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New method of differential calorimetry
Section 14. Physics
DOI: http://dx.doi.org/10.20534/ESR-17-1.2-253-255
Nadareishvili Malkhaz, Tbilisi State University, Institute of Physics, senior researcher E-mail: malkhaz.nadareishvili@tsu.ge Kiziria Evgeni,
Tbilisi State University, Institute of Physics, Leading researcher E-mail: evgenikiziria@hotmail.com Sokhadze Viktor,
Tbilisi State University, Institute of Physics, senior researcher
E-mail: vsokhadze@yahoo.com Tvauri Genadi,
Tbilisi State University, Institute of Physics, Engineer E-mail: gena-tvauri@yahoo.com Tsakadze Severian,
Tbilisi State University, Institute of Physics, senior researcher
E-mail: ztsakadze@gmail.com
New method of differential calorimetry
Abstract: The article discusses a developed by authors new method of differential calorimetry, the novelty of which consists in the use of pulse heating mode instead of continuous heating, which is usually used in modern differential calorimeters. This method eliminates the main drawback of modern differential calorimetry, allowing combine high heating rates with the providing the measurements in equilibrium conditions, which enable us sharp increase the sensitivity and accuracy of measurements and study those slight changes in thermal heat capacity of bodies that cannot be measured by common differential calomireters.
Keywords: Thermodynamic studies, a new thermodynamic method, improving the accuracy of measurement in thermodynamics.
Introduction
In the solution of the problems existing in modern science and technology, thermodynamic studies, which are widely used in physics, chemistry, biology, materials science, medicine [1-3] etc., including for diagnosing cancer [4] play an important role. For the studies of this kind, calorimeters are divided into two basic groups: classical calorimeters, measuring the absolute heat capacity of bodies in the impulsive regime and differential scanning calorimeters (DSC) measuring the heat capacity difference between the research sample and the standard in the continuous heating regime. It should be noted that DSC are characterized by higher sensitivity to the heat effects and by comparatively shorter time of measurements (that can be regulated by scanning rate) than the classical calorimeters, and they are used more widely [1]. But they have one important disadvantage, incompatibility of the high heating rate with the providing the measurements in equilibrium conditions, which does not allow studying many "fine" effects. This issue was considered in work [5].
Results and discussion
To eliminate the above-mentioned drawback of differential calorimetry, we elaborated a new method the novelty of which consists in the use of pulse heating mode instead of continuous heating, which is usually used in modern differential calorimeters. The cursory mention of the method is given in [6].
Let us consider the pulse method in more detail. In this method, the measuring container (Fig.1) of the differential calorimeter consists of two identical cells (1), in which a sample and a standard (5) are placed. The cells are connected via thermocouples (3) that measure the temperature difference between the cells and, at the same time, provide the required thermal link between them.
Figure 1. Container of the differential calorimeter: 1 - Cells, 2 - Heaters, 3 - Thermocouples, 4 - Thermometer, 5 - Samples, 6 - Radiation shields
Section 14. Physics
Before applying a heat pulse of At duration and after a certain time of relaxation T>>At, the sample under study and the standard are in thermal equilibrium and their temperatures are similar. During the entire process of measurement, the differential container is thermally isolated by radiation shields (6), and the process proceeds under adiabatic conditions. Similar heat pulses Q=IUAt are applied to both cells by means of electric heater (2). The change in cell temperature in time is described by the expressions:
1 1 k 1 T(t) - T = — \0(At -1 i)p(t l)dtl-—\ST (t i)dt,
0 0 (l) 1 t k t T2(t) - T — J 0 (At -11)p(t J )dt1 +—\ST (t J )dt1 C2 0 C2 0 where T = T1(0) = T2(0) is the initial temperature of cells before applying the heat pulse, ST(t1) is the instantaneous temperature difference between cell temperatures, k is the coefficient of heat conductivity of the thermocouples between the cells, p(t1) is the amount of heat power supplied to each cell during the action of the pulse, and d(t) is the step function determined by d(t) = 1 at t>0 and 0(t) = 0 at t < 0.
After relaxation, at the moment At + t, expression (1) takes the form
C1AT = IU At — AQ C2AT = IU At + AQ where AT = T^- T is the temperature increment for the sample and the standard, T = T1(At + t) = T2(At + t) is the final temperature of
f At
the cells after relaxation, IUAt = j p(t)dt is the heat released in each
0
At +t
cell during the action of the heat pulse, and AQ = k j ST(t)dt is
0
the amount of heat passed from one cell to the other (thanks to thermal link between the cells) due to temperature difference ST(t) at the transition from one equilibrium state to another. Finally, the difference in heat capacities is calculated according to
AC=2AQ/AT (3)
In the experiment, the increase in temperature AT can be measured with the help of a thermometer (4). The power transferring from the one cell to another can be calculated as follows:
AQ = kß J s(t)dt
(7)
(2)
AQ = J SP(t)dt
(4)
Where SP(t) is the power transferring from the one cell to another. As it is well-known,
SP(t)=kST (5)
Where k is the heat conductivity of the thermocouples connecting the cells, and ST is the difference between the temperatures of these cells. On the other hand,
ST=p£ (6)
Where e is the emf of the thermocouples between the cells emerging due to the difference between temperatures at its ends, and |3 is the factor of proportionality depending on the thermocouple material and the number of thermocouples in the cell. Finally, we get SP(t)=kfis and, substituting this expression in Eq. (4), we obtain
As it was said above, k and ft are the constants of the device depending on its design. They are determined by a special calibration experiment and remain constant from a test to a test. Then, having measured only the thermocouple emf e, one can calculate the AQ and the heat capacity difference between the samples.
Figure 2. The dependence of the emf of thermocouples versus time for a warm-Impulse
Before the heat pulse is supplied, the cells are in a thermal equilibrium, they have the same temperature, and the emf of thermocouples will be zero if parasitic emf in conducting wires is excluded. At moment t1 (Fig. 2) electric heaters 2 (Fig. 1) switch on, and the same amount of heat Q=IUAt enters the cells for the At=t2-t1 time (Fig. 2).The cells heat up unequally because of the difference in their thermal capacities. As a result, the temperature difference ST arises between them, which, as shows formula (6), will cause the emergence of emf at the ends of thermocouples connecting these cells. After switching off of the heaters at moment t2, the cell temperatures begin to level off due to a thermal link between the cells via the thermocouples. After a certain relaxation time T=t -t2, the cell temperatures will equalize, and the system will again come into thermal equilibrium. Having calculated the area under the curve by integration, we can calculate the amount of heat transferred from one ampoule into another according to Eq. (7). As you can see, the pulse heating method allows developing the high heating rate during a short pulse and, at the same time, carrying out the measurements under the equilibrium conditions, because the system is in the thermal equilibrium at the beginning and after the heat pulse.
Conclusions
The pulse heating method eliminates the main drawback of differential calorimetry, allowing combine high heating rates with the providing the measurements in equilibrium conditions, which will enable us to study those slight changes in thermal heat capacity that cannot be measured by common differential calomireters.
Acknowledgments: The authors express their gratitude to Prof. J. Monaselidze for very useful discussions.
The work was supported of Sh.Rustaveli Foundation grant № FR/500/6-130/13
2. 3.
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Thermodynamic properties of LSCO Cuprates in the Nonsuperconducting State
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DOI: http://dx.doi.org/10.20534/ESR-17-1.2-255-256
Nadareishvili Malkhaz, Tbilisi State University, Institute of Physics, senior researcher E-mail: malkhaz.nadareishvili@tsu.ge Kiziria Evgeni, Tbilisi State University, Institute of Physics, Leading researcher E-mail: evgenikiziria@hotmail.com Sokhadze Viktor, Tbilisi State University Institute of Physics, senior researcher E-mail: vsokhadze@yahoo.com Tvauri Genadi, Tbilisi State University Institute of Physics, Engineer E-mail: gena-tvauri@yahoo.com Tsakadze Severian, Tbilisi State University, Institute of Physics, senior researcher E-mail: ztsakadze@gmail.com
Thermodynamic properties of LSCO Cuprates in the Nonsuperconducting State
Abstract: The investigations of low-temperature heat capacity in pure (y=0) and Zn-doped La1 84Sr0 16Cu1-yZnyO4 samples (y=0.033 and 0.06) have been performed by high-precision differential pulsed calorimeter (DPC) measuring the heat capacities under the thermodinamicaly equilibrium conditions in contrast to the commonly used differential scanning calorimeters (DSC). The anomaly of a low-temperature heat capacity which has a wide peak form and is related with Zn impurity was observed in the nonsuperconducting state in agreement with the neutron scattering experiments. The shape of anomaly indicates that Zn-induced magnetic ordering transition is of the first order transition type in the investigated cases. The anomaly shifts to higher temperatures with the increase of Zn content as it is characteristic of the anomalies of magnetic nature in contrast to anomalies of phonon heat capacity.
Keywords: Calorimeter, differential calorimeter, High temperature Superconductors, Superconducting Cuprates.
Introduction
There exists the suggestion that the dynamic spin correlations (spin fluctuations) should play an important role in the mechanism of high-temperature superconductivity [1; 2]. To clarify the situation in this direction, the influence of magnetic and nonmagnetic impurities in the high-temperature superconducting cuprates La2xSrCuO4 (LSCO) have been intensively studied [3].
The neutron scattering experiments [4] show that in monocrys-talline La179Sr021Cu099Zn001O4 sample in the non superconducting state there appear the elastic peaks indicating that Zn influences on AF dynamic spin correlations and stabilizes them into the static ones.
In the ^SR investigations of Zn-dopd LSCO [5] it was also observed that the AF magnetic order appears in La^SrCuj yZnyO4
samples in non superconducting state at x=0.21 and y=0.01. The thermodynamic investigations of Zn-doped LSCO cuprates were carried out both with the usual pulsed calorimetric technique measuring the absolute heat capacity of samples [6], and with the differential scanning calorimetry (DSC) measuring the heat capacity difference between the investigated and the reference samples [7], however, the data of thermodynamic characteristics of this phenomenon are not available. The cause in our opinion is not sufficient precision of used techniques.
Results and Discussion
We made the measurements of low temperature heat capacity in pure and Zn-doped LSCO samples by the original, created with us, differential pulsed calorimeter (DPC) with high precision
