The thermodynamic description of the C-Cr-Ti ternary system has been reassessed. The main reason was to adjust the solubility limit of Cr in MC (M = Cr, Ti), but also to take the solubility of Ti in M3C2 and M7C3 into account. Another reason was that the thermodynamic descriptions of all the three constituent binary systems (C-Cr, C-Ti and Cr-Ti) had been revised after the previously published description of the C-Cr-Ti system. Important metastable end-members and interaction parameters were calculated using Density Functional Theory (DFT). For fcc-CrC and Ti3C2, DFT was used together with a recently published method to calculate the molar Gibbs energy as a function of temperature (Gm(T)). For fcc-CrC also the magnetic contribution and the magnetic transition temperature, i.e. the Curie temperature (TC), were included. DFT was also used to calculate Gibbs energy of formation at 0 K for Ti7C3 and to calculate the molar excess Gibbs energy contribution, and TC, as a function of Ti composition in MC. DFT calculated parameters were compared with experiments or previous assessments. Selected experimental information from literature was then used to optimize parameters that are difficult to calculate with DFT, e.g. interaction parameters for the liquid phase and temperature dependence for interaction parameters in the solid phases. The resulting thermodynamic description, which is based on critically reviewed binary descriptions, reproduces the experimental solidification sequence, found in literature, equally well as the previous description of the C-Cr-Ti system. Furthermore, in contrast to the previous description, the new description also reproduces the most recent experimentally determined solubility of Cr in MC and takes the solubility of Ti in M3C2 and M7C3 into account. Finally the new description uses DFT calculated metastable end-members and interaction parameters, which gives more reliable predictions, especially at low temperatures.

A method for calculation of finite temperature thermodynamic properties for magnetic allotropes has been developed. The developed method is based on quasi-harmonic approximations using the Debye-Gruneisen model. Electronic contributions are included and magnetic disordering contributions are added with the empiric model often used in CALPHAD (CALculation of PHAse Diagrams) databases. The developed method also includes two new ways to estimate the Debye temperature (theta(D)(V-0)) which enables calculation of finite temperature thermodynamic properties also for allotropes that are dynamically unstable at 0 K. Also a new CALPHAD approach for estimation of Curie- (T-C) or Neel- (T-N) temperatures is presented. The developed method was used to calculate Gibbs energy as a function of temperature (G(T)) and isobaric heat capacity as a function of temperature (C-P(T)) for the body-centred-cubic (bcc), the face-centred-cubic (fcc) and the hexagonal-closed-packed (hcp) allotropes of Fe, Co and Ni. The results were compared with the SGTE Unary database. By using the developed method the phase transitions in Fe and Co were predicted. The calculations of the metastable allotropes fcc-Fe, hcp-Fe and bcc-Ni in this work indicates that the descriptions of these allotropes in the SGTE Unary database need to be updated, especially regarding the magnetic parameters. Furthermore, contradictory to previously reported results in literature, the calculations in this work show that the magnetic ground state structure of fcc-Fe is the double layer antiferromagnetic structure (AFM-D) and not a spin-spiral. The final conclusion is that by using the developed method it is possible to calculate finite temperature thermodynamic properties, not only, for stable and metastable magnetic allotropes, but also for magnetic allotropes that are dynamically unstable at 0 K, which is very important for the development of thermodynamic databases.

The CALPHAD (CALculation of PHAse Diagrams) method consists of three cornerstones, i.e. experiments, computational methods (e.g. Density Functional Theory (DFT)) and thermodynamic models, which together are used to build CALPHAD descriptions. In this thesis the CALPHAD method, including all three parts, is used to study transition metals and their carbides, nitrides and carbonitrides. The focus is mainly on transition metals important for the steel and cemented carbide industries. Some of the weaknesses or uncertainties in existing thermodynamic descriptions of these transition metals are identified and investigated with either experiments or computational methods whereupon new descriptions are presented.

A method for calculation of the molar Gibbs energy as a function of temperature (G_m(T)) for metastable magnetic components is developed. The method uses DFT in combination with the Debye-Grüneisen model and the empirical magnetic model often used in CALPHAD. The developed method is also able to estimate the magnetic transition temperature (T_C or T_N). Furthermore, two new approaches for how to treat calculations on dynamically unstable allotropes are presented. This is important since this often is the reason why DFT calculations on metastable components fail. The method is developed and verified on bcc, fcc and hcp allotropes of Fe, Co and Ni, and is then used to calculate G_m(T) descriptions for fcc-TiC, fcc-CrC, fcc-CrN, hcp-Cr₂C and hcp-Cr₂N. Furthermore, the same method is also used to calculate the excess Gibbs energy at 0 K for the interactions CrC-TiC (fcc), CrC-CrN (fcc) and Cr₂C-Cr₂N (hcp), as well as T_C and T_N as a function of composition for the same composition ranges.

Experiments are performed at 1673 and 1773 K to determine the solubility of Cr in MC (M = Ti, Cr) and of Ti in M₃C₂ and M₇C₃, in the equilibria MC-M₃C₂-M₇C₃ and MC-M₃C₂-graphite of the C-Cr-Ti system. The solubilities are measured with EDS/WDS and verified with XRD/Rietveld refinement.

The experimental and computational results for the C-Cr-Ti system are used together with literature data to perform a reassessment of this system. Compared to the previous CALPHAD description, the new description also includes updated descriptions for two of the three constituent binary systems (C-Ti and Cr-Ti) and reproduces the experimental results in the TiC-Cr₃C₂ isoplethal section found in literature.

In summary, the outcome of this thesis is an updated CALPHAD description of the C-Cr-Ti system and calculated G_m(T) descriptions, including magnetic properties, for allotropes of Fe, Co, Ni, and several parameters in the C-Cr-N system. The developed method for calculation of G_m(T) for metastable magnetic compounds is also a useful tool for calculation of G_m(T) for many other transition metals and their carbides, nitrides, and carbonitrides.

CALPHAD (CALculation of PHAse Diagrams) metodiken består av tre hörnstenar, dvs. experiment, beräkningsmetoder (tex. Density Functional Theory (DFT)) och termodynamiska modeller, vilka tillsammans används för att skapa CALPHAD beskrivningar. I den här avhandlingen används CALPHAD-metodiken, inklusive alla tre delar, för att studera övergångsmetaller och deras karbider, nitrider och karbonitrider. Fokuset ligger i huvudsak på övergångsmetaller som är viktiga inom stål- och hårdmetallindustrin. Några av svagheterna och osäkerheterna i befintliga thermodynamiska beskrivningar av dessa övergångsmetaller identifieras och undersöks med hjälp av antingen experiment eller beräkningsmetoder, varpå nya beskrivningar presenteras.

En metod för beräkning av den molära Gibbsenergin som funktion av temperatur (G_m(T)) för metastabila magnetiska komponenter utvecklas. Metoden använder DFT i kombination med Debye-Grüneisen-modellen och den empiriska magnetiska modellen som ofta används inom CALPHAD. Den utvecklade metoden kan också användas för att uppskatta den magnetiska omvandlingstemperaturen (T_C eller T_N). Dessutom presenteras två nya tillvägagångssätt för hur man ska behandla beräkningar på dynamiskt instabila komponenter. Detta är viktigt eftersom det ofta är anledningen till att DFT-beräkningar på metastabila komponenter misslyckas. Metoden utvecklas och verifieras på bcc-, fcc- och hcp-allotroper av Fe, Co och Ni, och används sedan för att beräkna G_m(T) beskrivningar för fcc-TiC, fcc-CrC, fcc-CrN, hcp-Cr₂C och hcp-Cr₂N. Dessutom används samma metod också för att beräkna överskottet av Gibbs energi vid 0 K för interaktionerna CrC-TiC(fcc), CrC-CrN (fcc) och Cr₂C-Cr₂N (hcp), samt T_C och T_N som funktion av sammansättning för samma sammansättningsintervall.

Experiment utförs vid 1673 och 1773 K för att bestämma lösligheten av Cr i MC (M = Ti, Cr) och Ti i M₃C₂ och M₇C₃, i jämvikterna MC-M₃C₂-M₇C₃ och MC-M₃C₂-grafit i C-Cr-Ti-systemet. Lösligheterna mäts med EDS/WDS och verifieras med XRD/Rietveld-förfining.

De experimentella och beräknade resultaten för C-Cr-Ti-systemet används tillsammans med litteraturdata för att utföra en ny anpassning av detta system. Jämfört med den tidigare CALPHAD-beskrivningen innehåller den nya beskrivningen också uppdaterade beskrivningar för två av de tre ingående binära systemen (C-Ti och Cr-Ti) och reproducerar de experimentella resultaten i det isopleta snittet TiC-Cr₃C₂ som finns i litteraturen.

Sammanfattningsvis är resultatet av denna avhandling en uppdaterad CALPHAD-beskrivning av C-Cr-Ti-systemet och beräknade G_m(T)-beskrivningar, inklusive magnetiska egenskaper, för allotroper av Fe, Co, Ni och flera parametrar i C-Cr-N-systemet. Den utvecklade metoden för beräkning av G_m(T) för metastabila magnetiska komponenter är också ett användbart verktyg för beräkning av G_m(T) för många andra övergångsmetaller och deras karbider, nitrider och karbonitrider.

The Ti-Cr-C system has been studied by producing samples within the MC-M3C2-M7C3 (M=Ti, Cr) and MC-M3C2-graphite equilibria. The main purpose was to determine the solubility of Cr in MC; however, the solubility of Ti in M3C2 and M7C3 was also of interest, as well as the C content in MC. Heat treatments have been performed at 1673 and 1773 K for 300 h. Thereafter, the phase compositions have been measured with energy-dispersive X-ray spectroscopy (EDS) and wavelength-dispersive X-ray spectroscopy (WDS). X-ray diffraction (XRD), in combination with Rietveld refinement, has been used to determine the lattice parameter for MC. Density functional theory (DFT) calculations were performed to estimate the lattice parameter for MC as a function of composition, and the Rietveld refined lattice parameters for MC have then been recalculated to compositions in order to verify the EDS measurements. The results show that the EDS and XRD measurements give equal results. One conclusion is that, with the current conditions, 300 h is a sufficient heat treatment time in order to reach thermodynamic equilibrium. The other main conclusion is that the solubility of Cr in MC, in general, was overestimated by previous studies due to too short heat treatment times, but also that the solubility is very temperature dependent, especially for the MC-M3C2-graphite equilibrium. This clear temperature dependence was not taken into account in the existing thermodynamic description found in the literature.