Heat FLUX sensor with anisotropic thermoelectric material

Abstract

A heat flux sensor (10) and method of using the heat flux sensor (10). The heat flux sensor (10) includes thermoelectric element (12) having an anisotropic thermoelectric material with width, length, and thickness dimensions. The width and length dimensions define opposing first and second flux transceiving surfaces (16). The width and thickness dimensions define opposing first and second electrode surfaces (18). Each of the first and second electrode surfaces (18) are configured to intersect each of the first and second flux transceiving surfaces (16). The thermoelectric element (12) is configured so that a heat flux (32) passing between the first and second flux transceiving surfaces (16) causes a voltage to appear between the first and second electrode surfaces (18), and so that the length dimension is at least two times the thickness dimension.

Description

HEAT FLUX SENSOR WITH ANISOTROPIC THERMOELECTRIC MATERIALCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The present application claims the filing benefit of co-pending U.S. Provisional Application Serial No. 63 / 728,933, filed December 6, 2024, the disclosure of which is incorporated by reference herein in its entirety.GOVERNMENT RIGHTS

[0002] This invention was made with government support under grant / contract number DE-SC0020923 awarded by the Department of Energy and grant / contract number FA9550-21-1 -0268 awarded by the Air Force Office of Scientific Research. The government has certain rights in the invention.FIELD OF THE INVENTION

[0003] The present invention relates generally to heat flux sensors and, more particularly, to heat flux sensors that use anisotropic thermoelectric materials.BACKGROUND

[0004] Temperature sensors measure the local temperature of a thermocouple after the thermocouple has reached a uniform temperature. Typically, this measurement is based on a voltage difference between two different metals of the thermocouple. In contrast, heat flux sensors measure the flow of heat through a thickness of material that is part of the sensor. Heat flux sensors may be made from classical thermoelectric materials, in which case the heat flux passing through the sensor is determined based on a measurement of the temperature drop across the material. So that there is a sufficient temperature drop to measure accurately, this indirect measurement of heat flux requires a sufficient thickness of material to develop a sufficient temperature gradient. As a result, this type of heat flux sensor is both insensitive and slow to respond to changes in heat flux.

[0005] Heat flux sensors that measure heat flux using more direct methods can be made by utilizing materials which generate transverse thermoelectric voltages. In these types of materials, when a heat flux is applied across the material in one direction, the material generates a voltage in another direction orthogonal to the heat flux. This geometry enables the sensitivity of the sensor to be increased by increasing the length of a transverse dimension of the material.Attorney Docket No.: OSU-25098WOHowever, this necessitates a large difference in thermopower along different crystallographic directions.

[0006] Thus, there is a need for improved heat flux sensors having increased sensitivity, faster response times, and that operate at lower thermopower levels than known heat flux sensors.SUMMARY

[0007] According to one aspect of this disclosure, a heat flux sensor is provided. The heat flux sensor includes a thermoelectric element having an anisotropic thermoelectric material with a width dimension, a length dimension, and a thickness dimension. The width dimension and the length dimension define a first flux transceiving surface and a second flux transceiving surface opposite the first flux transceiving surface. The width dimension and the thickness dimension define a first electrode surface and a second electrode surface opposite the first electrode surface. Each of the first electrode surface and the second electrode surface intersects each of the first flux transceiving surface and the second flux transceiving surface. The thermoelectric element is configured so that a heat flux passing between the first flux transceiving surface and the second flux transceiving surface causes a voltage to appear between the first electrode surface and the second electrode surface, and so that the length dimension is at least two times the thickness dimension.

[0008] In some embodiments of the heat flux sensor, the anisotropic thermoelectric material may include Re4Si?.

[0009] In some embodiments of the heat flux sensor, the anisotropic thermoelectric material may have a crystalline structure defining a lattice plane, and the thermoelectric element may be configured so that the lattice plane of the crystalline structure is oriented at an angle of between 10 and 80 degrees relative to an in-plane direction and an out-of-plane direction of the crystalline structure.

[0010] In some embodiments of the heat flux sensor, the sensor may further include a voltage measurement circuit operatively coupled to each of the first electrode surface and the second electrode surface.

[0011] In some embodiments of the heat flux sensor, each of the first flux transceiving surface and the second flux transceiving surface may be orthogonal to each of the first electrode surface and the second electrode surface.Attorney Docket No.: OSU-25098WO

[0012] In some embodiments of the heat flux sensor, the sensor may further include a first thermal coupler configured to thermally couple the first flux transceiving surface to one portion of an external environment, and a second thermal coupler configured to thermally couple the second flux transceiving surface to another portion of the external environment.

[0013] In some embodiments of the heat flux sensor, the one portion of the external environment may be one of a heat sink or a heat source, and the other portion of the external environment may be the other of the heat sink or the heat source.

[0014] According to another aspect of this disclosure, a method of measuring heat flux is provided. The method includes providing a heat flux to the thermoelectric element including the anisotropic thermoelectric material having the width dimension, the length dimension, and the thickness dimension. The width dimension and the length dimension define the first flux transceiving surface and the second flux transceiving surface opposite the first flux transceiving surface. The width dimension and the thickness dimension define the first electrode surface and the second electrode surface opposite the first electrode surface. Each of the first electrode surface and the second electrode surface intersect each of the first flux transceiving surface and the second flux transceiving surface. The thermoelectric element is configured so that the heat flux passing between the first flux transceiving surface and the second flux transceiving surface causes the voltage to appear between the first electrode surface and the second electrode surface, and so that the length dimension is at least two times the thickness dimension.

[0015] In some embodiments of the method, the anisotropic thermoelectric material may include Re4Si?.

[0016] In some embodiments of the method, the anisotropic thermoelectric material may have a crystalline structure defining a lattice plane, and the method may further include configuring the thermoelectric element so that the lattice plane of the crystalline structure is oriented at an angle of between 10 and 80 degrees relative to the in-plane direction and the out-of-plane direction of the crystalline structure.

[0017] In some embodiments of the method, the method may further include operatively coupling the voltage measurement circuit to each of the first electrode surface and the second electrode surface.Attorney Docket No.: OSU-25098WO

[0018] In some embodiments of the method, each of the first flux transceiving surface and the second flux transceiving surface may be orthogonal to each of the first electrode surface and the second electrode surface.

[0019] In some embodiments of the method, the method may further include configuring the first thermal coupler to thermally couple the first flux transceiving surface to the one portion of the external environment, and configuring the second thermal coupler to thermally couple the second flux transceiving surface to the other portion of the external environment.

[0020] In some embodiments of the method, the one portion of the external environment may be one of the heat sink or the heat source, and the other portion of the external environment may be the other of the heat sink or the heat source.

[0021] The above summary presents a simplified overview of some embodiments of the invention to provide a basic understanding of certain aspects of the invention discussed herein. The summary is not intended to provide an extensive overview of the invention, nor is it intended to identify any key or critical elements, or delineate the scope of the invention. The sole purpose of the summary is merely to present some concepts in a simplified form as an introduction to the detailed description presented below.BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate various embodiments of the invention and, together with the general description of the invention given above, and the detailed description of the embodiments given below, serve to explain the embodiments of the invention.

[0023] FIG. 1 is a diagrammatic view of an exemplary heat flux sensor including a thermoelectric element in accordance with an embodiment of the invention.

[0024] FIG. 2 is a diagrammatic view of a stack of components including the heat flux sensor of FIG. 1.

[0025] FIG. 3 is a diagrammatic view of the crystal structure of a material that may be used to form the thermoelectric element of the heat flux sensor of FIG. 1.

[0026] FIG. 4 is a graphical view of measured thermopower for the material of FIG. 3 as a function of temperature along different crystallographic directions.

[0027] FIG. 5 a graphical view of thermopower along in-plane and cross-plane directions of the material of FIG. 3 as a function of temperature.Attorney Docket No.: OSU-25098WO

[0028] FTG. 6 is a diagrammatic view of an exemplary heat flux sensor fabricated using the material of FIGS. 3 and 5.

[0029] It should be understood that the appended drawings are not necessarily to scale, and may present a somewhat simplified representation of various features illustrative of the basic principles of the invention. The specific design features of the sequence of operations disclosed herein, including, for example, specific dimensions, orientations, locations, and shapes of various illustrated components, may be determined in part by the particular intended application and use environment. Certain features of the illustrated embodiments may have been enlarged or distorted relative to others to facilitate visualization and a clear understanding. In particular, thin features may be thickened, for example, for clarity or illustration.DETAILED DESCRIPTION

[0030] The present disclosure is believed to be the first to recognize materials which have different sign thermopowers along different crystallographic directions (referred to herein as anisotropic thermoelectric materials) can be used as the basis for improved heat flux sensors. Re4Si?, which is a silicon-deficient variant of rhenium silicide, has a particularly large thermopower anisotropy, with in-plane and cross-plane thermopowers approaching maximums of about +150 and -400 pV K-1(respectively) at 500 K in test samples. This difference of 550 p V K1represents a thermopower anisotropy which is almost twenty times that found in current state of the art materials.

[0031] Variants of Re4Si? that are silicon deficient (e.g., Re4Si?-x where x < 0.03, such as parts per million or parts per thousand) also demonstrate different thermopower anisotropies. Crystals of alloys of Re4-xMxSi7+o.25x (where M can be Mo, W) and Re4-xMnxSi7 have also shown different thermopower anisotropies. However, the largest thermopower anisotropy known to the Applicant is provided by the most stoichiometrically pure Re4Si? samples.

[0032] The thermopower anisotropy of the above described materials (e.g., Re4Si?) is leveraged by the thermal flux sensors disclosed herein to enhance the heat flux sensitivity and responsiveness thereof. Additionally, Re4Si7 has thermopower anisotropies that are stable over wide temperature ranges. This characteristic enables improved simplicity in calibration of the heat flux sensors as compared to conventional flux sensors. Furthermore, Re4Si? is thermally stable, with a 2000°C melting point. This characteristic enables flux sensors made from Re4Si? to be used over a much greater measurement range than conventional flux sensors. The presentAttorney Docket No.: OSU-25098WO disclosure is also believed to be the first to recognize the usefulness of transverse thermoelectric devices as heat flux sensors. Re4Si? crystals have a large transverse thermoelectric effect and can be used for generating electrical power. However, power generation is a fundamentally different application from sensing heat flux, and applying the design principles used for power generating devices does not produce a useful heat flux sensor. For example, power generation designs must apply voltage wires in the transverse direction to supply voltage and current to an electrical load. In contrast, the material used in the thermoelectric element of a heat flux sensor is configured with a geometry that is materially different from that of, and sub-optimal for, a power generation device.

[0033] FIG. 1 depicts an exemplary heat flux sensor 10 in accordance with an embodiment of the present invention. The heat flux sensor 10 includes a thermoelectric element 12 comprised of a suitable anisotropic thermoelectric material, such as Re4Si?, although other anisotropic thermoelectric materials may also be used, e.g., Re4Si?- , Re4-xMoxSi7+o.25x, Re4-xWxSi7+o.25x, and Re4-xMnxSi7. For reference purposes, a cartesian coordinate system 14 is depicted as having an x-axis, a y-axis, and a z-axis aligned with respective dimensions of the thermoelectric element 12. The thermoelectric element 12 has a dimension w in the z-axis direction (referred to herein as the width dimension), a dimension / in the -axis direction (referred to herein as the length dimension), and a dimension h in the x-axis direction (referred to herein as the thickness dimension). The thermoelectric element 12 may further include opposing (e.g., upper and lower) flux transceiving surfaces 16 and opposing (e.g., left and right) electrode surfaces 18. The flux transceiving surfaces 16 may either receive or transmit a heat flux 32 (depending on the direction of the heat flux 32), and have dimensions defined by the length I and width w of the thermoelectric element 12 of heat flux sensor 10. The electrode surfaces 18 may have dimensions defined by the width vv and thickness h of the thermoelectric element 12 of heat flux sensor 10. Each electrode surface 18 of thermoelectric element 12 may include an electrical contact 20 to which one or more conductors 22 can be coupled. The conductors 22 (e.g., wires made of copper, platinum, silver, gold, tungsten, nickel, rhenium, molybdenum, and / or suitable alloys such as stainless steel and / or various nickel-chromium combinations) may operatively couple the electrical contacts 20 to a voltage measurement circuit 24 that measures a voltage VOUT generated by the heat flux sensor 10. The voltage measurement circuit 24 may have a high input impedance (e.g., approaching infinity for a direct current (DC)) to avoid loading the heatAttorney Docket No.: OSU-25098WO flux sensor 10. The thermoelectric element 12 may have a crystalline structure and be configured so that a lattice plane 26 of the crystalline structure is oriented at an angle <f> to one of the flux transceiving surfaces 16 of thermoelectric element 12, e.g., the upper flux transceiving surface 16. The flux transceiving surfaces 16 of thermoelectric element 12 may be generally parallel to the y-z plane of coordinate system 14. The lattice plane 26 may have a cross-plane direction 28 oriented generally parallel to the z-axis, and an in-plane direction 30 perpendicular to the z-axis and oriented at the angle to the y-axis.

[0034] Embodiments of the heat flux sensor 10 may have many different geometrical variations, including variations in thickness, length, width, and shape. The thermoelectric element 12 of heat flux sensor 10 may be made from material grown as a thin film on a substrate, cut and lapped from a larger block of material, or using any other suitable method of fabrication. In an embodiment of the heat flux sensor 10, slabs of Re4Si? may be cut into the desired geometry. The heat flux 32 may be applied in a direction normal to one of the flux transceiving surfaces 16 of thermoelectric element 12. The thermoelectric element 12 of heat flux sensor 10 may be cut so that the angle 6 between the thickness dimension (shown as aligned with the x-axis) is between about 10 and 80 degrees, preferably between 40 and 50 degrees, and more preferably about 45 degrees relative to the in-plane and out-of-plane directions of the crystalline structure thereof. For the depicted embodiment, the maximum voltage may be achieved with an angle 6 of about 45 degrees.

[0035] The thermoelectric element 12 of heat flux sensor 10 may have different thicknesses depending on the application of the heat flux sensor 10. Exemplary thicknesses h may include, but are not limited to, 1.0 mm, 0.3 mm, 0.1 mm, 0.03 mm, and 0.01 mm. These dimensions may be achieved using conventional lapping and polishing instruments found in the semiconductor industry. Lower thicknesses h (e.g., from 10 pm down to the atomic level) may be achieved by growing films on a substrate, for example. For low-temperature operation (T < 450 K), the contacts 20 between conductors 22 and the thermoelectric element 12 may be provided by Ag- epoxy. For higher temperature operation, small-diameter wires (e.g., wire made of rhenium, molybdenum, or other suitable materials) may be laser welded to the thermoelectric element 12 of heat flux sensor 10.

[0036] As noted above, the optimal geometry for the heat flux sensor 10 may vary by application. Geometric parameters include the length / , width w, and thickness h of theAttorney Docket No.: OSU-25098WO thermoelectric element 12 of heat flux sensor 10. Figures of merit for the heat flux sensor 10 may include sensitivity and response time.

[0037] Sensitivity of the heat flux sensor 10 may be defined as the voltage out VOUT per unit of heat flux JQ (W / m2) passing through the sensor. The classical thermoelectric equations relate electric field and thermal gradients to heat and current fluxes as follows:

[0038] Unlike power generating devices, the voltage measurements are of an open circuit voltage - ideally with little or no current is flowing and jc = 0. As a result, Equation 1 relates electric fields to temperature gradients along the v-axis and y-axis directions.

[0039] The bottom line of Equation 1 also gives the Fourier equation for thermal conductivity:

[0040] If the heat flux 32 is applied to the heat flux sensor 10 via isothermal plates, VyT = 0 and Fourier’s law is provided by:]Q,X = -«VXT Eqn. 4

[0041] Equation 4 may be substituted into Equation 2 and the resulting equation solved for the electric field induced in the heat flux sensor 10 to produce:5Ey= SyxVxT = — —jQ,xEqn. 5 X"

[0042] The voltage output of the heat flux sensor 10 may be determined by integrating the electric field over the length I of the thermoelectric element 12 of heat flux sensor 10, to produce:Equation 6 indicates that the output voltage VOUT is linear with heat flux, is independent of the thickness h and the width w, and can be increased by increasing the length I of the thermoelectric element 12 of heat flux sensor 10.

[0043] The geometry of the heat flux sensor 10 may also affect response times of the sensor to changes in the amount of heat flux 32. When a pulse of heat is received by the flux transceiving surface 16 of thermoelectric element 12 at time t =0, the pulse of heat may penetrateAttorney Docket No.: OSU-25098WO the thermoelectric element 12 as a decaying exponential having characteristic length corresponding to the thermal diffusion length of the thermoelectric element 12. After a time delay T, the diffusion length Ldiff is given by:Ldiff = VOr Eqn. 7 where D is the thermal diffusivity of the thermoelectric element 12 of heat flux sensor 10. The thermal diffusivity D may be determined as,where C is the specific heat per unit volume of the thermoelectric element 12 of heat flux sensor 10. C is given by,C = Cwx p Eqn. 9 where Cwis the specific heat per unit weight and p is the density of the material from which the thermoelectric element 12 of heat flux sensor 10 is made, e.g., Re4Si?. The response time of the heat flux sensor 10 can be estimated by setting Ldiff - h and solving Equation 7 for the response time r to produce:

[0044] Equation 10 indicates that the thinner the thermoelectric element 12 of heat flux sensor 10, the faster the response time r, with the response time r improving quadratically with the inverse of the thickness h. The thickness h of the thermoelectric element 12 of heat flux sensor 10 may therefore preferably be small, as devices with smaller thicknesses h tend to have shorter thermal response times r. The thermal diffusivity D of Re4Si? is estimated to be about 0.2 cm2 / s, which indicates response times r of 5 ps for a thermoelectric element 12 having a thickness h - 0.01 mm, and 5 ns for a thermoelectric element 12 having a thickness h - 300 nm. The voltage output VOUT is independent of the thickness / ?, but increases with increasing length I. Therefore, even with suboptimal geometry, the lower bound for sensitivity of the heat flux sensor 10 is estimated to be superior to the sensitivities of state of the art conventional heat flux sensors.

[0045] Heat flux sensor transient characteristics may be measured at room temperature on an optical bench. By way of example, the thermoelectric element 12 of heat flux sensor 10 may be irradiated by a laser pulse, and the voltage output measured by an oscilloscope triggered by the laser pulse, e.g., from a 1 ns diode laser. For thicknesses h in the range 1000 pm > h > 0.2 pm, response times down to 3 ns may be achieved. This range of response times r can be measuredAttorney Docket No.: OSU-25098WO using a 300 MHz oscilloscope. Optical components (e.g., lenses) may be used to spread the laser pulse across the flux transceiving surface 16 of thermoelectric element 12. However, maintaining a uniform heat flux across the flux transceiving surface 16 of thermoelectric element 12 may be difficult. Accordingly, the above described transient response time measurement test may not provide sufficiently accurate sensitivity measurements in some situations.

[0046] Determining sensitivity of the heat flux sensor 10 may require measurements of VOUT and heat flux jg, which may be measured under steady state conditions. One difficulty may be caused by radiative heat losses, which can make a direct estimate of the heat flux j difficult to determine. Radiative losses follow the Stefan-Boltzmann law, and are thus proportional to the fourth power of the temperature T*. Below 200 K, radiative heat losses may be negligible, and thus ignored. Around room temperature (e.g., 293 K), radiative losses may siphon off about 30% of the heat input supplied to the flux transceiving surface 16 of thermoelectric element 12. Above 400 K, radiative losses may become dominant. Thus, sensitivity measurements over different temperature ranges may be made using different instrumentation.

[0047] Low temperature measurements (e.g., T < 200 K) may be made in a cryostat with the geometry used for classical heater- and- sink thermal conductivity measurements using Equation 4. The voltage VOUT across the electrical contacts 20 of thermoelectric element 12 may be monitored.

[0048] Referring now to FIG. 2, to measure sensitivity in a medium temperature range (e.g., 200 K < T< 400 K) the heat flux sensor 10 may be mounted between two calibrated commercially available heat flux sensors 38. As described above, a cryostat may be used with a modified measurement setup and measurement protocol. The device under test may be mounted in a stack of components 34 including a heat source 36 (e.g., a resistive heater), a commercially available heat flux sensor 38, the heat flux sensor 10 under test, another commercially available heat flux sensor 38, and a heat sink 40. The mount (not shown) may be configured to minimize the amount of the heat flux sensor 10 under test that is exposed to the vacuum along the sides of the stack of components 34, thus minimizing heat losses. The portions of the thermoelectric element 12 of heat flux sensor 10 exposed to the commercially available heat flux sensors 38 should not radiate away heat. Accordingly, the difference between the heat flux 32 going into the heat flux sensor 10 under test measured by the first commercially available heat flux sensor 38 and the heat flux 32 coming out of the heat flux sensor 10 under test measured by the secondAttorney Docket No.: OSU-25098WO commercially available heat flux sensor 38 may be used to estimate of the heat radiated away into the cryostat. The sensitivity measurements can then be corrected for that loss.

[0049] Commercially available heat flux sensors may not be able to withstand temperatures above 400 K. To measure sensitivity in the high temperature range (e.g., T> 400 K), heat flux may be determined by using suitable thermal resistor (e.g., a piece of electrolytic iron) whose thermal conductivity is stable and calibrated by a suitable standards body (e.g., the National Institute of Standards and Technology (NIST)). The resistor may be instrumented with a plurality of high temperature thermocouples, e.g., two Platinum-Rhodium thermocouples - one on each of two opposing surfaces through which the heat flux passes. The resistor / thermocouple device can then be mounted in a high-temperature instrument. Fourier’s law may then be used to estimate the heat flux flowing through the thermal resistor. The heat flux sensor under test can be mounted under the thermal resistor. Due to the high aspect-ratio of the thermoelectric element 12 of heat flux sensor 10, it may be presumed that most of the heat which flows through the thermal resistor is also passing through the heat flux sensor under test. Measurements in the high temperature range may overlap with medium range temperature testing to allow comparisons between collected data with each test setup. This comparison should enable the accuracy of the high temperature test setup to be confirmed for temperatures T < 400 K.

[0050] FIG. 3 depicts the crystal structure of Re4S i 7 viewed down the b-axis. Isolated dark spheres correspond to Re and bonded spheres correspond to Si. The cross-plane

[0101] and in-plane [7 0 -1] directions are shown. Experimental results have established that single crystals of Re4Si? and derivatives thereof may have the highest anisotropic thermopower values among all materials. Re4Si? adopts a layered monoclinic crystal structure (space group Cm) that is a defect-ordered silicon-deficient variant of the a-MoSi structure type, but with a (7a + c) x b x (c - a) supercell. As shown by FIG. 3, Re4Si? includes two-dimensional layers of square pyramidally bonded networks of Si atoms separated by planes of Re atoms. Furthermore, one Si atom is absent for every seven Si atoms, causing a slight monoclinic distortion (beta = 92.8°). The a-axis and c-axis are rotated from the in-plane and cross-plane directions by 22.1° and 19.3°, respectively. Two of the in-plane directions are the [7 0 -1] and the

[0010] directions, whereas the cross-plane direction corresponds to the

[0101] direction.

[0051] Stoichiometric Re4Si? has the largest thermopower anisotropy among known materials, followed by its doped derivatives (e.g., Re4Si?-x; x<0.2) or alloyed derivativesAttorney Docket No.: OSU-25098WO(Re4-xMxSi7+o.25x, where x<l and M = Mo, W; Re4-xMnxSi?; as well as Re4-o.25xSi7-i.33xTrx, where Tr = B, Al, or Ga). FIG. 4 depicts a graph of measured thermopower for a nominally undoped Re4Si? crystal along different crystallographic directions as a function of temperature, including the in-plane

[0010] and [7 0 -1] directions and the cross-plane

[0101] direction. As can be seen from FIG. 4, nominally undoped Re4Si? has a large thermopower anisotropy.

[0052] A prototype heat flux sensor was constructed from a doped single crystal of Re4Si?. The temperature dependent thermopower along each of the in-plane and cross-plane directions from this crystal is shown in FIG. 5, which depicts in-plane [7 0 -1] and cross-plane

[0101] thermopower measured for a doped Re4Si? crystal as a function of temperature. As shown by FIG. 5, at 560 K, the in-plane thermopower is 155 pV K1and the cross-plane thermopower is - 338 pV K1.

[0053] FIG. 6 depicts an exemplary heat flux sensor fabricated by dicing the crystal characterized by FIG. 5 into a rectangular shape having a thickness of 1.1 mm, a length of 3.7 mm, and a width of 2 mm. The crystal was oriented in such a way that the top face of the crystal was rotated -60 degrees away from the in-plane and toward the cross-plane direction. This angular orientation is represented by diagonal lines. Based on the above values and geometry, the device is expected to have a Syx= 213 pV K1at 560 K, and the length would be about 3.7 mm as determined using Equation 6. The thermal conductivity along the thickness direction was determined to be 4.1 W m-1K’1at 560 K. When a 1 K temperature difference was applied along the thickness in a steady state configuration, a 383 pV transverse voltage was measured.

[0054] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the embodiments of the invention. As used herein, the singular forms “a”, “an” and “the” are intended to include both the singular and plural forms, and the terms “and” and “or” are each intended to include both alternative and conjunctive combinations, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” or “comprising,” when used in this specification, specify the presence of stated features, integers, actions, steps, operations, elements, or components, but do not preclude the presence or addition of one or more other features, integers, actions, steps, operations, elements, components, or groups thereof. Furthermore, to the extent that the terms “includes”, “having”, “has”, “with”, “comprised of’, or variants thereof are used in either the detailedAttorney Docket No.: OSU-25098WO description or the claims, such terms are intended to be inclusive in a manner similar to the term “comprising”.

[0055] While all the invention has been illustrated by a description of various embodiments, and while these embodiments have been described in considerable detail, it is not the intention of the Applicant to restrict or in any way limit the scope of the appended claims to such detail. Additional advantages and modifications will readily appear to those skilled in the art. The invention in its broader aspects is therefore not limited to the specific details, representative apparatus and method, and illustrative examples shown and described. Accordingly, departures may be made from such details without departing from the spirit or scope of the Applicant’s general inventive concept.

Claims

Attorney Docket No.: OSU-25098WOCLAIMSWhat is claimed is:

1. A heat flux sensor, comprising: a thermoelectric element including an anisotropic thermoelectric material having a width dimension, a length dimension, and a thickness dimension, wherein: the width dimension and the length dimension define a first flux transceiving surface and a second flux transceiving surface opposite the first flux transceiving surface, the width dimension and the thickness dimension define a first electrode surface and a second electrode surface opposite the first electrode surface, each of the first electrode surface and the second electrode surface intersecting each of the first flux transceiving surface and the second flux transceiving surface, the thermoelectric element is configured so that a heat flux passing between the first flux transceiving surface and the second flux transceiving surface causes a voltage to appear between the first electrode surface and the second electrode surface, and the length dimension is at least two times the thickness dimension.

2. The heat flux sensor of claim 1, wherein the anisotropic thermoelectric material comprises Re4Si?.

3. The heat flux sensor of claim 1, wherein the anisotropic thermoelectric material has a crystalline structure defining a lattice plane, and the thermoelectric element is configured so that the lattice plane of the crystalline structure is oriented at an angle of between 10 and 80 degrees relative to an in-plane direction and an out-of-plane direction of the crystalline structure.

4. The heat flux sensor of claim 1, further comprising: a voltage measurement circuit operatively coupled to each of the first electrode surface and the second electrode surface.Attorney Docket No.: OSU-25098WO5. The heat flux sensor of claim 1 , wherein each of the first flux transceiving surface and the second flux transceiving surface is orthogonal to each of the first electrode surface and the second electrode surface.

6. The heat flux sensor of claim 1, further comprising: a first thermal coupler configured to thermally couple the first flux transceiving surface to one portion of an external environment, and a second thermal coupler configured to thermally couple the second flux transceiving surface to another portion of the external environment.

7. The heat flux sensor of claim 6, wherein the one portion of the external environment is one of a heat sink or a heat source, and the other portion of the external environment is the other of the heat sink or the heat source.

8. A method of measuring heat flux, comprising: providing a heat flux to a thermoelectric element including an anisotropic thermoelectric material having a width dimension, a length dimension, and a thickness dimension, wherein: the width dimension and the length dimension define a first flux transceiving surface and a second flux transceiving surface opposite the first flux transceiving surface, the width dimension and the thickness dimension define a first electrode surface and a second electrode surface opposite the first electrode surface, each of the first electrode surface and the second electrode surface intersecting each of the first flux transceiving surface and the second flux transceiving surface, the thermoelectric element is configured so that the heat flux passing between the first flux transceiving surface and the second flux transceiving surface causes a voltage to appear between the first electrode surface and the second electrode surface, and the length dimension is at least two times the thickness dimension.

9. The method of claim 8, wherein the anisotropic thermoelectric material comprises Re4Si?.Attorney Docket No.: OSU-25098WO10. The method of claim 8, wherein the anisotropic thermoelectric material has a crystalline structure defining a lattice plane, and further comprising: configuring the thermoelectric element so that the lattice plane of the crystalline structure is oriented at an angle of between 10 and 80 degrees relative to an in-plane direction and an out- of-plane direction of the crystalline structure.

11. The method of claim 8, further comprising: operatively coupling a voltage measurement circuit to each of the first electrode surface and the second electrode surface.

12. The method of claim 8, wherein each of the first flux transceiving surface and the second flux transceiving surface is orthogonal to each of the first electrode surface and the second electrode surface.

13. The method of claim 8, further comprising: configuring a first thermal coupler to thermally couple the first flux transceiving surface to one portion of an external environment, and configuring a second thermal coupler to thermally couple the second flux transceiving surface to another portion of the external environment.

14. The method of claim 13, wherein the one portion of the external environment is one of a heat sink or a heat source, and the other portion of the external environment is the other of the heat sink or the heat source.

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