Applied Innovative Research Vol. 2, September 2020, pp. 208-212 Theoretical investigation of structural phase transition and microwave dielectric properties in triglycine sulphate (TGS) crystal Muzaffar Iqbal Khan*, Pawan Singh & T C Upadhyay Department of Physics, H N B Garhwal University (A Central University) Srinagar (Garhwal) -246 174, India Received 7 September 2020 By using the extended two sublattice pseudospin coupled mode (PLCM) model by summing third-order and fourth-order anharmonic interactions as well as extra spin lattice interactions, direct spin-spin interaction and electric field terms is considered for triglycine sulphate crystal (TGS) crystal. With the help of double-time thermal dependent Green’s function method and Dyson’s equation, expressions for soft mode frequency dielectric constant and loss tangent for triglycine sulphate crystal. By fitting the model values in the theoretical expressions, thermal variations of soft mode frequency, dielectric constant and loss tangent are calculated and compare well with the experimental data of Bye et al. Keywords: Anharmonic interactions, Green function method, Triglycine sulphate Introduction Ferroelectric materials have great applications in memory devices, pyroelectric and infrared detectors, transducers, display devices, capacitors, piezoelectric devices etc. Triglycine sulphate (TGS) crystal is one of the pyroelectric materials, used as laser and transducer material and storage devices and one of the rare ferroelectrics which show isostructural phase transition. TGS received universal attention ever since Mathias et al. 1 have discovered its ferroelectric phase transition properties. The crystal structures are easily grown from aqueous water solution. It is uniaxial ferroelectric material with transition temperature 322K 1,2 . The crystal structure is monoclinic system in both polar and non-polar phases. The transition is second-order and order-disorder type ferroelectrics. Below the transition temperature    the space group of the TGS crystal is    of monoclinic structure and above the transition temperature  , it possesses the     which is centrosymmetric and thus is non- piezoelectric material 1,2 . After a transition mirror plane disappears and crystal belongs to isostructural phase transition. Triglycine sulphate crystal and its isomorphs such as TGSe, TGBe etc are very similar in their essential character to KDP-type crystal. The temperature expansion is also an important thermodynamic property of crystals, since it is a result of the interactions and excitation of their constituent elements. The spontaneous polarization arises parallel to b-axis of the monoclinic system. This b-axis cut plates of triglycine sulphate crystals are used for room temperature infrared detectors, radiation monitoring, earth exploration and astronomical telescopes. The dielectric properties, transition temperature and Curie-Weiss are not greatly affected by its deuteration showing that tunnelling effect is present in TGS crystal. Experimental explanations on TGS crystal have carried by Hoshino et al. 3 and determined the crystal structure of TGS by means of X-ray diffraction. Pasalov et al. 4 have studied the hysteresis loop measurements in TGS. Chan et al. 5 have explained the domain wall motion in triglycine sulphate crystal by using a pyroelectric probe. Sun et al. 6 have done the study of growth and pyroelectric properties of pure and doped TGS crystals. Lal and Batra 7 have studied the crystal structure growth and characterization studies on TGS crystal. Yamaguchi et al. 8 have done dilatometer studies on TGS down to cryogenic temperatures. Arago and Gonzalo 9 have studied the crystal growth and characterization of triglycine sulphate crystal. Alexandru and Berbecaru 10 have grown pure and doped triglycine sulphate crystals and studied its ferroelectric properties. Costache et al. 11 explained the pyroelectric properties of pure and doped TGS crystals. Dolino et al. 12 have done second harmonic generation studies experimentally in TGS crystal. Hill and Ichiki 13 have studied the polarization relaxation experimentally in TGS crystal. Aravazhi —————— *Corresponding author (E-mail: muzaffariqbalkhan786@gmail.com)