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Deng et al. Microstructures 2023;3:2023044  https://dx.doi.org/10.20517/microstructures.2023.42  Page 7 of 18

               Table 1. Magnetic structures and corresponding temperature ranges in antiperovskites
                Antiperovskites     Magnetic ordering     Spin configurations     Temperature range
                Mn GaC [52]         Ferromagnetic         Collinear               163.9 K < T < 248 K
                  3
                                    intermediate                                  160.1 K < T < 163.9 K
                                    antiferromagnetic                             T < 160.1 K
                     [58]                                  5g
                Mn3ZnN              Antiferromagnetic     Γ                       140 K < T < 183 K
                                                          Collinear               T < 140 K
                                                           5g
                                                               4g
                Mn NiN [54]         Antiferromagnetic     Γ  + Γ                  163 K < T < 266 K
                  3
                                                          Γ 5g                    T < 163 K
                Mn GaN [54]         Antiferromagnetic     Γ 5g                    T < 298 K
                  3
                     [54]                                  5g
                Mn AgN              Antiferromagnetic     Γ                       55 K <T < 290 K
                  3                                        5g  4g
                                                          Γ  + Γ                  T < 55 K
                Mn SnN [54]         Antiferromagnetic     Collinear               357 K < T < 475 K
                  3
                                                           5g
                                                          Γ  + Γ 4g               237 K < T< 357 K
                Mn CuN [54]         Ferrimagnetic         Non-coplanar            T < 143 K
                  3
               applications. In the past decade or so, a large number of physical properties correlated to magnetic
               structures have been reported.
               Anomalous thermal expansion in manganese-based antiperovskites
               Materials with zero thermal expansion (ZTE) and NTE behaviors have attracted widespread attention
               because of their broad applications in modern technology, such as high-precision optical instruments,
               microelectronics, aerospace devices, etc. [63-69] . A great deal of work has focused on the discovery of new
               materials and the improvement of thermal expansion properties. Nevertheless, the investigations for the
               mechanism of anomalous thermal expansion (ATE) (mainly including ZTE and NTE) are still needed. For
               ZrW O  and ScF , the mechanism associated with the soft phonon mode of the frame structure is
                      [67]
                                [68]
                   2
                     8
                               3
               adopted; moreover, the ATE behavior of the material has a strong coupling effect with other physical
                                                                                                [63]
               properties,  such  as  the  valence  state  change  in  LaCu Fe O 12 [69] , BiNiO 3 [70] , and  YbGaGe   and  the
                                                                  3
                                                                    4
               ferroelectric characteristics in PbTiO -BiFeO ; in addition, the ATE behavior emerges with magnetic
                                                       [71]
                                                       3
                                                3
                                                                                         [73]
               transitions in various materials, such as the NTE in La(Fe,Si,Co) 13 [72]  and Ca Ru Cr O  and near ZTE in
                                                                                   1−x
                                                                                       x
                                                                                2
                                                                                         4
                                     [75]
               FeNi Invar  and SrRuO . It is worth noting that although a large number of studies have shown that the
                        [74]
                                    3
               Invar effect is related to the magnetic properties of materials, an adequate understanding of this property is
               still required. Therefore, the exploration of new materials with ATE will contribute to the clarification of
               mechanisms [75-80] .
               Some manganese nitrogen compounds (such as Mn ZnN at 185 K, Mn GaN at 298 K, etc.) are accompanied
                                                           3
                                                                           3
               by a sudden change in volume during the magnetic transition, that is, the so-called magnetovolume effect.
               In 2005, Takenaka et al. reported the NTE behavior in the Ge-doped antiperovskite structure compound
               Mn Cu Ge N . For Mn CuN, the compound itself has no magnetovolume effect. Through the doping of
                           [5]
                     1-x
                         x
                  3
                                    3
               Ge, the discontinuous volume change caused by the magnetic volume effect is broadened, thereby realizing
               the regulation of the thermal expansion coefficient and temperature range of the NTE behavior. With
               increasing the doping amount of Ge, the magnetovolume effect of Mn Cu Ge N was broadened and moved
                                                                          3
                                                                                 x
                                                                             1-x
               to the high temperature region, resulting in NTE behavior near room temperature. As shown in Figure 7A
               and 7B, near room temperature, the linear expansion coefficient α of Mn Cu Ge N and Mn Cu Ge N
                                                                                                   0.5
                                                                                 0.53
                                                                                     0.47
                                                                                                3
                                                                                                       0.5
                                                                              3
                                        -6
                                           -1
                            -1
                         -6
               are -16 × 10  K  and -12 × 10  K , respectively. In order to further reduce the material cost, Takenaka et al.
               used Sn as the dopant, which is cheaper than Ge. The doping of Sn can also broaden the NTE behavior of
               antiperovskites .
                            [6]
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