Chinese Chemical Letters  2018, Vol. 29 Issue (5): 664-670   PDF    
Applications of low temperature calorimetry in material research
Xin Liu, Jipeng Luo, Nan Yin, Zhi-Cheng Tan, Quan Shi    
Thermochemistry Laboratory, Liaoning Province Key Laboratory of Thermochemistry for Energy and Materials, Dalian National Laboratory for Clean Energy, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China
Abstract: Low temperature calorimetry is an experimental method of heat capacity measurements, and heat capacity is one of the most important and fundamental thermodynamic properties of substances. The heat capacity can provide an average evaluation of the thermal property of a sample since it is a bulk property of substances. In the other hand, the condensed states of substances could be mainly controlled by the molecular motions, intermolecular interactions, and interplay among molecular structures. The physical property reflected in a material may be closely related to the energy changes in these three factors, which can be directly observed in a heat capacity curve. Therefore, low temperature calorimetry has been used not only to obtain heat capacity, entropy, enthalpy and Gibbs free energy, but also to investigate and understand lattice vibrations, metals, superconductivity, electronic and nuclear magnetism, dilute magnetic systems and structural transitions. In this review, we have presented the concept of low temperature calorimetry and its applications in the related field of material researches, such as nano-materials, magnetic materials, ferroelectric materials, phase change materials and other materials.
Key words: Low Temperature Calorimetry     Heat Capacity     Thermodynamics     Physical Propertie     Materials    
1. Introduction

Thermodynamics is concerned with heat and temperature and their relation to energy and work. It is one of the most important basic disciplines that human beings must follow in research of natural science and engineering. It has been generally used in the fields of Chemistry, Physics, Energy, Materials, Metallurgy, Biology, Engineering and so on. The heat capacity is one of basic thermodynamic properties related to the material structure and energy properties. Based on the heat capacity obtained from low temperature calorimetry, it can not only obtain the basic thermodynamic functions, such as enthalpy, entropy and Gibbs free energy, but also improve the understanding of the lattice vibrations, metals, superconductivity, electronic and nuclear magnetism, dilute magnetic systems and structural transitions in material research [1-21].

In the view of energy contribution, the heat capacity can be expressed as a sum of contributions from the lattice, electronic and magnetic properties of a substance. These contributions can be fitted to different theoretical models that may reveal the corresponding physical properties of a material. The lattice heat capacity is usually modeled using the classical Einstein and Debye functions at relatively high temperatures. The lattice heat below about 20 K, the lattice heat capacity Clat can be expressed by the harmonic lattice model [1-2, 20-22],

(1)

The contribution of electron heat capacity Celec is generally linear with the temperature,

(2)

The model of magnetic contribution of specific heat is different depending on the magnetic interaction. When the magnetic interaction is ferromagnetic or ferrimagnetic, the magnetic contribution of heat capacity Cmag is,

(3)

When the magnetic interaction is antiferromagnetic, the heat capacity contribution is,

(4)

where, the Bfsw and Basw representing the constants of ferromagnetic and antiferromagnetic contributions of heat capacity, respectively. When there is transition between the electron energy levels or atomic nucleus hyperfine structure, the system will be accompanied by Schottky effect, and the heat capacity contribution Csch is,

(5)

The total heat capacity obtained from low temperature calorimetric experiments can be expressed as the sum of all the above heat capacity contributions:

(6)

where, the Cother represents other contributions except those mentioned above. By using the above models, the various contributions of heat capacity can be extracted by fitting the experimental data, thus providing important information for the study of the physical property of materials [23-26].

There are four kinds of low temperature calorimetric methods for the heat capacity measurement of condensed matter: adiabatic calorimetry [27-30], relaxation calorimetry [31-35], alternating current (AC) calorimetry [36] and continuous calorimetry [37]. The temperature range is generally from liquid helium temperature (as low as mK) to room temperature, and the maximum temperature is generally no more than 400 K. This is due to that the temperature range of the heat capacity properties reflecting the material physical properties is generally less than 20 K. With increase of temperature, according to the Dulong-Petit law, the molar heat capacity of most solid matters tends to be consistent. Therefore, most of heat capacity studies using low temperature calorimetry are mainly performed in the temperature region below 300 K [38-51].

2. Nanomaterials

Nanomaterials have been a hot topic in material research field due to their entirely different chemical and physical properties from the bulk in the nanometer scale, which may have important research and application values for design and synthesize functional materials. The vast majority of researchers focus on the study of morphology and performance of nano-materials, but less of them attempt to understand and elaborate the nature of nano-materials from a thermodynamic view.

Tan and Wang studied the heat capacities of a series of nano metal oxides, metal and molecular sieve catalyst materials by means of adiabatic calorimetry. It was found that the heat capacity of these nanomaterials were larger than those of their bulk phases. For example, the differences of the heat capacity between the nano and bulk copper and molecular sieve ZSM-5 increase with the temperature increasing. This enhanced heat capacity behavior of nanomaterials was attributed to the factors of density, thermal expansion, impurities, surface adsorption and size effects, etc., and these impact factors may be different for different type of naomaterials [52].

Beorio-Goates et al. [53] studied the heat capacity of different nano-sized rutile and anatase TiO2 materials using adiabatic calorimetry in 2006, indicating that the enhanced heat capacity of namomaterials was mainly due to the significant amounts of water adsorbed on the material's surface. Also, they obtained the heat capacity of surface water by subtracting the lattice heat capacity for the total, and found that the heat capacity of water in inner and outer layers may have different behaviors.

And then, Shi et al. [54] performed heat capacity study on a series of SnO2 nanoparticles with different sizes using a relaxation calorimetry and inelastic neutron scattering technique (Fig. 1). It was found that the heat capacities of the SnO2 nanoparticles increased with their sizes decreasing, which may be attributed to that the smaller particles could absorb more surface water. Moreover, they found that the surface water on the different sizes of nanoparticles could exhibit different heat capacity behaviors.

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Fig. 1. The low-temperature heat capacities of nano and bulk SnO2 [54]. Reprinted with permition [54]. Copyright 2012, American Chemical Society.

In 2013, Beorio-Goates et al. [55] further studied the heat capacities of rutile and sharp TiO2 nanoparticles using semiadiabatic calorimetry. The results showed that the two nanoparticles exhibited a broad peak in the heat capacity curve below 5 K, and this heat capacity anomaly was attributed to Schottky effect originated from the water adsorbed at defect sites on the particle surfaces. They also found that the very low energies associated with the Schottky heat capacity maxima were consistent with tunnel splitting of ground state of a multiple-well potential.

3. Magnetic materials

Low temperature calorimetry is an important method to study the magnetic interaction of magnetic materials. Compared with the magnetic method, low temperature calorimetry can accurately detect the temperature region of the magnetic interaction occurring due to the high temperature control resolution usually employed in calorimetric instruments. More importantly, the magnetic contribution to the heat capacity can be expressed with different theoretical models, and therefore the corresponding magnetic property may be revealed by fitting the experimental heat capacity to these models. As for the magnetic transition, the transition entropy can be obtained by measuring the heat capacity in the transition temperature region. According to Boltzmann's principle, the entropy gain in the phase transition can be correlated with the following formula [1, 2, 6, 18],

(7)

where W is the number of energetically equivalent microscopic states, and when the phase transition occurs, the difference between the high temperature phase and the low temperature phase entropy is

(8)

where WH and WL represent the numbers of microscopic states of high and low temperature phases, respectively. In most cases, the general low temperature phase is in an ordered state when the phase change occurs, and hence WL = 1; thus, ΔS can be obtained by applying the number of microscopic states of the high temperature phase WH in Eq. (8).

3.1. Iron phosphates

Iron phosphates are widely used in agriculture as a fertilizer and insecticide component. In recent years, due to the excellent physical and chemical properties, these compounds have attracted the attention of material researchers [56-59]. Iron phosphates have two kinds of Fe valence of +2 and +3, which gives the rich magnetic properties of these compounds. However, the magnetic properties of these compounds are mostly studied by means of magnetic measurements, and the study on the understanding of magnetic properties in thermodynamics has not been reported. Shi et al. [60-62] studied the heat capacities of Fe(PO3)3, Fe3PO7, Fe4PO4, FePO4 and Fe3(P2O7)2 in the temperature range from 1.9 K to 300 K using relaxation calorimetry, and found that these samples showed a paramagnetic-antiferromagnetic phase transition in the measured temperature range. At temperature region below 10 K, the heat capacity data can be fitted with the following model:

(9)

where, γT is the contributions of the heat capacity from electrons, (B3T3 + B5T5) is the lattice heat capacity contribution, and BaswT3e-Δ/T is the magnetic heat capacity contribution. It can be seen that the magnetic heat capacity could be modeled using a T3 term, implying an antiferromagnetic ordering occurred in these compounds. Besides, for Fe3(P2O7)2, it is necessary to use a Schottky term to fit the heat capacity, indicating that the Schottky effect is present in this compound.

The lattice heat capacities of these compounds can be fitted using a combination of Einstein and Debye models:

(10)

where D(ΘD/T), E(ΘE, 1/T), E(ΘE, 2/T) are Debye, low temperature and high temperature Einstein Function, respectively.

In addition, a notable four-peak transition was detected in the heat capacity curve of Fe3(P2O7)2 (Fig. 2), which was different from the single peak obtained in the other five compounds. It is worth noting that iron ions in Fe3(P2O7)2 are mix valence, which lead the behavior more complicated during the magnetic phase transition. The Fe3(P2O7)2 sample was prepared by mixing FePO4, Fe2P2O7, Fe4(P2O7)3, and the phase transition behavior could be explained by comparing the magnetic phases of the three samples respectively. Fig. 2 shows the comparison of the heat capacity of Fe3(P2O7)2 and FePO4, Fe2P2O7, Fe4(P2O7)3 in the temperature range of the magnetic phase transition. It can be seen from the figure that the temperature range of first phase transition peak of Fe3(P2O7)2 coincide with the transition range of Fe2P2O7 which contains Fe2+; indicating that the transition peak is caused by the Fe2+; the third and fourth transition peaks coincide with FePO4 and Fe4(P2O7)3 phase transition temperature range respectively, indicating these two peaks are caused by the Fe3+; while the second transition peak is in the superposition range of Fe2P2O7 and FePO4, indicating this peak would be caused by both Fe2+ and Fe3+.

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Fig. 2. Plot of heat capacity comparison of Fe3(P2O7)2, FePO4, Fe2P2O7 and Fe3(P2O7)2 in the magnetic phase transition temperature region [60]. Reprinted with permition [60]. Copyright 2013, Elsevier Ltd.

3.2. Fe-Zn-O materials

ZnFe2O4 has a high surface area, low resistivity and excellent magnetic property, which were widely used in magnetic fluid, medical imaging, drug targeting, magnetic data storage and catalysis [63-65]. The molecular structure of ZnFe2O4 phase is spinel structure and nano ZnFe2O4 is generally considered to be a mixed spinel structure. Zhang et al. synthesized ZnFe2O4 nanoparticles with spinel structure using a simple coprecipitation method in their recent work [66]. The X ray diffraction, FTIR and transmission electron microscope characterization revealed that the nanoparticles have a crystal structure as same as bulk materials. Besides, the magnetic measurement results showed that the magnetic behavior of the nanoparticles were similar with the bulk phase, which was different with the found of nano zinc ferrite described in literature. The low temperature heat capacity study found that the Debye temperature of nanostructured samples was approximately the same with that of bulk phase reported by Westrum et al. [67], which further confirmed the nano zinc ferrite be a positive spinel structure that was consistent with that of the bulk material.

Subsequently, Liu et al. [68] further studied of the thermodynamic properties of a series of ZnxFe3-xO4, and heat capacity data below 10 K were fitted using a theoretical model including ferromagnetic and antiferromagnetic heat capacity contributions (Fig. 3):

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Fig. 3. Low temperature heat capacities of ZnxFe3-xO4 [68]. Reprinted with permition [68]. Copyright 2016, American Chemical Society.

(11)

The fitting parameters were obtained for these samples, and it can be seen that when the molar concentration of Zn is lower than 0.2, the ZnxFe3-xO4 appeared ferromagnetic properties, and with the increase of the content of Zn, the ferromagnetic interaction enhanced; when the content of Zn is higher than 0.5, the ZnxFe3-xO4 could appear an antiferromagnetic character, and with the increase of the content of Zn, the antiferromagnetic effect enhanced. These results were in line with those obtained from the magnetic measurement, suggesting that the thermodynamic and magnetic properties of Zn-doped Fe3O4 could be tunable by controlling the Zn doping amounts.

3.3. Molecular-based magnetic materials

Molecular-based magnetic material is a kind of magnetic compound synthesized by chemical methods of spontaneous assembly and control combination assembly mode with radical or paramagnetic ions (including transition metal and rare earth metal ions) and diamagnetic ligands. Molecular-based magnetic material is different from the traditional inorganic magnetic material involved with covalent bond, ionic bonds or metal bond, has the characteristics of low density, high transparency, good solubility, high plasticity, chemical good controllability, and become one of the hotspots in the field of physics, chemistry and materials [69, 70]. Most studies on molecular-based magnetic materials focus on material design, synthesis and magnetic property investigation using various techniques, however, the related thermodynamic study using low temperature calorimetry has seldom reported in literature.

Nakamoto et al. studied the heat capacity properties of molecular-based magnetic materials [Fe(2-pic)3] Cl2·MeOH (pic = 2-aminomethylpyridine) with spin cross phenomenon using adiabatic calorimetry in the temperature range from 12 K to 355 K [71]. A phase transition with a peak temperature of 150 K was detected in the temperature range of 80–250 K, and both low spin and high spin states of Fe in the phase change temperature region were confirmed by the Mössbauer spectrum. The phase change entropy calculated by the heat capacity (ΔS = 59.5 J K-1 mol-1) was much larger than the theoretical value (Rln5 = 13.4 J K-1 mol-1), which was mainly due to the fact that the phase change entropy was from the molecular vibration in addition to the magnetic contribution. The data analysis using domain model suggested by Sorai and Seki [72], indicated that this material has a weak cosynchronic effect when the spin crossover phenomenon occurs, which opened a new door for revealing the magnetic interaction mechanism of these materials.

Chen et al. [73] reported a low temperature heat capacity study of Mn(Ⅲ) Schiff base coordination molecular-based magnetic materials in 2014. The heat capacity curve of the sample obtained by the relaxation calorimetry is shown in Fig. 4. In order to reveal the physical properties of the sample at low temperature region, the heat capacity data below 20 K were fitted using the following model:

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Fig. 4. Low temperature heat capacities of the Mn(Ⅲ) Schiff-base coordination compound [73]. Reprinted with permition [73], Copyright 2013, Elsevier Ltd.

(12)

where, the last term is the Schottky heat capacity contribution, mainly from the contribution of the fine structure of Mn nucleus. Magnetic measurement in the low temperature region showed an antiferromagnetic behavior for this sample, which lead the heat capacity contribution to be proportional to the third power of the temperature. Although the fitting model contains a T3 term, the fitting coefficient B3 is very small and could only be regarded as lattice heat capacity contribution with other odds power of temperature, rather than antiferromagnetic contribution. In addition, the fitting model also contained an A-2T-2 term, which could be considered to be caused by the contribution of manganese nucleus or the phase transition in high temperature range. In order to further confirm whether it was the contribution of manganese nucleus, the internal magnetic field caused by the atomic nucleus of manganese was calculated to be 588 T, which was much larger than that 61 T reported in the literature [74]. Therefore, A-2T-2 was not caused by the nucleus of the manganese nucleus but the phase transition possibly occurred at lower temperatures.

3.4. Magnetic refrigeration materials

Magnetic refrigeration materials is a kind of magnetic functional material which is used for cooling by means of magnetocaloric effect, and it does not need compressor and has the advantages of low noise, small volume, light weight and no emission and so on. These materials have a wide range of applications in the field of space, nuclear technology and other areas of defense. Low temperature calorimetry can be used to measure the magnetic entropy generated by the magnetic phase transition, so as to provide an important basis for evaluation of the magnetocaloric effect of the material. For example, Zheng et al. [75] reported a Co-Ln metal phosphate with lattice and cage shape as a magnetic refrigeration material, and the heat capacity data of the sample was measured by low temperature calorimetry, furthermore, the entropy change of the sample under different magnetic field was calculated by the corresponding thermodynamic relationship, which could provide a strong support for this sample used as a magnetic refrigeration material.

4. Ferroelectric materials

Ferroelectric materials refer to a class of materials with ferroelectric effect. Ferroelectric effect refers to the positive and negative charge center is not coincident in some crystals due to the asymmetry of the crystal structure, which gives rise to the electric dipole, namely, the electrode strength is not zero and the crystal can spontaneously behave a electric polarization, and its direction can be reversed by the electric field or re-orientation. In addition to ferroelectric, ferroelectric materials can also show dielectric, piezoelectric, pyroelectric, sound light effects, photoelectric effects, nonlinear optical effects, photorefractive effects, and many other excellent physical properties, which can be widely used in capacitors, piezoelectric sensors, ferroelectric memory, waveguide, optical memory and other fields [76-78].

Shi et al. [79] studied the heat capacity properties of two ferroelectric compounds with similar crystal structures, Ba2TiSi2O8 and Sr2TiSi2O8, in the temperature range from 1.9 K to 300 K using a relaxation calorimetric method, and the results are shown in Fig. 5. For heat capacity below 10 K, the following model was used to fit the data:

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Fig. 5. Low temperature heat capacities of Ba2TiSi2O8 and Sr2TiSi2O8 [79]. Reprinted with permition [79], Copyright 2013, Elsevier Ltd.

(13)

where, Bfe is specific constant of ferromagnetic term. It can be seen that the T3/2 term contained in this model is generally considered as the contribution from ferromagnetic contribution. In fact, as early as in 1970s, Lawless [80] found that the low temperature heat capacity contribution of some ferroelectric materials was in proportional to T3/2 term, and it was attributed to quantized domain-wall oscillations or a surface excitation. And also, other researchers had proposed that the T3/2 contribution of heat capacity in ferroelectric material was caused by impurities or defects, rather than the ferroelectric behavior [81]. However, there is no further study of these impurities or defects to what extent that it could include T3/2 contribution in these materials. Therefore, this requires more calorimetric work to verify whether the low temperature heat capacity of the ferroelectric materials have a contribution of T3/2 contribution at low temperatures.

5. Phase change materials

Phase change materials are capable of storing or releasing thermal energy during the phase transition process at almost constant temperatures with the involved latent heats absorbed or released, respectively, which are generally several times larger than those commonly used in sensible heat storage materials, and thus these materials are generally used for thermal energy storage [82, 83]. The thermodynamic properties, such as phase transition temperature, enthalpy and entropy as well as heat capacity are significant parameters for evaluating the performance of thermal energy storage for phase change materials. These thermodynamic properties can be determined using the heat capacity measurement in the concerned temperature region.

The heat capacities of several new phase change materials were investigated using a precision automatic calorimeter by Lu et al. [84], and the phase transition temperature, enthalpy and entropy of the phase change materials could be obtained by progressive approach through stepwise heating method employed in adiabatic calorimetry [85]. The melting point determination principle is:

(14)

where, Tm is melting temperature of the sample, Ti' is a certain equilibrium temperature at which solid and liquid phase coexist in the melting region. Tf is a temperature slightly higher than the melting temperature, Q' is the total heat introduced by heating the sample and sample cell from Ti' to Tf, C0 is the average heat capacity of the cell in the temperature region from Ti' to Tf, Cp(L) is the liquid phase heat capacity of the sample at temperature of (Tf +Tm)/2, Cp(S+L) is the heat capacity of the solid-liquid coexistent system at temperature of (Tm + Ti')/2, and n is the number of moles of the sample. The measuring principle of phase change enthalpy and entropy are,

(15)
(16)

where Ti is a temperature point slightly below the starting melting temperature, Cp(S) is solid phase heat capacity of sample at temperature of (Ti + Tm)/2, C0 is the heat capacity of sample cell at temperature (Ti + Tf)/2, Q is the total heat introduced by heating the sample and sample cell from Ti to Tf. These thermodynamic properties can be accurately determined according to the above functions through the collected energy, temperature and heat capacity in the adiabatic calorimetric measurement.

In addition, according to the ideal solution law, the purity of the sample can be determined by measuring the heat capacity of the solid-liquid phase transition by means of adiabatic calorimetry [86]. The measurement principle is as follows,

(17)

where, T0 is the melting temperature of an absolute pure material; T1 is the melting point of the given sample, which can be obtained from Formula (11); F is melting faction, can be obtained by the heating energy of adiabatic calorimetry measurement. The equilibrium temperature T of the sample in the solid-liquid phase transition process is plotted against 1/F, and the line is extrapolated to 1/F = 1 and 1/F = 0 to obtain T0 and T1, respectively. Shi et al. measured the low temperature heat capacity of 4-dimethylami-nopyridine (DMAP) by adiabatic calorimetry [86]. The experimental results are shown in Fig. 6, The purity of the sample was calculated to be 99.964% by Eq. (17). The accuracy of the determination of the purity of organic compounds using adiabatic calorimetry is generally one order of magnitude higher than that measured by spectroscopy, and this technique can therefore be used as a standard method for the determination of the purity of such substances.

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Fig. 6. Low temperature heat capacities of DMAP (a) and the inset is the measured heat capacities in transition temperature region, the melting curve (b) of DMAP [86]. Reprinted with permition [86]. Copyright 2007, American Chemical Society.

6. Other applications

Low temperature calorimetry can also be applied in other materials to reveal some novel physical properties that possibly occurring in these materials. For example, Park et al. [87] has reported the measurement and study of heat capacity of pressuretuned unconventional superconductor CeRhIn5 at low temperatures, and they found that a line of quantum-phase transitions induced inside the superconducting state by an applied magnetic field, and established a common relationship among hidden magnetism, quantum criticality and unconventional superconductivity in copper oxides and heavy-electron systems. Kinast et al. [88] have performed a heat capacity study on strongly interacting Fermi gas of 6Li atoms that confined in an optical trap, characterized the nature of bosonic and fermionic excitations, and predicted the onset of super fluidity at the observed transition point. This study presents a new way to study the thermodynamic properties of the strongly interacting Fermi systems. Additionally, combining the measurements of magnetocaloric effect and heat capacity, Rost [89] studied the entropic landscape of Sr3Ru2O7 using magnetic field as running parameters. This allows studying the thermodynamic consequences of the formation of a novel electronic liquid crystalline phase in its vicinity.

7. Conclusions

Low temperature calorimetry has been developed for more than 100 years as a classical and important experimental method for measuring and studying the heat capacity and related thermodynamic properties of condensed matter in non reactive systems. Based on the above studies presented in this review, it can be concluded that low temperature calorimetry play a crucial role in understanding the macroscopic property of materials closely related to the microscopic energy schemes of molecular freedom degrees in a thermodynamic view. However, due to its classical and traditional nature, most researchers seem to ignore the application of this technique but to seek more fashionable experimental methods to study the physical properties of materials. To make low temperature caloimetry extensively used in the material researches, the calorimetrists should not only accurately measure the thermodynamic data using various calorimetric methods, but also reveal and explain the corresponding properties of materials in thermodynamics to attract the research interests of material researchers. On the other hand, it should break through the limitation of commercial instruments, and develop new calorimetric method, technique and devices to meet the increasing demand of material research.

Acknowledgments

This work was financially supported by the National Natural Science Foundation of China (Nos. 21473198, 11775226) and Natural Science Foundation of Liaoning Provincial (No. 201602741). Q. Shi would like to thank Hundred-Talent Program founded by Chinese Academy of Sciences.

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