – – 2_1)	(P222_1, _{(17)})
					(k)		(P – 2_1 – )	(P22_12, _{(17)})
					(k)	(l)	(P – 2_12_1)	(P22_12_1, _{(18)})
				(h)			(P2_1 – – )	(P2_122, _{(17)})
				(h)		(l)	(P2_1 – 2_1)	(P2_122_1, _{(18)})
				(h)	(k)		(P2_12_1 – )	(P2_12_12, _{(18)})
				(h)	(k)	(l)	(P2_12_12_1)	(P2_12_12_1, _{(19)})
			(h)	(h)			(P – – a)		(Pm2a, _{(28)}) ( P2_1ma, _{(26)})	(Pmma, _{(51)})
			(k)		(k)		(P – – b)		(Pm2_1b, _{(26)}) ( P2_1mb, _{(28)})	(Pmmb, _{(51)})
			(h + k)	(h)	(k)		(P – – n)		(Pm2_1n, _{(31)}) ( P2_1mn, _{(31)})	(Pmmn, _{(59)})
		(h)		(h)			(P – a – )		(Pma2, _{(28)}) ( P2_1am, _{(26)})	(Pmam, _{(51)})
		(h)	(h)	(h)			(P – aa)		(P2aa, _{(27)})	(Pmaa, _{(49)})
		(h)	(k)	(h)	(k)		(P – ab)		(P2_1ab, _{(29)})	(Pmab, _{(57)})
		(h)	(h + k)	(h)	(k)		(P – an)		(P2_1an, _{(30)})	(Pman, _{(53)})
		(l)				(l)	(P – c – )		(Pmc2_1, _{(26)}) ( P2cm, _{(28)})	(Pmcm, _{(51)})
		(l)	(h)	(h)		(l)	(P – ca)		(P2_1ca, _{(29)})	(Pmca, _{(57)})
		(l)	(k)		(k)	(l)	(P – cb)		(P2cb, _{(32)})	(Pmcb, _{(55)})
		(l)	(h + k)	(h)	(k)	(l)	(P – cn)		(P2_1cn, _{(33)})	(Pmcn, _{(62)})
		(h + l)		(h)		(l)	(P – n – )		(Pmn2_1, _{(31)}) ( P2_1nm, _{(31)})	(Pmnm, _{(59)})
		(h + l)	(h)	(h)		(l)	(P – na)		(P2na, _{(30)})	(Pmna, _{(53)})
		(h + l)	(k)	(h)	(k)	(l)	(P – nb)		(P2_1nb, _{(33)})	(Pmnb, _{(62)})
		(h + l)	(h + k)	(h)	(k)	(l)	(P – nn)		(P2nn, _{(34)})	(Pmnn, _{(58)})
	(k)				(k)		(Pb – – )		(Pbm2, _{(28)}) ( Pb2_1m, _{(26)})	(Pbmm, _{(51)})
	(k)		(h)	(h)	(k)		(Pb – a)		(Pb2_1a, _{(29)})	(Pbma, _{(57)})
	(k)		(k)		(k)		(Pb – b)		(Pb2b, _{(27)})	(Pbmb, _{(49)})
	(k)		(h + k)	(h)	(k)		(Pb – n)		(Pb2n, _{(30)})	(Pbmn, _{(53)})
	(k)	(h)		(h)	(k)		(Pba – )		(Pba2, _{(32)})	(Pbam, _{(55)})
	(k)	(h)	(h)	(h)	(k)		(Pbaa)			(Pbaa, _{(54)})
	(k)	(h)	(k)	(h)	(k)		(Pbab)			(Pbab, _{(54)})
	(k)	(h)	(h + k)	(h)	(k)		(Pban)			(Pban, _{(50)})
	(k)	(l)			(k)	(l)	(Pbc – )		(Pbc2_1, _{(29)})	(Pbcm, _{(57)})
	(k)	(l)	(h)	(h)	(k)	(l)	(Pbca)			(Pbca, _{(61)})
	(k)	(l)	(k)		(k)	(l)	(Pbcb)			(Pbcb, _{(54)})
	(k)	(l)	(h + k)	(h)	(k)	(l)	(Pbcn)			(Pbcn, _{(60)})
	(k)	(h + l)		(h)	(k)	(l)	(Pbn – )		(Pbn2_1, _{(33)})	(Pbnm, _{(62)})
	(k)	(h + l)	(h)	(h)	(k)	(l)	(Pbna)			(Pbna, _{(60)})
	(k)	(h + l)	(k)	(h)	(k)	(l)	(Pbnb)			(Pbnb, _{(56)})
	(k)	(h + l)	(h + k)	(h)	(k)	(l)	(Pbnn)			(Pbnn, _{(52)})
	(l)					(l)	(Pc – – )		(Pcm2_1, _{(26)}) ( Pc2m, _{(28)})	(Pcmm, _{(51)})
	(l)		(h)	(h)		(l)	(Pc – a)		(Pc2a, _{(32)})	(Pcma, _{(55)})
	(l)		(k)		(k)	(l)	(Pc – b)		(Pc2_1b, _{(29)})	(Pcmb, _{(57)})
	(l)		(h + k)	(h)	(k)	(l)	(Pc – n)		(Pc2_1n, _{(33)})	(Pcmn, _{(62)})
	(l)	(h)		(h)		(l)	(Pca – )		(Pca2_1, _{(29)})	(Pcam, _{(57)})
	(l)	(h)	(h)	(h)		(l)	(Pcaa)			(Pcaa, _{(54)})
	(l)	(h)	(k)	(h)	(k)	(l)	(Pcab)			(Pcab, _{(61)})
	(l)	(h)	(h + k)	(h)	(k)	(l)	(Pcan)			(Pcan, _{(60)})
	(l)	(l)				(l)	(Pcc – )		(Pcc2, _{(27)})	(Pccm, _{(49)})
	(l)	(l)	(h)	(h)		(l)	(Pcca)			(Pcca, _{(54)})
	(l)	(l)	(k)		(k)	(l)	(Pccb)			(Pccb, _{(54)})
	(l)	(l)	(h + k)	(h)	(k)	(l)	(Pccn)			(Pccn, _{(56)})
	(l)	(h + l)		(h)		(l)	(Pcn – )		(Pcn2, _{(30)})	(Pcnm, _{(53)})
	(l)	(h + l)	(h)	(h)		(l)	(Pcna)			(Pcna, _{(50)})
	(l)	(h + l)	(k)	(h)	(k)	(l)	(Pcnb)			(Pcnb, _{(60)})
	(l)	(h + l)	(h + k)	(h)	(k)	(l)	(Pcnn)			(Pcnn, _{(52)})
	(k + l)				(k)	(l)	(Pn – – )		(Pnm2_1, _{(31)}) ( Pn2_1m, _{(31)})	(Pnmm, _{(59)})
	(k + l)		(h)	(h)	(k)	(l)	(Pn – a)		(Pn2_1a, _{(33)})	(Pnma, _{(62)})
	(k + l)		(k)		(k)	(l)	(Pn – b)		(Pn2b, _{(30)})	(Pnmb, _{(53)})
	(k + l)		(h + k)	(h)	(k)	(l)	(Pn – n)		(Pn2n, _{(34)})	(Pnmn, _{(58)})
	(k + l)	(h)		(h)	(k)	(l)	(Pna – )		(Pna2_1, _{(33)})	(Pnam, _{(62)})
	(k + l)	(h)	(h)	(h)	(k)	(l)	(Pnaa)			(Pnaa, _{(56)})
	(k + l)	(h)	(k)	(h)	(k)	(l)	(Pnab)			(Pnab, _{(60)})
	(k + l)	(h)	(h + k)	(h)	(k)	(l)	(Pnan)			(Pnan, _{(52)})
	(k + l)	(l)			(k)	(l)	(Pnc – )		(Pnc2, _{(30)})	(Pncm, _{(53)})
	(k + l)	(l)	(h)	(h)	(k)	(l)	(Pnca)			(Pnca, _{(60)})
	(k + l)	(l)	(k)		(k)	(l)	(Pncb)			(Pncb, _{(50)})
	(k + l)	(l)	(h + k)	(h)	(k)	(l)	(Pncn)			(Pncn, _{(52)})
	(k + l)	(h + l)		(h)	(k)	(l)	(Pnn – )		(Pnn2, _{(34)})	(Pnnm, _{(58)})
	(k + l)	(h + l)	(h)	(h)	(k)	(l)	(Pnna)			(Pnna, _{(52)})
	(k + l)	(h + l)	(k)	(h)	(k)	(l)	(Pnnb)			(Pnnb, _{(52)})
	(k + l)	(h + l)	(h + k)	(h)	(k)	(l)	(Pnnn)			(Pnnn, _{(48)})
(h + k)	(k)	(h)	(h + k)	(h)	(k)		(C – – – )	(C222, _{(21)})	(Cmm2, _{(35)}) ( Cm2m, _{(38)}) ( C2mm, _{(38)})	(Cmmm, _{(65)})
(h + k)	(k)	(h)	(h + k)	(h)	(k)	(l)	(C – – 2_1)	(C222_1, _{(20)})
(h + k)	(k)	(h)	(h, k)	(h)	(k)		(C – – (ab))		(Cm2e, _{(39)}) ( C2me, _{(39)})	(Cmme, _{(67)})
(h + k)	(k)	(h, l)	(h + k)	(h)	(k)	(l)	(C – c – )		(Cmc2_1, _{(36)}) ( C2cm, _{(40)})	(Cmcm, _{(63)})
(h + k)	(k)	(h, l)	(h, k)	(h)	(k)	(l)	(C – c(ab))		(C2ce, _{(41)})	(Cmce, _{(64)})
(h + k)	(k. l)	(h)	(h + k)	(h)	(k)	(l)	(Cc – – )		(Ccm2_1, _{(36)}) ( Cc2m, _{(40)})	(Ccmm, _{(63)})
(h + k)	(k, l)	(h)	(h, k)	(h)	(k)	(l)	(Cc – (ab))		(Cc2e, _{(41)})	(Ccme, _{(64)})
(h + k)	(k. l)	(h, l)	(h + k)	(h)	(k)	(l)	(Ccc – )		(Ccc2, _{(37)})	(Cccm, _{(66)})
(h + k)	(k. l)	(h, l)	(h, k)	(h)	(k)	(l)	(Ccc(ab))			(Ccce, _{(68)})
(h + l)	(l)	(h + l)	(h)	(h)		(l)	(B – – – )	(B222, _{(21)})	(Bmm2, _{(38)}) (Bm2m, _{(35)}) (B2mm, _{(38)})	(Bmmm, _{(65)})
(h + l)	(l)	(h + l)	(h)	(h)	(k)	(l)	(B – 2_1 – )	(B22_12, _{(20)})
(h + l)	(l)	(h + l)	(h, k)	(h)	(k)	(l)	(B – – b)		(Bm2_1b, _{(36)}) (B2mb, _{(40)})	(Bmmb, _{(63)})
(h + l)	(l)	(h, l)	(h)	(h)		(l)	(B – (ac) – )		(Bme2, _{(39)}) (B2em, _{(39)})	(Bmem, _{(67)})
(h + l)	(l)	(h, l)	(h, k)	(h)	(k)	(l)	(B – (ac)b)		(B2eb, _{(41)})	(Bmeb, _{(64)})
(h + l)	(k. l)	(h + l)	(h)	(h)	(k)	(l)	(Bb – – )		(Bbm2, _{(40)}) ( Bb2_1m, _{(36)})	(Bbmm, _{(63)})
(h + l)	(k. l)	(h + l)	(h, k)	(h)	(k)	(l)	(Bb – b)		(Bb2b, _{(37)})	(Bbmb, _{(66)})
(h + l)	(k, l)	(h. l)	(h)	(h)	(k)	(l)	(Bb(ac) – )		(Bbe2, _{(41)})	(Bbem, _{(64)})
(h + l)	(k. l)	(h, l)	(h, k)	(h)	(k)	(l)	(Bb(ac)b)			(Bbeb, _{(68)})
(k + l)	(k + l)	(l)	(k)		(k)	(l)	(A – – – )	(A222, _{(21)})	(Amm2, _{(38)}) (Am2m, _{(38)}) (A2mm, _{(35)})	(Ammm, _{(65)})
(k + l)	(k + l)	(l)	(k)	(h)	(k)	(l)	(A2_1 – – )	(A2_122, _{(20)})
(k + l)	(k + l)	(l)	(h, k)	(h)	(k)	(l)	(A – – a)		(Am2a, _{(40)}) (A2_1ma, _{(36)})	(Amma, _{(63)})
(k + l)	(k + l)	(h, l)	(k)	(h)	(k)	(l)	(A – a – )		(Ama2, _{(40)}) (A2_1am, _{(36)})	(Amam, _{(63)})
(k + l)	(k + l)	(h, l)	(h, k)	(h)	(k)	(l)	(A – aa)		(A2aa, _{(37)})	(Amaa, _{(66)})
(k + l)	(k. l)	(l)	(k)		(k)	(l)	(A(bc) – – )		(Aem2, _{(39)}) (Ae2m, _{(39)})	(Aemm, _{(67)})
(k + l)	(k. l)	(l)	(h, k)	(h)	(k)	(l)	(A(bc) – a)		(Ae2a, _{(41)})	(Aema, _{(64)})
(k + l)	(k. l)	(h, l)	(k)	(h)	(k)	(l)	(A(bc)a – )		(Aea2, _{(41)})	(Aeam, _{(64)})
(k + l)	(k, l)	(h, l)	(h, k)	(h)	(k)	(l)	(A(bc)aa)			(Aeaa, _{(68)})
(h + k + l)	(k + l)	(h + l)	(h + k)	(h)	(k)	(l)	(I – – – )	(I222, _{(23)}) ( I2_12_12_1, _{(24)})	(Imm2, _{(44)}) ( Im2m, _{(44)}) ( I2mm, _{(44)})	(Immm, _{(71)})
(h + k + l)	(k + l)	(h + l)	(h, k)	(h)	(k)	(l)	(I – – (ab))		(Im2a, _{(46)}) ( I2mb, _{(46)})	(Imma, _{(74)}) ( Immb, _{(74)})
(h + k + l)	(k + l)	(h, l)	(h + k)	(h)	(k)	(l)	(I – (ac) – )		(Ima2, _{(46)}) ( I2cm, _{(46)})	(Imam, _{(74)}) ( Imcm, _{(74)})
(h + k + l)	(k + l)	(h, l)	(h, k)	(h)	(k)	(l)	(I – cb)		(I2cb, _{(45)})	(Imcb, _{(72)})
(h + k + l)	(k, l)	(h + l)	(h + k)	(h)	(k)	(l)	(I(bc) – – )		(Iem2, _{(46)}) ( Ie2m, _{(46)})	(Iemm, _{(74)})
(h + k + l)	(k, l)	(h + l)	(h, k)	(h)	(k)	(l)	(Ic – a)		(Ic2a, _{(45)})	(Icma, _{(72)})
(h + k + l)	(k, l)	(h, l)	(h + k)	(h)	(k)	(l)	(Iba – )		(Iba2, _{(45)})	(Ibam, _{(72)})
(h + k + l)	(k, l)	(h, l)	(h, k)	(h)	(k)	(l)	(Ibca)			(Ibca, _{(73)}) (Icab, _{(73)})
(h + k, h + l, ) (k + l)	(k, l)	(h, l)	(h, k)	(h)	(k)	(l)	(F – – – )	(F222, _{(22)})	(Fmm2, _{(42)}) (Fm2m, _{(42)}) ( F2mm, _{(42)})	(Fmmm, _{(69)})
(h + k, h + l,) ( k + l)	(k, l)	(h+l=4n;) ( h, l)	(h+k=4n;) ( h, k)	(h = 4n)	(k = 4n)	(l = 4n)	(F – dd)		(F2dd, _{(43)})
(h + k, h + l, ) (k + l)	(k+l=4n; ) (k, l)	(h, l)	(h+k = 4n;) ( h, k)	(h = 4n)	(k = 4n)	(l = 4n)	(Fd – d)		(Fd2d, _{(43)})
(h + k, h + l, ) (k + l)	(k+l=4n; ) (k, l)	(h+l=4n;) ( h, l)	(h, k)	(h = 4n)	(k = 4n)	(l = 4n)	(Fdd – )		(Fdd2, _{(43)})
(h + k, h + l, ) (k + l)	(k+l=4n; ) (k, l)	(h+l=4n; ) (h, l)	(h+k=4n;) ( h, k)	(h = 4n)	(k = 4n)	(l = 4n)	(Fddd)			(Fddd, _{(70)})

Tetragonal tetragonal crystal system

Reflection conditions							Extinction symbol	Laue class
								(4/m)			(4/mmm)
								Point group
(hkl)	(hk0)	(0kl)	(hhl)	(00l)	(0kl)	(hh0)		(4)	(bar{4})	(4/m)	(422)	(4mm)	(bar{4}2m), (bar{4}m2)	(4/mmm)
							(P – – – )	(P4, _{(75)})	(Pbar{4}, _{(81)})	(P4/m, _{(83)})	(P422, _{(89)})	(P4mm, _{(99)})	(Pbar{4}2m, _{(111)}) (Pbar{4}m2, _{(115)})	(P4/mnm, _{(123)})
					(k)		(P – 2_1 – )				(P42_12, _{(90)})		(Pbar{4}2_1m, _{(113)})
				(l)			(P4_2 – – )	(P4_2, _{(77)})		(P4_2/m, _{(84)})	(P4_222, _{(93)})
				(l)	(k)		(P4_22_1 – )				(P4_22_12, _{(94)})
				(l=) (4n)			(P4_1 – – )	(P4_1, _{(76)}) ( P4_3, _{(78)})			(P4_122, _{(91)}) ( P4_322, _{(95)})
				(l=) (4n)	(k)		(P412_1 – )				(P4_12_12, _{(92)}) ( P4_32_12, _{(96)})
			(l)	(l)			(P – – c)					(P4_2mc, _{(105)})	(Pbar{4}2c, _{(112)})	(P4_2/mmc, _{(131)})
			(l)	(l)	(k)		(P – 2_1c)						(Pbar{4}2_1c, _{(114)})
		(k)			(k)		(P – b – )					(P4bm, _{(100)})	(Pbar{4}b2, _{(117)})	(P4/mbm, _{(127)})
		(k)	(l)	(l)	(k)		(P – be)					(P4_2bc, _{(106)})		(P4_2/mbc, _{( 135)})
		(l)		(l)			(P – c – )					(P4_2cm, _{(101)})	(Pbar{4}c2, _{(116)})	(P4_2/mcm, _{( 132)})
		(l)	(l)	(l)			(P – cc)					(P4cc, _{(103)})		(P4/mcc, _{(124)})
		(k+l)		(l)	(k)		(P – n – )					(P4_2nm, _{(102)})	(Pbar{4}n2, _{(118)})	(P4_2/mnm, _{(136)})
		(k+l)	(l)	(l)	(k)		(P – nc)					(P4nc, _{(104)})		(P4/mnc, _{(128)})
	(h+k)				(k)		(Pn – – )			(P4/n, _{(85)})				(P4/nmm, _{(129)})
	(h+k)			(l)	(k)		(P4_2/n)			(P4_2/n, _{(86)})
	(h+k)		(l)	(l)	(k)		(Pn – c)							(P4_2/mnc, _{(137)})
	(h+k)	(k)			(k)		(Pnb – )							(P4/nbm, _{(125)})
	(h+k)	(k)	(l)	(l)	(k)		(Pnbc)							(P4_2/nbc, _{(133)})
	(h+k)	(l)	(l)	(l)	(k)		(Pnc – )							(P4_2/ncm, _{(138)})
	(h+k)	(l)	(l)	(l)	(k)		(Pncc)							(P4/ncc, _{(130)})
	(h+k)	(k+l)		(l)	(k)		(Pnn – )							(P4_2/nnm, _{(134)})
	(h+k)	(k+l)	(l)	(l)	(k)		(Pnnc)							(P4/nnc, _{(126)})
(h+k+l)	(h+k)	(k+l)	(l)	(l)	(k)		(I – – – )	(I4, _{(79)})	(Ibar{4}, _{(82)})	(I4/m, _{(87)})	(I422, _{(97)})	(I4mm, _{(107)})	(Ibar{4}2m, _{(121)}) (Ibar{4}m2, _{(119)})	(I4/mmm, _{(139)})
(h+k+l)	(h+k)	(k+l)	(l)	(l=) (4n)	(k)		(I4_1 – – )	(I4_1, _{(80)})			(I4_122, _{(98)})
(h+k+l)	(h+k)	(k+l)		(l=) (4n)	(k)	(h)	(I – – d)					(I4_1md, _{(109)})	(Ibar{4}2d, _{(122)})
(h+k+l)	(h+k)	(k, l)	(l)	(l)	(k)		(I – c – )					(I4cm, _{( 108)})	(Ibar{4}c2, _{(120)})	(I4/mcm, _{(140)})
(h+k+l)	(h+k)	(k, l)		(l=) (4n)	(k)	(h)	(I – cd)					(I4_1cd, _{(110)})
(h+k+l)	(h, k)	(k+l)	(l)	(l=) (4n)	(k)		(I4_1/a – – )			(I4_1/a, _{(88)})
(h+k+l)	(h, k)	(k+l)		(l=) (4n)	(k)	(h)	(Ia – d)							(I4_1/amd, _{(141)})
(h+k+l)	(h, k)	(k, l)		(l=) (4n)	(k)	(h)	(Iacd)							(I4_1/acd, _{(142)})

Trigonal trigonal crystal system

Hexagonal axes

Reflection conditions				Extinction symbol	Laue class
					(bar{3})		(bar{3}m1, (=bar{3},2/m,1), bar{3}m)			(bar{3}1m, (=bar{3},1, 2/m))
					Point group
(hkil)	(hh0l)	(h h overline{2h} l)	(000l)		(3)	(bar{3})	(321), (32)	(3m1), (3m)	(bar{3}m1), (bar{3}m)	(312)	(31m)	(bar{3}1m)
				(P – – – )	(P3, _{(143)})	(Pbar{3}, _{(147)})	(P321, _{(150)})	(P3m1, _{(156)})	(Pbar{3}m1, _{(164)})	(P312, _{(149)})	(P31m, _{(157)})	(Pbar{3}1m, _{(162)})
			(l) (=3n)	(P3_1 – – – )	(P3_1, _{(144)}) (P3_2, _{(145)})		(P3_121, _{(152)}) ( P3_221, _{(154)})			(P3_112, _{(151)}) ( P3_212, _{(153)})
		(l)	(l)	(P – – c)							(P31c, _{(159)})	(Pbar{3}1c, _{(163)})
	(l)		(l)	(P – c – )				(P3c1, _{(158)})	(Pbar{3}c1, _{(165)})
( -h+k+l) (=3n)	(h+l) (=3n)	(l) (=3n)	(l) (=3n)	(R(obv) – – )	(R3, _{(146)})	(Rbar{3}, _{(148)})	(R32, _{(155)})	(R3m, _{(160)})	(Rbar{3}m, _{(166)})
( -h+k+l) (=3n)	(h+l) (=3n; l)	(l) (=3n)	(l) (=6n)	(R(obv) – c)				(R3c, _{(161)})	(Rbar{3}c, _{(167)})
(h- k+l) (=3n)	( -h+l) (=3n)	(l) (=3n)	(l) (=3n)	(R(rev) – – )	(R3, _{(146)})	(Rbar{3}, _{(148)})	(R32, _{(155)}, )	(R3m, _{(160)})	(Rbar{3}m, _{(166)})
(h- k+l) (=3n)	( -h+l) (=3n; l)	(l) (=3n)	(l) (=3n)	(R(rev) – c)				(R3c, _{(161)})	(Rbar{3}c, _{(167)})

Rhombohedral axes

Reflection conditions			Extinction symbol	Point group
(hkl)	(hhl)	(hhh)	Extinction symbol	(3)	(bar{3})	(32)	(3m)	(bar{3}m)
			(R – – )	(R3, _{(146)})	(Rbar{3}, _{(148)})	(R32, _{(155)})	(R3m, _{(160)})	(Rbar{3}m, _{(166)})
	(l)	(h)	(R – c – )				(R3c, _{(161)})	(Rbar{3}c, _{(167)})

Hexagonal hexagonal crystal system

Reflection conditions			Extinction symbol	Laue class
				(6/m)			(6/mmm)
				Point group
(hh0l)	(hh2hl)	(000l)		(6)	(bar{6})	(6/m)	(622)	(6mm)	(bar{6}2m)	(6/mmm)
									(bar{6}m2)
			(P – – – )	(P6, _{(168)})	(Pbar{6}, _{(174)})	(P6/m, _{(175)})	(P622, _{(177)})	(P6mm, _{(183)})	(Pbar{6}2m, _{(189)})	(P6/mmm, _{(191)})
									(Pbar{6}m2, _{(187)})
		(l)	(P6_3 – – )	(P6_3, _{(173)})		(P6_3/m, _{(176)})	(P6_322, _{(182)})
		(l=3n)	(P6_2 – – )	(P6_2, _{(171)})			(P6_222, _{(180)})
				(P6_4, _{(172)})			(P6_422, _{(181)})
		(l=6n)	(P6_1 – – )	(P6_1, _{(169)})			(P6_122, _{(178)})
				(P6_5, _{(170)})			(P6_522, _{(179)})
	(l)	(l)	(P – – c)					(P6_3mc, _{(186)})	(Pbar{6}2c, _{(190)})	(P6_3/nmc, _{(194)})
(l)		(l)	(P – c – )					(P6_3cm, _{(185)})	(Pbar{6}c2, _{(188)})	(P6_3/mcm, _{(193)})
(l)	(l)	(l)	(P – cc)					(P6cc, _{(184)})		(P6/mcc, _{(192)})

Cubic cubic crystal system

Reflection conditions				Extinction symbol	Laue class
					(m3)		(m3m)
					Point group
(hkl)	(0kl)	(hhl)	(00l)		(23)	(mbar{3})	(432)	(bar{4}3m)	(mbar{3}m)
				(P – – – )	(P23, _{(195)})	(Pmbar{3}, _{(200)})	(P432, _{(207)})	(Pbar{4}3m, _{(215)})	(Pmbar{3}m, _{(221)})
			(l)	(P2_1 – -) (P4_2 – -)	(P2_13, _{(198)})		(P4_232, _{(208)})
			(l=4n)	(P4_1 – – )			(P4_132, _{(213)}) (P4_332, _{(212)})
		(l)	(l)	(P – – n)				(Pbar{4}3n, _{(218)})	(Pmbar{3}n, _{(223)})
	(k)		(l)	(Pa – – )		(Pabar{3}, _{(205)})
	(k+l)		(l)	(Pn – – )		(Pnbar{3}, _{(201)})			(Pnbar{3}m, _{(224)})
	(k+l)	(l)	(l)	(Pn – n)					(Pnbar{3}n, _{(222)})
(h+k+l)	(k+l)	(l)	(l)	(I – – – )	(I23, _{(197)}) (I2_13, _{(199)})	(Imbar{3}, _{(204)})	(I432, _{(211)})	(Ibar{4}3m, _{(217)})	(Imbar{3}m, _{(229)})
(h+k+l)	(k+l)	(l)	(l=4n)	(I4_1- -)			(I4_132, _{(214)})
(h+k+l)	(k+l)	(2h+l=4n, l)	(l=4n)	(I – – d)				(Ibar{4}3d, _{(220)})
(h+k+l)	(k, l)	(l)	(l)	(la – – )		(Iabar{3}, _{(206)})
(h+k+l)	(k, l)	(2h+l=4n, l)	(l=4n)	(Ia – d)					(Iabar{3}d, _{(230)})
(h+k, h+l,) ( k+l)	(k, l)	(h+l)	(l)	(F)	(F23, _{(196)})	(Fmbar{3}, _{(202)})	(F432, _{(209)})	(Fbar{4}3m, _{(216)})	(Fmbar{3}m, _{(225)})
(h+k, h+l,) ( k+l)	(k, l)	(h+l)	(l=4n)	(F4_1 – – )			(F4_132, _{(210)})
(h+k, h+l,) ( k+l)	(k, l)	(h, l)	(l)	(F – – c)				(Fbar{4}3c, _{(219)})	(Fmbar{3}c, _{(226)})
(h+k, h+l, ) (k+l)	(k+l=4n;) (k, l)	(h+l)	(l=4n)	(Fd – – )		(Fdbar{3}, _{(203)})			(Fdbar{3}m, _{(227)})
(h+k, h+l, ) (k+l)	(k+l=4n;) (k, l)	(h, l)	(l=4n)	(Fd-c)					(Fdbar{3}c, _{(228)})

これはX線や中性子線のような、散乱能が小さく試料中で高々1回程度しか散乱が起きないような入射波を使った場合に成立します。電子線のような散乱能の大きい波を用いた場合、複合格子並進に由来するpresence conditions/systematic absencesは満たすものの、らせん・映進に由来するpresence conditions/systematic absencesは満たされません。 ↩︎

Reflection conditions	Extinction symbol	Point group
Reflection conditions	Extinction symbol	(1)	(bar{1})
None	(P – )	(P1, _{(1)})	(Pbar{1}, _{(2)})