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We demonstrate that the isotope shift in isotopomers of diatomic molecules, where the nucleus of one of its constituent atoms is replaced by another isotope, can be expressed as the sum of a field shift and a mass shift, similar to the atomic case. We show that a linear relation holds between atomic and molecular isotopes shifts, thus extending the King-plot analysis to molecular isotope shifts. Optical isotope shifts in YbF and ZrO and infrared isotope shifts in SnH are analyzed with a molecular King-plot approach, utilizing Yb$^{+}$ and Zr$^{+}$ ionic isotope shifts and charge radii of Sn obtained with non-optical methods. The changes in the mean-squared nuclear charge radii $\delta \langle r^2 \rangle$ of $^{170-174,176}$Yb and $^{90-92,94,96}$Zr extracted from the molecular transitions are found to be in excellent agreement with the values from the spectroscopy of Yb$^{+}$ and Zr$^{+}$, respectively. On the contrary, in the case of the vibrational-rotational transition in SnH, no sensitivity to the nuclear volume could be deduced within the experimental resolution, which makes it unsuitable for the extraction of nuclear charge radii but provides insights into the molecular electronic wave function not accessible via other methods. The new opportunities offered by the molecular King-plot analysis for research in nuclear structure and molecular physics are discussed., Comment: Accepted at Physical Review X. Link to abstract: https://journals.aps.org/prx/accepted/be075Kf7E0c16505459d9fa833408356a593fd904

We present a comprehensive study shedding light on how thermal fluctuations affect correlations in a Bose gas with contact repulsive interactions in one spatial dimension. The pair correlation function, the static structure factor, and the one-body density matrix are calculated as a function of the interaction strength and temperature with the exact ab-initio Path Integral Monte Carlo method. We explore all possible gas regimes from weak to strong interactions and from low to high temperatures. We provide a detailed comparison with a number of theories, such as perturbative (Bogoliubov and decoherent classical), effective (Luttinger liquid) and exact (ground-state and thermal Bethe Ansatz) ones. Our Monte Carlo results exhibit an excellent agreement with the tractable limits and provide a fundamental benchmark for future observations which can be achieved in atomic gases, cavity quantum-electrodynamic and superconducting-circuit platforms., Main Text: 13 pages, 9 figures. Appendix: 1 page

At the familiar liquid-gas phase transition in water, the density jumps discontinuously at atmospheric pressure, but the line of these first-order transitions defined by increasing pressures terminates at the critical point, a concept ubiquitous in statistical thermodynamics. In correlated quantum materials, a critical point was predicted and measured terminating the line of Mott metal-insulator transitions, which are also first-order with a discontinuous charge density. In quantum spin systems, continuous quantum phase transitions (QPTs) have been investigated extensively, but discontinuous QPTs have received less attention. The frustrated quantum antiferromagnet SrCu$_2$(BO$_3$)$_2$ constitutes a near-exact realization of the paradigmatic Shastry-Sutherland model and displays exotic phenomena including magnetization plateaux, anomalous thermodynamics and discontinuous QPTs. We demonstrate by high-precision specific-heat measurements under pressure and applied magnetic field that, like water, the pressure-temperature phase diagram of SrCu$_2$(BO$_3$)$_2$ has an Ising critical point terminating a first-order transition line, which separates phases with different densities of magnetic particles (triplets). We achieve a quantitative explanation of our data by detailed numerical calculations using newly-developed finite-temperature tensor-network methods. These results open a new dimension in understanding the thermodynamics of quantum magnetic materials, where the anisotropic spin interactions producing topological properties for spintronic applications drive an increasing focus on first-order QPTs., 8+4 pages, 4+3 figures

The energy of ultra-dilute quantum many-body systems is known to exhibit a universal dependence on the gas parameter x=n a_0^dx=na0d, with nn the density, dd the dimensionality of the space (d=1,2,3d=1,2,3) and a_0a0 the ss-wave scattering length. The universal regime typically extends up to x\approx 0.001x≈0.001, while at larger values specific details of the interaction start to be relevant and different model potentials lead to different results. Dipolar systems are peculiar in this regard since the anisotropy of the interaction makes a_0a0 depend on the polarization angle \alphaα, so different combinations of n and \alphaα can lead to the same value of the gas parameter x. In this work we analyze the scaling properties of dipolar bosons in two dimensions as a function of the density and polarization dependent scattering length up to very large gas parameter values. Using Quantum Monte Carlo (QMC) methods we study the energy and the main structural and coherence properties of the ground state of a gas of dipolar bosons by varying the density and scattering length for a fixed gas parameter. We find that the dipolar interaction shows relevant scaling laws up to unusually large values of xx that hold almost to the boundaries in the phase diagram where a transition to a stripe phase takes place.

BaCuSi$_2$O$_6$ is a quasi-two-dimensional (2D) quantum antiferromagnet containing three different types of stacked, square-lattice bilayer hosting spin-1/2 dimers. Although this compound has been studied extensively over the last two decades, the critical applied magnetic field required to close the dimer spin gap and induce magnetic order, which exceeds 23 T, has to date precluded any kind of neutron scattering investigation. However, the HFM/EXED instrument at the Helmholtz-Zentrum Berlin made this possible at magnetic fields up to 25.9 T. Thus we have used HFM/EXED to investigate the field-induced ordered phase, in particular to look for quasi-2D physics arising from the layered structure and from the different bilayer types. From neutron diffraction data, we determined the global dependence of the magnetic order parameter on both magnetic field and temperature, finding a form consistent with 3D quantum critical scaling; from this we deduce that the quasi-2D interactions and nonuniform layering of BaCuSi$_2$O$_6$ are not anisotropic enough to induce hallmarks of 2D physics. From neutron spectroscopy data, we measured the dispersion of the strongly Zeeman-split magnetic excitations, finding good agreement with the zero-field interaction parameters of BaCuSi$_2$O$_6$. We conclude that HFM/EXED allowed a significant extension in the application of neutron scattering techniques to the field range above 20 T and in particular opened new horizons in the study of field-induced magnetic quantum phase transitions., 19 pages, 8 figures

We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of spatial periodicity. Our variational state is parameterized in terms of a permutationally-invariant part described by the Deep Sets neural-network architecture. The input coordinates to the Deep Sets are periodically transformed such that they are suitable to directly describe periodic bosonic systems. We show example applications to both one and two-dimensional interacting quantum gases with Gaussian interactions, as well as to $^4$He confined in a one-dimensional geometry. For the one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods., 8 pages, 6 figures

Advances in the field of stem cell-based models have in recent years lead to the development of blastocyst-like structures termed blastoids. Blastoids can be used to study key events in mammalian pre-implantation development, as they mimic the blastocyst morphologically and transcriptionally, can progress to the post-implantation stage and can be generated in large numbers. Blastoids were originally developed using mouse pluripotent stem cells, and since several groups have successfully generated blastocyst models of the human system. Here we provide a comparison of the mouse and human protocols with the aim of deriving the core requirements for blastoid formation, discuss the models’ current ability to mimic blastocysts and give an outlook on potential future applications.

The phase diagrams of highly frustrated quantum spin systems can exhibit first-order quantum phase transitions and thermal critical points even in the absence of any long-ranged magnetic order. However, all unbiased numerical techniques for investigating frustrated quantum magnets face significant challenges, and for generic quantum Monte Carlo methods the challenge is the sign problem. Here we report on a general quantum Monte Carlo approach with a loop-update scheme that operates in any basis, and we show that, with an appropriate choice of basis, it allows us to study a frustrated model of coupled spin-1/2 trimers: simulations of the trilayer Heisenberg antiferromagnet in the spin-trimer basis are sign-problem-free when the intertrimer couplings are fully frustrated. This model features a first-order quantum phase transition, from which a line of first-order transitions emerges at finite temperatures and terminates in a thermal critical point. The trimer unit cell hosts an internal degree of freedom that can be controlled to induce an extensive entropy jump at the quantum transition, which alters the shape of the first-order line. We explore the consequences for the thermal properties in the vicinity of the critical point, which include profound changes in the lines of maxima defined by the specific heat. Our findings reveal trimer quantum magnets as fundamental systems capturing in full the complex thermal physics of the strongly frustrated regime., 27 pages, 10 figures, Resubmission to SciPost

Triplet ground-state organic molecules are of interest with respect to several emerging technologies but usually show limited stability, especially as thin films. We report an organic diradical, consisting of two Blatter radicals, that possesses a triplet ground state with a singlet-triplet energy gap, ?EST? 0.4-0.5 kcal mol-1(2J/k ? 220-275 K). The diradical possesses robust thermal stability, with an onset of decomposition above 264 °C (TGA). In toluene/chloroform, glassy matrix, and fluid solution, an equilibrium between two conformations with ?EST? 0.4 kcal mol-1and ?EST? -0.7 kcal mol-1is observed, favoring the triplet ground state over the singlet ground-state conformation in the 110-330 K temperature range. The diradical with the triplet ground-state conformation is found exclusively in crystals and in a polystyrene matrix. The crystalline neutral diradical is a good electrical conductor with conductivity comparable to the thoroughly optimized bis(thiazolyl)-related monoradicals. This is surprising because the triplet ground state implies that the underlying ?-system is cross-conjugated and thus is not compatible with either good conductance or electron delocalization. The diradical is evaporated under ultra-high vacuum to form thin films, which are stable in air for at least 18 h, as demonstrated by X-ray photoelectron and electron paramagnetic resonance (EPR) spectroscopies

Using density matrix renormalization group simulations on open chains, we map out the wave vector in the incommensurate disordered phase of a realistic model of Rydberg chains with 1/r6 interactions, and we locate and characterize the points along the commensurate lines where the transition out of the period 3 and 4 phases is conformal. We confirm that it is three-state Potts for the period-3 phase, and we show that it is Ashkin-Teller with v similar or equal to 0.80 for the period-4 phase. We further show that close to these points, the transition is still continuous, but with a completely different scaling of the wave vector, in agreement with a chiral transition. Finally, we propose to use the conformal points as benchmarks for Kibble-Zurek experiments, defining a roadmap towards a conclusive identification of the chiral universality class.

This thesis deals with the study of a Gross-Clark-Schrödinger system which models the motion of an impurity in a Bose condensate. We have first shown that the Cauchy problem for this system is globally well posed in the associated energy space. The approach used is quite classical and is based on Strichartz type estimates and on a fixed point theorem. In a second step, we are interested in the travelling waves of this system. These special solutions have been studied since 1974 by physicists using formal asymptotic developments and some numerical simulations. In one dimension space the existence of these solutions and some properties have been rigorously established in 2006. Despite several attempts, there is no rigorous proof in the literature of the existence of travelling waves in dimension greater than or equal to two. We have used several approaches to show the existence, based on ideas and tools recently developed in Calculus of Variations. One of them consists in minimizing the energy associated to the system under two constraints, at constant mass and constant momentum. We have shown that minimizing travelling waves exist for any pair (moment, mass) that verifies a strict subadditivity condition of the minimal energy as a function of two variables. In parallel, we have performed numerical simulations that have well highlighted the travelling waves in the cases that correspond to the physical applications, we have obtained their profiles and we have calculated their energy levels. We have also studied other types of special solutions, including zero-momentum ground states and bubble-vortex solutions.; Cette thèse porte sur l'étude d'un système de Gross-Clark-Schrödinger qui modélise le mouvement d'une impureté dans un condensat de Bose. Nous avons d'abord montré que le problème de Cauchy pour ce système est globalement bien posé dans l'espace d'énergie associé. L'approche utilisée est assez classique et est basée sur des estimations de type Strichartz ainsi que sur l'utilisation d'un théorème de point fixe. Dans un second temps nous nous sommes intéressés aux ondes progressives de ce système. Ces solutions spéciales ont été étudiées dès 1974 par des physiciens à l'aide des développements asymptotiques formels et de quelques simulations numériques. En dimension un d'espace l'existence de ces solutions et quelques propriétés ont été établies rigoureusement en 2006. Malgré plusieurs tentatives, il n'existe dans la littérature aucune preuve rigoureuse de l'existence des ondes progressives en dimension supérieure ou égale à deux. Nous avons utilisé plusieurs approches pour montrer l'existence, basées sur des idées et des outils récemment développés en Calcul des Variations. Une d'elles consiste à minimiser l'énergie associée au système sous deux contraintes, à masse constante et à moment constant. Nous avons montré que les ondes progressives minimisantes existent pour tout couple (moment, masse) qui vérifie une condition de stricte sous-additivité de l'énergie minimale comme fonction de deux variables. En parallèle, nous avons effectué des simulations numériques qui ont bien mis en évidence les ondes progressives dans les cas qui correspondent aux applications physiques, nous avons obtenu leurs profils et nous avons calculé leurs niveaux d'énergie. Nous avons étudié également d'autres types de solutions spéciales, notamment les états fondamentaux de moment nul et les solutions de type bulle-vortex.

The cellular cytoskeleton provides the cell with a mechanical rigidity that allows mechanical interaction between cells and the extracellular environment. The actin structure plays a key role in mechanical events such as motility or the establishment of cell polarity. From the earliest stages of development, as represented by the ex vivo expansion of naïve embryonic stem cells (ESCs), the critical mechanical role of the actin structure is becoming recognized as a vital cue for correct segregation and lineage control of cells and as a regulatory structure that controls several transcription factors. Naïve ESCs have a characteristic morphology, and the ultrastructure that underlies this condition remains to be further investigated. Here, we investigate the 3D actin cytoskeleton of naïve mouse ESCs using super-resolution optical reconstruction microscopy (STORM). We investigate the morphological, cytoskeletal, and mechanical changes in cells cultured in 2i or Serum/LIF media reflecting, respectively, a homogeneous preimplantation cell state and a state that is closer to embarking on differentiation. STORM imaging showed that the peripheral actin structure undergoes a dramatic change between the two culturing conditions. We also detected micro-rheological differences in the cell periphery between the cells cultured in these two media correlating well with the observed nano-architecture of the ESCs in the two different culture conditions. These results pave the way for linking physical properties and cytoskeletal architecture to cell morphology during early development.

Reductive elimination is an elementary organometallic reaction step involving a formal oxidation state change of -2 at a transition-metal center. For a series of formal high-valent Ni-IV complexes, aryl-CF3 bond-forming reductive elimination was reported to occur readily (Bour et al. J. Am. Chem. Soc. 2015, 137, 8034-8037). We report a computational analysis of this reaction and find that, unexpectedly, the formal Ni-IV centers are better described as approaching a +II oxidation state, originating from highly covalent metal-ligand bonds, a phenomenon attributable to sigma-noninnocence. A direct consequence is that the elimination of aryl-CF3 products occurs in an essentially redox-neutral fashion, as opposed to a reductive elimination. This is supported by an electron flow analysis which shows that an anionic CF3 group is transferred to an electrophilic aryl group. The uncovered role of sigma-noninnocence in metal-ligand bonding, and of an essentially redox-neutral elimination as an elementary organometallic reaction step, may constitute concepts of broad relevance to organometallic chemistry.

Two isomeric ruthenium(II)/5,10,15,20-tetraphe-nylporphyrin complexes featuring axially coordinated redox-active, low-optical gap 2- or 6-isocyanoazulene ligands have been isolated and characterized by NMR, UV-vis, and magnetic circular dichroism (MCD) spectroscopic methods, high-resolution mass spectrometry, and single-crystal X-ray crystallography. The UV-vis and MCD spectra support the presence of the low-energy, azulene-centered transitions in the Q band region of the porphyrin chromophore. The first coordination sphere in new L2RuTPP complexes reflects compressed tetragonal geometry. The redox properties of the new compounds were assessed by electrochemical and spectroelectrochemical means and correlated with the electronic structures predicted by density functional theory and CASSCF calculations. Both experimental and theoretical data are consistent with the first two reduction processes involving the axial azulenic ligands, whereas the oxidation profile (in the direction of increasing potential) is exerted by the ruthenium ion, the porphyrin core, and the axial azulenic moieties.

Classical and quantum phase transitions (QPTs), with their accompanying concepts of criticality and universality, are a cornerstone of statistical thermodynamics. An exemplary controlled QPT is the field-induced magnetic ordering of a gapped quantum magnet. Although numerous "quasi-one-dimensional" coupled spin-chain and -ladder materials are known whose ordering transition is three-dimensional (3D), quasi-2D systems are special for several physical reasons. Motivated by the ancient pigment Han Purple (BaCuSi$_{2}$O$_{6}$), a quasi-2D material displaying anomalous critical properties, we present a complete analysis of Ba$_{0.9}$Sr$_{0.1}$CuSi$_{2}$O$_{6}$. We measure the zero-field magnetic excitations by neutron spectroscopy and deduce the magnetic Hamiltonian. We probe the field-induced transition by combining magnetization, specific-heat, torque and magnetocalorimetric measurements with low-temperature nuclear magnetic resonance studies near the QPT. By a Bayesian statistical analysis and large-scale Quantum Monte Carlo simulations, we demonstrate unambiguously that observable 3D quantum critical scaling is restored by the structural simplification arising from light Sr-substitution in Han Purple., 19 pages, 5 figures

Ideal magnetic frustration forms the basis for the emergence of exotic quantum spin states that are entirely nonmagnetic. Such singlet spin states are the defining feature of the Shastry-Sutherland model, and of its faithful materials realization in the quantum antiferromagnet SrCu$_2$(BO$_3$)$_2$. To address these states on ultrafast timescales, despite their lack of any microscopic order parameter, we introduce a nonlinear magnetophononic mechanism to alter the quantum spin dynamics by driving multiple optical phonon modes coherently and simultaneously. We apply intense terahertz pulses to create a nonequilibrium modulation of the magnetic interactions that breaks the ideal frustration of SrCu$_2$(BO$_3$)$_2$, such that previously forbidden physics can be driven in a coherent manner. Specifically, this driving populates a purely magnetic excitation, the singlet branch of the two-triplon bound state, by resonance with the difference frequency of two pumped phonons. Our results demonstrate how light-driven phonons can be used for the ultrafast and selective manipulation of interactions in condensed matter, even at frequencies far from those of the pump spectrum, offering valuable additional capabilities for the dynamical control of quantum many-body phenomena., 21 pages, 13 figures

Complex organic molecules with three carbon atoms are found in the earliest stages of star formation. In particular, propenal (C$_2$H$_3$CHO) is a species of interest due to its implication in the formation of more complex species and even biotic molecules. This study aims to search for the presence of C$_2$H$_3$CHO and other three-carbon species such as propylene (C$_3$H$_6$) in the hot corino region of the low-mass protostellar binary IRAS 16293--2422 to understand their formation pathways. We use ALMA observations in Band 6 and 7 from various surveys to search for the presence of C$_3$H$_6$ and C$_2$H$_3$CHO towards the protostar IRAS 16293--2422 B (IRAS 16293B). We report the detection of both C$_3$H$_6$ and C$_2$H$_3$CHO towards IRAS 16293B, however, no unblended lines were found towards the other component of the binary system, IRAS 16293A. We derive column density upper limits for C$_3$H$_8$, HCCCHO, n-C$_3$H$_7$OH, i-C$_3$H$_7$OH, C$_3$O, and cis-HC(O)CHO towards IRAS 16293B. We then use a three-phase chemical model to simulate the formation of these species in a typical prestellar environment followed by its hydrodynamical collapse until the birth of the central protostar. Different formation paths, such as successive hydrogenation and radical-radical additions on grain surfaces, are tested and compared to the observational results. The simulations reproduce the abundances within one order of magnitude from those observed towards IRAS 16293B, with the best agreement found for a rate of $10^{-12}$ cm$^3$ s$^{-1}$ for the gas-phase reaction C$_3$ + O $\rightarrow$ C$_2$ + CO. Successive hydrogenations of C$_3$, HC(O)CHO, and CH$_3$OCHO on grain surfaces are a major and crucial formation route of complex organics molecules, whereas both successive hydrogenation pathways and radical-radical addition reactions contribute to the formation of C$_2$H$_5$CHO., Comment: Accepted for publication in A&A. 24 pages, 17 figures

According to Landau's Fermi liquid theory, the main properties of the quasiparticle excitations of an electron gas are embodied in the effective mass $m^*$, which determines the energy of a single quasiparticle, and the Landau interaction function, which indicates how the energy of a quasiparticle is modified by the presence of other quasiparticles. This simple paradigm underlies most of our current understanding of the physical and chemical behavior of metallic systems. The quasiparticle effective mass of the three-dimensional homogeneous electron gas has been the subject of theoretical controversy and there is a lack of experimental data. In this work, we deploy diffusion Monte Carlo (DMC) methods to calculate $m^*$ as a function of density for paramagnetic and ferromagnetic three-dimensional homogeneous electron gases. The DMC results indicate that $m^*$ decreases when the density is reduced, especially in the ferromagnetic case. The DMC quasiparticle energy bands exclude the possibility of a reduction in the occupied bandwidth relative to that of the free-electron model at density parameter $r_s=4$, which corresponds to Na metal., Comment: Accepted for the publication

We describe the new version (v3.06h) of the code HFODD that solves the universal nonrelativistic nuclear DFT Hartree-Fock or Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we implemented the following new features: (i) zero-range three- and four-body central terms, (ii) zero-range three-body gradient terms, (iii) zero-range tensor terms, (iv) zero-range isospin-breaking terms, (v) finite-range higher-order regularized terms, (vi) finite-range separable terms, (vii) zero-range two-body pairing terms, (viii) multi-quasiparticle blocking, (ix) Pfaffian overlaps, (x) particle-number and parity symmetry restoration, (xi) axialization, (xii) Wigner functions, (xiii) choice of the harmonic-oscillator basis, (xiv) fixed Omega partitions, (xv) consistency formula between energy and fields, and we corrected several errors of the previous versions., Comment: 52 LaTeX pages, revised version

Temperature fluctuations of a finite system follows the Landau bound $\delta T^2 = T^2/C(T)$ where $C(T)$ is the heat capacity of the system. In turn, the same bound sets a limit to the precision of temperature estimation when the system itself is used as a thermometer. In this paper, we employ graph theory and the concept of Fisher information to assess the role of topology on the thermometric performance of a given system. We find that low connectivity is a resource to build precise thermometers working at low temperatures, whereas highly connected systems are suitable for higher temperatures. Upon modelling the thermometer as a set of vertices for the quantum walk of an excitation, we compare the precision achievable by position measurement to the optimal one, which itself corresponds to energy measurement., Comment: 16 pages, 8 figures, accepted version

Filopodia are actin-rich structures, present on the surface of practically every known eukaryotic cell. These structures play a pivotal role in specific cell-cell and cell-matrix interactions by allowing cells to explore their environment, generate mechanical forces, perform chemical signaling, or convey signals via intercellular tunneling nano-bridges. The dynamics of filopodia appear quite complex as they exhibit a rich behavior of buckling, pulling, length and shape changes. Here, we find that filopodia additionally explore their 3D extracellular space by combining growth and shrinking with axial twisting and buckling of their actin rich core. Importantly, we show the rotational dynamics of the filamentous actin inside filopodia for a range of highly distinct and cognate cell types spanning from earliest development to highly differentiated tissue cells. Non-equilibrium physical modeling of actin and myosin confirm that twist, and hence rotation, is an emergent phenomenon of active filaments confined in a narrow channel which points to a generic mechanism present in all cells. Our measurements confirm that filopodia exert traction forces and form helical buckles in a range of different cell types that can be ascribed to accumulation of sufficient twist. These results lead us to conclude that activity induced twisting of the actin shaft is a general mechanism underlying fundamental functions of filopodia.

Ab initio methods using weakly interacting nucleons give a good description of condensed nuclear matter up to densities comparable to the nuclear saturation density. At higher densities palpable strong interactions between overlapping nucleons become important; we propose that the interactions will continuously switch over to follow a holographic model in this region. In order to implement this, we construct hybrid equations of state (EoSs) where various models are used for low density nuclear matter, and the holographic V-QCD model is used for non-perturbative high density nuclear matter as well as for quark matter. We carefully examine all existing constraints from astrophysics of compact stars and discuss their implications for the hybrid EoSs. Thanks to the stiffness of the V-QCD EoS for nuclear matter, we obtain a large family of viable hybrid EoSs passing the constraints. We find that quark matter cores in neutron stars are unstable due to the strongly first order deconfinement transition, and predict bounds on the tidal deformability as well as on the radius of neutron stars. By relying on universal relations, we also constrain characteristic peak frequencies of gravitational waves produced in neutron star mergers., 40 pages, 19 figures; v2: analysis of I-Love-Q relations added

Nitriding of steels has been widely used for almost a century. However, insight in two important precipitating phases for low concentration through-thickness nitriding is still lacking, hindering further development of the process. Due to their metastable nature, manufacturing large homogeneous samples of Fe4N and Fe16N2 is very challenging. Consequently, measuring thermodynamic properties, such as heat capacity and free energy, has proven difficult at best. In this work, we have calculated those thermodynamic properties using density-functional theory (DFT) for Fe4N, Fe16N2 and ferrite with nitrogen in solid solution. This information is a prerequisite to improve the accuracy of larger-scale modeling approaches of iron nitrides. We used the free energies to construct the temperature/concentration phase diagram for low nitrogen concentrations from 0 K to 865 K . Both the range of metastability for Fe16N2 and the nitrogen solvus confirm the experimental data. On the other hand, it was concluded that the experimental Curie temperature for Fe16N2 is severely underestimated because of the thermodynamic instability above 400 K .