Liquid Crystals, Vol. 38, No. 5, May 2011, 663–668 Discovery of a novel ferrielectric phase of five-layer periodicity in binary mixtures of chiral smectic liquid crystals exhibiting unusual reversed phase sequence A.D.L. Chandani a,b , Atsuo Fukuda a , S. Kumar c , and Jagdish K. Vij a a Department of Electrical and Electronic Engineering, Trinity College, University of Dublin, Dublin 2, Ireland; b Department of Chemistry, Faculty of Science, University of Peradenia, Peradenia, Sri Lanka; c Raman Research Institute, Bangalore, India (Received 7 January 2011; final version received 24 February 2011) In a binary mixture system of ferroelectric and antiferroelectric liquid crystals whose major component shows an unusual reversed phase sequence of SmC ∗ A (1/2) - SmC ∗ , a new phase with ferrielectric order of five layers has been discovered by the electric field-induced birefringence (EFIB) measurements. The EFIB was measured using a photo-elastic modulator (PEM) set-up and by applying an in-plane electric field to a homeotropic aligned cell filled with the binary mixtures of compounds with ferroelectric and antiferroelectric compounds. The contours of constant birefringence in the electric field–temperature (E–T ) phase diagrams clearly indicate a distinct region corresponding to a new phase bordering the four-layer SmC ∗ (1/2) on the low temperature side and SmC ∗ α on the high temperature side. This new phase is unambiguously assigned to SmC ∗ (3/5) whose structure has been calculated by Osipov and Gorkunov. Keywords: anti Ferroelectrics (with five layer periodicity and a ferrielectric phase); chiral smectics; ferielectric phase of five layer periodicity; unusual reversed phase sequence 1. Introduction In chiral smectic liquid crystal materials exhibit- ing anticlinic antiferroelectric SmC ∗ A as well as synclinic ferroelectric SmC ∗ phases, several biaxial subphases may emerge in the clinicity frustration region between the main phases, SmC ∗ A and SmC ∗ [1– 8]. In the temperature region where the tilt angle is small, non-tilted SmA may also participate in the frustration as another main phase, and an opti- cally uniaxial subphase designated as SmC ∗ α may emerge, which is characterised by a microscopic heli- cal structure with an incommensurate short pitch [9–14]. Among them are the most common sub- phases, SmC ∗ A (1/3) and SmC ∗ A (1/2), with three- and four-layer superstructures. Additional subphases other than these two are also observed in the sequence of the temperature-induced phase tran- sitions. Drawing electric field–temperature (E–T ) phase diagrams with field-induced birefringence (EFIB) contours measured by a photoelastic mod- ulator has been established as a powerful technique in studying the subphases and main phases. The con- tours show characteristic patterns typical of uniaxial and biaxial subphases as well as the main phases, SmC ∗ A , SmC ∗ and SmA. When designating a subphase as SmC ∗ A (1/3) or SmC ∗ A (1/2), the number in parentheses refers to the q T value defined as ∗ Corresponding author. Email: jvij@tcd.ie q T = [F ] [A] + [F ] , (1) where [A] and [F ] are the numbers of quasi- anticlinic antiferroelectric and quasi-synclinic fer- roelectric orderings in a unit cell. The subphase has a microscopic distorted helical structure with its short-pitch p qT uniquely determined by q T is as follows |p qT |= 2 1 - q T . (2) If either of the denominator or numerator of q T (an irreducible fractional number) is even, the number of smectic layers contained in the unit cell is equal to twice the denominator and the subphase may be antiferrolectric; otherwise, the denominator directly indicates the size of the unit cell and the subphase must be ferrielectric. The number of smectic lay- ers in a unit cell of the subphase does not change monotonically with temperature. When use is made of q T instead to specify the subphase, it increases monotonically with temperature, as the emergence of subphases results from degeneracy lifting due to the weak long-range interlayer interactions (LRILIs) in the clinicity frustration region [8, 15]. In this paper where we consider the unusual reversed phase ISSN 0267-8292 print/ISSN 1366-5855 online c  2011 Taylor & Francis DOI: 10.1080/02678292.2011.566943 http://www.informaworld.com