DEVICE AND METHOD FOR SIMULTANEOUSLY DETERMINING TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY, THERMAL DIFFUSIVITY AND SPECIFIC HEAT CAPACITY

Abstract

The invention relates to a device and a method for simultaneously determining temperature-dependent thermal conductivity, thermal diffusivity and specific heat capacity and comprises a heat source for locally heating a solid body to be examined, a both locally and chronologically high-resolution line and/or surface detector for non-contact temperature measurement along the sample, and a cooling Circuit having a cooling liquid flowing around the lower sample edge, the temperature increase and flow rate of which cooling liquid are measured continuously. The thermal diffusivity is determined by means of the described method from the transient thermal States of the sample, which are adjusted in a controlled manner, during heating and cooling. The thermal conductivity is determined from the steady state with a constant heating output. The specific heat capacity of the sample material is calculated according to the temperature from the data sets relating to the thermal diffusivity and thermal conductivity, which data sets are determined directly and over a large temperature range. Because of the enormous savings in time as compared with the prior art, a large number of different solid bodies can be comprehensively characterized thermally for the first time by means of the invention.

Claims

1. A method for simultaneously determining thermal conductivity, thermal diffusivity and specific heat capacity, comprising the steps of locally heating a sample (3) to be examined at a sample end, performing non-contact temperature measurement along the sample (3), measuring the temperature change in a cooling liquid flowing around the other sample end, in order to measure transient and steady thermal states of the sample (3) and determine the thermal diffusivity from the transient thermal states and to determine the thermal conductivity from the steady state and then calculate the temperature-dependent specific heat capacity.

2. The method according to claim 1, characterized in that the thermal states are produced by heating an electrically conductive sample (3) on one side by means of a controlled power output of an induction furnace (1).

3. The method according to claim 1, characterized in that the thermal states are produced by heating an electrically conductive and/or semi-conductive and/or non-conductive sample (3) on one side by means of a controlled power output of an induction furnace (1) with the aid of a susceptor.

4. The method according to claim 1, characterized in that the thermal states are produced by heating an electrically conductive and/or semi-conductive and/or non-conductive sample (3) on one side by means of a controlled power output by a laser.

5. The method according to claim 1, characterized in that the thermal states are produced by heating an electrically conductive and/or semi-conductive and/or non-conductive sample (3) on one side by means of a controlled power output by a resistance-heated heater.

6. The method according to claim 1, characterized in that the thermal states in short samples (3), in particular samples smaller than 20 mm, are produced by heating on one side and cooling on both sides using a cooling body extending into the cooling liquid.

7. The method according to claim 1, characterized in that the temperature at the heated sample end is set by a PID controller (5).

8. The method according to claim 1, characterized in that the temperature-dependent thermal diffusivity is calculated by an inverse numerical method as a polynomial of the nth order, where n is an integer, preferably n=1.

9. The method according to claim 1, characterized in that the flow rate of the cooling liquid is controllable and/or is determined continuously with a flow meter (12).

10. A device for performing a method according to claim 1, comprising: an induction furnace (1) and/or an induction furnace (1) in conjunction with a susceptor and/or a laser and/or a resistance-heated heater for heating the sample (3), a pyrometer (4) and/or an infrared camera for determining the temperature at the heated sample end and/or for relaying to a controller, a PID controller (5) for setting defined heating and/or cooling rates and/or a constant temperature at the heated sample end, a thermal isolation (6) for avoiding lateral heat losses, an infrared camera (8) for measuring the temperature progressions along the sample (3) in thermally transient and/or steady states, one, two or more thermocouples, resistance thermometers and/or other thermal detectors for determining the coolant temperature, a swirler (10) for producing a homogeneous temperature of the cooling liquid behind the sample (3), a flow meter (12) for determining the flow rate of the coolant, and a control valve (15) for setting the flow rate of the cooling liquid.

Description

[0054] In the figures:

[0055] FIG. 1 shows a schematic overall view of the device for simultaneously determining temperature-dependent thermal conductivity, thermal diffusivity and specific heat capacity of a sample to be examined,

[0056] FIG. 2 shows exemplary transient temperature profiles during rapid heating of a sample end,

[0057] FIG. 3 shows exemplary temperature profiles of a sample in the steady state for different constant, controlled temperatures (T.sub.py) at the heated sample end,

[0058] FIG. 4 shows the temperature-dependent progression of thermal conductivity over a large temperature range in linearized form (as a first-order polynomial),

[0059] FIG. 5 shows the progression of thermal diffusivity determined experimentally from the transient states in linearized form (as a first-order polynomial),

[0060] FIG. 6 shows the temperature-dependent progression of specific heat capacity determined from the data sets in FIG. 4 and FIG. 5,

[0061] FIG. 7 shows by way of example the transition (in this case Curie temperature T.sub.c) detected from the temperature-dependent progression of thermal conductivity for pure nickel (Ni).

DETERMINING THERMAL DIFFUSIVITY

[0062] In order to transfer the sample 3 into different transient states which are characterized by temperature gradients ∂T/∂x which differ at any time along the sample axis, in one embodiment of the device in accordance with the invention the heating of the upper sample end to a temperature T.sub.py is achieved by means of PID-controlled power control of an induction furnace 1.

[0063] By reason of the rotationally symmetrical geometry of the induction coils 2 used in practice it is expedient also to provide the sample 3 to be examined with a rotationally symmetrical geometry. Since the production of rotationally symmetrical cylindrical rods is possible with little machine outlay, in one embodiment of the device in accordance with the invention the sample 3 to be examined should have a cylindrical geometry with a length between 20 and 80 mm and a diameter between 4 and 10 mm, but in particular a length of 50 to 60 mm and a diameter of 8 mm.

[0064] The upper end of the cylindrical sample 3 is positioned centrally in the induction coil 2. The primarily electrically conductive sample material inductively couples to the alternating field of the induction coil 2. As a result of this, the sample 3 is heated in a contactless manner owing to the induction currents generated in the material, and initially passes through a thermally transient state. Electrically semi-conductive or non-conductive materials can be heated with the aid of a susceptor and also using the induction coil 2.

[0065] In order to prevent the sample material melting inside the induction coil 2, the sample end is located over half the coil height and the maximum temperature of the sample 3 at the upper end face T.sub.py is measured continuously and in a contactless manner using a pyrometer 4. The measured temperature serves as an input for a PID controller 5 which controls the power of the induction furnace 1.

[0066] The heating output is varied during heating (e.g., by briefly switching the induction furnace 1 on or off and/or by sinusoidally modulated heating output of the induction furnace 1, which varies in amplitude). By means of the one-sided heating and varied heating output, the sample 3 is put into a thermally transient state at any time t and at any location x and, in contrast to the LFM, it is possible, within an extremely short time, to determine the temperature-dependent thermal diffusivity α(T) within a large temperature range.

[0067] The transient states are continually recorded using an infrared camera 8. Undesired lateral heat losses are prevented or greatly reduced by a thermal isolator 6. Furthermore, thermal radiation losses are minimized by silvering 7 applied to the thermal isolator 6. FIG. 2 shows different thermally transient states along the sample axis, which can be achieved during heating of a sample 3 (in this case Cu.sub.70Zn.sub.30). The illustrated temperature profiles are the arithmetic mean of a plurality of lines of the detector which extend in parallel with each other and which all lie within the just prepared surface along the sample axis.

[0068] The thermal diffusivity always results from two temperature profiles as illustrated in FIG. 2, and is determined multiple times according to the response time of the infrared camera 8 used in one embodiment of the invention. The capture rate of the infrared camera 8 during the analysis of the transient states amounts to 5 ms to I s, but more particularly 20 ms. High capture rates permit multiple determinations and subsequent averaging of the determined thermal diffusivities and increase the achievable accuracy of the method compared to the single determination.

[0069] In one modification of the method, in addition to the temperature profiles along the sample axis documented during heating, the transient thermal states are evaluated during the cooling process. The temperature profiles which can be evaluated are thereby multiplied, whereby the accuracy of the measurement of the thermal diffusivity is further increased.

[0070] The basis of the method described herein for determining thermal diffusivity forms an inverse numerical method, in which, starting from an initially freely selected starting value for the thermal diffusivity a, the following homogeneous thermal conductivity equation is iteratively solved.

[00001]$\frac{\partial T}{\partial t}=\frac{\partial }{\partial x}\left(\alpha .Math.\frac{\partial T}{\partial x}\right)\mathrm{with}\alpha =\frac{\lambda }{\rho .Math.c_p}$

[0071] The temperature-dependent thermal diffusivity is described by a polynomial of the nth order (n=1, 2, 3, . . . , but in particular for a moderate temperature range n=1). Once the thermal conductivity equation has been solved using the polynomial in an iteration step, the calculated temperature profiles are compared with the temperature profiles measured using the infrared camera. If calculated and measured profiles differ from each other, the parameters of the polynomial used to calculate the temperature-dependent thermal diffusivity are adapted and the thermal conductivity equation is solved again. The parameters are adapted using smallest error square methods. This procedure is repeated until the calculated temperature profiles match those measured by the infrared camera 8 to the best possible degree. The evaluation of the whole temperature profile therefore results in a temperature-dependent progression of the thermal diffusivity, as shown by way of example in FIG. 5.

[0072] Determining Thermal Conductivity

[0073] When the temperature distribution along the sample 3 no longer changes, the sample 3 is in the thermally steady state and the temperature-dependent thermal conductivity λ(T) of the sample material used can be determined using the heat flow {dot over (Q)}/A through the sample 3 and the evaluation of the temperature profile ∂T/∂x along the sample 3.

[0074] In order to achieve the thermally steady state, the temperature T.sub.py at the heated sample end is measured using a pyrometer 4 and kept constant by a suitable PID controller 5. The temperature of the cooling liquid (measured by thermal sensor 9a) is kept constant by means of a thermostat. At the cool sample end, the cooling liquid flows around the sample 3, the temperature of said liquid being raised by the amount of heat given off by the sample. In the steady state, the amount of heat {dot over (Q)} given off to the cooling liquid per unit of time no longer changes and the temperature change of the cooling liquid (Δ.sub.fT.sub.l) determined as the difference of the temperature of the thermal sensor behind the sample 9b and the temperature of the thermal sensor in front of the sample 9a is constant.

[0075] In the thermally steady state, the sample 3 has the same amount of heat flowing through it along the sample axis in each cross-section A. The heat which is supplied to the heated sample end by means of the induction furnace 1 flows in the direction of the cooled end of the sample, which is located in the closed cooling circuit 11. As the cooling liquid is flowing past the sample, the heat is fully transmitted to the cooling liquid. A swirler 10 then mixes the cooling liquid in order to ensure a homogeneous temperature distribution in the cooling liquid before the temperature increase is quantified by means of two thermal sensors 9. The temperature per cross-sectional surface area of the sample no longer changes and remains constant.

[0076] The heat flow {dot over (Q)}/A is defined as the amount of heat Q transmitted perpendicularly to the sample cross-sectional surface area A per unit of time t.

[0077] In the steady state, the relationship between the heat flow and the temperature profile ∂T/∂x resulting therefrom within the examined sample is described using the Fourier equation.

[00002]$\frac{\stackrel{.}{Q}}{A}=\lambda .Math.\frac{\partial T}{\partial x}$

[0078] In an isotropic medium, heat flow and temperature gradient are directly proportional to one another. The proportionality factor is the thermal conductivity λ.

[0079] By reason of the thermal isolation 6 lateral heat losses are negligible and the one-dimensionality of the heat flow along the sample axis is ensured.

[0080] The quantification of the amount of heat which flows through each sample cross-section and is given off to the cooling liquid is effected with knowledge of the temperatures of the cooling liquid in front of (measured by the thermal sensor 9a) and behind the sample (measured by thermal sensor 9b) and of the flow rate of the cooling liquid per time interval m.sub.f/.sub.1/Δt

[0081] With the aid of the infrared camera 8 integrated in one embodiment of the invention, the temperature distribution of the sample 3 to be examined is recorded in the steady state along the just prepared surface.

[0082] From the temperature distribution measured along the sample axis, individual temperature profiles, which are in parallel with each other and extend in the axial direction, are extracted and then averaged. With knowledge of the local resolution of the infrared camera 8 used, the captured pixels are converted into metric lengths. The averaged one-dimensional temperature distribution describes with high resolution the temperature gradient ∂T/∂x [K/m] along the sample axis. By way of example FIG. 3 illustrates temperature distributions determined by means of this method. For different control temperatures T.sub.py in each case the achievement of the steady state has been awaited and the temperature distribution along the sample axis has been determined.

[0083] The unheated sample end is integrated into the closed cooling circuit 11. In this case, cooling liquid flows around the sample 3 in flow direction 13. By reason of the lateral thermal isolation 6, the entire amount of heat generated at the upper sample end is given off to the cooling liquid.

[0084] The temperature of the cooling liquid changes by reason of the absorbed heat quantity Q. The temperature increase ΔT.sub.fl depends upon the specific heat capacity of the cooling liquid c.sub.p;fl, the amount of heat given off per time interval {dot over (Q)} and the flow rate of the cooling liquid per time interval m.sub.f/.sub.1/Δt. Therefore, the amount of heat given off to the cooling liquid per time interval {dot over (Q)} can be determined with the following equation:

[00003]$\stackrel{.}{Q}=\frac{\Delta Q}{\Delta t}=c_{p;\mathrm{fl}}.Math.\frac{m_{\mathrm{fl}}}{\Delta t}.Math.{\Delta T}_{\mathrm{fl}}$

[0085] The flow rate of the cooling liquid per time interval m.sub.f/.sub.1/Δt is determined continuously with a flow meter 12. Furthermore, a control valve 15 for setting the flow rate is integrated into the cooling circuit 11. This ensures that a sufficiently large temperature increase Δ.sub.fT is achieved between the thermal sensors 9a and 9b.

[0086] The heat flow {dot over (Q)}/A along the sample axis can be calculated with knowledge of the sample cross-sectional surface area A. With the aid of the measured temperature gradient ∂T/∂x, the temperature-dependent thermal conductivity λ(T) is calculated by transposing the Fourier equation. In order to increase the accuracy of the method, thermal conductivity is determined multiple times at one temperature by selecting the temperatures T.sub.py set at the heated end such that the different temperature ranges of the respective steady states overlap. The temperature-dependent thermal conductivities λ(T) determined with the aid of the method described in this case are illustrated by by way of example in FIG. 4. In addition, a linearly adapted curve is illustrated over the complete temperature range examined.

[0087] Determining Specific Heat Capacity

[0088] After determining temperature-dependent diffusivity α(T) from the transient states during heating or cooling and determining thermal conductivity λ(T) from steady states, the temperature-dependent specific heat capacity c.sub.p (T) of the sample is calculated with the aid of the following relationship:

[00004]$c_p\left(T\right)=\frac{\lambda \left(T\right)}{\rho .Math.\alpha \left(T\right)}$

[0089] FIG. 6 shows by way of example the temperature-dependent progression of specific heat capacity of

[00005]${\mathrm{Cu}}_{70}{\mathrm{Zn}}_{30}[p=8.65.Math.\frac{{10}^3\mathrm{kg}}{m^3}),$

as calculated with the aid of the temperature-dependent thermal diffusivity, determined in accordance with the invention, from FIG. 5 and the temperature-dependent thermal conductivities from FIG. 4.

[0090] Derived Properties

[0091] Further temperature-dependent properties of the examined sample material can be derived on the basis of the temperature-dependent progression of thermal diffusivity α(T), thermal conductivity λ(T) and/or specific heat capacity c.sub.p(T).

[0092] Abrupt and/or sudden changes and/or change in monotonicity and/or a change in the increase in the temperature-dependent progression of thermal diffusivity α(T), thermal conductivity λ(T) and/or specific thermal conductivity c.sub.p(T) are indications of phase transitions such as order transitions, allotropic or polymorphic transformations and/or magnetic transformations at the Curie temperature T.sub.c and/or Néel temperature T.sub.N and/or for the existence of different phases along the sample axis and/or concentration differences extending in the axial direction within a phase.

[0093] FIG. 7 shows by way of example the change in the increase in the progression of thermal conductivity of nickel at a temperature of T=630 . . . 640 K. In accordance with the literature, pure nickel undergoes a reversible transition at the Curie temperature of T.sub.c=633 K. Below the Curie temperature, pure nickel is ferromagnetic, and is paramagnetic above it.

[0094] The device and method for determining temperature-dependent thermal diffusivity, thermal conductivity and specific heat capacity described in this case can thus also be used for analyzing material-specific transitions, such as order transitions, allotropic or polymorphic transformations and/or magnetic transformations at the Curie temperature T.sub.c and/or Néel temperature T.sub.N and/or for analyzing different phases which occur along the sample axis and/or for evaluating concentration differences, extending in the axial direction, within a phase.

LIST OF REFERENCE SIGNS

[0095] 1 induction furnace [0096] 2 induction coil [0097] 3 sample [0098] 4 pyrometer [0099] 5 PID controller [0100] 6 thermal isolation [0101] 7 silvering [0102] 8 infrared camera [0103] 9 thermal sensor [0104] 10 swirler [0105] 11 closed cooling circuit with fluid cooling medium [0106] 12 flow meter [0107] 13 flow direction [0108] 14 computer [0109] 15 control valve