Dielectric Relaxation Modes Research Articles

Gd3+ substitution effects, electrical and AC impedance characterizations of Gd/Cr co-doped SrBi4Ti4O15 Aurivillius-phase ceramics

Gd/Cr co-doped SrBi4Ti4O15 (Sr1-xGdxBi4Ti4O15 + 0.2 wt% Cr2O3, x = 0∼0.08) Aurivillius-phase ceramics were prepared by the traditional solid-state reaction process, the influences of Gd3+ doping concentration (x) on the structures and electrical properties of SrBi4Ti4O15 were investigated, as well as the AC impedance characterizations of the ceramics were analyzed. The incorporation of Gd2O3 and Cr2O3 into SrBi4Ti4O15 induced the lattice distortion of its orthorhombic structure. The donor substitution of Gd3+ for Sr2+ at A-site improved the Curie temperature (TC) and decrease the temperature coefficient of dielectric constant (TKε), as well as change the relaxation activation energy (Earel) of SrBi4Ti4O15 through the lattice distortion caused. Between 425 °C and 700 °C, the DC conduction behaviors of the ceramics was found with a transition from the mixed conduction mechanism involved in both the single-ionized oxygen vacancy and the double-ionized one to the single mode dominated by the latter one. Above TC, the imaginary part of modulus (M″) gradually shifts towards higher frequencies with increasing temperature, indicating the emergence of a new dielectric relaxation mode related to the phase transition process of the ceramics. Owing to the co-doping effects of Gd3+ and Cr3+, the optimized composition with x = 0.03 achieved excellent electrical properties (TC = 550 °C and d33 = 30 pC/N) and good thermal stability (TKε = 4.19 × 10−3/°C between RT and 500 °C, and the lose in d33 is only 3.3% after being annealed at 500 °C for 4 h), which make it promising for stable applications below 500 °C in the high-temperature piezoelectric devices.

Anopore confinement in the cyanobiphenyl-based liquid crystal dimer CB7CB. A dielectric study

ABSTRACT We report an experimental work on the liquid crystal dimer 1’’,7’-bis(4-cyanobiphenyl-4’-yl) heptane (CB7CB) confined to Anopore membranes. We have studied the behaviour of the dielectric relaxation modes in the isotropic (I), nematic (N) and twist-bend nematic (NTB) phases by broadband dielectric spectroscopy and compared to the results of the bulk sample. We have found that the strength of the components of the static dielectric permittivity for bulk and confined samples diminishes when cooling but, once in the NTB phase, those of the confined CB7CB tend to decrease in a slower rate compared to the ones of bulk CB7CB. This work is meant to play a humble tribute to the first report on a cyanobiphenyl-based LC in its 50th anniversary.

Frequency response of dielectric relaxation modes in a room temperature antiferroelectric phase liquid crystalline mixture

Thermodynamic, optical, and electrical characterization of a newly formulated mixture of chiral mesogenic molecules has been carried out. The material exhibits different mesophases like paraelectric smectic (SmA*), ferroelectric chiral smectic (SmC*) with synclinic structure, and wide temperature range antiferroelectric chiral smectic (SmCa*) with anticlinic structure. These studies show that at room temperature, the SmCa* phase is present in a wide temperature range of ∼128 °C (from −35.0 °C to 92.6 °C) followed by the SmC* phase (from 92.6 °C to 110.8 °C) as well as SmA* phase (from 110.8 °C to 113.9 °C). Besides the wide temperature range, the SmCa* phase has also been optimized for high helical pitch length, which is useful for helix unwound cells through surface stabilization for application. Frequency-dependent dielectric parameters have been determined for the material in the frequency range of 1 Hz to 40 MHz. The dielectric spectroscopy shows six different relaxation modes in various phases due to the collective and individual molecular behavior. The SmA* phase exhibits soft mode relaxation associated with variations in the amplitude of the tilt angle. The identified soft mode is significantly temperature-dependent. Using the Curie-Weiss law, the transition temperature for the paraelectric SmA* phase to the ferroelectric SmC* phase (Tc) is found to be 111.4 °C. Two relaxation modes in the SmC* phase have been identified Goldstone mode and a domain mode. These modes have extremely high dielectric strength resulting in high permittivity in comparison with other modes. Three modes of relaxation have been detected in the antiferroelectric SmCa* phase. Different characteristic parameters of these modes are strongly temperature-dependent. This study signifies that the present room-temperature antiferroelectric liquid crystals may be a potential candidate for display applications.

An insight into the effect of carbon nanofillers in glass fibre epoxy nanocomposites through dielectric spectroscopy

Interfacial characteristics of nanocomposites are critical limiting factors in the design of polymer nanocomposites. The nanocomposites have complex structures and play a pivotal role in controlling functional properties. Analysis of interfacial layers in polymer nanocomposites, existing between the polymer matrix and the nanoparticles plays a major role in determining their characteristics. High-frequency analysis of electrical conductivity and dielectric properties of carbon nanofillers which are embedded in an epoxy matrix were analysed using alternating current dielectric spectra. This article provides a correlation between the electrical transport properties and dielectric behaviour of epoxy carbon nanocomposites at different temperatures are investigated with variations in frequency. Electrical transport properties of nanocomposites are primarily dictated by electron tunnelling and matrix, nanofillers conductivity. Dielectric spectroscopy in the frequency range 10 Hz–8 MHz has been performed on epoxy nanocomposites with and without hybrid carbon nanofillers at one weight percentage (2:3 ratio). Dominant dielectric relaxation mode is observed in the base composite at a low-frequency region (≥10 Hz), whereas nanocomposite with hybrid carbon nanofillers is observed to induce two dielectric relaxations in the kHz region. Increase in non-monotonic variations in dielectric spectra makes the nanocomposite suitable for high temperature low sag conductor core, aerospace and cryogenic engineering applications.

Tuning dielectric response of polyethylene by low gamma dose: Molecular mobility study improvement by dipolar probes implementation

Dynamic Dielectric Spectroscopy is a powerful method to study the molecular mobility of dipolar polymers. As Linear Low Density Polyethylene is globally non polar, the dielectric experimental signal needs to be seriously improved. The aim of this study is to implement carbonyl groups by gamma irradiation, that act as dipolar probes in order to increase the signal to noise ratio. A specific attention is paid to induce as less modification as possible. Films were gamma irradiated in dioxygen media with different absorbed doses from 0 kGy to 100 kGy. After irradiation, better signal to noise ratios have been obtain thanks to polar probes introduction. The study of dielectric relaxation modes is then possible, extended and much more precise. One should irradiate the polymer with the lowest dose, between 12.5 kGy and 25 kGy, to obtain satisfactory Dynamic Dielectric Spectroscopy results with virtually no chemical and physical changes in the gamma irradiated samples.

Impact of carbon quantum dots on self-assembly and dielectric relaxation modes of a room temperature tri-component fluorinated antiferroelectric liquid crystal mixture.

We investigated the impact of carbon quantum dots (CQDs) of sizes ∼2-5 nm in a room temperature tri-component fluorinated antiferroelectric liquid crystal (AFLC) mixture. The synthesised CQDs have been characterised by high-resolution transmission electron microscopy and X-ray diffraction spectroscopy. An increase in the transition temperature and enthalpy to the isotropic liquid phase indicates stabilization of the AFLC mixture in the presence of CQDs. The dielectric studies have been carried out in the frequency range of 1 Hz-40 MHz under the planar anchoring conditions of the molecules. An appreciable increase in the permittivity, dielectric strength, and conductivity has been observed owing to the existence of sp2/sp3 hybridization in the CQDs which form a strong coupling and develop a dipolar ordering in the systems. Various relaxation frequencies were increased with the incarceration of CQDs in the AFLC mixture. Overall, the different studies suggest that the doped CQDs are very well settled in between the host molecules without disturbing the molecular ordering of the hosts. Such results are encouraging and reveal the potential applicability of the CQD doped systems to produce highly efficient tuneable optical devices and other multifaceted applications.

Abnormal dielectric relaxations and giant permittivity in SrTiO3 ceramic prepared by plasma activated sintering

AbstractIn this study, the dielectric properties of SrTiO3 ceramics prepared by plasma‐activated sintering (PAS) were investigated. One of the striking findings is that the material exhibits giant room temperature permittivity (k∼3.5 × 104) and low dielectric loss (∼0.05) at 1 kHz, with the permittivity exceeding that of the conventionally prepared SrTiO3（ST） ceramics (k∼300) by two orders of magnitude. The enhancement of the polarizability was caused by the high concentration of defect dipoles. In this paper, two dielectric relaxation modes of the PAS ceramics below 0°C have been mainly discussed. One dielectric relaxation mode showed higher activation energy than that of the dielectric peak in the same temperature range for the conventional SrTiO3‐based ceramics. This mode was sensitive to humidity, and the strength of this mode was associated with the oxygen vacancies concentration in the ceramics. The other mode exhibited abnormal slowing down of relaxation rate with increasing temperature, which is contrary to the typical dielectric relaxation behavior, and the anomaly persisted over a narrow temperature range. Both modes were observed at the same interface between the grain and grain boundaries.

Dielectric and electrooptical properties of hockey-stick-shaped liquid crystal with a negative dielectric anisotropy

We investigated dielectric properties of a hockey-stick-shaped liquid crystal (HLC). Two dielectric relaxation modes were observed at 0.91 kHz and 4.51 MHz. The low frequency relaxation modes in isotropic, smectic, and nematic phases are related to the motion of ions, collective tilt fluctuation, and rotation around the long molecular axis, respectively. Meanwhile, the high frequency relaxation modes in nematic and smectic phases was due to the rotation around the short axis of the molecules and hindered by the resistance of the ITO layers. We also examined the electrooptical response of the 5.0 wt% HLC-doped commercial nematic liquid crystal (LC) mixtures. The birefringence of the LC mixture was slightly increased, while the falling time and the rotational viscosity was decreased in the nematic phase.

Catalysis with Earth-abundant Elements (Catalysis Series)

The continuous growing demand for nanoscience applications and the improvement in the performance of liquid crystal based devices has been extensively required by the technological world. Recent progress in the field of liquid crystals has found its practical implementation in various display and non display devices which experiences obstacle due to impurity effects that reduces its performance. The dispersion of nanoparticles in liquid crystal medium helps in the reduction of impurity ions and thus improving the performance of liquid crystal based devices. The present work is based on the collective dielectric relaxation processes that have been observed in antiferroelectric liquid crystal (AFLC) mixture W1000 dispersed with 0.1% wt/wt and 0.3% wt/wt concentrations of graphene oxide. Graphene oxide itself favors vertical alignment and the coupling of AFLC W1000 mixture with graphene oxide affects its molecular ordering. This has been confirmed from the polarizing optical micrographs. The dielectric relaxation modes have been observed with and without the application of bias voltage in SmC* to SmCA* phase transition during cooling cycle. The appearance and disappearance of PL, PH and X modes have been observed and are explained on the basis of molecular interactions. Graphene oxide dispersed system favors homeotropic alignment (dark state) and the application of bias field will convert it into homogenous alignment (bright state). Graphene oxide dispersion find prospective applications in good contrast display devices, supercapacitors, electronic gadgets, rechargeable batteries. Electro optical results unveil the faster response time, decreased rotational viscosity and spontaneous polarization with no change in tilt angle for the dispersed system. These observations can be exploited in photonic switches with sub millisecond response time which are required for fabricating faster liquid crystal devices.

Coupling between Structural and Dielectric Relaxations of Methanol and Ethanol Studied by Molecular Dynamics Simulation.

The microscopic origin of the fast dielectric relaxation modes and the integrated dielectric relaxation times of methanol and ethanol was investigated by means of cross-correlation analysis of molecular dynamics simulation. Random force on the fluctuation of collective dipole moment was correlated with the two-body density mode in both real and reciprocal spaces. A strong coupling was observed with the OH alternation mode at 30 nm-1, suggesting that alternating switching of the hydrogen bond within a hydrogen-bonding chain is the principal origin of the retarded friction on the collective dipole moment. The relaxation of the coupling was much slower than that of the partial intermediate scattering functions at the corresponding wavenumber, which suggests the breakdown of the factorization approximation employed in the mode-coupling theory. Although the prepeak structure is strongly coupled to the viscoelastic relaxation, its coupling with the dielectric relaxation is relatively weak. The difference between the viscoelastic and the dielectric relaxations was discussed in terms of the different symmetries of the shear stress tensor and the collective dipole moment.

Effect of graphene oxide dispersion in antiferroelectric liquid crystal mixture in the verge of SmC* to SmCA* phase transition

The continuous growing demand for nanoscience applications and the improvement in the performance of liquid crystal based devices has been extensively required by the technological world. Recent progress in the field of liquid crystals has found its practical implementation in various display and non display devices which experiences obstacle due to impurity effects that reduces its performance. The dispersion of nanoparticles in liquid crystal medium helps in the reduction of impurity ions and thus improving the performance of liquid crystal based devices. The present work is based on the collective dielectric relaxation processes that have been observed in antiferroelectric liquid crystal (AFLC) mixture W1000 dispersed with 0.1% wt/wt and 0.3% wt/wt concentrations of graphene oxide. Graphene oxide itself favors vertical alignment and the coupling of AFLC W1000 mixture with graphene oxide affects its molecular ordering. This has been confirmed from the polarizing optical micrographs. The dielectric relaxation modes have been observed with and without the application of bias voltage in SmC* to SmCA* phase transition during cooling cycle. The appearance and disappearance of PL, PH and X modes have been observed and are explained on the basis of molecular interactions. Graphene oxide dispersed system favors homeotropic alignment (dark state) and the application of bias field will convert it into homogenous alignment (bright state). Graphene oxide dispersion find prospective applications in good contrast display devices, supercapacitors, electronic gadgets, rechargeable batteries. Electro optical results unveil the faster response time, decreased rotational viscosity and spontaneous polarization with no change in tilt angle for the dispersed system. These observations can be exploited in photonic switches with sub millisecond response time which are required for fabricating faster liquid crystal devices.

Low-frequency dielectric processes in deformed helix ferroelectric liquid crystals

A low-frequency dielectric relaxation mode in deformed helix ferroelectric liquid crystal (DHFLC) has been observed at the interface of strongly rubbed substrates and DHFLC material which may find applications in low power consumption FLC devices. The surface-induced dielectric relaxation process at the interface of DHFLC and substrate is called the partially unwound helical mode (p-UHM) due to the unwinding of the helical structure at this interface. After investigation of the material under various parameters such as temperature, variation of the amplitude of probing ac voltage and dc bias voltage, the relaxation frequency of p-UHM is found to be shifted towards Goldstone mode and merged with it. The relaxation frequency of Goldstone mode is found to decrease, whereas the relaxation frequency of p-UHM process increases with the increase in temperature of DHFLC. Finally, both the modes merge and the resultant relaxation frequency is found to be lower than Goldstone mode in SmC* phase. It seems that phason mode and partial helical unwinding mode are coupled together due to dipole moment that is resulting in a new relaxation frequency. p-UHM process is significant for low-power displays and non-displays applications like a part of sensor where weak electric signal is required to be realized without pre-amplification.

Enhancement of dielectric and electro-optical parameters of a newly prepared ferroelectric liquid crystal mixture by dispersing nano-sized copper oxide

ABSTRACT Here, we present the effect of copper (II) oxide nanoparticles (nCuO) on dielectric and electro-optical parameters of a newly prepared ferroelectric liquid crystal (FLC) mixture, namely W302. The FLC mixture, comprising of pyrimidine compounds, was characterised through dielectric spectroscopy, differential scanning calorimetry (DSC), polarising optical microscopy (POM) and other electro-optical methods. The material parameters such as spontaneous polarisation, rotational viscosity, response time and tilt angle of W302 were found to be 14 nC/cm2, 240 mPa.s, 150 µs and 28ᴼ, respectively. The phase transition temperatures of W302 were observed through DSC and further confirmed by the dependence of dielectric loss factor in homogeneously aligned FLC sample with temperature. We also demonstrate the observance of a low-frequency dielectric relaxation mode due to the unwinding of the helix, called as partially unwound helical mode (p-UHM) along with Goldstone mode. The behaviour of p-UHM has been systematically studied with temperature and applied bias field. Further, dispersion of nCuO into host W302 has shown a significant increase in dielectric permittivity. Also, the p-UHM relaxation peak in the dielectric regime has disappeared with the incorporation of nCuO. These studies would be useful to fabricate better electro-optical devices for display, switching and beam steering applications. The formulation and characterization of a ferroelectric liquid crystal (FLC) mixture W302 composed of pyrimidine compounds is presented. Then, we observed the effect of copper (II) oxide nanoparticles (nCuO) on dielectric and electro-optical parameters of a newly prepared and characterized FLC mixture.

Ionic conductivity mediated by hydrogen bonding in liquid crystalline 4-n-alkoxybenzoic acids

We describe the dielectric response of a series of liquid crystalline 4-n-alkoxybenzoic acids, nOBAs, with different alkyl chains, n = 4, 5, 7 and 8, in planarly aligned cells, as potential anhydrous electrolytes for electrochemical cells. All nOBAs display two modes of dielectric relaxations and conductivity. At moderate-high frequencies, f ∼101–104 Hz, the so-called mode 1 involves fast dipole rearrangements leading to direct current, DC, conductivities in the σdc1 ∼ 10−5 S cm−1 range, which are eventually insensitive to bias fields. At lower frequencies, f ∼10−1 to 101 Hz, the so-called mode 2 is related to slower processes with lower DC conductivities, σdc2 ∼ 10−6 S cm−1, which are further facilitated under sufficiently strong bias fields. Whilst mode 1 can be associated to the presence (and motions) of asymmetric dimers stabilised by hydrogen bonding and free acids in the nematic phase, mode 2 may involve the extension of the hydrogen-bonded network to longer ranges, probably by the formation of catemeric species, and its conductivity increases on heating in both the nematic and isotropic phases. Even though the conductivity values fall below those of benchmark electrolytes used in fuel cells (σdc ∼ 0.1 S cm−1), our results are promising, particularly for non-doped/non-hydrated electrolytes, and highlight the potential of the nOBAs and other hydrogen-bonded liquid crystals as components of electrolytes for ion conductivity.

Relaxation phenomena and conductivity mechanisms in anion-exchange membranes derived from polyketone

A polyketone-b-poly[N-(4 methyl-methylpyridium)-ethylenepyrrole+][X−], with X− = I− or OH−, is investigated as an example of anion-exchange membrane with potential applications in fuel cells. The polyketone starting material PK and the functionalized polyketones Pyr-FPKmI and Pyr-FPKmOH are investigated via Broadband Electrical Spectroscopy (BES) to understand the conductivity mechanism. BES signals are collected in the frequency range of 10−2 – 107 Hz and from −100° to 120 °C. BES measurements reveal the presence of up to three interdomain polarizations phenomena, one electrode polarization event and two β dielectric relaxation modes for both wet Pyr-FPKmI and Pyr-FPKmOH. Ion conductivity for Pyr-FPKmI and Pyr-FPKmOH is found to be 0.0086 and 0.0105 S cm−1 at 80 °C, respectively. The overall conductivity mechanism is attributed to the superposition of two conduction pathways, via delocalization bodies and via interdomain percolation pathways, which are associated with two different physical phenomena.

Probing the impact of carbon quantum dots on partially unwound helical mode in ferroelectric liquid crystals

We report the modulation in dielectric properties of a ferroelectric liquid crystal (FLC) by using carbon quantum dots (CQDs) of size ∼4–5 nm. The appearance of a low frequency dielectric relaxation mode in the FLC, called the partially unwound helical mode (p-UHM), is controlled by CQDs with a FLC material in two different ways. Firstly, CQDs are dispersed into the bulk of the FLC before filling into a sample cell, and secondly, they are deposited onto the surface of a substrate. In both cases, the p-UHM has been found suppressed due to the modulation of a helicoidal structure at the interface of the FLC and the surface of the substrate of the sample cell. It has also been confirmed that CQDs at the interface of the FLC and the surface of the substrate have not affected the intrinsic properties of the FLC material. On the other hand, CQDs in the bulk of the FLC have shown remarkable variations in the fundamental properties of the FLC material. The suppression of the dielectric mode is confirmed by high-resolution dielectric spectroscopy, optical textures, and contact angle measurements. The concept of appearance and disappearance of the p-UHM process leads to the understanding of FLC systems in confined geometries for various display and non-display applications.

Chain dynamics of human dermis by Thermostimulated currents: A tool for new markers of aging.

The purpose of this clinical study was to identify dielectric markers to complete a previous thermal and vibrational study on the molecular and organizational changes in human dermis during intrinsic and extrinsic aging. Sun-exposed and non-exposed skin biopsies were collected from 28 women devised in two groups (20-30 and ≥60years old). The dielectric relaxation modes associated with localized and delocalized dynamics in the fresh and dehydrated state were determined by the Thermostimulated currents technique (TSC). Intrinsic and extrinsic aging induced significant evolution of some of the dielectric parameters of localized and delocalized dynamics of human skin. With photo-aging, freezable water forms a segregated phase in dermis and its dynamics is close to free water, what evidences the major role of extrinsic aging on water organization in human skin. Moreover, TSC indicators highlight the restriction of localized mobility with intrinsic aging due to glycation, and the cumulative effect of chronological aging and photo-exposition on the molecular mobility of the main structural proteins of the dermis at the mesoscopic scale. TSC is a well-suited technique to scan the molecular mobility of human skin. It can be uses as a relevant complement of vibrational and thermal characterization to follow human skin modifications with intrinsic and extrinsic aging.

Cooperative behavior of molecular motions giving rise to two glass transitions in the same supercooled mesophase of a smectogenic liquid crystal dimer.

In the present work, a detailed analysis of the glassy behavior and the relaxation dynamics of the liquid crystal dimer α-(4-cyanobiphenyl-4'-yloxy)-ω-(1-pyrenimine-benzylidene-4'-oxy) heptane (CBO7O.Py) throughout both nematic and smectic-A mesophases by means of broadband dielectric spectroscopy has been performed. CBO7O.Py shows three different dielectric relaxation modes and two glass transition (T_{g}) temperatures: The higher T_{g} is due to the freezing of the molecular motions responsible for the relaxation mode with the lowest frequency (μ_{1L}); the lower T_{g} is due to the motions responsible for the two relaxation modes with highest frequencies (μ_{1H} and μ_{2}), which converge just at their corresponding T_{g}. It is shown how the three modes follow a critical-like description via the dynamic scaling model. The two modes with lowest frequencies (μ_{1L} and μ_{1H}) are cooperative in the whole range of the mesophases, whereas the highest frequency mode (μ_{2}) is cooperative just below some crossover temperature. In terms of fragility, at the glass transition, the ensemble (μ_{1H}+μ_{2}) presents a value of the steepness index and μ_{1L} a different one, meaning that fragility is a property intrinsic to the molecular motion itself. Finally, the steepness index seems to have a universal behavior with temperature for the dielectric relaxation modes of liquid crystal dimers, being almost constant at high temperatures and increasing drastically when cooling the compound down to the glass transition from a temperature about 3/4T_{NI}.

Dielectric response of vulcanized natural rubber containing BaTiO3 filler: The role of particle functionalization

Natural rubber (NR) nanocomposites have been prepared with hydroxylated barium titanate filler (BaTiO3-OH), employing emulsion polymerization followed by vulcanization process. The addition of barium titanate, a compound with high dielectric permittivity, was envisaged to increase the insulating properties of NR films, thereby reducing the electrical stress and the possibility of undesired arcing on their surfaces. The content of perovskite particles greatly affected both, the mechanical and the electrical properties, of the vulcanized films. It was observed that the optimum functionalized nanoparticle concentration is around 0.25–0.50 phr, range in which the elongation of break was maintained between 874–935% and the tensile strength was between 4.40–4.80 MPa; whereas the dielectric permittivity (ɛ′) is slightly lower than the pristine NR or the NR compounded with high content of BaTiO3 nanoparticles. The dielectric study revealed the presence of two dielectric relaxation modes: (i) glass to rubber transition (α-relaxation) and (ii) interfacial polarization (IP), known as Maxwell−Wagner−Sillars (MWS) polarization. The comparison between small concentrations of non-functionalized and functionalized BaTiO3 inside NR polymeric films lead to the conclusion that the dielectric breakdown strength is high for non-functionalized fillers, supposedly due to less IP polarization phenomena.

Evidence of both unusual dielectric mode at low frequencies and the co-existence of antiferroelectric, ferroelectric and paraelectric phases in a novel antiferroelectric liquid crystals mixture

The dynamics of different collective and non-collective relaxation processes were investigated in a new mixture which displays ferroelectric and antiferroelectric properties by dielectric spectroscopy. The experimental data, collected in function of frequency, temperature and under bias filed, were analyzed using a generalized Havriliak-Negami expression, leading to many dielectric relaxation modes. The results obtained through the dielectric spectroscopy and optical microscopy suggest a coexistence of different phases and hereditary dielectric peaks. A deep penetration of the Goldstone mode also occurs during isotropic phase.