Theoretical Study Of The Negative Thermal Expansion And Regulatoin In Several Typical Materials

Most materials show normal thermal expansion properties on heating.So,the abnormal property-negative thermal expansion?NTE?-has attracted considerable attentions because of the rarity of the phenomenon and intriguing properties of NTE.Although the total numbers of NTE materials increase due to the persistent studying of the NTE and several mechanisms have already been proposed to explain this interesting property,however,the nature of NTE is complicated and remains challenging since it is entangled with some factors like magnetic transitions and Ferro-electricity,changes of the electronic configuration,etc.So more NTE materials need to be proposed and explored,and to reveal the negative thermal expansion mechanism.The theoretical simulation can reveal the property of the bonding,bonds strength and magnetism as well as electric polarization,so can comprehensively and reasonably explain the mechanism of NTE.But the theoretical simulation reports have been reported are less.In this work,using density functional first principles calculations combined with QHA,we intensively studied the mechanism in two NTE materials and predicted two types' new NTE materials.The obtained main results are given as follows.1)Generally speaking,the NTE of most open framework structures attributes to the transverse vibrations of non-metal?light?atoms,such as the bridge Oxygen atoms of metal oxides,bridge Fluorine atoms of ScF₃,the CN group of cyanides etc.While the NTE originating from the transverse vibrations of heavy metal atoms are seldom reported,the 2H CuScO₂ is such a case.By using the first-principles calculations,we found that 2H CuScO₂ show negative thermal expansion properties both along c axis and in volume.The low energy vibrational modes of 2H CuScO₂ show frequency softening phenomenon under compressive pressure but hardening phenomenon under tensile stress along c axis,while the high energy modes show the transverse phenomenon.The calculation show that the low frequency modes of E2 u,E2g and E1 u have the larger negative Grüneisen parameters and contribute mainly to the NTE.Although the vibrations of atoms in these three modes are different,these modes all lead to a contraction of 2H CuScO₂ parallel to the c axis.The vibrations in these three modes are called tension effects.It is cooperation of transverse vibrations of O and Cu atoms or tension effects that contribute to the NTE of 2H CuScO₂.2)KHgAs and KHgSb have been confirmed to be the “hourglass fermions” materials due to the hourglass-shaped dispersion relation.We all know that some layered compounds showed NTE only in the plane and almost all layered compounds show positive thermal expansion in the volume.But the hourglass fermions materials KHgX?X= As,Sb?show the different thermal expansion property.Based on the calculation,KHgAs and KHgSb not only show NTE in the plane but also in the volume.The ZA mode and the low energy optical modes have bigger negative Grüneisen parameters.It is the membrane and tension effects that contribute to the NTE.We find that NTE in volume relate closely to the metal plane in layered KHgAs and KHgSb.The intervening metal layers not only enlarge the distance between adjacent honeycomb layers,but also sufficiently screen the forces of the honeycomb layers.This may reduce an expansion perpendicular to the layer when the honeycomb layer contracted,leading to a volumetric NTE in KHgSb.Due to the Hg-As bond is stronger than the Hg-Sb bond,leading to a larger NTE in KHgSb compared to KHgAs.It also found that the heavy Rb atoms suppress the vibration of HgSb perpendicular to the honeycomb layer,thus leading to a much weaker NET behavior3)ScF₃ shows huge NTE and the magnitude of NTE can be tuned by doping.Except the ScF₃,only ZnF2 and Ti F3 exhibit smaller NTE behaviors.Other mono-metal fluorides such as Ca F2 and ZrF4 only show positive thermal expansion properties.Can the bi-metal fluorides composed of mono-metal fluorides show NTE behaviors? This study show that M^?X^?F₆?M = Mg,Ca,Sr,X = Zr,Hf?all display NTE behaviors,and the magnitudes of NTE increase with the atom number of both M and X.The calculations are in agreement with the experiment results,and the coefficients of NTE of SrHfF6 can reach up to 27×10-6K-1 which is almost as three times larger as that of the star NTE materials ZrW2O8.Through the calculation,we find that the lowest optical modes at the X and ? points in the Brillouin zone have the bigger negative Grüneisen parameters.Through the analysis of vibrational modes,the modes with negative Grüneisen parameters are the transverse vibration of fluorides;it is the cooperation of the two vibration lead to the NTE of M^?X^?F₆.With the increasing of the atoms number of both M and X atoms,the difference between the vibration frequency of X and ? points in the Brillouin zone decreases.SrHfF6 can resonate due to almost same frequency at X and ? points,so the NTE can reach the biggest magnitude.4)Due to the simple structure and the NTE properties,ReO₃ and ScF₃ are frequently cited in the introduction part of the works about NTE.Besides ReO₃ and ScF₃,there is no case in such simple structure showing NTE.The interest changes to the anti-ReO₃ struture,and the Li₃ N is the only case that has been reported using the density functional theory,but the NTE mechanism is not clear up to now.The thermodynamic property has been studied by using the first-principles calculations.It is interesting that the bulk modular of Li₃ N decreases with the temperature increasing.Li₃ N shows NTE in the temperature range of 0-300 K.The low energy optical modes and the phonon density of state show frequency softening phenomenon under compressive tension indicating that they contribute mainly to the NTE.The Grüneisen parameters of Li₃ N are the same as that of ReO₃ and Sc F3,all show big negative values at M and R in the Brillouin zone.Through the analysis of vibrational modes,it is the transverse vibration of bridge Li atom leads to theNTE in Li₃ N.