Method for determining thermal conductivity and thermoelectric quality of thermoelectric samples

Description

[0001] The present invention relates to a transient method for eliminating contact thermal resistance when measuring thermal conductivity or thermoelectric quality on thermoelectric samples.

[0002] Modern methods for determining thermal conductivity in bulk samples rely on a transient method for measuring thermal diffusivity (the flash method), which is non-contact and unaffected by heat transfer. However, non-contact methods are not feasible for simultaneous measurement methods that allow for the simultaneous determination of electrical and thermal conductivity. The thermal conductivity measurement is then fundamentally distorted by the usually unknown thermal resistance of the contact in the sample holder.

[0003] This thermal resistance is connected serially to the sample in the heat flow path. With well-reproducible contacting, i.e., with barely varying contact resistance during multiple fabrications, simultaneously with well-reproducible thermal ambient conditions and well-reproducible sample properties, and with a sufficiently producible sample size, it can be eliminated by varying the sample length. However, these prerequisites are often not met, making this approach either impractical or both complex and associated with considerable residual uncertainty.

[0004] Alternatively, the contact resistance can be eliminated in complex measurement setups analogous to an electrical 4-point measurement by precisely and non-interactingly measuring the temperatures of the heat source and heat sink, as well as the temperature on the sample surface, at multiple locations. This is extremely complex from a measurement technology perspective, as separate thermalization of all measuring points must reliably prevent temperature measurement distortion caused by incoming or outgoing heat flows. Such systems have already been demonstrated, but they are too complex for routine measurements in materials laboratories and are not implemented in commercial or standard laboratory systems.

[0005] The interfacial thermal resistance in composite materials can also be determined using the flash method if the thermophysical properties of the bonded materials / layers are known. However, the simultaneous determination of the thermal conductivity of a sample material and the thermal contact resistance is not possible, as both effects are additive in the serial configuration and cannot be separated.

[0006] Well-known contact methods for measuring thermal conductivity include the Kohlrausch method, which uses self-heating by Joule heat and evaluates the axial temperature distribution of a sample rod under the assumption of adiabatic closure in the radial direction, the Ioffe method as a dynamic absolute method in which the heat conduction through a sample is determined from the time course of the decay of an applied temperature difference, whereby the heat capacity of a reservoir connected to the sample and adiabatically insulated from the outside must be known, and stationary comparison methods in which a fixed heat flow flows serially to the sample through a reference sample with known thermal conductivity.All these methods are distorted by the influence of thermal contact resistance unless a temperature measurement is carried out on or in the sample itself, which would require a modification / processing of the sample itself, is prone to errors and is impractically complex for regular measurement operations.

[0007] In the historical Kohlrausch method, a specialized laboratory method, this extra effort was accepted, partly due to the lack of alternative methods at the time. However, this is not feasible for daily practice in materials laboratories, either for the Ioffe method and its variants or for stationary comparison methods. Contact resistance-corrected thermal conductivity measurements in contact-based measurement methods are not yet available.

[0008] A common method for determining the thermoelectric performance of thermoelectric converter materials is the Harman method, which implies a measurement of the thermal conductivity and is based on the balance between the Peltier heat pumped through the sample with an electric current and the returning Fourier heat due to the temperature difference building up under adiabatic closure.The position of this equilibrium, expressed by the equilibrium temperature difference, is independent of the thermal contact resistance. However, the established measurement methodology, which is based on the transient measurement of thermoelectric voltages to track this temperature difference and a temporal extrapolation of the measurement signals to the time of the Peltier current shutdown, does not consider the influence of the thermal contact resistance on the relaxation of the system. Therefore, the conventional evaluation results in an insufficient equilibrium temperature difference and, complementarily, an excessively large ohmic voltage drop, thus overestimating the influence of the thermal conductivity and underestimating the electrical conductivity. Both effects accumulate, resulting in an underestimation of the thermoelectric effectiveness by the conventional Harman measurement.

[0009] H. Kolb et al. (Review of Scientific Instruments 86, 073901 (2015)) disclose the simultaneous measurement of different thermoelectric properties of bulk materials in the temperature range from 300 to 600 K. This is based on the Harman method. B. Kwon et al. (Review of Scientific Instruments 85, 045108 (2014)) discloses the influence of parasitic thermal effects on thermoelectric properties. The determination of the thermoelectric properties is based on the Harman method.

[0010] Knowledge of the contact thermal resistance would allow a correction and thus a significantly more accurate measurement of the thermoelectric efficiency using the Harman method. At the same time, it would allow a correction of the thermal conductivity measurement in a contacted installation situation, which is essential for simultaneous measurement of electrical and thermal conductivity. However, a complementary or in-situ measurement of the thermal resistance is not known to date. The object of the present invention is to provide a corresponding method.

[0011] Surprisingly, it has been shown that the thermal contact resistance of a thermoelectric sample placed between two differently temperature-controlled blocks can be measured using the electrical measurement of thermoelectric voltages (electrical voltages associated with a temperature difference caused by the Seebeck effect) without the need to attach additional measuring elements (e.g., thermostatted probes) to the sample or require complex length variation. This is possible by evaluating the transient temporal behavior of the measurement signals over a short period of time immediately following a sudden change in the sample current from a steady thermal state.

[0012] In a first embodiment, the object underlying the present invention is therefore achieved by a method claimed in claim 1 for determining the thermal conductivity κ and the thermoelectric quality zT eliminating contact thermal resistance R C th< on a sample comprising a thermoelectric material, which is arranged between two blocks of different temperatures, which are adiabatically shielded from the environment, and connected to them via a contact material, with at least two electrical leads attached to each block, forming line pairs. Each of these leads serves to feed in a direct current, which flows from one block via the sample to the other block. With the help of the second pair of leads, the so-called voltage probes, the voltage is V 1 measured before and after changing (switching on or off or instantaneous change) the current.

[0013] The method according to the invention is therefore a method for determining the thermal conductivity κ and the thermoelectric quality zT eliminating contact thermal resistance R C th< on a sample (1) comprising a thermoelectric material, wherein the sample (1) has two spatially separated contact surfaces and the distance between these contact surfaces corresponds to the length / , comprising: a) bringing a first contact surface of the sample (1) into contact with a first block (2a) via a first contact material (3a), and b) bringing a second contact surface of the sample (1) into contact with a second block (2b) via a second contact material (3b), wherein the first block (2a) and the second block (2b) comprise a metal and / or a metallic coating, and at least one of the blocks is adiabatically shielded from the environment, c) applying at least one first pair of conductors to the first block (2a) and to the second block (2b) in such a way that they are electrically conductively connected to the respective contact material (3a, 3b) via the respective block (2a, 2b), so that a direct current can flow from one block through the sample into the other block, and applying at least one second pair of conductors consisting of voltage probes to the first and second blocks (2a, 2b),so that a voltage V can be measured between the voltage probe on the first block (2a) and the voltage probe on the second block (2b), d) achieving an equilibrium state between a Peltier heat, which is pumped with an electric current through the sample (1) via the first pair of lines, and a returning Fourier heat due to the temperature difference building up under adiabatic closure and measuring a voltage, V 1 via the second pair of lines consisting of voltage probes, e) change in current at the time t 0 and f) time-resolved measurement of the voltage V 1 between the voltage probes of the second pair of lines over a period immediately after the change in the current intensity in step e), wherein the period is at least one half-life of the rapid decay and at a sampling rate that allows at least 10 to 100 measured values ​​(voltage values) to be recorded within the first half-life, g) following the measurement according to step f), time-resolved measurement of the voltage V 1 between the voltage probes of the second line pair over a period of slow decay until the system has approximately adjusted to a new equilibrium state, with a data rate of at least 5, in particular at least 20, values ​​per half-life of the slow decay when entering the new equilibrium state, wherein the period in step f) is characterized by a rapid drop in the voltage compared to the period in step g), in which a uniform slow decay takes place according to an exponential law, h) numerical adaptation of data from the time-resolved measurement of the voltage V 1 from step g) by an exponential function or the sum of a linear and an exponential function and temporal extrapolation of this function of the measured voltage drop from step g) to obtain a baseline up to the time t 0 ,where the extrapolation of the measured voltage drop to the time t 0 an amplitude A 1 is determined, i) forming the difference between this baseline and the experimental data from step f), the difference being t 0 the amplitude A 2, and formation of the ratio A 2 / A 1 , which indicates the relative systematic error of a thermal resistance measurement on the sample caused by the thermal resistance of the contact, j) determination of the thermal conductivity κ and the thermoelectric quality factor zT taking into account the relative systematic error from step i).

[0014] First contact (3a) and first contact material (3a) are used synonymously in this application. While "contact" emphasizes the physical properties (establishing contact between the block and the sample), "contact material" focuses on the material from which these properties arise. The same applies. The same applies to the second contact (3b) and the second contact material (3b). If the first and second contact materials, or the first and second contacts, are included in a description, only "contacts" or "contact materials" are used. Likewise, the term "blocks" always includes both the first block (2a) and the second block (2b), unless explicitly stated otherwise.

[0015] The system consisting of blocks (2a, 2b), contact materials (3a, 3b), and sample (1) is in a state of equilibrium at the beginning of the measurement in step d). Changing the current also brings the system out of this equilibrium. After a certain period of time, the system then reaches a new equilibrium state.

[0016] According to the invention, the equilibrium state in step d) already occurs when a current is supplied.

[0017] Step d) therefore comprises applying a direct current across the blocks by means of a first pair of conductors so that the current flows from one block to the other, passing through the contact material, the sample, and again through the contact material, and maintaining the current flow until an equilibrium state is reached. After the equilibrium state is reached, the voltage V 1 measured via the other second pair of lines consisting of voltage probes.

[0018] In this case, the change in current intensity can cause the current to be completely switched off at the time t 0 which is also preferred according to the invention. However, it is also possible that the current intensity at the time t 0 is increased or decreased, i.e. a stronger or weaker current is applied.

[0019] The change in current strength occurs abruptly, i.e. the change does not occur continuously, but there is an immediate change to the new value or the immediate switching off of the current.

[0020] Step f) of the method according to the invention relates to the time-resolved measurement of the voltage over a short period immediately after a change in current strength. This is characterized by an initial, more rapid drop in the voltage compared to the subsequent phase of a uniform decay according to a simple exponential law analogous to capacitor discharge. The voltage measurement should be carried out over the duration of at least one half-life of the rapid decay and at a sampling rate high enough to allow at least 10 to 100 voltage values ​​to be recorded within the first half-life. This half-life depends on the magnitude of the contact resistance and is typically less than 1 s.

[0021] Step g) of the method according to the invention relates to the time-resolved voltage measurement following step f). This measurement is performed over a period of time in which the system has approximately adjusted to the new equilibrium state and at a data rate of at least 5 to 20 values ​​per half-life of the slow decay during temperature equalization (or arrival at the new equilibrium state). This half-life depends on the size and properties of the sample and blocks and is typically approximately 5 to 60 s in laboratory geometry with mm-sized blocks and samples, considerably longer for large systems; it is shorter for miniature or microsystems.

[0022] In step h) of the method according to the invention, the numerical fitting of the experimental data takes place. This depends on the data rate. At a sufficiently high data rate and signal quality, the fitting is carried out to a linear function starting after the initial, faster decay has subsided over a period of approximately 0.3 half-lives of the slower decay. A more precise fitting, starting after the initial, faster decay has subsided over a period of approximately 3 to 5 half-lives of the slower decay, is carried out to a functional approach. V 1 ( t ) = A 1 * exp(- t / τ 1 ). This is followed by a temporal extrapolation of this function of the measured voltage drop to obtain a baseline up to the time t 0 .

[0023] The method according to the invention thus enables a correct determination of thermal conductivity κ and thermoelectric quality zT , whereby the Harman method eliminates inherent errors. The thermoelectric quality zT depends on the thermal conductivity of the materials being measured. To analyze a thermoelectric sample, it is placed between two blocks and connected to them via a contact material.

[0024] In Fig. 1a ) shows a corresponding, conventional measurement setup schematically in an exploded view. The sample (1) is shown with a regular geometry. However, this is not fundamentally necessary for the invention. When selecting the geometry, it is only important to ensure that the contacts form isothermal lines if possible. Fig. 1a ) shows the schematic design of a sample holder for determining the thermal conductivity of a sample by temperature equalization between two metal blocks of known heat capacity, which also allows the Harman measurement to be carried out if at least one of the blocks of the holder is adiabatically sealed from the environment. The block temperatures are measured using thermocouples and can be varied from the initial / ambient temperature using integrated heaters. The temperature gradient across the sample required for the measurement must be generated by an applied direct current using the Peltier effect, not by the integrated heaters. When using metallic contacts, which have a vanishing Seebeck coefficient, the thermoelectric voltages V 1 or V 2 , measured between the blocks, is a measure of the temperature difference across the thermoelectric sample.

[0025] The probe has two opposing contact surfaces, each connected to the blocks (2a, 2b) via contact materials (3a, 3b). The blocks (2a, 2b) may have heating elements (4a, 4b), but this is not necessary. Furthermore, the blocks (2a, 2b) each have at least two electrical connection lines. If two probes are present, as in Fig. 1a As shown, one probe can be used to inject the current and the other to measure the voltage.

[0026] At least one of the blocks is adiabatically shielded from the environment. However, both blocks (2a, 2b) can also be adiabatically shielded.

[0027] Particularly good results are obtained when the thermal mass of the blocks is greater than the thermal mass of the sample. In particular, the ratio of the heat capacity of the blocks to the heat capacity of the sample is in the range of 2:1 to 50:1, especially from 5:1 to 20:1. For laboratory measurements on bulk samples, a sample to be examined typically has a length of 5 mm to 6 mm. Accordingly, a block with a size of approximately 15 mm is required. However, the method according to the invention is also applicable for sample and block dimensions that differ significantly from this, for example, even microsystems.

[0028] The process according to the invention can be carried out at room temperature (usually 20°C to 25°C). However, it is also possible to determine the temperature dependence of the relative or absolute contact thermal resistance by carrying out the process according to the invention at temperatures from 4 K to 1200 °C, preferably from 80 K to 600 °C, especially from room temperature to 300 °C. The process according to the invention is preferably carried out at temperatures from 4 K to 1500 K, in particular from 80 K to 900 K, preferably from 300 K to 600 K.

[0029] Preferably, the sample not only comprises a thermoelectric material, but consists essentially of it. The purity of the sample is not relevant for the method according to the invention. In principle, the sample should be as homogeneous as possible so that the ratio of electrical conductivity to thermal conductivity is not subject to large local fluctuations. However, if the electrical conductivity is not too low, this is generally already ensured by the Wiedemann-Franz law. Furthermore, this problem also arises with measurement methods known in the prior art.

[0030] The first block (2a) and the second block (2b) are essentially made of the same material or have the same coating. Contacts (3a, 3b), blocks (2a, 2b), and probes preferably have the same Seebeck coefficient. While the blocks (2a, 2b) and probes are selected accordingly, the Seebeck coefficient of the contacts (3a, 3b) is often unknown. However, with metallic contacts (3a, 3b), a sufficiently low Seebeck coefficient, typically less than 5 µV / K, can be expected and realized.

[0031] The Seebeck coefficient can generally assume both positive and negative values. Where values ​​for the Seebeck coefficient are mentioned in this document, these are to be understood as absolute values.

[0032] As a material for blocks (2a, 2b), contacts (3a, 3b) and probes, a material is selected in particular which has a Seebeck coefficient of 10 µV / K or less. Preferably, the Seebeck coefficient is S in terms of amount in the range from 0 µV / K to 10 µV / K, in particular from 0 µV / K to 8 µV / K or from 0 µV / K to 5 µV / K.

[0033] Blocks (2a, 2b), contacts (3a, 3b) and probes preferably have an electrical conductivity of at least 10 4< S / cm, preferably from 10 4< to 10 9< S / cm, in particular from 10 5< to 10 8< S / cm or from 10 5< to 10 7< S / cm.

[0034] Particularly preferably, blocks (2a, 2b), contacts (3a, 3b), and probes have a thermal conductivity of at least 10 W / (m K), in particular of at least 100 W / (m K). With a low Seebeck coefficient and equality between blocks (2a, 2b), contacts (3a, 3b), and probes with regard to the Seebeck coefficient, the thermal conductivity is not relevant.

[0035] Metallic materials within the meaning of the present invention are those elements located in the periodic table of elements to the left of and below a dividing line between boron and astatine. This also includes alloys and inner-metallic phases that exhibit, in particular, the aforementioned properties, namely a low Seebeck coefficient, electrical conductivity, and thermal conductivity. Characteristic of metallic material properties are high electrical conductivity, high thermal conductivity, and a low Seebeck coefficient.

[0036] Particularly suitable and preferred materials for blocks (2a, 2b) and probes are Cu, Ag, Au, Ni, Al, Sn, Zn, Pb, or mixtures thereof. Suitable materials include, for example, Bi, Sb, but also special thermocouple alloys such as constantan, chromel, and platinum-rhodium. If the present application refers to a material for the blocks (2a, 2b), the blocks can consist essentially of this material or have a coating of this material, which then defines the properties of the blocks (2a, 2b) for the method according to the invention.

[0037] The contact material (3a, 3b), like the material of the first and / or second block, is a metallic material that exhibits the aforementioned properties with regard to Seebeck coefficient, electrical conductivity, and thermal conductivity. Particularly preferably, the contact material is liquid at room temperature and atmospheric pressure. This enables easy handling during measurement. The sample can be easily inserted and removed between the block (2a, 2b) without subjecting the sample (1) and / or block (2a, 2b) to any particular mechanical stress. Thus, the mechanical stress on the sample is low, which is particularly relevant for thin samples (1).

[0038] The sample (1) comprises and, in particular, consists of a thermoelectric material. The Seebeck coefficient of the sample differs from that of the probes to enable measurement. Therefore, the Seebeck coefficient of the sample is preferably greater than 10 µV / K in magnitude, preferably in the range of 25 µV / K to 500 µV / K, in particular in the range of 50 µV / K to 300 µV / K or from 70 µV / K to 250 µV / K, especially from 100 µV / K to 200 µV / K.

[0039] The electrical conductivity of the sample (1) is preferably 10 4 < S / cm or less, in particular from 10 1 < to 10 4 < S / cm, preferably from 10 2 < to 10 3 < S / cm. The thermal conductivity of the sample is preferably 20 W / (m K) or less, in particular in the range from 0 to 15 W / (m K), preferably from 0.2 to 10 W / (m K), particularly preferably from 0.5 to 5 W / (m K). Preferably, the thermoelectric material of sample (1) is selected from skutterudites, clathrates, half-Heusler compounds, Zintl compounds, quaternary chalcogenides, tellurides, in particular bismuth telluride, PbTe, SnTe and their mixed crystals as well as nanomaterials based on them, for example LAST (lead silver antimony telluride), TAST (tin antimony silver telluride), BTST (bismuth tin silver telluride), etc.; silicides, in particular of the elements magnesium, manganese, iron, chromium and others; transition metals and their mixed crystals, in particular stannides and germanides; sulfides, in particular of titanium, tin, etc. and antimonides, in particular Zn 4 Sb 4 and ZnSb, MgAgSb, and many others.

[0040] Separating the thermal resistance of the sample and the contact from the time course of the measurement signal is possible due to the different ratios between thermal resistance and heat capacity in the sample and at the contact, respectively, in conjunction with the fact that the location of the release of the Peltier heat, which is transported with the sample current, is located directly at the interface between the thermoelectric material and the metallic contact, i.e., in the chain of thermal resistances between the contact resistance and the sample. The equilibrium between Peltier heat and Fourier heat is unaffected by the thermal contact resistance.

[0041] By way of example, an embodiment is now described below in which the change in current intensity is achieved by switching off and the system is in an equilibrium state after switching on direct current in step d).

[0042] To determine the thermoelectric quality, a current is passed from one block to the other. The current flows from one block (2a) through the contact material (3a) into the sample (1), and from there through the second contact material (3b) into the other block (2b). The sample (1) contains a thermoelectric material, so that with the current flow, a temperature difference is established inside the sample due to the associated Peltier effect. After usually a few minutes, an equilibrium state is reached. In this state, the sample exhibits a temperature gradient. The principle of Harman measurement requires that at least one of the blocks is adiabatically separated from the environment, i.e., its heat content can only change due to the heat flow through the sample. A constant temperature exists within the contact material and within blocks (2a, 2b).The temperature difference inside the sample (1) is caused by the Peltier effect.

[0043] If a sudden change in the current flow is made by changing the current at the time t = t 0 is switched off, the system is in a non-equilibrium state. In this state, the voltage initially drops rapidly, followed by a slower exponential decline. In the conventional evaluation, this slower exponential decline was limited to a point in time t = 0 extrapolated.

[0044] In Fig. 1b ) shows the time course of the total voltage across a thermoelectric sample when a direct current is switched on and then switched off through the sample. The current flow is accompanied by an ohmic voltage drop that is related to the electrical resistance of the sample. The Peltier heat transported by the current creates a temperature difference between the blocks, which stabilizes after a while when the returning Fourier heat compensates for the Peltier heat flow. According to the principle of Harman measurement, this is described as an equilibrium state. After the current is switched off, the temperature compensation can be monitored by the drop in the thermoelectric voltage.

[0045] However, it has been shown that within the first few moments immediately following the sudden change, and thus in the present exemplary embodiment after the current flow is switched off, a state exists in which a temperature change occurs within the contact material, which is influenced by the beginning temperature drop across the sample, while the temperature of the blocks has not yet changed significantly. However, this is not taken into account by the usual extrapolation, so that the thermal resistance of the contact material was not taken into account according to prior art methods.

[0046] In Fig. 2 A temperature profile across the blocks, contacts, and sample (1) is shown. The solid line shows the equilibrium state after switching on a current, as described in step d) of the inventive method. The dashed line shows the non-equilibrium state after switching off the current (step e)) after a short time, neglecting the more sluggish change in the block temperature.

[0047] It has now been shown that within an initial short phase after the current is switched off, the drop in thermoelectric voltage does not follow the subsequent simple exponential law. This deviation is measurable, so that, according to the invention, measurements are carried out at a high measuring rate over a period that is short compared to the half-life of the decay of the temperature difference. This means that an initial measurement is taken as immediately as possible after the current is switched off, followed by a further measurement after each short period of time (significantly shorter than the half-life of the first rapid voltage drop), and so on. Typically, the measurement is started before the current is switched off; for the Harman measurement, knowledge of the measuring voltage before the current is switched off or switched over is essential.After a short time, which is usually small compared to the half-life of the subsequent decay, the portion of the thermoelectric voltage attributable to the contact material is no longer measurable, and the voltage measurement is continued in the usual manner over a period of approximately 3 to 5 half-lives of the slow decay (step g) of the method according to the invention). The exponential decay of the voltage over time is then plotted.

[0048] From the extrapolation of the measured voltage drop to the time t 0 can have an amplitude A 1 Depending on the temperature control of the sample environment and other special features of the measurement setup, it may be necessary to superimpose a slightly inclined linear function on this essentially exponential decay in order to improve the accuracy of the method, namely when the entire sample holder is exposed to a slight drift of the mean temperature; this is also known in the conventional method and is not relevant for the invention. From the measurement immediately after switching off the current in step f) of the method according to the invention, an amplitude A 2, where appropriate, step g) also involves the extrapolation of the measured values ​​to the time t 0 A corresponding measurement process is shown in Fig. 3 shown.

[0049] The ratio A 2 / A 1 corresponds to the relative systematic error of the thermal resistance measurement on the sample, so that the thermal conductivity and the thermoelectric quality can now be determined taking this error into account.

[0050] The determination in the case of switching off the current as a sudden change after an equilibrium state has been reached under current flow is carried out according to the following formula: ZT = U S , true U Ohm = A 1 + A 2 U Ohm

[0051] The incorrect value determined by the standard method ZT old can be corrected as follows ZT old = A 1 U Ohm + A 2 ZT = ZT old A 1 + A 2 A 1 ∗ U ohm + A 2 U ohm

[0052] The usually from the time constant τ 1 Calculated thermal conductivity is determined too low due to the thermal contact resistances (series connection of the resistances of sample and contact). The corrected value x results from the measured κ meas through: κ = κ meas ∗ A 1 + A 2 A 1

[0053] Fig. 4shows the transient thermoelectric voltage between the blocks immediately after the direct current through the sample is switched off. An enlarged view of the initial signal curve is shown in the inset. The thermoelectric voltage represents the temperature difference across the sample (not the temperature difference between the blocks, because the metallic contact area does not contribute to the thermoelectric voltage). Temperature equilibration follows a simple exponential decay analogous to capacitor discharge when the heat capacity of the blocks is large compared to that of the sample. At the beginning of the relaxation, a small but significant deviation from the simple exponential curve is observed. The thermoelectric voltage initially drops more quickly. This is due to the rapid development of a temperature drop across the contact area after switching off.In the previous equilibrium state, there is no temperature difference across the contact because the Peltier heat is not released in the block but directly at the thermoelectric material. If a temperature difference between the blocks is generated by the integrated heaters, this initial, faster drop is not observed. The faster initial equilibration describes the beginning of temperature equalization across the sample synchronously with the formation of the temperature difference across the contacts, while the block temperatures initially do not change. The back extrapolation of the later, slower exponential decay to the switch-off time describes a state in which the equilibrium temperature difference between the blocks is distributed according to the thermal potentiometer ratio between the sample and the contacts.The amplitude of the rapidly decaying signal component compared to the slow relaxation voltage thus represents the ratio of the thermal resistance of contacts and sample, provided one of the blocks is adiabatically separated from the environment. Adiabatic isolation of both blocks is ideal for performing the measurement; if this occurs only on one side and the other block exchanges a significant heat flow with the environment, the exponential fit of the slow temperature compensation must also include a linear term. This improves the accuracy of the determination of the amplitude A 1 , but is not crucial to the core of the invention.

Claims

1. Method for determining the thermal conductivity κ and the thermoelectric quality zT with elimination of the contact thermal resistance RCth on a sample (1) which comprises a thermoelectric material, the sample (1) having two spatially separated contact surfaces and the distance between these contact surfaces corresponding to the length l, the method comprising the following steps: a) bringing a first contact surface of the sample (1) into contact with a first block (2a) via a first contact material (3a) and b) bringing a second contact surface of the sample (1) into contact with a second block (2b) via a second contact material (3b), wherein the first block (2a) and the second block (2b) comprise a metal and / or a metallic coating, wherein at least one of the blocks is adiabatically shielded from the environment, c) attaching at least one first pair of leads to the first block (2a) and to the second block (2b) such that they are electrically conductively connected to the respective contact material (3a, 3b) via the respective block (2a, 2b), so that a direct current can flow from one block through the sample into the other block, and applying at least one second pair of leads consisting of voltage probes to the first and second blocks (2a, 2b), so that a voltage V can be measured between the voltage probe on the first block (2a) and the voltage probe on the second block (2b), d) Achieving a state of equilibrium between a Peltier heat pumped with an electric current through the sample (1) via the first pair of conductors and a Fourier heat flowing back due to the temperature difference building up under adiabatic closure and measuring a voltage V1 via the second pair of conductors consisting of voltage probes, e) Change in the current at time t0, f) time-resolved measurement of the voltage V1 between the voltage probes of the second pair of conductors over a period of time immediately after the change in current intensity in step e), the period of time comprising at least one half-life of a rapid decay and the measurement of the voltage V1 being carried out at a sampling rate which makes it possible to record at least 10, in particular at least 100, measured values within the first half-life, g) subsequent to the measurement according to step f), time-resolved measurement of the voltage V1 between the voltage probes of the second pair of conductors over a period of slow decay until the system has approximately reached a new equilibrium state, with a data rate of at least 5, in particular at least 20, values per half-life of the slow decay when entering the new equilibrium state, whereby the period in step f) is characterized by a rapid drop in voltage compared to the period in step g), in which a uniform slow decay takes place according to an exponential law, h) numerical fitting of data of the time-resolved measurement of the voltage V1 from step g) by an exponential function or the sum of a linear and an exponential function and temporal extrapolation of this function of the measured voltage drop from step g) to obtain a baseline up to the time t0, an amplitude A1 being determined from the extrapolation of the measured voltage drop to the time t0, i) Forming the difference between this baseline and the experimental data from step f), whereby the difference at t0 corresponds to the amplitudeA2 , and forming the ratio A2 / A1, which indicates the relative systematic error of a thermal resistance measurement on the sample caused by the thermal resistance of the contact, j) Determination of the thermal conductivity κ and the thermoelectric quality zT, taking into account the relative systematic error from step i).

2. The method according to claim 1, characterized in that the equilibrium state in step d) is reached in a state in which a direct current is supplied via the blocks (2a, 2b) by means of the first pair of conductors so that the current flows from the first block (2a) to the second block (2b), the current flowing through the first contact material (3a), the sample (1) and the second contact material (3b).

3. Method according to claim 2, characterized in that the change in current intensity in step e) at time t0 is caused by switching off the current.

4. Method according to one of claims 1 to 3, characterized in that the first block (2a), second block (2b), first contact material (3a), second contact material (3b) and the voltage probes applied in step c) have a Seebeck coefficient S of 10 µV / K or less.

5. Method according to one of claims 1 to 4, characterized in that the first block (2a), second block (2b), first contact material (3a), second contact material (3b) and the voltage probes applied in step c) have an electrical conductivity of at least 104 S / cm.

6. Process according to one of claims 1 to 5, characterized in that it is carried out at temperatures of 4 K to 1500 K.

7. The method according to any one of claims 1 to 6, characterized in that the thermoelectric material of the sample (1) is selected from skutterudites, clathrates, half-Heusler compounds, Zintl compounds, quaternary chalcogenides, tellurides, silicides, transition metals and their solid solutions, sulfides, antimonides.