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Heat capacity magnetic transitions

Spin-state transitions have been studied by the application of numerous physical techniques such as the measurement of magnetic susceptibility, optical and vibrational spectroscopy, the Fe-Mbssbauer effect, EPR, NMR, and EXAFS spectroscopy, the measurement of heat capacity, and others. Most of these studies have been adequately reviewed. The somewhat older surveys [3, 19] cover the complete field of spin-state transitions. Several more recent review articles [20, 21, 22, 23, 24, 25] have been devoted exclusively to spin-state transitions in compounds of iron(II). Two reviews [26, 27] have considered inter alia the available theoretical models of spin-state transitions. Of particular interest is the determination of the X-ray crystal structures of spin transition compounds at two or more temperatures thus approaching the structures of the pure HS and LS electronic isomers. A recent survey [6] concentrates particularly on these studies. [Pg.58]

This drawback has been overcome by using rare-earth magnetic materials in the coldest part of the regenerator. These materials have a magnetic phase transitions below 15K, with an increase in their heat capacities (see Section 3.6). However, to find a material suitable for sub 4 K applications is still a challenge. [Pg.147]

Spin transitions have also been reported for Al0.33[Fe(5-Cl-thsa)2] [110] and H[Fe(5-Cl-thsa)2] [109, 110]. For both compounds, a relatively abrupt and almost complete spin crossover occurs with Ti/2=228 K for the Al derivative, and 226 K for the H derivative. Transition temperatures determined by variable temperature heat capacity measurements are in agreement with those obtained from the magnetic susceptibility measurements. [Pg.294]

The Inden model [20] is frequently used to describe second-order magnetic order-disorder transitions. Inden assumed that the heat capacity varied as a logarithmic function of temperature and used separate expressions above and below the magnetic order-disorder transition temperature (TtIS) in order to treat the effects of both long- and short-range order. Thus for z = (T/TtIS) < 1 ... [Pg.47]

Figure 8.24 Heat capacity of C03O4 [23-25]. The insert shows the magnetic order-disorder transition at around 30 K [24] in detail. Figure 8.24 Heat capacity of C03O4 [23-25]. The insert shows the magnetic order-disorder transition at around 30 K [24] in detail.
Figure 13.2 Heat capacities of (a), Hg near the melting temperature of 234.314 K showing the abrupt nature of the change in heat capacity for this first-order phase transition at this temperature [from R. H. Busey and W. F. Giauque, J. Am. Chem. Soc., 75, 61-64 (1953)] and (b), MnO showing the continuous magnetic transition (note inset). (Data obtained from Professor Brian Woodfield and co-workers at Brigham Young University.) The dashed line is an estimate of the lattice heat capacity of MnO. Figure 13.2 Heat capacities of (a), Hg near the melting temperature of 234.314 K showing the abrupt nature of the change in heat capacity for this first-order phase transition at this temperature [from R. H. Busey and W. F. Giauque, J. Am. Chem. Soc., 75, 61-64 (1953)] and (b), MnO showing the continuous magnetic transition (note inset). (Data obtained from Professor Brian Woodfield and co-workers at Brigham Young University.) The dashed line is an estimate of the lattice heat capacity of MnO.
Figure 13.18 (a) Entropy Sm and (b) heat capacity Cm of A1 in the normal and superconducting states as a function of temperature. The solid line represents the entropy or heat capacity of normal Al, while the dashed line represents values for the superconducting state. The results for normal Al below the superconducting transition temperature Tc of 1.1796 K were made in 0.03 Tesla magnetic field to suppress the superconduction transition. [Pg.99]

Not only do the thermodynamic properties follow similar power laws near the critical temperatures, but the exponents measured for a given property, such as heat capacity or the order parameter, are found to be the same within experimental error in a wide variety of substances. This can be seen in Table 13.3. It has been shown that the same set of exponents (a, (3, 7, v, etc.) are obtained for phase transitions that have the same spatial (d) and order parameter (n) dimensionalities. For example, (order + disorder) transitions, magnetic transitions with a single axis about which the magnetization orients, and the (liquid + gas) critical point have d= 3 and n — 1, and all have the same values for the critical exponents. Superconductors and the superfluid transition in 4He have d= 3 and n = 2, and they show different values for the set of exponents. Phase transitions are said to belong to different universality classes when their critical exponents belong to different sets. [Pg.106]

Ehrenfest s concept of the discontinuities at the transition point was that the discontinuities were finite, similar to the discontinuities in the entropy and volume for first-order transitions. Only one second-order transition, that of superconductors in zero magnetic field, has been found which is of this type. The others, such as the transition between liquid helium-I and liquid helium-II, the Curie point, the order-disorder transition in some alloys, and transition in certain crystals due to rotational phenomena all have discontinuities that are large and may be infinite. Such discontinuities are particularly evident in the behavior of the heat capacity at constant pressure in the region of the transition temperature. The curve of the heat capacity as a function of the temperature has the general form of the Greek letter lambda and, hence, the points are called lambda points. Except for liquid helium, the effect of pressure on the transition temperature is very small. The behavior of systems at these second-order transitions is not completely known, and further thermodynamic treatment must be based on molecular and statistical concepts. These concepts are beyond the scope of this book, and no further discussion of second-order transitions is given. [Pg.239]

NdRu4Sbi2 is metallic and undergoes some type of magnetic transition near 1.3 K. The magnetic susceptibility follows a Curie-Weiss law above 50 K with an effective moment of 3.45/u.b and a Weiss temperature of -28 K. Crystal fields likely effect the susceptibility and magnetic interactions for temperatures below 50 K. Low temperature heat capacity data confirm the bulk nature of the magnetic transition (Takeda and Ishikawa, 2000b). [Pg.23]

In Fig. 13 the result of the field dependent calculation of the heat capacity using Landau theory for fields within the tetragonal plane is shown. In agreement with the experiment (Fig. 5), the magnetic field broadens the anomaly observed at the Neel temperature TN and lowers the transition point T of the commensurate to incommensurate phase transition. The increase of the calculated heat capacity while lowering the temperature below T, is a consequence of the approach to the temperature T of the proper instability of the ferromagnetic subsystem. As such, the same increase is observed in the experimental data too and it is possible to assume that the broad maximum at low temperature is connected with the subsequent phase transition in the magnetic subsystem of copper metaborate. [Pg.64]


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