The Effect of X‐Ray Irradiation on Conductivity of C and 2C Polytype TlInS₂ Ferroelectrics

Abstract

Introductionβ-TlInS 2 crystals are the wide-gap semiconductor-ferroelectrics and belong to the class of low-dimensional thallium compounds TlMX 2 (M ¼ Ga, In; X ¼ Se, S, Te). At ambient conditions, β-TlInS 2 crystals are characterized by C2/c space symmetry group of the monoclinic crystal system; unit cell parameters are a ¼ 10.90 Å, b ¼ 10.94 Å, c ¼ 15.18 Å, β ¼ 100.21 . [1] Since TlInS 2 crystals are promising materials as detectors of electromagnetic radiation, their dielectric, optical, elastic properties, and electric transport have been actively studied in numerous works. [2][3][4][5] It was found that a number of anomalies of photoconductivity, permittivity, ultrasonic wave propagation velocity, and specific heat of TlInS 2 crystals which are due to the existence of phase transitions (PTs) in them with the formation of both commensurate and incommensurate modulated structures in temperature range of 170-240 K (as also in isostructural analog TlGaSe 2 but in temperature range 100-160 K). [2,6,7] However, despite numerous experimental studies, data on the characteristics and mechanisms of PT "paraelectric-incommensurate phase (IP)" and "IP-commensurate phase (CP)" in TlInS 2 are quite contradictory. For example, according to neutron diffraction data, [8] modulation satellites in corresponding to IP are observed in temperature range of T ¼ 200-216 K with a modulation vector qðδ, δ, 0.25Þ ðδ ¼ 0.012Þ. From another hand, the X-ray diffraction data in temperature range of T ¼ 194-214 K indicate the formation of incommensurate waves with the wave vector qð∓δ, 0, AE 0.25Þ ðδ ¼ 0.04Þ as the waves of static atomic displacements. [1,9] It was suggested that the incommensurate atomic displacements occur in the a-direction of monoclinic unit cell, therefore the wavelength of incommensurability is the irrational number λ a ¼ 1=δ ¼ 22.72 : : : . According to this model, atoms with the same value of Z-coordinate are displaced in the a-b-plane by the same value, and the Z-component of displacement is characterized by λ c ¼ 4c.To explain the discrepancy between neutron and X-ray diffraction data, as well as number of other contradictions, it was suggested to take into account the existence of a number of polytypes in the β-TlInS 2 crystals-C, 2C, 4C, and 8C with the unit cell parameter c ¼ c 0 , 2c 0 , 4c 0 , 8c 0 (c 0 % 15 Å), respectively. [10,11] In particular, for TlInS 2 crystals of 2C polytype, the absence of modulation satellites of IP and CP in temperature range of 170-300 K, which points to the absence of incommensurate and commensurate modulation waves, unlike the C polytype, was demonstrated with four circle X-ray diffractometry method. [9,12] Because of these differences of the C and 2C polytypes crystal lattice dynamics, it is crucial to compare the transport characteristics of these polytypes, in particular, their