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SPECIAL TOPIC — Structures and properties of materials under high pressure
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Pressure-induced superconductivity and phase transition in PbSe and PbTe
Yuyang Jiang(江宇阳), Cuiying Pei(裴翠颖), Qi Wang(王琦), Juefei Wu(吴珏霏), Lili Zhang(张丽丽), Chao Xiong(熊超), and Yanpeng Qi(齐彦鹏)
Chin. Phys. B, 2024, 33 (
12
): 126105. DOI:
10.1088/1674-1056/ad8ecc
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324
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The IV-VI semiconducting chalcogenides are a large material family with distinct physical behavior. Here, we systematically investigate the effect of pressure on the electronic and crystal structures of PbSe and PbTe by combining high-pressure electrical transport and synchrotron x-ray diffraction (XRD) measurements. The resistivity of PbSe and PbTe changes dramatically under high pressure and a non-monotonic evolution of $\rho (T)$ is observed. Both PbSe and PbTe are found to undergo semiconductor-metal transition upon compression and show superconductivity under higher pressure. The structural evolutions from the
Fm
$\bar{3}m$ to
Pnma
phase and then to the
Pm
$\bar{3}m$ phase in PbSe are verified by the x-ray diffraction. The present findings reveal the internal correlation between the structural evolution and the physical properties in lead chalcogenides.
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Pressure-induced structural transitions and metallization in ZrSe
2
Yiping Gao(高一平), Chenchen Liu(刘晨晨), Can Tian(田灿), Chengcheng Zhu(朱程程), Xiaoli Huang(黄晓丽), and Tian Cui(崔田)
Chin. Phys. B, 2024, 33 (
12
): 126104. DOI:
10.1088/1674-1056/ad8ec9
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287
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High-pressure studies of two-dimensional materials have revealed numerous novel properties and physical mechanisms behind them. As a typical material of transition metal dichalcogenides (TMDs), ZrSe$_{2}$ exhibits high carrier mobility, rich electronic states regulated by doping, and high potential in applications at ambient pressure. However, the properties of ZrSe$_{2}$ under pressure are still not clear, especially for the structural and electrical properties. Here, we report the investigation of ZrSe$_{2}$ under pressure up to 66.5 GPa by
in-situ
x-ray diffraction, Raman, electrical transport measurements, and first-principles calculations. Two structural phase transitions occur in ZrSe$_{2}$ at 8.3 GPa and 31.5 GPa, from $P$-3$m$1 symmetry to $P$2$_{1}$/$m$ symmetry, and finally transformed into a non-layer $I$4/
mmm
symmetry structure. Pressure-induced metallic transition is observed at around 19.4 GPa in phase II which aligns well with the results of the calculation. Our work will help to improve the understanding of the evolution of the structure and electrical transport properties of two-dimensional materials.
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Design of superconducting compounds at lower pressure via intercalating
X
H
4
molecules (
X
= B, C, and N) into fcc lattices
Yue Zhao(赵玥), Sihan Liu(刘思涵), Jiao Liu(刘骄), Tingting Gu(顾婷婷), Jian Hao(郝健), Jingming Shi(石景明), Wenwen Cui(崔文文), and Yinwei Li(李印威)
Chin. Phys. B, 2024, 33 (
12
): 127101. DOI:
10.1088/1674-1056/ad7c31
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285
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Recently, many encouraging experimental advances have been achieved in ternary hydrides superconductors under high pressure. However, the extreme pressure required is indeed a challenge for practical application, which promotes a further exploration for high temperature ($T_{\rm c}$) superconductors at relatively low pressure. Herein, we performed a systematic theoretical investigation on a series of ternary hydrides with stoichiometry $AX_2$H$_8$, which is constructed by interacting molecular $X$H$_4$ ($X=$ B, C, and N) into the fcc metal $A$ lattice under low pressure of 0-150 GPa. We uncovered five compounds which are dynamically stable below 100 GPa, e.g., AcB$_2$H$_8$ (25 GPa), LaB$_2$H$_8$ (40 GPa), RbC$_2$H$_8$ (40 GPa), CsC$_2$H$_8$ (60 GPa), and SrC$_2$H$_8$ (65 GPa). Among them, AcB$_2$H$_8$, which is energetically stable above 2.5 GPa, exhibits the highest $T_{\rm c}$ of 32 K at 25 GPa. The superconductivity originates mainly from the coupling between the electron of Ac atoms and the associated low-frequency phonons, distinct from the previous typical hydrides with H-derived superconductivity. Our results shed light on the future exploration of superconductivity among ternary compounds at low pressure.
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Novel high-temperature-resistant material SbLaO
3
with superior hardness under high pressure
Haoqi Chen(陈浩琦), Haowen Jiang(姜皓文), Xuehui Jiang(姜雪辉), Jialin Wang(王佳琳), Chengyao Zhang(张铖瑶), Defang Duan(段德芳), Jing Dong(董晶), and Yanbin Ma(马艳斌)
Chin. Phys. B, 2025, 34 (
2
): 026201. DOI:
10.1088/1674-1056/ad989e
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227
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Perovskites have garnered significant attention in recent years. However, the presence of La atoms at the $B$-site in $ABX_3$ structures has not yet been observed. Under high pressure, perovskites exhibit unexpected phase transitions. In this study, we report the discovery of SbLaO$_3$ under ambient pressure, with a space group of $R3m$. Mechanical property calculations indicate that it is a brittle material, and it possesses a band gap of 4.0266 eV, classifying it as an insulator. We also investigate the phase at 300 GPa, where the space group shifts to $P2_{1}/m$. Additionally, the $P2_{1}/m$ phase of LaInO$_3$ under 300 GPa is explored.
Ab initio
molecular dynamics calculations reveal that the melting point of SbLaO$_3$ is exceptionally high. The inclusion of Sb alters the electronic structure compared with LaInO$_3$, and the Vickers hardness ($H_{\rm v}$) is estimated to reach 20.97 GPa. This research provides insights into the phase transitions of perovskites under high pressure.
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Structural and transport properties of (Mg,Fe)SiO
3
at high temperature and high pressure
Shu Huang(黄澍), Zhiyang Xiang(向志洋), Shi He(何适), Luhan Yin(尹路寒), Shihe Zhang(张时赫), Chen Chen(陈晨), Kaihua He(何开华), and Cheng Lu(卢成)
Chin. Phys. B, 2025, 34 (
3
): 036102. DOI:
10.1088/1674-1056/ada759
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225
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(Mg,Fe)SiO$_3$ is primarily located in the mantle and has a substantial impact on geophysical and geochemical processes. Here, we employ molecular dynamics simulations to investigate the structural and transport properties of (Mg,Fe)SiO$_3$ with varying iron contents at temperatures up to 5000 K and pressures up to 135 GPa. We thoroughly examine the effects of pressure, temperature, and iron content on the bond lengths, coordination numbers, viscosities, and electrical conductivities of (Mg,Fe)SiO$_3$. Our calculations indicate that the increase of pressure leads to the shortening of the O-O and Mg-O bond lengths, while the Si-O bond lengths exhibit the initial increase with pressure up to 40 GPa, after which they are almost unchanged. The coordination numbers of Si transition from four-fold to six-fold and eventually reach eight-fold coordination at 135 GPa. The enhanced pressure causes the decrease of the diffusion coefficients and the increase of the viscosities of (Mg,Fe)SiO$_3$. The increased temperatures slightly decrease the coordination numbers and viscosities, as well as obviously increase the diffusion coefficients and electrical conductivities of (Mg,Fe)SiO$_3$. Additionally, iron doping facilitates the diffusion of Si and O, reduces the viscosities, and enhances the electrical conductivities of (Mg,Fe)SiO$_3$. These findings advance fundamental understanding of the structural and transport properties of (Mg,Fe)SiO$_3$ under high temperature and high pressure, which provide novel insights for unraveling the complexities of geological processes within the Earth's mantle.
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Exploring Lifshitz transition and superconductivity in 3R-NbS
2
under pressure
Kun Chen(陈坤), Xindeng Lv(吕心邓), Simin Li(李思敏), Yanping Huang(黄艳萍), and Tian Cui(崔田)
Chin. Phys. B, 2025, 34 (
3
): 037403. DOI:
10.1088/1674-1056/adacd2
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194
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The interplay between electronic topological phase transitions and superconductivity in the field of condensed matter physics has consistently captivated researchers. Here we have succeeded in modulating the Lifshitz transition by pressure and realized superconductivity. At 25.7 GPa, superconductivity with a transition temperature of 1.9 K has been observed in 3R-NbS$_{2}$. The Hall coefficient changes from negative to positive at 14 GPa, indicating a Lifshitz transition in 3R-NbS$_{2}$, and the carrier concentration continues to increase with increasing pressure. X-ray diffraction results indicate that the appearance of superconductivity cannot be attributable to structural transitions. Based on theoretical calculations, the emergence of a new band is attributed to the Lifshitz transition and the new band coincides with the Fermi surface at the pressure of 30 GPa. These findings provide new insights into the relationship between the Lifshitz transition and superconductivity.
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First-principles insights into the high-pressure stability and electronic characteristics of molybdenum nitride
Tao Wang(王涛), Ming-Hong Wen(温铭洪), Xin-Xin Zhang(张新欣), Wei-Hua Wang(王伟华), Jia-Mei Liu(刘佳美), Xu-Ying Wang(王旭颖), and Pei-Fang Li(李培芳)
Chin. Phys. B, 2025, 34 (
3
): 036104. DOI:
10.1088/1674-1056/adab66
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200
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Molybdenum nitride, renowned for its exceptional physical and chemical properties, has garnered extensive attention and research interest. In this study, we employed first-principles calculations and the CALYPSO structure prediction method to conduct a comprehensive analysis of the crystal structures and electronic properties of molybdenum nitride (Mo$_{x}$N$_{1-x}$) under high pressure. We discovered two novel high-pressure phases:
Imm
2-MoN$_{3}$ and
Cmmm
-MoN$_{4}$, and confirmed their stability through the analysis of elastic constants and phonon dispersion curves. Notably, the MoN$_{4}$ phase, with its high Vickers hardness of 36.9 GPa, demonstrates potential as a hard material. The results of this study have broadened the range of known high-pressure phases of molybdenum nitride, providing the groundwork for future theoretical and experimental researches.
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Insights to unusual antiferromagnetic behavior and exchange coupling interactions in Mn
23
C
6
Ze-Kun Yu(于泽坤), Chao Zhou(周超), Kuo Bao(包括), Zhao-Qing Wang(王兆卿), En-Xuan Li(李恩萱), Jin-Ming Zhu(朱金铭), Yuan Qin(秦源), Yu-Han Meng(孟钰涵), Pin-Wen Zhu(朱品文), Qiang Tao(陶强), and Tian Cui(崔田)
Chin. Phys. B, 2025, 34 (
3
): 037101. DOI:
10.1088/1674-1056/adaadd
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184
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We report the structural, mechanical and electromagnetic properties of the intermetallic compound Mn$_{23}$C$_{6}$. The bulk Mn$_{23}$C$_{6}$ sample was synthesized using high temperature high pressure quenching method (HTHPQM), and investigated in detail by x-ray diffraction, electron microscope, magnetization and electrical resistivity measurements, etc. First-principles calculation based on density functional theory
ab intio
simulation was carried out to calculate the bonding and electromagnetic properties of Mn$_{23}$C$_{6}$. Based on our experimental and simulated results, the Mn$_{23}$C$_{6}$ in this work is single phase of a faced-centered cubic structure with space group
Fm
-3$m$ (No. 225). Determined by SEM and TEM, the bulk sample consists of monocrystal Mn$_{23}$C$_{6}$ crystals with 2-15 μm grain sizes, it is the quick quenching method in the synthesizing process that brings such small crystal grain size. Archimedes method gives its density of 7.14 g/cm$^{3}$, 95.74% of its theoretically calculated density 7.458 g/cm$^{3}$. Owing to the abundant Mn 3d electrons and a framework of strongly linked Mn atoms in Mn$_{23}$C$_{6}$, the electrical conductivity is up to $8.47\times 10^{-4}$ $\Omega \cdot $m, which shows that Mn$_{23}$C$_{6}$ is a good conductor. Our magnetic susceptibility analyses reveal a magnetization peak in the $M$-$T$ curve at 104 K, combined with the $M$-$H$ curve and Curie-Weiss law, this peak usually means the transformation between paramagnetic and antiferromagnetic orders. To gain an insight into the mechanism of the magnetic phase transition, we calculated the magnetic properties, and the results show that different from normal antiferromagnetic order, the magnetic orders in Mn$_{23}$C$_{6}$ consist of three parts, the direct ferromagnetic and antiferromagnetic exchange coupling interactions between Mn atoms, and the indirect antiferromagnetic super-exchange interaction between Mn and C atoms. Therefore, we reveal that the Mn$_{23}$C$_{6}$ is a complex magnetic competition system including different magnetic orders and interactions, instead of the normal long-range antiferromagnetic order.
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Pressure-promoted ligand to metal energy transfer for emission enhancement of [Tb
2
(BDC)
3
(DMF)
2
(H
2
O)
2
]
n
metal-organic framework
Yunfeng Yang(杨云峰), Kaiyan Yuan(袁开岩), Binhao Yang(杨斌豪), Qing Yang(杨青), Yixuan Wang(王艺璇), and Xinyi Yang(杨新一)§
Chin. Phys. B, 2025, 34 (
3
): 036101. DOI:
10.1088/1674-1056/ada755
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161
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Lanthanide metal-organic frameworks (Ln-MOFs) have received extensive attention in the development of photoluminescent (PL) materials due to their stable structures and unique line-like emission spectroscopic properties. However, in order to prepare Ln-MOFs with high PL quantum yield (PLQY), further improving the sensitization efficiency of the "antenna effect" is essential. Herein, remarkably enhanced PL in [Tb$_{2}$(BDC)$_{3}$(DMF)$_{2}$(H$_{2}$O)$_{2}$]$_{n}$ MOF is successfully achieved via high-pressure engineering at room temperature. Notably, the PL intensity continues to increase as the pressure increases, reaching its peak at 12.0 GPa, which is 4.4 times that of the initial state. Detailed experimental and theoretical calculations have demonstrated that pressure engineering significantly narrows the bandgap of [Tb$_{2}$(BDC)$_{3}$(DMF)$_{2}$(H$_{2}$O)$_{2}$]$_{n}$, optimizing both singlet and triplet energy levels. Ultimately, higher antenna effect sensitization efficiency is achieved by promoting intersystem crossing and energy transfer processes. Our work provides a promising strategy for the development of high PLQY Ln-MOFs.
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Exploring superconductivity in dynamically stable carbon-boron clathrates trapping molecular hydrogen
Akinwumi Akinpelu, Mangladeep Bhullar, Timothy A. Strobel, and Yansun Yao
Chin. Phys. B, 2025, 34 (
3
): 036103. DOI:
10.1088/1674-1056/ada757
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170
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The recent discovery of type-VII boron-carbon clathrates with calculated superconducting transition temperatures approaching $\sim 100 $ K has sparked interest in exploring new conventional superconductors that may be stabilized at ambient pressure. The electronic structure of the clathrate is highly tunable based on the ability to substitute different metal atoms within the cages, which may also be large enough to host small molecules. Here we introduce molecular hydrogen (H$_{2}$) within the clathrate cages and investigate its impact on electron-phonon coupling interactions and the superconducting transition temperature ($T_{\rm c}$). Our approach involves combining molecular hydrogen with the new diamond-like covalent framework, resulting in a hydrogen-encapsulated clathrate, (H$_{2}$)B$_{3}$C$_{3}$. A notable characteristic of (H$_{2}$)B$_{3}$C$_{3}$ is the dynamic behavior of the H$_{2}$ molecules, which exhibit nearly free rotations within the B-C cages, resulting in a dynamic structure that remains cubic on average. The static structure of (H$_{2}$)B$_{3}$C$_{3}$ (a snapshot in its dynamic trajectory) is calculated to be dynamically stable at ambient and low pressures. Topological analysis of the electron density reveals weak van der Waals interactions between molecular hydrogen and the B-C cages, marginally influencing the electronic structure of the material. The electron count and electronic structure calculations indicate that (H$_{2}$)B$_{3}$C$_{3}$ is a hole conductor, in which H$_{2}$ molecules donate a portion of their valence electron density to the metallic cage framework. Electron-phonon coupling calculation using the Migdal-Eliashberg theory predicts that (H$_{2}$)B$_{3}$C$_{3}$ possesses a $T_{\rm c}$ of 46 K under ambient pressure. These results indicate potential for additional light-element substitutions within the type-VII clathrate framework and suggest the possibility of molecular hydrogen as a new approach to optimizing the electronic structures of this new class of superconducting materials.
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Strain rate effects on pressure-induced amorphous-to-amorphous transformation in fused silica
Wenhao Song(宋文豪), Bo Gan(甘波), Dongxiao Liu(刘东晓), Jie Wu(吴杰), Martin T. Dove, and Youjun Zhang(张友君)
Chin. Phys. B, 2025, 34 (
4
): 046101. DOI:
10.1088/1674-1056/adb38f
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207
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Fused silica (SiO$_2$ glass), a key amorphous component of Earth's silicate minerals, undergoes coordination and phase transformations under high pressure. Although extensive studies have been conducted, discrepancies between theoretical and experimental studies remain, particularly regarding strain rate effects during compression. Here, we examine strain rate influences on the shock-induced amorphous-amorphous phase transitions in fused silica by measuring its Hugoniot equation of state and longitudinal sound velocity ($C_{\rm L}$) up to 7 GPa at strain rates of 10$^6$-10$^7$ s$^{-1}$ using a one-stage light-gas gun. A discontinuity in the relationship between shock velocity ($U_{\rm S}$) and particle velocity ($U_{\rm P}$) and a significant softening in $C_{\rm L}$ of fused silica were observed near $\sim 5 $ GPa under shock loading. Our results indicate that high strain rates restrict Si-O-Si rotation in fused silica, modifying their bonds and increasing silicon coordination. The transition pressure by shock compression is significantly higher than that under static high-pressure conditions (2-3 GPa), which agrees with some recent theoretical predictions with high compression rates, reflecting the greater pressure needed to overcome energy barriers with the strain rate increase. These findings offer insights into strain rate-dependent phase transitions in fused silica and other silicate minerals (e.g., quartz, olivine, and forsterite), bridging gaps between theoretical simulations and experiments.
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Well defined phase boundaries and superconductivity with high
T
c
in PbSe single crystal
Jiawei Hu(胡佳玮), Yanghao Meng(孟养浩), He Zhang(张赫), Wei Zhong(钟韦), Hang Zhai(翟航), Xiaohui Yu(于晓辉), Binbin Yue(岳彬彬), and Fang Hong(洪芳)
Chin. Phys. B, 2025, 34 (
4
): 046102. DOI:
10.1088/1674-1056/adb272
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180
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Lead chalcogenides represent a significant class of materials that exhibit intriguing physical phenomena, including remarkable thermoelectric properties and superconductivity. In this study, we present a comprehensive investigation on the superconductivity of PbSe single crystal under high pressure. The signature of superconducting (SC) transition starts to appear at 7.2 K under 16.5 GPa. Upon further compression, the SC temperature ($T_{\rm c}$) decreases, and it is reduced to 3.5 K at 45.0 GPa. The negative pressure dependent behavior of $T_{\rm c}$ is consistent with the trend of $T_{\rm c}$-$P$ relations observed in other lead chalcogenides. The highest $T_{\rm c}$ is 8.0 K observed at 20.5 GPa during decompression process, which is also the highest record among all other PbSe derivatives, such as doped samples, superlattices, and so on. The phase boundaries of the structural and electronic transitions are well defined by Raman spectroscopy, and then phase diagrams are plotted for both compression and decompression processes. This work corrects the previous claim of positive pressure dependence of $T_{\rm c}$ in PbSe and provides clear phase diagrams for intrinsic superconductivity in PbSe under pressure.
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Robustness of ferromagnetism in van der Waals magnet Fe
3
GeTe
2
to hydrostatic pressure
Yonglin Wang(王涌霖), Xu-Tao Zeng(曾旭涛), Bo Li(李博), Cheng Su(宿程), Takanori Hattori, Xian-Lei Sheng(胜献雷), and Wentao Jin(金文涛)
Chin. Phys. B, 2025, 34 (
4
): 046203. DOI:
10.1088/1674-1056/adb26f
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175
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Two-dimensional van der Waals ferromagnet Fe$_3$GeTe$_2$ (FGT) holds a great potential for applications in spintronic devices due to its high Curie temperature, easy tunability, and excellent structural stability in air. Theoretical studies have shown that pressure, as an external parameter, significantly affects its ferromagnetic properties. In this study, we have performed comprehensive high-pressure neutron powder diffraction (NPD) experiments on FGT up to 5 GPa to investigate the evolution of its structural and magnetic properties with hydrostatic pressure. The NPD data clearly reveal the robustness of the ferromagnetism in FGT, despite of an apparent suppression by hydrostatic pressure. As the pressure increases from 0 to 5 GPa, the Curie temperature is found to decrease monotonically from 225(5) K to 175(5) K, together with a dramatically suppressed ordered moment of Fe, which is well supported by the first-principles calculations. Although no pressure-driven structural phase transition is observed up to 5 GPa, quantitative analysis on the changes of bond lengths and bond angles indicates a significant modification of the exchange interactions, which accounts for the pressure-induced suppression of the ferromagnetism in FGT.
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Pressure-driven crystal structure evolution in RbB
2
C
4
compounds
Jinyu Liu(刘金禹), Ailing Liu(刘爱玲), Yujia Wang(王雨佳), Lili Gao(高丽丽), Xiangyi Luo(罗香怡), and Miao Zhang(张淼)
Chin. Phys. B, 2025, 34 (
4
): 046201. DOI:
10.1088/1674-1056/adb271
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108
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As an extreme physical condition, high pressure serves as a potent means to substantially modify the interatomic distances and bonding patterns within condensed matter, thereby enabling the macroscopic manipulation of material properties. We employed the CALYPSO method to predict the stable structures of RbB$_{2}$C$_{4}$ across the pressure range from 0 GPa to 100 GPa and investigated its physical properties through first-principles calculations. Specially, we found four novel structures, namely, $P$6$_{3}$/
mcm
-,
Amm
2-, $P$1-, and $I$4/
mmm
-RbB$_{2}$C$_{4}$. Under pressure conditions, electronic structure calculations reveal that all of them exhibit metallic characteristics. The calculation results of formation enthalpy show that the $P$6$_{3}$/
mcm
structure can be synthesized within the pressure range of 0-40 GPa. Specially, the
Amm
2, $P1$, and $I$4/
mmm
structures can be synthesized above 4 GPa, 6 GPa, 10 GPa, respectively. Moreover, the estimated Vickers hardness value of $I$4/
mmm
-RbB$_{2}$C$_{4}$ compound is 47 GPa, suggesting that it is a superhard material. Interestingly, this study uncovers the continuous transformation of the crystal structure of RbB$_{2}$C$_{4}$ from a layered configuration to folded and tubular forms, ultimately attaining a stabilized cage-like structure under the pressure span of 0-100 GPa. The application of pressure offers a formidable impetus for the advancement and innovation in condensed matter physics, facilitating the exploration of novel states and functions of matter.
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Stoichiometric change and solid decomposition in Ca-S compounds under high pressure
Yang Lv(吕阳), Jian-Fu Li(李建福), Zhao-Bin Zhang(张钊彬), Yong Liu(刘勇), Jia-Nan Yuan(袁嘉男), Jia-Ni Lin(林佳妮), and Xiao-Li Wang(王晓丽)
Chin. Phys. B, 2025, 34 (
4
): 046202. DOI:
10.1088/1674-1056/adb38e
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125
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As an independent thermodynamic parameter, pressure significantly influences interatomic distances, leading to an increase in material density. In this work, we employ the CALYPSO structure search and density functional theory calculations to explore the structural phase transitions and electronic properties of calcium-sulfur compounds (Ca$_{x}$S$_{1-x}$, where $x = 1/4$, 1/3, 1/2, 2/3, 3/4, 4/5) under 0-1200 GPa. The calculated formation enthalpies suggest that Ca$_{x}$S$_{1-x}$ compounds undergo multiple phase transitions and eventually decompose into elemental Ca and S, challenging the traditional view that pressure stabilizes and densifies compounds. The analysis of formation enthalpy indicates that an increase in pressure leads to a rise in internal energy and the $PV$ term, resulting in thermodynamic instability. Bader charge analysis reveals that this phenomenon is attributed to a decrease in charge transfer under high pressure. The activation of Ca-3d orbitals is significantly enhanced under pressure, leading to competition with Ca-4s orbitals and S-3p orbitals. This may cause the formation enthalpy minimum on the convex hull to shift sequentially from CaS to CaS$_{3}$, then to Ca$_{3}$S and Ca$_{2}$S, and finally back to CaS. These findings provide critical insights into the behavior of alkaline-earth metal sulfides under high pressure, with implications for the synthesis and application of novel materials under extreme conditions and for understanding element distribution in planetary interiors.