High-temperature phase transitions and domain structures of KLiSO₄: studied by polarisation-optics, X-ray topography and liquid–crystal surface decoration

(1) Structure types of KLiSO₄

For more than 100 years KLiSO₄ has been one of the well-known and often investigated compounds, because of its rich collection of polymorphs (modifications) and the different types of phase transitions (cf. Tomaszewski [9]) between them. Beyond this wealth, however, KLiSO₄ plays an even more special role among the group of related compounds MLiSO₄ with M=K¹⁺NH₄¹⁺, Rb¹⁺ and Cs¹⁺ in that it exhibits among its five polymorphs two different structure types, hexagonal (stuffed) tridymite and orthorhombic Icmm [10], [11], [13], whereas the other compounds (although also exhibiting polymorphism) have only one of these structure types.^[10]

In addition, the nature of the KLiSO₄ phase transitions is quite diverse, ranging from fast, displacive group-subgroup transitions to slow reconstructive transitions without symmetry relations. In the present paper only the three “high-temperature” polymorphs III, II and I and their phase transitions and domains structures are discussed, whereas the “low-temperature” phases III, VI and V and their transitions are extensively treated in the first publication of this series [17].

The “prototype structures” of the tridymite and the Icmm type are presented in Figure 15 in an idealised fashion (equal tetrahedra, no disorder) and highest symmetry: space groups P6₃/mmc (194^[11]) for the tridymite and Icmm (74¹¹ ) for the Icmm type. If two (oppositely linked) different tetrahedra, SO₄ and LiO₄, are considered, the space group of the tridymite type is (polar) P6₃mc (186), index [2], if the tetrahedra are fully ordered, or P6₃ (173), index [4], if chiral order (enantiomorphism) is admitted. For the Icmm polymorphs the symmetry reduces for two types of tetrahedra to the (still centrosymmetric) space group Pcmn (62), index [2], with polar pairs of SO₄- and LiO₄-tetrahedra along [001]. These pairs, however, are ordered antiparallel due to the n-glide perpendicular to [001].

(2) Order and disorder of the KLiSO₄ polymorphs

Starting from the polar and chiral ordered room-temperature phase III of space group P6₃ (173) [1], [12], [13], [14], [15], [16], [26] the disorder of the high-temperature phase I (space group P6₃/mmc (194), supergroup index [4], [13], [32]) can be described as follows:

• due to the centrosymmetry the polarity of phase III is lost;

• due to the mirror planes in z=¼ and ¾ of supergroup P6₃/mmc (194) the tetrahedral apices of both O4 and LiO₄ tetrahedra are half up and half down along the c-axis, i.e. each tetrahedral site is now a superposition of two equal but oppositely oriented half tetrahedra, related by a mirror plane in xy¼ or xy ¾.

• The vertical mirror planes in P6₃/mmc cause a further disorder of the structure of phase I: the tetrahedral bases are “split” into two, i.e. instead of a single triangular basis there is now a superposition of two triangles, rotated by about 30° around [001]. Considering both disorders in b) and c), each single SO₄ and LiO₄ tetrahedron in phase III is split in phase I into four disordered tetrahedra, each of “weight ¼”, thus resembling the supergroup index [4].

• There is a small further disorder effect which occurs in all polymorphs of KLiSO₄, including the ordered form III: the distance between the S- and the Li–atoms along c (≈3.33 Å) is shorter than the sum of the “standard” bond lengths S–O (≈1.47 Å) and Li–O (≈1.92 Å), which is ≈3.39 Å. As a result, the O atom, forming the joint apex of each pair of tetrahedra, is “pushed out” from its ideal position on the c-axis by about 0.27 Å, thus adding another, rather small three-fold disorder effect. This leads in phase III to an inclined S–O–Li bond with an (S–O–Li) angle of ≈155° instead of 180°.

• For the intermediate (orthorhombic) phase II with space group Pcmn (62) [13], [26], [31] significantly less disorder is found, compared to phase I. Again, the polarity of III is lost because of the centrosymmetry of II and, again, the mirror plane m perpendicular to [010] and parallel to c causes a two-fold splitting of the tetrahedra as in phase I, i.e. a rotation of the basis planes of the tetrahedra around [001] by about 30°. Also the disorder of the O atoms (tetrahedral apices) occurs as in phases III and I. However, the major disorder effect of phase I, the reversal of half the tetrahedral orientations and the superposition of the disordered SO₄/LiO₄ pairs (due to the mirror planes in xy¼ and xy¾) [see (b) above] does not occur in II. Instead, the glide planes n in xy¼ and xy¾ still reverse the pairs of SO₄- and LiO₄-tetrahdedra, however not in the same site (as in phase I), but in sites related by the translation ½ ½ 0. This results in a well-ordered non-polar arrangement of tetrahedra. Hence, with respect to tetrahedral order/disorder, polymorph II is a well-defined intermediary between the ordered polar phase III and the strongly disordered phase I.^[13]

It should be noted that the n-glide and its effect in phase II remain unchanged if instead of the centrosymmetric space group Pcmn (62) its non-centrosymmetric alternative Pc2₁n is chosen.

(3) Phase transitions between KLiSO₄ polymorphs

• We begin with a hypothetical, not realised case, the non-existence of phase II, i.e. the non-existence of the Icmm structure among the KLiSO₄ polymorphs. Then the resulting phase transition of index [4] at 708 K

  Phase III (P63, 173)←→Phase I (P63/mmc, 194),

  has almost textbook character, with the following essential features:

  • both polymorphs are of the tridymite type;

  • the transition would be non-ferroelastic, i.e. group and subgroup belong to the same crystal family (here hexagonal); both modifications have the same lattice. The point group of the supergroup, 6/mmm, is the hexagonal holohedry, the point group of the subgroup, 6, is of index [4];

  • all twins of this phase transition would be strictly merohedral (Σ1);

  • the phase transitions (in both directions) would involve a reversal of the tetrahedral apices by one half of the SO₄- as well as of the LiO₄-tetraheda in order to achieve either complete disorder (III→I) or complete polar order (I→III).

  It should be noted that a reversal of the apex of a tetrahedron does not require a rotation of 180° of the tetrahedron (up→down orientation) but only of 70.5° (180°–109.5°), thus making the order-disorder transition much easier to achieve.

• The discussion above of the (hypothetical) simple phase transition III←→I makes it easier to grasp which unusual complexities are introduced by the “insertion” of the Icmm phase II with orthorhombic space group Pcmn (62), leading to the sequence

  III (P63, 175) ←708 K→ II (Pcmn, 62)  ←949 K→ I (P63/mmc, 194).

  The following important aspects are emphasised:

  • there is practically no symmetry (and structure) relation between P6₃ and Pcmn, any group-subgroup tree would have to go up to P6₃/mmc (supergroup index [4]) and down to Pcmn (subgroup index [6], see below);

  • For the way down, from P6₃/mmc to Pcmn, there is a direct subgroup relation of index [6=3×2], as follows:

    P63/mmc (194) ←[3]→ Ccmm (63)  ←[2]→Pcmn (62)

    The index [6] is rather high, but there is another important aspect: The orthorhombic subgroup Ccmm occurs as three (120°) conjugate subgroups of the hexagonal supergroup P6₃/mmc, thus determining already the 120°-orientations of the of the three domain structures of Pcmn, which result from the above transition (cf. Figure 7);

  • Phase II with Pcmn is centrosymmetric with opposite, but well-ordered pairs of tetrahedral apices due to the n-glide, in contrast to the disordered phase I and the polar phase III, thus phase II is well suited as an intermediate form between III and I. In both transitions, from P6₃ on heating and from P6₃/mmc on cooling, 50% of both, SO₄ and LiO₄ tetrahedra must change their apex orientation;

  • The further geometric disorder of the structure of II is similar to that of phase I: splitting of the triangular bases due to m||[001] and small disorder of O in the S–O–Li bond chain along [001].