high temperature specific heat measurement using quasi

Transactions, SMiRT-23

Manchester, United Kingdom - August 10-14, 2015

Division I, Paper ID 218

High temperature specific heat measurement using quasi-adiabatic calorimetry

Mark Kirkham1,, Klaus Nuemann

2, Andrew Wisbey

1, and Bryan Daniels

2

1 Amec Foster Wheeler, Clean Energy, Walton House, Birchwood Park, Warrington, Cheshire,, UK

2 Physics Department Loughborough University, UK

ABSTRACT The measurement of specific heat capacity above ambient temperatures is normally performed using

differential scanning calorimeters (DSC’s), which typically use small samples (5 mm x 1 mm, up to 5 mm

x 15 mm). However, some materials (e.g. graphite, complex alloys, polymers and composites) require a

large number of grains, or large volumes, for measurements to be representative of a material’s bulk

properties. For these types of material DSC measurements are not ideal and traditional modelling (i.e.

Kopp-Neumann, method of mixtures) has only limited applications and is not always applicable,

especially if phase changes take place, or the sample melts.

Low temperature specific heat capacity has been successfully measured using Nernst-type (heat pulse)

adiabatic calorimetry. This technique has potentially the best accuracy of available techniques and a large

freedom on sample size. Therefore, a high temperature quasi-adiabatic calorimeter was developed.

The developed system uses a quasi-adiabatic sample mounting arrangement to measure specific heat,

using an integrated temperature sensor and heater arrangement for improved sensitivity. During the

development of the measurement system two methods of heat pulse analysis were produced; 1.traditional

post-pulse regression/interpolation, and 2. a simplified finite element modelling technique The system

and both analysis techniques produced reproducible specific heat capacity data between room temperature

and 1000°C on samples sizes between 2 g to 50 g for graphite, copper, stainless steel, and molybdenum

samples. This data compared well with accepted values for these materials.

INTRODUCTION As part of a programme of research investigating the shape memory effect in the ferritic shape memory

alloy Ni2MnGa at Loughborough University Physics department a method of determining the high

temperature order-disorder phase transition (V. Recarte, 2012) (Khovailo, et al., 2001) of as cast non-

stoichimetric compositions of Ni2MnGa (Reece, 2007) using specific heat capacity was required

(Kirkham, 2014). The relatively large grain structure and potential for segregation that can occur in cast

Ni2MnGa (Cherneko, et al., 1994) meant that DSC measurements were not considered ideal, as this

technique would limit sample size and potentially skew results. To allow for a larger sample size and

potentially increase resolution at the transition temperature, a system for the measurement of specific heat

adiabatically was developed. The following sections of this paper detail the apparatus used, the analysis

techniques applied and the results of commissioning tests performed with a range of material.

METHODOLOGY The high temperature adiabatic calorimeter (referred to as the HTCP system) measures specific heat using

the Nernst-type pulsed technique (Nernst, 1911). This consists of a sample being heated/cooled to the

required measurement temperature, once stable, a known amount of energy is supplied to the sample (the

heat pulse) and the resultant change in temperature recorded. If the sample is perfectly thermally isolated

during the measurement (adiabatic) the specific heat capacity can be determined directly using the

equation below:

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dT

dQ

mCP

1= (1)

Where m = mass, dQ = supplied energy, and dT = change in sample temperature

In practise the sample is never perfectly thermally isolated and there is always some heat loss from the

sample and much of the design and development effort for the HTCP system focused on minimizing heat

loss and correcting for unpreventable heat loss and other practical considerations (e.g. additional thermal

mass due to heater and measurement apparatus).

Description of Apparatus The HTCP system consists of: a furnace to heat the sample to the measurement temperature; a vacuum

tube, in which the measurement apparatus is located: a number of radiations shields and internal supports;

and the sample head, containing the sample and measurement apparatus (i.e. thermocouples, sample

heater, etc). Figure 1 shows a cross section of the test apparatus.

(a) (b)

Figure 1: Cross sections of (a) the HTCP test chamber, and (b) the sample head containing the sample and

measurement apparatus.

All measurements were performed inside the vacuum tube, evacuated to <2x10-3

mbar, to prevent

convective heat loss from the sample. Testing in vacuum also reduced oxidation to the samples and the

internal supports when at high temperature. The inserts supporting the sample head and radiation shields

(Figure 1a) were all made of thin walled stainless steel tube to minimise longitudinal heat transfer and

permit the sample can to remain at a stable temperature. The horizontal radiation shields/baffles along the

tube (Figure 1a) were made of thin molybdenum foil, these components minimise longitudinal heat

transfer away from the sample head due to radiation.

The sample head (Figure 1b) containing the sample and measurement apparatus was positioned at the

mid-point of the furnace hot zone (Figure 1a), where the temperature was uniform and stable. The hot

zone extended 200 mm above and below the ends of the head. The outer surface of the sample head was

made of thick ceramic (alumina and boron nitride) with molybdenum attachments. The thickness of the

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outer shell (4 mm alumina, and 8 mm boron nitride) was maximised to increase thermal mass and heat

transfer time to prevent any short term temperature fluctuation affecting the sample and to allow for a

more stable internal temperature.

Inside the ceramic outer shell of the sample head a number of floating molybdenum and tantalum

radiation shields were mounted concentrically around the sample to minimize radiative heat loss from the

sample during pulse measurements. To reduce conductive heat loss during pulse measurements the

sample was suspended from fine wires welded to the sample surface. To reduce the sample connections,

these support wires double as thermocouples used to measure the sample surface temperature.

A small wire wound platinum resistance thermometer (PT100) was cemented in a hole drilled in the

centre of the sample to act as a combined temperature sensor and sample heater element (See Figure 1b).

The sample heater was connected using the four-point probe configuration to permit accurate

determination of the sensor resistance and the power supplied during heating, without the resistance of the

connecting wires having an effect.

The instrumentation in the sample head (2 off K-type thermocouples and 4 off wires connected to PT100

thermometer) was connected through water cooled lead-throughs in the vacuum tube head to a

multiplexer unit, power source and measurement instrumentation. A computer connected to these

components control the system and records all measurements in real-time.

Initial Trials During initial trials two aspects of the measurement approach required further consideration. These were

the sample temperature measurements and sample temperature stability (due to thermal isolation).

Figure 2: HTCP heat pulse signal with thermocouple (red) and platinum resistance thermometer (blue)

temperature data.

Sample Temperature:

Nernst-type heat pulse calorimeters determine the change in temperature (dT) due to a heat pulse by

measuring the sample temperature after a heat pulse and subtracting a baseline temperature determined

from the pre-heat pulse stage of a measurement. Figure 2 shows a heat pulse for copper at room

temperature, as can be seen the change in sample temperature recorded by the thermocouple (red line,

Figure 2) is much lower than observed in PT100 resistor data (blue line, Figure 2). Analysis of both data

sets below shows an error of 22% on the specific heat derived from the thermocouple data but only 1.2%

for that based upon the PT100 sensor. This suggests that the surface thermocouple was insufficiently

sensitive to accurately determine the sample temperature change during a heat pulse. Hence the heater

element (PT100 resistance thermometer) was used. While the surface mounted thermocouples were of

limited application for determining the sample dT for a heat pulse, they were useful in calibrating each

PT100 sensor used.

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

��

Time (s)

dT (K

)

RST offset

Sample

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Sample temperature stability (due to thermal isolation):

The configuration of the HTCP system, and location of the sample (Figure 1) gave excellent thermal

isolation of the sample from the furnace but the time taken for the sample to stabilise after a 10 K change

in furnace temperature was in excess of 2 hours. Under this configuration, the long delay between heat

pulse measurements (due to slow stabilising rate) would mean that a specific heat measurement between

room temperature and 1300 K (measurements made every 10 K), would take more than 16 days (for both

heating and cooling phases). This time does not include the time taken for the pulse measurements. This

is clearly impractical for most purposes and limits the observations possible.

To address this problem and reduce the test time and also increase resolution it was proposed that instead

of allowing the sample to stabilise at a specific temperature before making the measurement, the furnace

and sample should be heated linearly and the pulse measurements made continuously with a suitable gap

to allow the residual heat from any heat pulse to dissipate and the sample to return a pre-heat pulse

thermal drift (Figure 3).

Figure 3: Schematic of a heat pulse made with a linearly drifting baseline.

The advantage of the linearly drifting baseline is that not only does it reduce measurement time (without

affecting resolution), but it also allows for the measurement of dynamic processes. However, this

approach does mean that there are additional potential sources of error in the measurement and the system

cannot be described as truly adiabatic.

Finite element modelling of the system under both stable and drifting ambient temperature conditions

showed that there was a slight difference between the two measurement conditions (Figure 4 and 5). Thus

the dT of the sample with a drifting baseline (Figure 5b) stabilising at a temperature above dT=0, while

the dT for the sample with a stable baseline (Figure 4b) continues to decay towards dT=0. However, this

difference can be accounted for during the analysis of the pulse.

(a) (b)

Figure 4: FE modelled data for a steel sample at a stable ambient temperature of 376.9 K showing (a) the

absolute temperature data and (b) temperature data with linear baseline subtracted.

Model data: Stable Ambient Temperature

376.85

376.9

376.95

377

377.05

377.1

377.15

0 100 200 300 400 500 600 700 800 900

Time (s)

Te

mp

era

ture

(K

)

Heater

Skin

Ambient

Model data: Stable Ambient Temperature

0

0.05

0.1

0.15

0.2

0.25

0.3

0 100 200 300 400 500 600 700 800 900

Time (s)

dT

(K

)

Heater

Skin

Ambient

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(a) (b)

Figure 5: FE modelled data for a steel sample for a constant drift of +10 K/hr, starting at 376.9 K and,

showing (a) the absolute temperature data and (b) temperature data with linear baseline subtracted.

The modelling of the HTCP system with a drifting baseline also showed that the selection of an

appropriate baseline function, to produce a suitable change in sample temperature data (dT), required

additional consideration for some of the analysis techniques applied. Trials were undertaken with linear,

polynomial and exponential baseline functions, but for consistency of results this paper only reports

results determined using baselines calculated using linear regression on the measured pre-pulse data. The

trials of alternative baseline functions, and using a measured baselines (extrapolated from the shield

temperature), showed some success but require additional investigation to improve repeatability.

Data Analysis A heat pulse measurement consists of: a pre-pulse phase, during which baseline data is recorded; the

heating phase, when the heat pulse is supplied; and the post-pulse phase as the sample cools back to the

baseline.

The measurement of the heat pulse energy supplied to the sample during the heating phase was assumed

to be 100% of the electrical power supplied to the heater element (determined from P=IV, and the

duration the heater was on), but since no real measurement system is truly adiabatic simply measuring dT

and using equation 1 was not sufficient to produce accurate Cp results. During the initial trials three

analysis techniques were developed, although only the first two are discussed here:

1. Post-pulse regression

2. Simple Finite Element Modelling (FEM)

3. Heat-pulse analysis (limited data, not discussed in this paper)

Post pulse regression fits an exponential polynomial to the data recorded in the post-pulse stage of the

measurements, after a suitable baseline has been subtracted (see Figure 6). To account for heat loss from

the sample during the heat pulse, the measured change in sample temperature due to the heat pulse is

calculated from the regression line (fit to post pulse data) extrapolated to the mid point of the heating

pulse (See Figure 6).

The heat capacity of the sample and heater arrangement can then be calculated (eqn 1), with the specific

heat of the sample determined by subtracting the heat capacity of the sample heater and cement. This

addenda heat capacity was determined from calculated values based on heater compositions and the

Nuemann-Kopp (Gramvall, 1999) method of mixtures (eqn 2 below), supported by initial trial data.

sample

i

iimeasured

sample

addendameasuredsample

m

CmH

m

HHC

�−

=

−

= (2)

With Ci = specific heat of the ith component, H = heat capacity and mi = the mass of the i

th component.

376.5

377

377.5

378

378.5

379

379.5

380

380.5

0 100 200 300 400 500 600 700 800 900

Time (s)

Tem

pe

ratu

re (

K)

Heater

Skin

Ambient

Model data: Constant Drift (10 K per Hour)

0

0.05

0.1

0.15

0.2

0.25

0.3

0 100 200 300 400 500 600 700 800 900

Time (s)

dT

(K

)

Heater

Skin

Ambient

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(a) (b)

Figure 6: Temperature pulse measurement with a linear baseline subtracted for copper, showing (a) the

change in sample temperature, dT and (b) the dT data on a logarithmic scale, ln(dT).

The regression analysis of data in Figure 6 produced the following results for copper at room temperature:

Calculated Cp – from sample thermocouple: 471.2 J.kg-1

.K-1

Calculated Cp – from sample resistance thermometer: 389.8 J.kg-1

.K-1

The accepted specific heat capacity of copper at 293 K is 385 J.kg-1

.K-1

(Y.S. Toulokian, 1970) and as

noted above, the HTCP system derived values for the sample thermocouple and resistance heater differ

from the reference data by 22% and 1.2%, respectively.

Modelling and observed results showed that the post pulse data were best approximated with exponential

curves with polynomial exponents, where the polynomial order decreases as the temperature rises. The

exact polynomial order is sample and test specific. Figure 7 shows the decreasing order of polynomials

required as temperature increases.

(a) (b)

Figure 7: (a) Example of the modelled dT pulse data, with post pulse regression for at three temperature

(300 K (blue), 800 K (pink) and 1200 K (green)) and (b) ln(dT) post pulse data with the lowest order

polynomial fit with R2 = 1 to 4 DP.

The post pulse regression analysis was very dependent on the range over which the regression is taken,

attempts to automate the analysis proved difficult and the analysis had to be performed manually, with the

inherent issues of user inputs/interpretation. A design modification to use two temperature sensors may

resolve this issue but requires confirmation.

Finite element modelling (FEM) analysis was undertaken by fitting a simple 2-body finite element model

to the measured data by tuning the heat capacity of the sample and heat transfer coefficient between the

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 200 400 600 800 1000 1200 1400

Time (s)

Tem

pera

ture

(K

)

SampleTC

Sample RST

Reg. Sample TC

Reg. Sample RST

0

0.1

0.2

0.3

0.4

0.5

0.6

0 100 200 300 400 500 600 700 800

Time (s)

dT

(K

)

300K

800K

1200K

dT absolute

curve fit 300K

curve fit 800K

curve fit 1200K

ln(dT-1200K) = -0.0098 t + 0.2071

R2 = 1.0000

ln(dT-800K)= 2.7173E-09 t3 - 2.5117E-06 t

2 -

5.2178E-03 t - 3.6540E-01

R2 = 1.0000E+00

ln(dT-300K) = 1.5154E-12 t4 - 1.9419E-10 t

3 +

5.5209E-09 t2 - 4.4513E-03 t -

4.8860E-01

R2 = 1.0000E+00

-8

-7

-6

-5

-4

-3

-2

-1

0

0 200 400 600 800

Time (S)

ln(d

T)

300 K model, post pulse data only



Linear (1200 K model, post pulse dataonly)

Poly. (800 K model, post pulse data only)

Poly. (300 K model, post pulse data only)

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Division I

sample and heater. Figure 8 shows a copper sample heat pulse and a simple two body FEM analysis. The

FEM analysis of the data in Figure 8, produced a specific heat of Cp = 386 J.kg-1

.K-1

, reference data for

Copper Cp = 385 J.kg-1

.K-1

(Y.S. Toulokian, 1970) – clearly a good result.

Figure 8: Example of an analysis of a measured heat pulse for a copper sample using the two body model.

This technique is open to misinterpretation, by inputting impractical heat transfer coefficients. However,

the fact that the two-body model is optimized for more of the measured data means that it is a more robust

analysis technique than post-pulse regression.

The use of more complex models (splitting the sample/heater assembly into more than two nodes/bodies)

would improve the fit of the model but would introduce another unknown variable (thermal conductivity

of the sample). This would have a significant effect on the tuning of the model, since it would be possible

to produce identical heat pulse data with different specific heats using different thermal conductivities.

RESULTS & DISCUSSION After the initial testing was performed to refine the methodology and the analysis approach finalised, four

materials were selected to test the system. The variety of the samples also served to investigate the scope

of application for the HTCP system. The samples tested were in two forms: three of the four test samples

were cylindrical and the fourth was rectangular. Tables 1 and 2 below detail the test sample information:

Table 1: Cylindrical sample information

Sample

No. Material

Sample information

Diameter (mm) Length (mm) Mass (g)

1* Stainless Steel (Type 304) 7.905 18.244 6.235

2* Stainless Steel (Type 304) 7.905 14.353 5.785

3 Copper 8.536 17.259 7.900

4 Molybdenum 16.015 25.005 51.800 * sample 1 and 2 are the same piece of material with testing performed on the larger 6.235g sample (1) then the

sample reduced in size to produce the smaller 5.7859g sample (2)

Table 2: Rectangular sample information.

Sample

No. Material

Sample information

Width (mm) Depth (mm) Length (mm) Mass (g)

5 Graphite 5.935 5.802 15.325 0.983

Each sample underwent a range of heating and cooling rates between 1 K/hr and 10 K/hr and using

different heat pulse durations and powers, as well as recording data over varying pre-pulse and post pulse

durations. The results of the four materials are shown in Figures 9-12.

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��

Figure 9: Measured specific heat capacity of copper using (a) post pulse regression on both the sample

thermocouple (blue) and the platinum resistance thermometer (red), and (b) using FEM analysis. Standard

reference data taken from (Y.S. Toulokian, 1970)

�

��

Figure 10: Measured specific heat capacity of stainless steel samples 1 and 2, using (a) post pulse

regression and (b) using FEM analysis. Standard reference data taken from (Y.S. Toulokian, 1970)

The conventional regression analysis for both the copper (Figure 9a) and the stainless steel

(Figure 10a) samples generally gave specific heats very comparable with the literature (Y.S.

Toulokian, 1970). However, it should be noted that above ~900K there was considerable scatter in the

values obtained for the stainless steel (Figure 10a) and this was thought to be associated with the sample

heater failing.

During the measurement of the graphite sample (Figure 11), a seal on the vacuum system failed, and the

sample oxidised when the temperature exceed 480 K, with the sample finally failing at 540 K. At the

temperature oxidation started, the measured Cp data begins to deviate from the reference data as would be

expected. If the heat capacity to specific heat conversion equation (eqn 2) is corrected for mass loss

(assuming linear mass loss due to oxidation with respect to temperature/time) the corrected measured Cp

0

100

200

300

400

500

600

700

292.5 293.0 293.5 294.0 294.5 295.0

Specific

Heat (J

.kg

-1.K

-1)

Temperature (K)

Cp TC

Cp RST

Cu Std Refrence data*330

340

350

360

370

380

390

400

410

420

293 293.5 294 294.5 295

Specific

Heat (J

.kg

-1.K

-1)

Temperature (K)

Copper FEM analysis

Copper Reference data*

0

100

200

300

400

500

600

700

800

900

1000

280 480 680 880 1080 1280

Specific

Heat (J

.Kg-1

.K-1

)

Temperature (K)

S.Steel 1, 10 K/hr-RST-heating

S.Steel 1, 10 K/hr-RST-cooling

S.Steel 1, 6 K/hr-RST heating

S.Steel 2, 10 K/hr-RST

Std Reference data

0

100

200

300

400

500

600

700

800

280 380 480 580 680

Specific

Heat (J

.kg

-1K

-1)

Temperature (K)

Stainless Steel, FEM Analysis

Std Reference Data [ref]

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once again agrees reasonably with the reference data (orange markers on Figure 11a). Here the FEM

analysis of the data appears to have been particularly successful (Figure 11b), with both the value and

shape of the specific heat variation well captured, up until the oxidation problem was reached.

��

Figure 11: Measured specific heat capacity of graphite, using (a) post pulse regression and (b) using FEM

analysis.. Standard reference data taken from (Y.S. Toulokian, 1970)

(a) (b)

Figure 12: Measured specific heat capacity of molybdenum, using (a) post pulse regression and (b) using

FEM analysis. Standard reference data taken from (Y.S. Toulokian, 1970)

As with the other materials, the specific heat values obtained for the molybdenum (Figure 12) generally

compared well with the literature (Y.S. Toulokian, 1970). There was some scatter in the data obtained by

both the regression and FEM analyses approaches and the regression data gave the more reliable fit to the

literature.

The limiting factor on most measurements (i.e. maximum temperature at which a measurement was

made) was component failure, usually the support wires or sample heater connections failing. These

failures not only limited the testing but results in increased scatter on the data prior to failure. There is

clearly work to be done in enhancing the robustness of the current experimental arrangement.

0

200

400

600

800

1000

1200

1400

280 330 380 430 480 530

Specific

Heat (J

.kg

-1.K

-1)

Temperature (K)

Measured Graphite (corrected)

Measured Graphite (un-corrected)

Std Refernce Data [ref] 0

200

400

600

800

1000

1200

1400

280 330 380 430 480 530

Specific

Heat (J

.kg

-1K

-1)

Temperature (K)

Graphite, FEM Analysis


0

50

100

150

200

250

300

350

280 480 680 880 1080 1280

Cp (

J.K

g-1

.K-1

)

Temperature (K)

Measure Cp - stable

Measured Cp- Drift 10K/hr


0

50

100

150

200

250

300

350

280 480 680 880

Specific

Heat (J

.kg

-1.K

-1)

Temperature (K)

Molybdenum, FEM AnalysisStd Reference Data [ref]

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Division I

The data recorded and analysed for all four samples compares well to standard reference data over the

temperature range measured (Figures 9 to 12), even showing good repeatability with multiple

measurements using varying measurement parameters e.g. heating rates, sample mass, pulse duration,

sample heater power, etc. (Figure 10). The new FE modelling analysis technique produced data that

compared well with both reference data and the results of the more traditional regression analysis, and

shows promise for further development. However, as the system currently stands the results show more

scatter than would be observed with DSC measurements but the physical advantages (size, geometry,

surface finish) of the HTCP make it applicable for some materials and applications. There are also further

developments that could enhance the HTCP system and improve the reliability of measurements,

including engineering improvements and analysis methodologies.

SUMMARY A high temperature quasi-adiabatic calorimeter (HTCP) has been successfully developed, along with the

required novel data analysis techniques.

The specific heat data produced by the HTCP system for the four materials were in good agreement with

the reference data. Of the four samples measured the smallest sample (graphite) producing the most

accurate data (until oxidation of the sample invalidated the measurement).

The commissioning testing, while not complete, has shown that a wide range of sample sizes, geometries

and types are can be measured, unlike other Cp measurement approaches, and it has the potential for a

high level of accuracy even in non-ideal conditions. However, there remains considerable development

required to automate the technique and improve repeatability.

REFERENCES

�� Cherneko, V., Kokorin, V. & Vitenko, I., 1994. Brief Communication: Properties of ribbon made from

shape memory alloy Ni2MnGa by quenching from liquid state. Smart Mater Struct. 3, pp. 80-82.

Gramvall, G., 1999. Thermal Phsyical Properties of Materials. North-Holland: Elsevier Science B.V..

IRCP, 1996. Chapter 1: Specific heat measurement techniques. In: International materials database.

s.l.:IRCP, p. i to xi.

Khovailo, V. V. et al., 2001. On order-disorder (L21/B2’) phase transition in Ni2+xMn1-xGa Heusler

alloys. Physica Status Solidi A-Applied Research, 183, pp. R1-R3.

Kirkham, M., 2014. High temperature specific heat capacity measuement of Ni2-XMn1+XGa, s.l.:

Loughbourough University.

Nernst, W., 1911. The energy content of solids. Ann Physic 36, pp. 395-439.

Neumann, K. et al., 2009. The Average Valence Electron Number: Is it a relevant parameter for

Ni2MnGa Alloys?. MRS Proceedings, Volume 1200.

Reece, P., 2007. Progress in Smart Materials ans Structures, s.l.: Nova Publishing.

V. Recarte, J. P.-L. V. S.-A. a. J. R.-V., 2012. Dependence of the martensitic transformation and magnetic

transition on the atomic. Acta Materialia, Vol 60, Issue 5, p. 937–1945.

Y.S. Toulokian, R. P. C. H. a. P., 1970. Thermophsycal properties of matter, The TPRC Data Series. New

York and Washington: IFI/Plenum.

high temperature specific heat measurement using quasi

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