NTC composition, thermistor, multilayer thermistor, multilayer thin-film thermistor, use of a formula for determining material properties and material optimization, and method for material property optimization of NTCs in ceramics

Abstract

NTC composition, thermistor, multilayer thermistor, multilayer thin-film thermistor, use of a formula for determining material properties and material optimization, and method for material property optimization of NTCs in ceramics A manganese cobalt oxide spinel based NTC composition is provided, which corresponds to the molecular formula Mn 3-x-y-z Co x Al y Cu z O4, where 0.80 ≤ x ≤ 1.40, 0.50 ≤ y ≤ 1.10 and 0.15 ≤ z ≤ 0.35, or the proportions of an addition of Al and Cu using the formulas B(T) = B max × tanhyp(3 T / T0) and T0 = (h × v0) / (2 k arcsinh γ), whereby the proportions are adjusted so that a value B max from 3400 to 4000 K and / or a lower limit temperature T0 ≤ 600 Kelvin is reached.

Description

NTC composition, thermistor, multilayer thermistor, multilayer thin-film thermistor, use of a formula for ascertaining material properties and for material optimization, and methods for material property optimization of NTCs in ceramicsThe present application relates to an NTC composition, a thermistor comprising these, a multilayer thermistor comprising these, and a multilayer thin-film thermistor comprising these. The application further relates to the use of a formula for ascertaining material properties and to the use of the formula for material property optimization and to a method for material property optimization.NTC ceramics are used in thermistors. Such thermistors are generally used for a large number of applications, for example in electronics, but also in combustion automobiles or electric automobiles. For some applications, components that are as small as possible may be advantageous. Some applications require as broad a temperature detection as possible over a wide range. Again, some applications require temperature sensing at low temperatures.In view of the above requirements, an improved NTC composition and a thermistor with it should be provided.The object is at least partially achieved by an NTC composition according to claim 1 or according to claim 2. Further preferred embodiments are given in dependent claims. Other objects are claimed in the subordinate claims or described below.According to one embodiment, an NTC composition having a main component based on manganese-cobalt oxide-spinel is described. This has aluminum with the element symbol Al and copper with the element symbol Cu as additives. The corresponding composition can be described, for example, by the empirical formula Mn 3-x-y-z Co x Al y Cu z O 4. The composition may have oxygen vacancies, but preferably does not have oxygen vacancies.The NTC composition may contain, in addition to the main component constituting the main portion of the NTC composition, also a portion of a second phase as what is known as a precipitate. Precipitates can form during sintering, in particular if sintering is carried out at too high a sintering temperature. The ceramic is preferably selected with regard to its starting materials as if, at the end, the entire NTC composition consisted of the main component as main phase. In the production, however, a precipitation phase or precipitation phases can be formed in addition to the main component, wherein still portions of the ceramic meet the target composition, which then represent the main component. Preferably, the precipitate constitutes a small proportion of the composition. Preferably, the main component has a phase content of more than 90%, i.e. in the case of the reproduction of the main component by Mn 3-x-y-z Co x Al y Cu z O 4 this spinel component has a phase content of more than 90%. More preferably, it constitutes a proportion of over 95%. With careful sintering, it can also be produced substantially in one phase, for example with a phase proportion of more than 99%.According to one embodiment, the proportion of the addition of Al and Cu can be determined with the aid of the formulae B(T)=B max×tanhyp(3T / T 0) and T 0= ( h×v 0) / (2 k arcsinh.gamma.). Here, B(T) is the temperature-dependent B value of the ceramic, T is the temperature, B max is the temperature-independent B value of the dominant small polaron hopping line, T 0 is the lower limit temperature of the dominant small polaron hopping line (SPH line for short), h is the Planck constant, v 0 is the characteristic oscillation frequency of the crystal lattice, k is the Boltzmann constant, and γ is the coupling constant. The B value is a variable which is fundamentally known in the NTC ceramic range and represents a characteristic measure for the composition or a thermistor produced therewith or can be used as a measure for the measurement sensitivity of a thermistor produced therewith. Small Polaron Hopping conduction is the generally accepted dominant conduction mechanism in NTC thermistor ceramics. In addition to the SPH line, a certain temperature-dependent proportion of the charge carriers is also transported by band half-line. Both mechanisms operate in parallel, resulting in some deviation from linear behavior.In particular, the use of the formulae enables the otherwise poorly accessible material parameters B max, T o and γ to be determined easily, accurately and reproducibly. For example, material optimization can be performed in a short time.According to one embodiment, quantitative proportions of ceramic components or, in particular, the quantitative proportions of Al and Cu are adjusted with the aid of the formulae mentioned above such that a value B is max3400 to 4000 K. According to a preferred embodiment, the quantitative proportions are adjusted such that a value B is max3500 to 3800 K. According to a particularly preferred embodiment, the quantitative proportions are adjusted such that a value B is max3500 to 3600 K.According to one embodiment, quantitative proportions of ceramic components or, in particular, the quantitative proportions of Al and Cu are adjusted with the aid of the formulae mentioned above such that a value T 0 of not more than 600 K. According to a preferred embodiment, quantitative proportions are set such that a value T 0 is at most 550 K. According to a particularly preferred embodiment, quantitative proportions are set such that a value T 0 of at most 500 K.A manganese-cobalt oxide spinel with Al and Cu as additives, which has a value B max of 3400 to 4000 K and / or a value T 0 of max. 600 K may be suitable for use at temperatures below 0° C. For such a thermistor, for example, at temperatures below 0°C, a B value may more easily remain above a value of 3000 K. Furthermore, the linear range of the B value may be more extended and extend, for example, towards lower temperatures. Such a thermistor can thus be particularly well suited for expanding the technically meaningful measurement range into temperature ranges below 0° C.A manganese-cobalt oxide spinel with Al and Cu as additives can also be used in a meaningful manner, for example, in particular in a temperature range in which typical thermistors from the prior art, which are based on a manganese-iron-nickel oxide spinel with Cu as additive, for example, can no longer be used in a meaningful manner. Such manganese-iron-nickel oxide spinels from the prior art, for example Mn 3-x-y-z Fe x Ni y Cu z O 4 with 0.80≤x≤0.85 and 0.60≤y≤0.65 and 0.001≤z≤0.10, have poor linearity and sensitivity of the measurement signal below 0° C. and therefore cannot be used meaningfully in this measurement range.According to one embodiment, the B value of the manganese-cobalt-oxide-spinel-based NTC composition can be adjusted via the Cu fraction. The addition of Al makes it possible to increase the resistivity of the composition. For example, the Cu additive may increase conductivity. Thus, the inventors have recognized that the composition can be optimized via the targeted interaction of these components, the proportions of which are adjusted, for example, with the aid of the formulae mentioned above. Thus, these two components can introduce preferred properties and in each case balance less preferred properties with respect to one another. Consequently, alternatively and independently of the features mentioned above or below, an NTC composition having a main component based on manganese-cobalt-oxide-spinel with an addition of aluminum and copper is also disclosed in general. This may include further features of other embodiments.According to an embodiment, the ceramic is set to a specific resistance of 200 Ω·cm or more.Preferably, to a value of 250 Ω·cm or more, and more preferably, to a value of 400 Ω·cm or more. Still more preferably, a value of 800 Ω·cm or higher is used. Higher resistivities allow thermistors to be miniaturized or to reduce film thicknesses in multilayer thermistors. In particular, a ceramic having the above-mentioned B values and the specific resistances described herein is preferred.Further, an NTC ceramic composition having a main component with the empirical formula Mn 3-x-y-z Co x Al y Cu z O 4 is described as a further embodiment. In this, 0.8≤x≤1.4, 0.5≤y≤1.1 and 0.15≤z≤0.35.According to one embodiment, 0.90≤x≤1.30, 0.55≤y≤1.00, and 0.15≤z≤0.35.The aforementioned features can be combined with one another and also with features mentioned below. In particular, a composition adjusted by the above formulae may have the present properties or the properties set out below.The inventors of the present invention have recognized that with such a composition, improved performance of the NTC composition or of a thermistor formed therefrom can be achieved. For example, the B value may have a better linearity, i.e., linearly approximated in a different or broader range without large errors. Further, too large a decrease in the resistance of such a ceramic composition can be prevented. In addition, a thermistor can be provided which enables improved temperature measurement at low temperatures. In particular, the sensitivity at low temperatures can be improved.According to a preferred embodiment, z is 0.15 ≤ z ≤ 0.30. more preferably, 0.15 ≤ z < 0.29 and even more preferably, 0.15 ≤ z ≤ 0.28.It has been recognized that z≤0.35 can prevent the composition from dropping too much resistivity. For values of z≤0.28 or even slightly smaller, it has been recognized that such an NTC composition has a preferably high specific resistance. In particular, by means of a composition for which x and y correspond to the values mentioned above and z corresponds to those mentioned here, it is easier to obtain an NTC composition which has a high B value at low temperatures and at the same time has a high specific resistance. The lower limits for z given have proven to be preferred since these help to set the B value.Preferred ranges for x are 0.90 ≤ x ≤ 1.30, such as 0.95 ≤ x ≤ 1.25, more preferred are, for example, 1.00 ≤ x ≤ 1.10.For y, the range of 0.55 ≤ y ≤ 0.95 was considered preferable. Even more preferably, a range of 0.60≤y≤0.95 or 0.60≤y≤0.90 or of 0.70<y≤0.95 or of 0.75≤y≤0.85 is found.In particular, all material compositions have been recognized as preferred in which two or more preferably three of x, y and z assume a preferred value or a very preferred value.According to a further embodiment, an NTC composition having a main component based on manganese-cobalt oxide spinel, to which aluminum and copper are added and in which the ratio of aluminum to copper is >2.4, is described. With such an amount ratio of Al to Cu, preferable characteristics of B value as well as resistivity can be obtained.When an NTC composition having a main component with the empirical formula Mn 3-x-y-z C Ox Al y Cu z O 4 is considered as an embodiment of the manganese-cobalt oxide-spinel-based NTC composition, in the case of the preceding exemplary embodiment y:z>2.4. x can assume the values described above. y can assume the values described above and z can result according to the ratio of y:z. Alternatively, z can also assume the values described above and y can result from the ratio of y:z. According to a preferred embodiment, the NTC composition having the empirical formula Mn 3-x-y-z Co x Al y Cu z O 4 satisfies both the values described above for x, y and z and the ratio y:z>2.4.According to one embodiment, the composition is free of nickel, except for unavoidable impurities.A thermistor is also disclosed. This has the above-mentioned NTC composition in an NTC ceramic. This means that the NTC ceramic composition makes up at least a portion or a partial volume of the ceramic of a thermistor.According to an embodiment, the thermistor may be a monolithic NTC thermistor or a multilayer thermistor. A monolithic NTC thermistor can mean here both a component sintered from one piece and a component formed and sintered from individual layers, which, however, has no internal electrodes in contrast to a multilayer thermistor.According to another embodiment, the thermistor may be a single-layer NTC thin-film thermistor or a multilayer thin-film thermistor. A monolayer NTC thin-film thermistor can mean here both a component manufactured from a single thin-film layer and a component composed of a plurality of individual thin-film layers stacked one above the other, even in successive manufacturing steps, but which, in contrast to a multilayer thin-film thermistor, has no internal electrodes.The ceramic composition allows the thermistors mentioned to have small designs because it enables a sufficiently high specific resistance. In particular, miniaturization of the components can thereby be achieved. For example, according to an embodiment, a multilayer thermistor having a volume between 0.075 to 10 mm 3 may be obtained. According to a preferred embodiment, a volume of such a multilayer thermistor can be 0.3 to 5.5 mm 3.According to one embodiment, at least one ceramic layer which contains or consists of the NTC composition is contained in a multilayer thermistor. A similar embodiment can also be embodied as a multilayer thin-film thermistor, wherein the multilayer thin-film thermistor contains a ceramic thin-film layer with or made of the NTC composition.According to an embodiment, a ceramic layer may have a thickness of 10 to 100 μm, and preferably of 20 to 50 μm. According to an embodiment, a thin film layer may have a thickness of 0.001 to 10 μm, and preferably of 0.01 to 1 μm.In particular, a ceramic composition having the above-mentioned values for z, such as 0.20≤z≤0.30, has particularly suitable properties in order to ensure a sufficiently high resistance for corresponding layer thicknesses.In particular, such a composition can be used for thermistors having rated resistances at 25° C. of 1 to 20 kΩ. In particular, a rated resistance at 25° C. may be 10 kΩ. The thermistors and in particular the multilayer thermistors can be designed as SMD components (surface mounted device components). The (thin-film thermistors, regardless of whether embodied in multilayer construction or as a monolayer thin-film thermistor, can also be applied to or in substrates or be suitable for embedding (SESUB technology) or be provided as a component for a MEMS component.Furthermore, the use of the formula B(T)=B max×tanhyp(3T / T 0) for ascertaining the material properties of an NTC spinel ceramic is described. Here, B(T), B max, T and T 0 correspond to the above-described sizes.Up to now, NTC spinel ceramics, such as nickel-manganese spinels or nickel-cobalt spinels, have often been described exclusively by the linear approximation B(T1, T2)=ln(R2 / R1) / (1 / T2-1 / T1). In this case, for example, T1=25 °C and T2=100 °C, wherein R1, R2are resistances at T1, T2. Thus, only the ideal RT characteristic curve of a thermistor ceramic was considered. This simplified view does not, however, meet such ceramics, in particular not for lower temperatures. In the linear range, the generally accepted conduction mechanism of small polaron hopping (SPH for short) predominates. This predominates in particular at higher temperatures, since here sufficient thermal energy is available for exciting the crystal oscillations. At room temperature and above all below this is no longer complete. In addition to the SPH line, a smaller proportion of the charge carriers is also transported by band half-conduction. Both mechanisms operate in parallel. This results in a deviation from the linear approximation. If the B(T1, T2) value is calculated in this temperature range, this value is lower the lower T1 is selected. If a close-mesh detection of T1 and T2 is selected, a constant drop of the B(T1, T2) value to low temperatures is shown.Up to now, mechanisms and parameters have been detected only extremely inaccurately. The method described by Casado et al. (J. Phys.: Condens. Matter 6 (1994) 4685-4698), however, physical description provides only an insufficient basis for detecting material properties in technically relevant systems. Thus, according to Casado et al. of the formulae T o= ( h·v o) / (2 k arcsinh γ) and B max= ( γ·h·v o) / (2 k) are used. Here, T 0 is the lower limit temperature of the dominant SPH line, B max is the constant B value of the dominant SPH line, v o is the characteristic oscillation frequency of the crystal lattice, h is the Planck constant, k is the Boltzmann constant, y is the coupling constant of the oscillation energy with the electrical energy.Although the formula B max= ( γ·h·y o) / (2 k) contributes much to understanding the deviation from the linearity at low temperatures, the parameters T 0, B max and y are difficult to determine with this. Up to now, as a rule, a graphic method has been used in which Ln(R) is applied over (1 / T) in a temperature range as large as possible. In the range of smaller (1 / T) values, a straight line is adapted as asymptotic curve. Thus, the values T o( the coincidence of the RT values with the straight line) and B max( the slope of the asymptotic curve) can be estimated. However, the placement of the straight lines and their drawing is partially arbitrary and at least subject to great uncertainty.The approach according to the invention using the formula B(T)=B max×tanhyp(3T / T 0) provides an improved, simple and accurate method here. The inventors have recognized in the analysis of the B(T1, T2) curve that this is very well reflected by the tan gene hyperbolic function.Moreover, the tangent hyperbolic function has the physically correct behavior: as the temperature rises, the function value asymptotically approaches a constant final value. This final value corresponds to B max.Since B(T) asymptotically (T→∞) approaches B max it is possible to define which approach is defined as sufficient according to one embodiment. For practical application, T 0 can be defined to be reached when 99.5% of the final value for B (i.e., B max) is reached. The result is: B (T 0) = tanhyp(3)·B max= 0.995- B maxThe interpolation points for B(T2,T1) to which an adaptation according to the formula B(T)=B max×tanhyp(3T / T 0) is carried out are preferably chosen to be close-mesh. Thus, a distance between the supporting points with T2-T1≤10K over a measurement range of -50° C. to 200° C. is preferably selected. However, T2-T1 can also be selected to be of a wider mesh. T2-T1can accordingly be ≤25K, with good matching still being obtained. This is particularly successful if at least 9 interpolation points are present in the measurement range -50° C. to 150° C.According to an embodiment, the coupling constant over T 0= ( h×v 0) / (2 k arcsineh γ) may be obtained.With the described procedure, material properties can be determined quickly and easily. In particular, it facilitates the evaluation of large data sets. In addition, the procedure can be used automatically.According to one embodiment, the use of the formula B(T)=B max×tanhyp(3T / T 0) for material property optimization of NTC spinel ceramics is described.Since the above-described procedure enables improved capture of material properties, this allows material development including material property optimization to take place in a targeted manner.Further, a method using formula B max × tanhyp(3T / T 0) is described. This can have the features described above.According to one embodiment, the method is a method for optimizing the material property of NTC spinel ceramics, wherein an adaptation (fit) is applied to a curve of the B value of a starting material composition with the aid of the formula B(T)=B max×tanhyp(3T / T 0). Together with the formula T 0= ( h×v 0) / (2 k arcsinh.gamma.), a determination of starting material properties of the starting material composition takes place. Starting from these starting material properties, additives are selected which specifically influence the B value at a specific temperature, the T 0- value and / or the specific resistance.Thus, starting from a starting composition, material optimization can be carried out, wherein the above-mentioned advantages are met.According to one embodiment, the process can be carried out as a multistage process. In this case, the composition already optimized by the method once again passes through the method by being subjected again to the process sequence as starting material composition. In other words, the ceramic composition already optimized by additions is again subjected to the described process sequence as starting material composition at least once.Also provided is a method of manufacturing a multilayer thermistor. According to this, starting materials for a ceramic composition having the empirical formula Mn 3-x-y-z Co x Al y Cu z O 4 are first provided. These starting materials can be, for example, oxides, carbonates or hydroxides or the like of the metal atoms mentioned in Mn 3-x-y-z Co x Al y Cu z O 4. The starting materials are weighed in such a way that 0.8≤x≤1.4, 0.5≤y≤1.1 and 0.15≤z≤0.35 are obtained for the ceramic composition. After the initial material has been weighed in, the starting materials are ground and subsequently calcined. The grinding may be, for example, a wet grinding. Thus, an average grain size of between 0.5 and 1.5 μm, and preferably of 0.7 to 1.0 μm, can be obtained. Calcination may be carried out at 800° C. to 1000° C., for example at 825 to 925° C. The resulting calcite is subsequently ground, which may be referred to as post-grinding. The targeted grain sizes can correspond to those of the first paint step. Green sheets are then prepared with the ground calcinate. In this case, the calcite can be admixed with additives such as binders, wetting agents or dispersants or the like. This mixture can be applied to a carrier film. The green sheets are then stacked. Stacking is performed together with raw materials for internal electrode layers. For example, the starting material for internal electrodes can be a metal paste and these can be printed on some green sheets before stacking. From the stack thus obtained, one or more green thermistor elements are cut out. This or these are subsequently debindered. The debindered green thermistor devices are sintered. The sintering is preferably carried out at 1000 to 1200° C. At this temperature, as few secondary phases as possible and as much main phase as possible are formed in the resulting ceramic. Decomposition can be reduced accordingly. In this regard, a range from 1050° C. to 1150° C. is preferred. Furthermore, external electrodes are applied, which each contact internal electrodes.Similarly, a monolithic thermistor can also be obtained. For this purpose, the steps for forming inner electrodes are omitted, for example.Furthermore, the ceramic obtained by the method can have the above-mentioned properties.Embodiments are listed below which are referred to below as "shape". These are numbered to better emphasize the relationship of these embodiments and the relationship of the features of these embodiments to each other, respectively. The numbered embodiments may also be modified by features of further features of this specification, which may result in further embodiments. The invention is not limited to these embodiments.Form 1: NTC composition comprising a main component based on manganese-cobalt oxide-spinel, wherein quantitative proportions of an additive of Al and Cu are determined with the aid of the formulae B(T)=B max×tanhyp(3 T / T 0) and T 0= ( h×v 0) / (2 k arcsineh γ), wherein B(T) is the B value of the ceramic, T is the temperature, T 0 is the lower limit temperature of the dominant small polaron hopping line, h is Planck constant, v 0 is the characteristic oscillation frequency of the crystal lattice, k is the Boltzmann constant and γ is the coupling constant, B max is the temperature-independent B value of the dominant small polaron hopping line, wherein the quantitative proportions are adjusted such that a value B is max3400 to 4000 K or / and a lower limit temperature T 0 ≤600 Kelvin is reached.Form 2: NTC composition comprising a main component having the empirical formula Mn 3-x-y-z Co x Al y Cu z O 4, where 0.8≤×≤1.4, 0.5≤y≤1, 1 and 0.15≤z≤0.35.Form 3: NTC composition according to Form 2, wherein 0.15≤z≤0.30, or preferably 0.15≤z≤0.28.Form 4: NTC composition according to Form 2 or 3, wherein y:z>2.4.Form 5: NTC composition according to any one of Forms 2 to 4, wherein 0.90≤x≤1.30, or preferably 0.95<x≤1.25.Form 6: NTC composition according to one of Forms 2 to 5, wherein 0.55≤y≤0.95 or preferably 0.60≤y≤0.95.Form 7: NTC composition according to any of Forms 1 to 6, wherein the main component makes up at least 90% of the phases of the NTC composition.Form 8: A thermistor comprising the NTC composition according to any one of Forms 1 to 7.Form 9: Multilayer thermistor comprising a ceramic layer comprising the NTC composition according to one of Forms 1 to 7.Mold 10: Multilayer thermistor according to Mold 9, wherein said multilayer thermistor has a volume of 0.075 to 10 mm 3.Mold 11: Multilayer thermistor according to Mold 9 or Mold 10, wherein the ceramic layer has a thickness of 10 to 100 μm, and the thermistor is composed of one or more layers.Form 12: Multilayer thermistor according to one of forms 9 to 11, which has a rated resistance at 25° C. of 1 to 20 kΩ.Mold 13: Multilayer thin film thermistor comprising a ceramic layer comprising the NTC composition according to one of Molds 1 to 7.Form 14: A method for producing a multilayer thermistor, wherein starting materials for a ceramic composition having the empirical formula Mn 3-x-y-z Co x Al y Cu z O 4 are provided, wherein the starting materials are weighed in such a way that 0.8≤x≤1.4, 0.5≤y≤1.1 and 0.15≤z≤0.35 are obtained for the ceramic composition, the starting materials are ground, the powder obtained after grinding the starting materials is calcined, the resulting calcite is ground, green foils are produced with the ground calcite, the green foils are stacked together with starting materials for internal electrodes, green thermistor components are cut from the stack, the green thermistor components are debindered, the debindered green thermistor devices are sintered into sintered thermistor devices at 1000-1200°C and external electrodes are applied to the sintered thermistor devices.Mold 15: The method according to Mold 14, wherein the raw material for internal electrodes is a metal paste, and is printed on some green sheets before stacking.Mold 16: The method according to Mold 14 or Mold 15, wherein the sintering is performed at 1050° C. to 1150° C.Form 17: Use of formula B (T 0) = B max × tanhyp(3T / T 0), wherein B(T) is the B value of the ceramic, B max is the temperature independent B value of the dominant small polaron hopping conduit, T is the temperature, T 0 is the lower limit temperature of the dominant small polaron hopping conduit, for determining the material properties of an NTC spinel ceramic.Form 18: Use of the formula B(T)=B max×tanhyp(3T / T 0), wherein B(T) is the B value of the ceramic, B max is the temperature-independent B value of the dominant small polaron hopping line, T is the temperature, T 0 is the lower limit temperature of the dominant small polaron hopping line, for material property optimization of NTC spinel ceramics.Form 19: Use according to Form 17 or Form 18, wherein T 0 is defined as being reached when B(T)=tanhyp(3)·B max= 0.995 ·B max holds.Form 20: A method for material property optimization of NTC spinel ceramics, wherein an adjustment is applied to a curve of the B value of a starting material composition with the aid of the formula B(T)=B max × tanhyp(3T / T 0) wherein B(T) is the B value of the ceramic, B max is the temperature-independent B value of the dominant small polaron hopping line, T is the temperature, T 0 is the lower limit temperature of the dominant small polaron hopping line, Together with the formula T 0= ( h×v 0) / (2 k arcsineh γ), wherein h is Planck constant, v 0 is the characteristic oscillation frequency of the crystal lattice, k is the Boltzmann constant, and γ is the coupling constant, a determination of starting material properties of the starting material composition is obtained, and starting from these starting material properties additions are selected which specifically influence the B value at a specific temperature, the T 0- value and / or the specific resistance.Mould 21: Process according to Mould 20, wherein the process is carried out as a multistage process, wherein the ceramic composition, already optimized by additions, as starting material composition is again subjected to the process sequence described at least once.The invention is described below with reference to exemplary embodiments and figures. Schematic representations of components are not true to scale. Portions thereof may be distorted in size, length, or aspect ratio as compared to other components. Accordingly, no variables or relationships can be gathered from the schematic drawings. Similar or similarly acting components are provided with the same reference numerals. It cannot be deduced therefrom that all features of these components are always identical or the invention is limited to the features of the exemplary embodiments specifically described for this purpose FIG. 1 schematically shows a first exemplary embodiment of an NTC thermistor in cross section. FIG. 2 shows a cross-sectional micrograph of a second embodiment of an NTC thermistor. FIG. 3 shows the curve B(T) for a first thermistor ceramic and a matching curve. FIG. 4 shows the curve B(T) for a second thermistor ceramic and a matching curve. FIG. 5 shows the curve B(T) for a third thermistor ceramic and a matching curve. FIG. 6 shows the curve B(T) for a fourth thermistor ceramic and a matching curve. FIG. 7 shows a cross-sectional micrograph of a third embodiment of an NTC thermistor. FIG. 8 shows the comparison of the curves of B(T) for the first and fourth thermistor ceramics.FIGS. 1 and 2 each show two exemplary embodiments of a multilayer thermistor 1. FIG. 1 shows a schematic cross-sectional view and FIG. 2 shows a cross-sectional microscopy image recorded with a scanning electron microscope.Both exemplary embodiments of the multilayer thermistor 1 have a plurality of ceramic layers 2 which are alternately stacked with inner electrode layers 3. The ceramic layers 2 consist of a ceramic material, as described below with reference to FIGS. 4 to 6. The inner electrode layers 3 consist of a palladium-silver alloy. The ceramic layers 2 and the inner electrode layers 3 can be obtained by usual multilayer technology. They can thus be formed from green foils and by applying metallizations. For a ceramic layer 2, one or more green sheets may be laminated. In the stacking-related layer direction, termination regions 5 are located at the top and bottom of the layer stack. Even if no sizes or size relationships can be derived from the schematic FIG. 1, it can nevertheless be recognized that, depending on the embodiment, possible termination regions 5 can be selected to be of different thicknesses. Furthermore, both multilayer thermistors 1 have external electrodes 4, which are obtainable by customary metallization methods.The multilayer thermistors 1 according to FIG. 1 or 2 have dimensions of length×thlow×height=(1.0±0.1) mm×(0.5±0.05) mm×0.6 mm or of length×thlow×height=(1.6±0.15) mm×(0.8±0.15) mm×0.9 mm. The ceramic layers in FIG. 2 have a thickness of 30 μm.FIG. 3 shows the curve for B(T1, T2) for a ceramic composition with the sample number 2917. This is a manganese-iron-nickel-copper spinel, which was sintered at 1070° C. This is an NTC ceramic material, which is customary in the prior art and mentioned at the outset, and which does not meet the desired requirements, in particular in the temperature range below 0° C. In the prior art, sufficient data regarding the relevant parameters describing an NTC thermistor with regard to its properties are known for this ceramic in order also to provide a basis for comparison for the improved determination method according to the invention for these parameters.The composition has a B(25° C., 100° C.) value of 3454 K and a specific resistance of 1700 Ω·cm, as acquired in a linear approximation with B(T1, T2)=ln(R2 / R1) / (1 / T2-1 / T1). It was possible to produce a component with a rated resistance of 10 kΩ. Numerous interpolation nodes (T2-T1≤10K) were detected.An adaptation (fit) was applied to the measurement data on the basis of the function B(T)=B max×tanhyp(3T / T 0). Here, B(T) is the B value of the ceramic, T is the temperature and T 0 is the lower limit temperature of the dominant small polaron hopping line (SPH line for short). The following approximation was also used: T 0 is achieved when B(T 0) = tanhyp(3)·B max= 0. 995·B max, i.e. when 99.5% of the final value is reached.B max= 3870 K and T 0= 680 K (407° C.) were able to be determined in this way.Furthermore, it was also possible to determine the coupling constant γ with the aid of T 0= ( h×v 0) / (2 k arcsinh γ), which is 3.10. Here, h is the Planck constant, v 0 is the characteristic oscillation frequency of the crystal lattice, and k is the Boltzmann constant.Thus, relevant material parameters can be obtained. The composition shows unsatisfactory linearity and unsatisfactory sensitivity at T<0° C. B(T) decreases below 3000 K in the region analyzed. The analysis reveals which parameters have improvement potential: in order to obtain a lower T o the coupling factor y should both be increased in the direction 4 and B max should be reduced, for example to approximately 3400 to 4000 K or preferably to 3500-3600 Kelvin. It should thus be possible to obtain a B(T1, T2) value of >3000 Kelvin at minus degrees and to improve the linearity of the RT characteristic curve.With this approach, a less reliable approach used hitherto can be detached. Heretofore, material properties have been evaluated according to results of basic research by Casado et al (J. Phys.: Condens. Matter 6 (1994), 4685 - 4698) by T 0= ( h·v o) / (2 k arcsinh γ) and B max= ( γ·h·v o) / (2 k). Here, T 0 is the lower limit temperature of the dominant SPH line, v o is the characteristic oscillation frequency of the crystal lattice, h is the Planck constant, k is the Boltzmann constant, y is the coupling constant of the oscillation energy with the electrical energy. Although B max= ( γ·h·v o) / (2 k) contributes much to understanding the deviation from linearity at low temperatures, the parameters T o, B max and γ are difficult to determine therefrom. In the literature, a graphic method is used in which In(R) is applied over (1 / T) in a (largest possible) temperature range. In the range of smaller (1 / T) values, a straight line is adapted as asymptotic curve. Thus, the values T o( the coincidence of the RT values with the straight line) and B max( the slope of the asymptotic curve) can be estimated. But finally, the drawing of the straight lines is arbitrary and has great uncertainty.For this reason, the improved and more accurate method presented above has been developed, which is based on the analysis of the B(T1, T2) curve. It has been recognized that the B-value curve (FIG. 3 ) is very well reproduced by the tangent hyperbolic function. Moreover, the tannerhyperbolicus function has the physically correct behavior: as the temperature rises, the function value asymptotically approaches a constant final value.FIG. 4 shows the B(T1, T2) curve for a ceramic composition according to the invention and an approximation with the aid of the method described above. The composition follows the empirical formula Mn 3-x-y-z Co x Al y Cu z O 4, wherein x=1.18, y=0.60 and z=0.28, i.e. contains a main phase with this composition. The composition was sintered at 1150°C. The composition is assigned the sample number 15.This composition shows improved values compared to Sample 2917 which is conventional in the art. The resistivity is 280 Ω·cm, the B(25,100) value is 3441 K, B max is 3549 K, T 0 is 467 K, and y is 3.7. thus, as compared with Sample 2917, the coupling factor y was increased in the direction 4, as well as B max was reduced to a value of 3500-3600 K. This has made it possible to obtain a B(T1, T2) value of >3000 Kelvin at minus degrees and to improve the linearity of the RT characteristic curve, as can be seen from FIG. 4. Also, excessive decrease of the resistivity could be prevented. However, this could be improved still further.FIG. 5 shows the B(T1, T2) curve for a ceramic composition according to the invention and also preferred and an approximation with the aid of the method described above. The composition follows the empirical formula Mn 3-x-y-z Co x Al y Cu z O 4, where x=1.21, y=0.90 and z=0.22. The composition was sintered at 1100°C. The composition is assigned the sample number 31.This composition shows at least partially improved values compared with sample 2917 and also with sample 15. The resistivity is 1049 Ω·cm, the B(25,100) value is 3581 K, B max is between 3700 K and 3800 K, as can be approximately read from the figure, T is 0 543 K, and y is 3.5. the coupling factor is slightly reduced, but the resistivity is greatly improved as compared with Sample 15. This makes it easy to achieve a component with a rated resistance of 10 kΩ.FIG. 6 shows the B(T1, T2) curve for a particularly preferred ceramic composition according to the invention and an approximation with the aid of the method described above. The composition follows the empirical formula Mn 3-x-y-z Co x Al y Cu z O 4, where x=1.02, y=0.80 and z=0.27. The composition was sintered at 1100°C. The composition is assigned the sample number 49.This composition again shows at least partly improved properties compared with the samples described above. The resistivity is 832 Ω·cm, the B(25.100) value is 3446 K, B max is 3542 K, T 0 is 457 K, and y is 3.8, and thus the sample has a very good balance of material properties.The production is also explained with reference to the sample 49.First, a powder is prepared. The initial weight and materials used for an 80 kg powder batch can be found in Table 1. Table 1 Table 1AluminumAl 2 O 3, Aluminum oxide15,3 kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kgManganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese Manganese ManganeseMn 3 O 4, Manganese oxide26,0 kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kgCobalt Cobalt Cobalt Cobalt Cobalt CobaltCo 3 O 4, cobalt oxide30,6 kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kgCopper CopperCuO, copper oxide8,1 kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kgSum:80 kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kg kgSubsequently, the components were mixed with water and milled in an agitator ball mill until a target grain size d(50%) of 0.7 to 1.0 μm was obtained. After obtaining the target grain size, the suspension was dried and sieved.The powder is then calcined. For this purpose, the powder was filled into cordierite capsules and reacted in a stand furnace. The heating rate was 5 K / min, the top temperature was 875°C, the holding time was 8 hours, and the cooling rate was -5 K / min. XRD measurement gave a degree of conversion >90%.Subsequently, post-grinding of the reacted powder was carried out. The calcite was first sieved dry and then mixed with water and reground until a target grain size d(50%) of 0.7 to 1.0 μm was obtained. After the target grain size was obtained, the suspension was dried again and sieved.Green sheets were then produced. For this purpose, the powder is mixed with organic solvents and auxiliaries (binders, wetting agents, dispersants, etc.) customary for this technology are added. After the suitable viscosity has been established and the suspension has been degassed, a ceramic film is produced on a carrier film by means of a film-drawing machine, which can be further processed by means of multilayer technology.In the specific embodiment, a film was made having a nominal thickness ("green thickness") of 28.5 μm.Then, the sintered body is produced. This is explained first on the representation in FIG. 7, which shows an SEM image of a sintered component in the longitudinal section. In this embodiment, the so-called "tip design" has been applied. In this case, two inner electrode layers 3 (electrode tips) protrude from each outer electrode 4 into the component, but without the inner electrode layers 3 overlapping. The current flow therefore takes place mainly from the electrode tips to the opposite electrode tips of the counter electrode. This minimizes the cross section of the current flow. The farther the electrode tips are from each other, the higher the resistance.First, internal electrodes were realized by printing on the ceramic film. For this purpose, an AgPd paste (60% Ag, 40% Pd) is applied at the intended locations by screen printing.Subsequently, the printed and non-printed films are stacked one above the other in a defined sequence.Stacking Sequence Based on the Exemplary Embodiment Illustrated in FIG. 714 non-printed films (form one of the lower end regions 5)1 printed film (inner electrode tips of one plane 1)5 non-printed films (intermediate space to a plane 2)1 printed film (inner electrode tips of plane 2)13 Non-printed films (form the upper cover layer)The stacked films are then pressed (laminated) in order to ensure stable adhesion of the individual layers to one another.The stack was then cut, components ("green parts") being cut from the stack. The dimension of the unsintered members (green members) is 1.8×0.9 mm (L×B).The components are then debindered. The binders required for the green processes are burnt out before sintering. For this purpose, the components are heated slowly (<1 K / min) to 450° C. under air flushing (holding time 6 hours).The components are then sintered. The components were sintered in an air atmosphere with the following sintering conditions:Heating Rate=5 K / minTop temperature=110°C (1080°C - 1140°C possible)Holding time= 2 hoursCooling Rate= -5 K / minFor the evaluation measurements, the two external electrodes are applied. For this purpose, the caps are provided with silver paste and fired. The configuration of the metallization caps can be clearly seen from the SEM image in FIG. 7.Furthermore, the components of the exemplary embodiment were passivated on the surface (glass cladding) and nickel-plated and tin-plated on the caps by means of electroplating in order to be easily solderable.Finally, the comparison of the B(T) curves for samples 49 and 2917 can be seen in FIG. 8. Sample 49 shows clearly improved low temperature B-value and linearity properties. Sample 49 thus has significantly improved properties compared to the NTC ceramics usually used in the prior art, corresponding to sample 2917, and can therefore extend the technically meaningful measurement range for NTC thermistors into the temperature range far below 0° C.List of reference characters1 Multilayer thermistor 2 Ceramic layer 3 Inner electrode layer 4 Outer electrode 5 Termination regionReferences included in the specificationThis list of documents cited by the applicant has been produced in an automated manner and is only included for the better information of the reader. The list is not part of the German patent application or utility model application. The DPMA does not take any adhesion for any faults or omissions.Cited Non-Patent LiteratureCasado et al. (J. Phys.: Condens. Matter 6 (1994) 4685 - 4698

[0039] Casado et al (J. Phys.: Condens. Matter 6 (1994) 4685 - 4698

[0088]

Claims

NTC composition comprising a main component described by Mn 3-x-y-z Co x Al y Cu z O 4 where 0.60<y≤1.1, and where proportions of an additive of Al and Cu are determined with the aid of the formulae B (T)=B max×tanhyp (3 T / T 0) and T 0=(h×v0) / (2 k acrsinh γ) where B(T) is the B value of the ceramic, T is the temperature, T 0 is the lower limit temperature of the dominant small polaron hopping line, h is the Planck constant, v 0 is the characteristic oscillation frequency of the crystal lattice, k is the Boltzmann constant, and γ is the coupling constant, B max is the temperature-independent B value of the dominant small polaron hopping line, wherein the quantitative proportions are set such that a value B is max3400 to 4000 K or / and a lower limit temperature T 0 ≤ 600 Kelvin is achieved.NTC composition comprising a main component described by Mn 3-x-y-z Co x Al y Cu z O 4 where 0.22≤z≤0.3, and where proportions of an additive of Al and Cu are determined with the aid of the formulae B (T)=B max×tanhyp (3T / T 0) and T 0=(h×v0) / (2 k arcsinhγ) where B(T) is the B value of the ceramic, T is the temperature, T 0 is the lower limit temperature of the dominant small polaron hopping line, h is the Planck constant, v 0 is the characteristic oscillation frequency of the crystal lattice, k is the Boltzmann constant, and γ is the coupling constant, B max is the temperature-independent B value of the dominant small polaron hopping line, wherein the quantitative proportions are set such that a value B is max3400 to 4000 K or / and a lower limit temperature T 0 ≤ 600 Kelvin is achieved.NTC composition comprising a main component having the empirical formula Mn 3-x-y-z Co x Al y Cu z O 4, where 0.8≤x≤1.4, 0.6<y≤1, 1 and 0.15≤z≤0.35.NTC composition comprising a main component having the empirical formula Mn 3-x-y-z Co x Al y Cu z O 4, where 0.8≤x≤1.4, 0.5≤y≤1, 1 and 0.22≤z≤0.3.The NTC composition according to claim 3 or 4, wherein z ≤ 0.28.The NTC composition of any one of claims 3 to 5, wherein y:z > 2.4.The NTC composition according to any one of claims 3 to 6, wherein 0.90 ≤ x ≤ 1.30, or preferably 0.95 < x ≤ 1.25.The NTC composition according to any one of claims 3 to 7, wherein 0.55 ≤ y ≤ 0.95 or preferably 0.60 ≤ y ≤ 0.95.The NTC composition according to any one of claims 1 to 8, wherein the main component constitutes at least 90% of the phases of the NTC composition.A thermistor comprising the NTC composition according to any one of claims 1 to 9.A multilayer thermistor comprising a ceramic layer comprising the NTC composition according to any one of claims 1 to 9.The multilayer thermistor according to claim 11, wherein it has a volume of 0.075 to 10 mm 3.The multilayer thermistor according to claim 11 or 12, wherein the ceramic layer has a thickness of 10 to 100 μm, and the thermistor is composed of one or more layers.Multilayer thermistor according to one of claims 11 to 13, which has a rated resistance at 25°C of 1 to 20 kΩ.A multilayer thin film thermistor comprising a ceramic layer comprising the NTC composition according to any one of claims 1 to 9.A process for producing a multilayer thermistor, wherein starting materials for a ceramic composition having the empirical formula Mn 3-x-y-z Co x Al y Cu z O 4 are provided, wherein the starting materials are weighed in such a way that 0.8 ≤ x ≤ 1.4, 0.5 ≤ y ≤ 1.1 and 0.22 ≤ z ≤ 0.30 are obtained for the ceramic composition, the starting materials are ground, the powder obtained after grinding the starting materials is calcined, the resulting calcite is ground, green films are produced with the ground calcite, the green films are stacked together with starting materials for internal electrodes, green thermistor components are cut from the stack, the green thermistor components are debindered, the debindered green thermistor devices are sintered into sintered thermistor devices at 1000-1200°C and external electrodes are applied to the sintered thermistor devices.The method according to claim 16, wherein the starting material for internal electrodes is a metal paste and is printed on some green sheets before stacking.The method according to claim 16 or 17, wherein the sintering is performed at 1050°C to 1150°C.A method for determining material properties of an NTC spinel ceramic using the formula B(T)=B max × tanhyp(3T / T 0), wherein B(T) is the B value of the ceramic, B max is the temperature-independent B value of the dominant small polaron hopping line, T is the temperature, T 0 is the lower limit temperature of the dominant small polaron hopping line.A method for optimizing material properties of NTC spinel ceramics using the formula B(T)=B max × tanhyp(3T / T 0), wherein B(T) is the B value of the ceramic, B max is the temperature-independent B value of the dominant small polaron hopping line, T is the temperature, T 0 is the lower limit temperature of the dominant small polaron hopping line.The method according to claim 19 or 20, wherein T 0 is defined as being reached when B (T) = tanhyp (3)·B max= 0.995 ·B max holds.The method according to any one of claims 19 to 21, wherein an adaptation to a curve of the B value of a ceramic material composition is applied with the aid of the formula B(T) = B max × tanhyp(3 T / T 0).A method for optimizing material properties of NTC spinel ceramics, wherein an adaptation is applied to a curve of the B value of a starting material composition with the aid of the formula B(T)=B max × tanhyp(3 T / T 0) wherein B(T) is the B value of the ceramic, B max is the temperature-independent B value of the dominant small polaron hopping line, T is the temperature, T 0 is the lower limit temperature of the dominant small polaron hopping line, Together with the formula T 0= ( h×v 0) / (2 k arcsineh γ), wherein h is Planck constant, v 0 is the characteristic oscillation frequency of the crystal lattice, k is the Boltzmann constant, and γ is the coupling constant, a determination of starting material properties of the starting material composition is obtained, and starting from these starting material properties additions are selected which specifically influence the B value at a specific temperature, the T 0- value and / or the specific resistance.Method according to claim 23, wherein the method is carried out as a multistage method, wherein the ceramic composition already optimized by additions is again subjected to the described process sequence at least once as starting material composition.Automated determination of material properties of several data sets of NTC spinel ceramics using the formula B(T)=B max × tanhyp(3T / T 0), wherein B(T) is the B value of the ceramic, B max is the temperature-independent B value of the dominant small polaron hopping line, T is the temperature, T 0 is the lower limit temperature of the dominant small polaron hopping line.

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