EP4686902A1

EP4686902A1 - Method for determining temperature distribution data and providing position arrangement data in a furnace

Info

Publication number: EP4686902A1
Application number: EP24192564.3A
Authority: EP
Inventors: Robert Matthew LEE; Christoph ARIAANS; Daniel JALALPOOR; Philipp THOMI; Dordije Nenad Tripkovic
Original assignee: BASF SE
Current assignee: BASF SE
Priority date: 2024-08-02
Filing date: 2024-08-02
Publication date: 2026-02-04

Abstract

It is disclosed a method for determining temperature distribution data (20) associated with a temperature distribution inside an oven (12, 13) having spatially distributed sample positions (18), having the steps of: providing calibration temperature values (T^calib ) at the sample positions (18) for predetermined setpoint temperature values (T^sp ) of the oven (12, 13); providing a selected setpoint temperature value (T^sp ) of the oven (12, 13) from a continuously adjustable setpoint temperature value (T^sp ); and determining the temperature distribution data (20) in the oven (12, 13) based on the calibration temperature values (T^calib ) and the selected setpoint temperature value (T^sp ), wherein the temperature distribution data (20) includes for the selected setpoint temperature value (T^sp ) a determined temperature value (T^exp ) at each sample position (18).

Description

TECHNICAL FIELD

The invention relates to a method for determining temperature distribution data and providing position arrangement data, arranging one or more samples in one or more ovens, and determining one or more samples out of the heat-treated samples. Furthermore, the invention also relates to a cathode, an oven arrangement, and the use of one or more ovens for heat treatment of two or more samples.

TECHNICAL BACKGROUND

Heat treatment of materials using high-temperature ovens is state of the art both in laboratory operations and in production processes. WO 2023/198804 A1 discloses such an oven, which can be used for heat treatment, in particular the calcination, of materials.
Calcining is a thermal treatment process characterized by the controlled application of heat to a material, typically in the absence or limited presence of air, leading to the removal of volatile components, phase transformations, or the activation of desired chemical reactions. This technique is widely utilized in various industries, including chemistry, to enhance material properties and achieve specific chemical outcomes.

SUMMARY

In an aspect, this disclosure relates to a method for determining temperature distribution data associated with a temperature distribution inside an oven having inside spatially distributed sample positions, the method comprising: providing calibration temperature values at the sample positions for predetermined setpoint temperature values of the oven; providing a selected setpoint temperature value of the oven from a continuously adjustable setpoint temperature value; determining the temperature distribution data based on the calibration temperature values and/or the selected setpoint temperature value, wherein for the selected setpoint temperature value, the temperature distribution data includes a determined temperature value at each sample position.
This approach is particularly advantageous, as calculating local temperature value at different position allows predicting which temperature samples may experience, and thus, providing foundation for an optimization approach as described herein. Additionally or alternatively, it is beneficial, as it provides basis for monitoring and/or checking that a given oven is behaving the same as when calibration data were gathered.
Predetermined setpoints are intended to refer to predetermined setpoints from, for instance, a calibration and/or training data, which may be collected in advance of a synthesis to be performed. Selected setpoint temperature is intended to refer to a temperature chosen for a material synthesis in question.
In another aspect, the disclosure relates to a method for providing position arrangement data associated with arranging one or more samples in one or more ovens at spatially distributed sample positions, the comprising: providing a target temperature value for each sample; determining temperature distribution data for a given oven according to aforementioned method; providing position arrangement data associated with a sample of the one or more samples, wherein the sample is to be arranged at a sample position dependent on the target temperature value of sample and/or the determined temperature distribution data.
In another aspect, the disclosure relates to a method for providing position arrangement data associated with arranging one or more samples in one or more ovens at spatially distributed sample positions, the comprising: providing a target temperature value for each sample; providing a selected setpoint temperature of a given oven; determining temperature distribution data for a given oven according to aforementioned method; providing position arrangement data associated with a sample of the one or more samples, wherein the sample is to be arranged at a sample position dependent on the target temperature value of sample and/or the determined temperature distribution data.
This approach is particularly beneficial, as it allows achieving of pre-determined experimental conditions rather than relying on a fixed oven setpoint with the expectation that each sample experiences a temperature close to the desired one. This eliminates the need for trial-and-error methods, resulting in increased efficiency and more informative experimental studies. Furthermore, it provides greater control over the experimental conditions, ensuring that each sample experiences the specific temperature required by the experimental plan, which is advantageous, as it eliminates the uncertainty and variability that can occur when relying solely on a fixed oven setpoint. Ultimately this makes experimental studies more efficient and informative.
In another aspect, the disclosure relates to a method for arranging one or more samples in one or more ovens at assigned sample positions based on the position arrangement data generated according to the aforementioned method. This is advantageous, as it allows for the maximization of each oven's sample capacity, which may be achieved by utilizing the pre-determined experimental conditions, which optimizes the use of available resources while maintaining the accuracy and reliability of results.
In another aspect, the disclosure relates to a method for determining one or more samples out of heat-treated samples, the method comprising: Arranging samples in one or more ovens according to the method for arranging one or more samples in one or more ovens as recited herein; performing a firing run by a given oven of the one or more ovens; and determining one or more samples out of the heat-treated samples based on at least one performance parameter. This approach is advantageous, as it allows optimization of laboratory resources by minimizing number of materials that need to be synthesized, which reduces need for extensive synthesis processes, saving time, energy and materials.
In another aspect, the disclosure relates to a cathode comprising at least partially a material of the determined heat-treated sample obtained by the method for determining one or more samples out of the heat-treated samples as recited herein. This approach is beneficial, as, for instance, it minimizes the number of electrochemical cells that need to be built and tested.
In another aspect, the disclosure relates to a computer program for performing at least one of the aforementioned methods, such as method for determining temperature distribution data and method for providing position arrangement data. This is particular advantageous, as automation of the above-mentioned makes them feasible for a modern laboratory workflow and enables their scalability, in particular, by permitting applicability to experiments at large scale such experiments comprising at least hundreds, preferably at least thousands of samples.
In another aspect, the disclosure relates to an oven arrangement having an oven and a computing device configured to execute at least one of the aforementioned methods, such as method for determining temperature distribution data and method for providing position arrangement data. This is particular advantageous, as automation of the above-mentioned makes them feasible for a modern laboratory workflow and enables their scalability, in particular, by permitting applicability to experiments at large scale such experiments comprising at least hundreds, preferably at least thousands of samples.
In another aspect, the disclosure relates to a use of one oven for heat treatment of two or more samples arranged at spatially distributed sample positions, wherein at least two of the samples demand heat treatment temperatures differing from each other. For instance, use of one oven for heat treatment, in particular calcining, of two or more samples arranged at spatially distributed sample positions, wherein at least two of the samples demand heat treatment, in particular calcination, temperatures differing from each other. This approach is particularly advantageous, as it allows to dispense with multiple firing runs to perform such experiments. Consequently, this approach is beneficial, as it allows treating multiple samples using only a single firing run, thus requiring less energy and time.
Any disclosure, embodiments and examples described herein relate to the method for determining temperature distribution data, the method for providing position arrangement data, a method for arranging one or more samples in one or more ovens, a method for determining one or more samples out of the heat-treated samples, a cathode, the computer program, the oven arrangement and the use of one oven lined out above and below. Advantageously, the benefits provided by any of the embodiments and examples equally apply to all other embodiments and examples.

EMBODIMENTS

In the following, terminology as used herein and/or the technical field of the present disclosure will be outlined by ways of definitions and/or examples. Where examples are given, it is to be understood that the present disclosure is not limited to said examples.
In accordance with the invention, it has been recognized that precise temperature control throughout the heat treatment process of the samples is critical as it affects the material quality of the final product. Thus, the temperature actually acting on a sample during a firing run has to match the demanded target temperature as accurately as possible. Achieving this is particularly difficult, because for a given oven setpoint temperature there are at least partially temperature heterogeneities inside the oven. For example, the oven has a lower temperature in the area next to the oven door than in the center of the oven.
It is therefore an object of the present invention to provide a method which improves the material quality of the heat-treated samples in the oven.
As mentioned above, in an aspect of the present invention, the disclosure relates to a method for determining temperature distribution data associated with a temperature distribution inside an oven having inside spatially distributed sample positions, the method comprising: providing calibration temperature values at the sample positions for predetermined setpoint temperature values of the oven; providing a selected setpoint temperature value of the oven from a continuously adjustable setpoint temperature value; determining the temperature distribution data based on the calibration temperature values and/or the selected setpoint temperature value, wherein for the selected setpoint temperature value, the temperature distribution data includes a determined temperature value at each sample position. Due to the fact that for several oven setpoint temperatures calibration temperatures at spatially distributed sample positions are provided based on which temperature distribution data having determined temperatures at the sample positions can be determined, for a sample to be heat treated an oven setpoint temperature and a sample position in the oven can be chosen such that the temperature acting on the sample is as close as possible to the demanded target temperature of the sample. This prevents an unwanted variation in the material quality of heat-treated samples.
In accordance with the invention, it has further been recognized that the at least partially prevailing temperature heterogeneities inside the oven can be utilized to the effect that several samples demanding for treatment temperatures at least partially different from each other, can be heat treated in a single oven.
As mentioned above, in another aspect of the present invention, the disclosure relates to a method for providing position arrangement data associated with arranging one or more samples in one or more ovens at spatially distributed sample positions, the comprising: providing a target temperature value for each sample; determining temperature distribution data for a given oven according to aforementioned method; providing position arrangement data associated with a sample of the one or more samples, wherein the sample is to be arranged at a sample position dependent on the target temperature value of sample and/or the determined temperature distribution data. Due to the fact that a method for providing position arrangement data is provided, wherein the position arrangement data is determined based on the demanded target temperatures of the samples and the determined temperature distribution data, for samples to be heat treated at least an oven setpoint temperature and sample positions in the oven are suggested such that the temperature acting on the respective sample is as close as possible to the demanded target temperature of this sample. Heat treatment of several samples in one oven run increases the sample throughput and therefore saves time.
These and other objects, which become apparent upon reading the following description, are solved by the subject matters of the independent claims. The dependent claims refer to embodiments of the invention.
The temperature distribution data may be associated with a collection of data regarding the temperature distribution inside an oven. The temperature distribution may be indicative of the variation of temperature inside the oven over a specific area of the oven interior. The temperature distribution may refer to a plurality of determined temperatures at sample positions spatially distributed over the specific area of the oven interior. The specific area may be the entire oven interior. The temperature distribution may relate to the setpoint temperature and the calibration temperature values. The temperature distribution may be an output of an interpolating function, which is generated by fitting a temperature distribution model to the calibration temperature values for a given setpoint temperature of the oven. The temperature distribution may be an output of an interpolating function, which is generated by fitting a temperature distribution model to the calibration temperature values for multiple setpoints temperature of the oven.
The oven may be a firing oven, in particular a calcination oven. The oven may have sample positions and a heating source, which are arranged immovable to each other during a firing run. Alternatively, the oven may have means for transporting the samples in relation to the heating source during a firing run, such as a conveyor belt. The heating source may be heating elements or a hot air blower. Additionally, the oven may have cooling means at the front door. In particular based on the interaction of the heating means and the cooling means the oven has inside a temperature distribution.
The sample to be heat treated may be a so-called P-CAM (precursor cathode active material). The P-CAM may be a composition of educts for producing cathode materials (CAM) of batteries as end products. Preferably the respective educt is in form of a powder. The respective composition of educts may include at least one of the following: a Nickel Cobalt Manganese hydroxide (NCM) precursor, a lithium salt and a at least one dopant. The lithium salt may be lithium hydroxide (LiOH). The dopant may be provided in a quantity of 0 to 5 mol%, such as 0 to 3 mol%, such as 2.5 mol%. The respective dopant may be zirconium (Zr), titanium (Ti), magnesium (Mg) and/or aluminum (Al). The educts are mixed in order to obtain the powdery composition of educts and then the composition is filled into a crucible. The crucibles may be arranged on a tablet that is inserted into the oven interior. The crucibles may be chessboard-like arranged on the tablet. During calcining the composition of educts gas, in particular oxygen, may be fed to the oven interior.
The calibration temperature values may be associated with temperature values that are determined based on measured temperatures inside the oven at spatially distributed positions during a calibration run of the oven for a given setpoint temperature value of the oven. For measuring the temperatures there may be provided fewer temperature sensors inside the oven than sample positions inside the oven. The determination of the calibration temperature values at the sample positions may be performed by interpolating the measured temperatures. The calibration temperature is dependent on the sample position and the temperature at this sample position that is dependent on at least one of the measured temperatures.
The setpoint temperature value of the oven may be associated with the temperature value to which the entire oven is set. Despite that the set point temperature is set, inside the oven a temperature distribution may be prevailing having at least one determined temperature that differs from the setpoint temperature. The set point temperature may depend on the use of the oven. The use of the oven may be for calcining cathode materials of batteries. For said use the set point temperature may be in the range of about 700 to 900 degrees Celsius.
The determined temperature may be associated with the temperature at a respective sample position for a respective setpoint temperature of the oven. The determined temperature may be related to the setpoint temperature and the calibration temperature values. The determined temperature for a setpoint temperature may be interpolated based on the calibration temperature values.
Determining one or more samples out of the heat-treated samples is associated with choosing that respective sample that has for an intended use a predetermined quality indicated by reaching a threshold by the at least one performance parameter. In particular a heat-treated sample is chosen that is suitable for usage as a cathode material in a battery.
In an embodiment, the calibration temperature values are determined based on temperature measurements in the oven during calibration runs of the oven for given setpoint temperature values of the oven. Before performing any of the claimed methods calibration runs of the oven may be performed. In these calibration runs the oven setpoint temperature may be varied in several temperature steps across a relevant range. The relevant range may be depending on the intend use of the oven. At present the intended use may be calcining cathode materials of batteries. For this intended use the relevant range may be about 700 to 900 degrees Celsius. During a calibration run the temperatures may be measured inside the oven by temperature sensors at spatially distributed positions. The measured temperatures may be used to calculate, in particular interpolate, the calibration temperatures at the sample positions.
In an embodiment, the temperature distribution data depends additionally on the sample position in the oven. Since the temperature distribution data includes for each setpoint temperature a determined temperature at each sample position, the determined temperature also depends on the following temperatures: the respective setpoint temperature, the calibration temperature and in particular the sample position.
In an embodiment, for providing the selected setpoint temperature this temperature for each oven is determined using the calibration temperatures and in particular the target temperatures and/or at least a constant. Preferably, for determining the setpoint temperature an interval having an upper bound and a lower bound is determined, wherein the setpoint temperature is arranged in the interval, and wherein the bounds are each dependent on at least one of following: the target temperatures, the calibration temperatures, at least a constant and the maximum reachable temperature of the given oven. Preferably, the bounds are dependent each on the target temperatures, the calibration temperatures and in particular the constant. In detail, the upper bound is either a highest calibration temperature or a sum of a highest target temperature and a constant; whichever is lower, and the lower bound is a lowest calibration temperature or a sum of a lowest target temperature and a further constant; whichever is lower.
In an embodiment, for determining the respective setpoint temperature within the interval said setpoint temperature is varied in the interval in order to minimize a loss function. For varying the setpoint temperature the Nelder-Mead method known in the state of the art may be used. The loss function may be provided depending on the respective target temperature and the respective temperature distribution data. For calculating this loss function the determined temperature vector is subtracted from the target temperature vector, wherein this difference is squared and summed up over all samples. Preferably, for varying the at least one setpoint temperature an initial value of this setpoint temperature is uniformly distributed within the interval. In more simple words, if there are multiple setpoints to be determined, these may be spaced on a uniform grid within a given interval. If only a single setpoint is to be determined, this may be put at the center point.
Moreover, for determining the setpoint temperature value within the interval, the setpoint temperature value may be varied in the interval to minimize a loss function depending on the target temperature value and/or the temperature distribution data. Additionally or alternatively, for varying the at least one setpoint temperature an initial value of this setpoint temperature is uniformly distributed within the interval. Furthermore, for minimizing the loss function each of the samples may be consecutively assigned to a given sample position in the given oven, at which the target temperature value is closest to the determined temperature value of the temperature distribution data.
In an embodiment, for minimizing the loss function the respective samples one after the other are assigned to that respective sample position in the respective oven, at which the target temperature is closest to the determined temperature of the temperature distribution data and at which no sample has already been assigned to. In the end that setpoint temperature is chosen that minimizes the loss function at least in a local minimum.
In an embodiment, for providing the position arrangement data the positioning of the samples is varied in order to minimize a further loss function, and wherein that position arrangement is chosen that minimizes the further loss function. For varying the positioning of the samples, the simplex algorithm known from the state of the art may be used.
In an embodiment, for determining the respective setpoint temperature and for providing the position arrangement data the setpoint temperature is varied within the interval and at the same time the positioning of the samples is varied in order to minimize a further loss function, and wherein that at least one setpoint temperature in combination with that position arrangement is chosen that minimizes this further loss function. For varying the setpoint temperatures at the same time as the positioning of the samples a branch-and-bound algorithm known in the state of the art may be deployed. Varying the setpoint temperatures at the same time as the positioning of the samples has the advantages that the computing time is reduced.
In an embodiment, at most one sample is assigned to a respective sample position, and wherein a total number of sample positions is greater than or equal to a total number of the samples.
In a further embodiment, any of the method as recited herein is a computer-implemented invention.

BRIEF DESCRIPTION OF THE DRAWINGS

In the following, the present disclosure is further described with reference to the enclosed figures. The same reference numbers in the drawings and this disclosure are intended to refer to the same or like elements, components, and/or parts.

Fig. 1: schematically illustrates an oven arrangement according to the invention;
Fig. 2: schematically illustrates sample positions inside an oven;
Fig. 3: shows a flowchart illustrating a method for determining temperature distribution data;
Fig. 4: schematically illustrates a temperature distribution inside an oven during a firing run;
Fig. 5: shows a flowchart illustrating a method for providing position arrangement data;
Fig. 6: schematically shows an assignment of samples to sample positions;
Fig. 7: shows a method for arranging one or more samples in one or more ovens; and
Fig. 8: shows a method for determining a sample out of heat-treated samples.

DETAILED DESCRIPTION

The following embodiments are mere examples for implementing the methods, the program, the oven arrangement, and the use disclosed herein and shall not be considered limiting.
Fig. 1 shows an oven arrangement 10 according to the invention, which comprises two firing, in particular calcination, ovens 12, 13 and a computing unit 14 in form of a cloud server. Ovens 12, 13 or a given oven 12, 13 may be a heat treatment device according to the disclosure of WO 2023/198804 A1 . The computing unit 14 is communicatively connected to two personal computers 16 each being arranged with an end user. On the computing unit 14 a software back end is implemented, wherein the assigned software front end is accessible for an end user via each personal computer 16. The methods according to the invention are executed on the computing unit 14. Via a personal computer 16 an end user has access separated from each other to the computing unit 14 as well as to a control unit of a given oven 12,13.
Each oven has inside several positions 18 for crucibles (not shown) which contain material to be heat treated, in particular, material to be calcinated. The crucibles are arranged inside the oven on a tablet such that the sample positions 18 are spatially distributed and chessboard-like arranged.
Fig. 2 conceptually depicts sample position references 19 of a given oven 12, 13. On the right, the expected temperature for each position reference from front-to-back and left-to-right is shown.
The sample material to be heat treated may be a composition of educt materials for the production of battery cathodes by calcining.
Fig. 3 schematically depicts a method 100 for determining temperature distribution data 20 according to embodiment of the present invention.
At first calibration runs of the respective oven 12, 13 re performed, wherein this oven 12, 13 is set to setpoint temperature values T^sp across a relevant range. E. g. the relevant range for battery materials is 700-900°C and the setpoint temperature values T^sp are chosen to be equidistantly arranged in this range; for example, in steps of 10°C or 20°C or 30°C. For a respective oven setpoint temperature value T^sp calibration temperature values T^calib at the sample positions are determined. The setpoint temperature values T^sp are stored together with calibration temperature values T^calib. In a first step S1 these setpoint temperature values T^sp together with the calibration temperatures T^calib are provided.
In a next step S2 the user chooses for each oven 12, 13 an oven setpoint temperature T^sp from continuously adjustable oven setpoint temperatures T^sp .
After that in a next step S3 based on the calibration temperatures T^calib and the selected oven setpoint temperature T^sp for each oven 12, 13 temperature distribution data 20 (see Fig. 4) is determined, in particular interpolated, that includes for each sample position 18 a determined temperature value T^exp. The temperature distribution data 20 is calculated by the function $T_{ij}^{\exp} = f_{interp} (T_{i}^{sp}, T_{i}^{calib}, a_{j}, b_{j}) \forall i \in [N_{ovens}], \forall j \in$ [N_pos ], wherein i is the respective firing run, in particular oven, j is the respective sample position, $T_{ij}^{\exp}$ is a vector having the determined temperatures, $T_{i}^{sp}$ is a vector having the setpoint temperatures and $T_{i}^{calib}$ is a vector having the calibration temperatures. Since the sample positions inside the oven are arranged chessboard-like in a cartesian coordinate system a_j is the sample position in the direction of the x-axis of the coordinate system and b_j is the sample position in the direction of the y-axis.
In a next step S4 the temperature distribution data 20 having determined temperatures T^exp for each sample position 18 may be shown to the end user. The end user may use this temperature distribution data 20 to arrange the respective sample at the respective sample position 18 in the respective oven 12, 13 such that the respective determined temperature T^exp of the temperature distribution data 20 is as close as possible to the target temperature T^targ of the respective sample.
Fig. 5 depicts a method a method 200 for providing position arrangement data according to embodiments of the present invention.
In a first step S10 a target temperature T^targ for each sample is provided. The target temperature T^targ is the desired temperature to which the sample should be exposed during a firing run of the oven. The target temperatures T^targ may be given by the user as a range of target temperatures T^targ and the target temperature T^targ for each sample may be determined dependent on this temperature range.
Also, in the first step S10 the user may together with the target temperatures T^targ provide other inputs. E.g., the user may specify the educt mixture to be heat treated by giving concrete values or ranges for at least some of the components of the mixture. In dependence on these inputs the number of samples to be heat treated and/or the number of differing educt mixtures and/or the number of component variations in a respective range may be determined. It is also possible that the user chooses the number of samples to be heat treated and/or the number of differing educt mixtures and/or the number of component variations in the respective range. Furthermore, the user may select how many oven runs to be performed. For example, two oven runs may be performed with one oven one after another or with two ovens at the same time.
In next steps S11 to S13 temperature distribution data 20 for each oven is determined according to steps S1 to S3, wherein in step S12 for providing the selected setpoint temperature T^sp . This temperature T^sp for the respective oven 12, 13 is determined dependent on the calibration temperatures T^calib and the target temperatures T^targ as described in the following.
For determining the setpoint temperatures T^sp in a step S12-1 an upper bound and a lower bound for the setpoint temperatures T^sp are determined. The upper bound is the lowest value of a highest calibration temperature T^calib as well as a sum of a highest target temperature T^targ and a constant S ₁, which is expressed by formula: min(max(T^calib ) , max(T^targ + S ₁)). The lower bound is the highest value of a lowest calibration temperature T^calib as well as a sum of a lowest target temperature T^targ and a further constant S ₂, which is expressed by formula: max (min(T^calib ) , min(T^targ + S ₂)), wherein T^calib is a vector having the calibration temperatures, T^targ is a vector having the target temperatures and S ₁, S ₂ are heuristically determined values and may be each 10 to 50% of the largest temperature difference within a respective provided temperature distribution 20. In Fig. 4 the largest temperature difference within the temperature distribution 20 is 40°C (=750°C-710°C) and accordingly S ₁, S ₂ may be 4 to 20°C each.
In a next step S12-2 initial values for the setpoint temperatures T^sp are chosen to be uniformly distributed within the interval in dependence of the number of firing runs to be performed. E. g.: If the interval is 700 to 790°C the initial setpoint temperature value T^sp for the firing run of the first oven 12 may be 730°C and the initial setpoint temperature value T^sp for the firing run of the second oven 13 may be 760°C.
In a next step S13 to this initial setpoint values T^sp the function $T_{ij}^{\exp} = f_{interp} (T_{i}^{sp}, T_{i}^{calib}, a_{j}, b_{j})$ is applied in order to obtain the temperature distribution data 20 having the determined temperatures $T_{ij}^{\exp}$ .
In a next step S14 the samples are assigned one after the other to that sample position in the oven 12, 13, for which the determined temperature T^exp of the respective sample position is closest to the respective target temperature T^targ of the sample and to which no sample has been assigned yet.
In a next step S15 the determined temperatures $T_{ij}^{\exp}$ and the target temperatures T^targ are used to determine a loss function L ₁. For calculating the loss function L ₁ the determined temperatures $T_{ij}^{\exp}$ are subtracted from the target temperatures T^targ and this difference is squared and added up for all samples. This loss function L ₁ is represented by the formula $L_{1} = \sum_{k = 1}^{N_{samples}} {(T_{k}^{targ} - T_{k}^{\exp})}^{2}$ , wherein T^targ is a vector having the target temperatures and $T_{k}^{\exp}$ is a vector having the determined temperatures.
To minimize the loss function the steps S13 to S15 are repeated several times with a differing initial value of the setpoint temperature T^sp within the interval, wherein in the end that setpoint temperature T^sp is chosen, for which the loss function gives out at least a local minimum. For varying the setpoint temperature T^sp the Nelder-Mead method may be applied.
In a next step S16 for providing the position arrangement data the positioning of the samples is varied in order to minimize a further loss function L ₂, which is expressed by formula $L_{2} = \begin{matrix} \min \\ x \end{matrix} \sum_{i = 1}^{N_{ovens}} \sum_{j = 1}^{N_{pos}} \sum_{k = 1}^{N_{samples}} [x_{ijk} {(T_{k}^{targ} - T_{ij}^{\exp})}^{2}]$ $\begin{matrix} T_{ij}^{\exp} = f_{interp} (T_{i}^{sp}, T_{i}^{calib}, a_{j}, b_{j}) & \forall i \in [N_{ovens}], \forall j \in [N_{pos}] \end{matrix}$ $\begin{matrix} \sum_{k = 1}^{N_{samples}} x_{ijk} \leq 1 & \forall i \in [N_{ovens}], \forall j \in [N_{pos}] \end{matrix}$ $\begin{matrix} \sum_{i = 1}^{N_{ovens}} \sum_{j = 1}^{N_{pos}} x_{ijk} = 1 & \forall k \in [N_{samples}] \end{matrix}$ $x_{ijk} \in \{0,1\} \forall i \in [N_{ovens}], \forall j \in [N_{pos}], \forall k \in [N_{samples}],$
Wherein x_ijk is a variable, which is 1 if the position j in firing run i is occupied by a sample (for instance, a material to be calcinated) and otherwise 0. For varying the positioning of the samples, the simplex algorithm may be applied.
This approach allows improvements of planned calcination temperatures of each material subject to practical constraints, such as allowing each position of the oven to be occupied by only a single crucible.
The function $f_{interp} (T_{i}^{sp}, T_{i}^{calib}, a_{j}, b_{j})$ give the estimate of the temperature experience by a sample at position j in an oven set to run at a temperature $T_{i}^{sp}, T_{i}^{calib}$ . The function /may, for instance, be generated by fitting an appropriate model to calibration data in which a range of temperatures is scanned.
Alternatively, for determining the respective setpoint temperature T^sp and for providing the position arrangement data the setpoint temperature T^sp is varied within the interval and at the same time the positioning of the samples is varied in order to minimize a further loss function, and wherein that at least one setpoint temperature T^sp in combination with that position arrangement is chosen that minimizes this further loss function. This further loss function may be the loss function L ₂. For varying the setpoint temperatures T^sp at the same time as the positioning of the samples a branch-and-bound algorithm known in the state of the art may be deployed.
In a next step S17 the assignment 26, 28 of samples to the sample positions 18 and the ovens 12, 13 (see Fig. 6) are shown to the end user. In this assignment the sample ID 22, the determined temperature T^exp 30 and the temperature difference 24 between the determined temperature T^exp and the target temperature T^targ is visualized to the end user.
Fig. 7 depicts a method 300 for arranging one or more samples in one or more ovens.
In steps S20 to S27 the method for providing position arrangement data is conducted according to steps S10 to S17.
Thereafter in a step S28 according to the assignment data the end user arranges the samples in the respective oven 12, 13. It is also conceivable that this arrangement is done by an arm of a robot.
Fig. 8 depicts a method 400 for determining a sample out of heat-treated samples.
In steps S30 to S38 the method for arranging samples in one or more ovens is performed according to steps S20 to S28.Thereafter the user parameterizes the ovens, in particular sets the setpoint temperature, via a personal computer 16 and starts the firing runs.
In a next step 39 during the firing run the samples may be lithiated, which means that lithium goes from LiOH into the crystal structure, and/or the hydroxide groups may be removed from the sample material. The structure itself of the material can also change (different crystal phases can be achieved for example).
After the firing run in a next step 40 posttreatment may be done, which involves mechanically breaking up the heat-treated sample material (CAM) so it can be processed more easily, and/or coat the heat-treated sample material to improve the properties of the particle surfaces. Then in a next step 41 the heat-treated sample material is mixed with a solvent, carbon and binder to make a slurry, which in a next step 42 can be applied to an aluminum part in order to obtain a cathode. This cathode in a next step 43 is combined with an inert porous separator, a liquid electrolyte, and another electrode (the anode = graphite or metallic lithium) in a sandwich-like structure as an electrochemical cell.
In a next step 44 this cell is tested in a device to measure at least one performance parameter of the cell, for example the capacity (how much charge does it hold and can be transferred), the energy density and/or the lifetime. In a next step 45 based on the respective performance parameter a decision is made about which materials are worth pursuing in research and are potentially sent to customers.
The present disclosure has been described in conjunction with preferred embodiments and examples as well. However, other variations can be understood and effected by those persons skilled in the art and practicing the claimed invention, from the studies of the drawings, this disclosure, and the claims.
As used herein "determining" also includes "initiating or causing to determine" and "providing" also includes "initiating or causing to determine, generate, select, send and/or receive". "initiating or causing to perform an action" includes any processing signal that triggers a computing node or device to perform the respective action.
In the claims as well as in the description the word "comprising" or "including" or similar wording does not exclude other elements or steps and shall not be construed limiting to the elements or steps lined out. The indefinite article "a" or "an" does not exclude a plurality. A single element or other unit may fulfill the functions of several entities or items recited in the claims. The mere fact that certain measures are recited in the mutual different dependent claims does not indicate that a combination of these measures cannot be used in an advantageous implementation or further elements may be included.
Providing in the scope of this disclosure may include any interface configured to provide data. This may include an application programming interface, a human-machine interface such as a display and/or a software module interface. Providing may include communication of data or submission of data to the interface, in particular display to a user or use of the data by the receiving node, entity or interface.
Various units, circuits, entities, nodes or other computing components may be described as "configured to" perform a task or tasks. Configured to shall recite structure meaning "having circuitry that" performs the task or tasks on operation. The units, circuits, entities, nodes or other computing components can be configured to perform the task even when the unit/circuit/component is not operating. The units, circuits, entities, nodes or other computing components that form the structure corresponding to "configured to" may include hardware circuits and/or memory storing program instructions executable to implement the operation. The units, circuits, entities, nodes or other computing components may be described as performing a task or tasks, for convenience in the description. Such descriptions shall be interpreted as including the phrase "configured to." Any recitation of "configured to" is expressly intended not to invoke 35 U.S.C. § 112(f) interpretation.
In general, the methods, apparatuses, systems, computer elements, nodes or other computing components described herein may include memory, software components and hardware components. The memory can include volatile memory such as static or dynamic random-access memory and/or nonvolatile memory such as optical or magnetic disk storage, flash memory, programmable read-only memories, etc. The hardware components may include any combination of combinatorial logic circuitry, clocked storage devices such as flops, registers, latches, etc., finite state machines, memory such as static random-access memory or embedded dynamic random-access memory, custom designed circuitry, programmable logic arrays, etc.
Any disclosure and embodiments described herein relate to the methods, the systems, apparatuses, devices, chemicals, materials, computer program elements lined out above and vice versa. Advantageously, the benefits provided by any of the embodiments and examples equally apply to all other embodiments and examples and vice versa.
All terms and definitions used herein are understood broadly and have their general meaning.

Claims

A method for determining temperature distribution data (20) associated with a temperature distribution inside an oven (12, 13) having spatially distributed sample positions (18), the method comprising:
- providing calibration temperature values (T^calib ) at the sample positions (18) for predetermined setpoint temperature values (T^sp ) of the oven (12, 13);

- providing a selected setpoint temperature value (T^sp ) of the oven (12, 13) from a continuously adjustable setpoint temperature value (T^sp ); and

- determining the temperature distribution data (20) based on the calibration temperature values (T^calib ) and/or the selected setpoint temperature value (T^sp ), wherein for the selected setpoint temperature value (T^sp ), the temperature distribution data (20) includes a determined temperature value (T^exp ) at each sample position (18).
The method according to claim 1, wherein the calibration temperature values (T^calib ) are determined based on temperature measurements in the oven (12, 13) during calibration runs of the oven (12, 13) for given setpoint temperature values (T^sp ) of the oven (12, 13).
The method according to claim 1 or 2, wherein the temperature distribution data (20) depends additionally on the sample position (18) in the oven (12, 13).
A method for providing position arrangement data associated with arranging one or more samples in one or more ovens (12, 13) at spatially distributed sample positions (18), the method comprising:
- providing a target temperature value (T^targ ) for each sample;

- providing a selected setpoint temperature (T^sp ) of a given oven (12, 13);

- determining temperature distribution data (20) for a given oven (12,13) according to any of the preceding claims;

- providing position arrangement data associated with a sample of the one or more samples, wherein the sample is to be arranged at a sample position (18) dependent on the target temperature value (T^targ ) of the sample and/or the determined temperature distribution data (20).
The method according to the preceding claim, wherein for providing the selected setpoint temperature value (T^sp ), the selected setpoint temperature value (T^sp ) for the given oven (12, 13) is determined using the calibration temperature values (T^calib ) and/or the target temperature value (T^targ ).
The method according to the preceding claim, wherein for determining the selected setpoint temperature value (T^sp ), an interval having an upper bound and a lower bound is determined, wherein the setpoint temperature value (T^sp ) is arranged in the interval, and wherein the upper and lower bounds are each dependent on at least one of: the target temperature value (T^targ ), the calibration temperature value (T^calib ), the sample position (18) and a maximum reachable temperature of the given oven (12, 13).
The method according to the preceding claim, wherein for determining the setpoint temperature value (T^sp ) within the interval, the setpoint temperature value (T^sp ) is varied in the interval to minimize a loss function (L ₁) depending on the target temperature value (T^targ ) and/or the temperature distribution data (20).
The method according to the preceding claim, wherein for minimizing the loss function (L ₁) each of the samples are consecutively assigned to a given sample position (18) in the given oven (12, 13), at which the target temperature value (T^targ ) is closest to the determined temperature value (T^exp ) of the temperature distribution data (20).
The method according to any of claims 4 to 8, wherein for providing the position arrangement data, the positioning of the samples is varied to minimize a further loss function (L ₂), and wherein that position arrangement is chosen that minimizes the further loss function (L ₂).
The method according to claim 6, wherein for determining the setpoint temperature value (T^sp ) and for providing the position arrangement data, the setpoint temperature value (T^sp ) is varied within the interval and at the same time the positioning of the samples is varied to minimize a further loss function (L ₂), and wherein that at least one setpoint temperature value (T^sp ) in combination with that position arrangement is chosen that minimizes the further loss function (L ₂).
The method according to any of the preceding claims, wherein at most one sample is assigned to a sample position (18), and wherein a total number of sample positions (18) is greater than or equal to a total number of the samples.
A method for arranging one or more samples in one or more ovens (12, 13) at assigned sample positions (18) based on the position arrangement data generated according to any of claims 4 to 11.
A method for determining one or more samples out of heat-treated samples the method comprising:
- arranging samples in one or more ovens (12, 13) according to the method of claim 12,

- performing a firing run by a given oven of the one or more ovens (12, 13),

- determining one or more samples out of the heat-treated samples based on at least one performance parameter.
A cathode comprising an electrode comprising at least partially a material of the determined heat-treated sample obtained by claim 13.
An oven arrangement having an oven (12, 13) and a computing device (14) configured to execute at least one of the methods according to any of claims 1 to 13.