International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. C. ch. 2.6, p. 92

Table 2.6.1.1 

O. Glattera

Table 2.6.1.1 | top | pdf |
Formulae for the various parameters for h (left) and m (right) scales

[\eqalign{R&=K\surd\tan \alpha\cr \tan \alpha &={\textstyle \Delta \log I(h) \over\textstyle\Delta h^2}\cr}] [\eqalign{R&=K{\textstyle\lambda a\over \textstyle2\pi}\surd\tan \alpha\cr \tan \alpha&={\textstyle\Delta \log I(m) \over \textstyle\Delta m^2}}]
[K=\surd {{3\over \log {\rm e}}} = 2.628]
[\eqalign{R_c&=K_c\surd\tan \alpha\cr \tan \alpha &={\textstyle \Delta \log [I(h)h] \over\textstyle\Delta h^2}\cr}] [\eqalign{R_c&=K_c{\textstyle\lambda a\over \textstyle2\pi}\surd\tan \alpha\cr \tan \alpha&={\textstyle\Delta \log [I(m)m] \over \textstyle\Delta m^2}}]
[K_c=\surd {\textstyle 2\over \log {\rm e}}=2.146]
[\eqalign{R_t&=K_t\surd\tan \alpha\cr \tan \alpha &={\textstyle \Delta \log [I(h)h^2] \over\textstyle\Delta h^2}\cr}] [\eqalign{R_t&=K_t{\textstyle\lambda a\over \textstyle2\pi}\surd\tan \alpha\cr \tan \alpha&={\textstyle\Delta \log [I(m)m^2] \over \textstyle\Delta m^2}}]
[K_t=\surd {\textstyle 1\over \log {\rm e}}=1.517]
[\eqalign{V&=2\pi^2{I(0)\over Q}\cr Q&=\int I(h)h^2\,{\rm d}h\cr}] [\eqalign{V&={\textstyle \lambda^3 a^3\over 4\pi}\ {\textstyle I(0)\over Q_m}\cr Q_m&=\int I(m)m^2{\,\rm d}m}]
[A=2\pi{\textstyle [I(h)h]_0\over Q}] [A={\textstyle \lambda^2a^2\over 2\pi}\ {\textstyle [I(m)m]_0\over Q_m}]
[T=\pi{\textstyle [I(h)h^2]_0\over Q}] [T={\textstyle \lambda a\over 2}\ {\textstyle [I(m)m^2]_0\over Q_m}]
[M={\textstyle I(0)\over P}K{\textstyle a^2\over cd(\Delta z)^2}] [K={\textstyle 1\over I_eN_L}=21.0]
[M_c={\textstyle [I(h)h]_0 \over P}\ {\textstyle K\over \pi}\ {\textstyle a^2 \over cd(\Delta z)^2}] [M_c={\textstyle [I(m)m]_0\over P}\ {\textstyle 2K\over \lambda}\ {\textstyle a\over cd(\Delta z)^2}]
[M_t={\textstyle [I(h)h^2]_0 \over P}\ {\textstyle K\over 2\pi}\ {\textstyle a^2 \over cd(\Delta z)^2}] [M_t={\textstyle [I(m)m^2]_0\over P}\ {\textstyle 2\pi K\over \lambda^2}\ {\textstyle 1\over cd(\Delta z)^2}]
[\overline {(\Delta\rho)^2}={\textstyle Q\over P}\ {\textstyle a^2\over 2\pi^2d}K] [ \overline {(\Delta\rho)^2}={\textstyle Q_m\over P}\ {\textstyle 4\pi\over \lambda^3ad}K]
[\eqalign{K&=10^{24}/I_e\cr (10^{24}&=[{\rm cm}/{\rm \AA}]^3)}]
[\eqalign{O_s&=\pi {\textstyle K\over Q}\cr K&= \lim\limits_{h \rightarrow \infty} I(h)h^4\cr}] [\eqalign{O_s&={\textstyle 2\pi ^2\over \lambda a}\ {\textstyle K_m\over Q_m}\cr K&= \lim\limits_{m \rightarrow \infty} I(m)m^4}]