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Subsections

• 4.1. Barium titanate (BaTiO₃) (Hewatt, 1974; Johnson, 1965) (see also Note added in proof)
• 4.2. Potassium tellurium bromide (K₂TeBr₆) Abrahams et al., 1984; Ihringer & Abrahams, 1984)
• 4.3. Lead aluminium fluoride (Pb₅Al₃F₁₉) (Andriamampianina et al., 1994; Sarraute et al., 1995, 1996; Omari et al., 1998)
• 4.4. Lead niobate (PbNb₂O₆) (Roth, 1959, 1968; Labbé et al., 1977; Mahé, 1967)
• 4.5. Tellurium dioxide (TeO₂) (Peercy & Fritz, 1974; Worlton & Beyerlein, 1975; Thomas, 1988)
• 4.6. Dicalcium silicate (Ca₂SiO₄) (Eysel & Hahn, 1970)
• 4.7. Iron (Fe) (Donohue, 1974)
• 4.8. Yttrium (Y) (Grosshans et al., 1992)
• 4.9. Caesium boron tetrafluoride (CsBF₄) (Richter & Pistorius 1971)

4. Examples

4.1. Barium titanate (BaTiO₃) (Hewatt, 1974; Johnson, 1965) (see also Note added in proof)

6H $\vert \gt \,$1733 K $\vert$P6₃/mmc (194) $\vert$Z = 6 $\vert$non-ferroic $\vert$metastable at 300 K if cooled rapidly; stabilized by certain impurities.

I $\vert$1733-403 K $\vert$Pm$\bar 3$m (221) $\vert$Z = 1 $\vert$non-ferroic $\vert$Type = CaTiO₃ idealized. May exist up to melting if phase 6H is not stabilized.

II $\vert$403-278 K $\vert$P4mm (99) $\vert$Z = 1 $\vert$ferroelectric, ferroelastic $\vert$6 ferroelectric, 3 ferroelastic variants.

III $\vert$278-183 K $\vert$Amm2 (38) $\vert$Z = 2 $\vert$ferroelectric, ferroelastic $\vert$12 ferroelectric, 6 ferroelastic variants.

IV $\vert$<$\,$183 K $\vert$R3m (160) $\vert$Z = 3 $\vert$ferroelectric, ferroelastic $\vert$8 ferroelectric, 4 ferroelastic variants.

4.2. Potassium tellurium bromide (K₂TeBr₆) Abrahams et al., 1984; Ihringer & Abrahams, 1984)

I $\vert \gt \,$434 K $\vert$Fm$\bar 3$m (225) $\vert$Z = 4 $\vert$non-ferroic $\vert$Type = K₂PtCl₆. Decomposes above $\sim$590 K.

II $\vert$434-400 K $\vert$P4/mnc (128) $\vert$Z = 2 $\vert$ferroelastic $\vert$3 variants.

III $\vert$< 400 K $\vert$P2₁/n (14) $\vert$Z = 2 $\vert$ferroelastic $\vert$12 variants.

4.3. Lead aluminium fluoride (Pb₅Al₃F₁₉) (Andriamampianina et al., 1994; Sarraute et al., 1995, 1996; Omari et al., 1998)

I $\vert \gt 670~K \vert$I4/mcm (140) $\vert$Z = 4 $\vert$non-ferroic $\vert$structure not yet unambiguously determined.

II $\vert$670-360 K $\vert$I4/m (87) $\vert$Z = 4 $\vert$ferroic^* $\vert$2 variants differing in elastic properties.

III $\vert$360-320 K $\vert$I2/c (15) $\vert$Z = 4 $\vert$ferroelastic $\vert$4 variants.

IV $\vert$320-270 K $\vert$P4/n (85) $\vert$Z = 8 $\vert$ferroic^* $\vert$antiferroelectric. ^*As in phase II.

V $\vert$< 270 K $\vert$I4cm (108) $\vert$Z = 4 $\vert$ferroelectric $\vert$2 variants.

4.4. Lead niobate (PbNb₂O₆) (Roth, 1959, 1968; Labbé et al., 1977; Mahé, 1967)

I $\vert \gt \,$1423 K $\vert$tetragonal $\vert$- $\vert$nonferroic $\vert$metastable from 1423 to 873 K if cooled rapidly.

II $\vert$<$\,$873 K $\vert$Bb2₁m (36) $\vert$Z = 40 $\vert$ferroelectric $\vert$metastable at room temperature if cooled rapidly from > 1423 K.

III $\vert$<$\,$1423 K $\vert$R3m (160) $\vert$Z = 9 $\vert$non-ferroic $\vert$the stable phase at all temperatures below 1423 K.

4.5. Tellurium dioxide (TeO₂) (Peercy & Fritz, 1974; Worlton & Beyerlein, 1975; Thomas, 1988)

$\alpha$ $\vert$<$\,$0.8 GPa $\vert$P4₁2₁2 (92) $\vert$Z = 4 $\vert$non-ferroic $\vert$room temperature structure determination.

$\beta$ $\vert \gt \,$0.8 GPa $\vert$P2₁2₁2 (19) $\vert$Z = 4 $\vert$ferroelastic $\vert$2 variants, room-temperature structure determined at 2 GPa.

4.6. Dicalcium silicate (Ca₂SiO₄) (Eysel & Hahn, 1970)

$\alpha$ $\vert$2400-1720 K $\vert$P6₃mc (186) or P6₃/mmc (194) $\vert$Z = 2 $\vert$non ferroic $\vert$Type = K₂SO₄ high. Stable.

$\alpha$$^\prime$-_H $\vert$1720-1430 K $\vert$Pcmn (62) $\vert$Z = 4 $\vert$ferroelastic $\vert$Type = K₂SO₄ low. Stable.

$\alpha$$^\prime$-_L $\vert$1430-950 K $\vert$Ccm2₁^* (36) $\vert$Z = 16 $\vert$- $\vert$Type = K₂SO₄ low, slightly deformed. Stable. ^*Other space groups are possible.

$\beta$ $\vert$<$\,$950 K $\vert$P2₁/n (14) $\vert$Z = 4 $\vert$- $\vert$Type = K₂SO₄ low, strongly deformed. Metastable with respect to $\gamma$.

$\gamma$ $\vert$<$\,$1000 K $\vert$Pcmn (62) $\vert$Z = 4 $\vert$ - $\vert$Type = olivine. Stable.

4.7. Iron (Fe) (Donohue, 1974)

$\delta$$\vert \gt \,$1663 K $\vert$Im$\bar 3$m (229) $\vert$Z = 2 $\vert$non-ferroic $\vert$Type = W. Melting at 1808 K.

$\gamma$$\vert$1663-1183 K $\vert$Fm$\bar 3$m (225) $\vert$Z = 4 $\vert$non-ferroic $\vert$Type = Cu.

$\beta$ $\vert$1183-1043 K $\vert$Im$\bar 3$m (229) $\vert$Z = 2 $\vert$paramagnetic $\vert$Type = W.

$\alpha$$\vert$<$\,$1043 K $\vert$Im$\bar 3$m (229)^* $\vert$Z = 2 $\vert$ferromagnetic $\vert$Type = W. ^*Magnetic structure is pseudocubic.

$\varepsilon$ $\vert \gt \,$13 GPa $\vert$P6₃/mmc (194) $\vert$Z = 2 $\vert$- $\vert$Type = Mg.

4.8. Yttrium (Y) (Grosshans et al., 1992)

- $\vert \gt \,$46 GPa $\vert$Fm$\bar 3$m (225) $\vert$Z = 4 $\vert$non-ferroic $\vert$Type = Cu.

- $\vert$46-26 GPa $\vert$P6₃/mmc (194) $\vert$Z = 4 $\vert$non-ferroic $\vert$Type = Nd $\alpha$.

- $\vert$26-12 GPa $\vert$R$\bar 3$m (166) $\vert$Z = 9 $\vert$- $\vert$Type = Sm $\alpha$.

- $\vert$<$\,$12 GPa $\vert$P6₃/mmc (194) $\vert$Z = 2 $\vert$- $\vert$Type = Mg.

4.9. Caesium boron tetrafluoride (CsBF₄) (Richter & Pistorius 1971)

This example is chosen to illustrate a situation in which the phase diagram is an intricate function of temperature and pressure. The proposed notation specifies a rectangular (T, p) area for each phase, approximately superimposed on the actual range of the phase. Such a rough indication is generally insufficient to reconstruct, even approximately, the shape of the phase diagram. However, it provides the approximate stability range for the various phases and may be considered a first step in their identification. Only the three phases with identified crystal symmetries are listed below (labelled I, II, III in the published diagram) and only the first three fields of the nomenclature are entered:

I $\vert$900-670 K; <$\,$3 GPa $\vert$cubic $\vert$$\dots$

II $\vert$670-500 K; <$\,$0.8 GPa $\vert$cubic $\vert$$\dots$

III $\vert$500-270 K; <$\,$0.5 GPa $\vert$orthorhombic $\vert$$\dots$.

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