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, p. 7

Section 1.2.4. Tetragonal crystal system

E. Kocha

aInstitut für Mineralogie, Petrologie und Kristallographie, Universität Marburg, Hans-Meerwein-Strasse, D-35032 Marburg, Germany

1.2.4. Tetragonal crystal system

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

Bravais lattice types: tP, tI

Symmetry of lattice points: 4/mmm

Simplified formulae: [V=({\bf abc})=\left[\left| \matrix{ a^2&0&0 \cr 0&a^2&0 \cr 0&0&c^2}\right|\right]^{1/2}=a^2c, \eqno(1.1.1.1d)] [a^*=b^*={1\over a}, \quad c^*={1\over c}, \quad \alpha^*=\beta^*=\gamma^*=90^\circ, \eqno (1.1.1.3d)] [\eqalignno{\qquad\qquad V^*& =({\bf a}^*{\bf b}^*{\bf c}^*)=\left[\left| \matrix{ a^{*2}&0&0 \cr 0&a^{*2}&0 \cr 0&0&c^{*2}}\right|\right]^{1/2} \cr &=a^{*2}c^*=a^{-2}c^{-1}, & (1.1.1.4d)}] [a=b={1\over a^*}, \quad c={1\over c^*}, \quad \alpha=\beta=\gamma=90^\circ, \eqno (1.1.1.7d)] [t^2=(u^2+v^2)a^2+w^2c^2, \eqno (1.1.2.1d)] [r^{*2}=(h^2+k^2)a^{*2}+l ^2c^{*2}=sa^{*2}+l ^2c^{*2} \eqno (1.1.2.2d)]with [s=h^2+k^2.]For each value of [s\le100], all corresponding pairs h, k are listed in Table 1.2.4.1[link]. [{u\over h}={v\over k}={c^2w \over a^2l}, \eqno (1.1.2.12d)] [{\bf t}_1\cdot {\bf t}_2 = (u_1u_2+v_1v_2)a^2+w_1w_2c^2, \eqno (1.1.3.4d)] [{\bf r}^*_1\cdot{\bf r}^*_2 = (h_1h_2+k_1k_2)a^{*2}+l_1l_2c^{*2}. \eqno (1.1.3.7d)]

Table 1.2.4.1| top | pdf |
Assignment of integers [s\le 100] to pairs h, k with [s=h^2+k^2]

Each pair h, k represents all eight pairs which result from permutation and different sign combinations.

shkshkshk
1 1 0 32 4 4 68 8 2
2 1 1 34 5 3 72 6 6
4 2 0 36 6 0 73 8 3
5 2 1 37 6 1 74 7 5
8 2 2 40 6 2 80 8 4
9 3 0 41 5 4 81 9 0
10 3 1 45 6 3 82 9 1
13 3 2 49 7 0 85 9 2
16 4 0 50 7 1 7 6
17 4 1 5 5 89 8 5
18 3 3 52 6 4 90 9 3
20 4 2 53 7 2 97 9 4
25 5 0 58 7 3 98 7 7
4 3 61 6 5 100 10 0
26 5 1 64 8 0 8 6
29 5 2 65 8 1  
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