Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved International Review of Mechanical Engineering, Vol. 5, N. 2 Special Issue on Heat Transfer
227 elements with increased sensitivity or Seebeck effect.
The technological needs of an efficient analysis using an extremely reduced quantity of expensive substances,
imposes the reduction miniaturization of the detecting surface in all devices in temperature programmed as
well as in isothermal devices. The differences between the heat generation in standard calibrations and the
intrinsic characteristics of the actual dissipation produce a systematic error. For each configuration of the
dissipation location in the sample, power only a particular fraction of the heat is detected. The position of
the heat sources modifies the output signal st or thermogram and, also the energy evaluated from
1 sdt
S
∞
∫
, using the sensitivity S. In isothermal work with miniaturized systems several problems converge
simultaneously. In the first place, the standard ideas [1], [9], [10] need to be modified. The positioning effects can
be studied and, eventually, systematized to establish experimental rules for each type of device. Also, from
the heat transfer equation Fourier equation, the classical elementary models [1], [9], [11] need to be
improved. For instance, in liquid mixtures arising from a continuous flow of reactants, the energy measurement
suffers two essential limitations: the reaction is not carried out completely and part of the produced energy
moves outside of the detection area due to the fluid flow.
As the new devices use flat detectors, the system works mainly as a local temperature sensor. It is a poor
detector of the heat flux transmitted between the crucible walls and the surroundings. These calorimeter use
heaters for standard calibration as the old devices did. Notwithstanding, to increase the accuracy it is necessary
to perform more complex calibration procedures with a clear knowledge of the positioning effects and the
coupling of the different elements of the device. These complex models have to reproduce the effect of the
dissipation of heat inside any point of the sample, i.e. expressed in x, y, z coordinates.
The relatively recent availability of solid integrated thermopile chips allows the construction of miniaturized
calorimeters for a wide variety of applications as, for example, for the detection of heats of reactions in micro-
liter samples, and also for the measurement of heats associated to adsorbtionabsorbtion gas-solid
equilibrium. These systems present the same calibration problems.
II. The In Calibration Difficulties
When the target is the evaluation of the exchanged energies, the results obtained from melting an indium
sample 19.0 mg using temperature programmed devices can show relevant differences depending on the
sample positioning [12]. Figs. 2 show the change in the measured energy using a classical Differential Scanning
Calorimeter 2910 MDSC, TA Instruments, 1997. The energy depends on the radial position of the
indium sample inside the container see Fig. 2a. The results also depend on the z-axis position of the sample.
To vary the z-axis position, a thin cylindrical slide of memory steel was located between the crucible and the
sample. The sensitivity also changed with the degree of cold working introduced in the steel slide. Intermediate
thicknesses were obtained by polishing the slide. The structural changes induced by the cold work, probably
modified the thermal conductivity. In Fig. 2b, the extreme changes of the measured energy with or without
the 1 mm thick slide are close to 7 per cent. For each point the error bars represent the experimental dispersion
of the measurements. The manufacturer’s method only furnishes the value indicated by the arrow. In addition,
the calibration is related to a slid-liquid phase transformation, with an extremely narrow temperature
span i.e. some tenths of K. In the solid-solid transformations, as for example SMA, with a
temperature span of about 20-30 K, bad results are to be expected, related to mass, sample geometry and previous
cold work or other thermo-mechanical treatments on the samples. The differences between the standard
calibration and the intrinsic characteristics of the actual dissipation therefore induce systematic errors.
Figs. 2. Calibration procedures in a classical DSC system by melting an indium sample a: changes due to a radial shift of the sample inside the
crucible. b: dependence with the thickness of a steel slide situated between the indium sample and the crucible bottom. Open squares:
cold worked on steel slides one step. Full squares: two steps of cold working. Arrow: standard result obtained with the method provided by
the manufacturer
The changes of the sensitivity as a function of the “heater” position are evident when the mathematical
formulation of heat transfer is raised. The dissipation of heat in a network of N heat
capacities C
i
, with thermal couplings P
ik
, can be written as:
i i
i ik
i k
i i
k i
dT W
C P
T T
P T T
dt
≠
= +
− +
−
∑
1 where P
i
is the coupling to the sink at temperature T eventually for programmed temperature devices T
= T t.
Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved International Review of Mechanical Engineering, Vol. 5, N. 2 Special Issue on Heat Transfer
228 The calorimetric output st can be written as:
s r
s rpairs
s t T
T
α
−
= −
∑
2 The calorimetric output st simulated by numerical
methods [13], [14] changes when the dissipation w
i
modifies its position. The heater furnished by Xensor is a thin squared “o-
ring” near the thermocouples connection. In a strictly bi- dimensional system each position inside the squared
inner part is equivalent from the sensitivity evaluation but in dynamic measurements the heater response is
faster when a heater is situated in the center of the chip. In the actual 3-D conditions, each position of the x-y
coordinates furnishes different sensitivities and dynamic behavior associated to different heat losses to the
surroundings.
III. Aging in NiTi
