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The high-temperature and high-pressure response of magnesium has been investigated through shock-release experiments performed up to shock melting. The longitudinal and bulk sound speeds of Mg are reported along the Hugoniot from 25 to 56 GPa and used to determine the elastic properties and Gr\"uneisen parameter. The hexagonal close-packed (hcp)--body-centered cubic (bcc) phase transition is marked by a reduction in the determined shear wave speed. Thermal softening is observed to begin between 40 and 44 GPa, with incipient melt at 55.5 GPa, in close agreement with previous diffraction measurements under laser shock loading. Examination of the release profiles showed that two different responses were observed, depending on the peak stress. When plotted in a stress-energy phase diagram, the two responses are observed to form separate lines that intersect the static hcp-bcc phase transition and incipient melt. The results indicate that the hcp-bcc transition occurs on the Hugoniot at 28.4 GPa and place the hcp-bcc-liquid triple point \ensuremath{\sim}20 GPa. A multiphase equation of state is developed which places the melt boundary below the previously reported static measurements.

We use first principles molecular dynamics simulations coupled to the thermodynamic integration method to study the hcp-bcc transition and melting of beryllium up to a pressure of 1600~GPa. We derive the melting line by equating solid and liquid Gibbs free energies, and represent it by a Simon Glatzel fit $T_m= 1564~\text{K} (1 + P/(15.6032 ~\text{GPa}))^{0.383}$, which is in good agreement with previous two-phase simulations below 6000~K. We also derive the hcp-bcc solid-solid phase boundary and show the quasiharmonic approximation underestimates the stability of the hcp structure, predicting lower transition pressures between hcp and bcc phases. However, our results are consistent with the stability regime predicted by the phonon quasiparticle method. We also predict that hcp-bcc-liquid triple point is located at 164.7~GPa and 4314~K. In addition, we compute the shock Hugoniot curve, and show that it is in good agreement with experiments, intersecting our derived melting curve at $\sim$235~GPa at 4900~K. Finally, we show that an isentropic compression path that intersects the melting curve at both low and high temperature in the liquid regime, can reappear in the solid after a gap as large as 7000~K. Therefore, we predict that a large section of the melting curve could be sampled, in principle, by a ramp compression experiment, where solid and liquid Be would coexist as the sample is compressed., Comment: 15 pages, 13 figures

We study a class of topological materials which in their momentum-space band structure exhibit threefold degeneracies known as triple points. Focusing specifically on PT-symmetric crystalline solids with negligible spin-orbit coupling, we find that such triple points can be stabilized by little groups containing a three-, four-, or sixfold rotation axis, and we develop a classification of all possible triple points as type A vs type B according to the absence vs presence of attached nodal-line arcs. Furthermore, by employing the recently discovered non-Abelian band topology, we argue that a rotation-symmetry-breaking strain transforms type-A triple points into multiband nodal links. Although multiband nodal-line compositions were previously theoretically conceived and related to topological monopole charges, a practical condensed-matter platform for their manipulation and inspection has hitherto been missing. By reviewing the known triple-point materials with weak spin-orbit coupling and by performing first-principles calculations to predict new ones, we identify suitable candidates for the realization of multiband nodal links in applied strain. In particular, we report that an ideal compound to study this phenomenon is Li2NaN, in which the conversion of triple points to multiband nodal links facilitates a largely tunable density of states and optical conductivity with doping and strain, respectively., Physical Review B, 103 (12), ISSN:1098-0121, ISSN:0163-1829, ISSN:1550-235X, ISSN:0556-2805, ISSN:2469-9969, ISSN:1095-3795, ISSN:2469-9950

We report the discovery of a codimension-two phenomenon in the phase diagram of a second-order self-sustained nonlinear oscillator subject to a constant external periodic forcing, around which three regimes associated with the synchronization phenomenon exist, namely phase-locking, frequency-locking without phase-locking, and frequency-unlocking states. The triple point of synchronization arises when a saddle-node homoclinic cycle collides with the zero-amplitude state of the forced oscillator. A line on the phase diagram where limit-cycle solutions contain a phase singularity departs from the triple point, giving rise to a codimension-one transition between the regimes of frequency unlocking and frequency locking without phase locking. At the parameter values where the critical transition occurs, the forced oscillator exhibits a separatrix with a $\ensuremath{\pi}$ phase jump, i.e., a particular trajectory in phase space that separates two distinct behaviors of the phase dynamics. Close to the triple point, noise induces excitable pulses where the two variants of type-I excitability, i.e., pulses with and without $2\ensuremath{\pi}$ phase slips, appear stochastically. The impacts of weak noise and some other dynamical aspects associated with the transition induced by the singular phenomenon are also discussed.

Evolution of magnetism in single crystals of the van der Waals compound $\mathrm{V}{\mathrm{I}}_{3}$ in external pressure up to 7.3 GPa studied by measuring magnetization and ac magnetic susceptibility is reported. Four magnetic phase transitions, at ${T}_{1}=54.5\phantom{\rule{0.16em}{0ex}}\mathrm{K}, {T}_{2}=53\phantom{\rule{0.16em}{0ex}}\mathrm{K}, {T}_{\mathrm{C}}=49.5\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, and ${T}_{\mathrm{FM}}=26\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, respectively, have been observed at ambient pressure. The first two have been attributed to the onset of ferromagnetism in specific crystal-surface layers. The bulk ferromagnetism is characterized by the magnetic ordering transition at Curie temperature ${T}_{\mathrm{C}}$ and the transition between two different ferromagnetic phases ${T}_{\mathrm{FM}}$, accompanied by a structure transition from monoclinic to triclinic symmetry upon cooling. The pressure effects on magnetic parameters were studied with three independent techniques. ${T}_{\mathrm{C}}$ was found to be almost unaffected by pressures up to 0.6 GPa whereas ${T}_{\mathrm{FM}}$ increases rapidly with increasing pressure and reaches ${T}_{\mathrm{C}}$ at a triple point at \ensuremath{\approx} 0.85 GPa. At higher pressures, only one magnetic phase transition is observed moving to higher temperatures with increasing pressure to reach 99 K at 7.3 GPa. In contrast, the low-temperature bulk magnetization is significantly reduced by applying pressure (by more than 50% at 2.5 GPa) suggesting a possible pressure-induced reduction of vanadium magnetic moment. First-principles calculations of $\mathrm{V}{\mathrm{I}}_{3}$ under pressure allow us to ascribe the evolution of ${T}_{\mathrm{C}}$ with pressure to the reduction of interplanar distance, including the observed slope change at 0.6 GPa. These calculations also describe the associated band gap closing, showing that with a modest compression the material would become metallic. Overall, the large pressure range covered corresponds to a significant change of interplanar interactions. The obtained data thus allow us to shed light on how does the transition between the three-dimensional (3D) and quasi-2D system affect magnetic interactions in the system.

Tricritical phenomenon appearing in multiple phases is a fundamental and attractive issue in condensed-matter physics. Monopnictide DySb, a candidate for potential magnetic topological semimetal with an antiferromagnetic ground state, has been found to possess complex and intriguing field-induced magnetic phase transitions. In this work, critical behaviors of single-crystal DySb are investigated systematically, which generate a series of critical exponents including $\ensuremath{\beta}=0.244(2)$, $\ensuremath{\gamma}=0.827(2)$, and $\ensuremath{\delta}=4.425(1)$ for $H\ensuremath{\parallel}[001]$. The deduced critical exponents verified by Widom law and scaling equations are close to a tricritical mean-field model, suggesting a field-induced tricritical phenomenon in DySb. Based on the universality principle, a detailed $H\text{\ensuremath{-}}T$ phase diagram around the phase transition is constructed for $H\ensuremath{\parallel}[001]$, in which a tricritical point is revealed at temperature and field of (7.5 K, 51.4 kOe) on intersected boundaries of antiferromagnetic, forced ferromagnetic, and paramagnetic phases. Moreover, a triple point is found at the intersection (9.2 K, 19.7 kOe) of paramagnetic and two kinds of antiferromagnetic states. Such a fascinating phase diagram is indicative of delicate competition and balance between multiple magnetic interactions in this system, and lays a solid foundation for future research in topological transition and criticality.

With density functional molecular dynamics simulations, we computed the phase diagram of MgO from 50 to 2000 GPa up to 20 000 K. Via thermodynamic integration (TDI), we derive the Gibbs free energies of the B1, B2, and liquid phases and determine their phase boundaries. With TDI and a pseudo-quasi-harmonic approach, we show that anharmonic effects are important and stabilize the B1 phase in particular. As a result, the B1-B2 transition boundary in the pressure-temperature plane exhibits a steep slope. We predict the B1-B2-liquid triple point to occur at approximately $T=10000\text{ }\text{ }\mathrm{K}$ and $P=370\text{ }\text{ }\mathrm{GPa}$, which is higher in pressure than was inferred with quasiharmonic methods alone. We predict the principal shock Hugoniot curve to enter the B2 phase stability domain but only over a very small range of parameters. This may render it difficult to observe this phase with shock experiments because of kinetic effects.

Materials with tunable topological features, simple crystal structure, and flexible synthesis are in extraordinary demand towards the technological exploitation of unique properties of topological nodal points. The controlled design of the lattice geometry of light elements is determined by utilizing density functional theory and the effective Hamiltonian model together with the symmetry analysis. This provides an intriguing venue for reasonably achieving various distinct types of novel fermions. We, therefore, show that a nodal line (types I and II), Dirac fermion, and triple point fermionic excitation can potentially appear as a direct result of a band inversion in group-I nitrides with $\ensuremath{\alpha}\ensuremath{-}{\mathrm{Li}}_{3}\mathrm{N}$-type crystal structure. The imposed strain is exclusively significant for these compounds, and it invariably leads to the considerable modification of the nodal line type. Most importantly, a type-II nodal loop can be realized in the system under strain. These unique characteristics make $\ensuremath{\alpha}\ensuremath{-}{\mathrm{Li}}_{3}\mathrm{N}$-type crystal structure an ideal playground to achieve various types of novel fermions well-suited for technological applications.

We develop a phenomenological mean-field theory describing the hidden-order phase in $\mathrm{U}{\mathrm{Ru}}_{2}{\mathrm{Si}}_{2}$ as a nematic of the ${B}_{1g}$ representation staggered along the $c$ axis. Several experimental features are reproduced by this theory: the topology of the temperature-pressure phase diagram, the response of the elastic modulus $({C}_{11}\ensuremath{-}{C}_{12})/2$ above the transition at ambient pressure, and orthorhombic symmetry breaking in the high-pressure antiferromagnetic phase. In this scenario, hidden order is characterized by broken rotational symmetry that is modulated along the $c$ axis, the primary order of the high-pressure phase is an unmodulated nematic, and the triple point joining those two phases with the high-temperature paramagnetic phase is a Lifshitz point.

The dynamic evolution of a highly underexpanded transient supersonic jet at the exit of a pulse detonation engine is investigated via high-resolution time-resolved schlieren and numerical simulations. Experimental evidence is provided for the presence of a second triple shock configuration along with a shocklet between the reflected shock and the slipstream, which has no analogue in a steady-state underexpanded jet. A pseudo-steady model is developed, which allows for the determination of the post-shock flow condition for a transient propagating oblique shock. This model is applied to the numerical simulations to reveal the mechanism leading to the formation of the second triple point. Accordingly, the formation of the triple point is initiated by the transient motion of the reflected shock, which is induced by the convection of the vortex ring. While the vortex ring embedded shock move essentially as a translating strong oblique shock, the reflected shock is rotating towards its steady state position. This results in a pressure discontinuity that must be resolved by the formation of a shocklet.

The experimental study of the ${\mathrm{CO}}_{2}$ phase diagram is hampered by strong kinetic effects leading to wide regions of metastability and to large uncertainties in the location of some phase boundaries. Here, we determine ${\mathrm{CO}}_{2}$'s thermodynamic phase boundaries by means of ab initio calculations of the Gibbs free energy of several solid phases of ${\mathrm{CO}}_{2}$ up to 50 Gigapascals. Temperature effects are included in the quasiharmonic approximation. Contrary to previous suggestions, we find that the boundary between molecular forms and the nonmolecular phase V has, indeed, a positive slope and starts at 21.5 GPa at $T=0\text{ }\text{ }\mathrm{K}$. A triple point between phase IV, V, and the liquid phase is found at 35 GPa and 1600 K, indicating a broader region of stability for the nonmolecular form than previously thought. The experimentally determined boundary line between ${\mathrm{CO}}_{2}\text{\ensuremath{-}}\mathrm{II}$ and ${\mathrm{CO}}_{2}\text{\ensuremath{-}}\mathrm{IV}$ phases is reproduced by our calculations, indicating that kinetic effects do not play a major role in that particular transition. Our results also show that ${\mathrm{CO}}_{2}\text{\ensuremath{-}}\mathrm{III}$ is stabilized at high temperature and its stability region coincides with the $P\text{\ensuremath{-}}T$ conditions where phase VII has been reported experimentally; instead, phase II is the most stable molecular phase at low temperatures, extending its region of stability to every $P\text{\ensuremath{-}}T$ condition where phase III is reported experimentally.

We present a theoretical calculation of the pressure-temperature-field phase diagram for the vortex phases of rotating superfluid $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{B}$. Based on a strong-coupling Ginzburg-Landau functional that accounts for the relative stability of the bulk A and B phases of $^{3}\mathrm{He}$ at all pressures, we report calculations for the internal structure and free energies of distinct broken-symmetry vortices in rotating superfluid $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{B}$. Theoretical results for the equilibrium vortex phase diagram in zero field and an external field of $H=284\phantom{\rule{0.16em}{0ex}}\text{G}$ parallel to the rotation axis, $\mathbf{H}\ensuremath{\parallel}\mathbit{\ensuremath{\Omega}}$, are reported, as well as the supercooling transition line, ${T}_{\text{V}}^{*}(p,H)$. In zero field the vortex phases of $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{B}$ are separated by a first-order phase transition line ${T}_{\text{V}}(p)$ that terminates on the bulk critical line ${T}_{c}(p)$ at a triple point. The low-pressure, low-temperature phase is characterized by an array of singly quantized vortices that spontaneously breaks axial rotation symmetry, exhibits anisotropic vortex currents and an axial current anomaly (D-core phase). The high-pressure, high-temperature phase is characterized by vortices with both bulk A phase and $\ensuremath{\beta}$ phase in their cores (A-core phase). We show that this phase is metastable and supercools down to a minimum temperature, ${T}_{\text{V}}^{*}(p,H)$, below which it is globally unstable to an array of D-core vortices. For $H\ensuremath{\gtrsim}60\phantom{\rule{0.16em}{0ex}}\text{G}$ external magnetic fields aligned along the axis of rotation increase the region of stability of the A-core phase of rotating $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{B}$, opening a window of stability down to low pressures. These results are compared with the experimentally reported phase transitions in rotating $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{B}$.

Molecular hydrogen is a fascinating candidate for quantum fluid showing bosonic and fermionic superfluidity. We have studied diffusion dynamics of thin films of H$_2$, HD and D$_2$ adsorbed on a glass substrate by measurements of elasticity. The elasticity shows multiple anomalies well below bulk triple point. They are attributed to three different diffusion mechanisms of admolecules and their "freezing" into localized state: classical thermal diffusion of vacancies, quantum tunneling of vacancies, and diffusion of molecules in the uppermost surface. The surface diffusion is active down to 1 K, below which the molecules become localized. This suggests that the surface layer of hydrogen films is on the verge of quantum phase transition to superfluid state., 5 pages, 3 figures

Peculiar features exist in the stress-temperature phase stability diagram of ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$, such as a first-order phase transition between the paramagnetic insulating and metallic phases that ends with a critical point, quantum phase transition, and a triple point. These features remain largely unexplored, and the exact nature of the phase transitions is not clear due to very limited control over the stress in bulk or film samples. Here, we show the synthesis of single-crystal ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$ nanoplates using chemical vapor deposition via van der Waals epitaxy. Thickness of the ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$ nanoplates range from a few to hundreds of nanometers, and they can be mechanically exfoliated from the growth substrate. Using Raman spectroscopy on the nanoplates, we reveal that, upon heating, ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$ enters a supercritical state for both tensile strained and relaxed crystals with a similar out-of-plane response. Transmission electron microscopy on ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$ nanoplates hints at the existence of a structural change when the crystals are heated. Our results show that ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$ nanoplates should be useful for studying the physics of the supercritical state and the phase stability of ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$ to enable new horizons in applications.

We investigate phase transitions in the two-dimensional dipolar Heisenberg model with uniaxial anisotropy with a specific ratio between the exchange and dipolar constants, $\delta=1$. We obtain the $\eta$--$T$ (anisotropy vs. temperature) phase diagrams for typical values of magnetic field by a Monte Carlo method with an $O(N)$ algorithm. We find that at lower fields, the $\eta$--$T$ phase diagram consists of the planar ferromagnetic (F), (perpendicular) stripe-ordered (SO), and paramagnetic (P) phases, and is characterized by the triple point. In the SO phase realized at larger $\eta$ and smaller $T$, the SO pattern changes depending on the field. On the other hand, we find that at higher fields, the SO phase does not exist, while the planer F phase robustly remains. We study the properties of the phase boundaries by employing finite-size-scaling analyses. We find that the slope of the spin-reorientation-transition line is positive with and without field, i.e., $\frac{d\eta}{dT}>0$, which implies that the planar F phase changes to the SO phase with lowering temperature. In the phase diagrams we observe a characteristic shape of the P--planer F phase-transition line, whose maximum point of $\eta$ is located at an intermediate temperature. This structure leads to the temperature-induced reentrant transition associated with P and planar F phases, which appears in successive phase transitions with lowering temperature: P $\rightarrow$ planar F $\rightarrow$ P $\rightarrow$ SO phase at lower fields and P $\rightarrow$ planar F $\rightarrow$ P phases at higher fields., Comment: 9 pages, 14 figures

We conduct an in-depth analysis of the electroclinic effect in chiral, ferroelectric liquid crystal systems that have a first-order smectic-A^{*}-smectic-C^{*} (Sm-A^{*}-Sm-C^{*}) transition, and show that such systems can be either type I or type II. In temperature-field parameter space type-I systems exhibit a macroscopically achiral (in which the Sm-C_{M}^{*} helical superstructure is expelled) low-tilt (LT) Sm-C_{U}^{*}-high-tilt (HT) Sm-C_{U}^{*} critical point, which terminates a LT Sm-C_{U}^{*}-HT Sm-^{*}C_{U} first-order boundary. Notationally, Sm-C_{M}^{*} or Sm-C_{U}^{*} denotes the Sm-C^{*} phase with or without a modulated superstructure. This boundary extends to an achiral-chiral triple point at which the macroscopically achiral LT Sm-C_{U}^{*} and HT Sm-C_{U}^{*} phases coexist along with the chiral Sm-C_{M}^{*} phase. In type-II systems the critical point, triple point, and first-order boundary are replaced by a Sm-C_{M}^{*} region, sandwiched between LT and HT Sm-C_{U}^{*} phases, at low and high fields, respectively. Correspondingly, as the field is ramped up, the type-II system will display a reentrant Sm-C_{U}^{*}-Sm-C_{M}^{*}-Sm-C_{U}^{*} phase sequence. Moreover, discontinuity in the tilt of the optical axis at each of the two phase transitions means the type-II system is tristable, in contrast to the bistable nature of the LT Sm-C_{U}^{*}-HT Sm-C_{U}^{*} transition in type-I systems. Whether the system is type I or type II is determined by the ratio of two length scales, one of which is the zero-field Sm-C^{*} helical pitch. The other length scale depends on the size of the discontinuity (and thus the latent heat) at the zero-field first-order Sm-A^{*}-Sm-C^{*} transition. We note that this type-I vs type-II behavior in this ferroelectric smectic is the Ising universality class analog of type-I vs type-II behavior in XY universality class systems. Lastly, we make a complete mapping of the phase boundaries in all regions of temperature-field-enantiomeric-excess parameter space (not just near the critical point) and show that various interesting features are possible, including a multicritical point, tricritical points, and a doubly reentrant Sm-C_{U}^{*}-Sm-C_{M}^{*}-Sm-C_{U}^{*}-Sm-C_{M}^{*} phase sequence.

We investigate the phase diagram of lithium at temperatures of 200 to 400 K, to pressures over 100 GPa using x-ray diffraction in diamond anvil cells, covering the region in which the melting curve is disputed. To overcome degradation of the diamond anvils by dense lithium we utilize a rapid compression scheme taking advantage of the high flux available at modern synchrotrons. Our results show the $hR1$ and $cI16$ phases to be stable to higher temperature than previously reported. The melting minima of lithium is found to be close to room temperature between 40 and 60 GPa, below which the solid is crystalline. Analysis of the stability fields of the $cI16$ and $oC88$ phases suggest the existence of a triple point between these and an undetermined solid phase at 60 GPa between 220 and 255 K.

We combined laser shock compression with in situ x-ray diffraction to probe the crystallographic state of gold (Au) on its principal shock Hugoniot. Au has long been recognized as an important calibration standard in diamond anvil cell experiments due to the stability of its face-centered cubic (fcc) structure to extremely high pressures ($P\text{ }g600\text{ }\text{ }\mathrm{GPa}$ at 300 K). This is in contrast to density functional theory and first principles calculations of the high-pressure phases of Au that predict a variety of fcc-like structures with different stacking arrangements at intermediate pressures. In this Letter, we probe high-pressure and high-temperature conditions on the shock Hugoniot and observe fcc Au at 169 GPa and the first evidence of body-centered cubic (bcc) Au at 223 GPa. Upon further compression, the bcc phase is observed in coexistence with liquid scattering as the Hugoniot crosses the Au melt curve before 322 GPa. The results suggest a triple point on the Au phase diagram that lies very close to the principal shock Hugoniot near $\ensuremath{\sim}220\text{ }\text{ }\mathrm{GPa}$.

We investigate topological characteristics of the photon-dressed band structure of the $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathcal{T}}_{3}$ lattice on being driven by off-resonant circularly polarized radiation. We obtain exact analytical expressions of the quasienergy bands over the first Brillouin zone. The broken time-reversal symmetry caused by the circularly polarized light lifts the triple point degeneracy completely at both the Dirac points. The gaps become unequal at $\mathbf{K}$ and ${\mathbf{K}}^{\ensuremath{'}}$ (except at $\ensuremath{\alpha}=0$ and 1), which reveals the absence of inversion symmetry in the system. At $\ensuremath{\alpha}=1/\sqrt{2}$, the gap between the flat and valence bands closes at $\mathbf{K}$, while that between the conduction and flat bands closes at ${\mathbf{K}}^{\ensuremath{'}}$, thereby restoring a semimetalic phase. At the gap closing point ($\ensuremath{\alpha}=1/\sqrt{2}$) which is independent of the radiation amplitude, there is a reappearance of low-energy Dirac cones around $\mathbf{K}$ and ${\mathbf{K}}^{\ensuremath{'}}$ points. Under the influence of the circularly polarized radiation, the $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathcal{T}}_{3}$ lattice is transformed from semimetal to a Haldane-like Chern insulator characterized by nonzero Chern number. The system undergoes a topological phase transition from $\mathcal{C}=1(\ensuremath{-}1)$ to $\mathcal{C}=2(\ensuremath{-}2)$ at $\ensuremath{\alpha}=1/\sqrt{2}$, where $\mathcal{C}$ is the Chern number of the valence (conduction) band. This sets an example of a multiband system having larger Chern number. These results are supported by the appearance of chiral edge states in an irradiated $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathcal{T}}_{3}$ nanoribbon.

Gallium metal possesses a complex phase diagram and it has been the subject of many experimental and theoretical studies. Nevertheless, hyperfine properties of its phases requiring higher pressure beyond the liquid-I-II triple point were seldom examined. In this work, hyperfine parameters of liquid and solid gallium metal under pressure are investigated by nuclear magnetic resonance (NMR) measurements and ab initio calculations. The electric field gradient and NMR shift of the Ga-III phase are both measured and calculated and their relation to electronic structure is interpreted. Further, calculations of pressure dependencies of the hyperfine parameters of several other solid gallium phases are presented.

We investigate the hcp to bcc phase transition in beryllium (Be) at high-pressure and -temperature ($PT$) conditions. A recently developed hybrid approach that combines first-principles molecular dynamics and lattice dynamics is used to account for anharmonic contributions to the free energy. Anharmonic effects are shown to be strong at high $T$ in both hcp and bcc Be. They are stronger in hcp Be than in bcc Be, as evidenced by the larger anharmonic vibrational entropy of hcp Be. We find that anharmonicity has a significant influence on the hcp to bcc transition at high-$PT$ conditions. It substantially enlarges the stability domain of hcp Be at high $T$ compared with that calculated under the quasiharmonic approximation (QHA), as a result bringing theoretical predictions into good consistency with recent experimental observations. After considering anharmonic effects, the calculated pressure and temperature of the hcp/bcc/liquid triple point increase from about 85 to 165 GPa, and from about 3300 to 4200 K, respectively, and the predicted Clapeyron slope at the triple point takes a value of $\ensuremath{-}7.4\ifmmode\pm\else\textpm\fi{}0.7\phantom{\rule{0.28em}{0ex}}\mathrm{K}/\mathrm{GPa}$, noticeably larger in magnitude than previous QHA results in the range of $\ensuremath{-}3$ to 2 K/GPa.

X-ray powder diffraction experiments using resistively heated diamond anvil cells have been conducted in order to establish the phase behavior of antimony up to 31 GPa and 835 K. The dip in the melting curve at 5.7 GPa and 840 K is identified as the triple point between the Sb-I, incommensurate Sb-II, and liquid phases. No evidence of the previously reported simple cubic phase was observed. Determination of the phase boundary between Sb-II and Sb-III suggests the existence of a second triple point in the region of 13 GPa and 1200 K. The incommensurate composite structure of Sb-II was found to remain ordered to the highest temperatures studies-no evidence of disordering of the guest-atom chains was observed. Indeed, the modulation reflections that arise from interactions between the host and guest subsystems were found to be present to the highest temperatures, suggesting such interactions remain relatively strong in Sb even in the presence of increased thermal motion. Finally, we show that the incommensurately modulated structure recently reported as giving an improved fit to diffraction data from incommensurate Ba-IV can be rejected as the structure of Sb-II using a simple density argument.

Based on first-principles calculations and effective model analysis, a Dirac nodal-net semimetal state is recognized in ${\mathrm{AlB}}_{2}$-type ${\mathrm{TiB}}_{2}$ and ${\mathrm{ZrB}}_{2}$ when spin-orbit coupling (SOC) is ignored. Taking ${\mathrm{TiB}}_{2}$ as an example, several topological novel states have been found in this nodal-net structure including triple point, nexus, and nodal link, which are protected by the coexistence of spatial-inversion symmetry and time-reversal symmetry. In addition, linearly and quadratically dispersed two-dimensional surface Dirac points have been identified as getting on the B-terminated and Ti-terminated (001) surfaces of ${\mathrm{TiB}}_{2}$, respectively, which are analogous to those of monolayer and bilayer graphene.

In low-temperature metallic magnets, ferromagnetic (FM) and antiferromagnetic (AFM) orders can exist in a single system in different parts of the phase diagram as a function of some control parameter. These phases can be adjacent, or exist concurrently, resulting in a phase transition between a FM phase and an AFM one, or between a phase of concurrent FM and AFM order and either of the pure phases. We show that universal quantum fluctuations qualitatively alter the known phase diagrams for classical magnets: They shrink the region of concurrent FM and AFM order, change various transitions from second to first order, and, in the presence of a magnetic field, lead to either a quantum triple point where the FM, AFM and paramagnetic phases coexist, or to a quantum critical end point., 5pp, 4 figs

At the triple point of a repulsive screened Coulomb system, a face-centered-cubic (fcc) crystal, a body-centered-cubic (bcc) crystal and a fluid phase coexist. At their intersection, these three phases form a liquid groove, the triple junction. Using confocal microscopy, we resolve the triple junction on a single particle level in a model system of charged PMMA colloids in a nonpolar solvent. The groove is found to be extremely deep and the incommensurate solid-solid interface to be very broad. Thermal fluctuations hence appear to dominate the solid-solid interface. This indicates a very low interfacial energy. The fcc-bcc interfacial energy is quantitatively determined based on Young's equation and, indeed, it is only about 1.3 times higher than the fcc-fluid interfacial energy close to the triple point.

The phase diagram of the spin-1 chain with bilinear-biquadratic and next-nearest neighbor inter- actions, recently investigated by Pixley, Shashi and Nevidomskyy [Phys. Rev. B 90, 214426 (2014)], has been revisited in the light of results we have recently obtained on a similar model. Combining extensive Density Matrix Renormalization Group (DMRG) simulations with conformal-field theory arguments, we confirm the presence of the three phases identified by Pixley et al, a Haldane phase, a next-nearest neighbor (NNN) Haldane phase, and a dimerized phase, but we come to significantly different conclusions regarding the nature of the phase transitions to the dimerized phase: i) We provide numerical evidence of a continuous Ising transition between the NNN-Haldane phase and the dimerized phase; ii) We show that the tri-critical end point, where the continuous transition between the Haldane phase and the dimerized phase turns into a first order transition, is distinct from the triple point where the three phases meet; iii) Finally, we demonstrate that the tri-critical end point is in the same Wess-Zumino-Witten (WZW) SU(2) level 2 universality class as the continuous transition line that ends at this point, 4 pages, 6 figures

The phase structure and the infrared behaviour of the Euclidean 3-dimensional $O(2)$ symmetric ghost scalar field $\phi$ has been investigated in Wegner and Houghton's renormalization group framework, including higher-derivatives in the kinetic term. It is pointed out that higher-derivative coupling provides three phases and leads to a triple point in that RG scheme. The types of the phase transitions have also been identified.

In this paper, we exactly solve, within the grand canonical ensemble, a minimal spin model with the hybrid phase transition. We call the model "diffusion-based" because its hamiltonian can be recovered from a simple dynamic procedure, which can be seen as an equilibrium statistical mechanics representation of a biased random walk. We outline the derivation of the phase diagram of the model, in which the triple point has the hallmarks of the hybrid transition: discontinuity in the average magnetization and algebraically diverging susceptibilities. At this point, two second-order transition curves meet in equilibrium with the first-order curve, resulting in a prototypical mixed-order behavior.

Spectroscopic parameters (line intensity factor, pressure self-broadening, and shifting coefficients) of ${\mathrm{C}}_{2}{\mathrm{H}}_{2}$ at $1.4\ensuremath{\mu}\mathrm{m}$ were accurately measured using a dual-laser approach, based upon the technique of optical phase locking. This generated an absolute frequency scale underneath the absorption spectra. A pair of extended-cavity diode lasers was used. One of them, the probe laser, is forced to maintain a precise frequency offset from a reference laser, which is an optical frequency standard based on noise-immune cavity-enhanced optical heterodyne molecular spectroscopy. Laser-gas interaction takes place inside an isothermal multipass cell that is stabilized at the temperature of the triple point of water. The fidelity in the observation of the shape associated to the ${P}_{e}$(14) line of the $2{\ensuremath{\nu}}_{3}+{\ensuremath{\nu}}_{5}$ band allowed us to measure the spectroscopic parameters, with a global uncertainty for the line strength of 0.22%.

In this article we provide a multitrace analysis of the theory of noncommutative ${\mathrm{\ensuremath{\Phi}}}^{4}$ in two dimensions on the fuzzy sphere ${\mathbf{S}}_{N,\mathrm{\ensuremath{\Omega}}}^{2}$, and on the Moyal-Weyl plane ${\mathbf{R}}_{\ensuremath{\theta},\mathrm{\ensuremath{\Omega}}}^{2}$, with a nonzero harmonic oscillator term added. The double-trace matrix model symmetric under $M\ensuremath{\rightarrow}\ensuremath{-}M$ is solved in closed form. An analytical prediction for the disordered-to-nonuniform-ordered phase transition and an estimation of the triple point, from the termination point of the critical boundary, are derived and compared with previous Monte Carlo measurement.

The phase behavior of sorbed CO{2} in an ordered mesoporous silica sample (SBA-15) was studied by neutron diffraction. Surprisingly, upon cooling our sample below the bulk critical point, confined CO{2} molecules neither freeze nor remain liquid as expected, but escape from the pores. The phenomenon has additionally been confirmed gravimetrically. The process is reversible and during heating CO{2} refills the pores, albeit with hysteresis. This depletion was for the first time observed in an ordered mesoporous molecular sieve and provides new insight on the phase behavior of nanoconfined fluids.

Simulation evidence of an incipient triple point is reported for xenon submonolayers adsorbed on the (111) surface of platinum. This is in stark contrast to the "normal" triple point found in simulations and experiments for xenon on the basal plane surface of graphite. The motions of the atoms in the surface plane are treated with standard 2D "NVE" molecular dynamics simulations using modern interactions. The simulation evidence strongly suggests an incipient triple point in the 120-150 K range for adsorption on the Pt (111) surface while the adsorption on graphite shows a normal triple point at about 100 K., 5 pages, 4 figures

The phase transitions of liquid 3He are described by truncations of an exact nonperturbative renormalization group equation. The location of the first-order transition lines and the jump in the order parameter are computed quantitatively. At the triple point we find indications of partially universal behavior. We suggest experiments that could help to determine the effective interactions between fermion pairs.

We present here results of high resolution synchrotron x-ray diffraction (SXRD) and dielectric studies in conjunction with Landau theory considerations on (Pb0.94Sr0.06)(ZrxTi1-x)O3 compositions in the vicinity of the morphotropic phase boundary (MPB) to find evidence for the flattening of the free energy surface at the MPB proposed in recent ab-initio studies on strongly piezoelectric ceramics. SXRD results reveal that the tetragonal and pseudorhombohedral monoclinic compositions with x=0.515 and 0.550 transform directly into the cubic paraelectric phase, whereas for 0.520

Many real-world networks depend on other networks, often in nontrivial ways, to maintain their functionality. These interdependent “networks of networks” are often extremely fragile. When a fraction 1 − p of nodes in one network randomly fails, the damage propagates to nodes in networks that are interdependent and a dynamic failure cascade occurs that affects the entire system. We present dynamic equations for two interdependent networks that allow us to reproduce the failure cascade for an arbitrary pattern of interdependency. We study the “rich club” effect found in many real interdependent network systems in which the high-degree nodes are extremely interdependent, correlating a fraction α of the higher-degree nodes on each network. We find a rich phase diagram in the plane p-α, with a triple point reminiscent of the triple point of liquids that separates a nonfunctional phase from two functional phases. Fil: Valdez, Lucas Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata; Argentina Fil: Macri, Pablo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata; Argentina. Boston University. Center for Polymer Studies; Estados Unidos Fil: Stanley, H. E.. Boston University. Center for Polymer Studies; Estados Unidos Fil: Braunstein, Lidia Adriana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata; Argentina

The freezing transition of a strongly dipolar Lennard-Jones fluid is investigated using Monte Carlo simulation. It is found that the system undergoes a ferroelectric liquid-to-solid transition when cooled under a constant pressure. Near the triple point the stable solid phase is a body-centered orthorhombic ferroelectric crystal; a metastable ferroelectric solid phase with distorted hexagonal lattice structure is also discovered. To locate the freezing point, Gibbs free energies of the solid and liquid phase are determined using a thermodynamic integration method.

We have performed high sensitivity quartz microbalance measurements of argon and methane adsorbed on gold. On smooth and flat gold electrodes we have found that both of these systems undergo the common triple-point wetting. Vice versa, on some heterogeneous gold electrodes the temperature scans of argon along the solid-vapor coexistence line show pronounced hysteresis loops between cooling and heating, while those of methane were, within the experimental resolution, reproducible.

We develop a methodology for the construction of two-dimensional discrete breather excitations. Application to the discrete nonlinear Schroedinger equation on a square lattice reveals three different types of breathers. Considering an elementary plaquette, the most unstable mode is centered on the plaquette, the most stable mode is centered on its vertices, while the intermediate (but also unstable) mode is centered at the middle of one of the edges. Below the turning points of each branch in a frequency-power phase diagram, the construction methodology fails and a continuation method is used to obtain the unstable branches of the solutions until a triple point is reached. At this triple point, the branches meet and subsequently bifurcate into the final state of an extended phonon mode. (c) 2000 The American Physical Society.

Sterical effects and the coupling between the cationic dynamics and the anionic-supralattice distortions lead to a series of phase transitions in the crystals of diguanidinium tetraiodoplumbate, $[\mathrm{C}({\mathrm{NH}}_{2}{)}_{3}{]}_{2}^{+}\ensuremath{\cdot}{\mathrm{PbI}}_{4}^{2\ensuremath{-}}.$ The crystals have been characterized by dielectric and calorimetric measurements at ambient and high hydrostatic pressures, as well as by single-crystal x-ray and neutron-powder diffraction at varied temperatures. At 287 K the crystal structure is monoclinic, but the strongly corrugated polyanionic sheets approximate the orthorhombic symmetry of the high-temperature phases. Guanidinium cations are enclosed in voids within the polyanions, and in channels between the neighboring sheets. At 0.1 MPa and 307 K the monoclinic phase undergoes a ferroelastic second-order transition to the orthorhombic phase, and at 356 K another continuous transition to the orthorhombic phase with the unit cell reduced four times in volume. The phase diagram reveals an unusual character of the pressure-induced transition with a critical point at 245 K and 270 MPa. Also a triple point at 358 K and 780 MPa has been detected. The mechanisms of the phase transitions have been postulated.

The dynamical properties of liquid lithium at several thermodynamic states near the triple point have been studied within the framework of the mode-coupling theory. We present a self-consistent scheme which, starting from the knowledge of the static structural properties of the liquid system, allows the theoretical calculation of several single particle and collective dynamical properties. The study is complemented by performing molecular-dynamics simulations and the obtained results are compared with the available experimental data.

A Stokes-Einstein-type relation is derived for the potential part of the shear viscosity of a simple liquid by means of statistical mechanics. The product of the shear viscosity and the self-diffusion coefficient is shown to be expressible in terms of the pair correlation function and the intermolecular force as well as the density. The shear viscosity formula, consisting of kinetic and potential parts and given in terms of the self-diffusion coefficient, is tested against experimental data with regard to the temperature and density dependence of the shear viscosity. Given the self-diffusion coefficient determined by experiment or simulations, the viscosity formula involving the Stokes-Einstein relation obtained produces the shear viscosity of argon, krypton, and xenon, in good agreement with experiment in the case of temperatures well away from the triple point. However, in the neighborhood of the triple point of argon examined, a cutoff parameter, which is a measure of the range of density variation, is needed to account for the experimental data. The applicability of the Stokes-Einstein relation to molecular particles is assessed, and it is found to remain applicable in the range of density and temperature examined.

We have used multiple-beam interferometry to study the temperature dependence of tert-butanol adsorption from vapor on mica, at an isolated surface and in a slit pore. The film thickness at one surface increases from 2 nm for 17--24 \ifmmode^\circ\else\textdegree\fi{}C to $g7\mathrm{nm}$ above the triple point ${T}_{\mathrm{tr}}$ (25.5 \ifmmode^\circ\else\textdegree\fi{}C). Concomitantly, the surface separation at which the slit fills with liquid increases from 11 to 27 nm. These results show for the first time how a continuous triple-point wetting transition at one surface and suppression of the freezing transition in a slit pore affect capillary condensation near ${T}_{\mathrm{tr}}$

The phenomenological analysis of the pressure-temperature $(P\ensuremath{-}T)$ phase diagram of ${[\mathrm{N}(\mathrm{C}\mathrm{H}}_{3}{)}_{4}{]}_{2}{\mathrm{CuCl}}_{4}$ (TMATC-Cu) crystals is presented. It is shown that serious disagreement between the experimental results and theory may be removed assuming that the coefficient of the Landau free energy expansion $\ensuremath{\kappa}$ at the gradient term ${(dq/dz)(dq}^{*}/dz)$ changes the sign in the experimental range of pressures. The phase diagram in the $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\kappa}$ phase plane is characterized by infinite Lifshitz point (at $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\kappa}}\ensuremath{\infty})$ in which both lines of the phase transitions into the incommensurate phase merge together, whereas the incommensurate wave vector approaches its zero value. The triple point ${(P}_{K}\ensuremath{\approx}55\mathrm{MPa},$ ${T}_{K}\ensuremath{\approx}304\mathrm{K})$ observed in these crystals may be considered as an artificial point, which results from the limitation of experimental resolution. Therefore, even above ${P}_{K}$ there still exist two very close (unresolved) lines of the incommensurate phase transitions.

Vibrational phase relaxation near gas-liquid and liquid-solid phase coexistence has been studied by molecular dynamics simulations of N-N stretch in N-2. Experimentally observed pronounced insensitivity of phase relaxation from the triple point to beyond the boiling point is found to originate from a competition between density relaxation and resonant-energy transfer terms. The sharp rise in relaxation rate near the critical point (CP) can be attributed at least partly to the sharp, rise in vibration-rotation coupling contribution. Substantial subquadratic quantum number dependence of overtone dephasing rate is found near the CP and in supercritical fluids. [S0031-9007 (99)09318-7].

A first order phase transition is found in liquid carbon using atomistic simulation methods and Brenner{close_quote}s bond order potential. The phase line is terminated by a critical point at 8801thinspthinspK and 10.56thinspthinspGPa and by a triple point on the graphite melting line at 5133thinspthinspK and 1.88thinspthinspGPa. The phase change is associated with density and structural changes. The low-density liquid is predominantly sp bonded with little sp{sup 3} character. The high-density liquid is mostly sp{sup 3} bonded with little sp character. This is the first nonempirical evidence of a liquid-liquid transition between thermodynamically stable fluids. {copyright} {ital 1999} {ital The American Physical Society}

A nonequilibrium method for calculating the shear viscosity is presented. It reverses the cause-and-effect picture customarily used in nonequilibrium molecular dynamics: the effect, the momentum flux or stress, is imposed, whereas the cause, the velocity gradient or shear rate, is obtained from the simulation. It differs from other Norton-ensemble methods by the way in which the steady-state momentum flux is maintained. This method involves a simple exchange of particle momenta, which is easy to implement. Moreover, it can be made to conserve the total energy as well as the total linear momentum, so no coupling to an external temperature bath is needed. The resulting raw data, the velocity profile, is a robust and rapidly converging property. The method is tested on the Lennard-Jones fluid near its triple point. It yields a viscosity of 3.2-3.3, in Lennard-Jones reduced units, in agreement with literature results.

A two-band model which includes the magnetoelastic interaction is used to study the magnetization and spin dynamics of {gamma}-Mn alloys. As previously believed, single (S), double (D), and triple (T) spin-density wave (SDW) states are found in fct (c{lt}a and c{gt}a) and fcc (c=a) lattices, respectively. When the magnetoelastic coupling constant {kappa} exceeds the critical value {kappa}{sub c}, both the structural and magnetic phase transitions become first order. This critical value drops to zero at the triple point, where the commensurate and incommensurate SDW phase boundaries meet. In agreement with experiments on fct MnNi and fcc FeMn alloys, we find that the gap {Delta}{sub sw}(T) in the spin-wave dispersion is proportional to the 3/2 power of the sublattice magnetization M(T). For the noncollinear D and T SDW magnetic phases observed in MnNi and FeMn alloys, we find an additional class of collective modes. This class includes a Goldstone mode which is produced by the modified dispersion of holes not directly involved in the SDW. We also find high-frequency excitations with energies of order {Delta}, where 2{Delta}{approx}2 eV is the energy gap in the quasiparticle spectrum. Although these incoherent excitations have the same frequencies in the D and T SDW phases,more » their neutron-scattering cross sections should be 33{percent} larger in the TSDW phase. {copyright} {ital 1999} {ital The American Physical Society}« less

High-resolution volumetric adsorption isotherms of ammonia-on-MgO(100) surfaces have been recorded over the temperature range 160--200 K (using powder prepared by a recently introduced process). Evidence is presented that indicates that multilayer formation is possible at $Tg~173\mathrm{K}$ (at least three layers). We have observed a series of layering transitions including a crossover from incomplete to complete wetting near the triple point of ammonia. The isothermal compressibility and isosteric heat of adsorption are determined. These data are compared with earlier results obtained for ammonia on graphite and used to describe the status of the film with regard to temperature and coverage. The importance of high-quality MgO substrates is discussed and areas for further study using structural methods are mentioned.

We have measured, using time-of-flight neutron diffraction, the thermodynamic derivatives of the microscopic structure factor of liquid parahydrogen in the vicinity of the triple point. Experiments have been carried out on the $T=17.1$ K isotherm and on the $n=22.2 {\mathrm{nm}}^{\ensuremath{-}3}$ isochore so that the thermodynamic derivatives at constant temperature and density could be evaluated. The hydrogen data have been compared with the corresponding quantities for deuterium and quantitatively significant differences have been observed. Assuming that hydrogen and deuterium experience the same intermolecular potential, these differences can only be attributed to the different quantum behaviors of the two molecules.

The magnetic phase diagram of the doped inorganic spin-Peierls compound ${\mathrm{CuGe}}_{1\ensuremath{-}x}{Y}_{x}{\mathrm{O}}_{3}$ ($Y=\mathrm{Sn}$ or Al) is studied in magnetic fields up to $B\ensuremath{\sim}50 \mathrm{T}$ at temperatures 0.32\char21{}20 K. The comparative analysis of the magnetization data and the resonant magnetoabsorption spectra for the frequency range 20\char21{}120 GHz shows that the spin-Peierls phase is not destroyed up to ${x}_{\mathrm{Sn}}=0.01$ and ${x}_{\mathrm{Al}}=0.02.$ The strong effects of doping on the magnetic phase transition between the spin-Peierls (D) and the incommensurate (M) phases are observed. The temperature dependence of the transition field ${B}_{\mathrm{DM}}(T)$ demonstrates a nonmonotonous behavior with a maximum at $T\ensuremath{\sim}9 \mathrm{K}.$ Doping by Sn and Al reduces the amplitude of the ${B}_{\mathrm{DM}}(T)$ maximum by a factor of 2 with respect to the undoped crystal. The magnetic hysteresis width $\ensuremath{\Delta}B(T)$ at $Tl1 \mathrm{K}$ increases substantially in both the Al- and Sn-doped crystals. The magnitude \ensuremath{\chi} of the magnetic transition along the phase boundary ${B}_{\mathrm{DM}}(T)$ follows a critical behavior similar to that of the superlattice peak: $\ensuremath{\chi}={\ensuremath{\chi}}_{0}[1\ensuremath{-}{(T/T}^{*}){]}^{\ensuremath{\beta}},$ where ${T}^{*}\ensuremath{\approx}12 \mathrm{K}$ is the temperature of the triple point and $\ensuremath{\beta}=0.75\ifmmode\pm\else\textpm\fi{}0.04.$ A model of the magnetic hysteresis in the spin-Peierls compounds based on a universal scaling of the magnetic phase diagram and g-factor renormalization in the transition region $B\ensuremath{\sim}{B}_{\mathrm{DM}}$ is suggested. The influence of disorder on the properties of the ${\mathrm{CuGeO}}_{3}$ crystals is discussed.