The Kuramoto model for Synchronization

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Any: 2015, Tutor: Conrad J. Pérez VicenteThe aim of this project is to reformulate Kuramoto's equations for N-coupled oscilla-tors in a cycle limited boundary, both for the noise-free case (D = 0) and for the noisy one (D6=0). We will see that solving integro-differential equations is needed to finally get the approximate value of Kc, which sets the phase transition. To prove this phenomena I will also program a simulation and compare both results

Barocaloric effects at first-order phase transitions

Aplicat embargament des de la data de defensa fins el dia 36/6/222Current refrigeration devices, based on vapour-compression cycles, employ refrigerants such as HFCs, which exhibit a global warming potential a thousand times higher than the one produced by CO2,. Furthermore, the increasing middle class, associated with their refrigeration needs, urges for research in new environmentally friendly refrigerant alternatives. Solid-state caloric effects have been proposed as potential alternatives to replace the vapour-compression refrigeration technologies. They may become giant under the cyclic application and removal of an external field which induces changes in entropy and temperature associated with the occurrence of a first-order phase transition. In this work we specifically focus on caloric effects driven by means of hydrostatic pressure (barocaloric effects, BCEs), which allow us to operate with powder compounds, avoiding fatigue upon cycling. Additionally, a wide variety of materials can be used with BC purposes, due to the possibility of working with powdered samples and to the emergence of BCE associated with any transition volume change. In this dissertation we carried out the study of the BC performance of a series of compounds belonging to four different material families: Plastic crystals (PC), hybrid organic-inorganic perovskites (HOIPs), magnetic alloys and a superionic conductor. The election of these materials is not arbitrary, but relies on several features which anticipate good BCEs, such as large transition entropy changes, pressure sensitivity of the transition temperature and small thermal hysteresis. The small hysteresis avoids losses related with the refrigeration cycle and ensures smaller pressures under which reversibility is observed (which at the same time enable smaller applied work to the refrigerant). Finally, other properties must also be taken into account when designing a refrigeration device: Density, thermal conductivity and costs of production. BCEs are determined by means of a combination of quasi-direct and indirect methods. Firstly, we conduct measurements of atmospheric pressure and high-pressure calorimetry (DSC and DTA, respectively), along with experiments of X-ray diffraction and dilatometry. Then, the isobaric entropy curves are constructed, from which by means of curves subtraction the BCEs can be obtained. Additionally, special attention has been put on reversibility, since cyclability is mandatory for a real refrigeration device. Among the family of PC, derivatives from adamantane (1- and 2-adamantanol) and neopentane (neopentylglycol, neopentyl alcohol, pentaglycerine, tris(hydroxymethyl)aminomethane and 2-amino-2-methyl-1,3-propanediol) have been studied. Results for reversible isothermal entropy changes reach colossal values between 300-500 JK-1kg-1 and 150-500 JK-1kg-1 for neopentane and adamantane derivatives, respectively. These values are associated with adiabatic temperature changes among 10-20 K for pressure changes of ~2.5 kbar. The studied HOIPs ([TMA](Mn(N3)3) and [TMA]2(NaFe(N3)6)) exhibit giant values of ~100 J K-1 kg-1 with temperature changes between 15-20 K for pressure changes of ~2 kbar. It is important to highlight the small pressure required in order to obtain reversibility for these compounds, which is about only ~0.1 kbar. Magnetic alloys MnCoGeB0.03, Mn3NiN, Mn3(Zn0.45In0.55)N and Ni50Mn31.5Ti18.5 have been analysed. Nonetheless, only MnCoGeB0.03 and Mn3(Zn0.45In0.55)N show reversibility. They exhibit ~25 J K-1 kg-1 and 4-10 K under pressure changes of ~3 kbar. Finally, AgI, the only superionic conductor studied in this dissertation, reaches ~50 J K-1 kg-1 and ~10 K under pressure changes of 2 kbar. These results become the most outstanding presented in this thesis when normalized by volume. Finally, several figures of merit are presented, in which the studied materials are put into comparison with each other and with other already reported compounds.Els sistemes de refrigeració actuals, basats en cicles de compressió de gasos, fan servir refrigerants com els HFCs, que presenten un PEG (potencial d’escalfament global) milers de vegades major que el del CO2. Atesa la necessitat de frenar l’emissió de gasos d’efecte hivernacle, especialment en un context de creixent demanda mundial de refrigeració, la recerca de materials ecològics esdevé urgent. Els efectes calòrics en l’estat sòlid han estat proposats com a potencials alternatives a les tecnologies de refrigeració actuals. Aquests efectes poden esdevenir gegants sota l’aplicació cíclica d¿un camp extern, que indueix canvis en l’entropia i la temperatura associades a una transició de fase de primer ordre. En aquesta tesi ens enfoquem en els efectes calòrics obtinguts mitjançant pressió hidrostàtica (barocalòrics, BC), que permeten treballar amb pols i que per tant eviten problemes relacionats amb la fatiga. Altrament, gran varietat de materials amb efectes BC poden ser emprats amb finalitats refrigeratives degut a la possibilitat de treballar amb pols i a que aquests efectes estan associats a qualsevol transició de fase que impliqui un canvi de volum. S’ha dut a terme l’estudi BC de materials pertanyents a 4 famílies de compostos: Cristalls plàstics (PC), perovskites híbrides orgàniques-inorgàniques (HOIP), aliatges magnètics i un conductor superiònic. La selecció dels compostos no és arbitrària, sinó que recau en característiques que ens anticipen un bon comportament BC, com grans canvis d’entropia a la transició, sensibilitat de la temperatura de transició respecte la pressió i histèresis tèrmiques petites. Una histèresi petita evita pèrdues relacionades amb el cicle de refrigeració i assegura canvis de pressió més petits a partir de les quals observem reversibilitat. Finalment, altres propietats s’han de considerar al dissenyar un equip de refrigeració: la densitat, conductivitat tèrmica i costos de producció. Els efectes BC són obtinguts mitjançant la combinació dels mètodes quasi-directe i indirecte. Primer, es duen a terme mesures de calorimetria a pressió atmosfèrica i a altes pressions (DSC i DTA, respectivament), juntament amb experiments de rajos-X i dilatometria. Aleshores podem construir les corbes d’entropia isobàriques, a partir de les quals s’obtenen els efectes BC. A més, hem posat especial èmfasi en la reversibilitat, ja que ha de ser possible dur a terme cicles complets en un sistema de refrigeració real. Dins la família dels PC, hem estudiat materials derivats de l’adamantà (1- and 2-adamantanol) i del neopentà (neopentylglycol, neopentyl alcohol, pentaglycerine, tris(hydroxymethyl)aminomethane and 2-amino-2-methyl-1,3-propanediol). S’han obtingut resultats colossals de canvis d’entropia reversibles isoterms entre 300-500 JK-1kg-1 i 150-500 JK-1kg-1 pels derivats del neopentà i adamantà respectivament. Aquest valors estan associats amb canvis de temperatura adiabàtics entre 10-20 K per canvis de pressió de ~2.5 kbar. Els compostos estudiats de la família dels HOIPs ([TMA](Mn(N3)3) and [TMA]2(NaFe(N3)6)) presenten valors gegants de ~100 J K-1 kg-1 amb 15-20 K per canvis de pressió de ~2 kbar. És important emfatitzar els baixos canvis de pressió necessaris per obtenir reversibilitat, que són ~0.1 kbar. Pel que fa als aliatges magnètics, s’han estudiat el MnCoGeB0.03, Mn3NiN, Mn3(Zn0.45In0.55)N i Ni50Mn31.5Ti18.5. No obstant, només el MnCoGeB0.03 i el Mn3(Zn0.45In0.55)N presenten reversibilitat. Mostren valors ~25 J K-1 kg-1 i 4-10 K per canvis de pressió de ~3 kbar. Per acabar, el AgI, l’únic conductor superiònic, assoleix ~50 J K-1 kg-1 i ~10 K per canvis de pressió de 2 kbar. Aquest resultats esdevenen els més destacats quan es normalitzen pel volum. Finalment, hem representat vàries figures comparatives en que avaluem els materials estudiats entre ells i amb altres compostos prèviament públicPostprint (published version

Melting of orientational degrees of freedom

We use calorimetry and dilatometry under hydrostatic pressure, X-ray powder diffraction and available literature data in a series of composition-related orientationally disordered (plastic) crystals to characterize both the plastic and melting transitions and investigate relationships between associated thermodynamic properties. First, general common trends are identified: (i) The temperature range of stability of the plastic phase Tm-Tt (where Tt and Tm are the plastic and melting transition temperatures, respectively) increases with increasing pressure and (ii) both the rate of this increase, d(Tm-Tt)/dp, and the entropy change across the plastic transition analyzed as function of the ratio Tt/Tm are quite independent of the particular compound. However, the dependence of the entropy change at the melting transition on Tt/Tm at high pressures deviates from the behavior observed at normal pressure for these and other plastic crystals. Second, we find that the usual errors associated with the estimations of second-order contributions in the Clausius-Clapeyron equation are high and thus these terms can be disregarded in practice. Instead, we successfully test the validity of the Clausius-Clapeyron equation at high pressure from direct measurements. ReferencesPeer ReviewedPostprint (published version

Giant and reversible inverse barocaloric effects near room temperature in ferromagnetic MnCoGeB0.03

Hydrostatic pressure represents an inexpensive and practical method of driving caloric effects in brittle magnetocaloric materials, which display first-order magnetostructural phase transitions whose large latent heats are traditionally accessed using applied magnetic fields. Here, moderate changes of hydrostatic pressure are used to drive giant and reversible inverse barocaloric effects near room temperature in the notoriously brittle magnetocaloric material MnCoGeB0.03. The barocaloric effects compare favorably with those observed in barocaloric materials that are magnetic. The inevitable fragmentation provides a large surface for heat exchange with pressure-transmitting media, permitting good access to barocaloric effects in cooling devices.Peer ReviewedPostprint (author's final draft

Colossal barocaloric effects in adamantane derivatives for thermal management

Plastic crystals are currently attracting interest because their solid-state caloric functionality could be used to tackle climate change in two critical areas: (i) more environmentally friendly cooling and heating driven by pressure and (ii) passive waste heat management. Here, we suggest that plastic crystals could also be used for active pressure-assisted (i.e., barocaloric) waste heat management. In contrast to the barocaloric cooling/heating cycle, for active barocaloric waste heat management, the hysteresis may not be a constraint and transition temperatures above ambient are usually desired. In contrast to passive waste heat management, the application of pressure can be an advantage to actively control the absorption and delivery of heat by the plastic crystal. Here, we have investigated the pressure-induced caloric response at the first-order phase transitions occurring above room temperature of three plastic crystals derived from adamantane: 1-adamantanol, 2-adamantanol, and 2-methyl-2-adamantanol. Colossal barocaloric effects have been found for two of them under small pressure changes of 50 MPa. This behavior occurs thanks to a colossal transition entropy change and a large transition sensitivity to pressure, which can simultaneously take place due to enormous transition volume changes. The balance between configurational and volumic entropy changes at the transition has also been discussed. For 2-adamantanol, in addition to the transition to the plastic phase, the less energetic triclinic-to-monoclinic transition at lower temperatures has also been analyzed. The transition temperatures above ambient make these compounds suitable for waste heat management and, thanks to a small hysteresis, also for industrial cooling and heat pumping.Peer ReviewedPostprint (published version

Giant barocaloric effect in all-d-metal Heusler shape memory alloys

We have studied the barocaloric properties associated with the martensitic transition of a shape memory Heulser alloy Ni50Mn31.5Ti18.5 which is composed of all-d-metal elements. The composition of the sample has been tailored to avoid long range ferromagnetic order in both ausenite and martensite. The lack of ferromagnetism results in a weak magnetic contribution to the total entropy change thereby leading to a large transition entropy change. The combination of such a large entropy change and a relatively large volume change at the martensitic transition gives rise to giant barocaloric properties in this alloy. When compared to other shape memory Heusler alloys, our material exhibits values for adiabatic temperature and isothermal entropy changes significantly larger than values reported so far for this class of materials. Furthermore, our Ni50Mn31.5Ti18.5 also compares favourably to the best state-of-the-art magnetic barocaloric materials.Peer ReviewedPostprint (author's final draft

Barocaloric response of plastic crystal 2-methyl-2-nitro-1-propanol across and far from the solid-solid phase transition

Plastic crystals have emerged as benchmark barocaloric (BC) materials for potential solid-state cooling and heating applications due to huge isothermal entropy changes and adiabatic temperature changes driven by pressure. In this work we investigate the BC response of the neopentane derivative 2-methyl-2-nitro-1-propanol (NO2C(CH3)2CH2OH) in a wide temperature range using x-ray diffraction, dilatometry and pressure-dependent differential thermal analysis. Near the ordered-to-plastic transition, we find colossal BC effects of $\simeq$400¿J¿K-1¿kg-1 and $\simeq$5¿K upon pressure changes of 100¿MPa. Although reversible effects at the transition are obtained only from higher pressure changes due to hysteretic effects, we do obtain fully reversible BC effects from any pressure change in individual phases, that become giant at moderate pressures due to very large thermal expansion, especially in the plastic phase. From our measurements, we also determine the crystal structure of the low-temperature phase and estimate the contribution of the configurational disorder and the volume change to the total transition entropy change.Peer ReviewedPostprint (author's final draft

Barocaloric properties of quaternary Mn3(Zn,In)N for room-temperature refrigeration applications

The magnetically frustrated manganese nitride antiperovskite family displays significant changes of entropy under hydrostatic pressure that can be useful for the emerging field of barocaloric cooling. Here we show that barocaloric properties of metallic antiperovskite Mn nitrides can be tailored for room-temperature application through quaternary alloying. We find an enhanced entropy change of |¿St|=37JK-1kg-1 at the Tt=300K antiferromagnetic transition of quaternary Mn3Zn0.5In0.5N relative to the ternary end members. The pressure-driven barocaloric entropy change of Mn3Zn0.5In0.5N reaches |¿SBCE|=20JK-1kg-1 in 2.9 kbar. Our results open up a large phase space where compounds with improved barocaloric properties may be found.Peer ReviewedPostprint (author's final draft

Relationship between the two-component system 1-Br-adamantane + 1-Cl-adamantane and the high-pressure properties of the pure components

The temperature-composition phase diagram of the two-component system 1-Br-adamantane and 1-Cl-adamantane has been determined by means of thermal analysis techniques and X-ray powder diffraction from the low-temperature phase to the liquid state. The crossed isopolymorphism formalism has been applied to the two-component system to infer the normal pressure properties of the orthorhombic metastable phase of 1-Cl-adamantane at normal pressure. The experimental pressure-temperature phase diagrams for the involved compounds are related to the two-phase equilibria determined at normal pressure and inferences about the monotropic behavior of the aforementioned orthorhombic phase are discussed.Peer ReviewedPostprint (author's final draft

Heterogeneous or Homogeneous dynamics? : A Bayesian model selection problem

Universitat Politècniaca de Catalun