Basic&Laboratory&

Materials&Science&and&Engineering&&

Differential&Thermal&Analysis& M110&

As of: 05.09.2011

Aim: Determination of THE thermal dehydration of crystal water with thermal analysis, as

an example Gypsum CaSO4.2H2O. 1. Introduction ......................................................................................................................... 1 2. Basics .................................................................................................................................. 1 2.1. Thermodynamic Background .......................................................................................... 1 2.2. Differential Thermal Analysis ......................................................................................... 5

2.2.1. Influence of the Furnace Atmosphere ...................................................................... 6 2.2.2. Influence of the Heating Rate ................................................................................... 7 2.2.3. Influence of the Reference Substances ..................................................................... 9

3. Technical Importance / Practical Use ................................................................................ 10 4. Experimental Steps ............................................................................................................ 12 4.1. Equipment ...................................................................................................................... 12 4.2. Procedures ..................................................................................................................... 12

4.2.1. Starting the Control Unit ........................................................................................ 12 4.2.2. Temperature Program ............................................................................................. 12 4.2.3. Measurements ......................................................................................................... 12 4.2.4. Reference Measurement ......................................................................................... 13 4.2.5. Measuring the Sample Material ............................................................................. 13

5. Analysis ............................................................................................................................. 13 6. Questions ........................................................................................................................... 13 5. Bibliography ...................................................................................................................... 14

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1. Introduction In most cases, heating a system (an element, a compound, a mixture) causes physical and chemical changes. Possible transformations are summarized in the following table: Physical changes Examples Chemical changes Examples change in modification

α-Fe, γ-Fe, δ-Fe chemisorption H2 on Pt

melting ice → water desolvation (e.g. dehydration)

CuSO4.5H2O Na2CO3.10H2O

evaporation water, ethanol decomposition NaHCO3 → Na2CO3 sublimation ammonium chloride oxidation Cu + O2 → CuO absorption gas in water solid state reaction PZT Pb(Zr, Ti)O3 desorption gas in oxides reactions with a gas

phase NiJ + H2 → Ni + 2 HJ

crystallization NaCl from solution

Table 1: Thermal transfomations Knowledge of these properties and changes are important for scientific and practical interest, especially for material preparation, determination of phase diagrams and phase stability.

2. Basics 2.1. Thermodynamic Background

Measuring methods that measure physical or chemical properties of a substance, a mixture of substances and/or reaction mixtures as a function of temperature are defined as Thermal Analysis (DIN 51005, ICTA-International Conferation for Thermal Analysis). In a Differential Thermal Analysis experiment (DTA experiment), the temperature difference between the sample under investigation and an inert reference material is measured as a function of temperature. Both samples are treated with the same temperature program and the same heating and cooling rates. When heating a sample of mass m, the sample receives energy. In consequence, the state of the sample might change. Either a phase transition occurs or the internal energy changes. Without a phase transition, the received quantity of heat, δq, is proportional to the temperature increase, δT: δq = mCδT (1) with C = specific heat capacity. The heat capacity depends on the conditions under which the system is treated. If the heat transfer is measured at constant volume, the heat capacity is defined as CV. If the heat capacity is measured at constant pressure, the heat capacity is

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defined as Cp. In the case of constant pressure, the volume changes. Therefore Cp and CV are different:

!! − !! = ! !"!" !

!"!" !

(2)

An important state variable, the enthalpy H, can be defined as

H = U + pV (3)

with U = internal energy, p = pressure and V = volume. At constant pressure (dp = 0; subscript p) the increase in H is equal to the received heat (besides the change in volume): dH = (dq)p

(4)

→ !! = !"

!" ! (5)

the change of the enthalpy while heating the system from T1 to T2 is then: → ∆! = !!!"!!

!! (6)

where Cp is a function of temperature as well. The transformation of a substance from one modification to another causes a change of the enthalpy ΔHU. If a substance is continuously heated, the temperature increases until the transfomation temperature TU is reached. Additional heat is used as latent heat for the transformation. During the transformation process the temperature is constant. After the transformation, the temperature increases regularly again: ΔH = CP dT +ΔHUT1

TU∫ + CPTU

T2∫ dT (7)

Upon cooling, the same transition heat is released. The temperature decreases before and after the transition point, but is constant during the transition. Thermograms can be calculated from the cooling curves of melts from different concentrations of the system under investigation. Figure 1 shows the temperature differences of an iron sample and a platinum sample as a function of time while cooling together in a furnance. At a temperature of 906 °C, the iron cooling slows down, because here the γ-form (fcc) transforms into the α-form (bcc). There is a jumpwise increment in the temperature difference between iron and platinum. The second noticeable phenomenon at 768 °C is the ferromagnetic transition in α-iron (paramagnetic to ferromagnetic). The crystallographic order of the atoms (bcc) doesn’t change during this transition. This transition temperature is called Curie-temperature. At this transition point, the 3d-electron spins turn parallel and energy is released. The type of phase transition at the curie point can be investigated with DTA measurements.

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Figure 1. Time-dependent cooling-curve of iron Figure 2 shows a schemetic curve for the specific heat for α-iron and γ-iron (TCF: ferromagnetic Curie-temperature, TCAF: antiferromagnetic Curie-temperature). The strong increase of the specific heat before and the following abrupt decrease at the curie point cause a similar trend in the DTA curve (Figure 3, curve 3). In the cooling curve, the same effect occurs, but with opposite sign.

Figure 2. Specific heat CV per mol for α- and γ-iron

Figure 3. DTA-curve (3) heating, (4) cooling of a ferromagnetic substance

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Transitions of this kind are called transitions of higher order. In contrast to transitions of first order, no latent heat is consumed or released. The changes in heat capacity Cp, heat conductivity and thermal expansion of the substance are discontinuous. Glass transitions of amorphous substances are phase transitions of higher order, too. Phase transitions of first order are, for example, melting, boiling and most of the modification changes. Phase transition α→β: With G=H-TS results:

,STG

P

−="#

$%&

'∂∂ V

PG

T

=!"

#$%

&∂∂ (8)

The chemical potentials µα and µβ for the phases α and β can be calculated as follows:

,0≠Δ=#$

%&'

( Δ=#

$

%&'

(−##

$

%&&'

(m

TTT

ß VPPP ∂µ∂

∂∂µ

∂

∂µα (9)

.0≠"#

$%&

' Δ−=Δ−="

#

$%&

' Δ="

#

$%&

'−""

#

$%%&

'

T

mm

PPP

ß

THS

TTT ∂µ∂

∂∂µ

∂

∂µα (10)

If the first derivative of the chemical potentials changes with a jump (discontinously) at the transition point, it is a transition of first order. If the first derivative of the chemical potentials changes continously and the second derivative changes with a jump, it is a transition of second order. Figure 4 shows the changes of the thermodynamic quantities at the phase transitions.

Figure 4a. Changes of the thermodynamic quantities for a first order transition

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Figure 4b. Changes of the thermodynamic quantities for a second order transition

2.2. Differential Thermal Analysis Figure 5 shows a schematic setup of the DTA. The substance under investigaton and an inert reference are heated under the same conditions simultaneously in a furnance. The increase of the temperature in the furnance should be linear. Both sample and reference are connected to thermocouples. These thermocouples are connected to each other. The difference of the voltages, which are correlated to the differences of the temperatures, are measured. As shown in Figure 6, the control unit shows no thermovoltage as long as there is no heat consumed or released, because there is the same temperature Ts = Ti in the sample and in the inert reference and hence ΔT = 0. If there is an endothermic reaction in the sample, the sample temperature increases slower than the reference temperature (Ts1 < Ti1) and the gauge shows a thermovoltage according to a temperature difference ΔT1 = Ts1 - Ti1, which is negative. If there is an exothemic reaction in the sample, the sample temperature increases faster than the reference temperature (Ts2 > Ti2) and the gauge shows a thermovoltage according to a temperature difference ΔT2 = Ts2 -Ti2, which is positive. The DTA curve can be determined by substraction of the curve Ts and Ti (Figure 6b).

Figure 5. Schematic setup for the DTA: 1. furnance, 2. sample substance, 3. inert reference, 4. control unit for heating, 5. temperature difference gauge, 6. temperature gauge

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Figure 6. DTA curves: a) Ts: temperature-time-curve of the sample, Ti: temperature-time-curve of the reference, b) temperature difference-time-curve In the following chapters, some of the factors which may influence the results of the DTA experiments will be explained.

2.2.1. Influence of the Furnace Atmosphere The equilibrium temperature of reversible transitions is dependent on the pressure in the furnance or the partial pressures of the components. A pressure change results mainly in a temperature shift of the peak. Secondly, the gases of the furnance atmosphere may react with the substance or with volatile products from decomposition of the sample. With a change of the composition of the furnance atmosphere, some characteristic peaks may disappear or extra peaks may appear. The mechanisms of many chemical reactions are influenced by the atmosphere and in particular by the gas pressure. Figure 7 shows DTA-curves of gypsum in a streaming nitrogen-steam-atmosphere with different steam partial pressures. The dehydration reaction occurs in two steps: CaSO4.2H2O ⇄ CaSO4.0.5H2O + 1.5 H2O (11) CaSO4.0.5H2O ⇄ CaSO4 + 0.5 H2O (12)

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Figure 7. DTA curve of gypsum with different steam partial pressures With increasing steam partial pressure, the second step of the dehydration reaction moves to higher temperatures. With higher steam partial pressure, the DTA effects are more pronounced and the peaks are narrower. The steam formed by the decomposition reaction diffuses slower into the furnace atmosphere than new steam is produced. Above the sample surface the partial pressure of steam increases. Consequently, the equilibrium temperature of the dehydration process increases. The DTA peak is broadened. The local steam pressure can only increase up to the total pressure in the furnace. The lower the given initial steam pressure is, the more the local steam pressure may increase. Due to sluggish diffusion, there are locally different partial pressures of the gaseous decomposition product.

2.2.2. Influence of the Heating Rate As the substance turnover per unit time increases with faster temperature rise, with increasing heating rate the peaks grow. The temperature difference ΔT is approximately proportional to the substance turnover (Figure 8). In addition, the DTA peaks as a function of temperature T are broadened, because the temperature gradient in the sample increases at higher heating rates. As a function of time t, the peaks seem to get narrower (Figure 9). At faster temperature rises, the turnover needs less time, but the temperature difference ΔT is increasing. Therefore the area is constant.

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Figure 8. Influence of increasing temperature rate as a function ΔT=f(T)

Figure 9. Influence of increasing temperature rise as a function ΔT=f(t). The vertical marks show the same sample temperatures.

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At a higher heating rate, the DTA-peaks of chemical reactions move to higher temperatures. In addition, there may be local changes in the furnance atmosphere and on the sample surface as a result of the temperature dependence of the reaction rate. The higher the heating rate, the less gas diffuses out of the sample environement during the decomposition process. Consequently, the partial pressure is locally higher and the decomposition temperature increases. The broadening and the different shifting effects of the DTA at high heating rates may result in overlapping of normal successively effects. For higher resolution of the DTA curves, the peak temperatures are near the thermodynamic equilibrium temperatures, thus, the heating rate should be as low as possible. It is useful to notice that the peaks become flatter.

2.2.3. Influence of the Reference Substances A reference substance for DTA measurements has to fulfill the following conditions: 1. no transitions in the measured temperature range 2. similar heat conductivity and heat capacity as the measured substance

If the reference material is mixed into the sample to achieve similar heat conductivity and heat capacity of the sample and the reference chamber, the constitutents (sample and a reference material) should not be able to react with each other. In general, it is impossible to fulfill both conditions 1 and 2 simultaneouly, because during the transition, heat capacity and heat conductivity are changing in the sample substance. Therefore, a reference is often chosen that remains as the product after heating the sample, for example caoline for clay minerals. For measuring small samples, no inert substance is used. The reference temperature is measured with an empty sample holder. These are only a few parameters which influence the DTA results. Nevertheless, comparing diagrams of different DTA-apparatuses is difficult. There are standards for the experiments, but these standards are often different from the best actual conditions. So it is useful to note the experimental conditions.

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3. Technical Importance / Practical Use Differential thermal analysis shows at which temperatures a substance reacts and if the heat change is positive or negative. Nevertheless, it is impossible to determine with DTA measurements what kind of reaction has taken place. DTA is a dynamical method; equilibrium conditions cannot be established. With DTA, determined reactions or equilibrium temperatures are dependent on the measurement conditions. So they may differ from the equilibrium temperatures. It is important to use other measuring methods. Information about the same sample at the same conditions as in the DTA measurements in very useful. For this reason, there are combination devices which can register simultaneously the following additional parameters: • weight change • rate of weight change • evolving gases However, differential thermal analysis is used for explaining many questions in physics and chemistry. Examples are homogenous and heterogenous chemical reactions in liquid and solid phases, determination of phase transitions, thermal decomposition, calorimetric and kinetic data. Differential thermal analysis is a quick method which does not require complicated instruments. With modern DTAs, the measurements can be automated so that the analysis is less time-consuming. During heating and cooling of one-component systems, only simple phase transitions occur. In multicomponent systems there are additional phenomena, such as formation and decomposition of mixtures, formation of compounds, etc. By measuring with DTA these transitions as a function of composition, it is possible to determine the corresponding phase diagrams. Figure 10 shows DTA curves of some mixtures in the Na2SO4-NaCl-system. Temperature, form, and height of these thermal effects depend in a characteristic manner on the composition of the mixture. If a melt has a eutectic composition, the DTA curve looks like a curve of a pure phase. To determine liquidus temperatures, cooling curves should be used, whereas for solidus temperatures, heating curves are more useful. For determination of complex phase diagrams, a great number of DTA curves at different compositions have to be measured. For explanation of the thermal effects, further methods such as X-ray diffraction or microscopy are needed.

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Figure 10. Phase diagram and DTA-curves of the Na2SO4-NaCl-system Differential thermal analysis can be used for determination of caloric data. The holding time in temperature-time curves is often used as a semiquantitative evaluation method for the transition heat. This time is equal to the time from the beginning of the thermal effect to the time of the peak maximum. During the phase transition, the temperature is constant for this time. The peak area is a useful value for the determination of heat capacities. In a DTA-diagram, the heat of reaction ΔH is proportional to the area between the baseline and the DTA curve (Figure 11), ΔH=KF. The factor K is dependent on the apparatus, the chosen sensitivity and the temperature and has to be determined by calibration measurements. Another direct quantitative method for the determination of the amount of heat conversion or the enthalpy change is DSC (differential scanning calorimetry). In DSC, a sample and a reference are heated. The difference in heating energy between the sample and the reference during a phase transition is measured.

Figure 11. DTA diagram, schematic

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Another important application for DTA is the characterization of ceramic materials. The starting materials for fine ceramics can be very different in their mineral composition. Sometime they contain large amount of impurities. This results in different product qualities. Pure caolin segregates water at 500 °C. At 987 °C a solid state reaction occurs, Al-Si-spinell phase and amorphous SiO2 are formed from metacaolin. On the other hand, caolin contaminated with illite shows three endotherm dehydration peaks in the thermal analysis, at 67 °C, 268 °C and 499 °C.

4. Experimental Steps 4.1. Equipment

For this experiment, the DTA typ 701 from Bähr Thermoanalyse GmbH is used. Read the instructions first! Before beginning your measurements, the cooling circuit has to be switched on. After finishing your measurements, it has to be switched off.

4.2. Procedures 4.2.1. Starting the Control Unit

After switching on the control unit, there is the main menu (Hauptmenü) for DIL 801 on the monitor. When the dilatometer program finishes, the main menu for DTA 701 is opened.

4.2.2. Temperature Program In the main menu for DTA 701, the menu “Programm erzeugen“ (generate program) has to be selected. If there is no useful program for the measument, the temperature program has to be written. The temperature program includes the following parameters: temperature (Temperatur), heating rate (Heizrate), segment time (Segmentzeit) [hh:mm:ss] and values (Werte) [%]. To hold the temperature constant, the heating rate is 0; for cooling, the values are negative. For entering the segment, the “Enter” key has to be pressed. Then the temperature program is saved. There are two temperature programs needed: Program 1: 1) Segment 1: 250 °C; 20 K/min; 12 min; 40 % 2) Segment 2: 250 °C; 0 K/min; 10 min; 10 % 3) Segment 3: 20 °C; -20K/min; 12 min; 40 % 4) Segment 4: 20 °C; 0 K/min; 10 min; 10 % Program 2: 1) Segment 1: 250 °C; 5 K/min; 46 min; 40 % 2) Segment 2: 250 °C; 0 K/min; 10 min; 10 % 3) Segment 3: 20 °C; -5 K/min; 46 min; 40 % 4) Segment 4: 20 °C; 0 K/min; 10 min; 10 %

4.2.3. Measurements

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Open the menu „messen„ (measuring). Fill in the following data: temperature program (Temperaturprogramm), lab name (Versuchsname), sample material (Probenmaterial), sample weight (Probengewicht), reference material (Referenzmaterial), reference weight (Referenzgewicht), date (Datum), atmosphere (Atmosphäre), crucible material (Tiegelmaterial). By pressing the icon “Ofen öffnen“ (open furnance), the furnance will be unlocked and can be opened within 10 seconds. The furnance can’t be opened when the temperature is higher than 200 °C. The measuring cell should be open as short as possible to avoid pollution and damage.

4.2.4. Reference Measurement For the reference measurement, two empty aluminium oxide crucibles are used. Thus sample and reference material are the same. The temperature program is started by pressing the icon “Messung starten“. This reference measurement has to be stored when it is finished. For both temperature programs reference measurements are needed.

4.2.5. Measuring the Sample Material Gypsum CaSO4.2H2O is used as sample material. Gypsum is an important construction material. It is used in the cement industry, in the building industry, and in the medical field. Due to low dehydration temperatures, gypsum is suitable for DTA measurements. The aluminium oxide crucible has to be filled half way up and then weighed. The measurements are done with the above described programs, in air. For each measurement, new samples should be used. After the measurement is done, the samples are weighed again to determine the weight reduction. The crucible has to be put on the left sample plate and the reference on the right. It is important to avoid material (sample) particles on the outside of the crucible, otherwise the crucible may stick on the plate. To avoid contamination of the crucible, it has to be handled with tweezers.

5. Analysis • For analysis of the experiments, the reference measurements are used for correction. The

DTA curves of the sample material have to be subtracted from the reference curves. These calculations have to be done direct on the computer with the DTA-software.

• The dehydration temperatures should be determinated. • Discuss the influence of the different temperature curves. • Answer the following questions

6. Questions 1. Describe the correlation between the up-take and release of heat and the corresponding

changes of the thermodynamic state of the sample. 2. Describe the different types of phase transitions. 3. Describe the principle of differential thermal analysis. 4. Which test conditions can influence the results of the DTA? How are the results dependent

on parameters like heat conductivity, temperature conductivity, density and geometry of the samples, sample weight, geometry of the thermocouples and latent heat of reactions?

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5. Bibliography 1. P.W. Atkins Physical Chemistry VCH Verlagsgesellschaft mbH, Weinheim 1987, 1988, 1990, ... 2. E. Post, S. Winkler TA for ceramic materials Netsch Industrial Applications Volume 6/93 3. R.F. Speyer Thermal analysis of materials Marcel Dekker, Inc., New York, 1994 4. T. Hatakeyama, Zhenhai Liu Handbook of thermal analysis Wiley, Chichester, 1998 5. D. Schultze Differentialthermoanalyse Verlag Chemie GmbH Weinheim/Bergstr., 1972 6. W. Schatt Einführung in die Werkstoffwissenschaft Deutscher Verlag für Grundstoffindustrie, Leipzig 1972