Orthorhombic crystal system

Koch, E.

doi:10.1107/97809553602060000573

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

International Tables for Crystallography (2006). Vol. C. ch. 1.2, pp. 6-7

Section 1.2.3. Orthorhombic crystal system

E. Koch^a

^a Institut für Mineralogie, Petrologie und Kristallographie, Universität Marburg, Hans-Meerwein-Strasse, D-35032 Marburg, Germany

1.2.3. Orthorhombic crystal system

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Metrical conditions: a, b, c arbitrary; α = β = γ = 90°

Bravais lattice types: oP, oS (oC, oA), oI, oF

Symmetry of lattice points: mmm

Simplified formulae: $[V=({\bf abc})=\left[\left| \matrix{ a^2&0&0 \cr 0&b^2&0 \cr 0&0&c^2}\right|\right]^{1/2}=abc, \eqno (1.1.1.1c)]$ $[a^*={1\over a}, \quad b^*={1\over b}, \quad c^*={1\over c},\quad \alpha^*=\beta^*=\gamma^*=90^\circ, \eqno (1.1.1.3c)]$ $[\eqalignno{ V^*&=({\bf a}^*{\bf b}^*{\bf c}^*)=\left [\left| \matrix{ a^{*2}&0&0 \cr 0&b^{*2}&0 \cr 0&0&c^{*2}}\right |\right] ^{1/2} \cr &=a^*b^*c^*=a^{-1}b^{-1}c^{-1}, &(1.1.1.4c)}]$ $[a={1\over a^*}, \quad b={1\over b^*}, \quad c={1\over c^*}, \quad\alpha=\beta=\gamma=90^\circ, \eqno (1.1.1.7c)]$ $[t^2=u^2a^2+v^2b^2+w^2c^2, \eqno (1.1.2.1c)]$ $[r^{*2}=h^2a^{*2}+k^2b^{*2}+l^2w^{*2}, \eqno (1.1.2.2c)]$ $[{a^2u\over h}={b^2v\over k}={c^2w\over l}, \eqno (1.1.2.12c)]$ $[{\bf t}_1\cdot{\bf t}_2=u_1u_2a^2+v_1v_2b^2+w_1w_2c^2, \eqno (1.1.3.4c)]$ $[{\bf r}^*_1\cdot {\bf r}^*_2=h_1h_2a^{*2}+k_1k_2b^{*2}+l_1l_2c^{*2}. \eqno (1.1.3.7c)]$

References

International Tables for Crystallography (2006). Vol. C. ch. 1.2, pp. 6-7