A dual-ridge four-probe method and apparatus for low resistance metal resistivity comparison

Abstract

The application discloses a double-ratio-arm four-probe method and device for low-resistance metal resistivity comparison. The method connects a regular cylindrical or cuboid standard sample for low-resistance metal resistivity comparison measurement and a sample to be tested into a ratio bridge with a main ratio arm and an inner ratio arm in a linear four-probe mode, carries out zero balance under forward current and reverse current, converts the resistivity ratio of the standard sample and the sample to be tested according to a four-probe block material formula and a geometric correction relationship, and outputs a resistivity relative change rate. The method can reduce lead resistance, contact resistance, thermoelectric potential and temperature drift error through four-probe resistivity measurement, double-ratio-arm bridge balance, forward and reverse current average and temperature gating, and is suitable for low-resistance metal and small resistivity change measurement.

Description

Technical Field

[0001] This invention belongs to the field of electrical performance testing technology for metallic materials, and particularly relates to a dual-arm four-probe method and apparatus for comparing the resistivity of low-resistivity metals. Background Technology

[0002] During heat treatment, electrical treatment, welding, surface treatment, plastic deformation, and service damage, metallic materials undergo changes in grain size, dislocation density, precipitates, phase interfaces, residual stress, microcracks, and oxidation corrosion. These changes in microstructure affect electron scattering behavior and are reflected in changes in resistivity. Therefore, resistivity can serve as a sensitive physical quantity for evaluating the processing condition, batch consistency, damage evolution, and microstructure changes of metallic materials.

[0003] For bulk metallic materials, the equivalent resistance of the sample is typically in the micro-ohm to milliohm range. The measured voltage signal is small and easily affected by lead resistance, probe contact resistance, clamp resistance, switch contact resistance, thermoelectric potential, ambient temperature fluctuations, sample self-heating, and instrument zero drift. The ordinary two-wire method directly superimposes the lead and contact resistance into the measurement result, making it unsuitable for precise measurements of low-resistivity metals. While the ordinary four-wire method or the linear four-probe method can reduce the influence of current-end contact resistance on voltage sampling, it is usually designed for absolute measurements of a single sample. Even if the standard sample and the test sample are measured separately and then compared, errors caused by different clamping conditions, time and temperature variations, and different instrument zero points will still be introduced.

[0004] Existing low-resistance bridges or resistance comparators can achieve low resistance ratio measurements, but they are usually based on standard resistors and the resistors under test, and do not provide a complete solution for the geometry of linear four-probes for bulk metals, finite size correction, probe pressure consistency, and relative resistivity output for batch process samples.

[0005] The following problems exist in the existing technology for measuring low resistance or small resistivity changes in bulk metals:

[0006] Firstly, bulk metals have low equivalent resistance, and traditional two-wire methods and ordinary single-sample measurements are easily affected by lead resistance and contact resistance, making them difficult to use for reliable comparison of resistances in the micro-ohm to milliohm range.

[0007] Secondly, when the standard sample and the sample to be tested are measured separately, inconsistencies in clamping conditions, temperature conditions, and instrument zero point can lead to comparison errors.

[0008] Third, the conventional four-probe method does not integrate low-resistance connection link compensation, forward and reverse current cancellation thermoelectric potential, temperature gating, and geometric correction into the same ratio measurement process;

[0009] Fourth, existing methods cannot directly output the percentage change in resistivity of the process sequence sample relative to the standard sample.

[0010] Therefore, a measurement method that can simultaneously take into account the geometric correction of four probes and the zero-point comparison of the bridge ratio is needed to improve the stability and repeatability of comparing small resistivity changes in bulk low-resistivity metals. Summary of the Invention

[0011] Purpose of the invention: The purpose of this invention is to provide a dual-arm four-probe method and apparatus for comparing the resistivity of low-resistivity metals.

[0012] Technical solution: The present invention provides a dual-arm four-probe method for comparing the resistivity of low-resistivity metals, comprising the following steps:

[0013] Step 1: The standard sample S and the test sample X, which are regular cylindrical or cuboid blocks used for the comparative measurement of resistivity of low-resistivity metals, are respectively clamped in the first straight four-probe fixture and the second straight four-probe fixture. The four probes of each fixture are arranged along the same straight line. The two outer probes are used as current terminals and the two inner probes are used as voltage terminals. Record the sample geometry, test surface orientation, spacing between adjacent probes and temperature.

[0014] Step 2, measure the equivalent resistance R of the four terminals of the standard sample S. S The equivalent resistance R of the four terminals of the test sample X X As the low-resistance arm being compared is connected to the dual-arm ratio bridge via a straight four-probe shielded wire, the dual-arm ratio bridge includes main arms A and B, inner arms a and b, and a zero-position detector G.

[0015] Step 3: Apply test current I to the two outer probes through a bipolar constant current source, adjust the main comparison arms A and B and the inner comparison arms a and b so that A / B and a / b meet the preset matching conditions, and adjust the output voltage U of the zero-position detector G. G The preset zero position condition is met;

[0016] Step 4: Perform zero-point balance under both forward current +I and reverse current -I to obtain the ratio of the equivalent resistances of the four terminals under forward bias, k. + Find the ratio of the reverse four-terminal equivalent resistance k-, and calculate the four-terminal equivalent resistance ratio:

[0017]

[0018] Where k represents R X / R S ;

[0019] Step 5: Calculate the resistivity ratio K of the test sample X relative to the standard sample S according to the resistivity formula and geometric correction factor formula for linear four-probe bulk materials, and output the percentage change in resistivity:

[0020] .

[0021] Furthermore, in step 2, the dual-arm ratio bridge is configured as follows: the main arms A and B establish the main potential ratio between the standard sample S and the test sample X; the inner arms a and b proportionally compensate for the potential drop of the low-resistance connection link connecting the lower-resistance arm being compared; the balance formula is:

[0022]

[0023] Among them, the low-resistance connection link between the resistor under test and the standard resistor has its first-order influence on the resistance ratio weakened when A / B and a / b meet the preset matching conditions.

[0024] Furthermore, the preset matching conditions satisfy the following: Main arms A and B and inner arms a and b:

[0025]

[0026] Or it satisfies:

[0027]

[0028] This reduces the first-order effect of low-resistance connection links on the resistance ratio.

[0029] Furthermore, in step 3, the preset zero-position condition specifically refers to:

[0030]

[0031] Among them, U G U0 is the output voltage of the zero-position detector G, ranging from 10 nV to 1 μV. When the output voltage of the zero-position detector G does not meet the preset zero-position condition, the main comparison arms A and B and the inner comparison arms a and b are readjusted, or the current and temperature are stabilized before sampling is performed again.

[0032] Furthermore, in step 4, when zero-point balance is achieved under forward current +I and reverse current -I, the amplitudes of the forward current and reverse current are the same; k + With k - The bridge balance ratio arms A / B are determined based on the corresponding forward current +I and reverse current -I, respectively. When A / B and a / b meet the preset matching conditions, k + With k -It is approximately equal to the A / B value under the corresponding current polarity; the thermoelectric potential, contact thermoelectric potential and zero drift, which are independent of the test current direction, are weakened as bias terms through the processing of equation (1).

[0033] Furthermore, in step 5, the resistivity formula for the linear four-probe bulk material is:

[0034]

[0035] Where ρ is the sample resistivity, s is the distance between adjacent probes, U is the voltage between the two inner voltage probes, I is the test current between the two outer current probes, and F is the geometry correction factor, which is equal to the product of the thickness correction factor F1 and the edge correction factor F2.

[0036]

[0037] Once k is calculated using equation (3) that satisfies the preset matching condition, the resistivity ratio K is calculated using the following formula:

[0038]

[0039] Among them, s S s X F represents the distance between adjacent probes of the standard sample S and the test sample X, respectively. S F X These are the corresponding geometric correction factors; when the geometric dimensions, boundary conditions, and probe spacing of the standard sample S and the test sample X are the same, no geometric correction is required, therefore K=k.

[0040] Furthermore, the geometric correction factor F is used to correct the current field boundary effect caused by the finite thickness, finite width, finite length and probe-to-boundary distance of the bulk sample; the geometric correction factor F is obtained through a four-probe correction table, standard sample calibration, analytical approximation or finite element calculation.

[0041] Furthermore, the method also includes a temperature gating step: synchronously acquiring the standard sample temperature T. S Temperature T of the sample to be tested X and base temperature T B The sample enters the valid sampling window when the following conditions are met simultaneously:

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] Where θ T The temperature ranges from 0.05℃ to 0.5℃, θ R The range is 0.001℃ / s to 0.1℃ / s; when the temperature gating condition is not met, the corresponding sampling window is marked as invalid, and the process waits for thermal equilibrium, rebalancing of the bridge, or correction to the reference temperature based on the material resistance temperature coefficient.

[0048] Furthermore, the spacing between adjacent probes of the linear four-probe fixture is 0.5 mm to 2 mm; the probe contact pressure is 0.2 N to 1 N; and the probe material is tungsten, tungsten steel, gold-plated tungsten needle, platinum-iridium alloy, or hard conductive alloy.

[0049] A dual-arm four-probe device for comparing the resistivity of low-resistivity metals includes a bipolar constant current source meter, a dual-arm ratio bridge, a zero-point detector G, a dual-sample linear four-probe fixture for a standard sample and a test sample, a temperature monitoring module, and a control and calculation unit; wherein, the standard sample linear four-probe fixture and the test sample linear four-probe fixture are respectively used to form the four-terminal equivalent resistance R of the standard sample S and the test sample X. S R X The dual-arm ratio bridge includes main ratio arms A and B and inner ratio arms a and b, and is configured to compare R... S With R X Zero-point ratio comparison is performed; the control and calculation unit is used to control current reversal, bridge circuit balancing, temperature gating, geometric correction, and resistivity change percentage output.

[0050] The dual-sample linear four-probe fixture includes an insulating base, a standard sample support position, a test sample support position, a first elastically loaded four-probe corresponding to the standard sample support position, a second elastically loaded four-probe corresponding to the test sample support position, a contact pressure adjustment knob, shielded leads, and a temperature sensor near the test surface; the contact pressure adjustment mechanism is configured to keep the probe contact pressure of each sample within a preset range during batch measurement.

[0051] The control and computing unit stores a computer program, which, when executed by the processor, performs the following operations: acquiring U... G A / B, a / b, T S T X and T BDetermine the zero-point condition and temperature gating condition; record k. + and k - Calculate k, K, and Δ; and generate a result table and variation curves for batch samples.

[0052] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0053] (1) The present invention incorporates the standard sample S and the test sample X into the same double-arm ratio bridge at the same time, so that the comparison process is changed from two independent absolute measurements to zero-point ratio measurement in the same bridge circuit, thereby reducing the influence of instrument gain, zero point and reading deviation on the comparison results;

[0054] (2) The present invention uses four probes for four-end sampling, with the outer probe carrying current and the inner probe taking voltage, so that the voltage sampling circuit is separated from the current contact circuit, thereby reducing the direct influence of the current end contact resistance and lead resistance on the measurement of low-resistance metals;

[0055] (3) The present invention sets the main comparison arms A and B and the inner comparison arms a and b, and makes A / B match a / b, thereby reducing the first-order influence of the low-resistance connection link on the resistance ratio through the dual comparison arm ratio compensation;

[0056] (4) The present invention uses forward and reverse currents to balance and average them, which can reduce the influence of thermoelectric potential, contact thermoelectric potential and zero drift on the judgment of small resistivity changes that are independent of the current direction.

[0057] (5) The present invention incorporates temperature sensor, temperature gating and geometric correction factor into the same calculation process, which can obtain comparable resistivity ratio K and percentage change Δ when there are differences in the geometry and temperature conditions of the bulk sample;

[0058] (6) This invention is applicable to batch process sample testing. Keeping the standard sample, bridge circuit, and main leads unchanged, the sample to be tested X is replaced sequentially. i K can then be output. i Δ i And the curves showing the changes in sample parameters under different processes. Attached Figure Description

[0059] Figure 1 This is a schematic diagram of the four-probe bridge measurement system of the present invention;

[0060] Figure 2 This is a structural diagram of the probe holder for simultaneous measurement of two samples according to the present invention. The labels in the diagram are as follows: 1—base; 2—sample; 3—probe clamp; 4—elastically loaded four probes; 5—height adjustment screw;

[0061] Figure 3 This is a schematic diagram of the ratio bridge circuit of the present invention;

[0062] Figure 4 This is a flowchart of the measurement and calculation process of the present invention. Detailed Implementation

[0063] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0064] like Figures 1 to 4 As shown, Figure 1 The diagram shows the overall connection framework between the control and calculation unit, bipolar constant current source meter, temperature sensing unit, dual-sample four-probe fixture, and dual-ratio arm bridge module. Figure 2 The dual-sample four-probe fixture structure for standard sample S and test sample X is shown. Figure 3 This illustrates a double-arm ratio bridge consisting of main ratio arms A and B and inner ratio arms a and b. Figure 4 The measurement and calculation process is illustrated. In this invention, R... S R is the equivalent resistance of the four terminals of the standard sample S. X Let ρ be the equivalent resistance of the four terminals of the sample X to be tested. S Let ρ be the resistivity of the standard sample S. X Let X be the resistivity of the sample to be tested, and k be R. X / R S The corresponding four-terminal equivalent resistance ratio, K is ρ X / ρ S The corresponding resistivity ratio, where Δ is the percentage change in resistivity, and T S T X T B These represent the standard sample, the sample to be tested, and the base temperature, respectively. The testing procedure of this invention is as follows:

[0065] Step 1: Sample pretreatment, recording sample geometry and test temperature. The test surfaces of the standard sample S and the sample X to be tested are uniformly ground and polished to remove the influence of surface oxide layers, contaminant layers, and localized rough contact on low-resistivity measurements. The sample number, material, length, width, thickness, test surface orientation, and spacing s between adjacent probes are recorded. S and s X And the test temperature, and input the above parameters. Figure 1 The control and calculation unit shown serves as the basis for subsequent temperature gating, geometric correction, and result output.

[0066] Step 2: Mount the standard sample and the test sample using a dual-sample, four-probe clamp. (Combined with...) Figure 2 The dual-sample synchronous measurement probe holder shown places the standard sample S and the test sample X in their respective sample bearing positions. The probe positions and contact pressure are adjusted using the probe clamp 3, the elastically loaded four probes 4, and the height adjustment screw 5. Each group of four probes is arranged in a straight line, with the two outer probes serving as current terminals and the two inner probes serving as voltage terminals, thus creating a four-terminal equivalent resistance R for the standard sample S.S The test sample X forms a four-terminal equivalent resistance R. X Two sets of four-probe terminals are connected via shielded leads. Figure 1 The measurement system shown separates the current contact circuit from the voltage sampling circuit, thereby reducing the direct impact of current terminal contact resistance and lead resistance on the measurement of low-resistance metals.

[0067] Step 3: Temperature gating to determine the valid measurement window. (Combined with...) Figure 1 The temperature monitoring module in the middle collects the temperature T of the standard sample in real time. S Temperature T of the sample to be tested X and base temperature T B The control and calculation unit determines whether the temperature difference between samples, the temperature difference between samples and the base, and the rate of temperature change meet the preset temperature gating conditions.

[0068] Step 4: Balance the bridge circuit under forward current +I. Within the effective measurement window, through... Figure 1 The bipolar constant current source shown is directed towards Figure 2 The outer current probes of the two sets of four probes in the middle are connected to a positive test current +I, and the voltage terminal signals of the standard sample S and the test sample X are connected to the middle probes. Figure 3 The dual-arm ratio bridge shown uses main arms A and B to establish the main potential ratio between the standard sample S and the test sample X, and inner arms a and b to proportionally compensate for the potential drop of the low-resistance connection link connecting the lower-resistance arm being compared. Adjusting the main arms A and B and the inner arms a and b ensures that A / B and a / b meet preset matching conditions, and that the output voltage U of the zero-position detector G is adjusted. G Once the preset zero-position condition is met and the bridge circuit reaches zero-position balance, the control and calculation unit records the ratio of the equivalent resistances k of the four positive terminals. + And the corresponding A / B, a / b and U G .

[0069] Step 5: Balance the bridge under reverse current -I. Figure 1 The system connections shown Figure 2 The dual-sample four-probe clamping state shown and Figure 3 The structure of the dual-arm ratio bridge remains unchanged. Switch the output of the bipolar constant current source meter to a reverse test current -I, which has the same amplitude but opposite direction to the forward test current. Adjust the main ratio arms A and B and the inner ratio arms a and b again to achieve zero-point balance, and record the ratio of the reverse four-terminal equivalent resistance k. - .

[0070] Step Six: Averaging the forward and reverse resistance ratios. The control and calculation unit reads the equivalent resistance ratio k of the four forward terminals. + The ratio of the reverse four-terminal equivalent resistance k - ,according to Figure 4The relationship shown is used to calculate the equivalent resistance ratio k of the four terminals. By averaging the forward and reverse results, the influence of thermoelectric potential, contact thermoelectric potential, and zero drift that coexist in the two current polarity measurements on the comparison of low resistance ratios can be reduced, and the subsequent resistivity conversion can be based on the same clamping condition, the same bridge condition, and the same temperature gating condition.

[0071] Step 7: Geometric Correction. The control and calculation unit, based on the resistivity formula and geometric correction relationship of the linear four-probe bulk material, converts the resistance ratio k into the resistivity ratio K of the test sample X relative to the standard sample S. F can be determined by the thickness correction factor F1 and the edge correction factor F2, used to correct for the current field boundary effects caused by the finite thickness, finite width, finite length of the bulk sample, and the distance from the probe to the boundary.

[0072] Step 8: Result Output. The control and calculation unit converts the resistivity ratio K into a percentage change in resistivity Δ, and generates a result including the test current I, probe spacing, probe pressure, main comparison arm A / B, inner comparison arm a / b, zero threshold U0, and k. + k - , k, K, Δ, T S T X T B The results of the geometric correction factor F and the standard deviation of repeated measures.

[0073] During batch measurements, maintain the positions of the standard sample S, main leads, and temperature sensor. Figure 2 The clamping reference shown is as follows Figure 3 The bridge connections remain unchanged; the test sample X is replaced sequentially. i Output K i Δ i The results of these parameters, along with variations in different process parameters, are used to evaluate the process status, batch consistency, damage evolution, or microstructure changes of low-resistivity metals.

[0074] Example 1: Comparative Differential Measurement of Resistivity of Typical Metal Samples

[0075] (1) Sample preparation: Select the metal sample X to be tested and the standard sample S, wherein the standard sample S and the metal sample X to be tested are samples with the same material system, the same geometric dimensions and in the standard process state. The test surfaces of samples X and S are wet-ground stepwise with 400#, 800#, 1200# and 2000# sandpaper, respectively. Then, they are mirror-polished with 1 μm and 0.25 μm diamond suspension to remove the surface layer and form a flat exposed metal surface. Then, they are ultrasonically cleaned with anhydrous ethanol or acetone for 1~5 min and dried.

[0076] (2) Four-probe clamping: The metal sample X to be tested and the standard sample S are clamped in a linear four-probe clamp. The two outer probes are current terminals, and the two inner probes are voltage terminals. The probe spacing s is 1 mm or 2 mm; the probe pressure can be 0.2 N to 1 N; the probe material can be tungsten carbide alloy. The leads are coaxial and are wired at the same temperature as much as possible.

[0077] (3) Temperature gating and repeatability determination: The sample temperature T is collected simultaneously. X Standard sample S temperature T S and base temperature T B When the temperature satisfies equations (10) to (13), it enters the effective sampling window; where θ T 0.05℃, θ R It is 0.001℃ / s.

[0078] (4) Positive current bridge balancing: Start the bipolar constant current source meter to output a constant current +I that does not cause significant self-heating. After the temperature stabilizes, adjust the main ratio arms A and B and the inner ratio arms a and b of the ratio bridge so that A / B and a / b satisfy equation (4) or equation (5), and make the zero-position detector G output |U G If |≤U0, record the forward resistance ratio k. + In this example, U0 is 1 μV.

[0079] (5) Reverse current bridge balancing: Switch the current to -I and repeat the bridge balancing process to obtain k - .

[0080] (6) Average forward and reverse resistance ratio: The resistance ratio of the metal sample to be tested relative to the standard sample is:

[0081]

[0082] (7) Calculation of resistivity of a block sample with four probes arranged in a straight line at equal intervals: The resistivity is _____.

[0083]

[0084] Introducing probe spacing and geometric correction factors, the resistivity ratio is calculated as follows:

[0085]

[0086] And calculate the percentage change in resistivity:

[0087]

[0088] (8) Output of results: The control and calculation unit outputs the percentage change in resistivity Δ. Record the test current I, probe spacing s, probe pressure, main comparison arm A / B, inner comparison arm a / b, zero threshold U0, and positive result k. + Reverse result k - Temperature T S T X T B Geometric correction factor F S and F X , and the standard deviation of repeated measures.

[0089] Example 2: Comparative Measurement of Resistivity Difference in TC11 Titanium Alloy Samples After Electrical Treatment

[0090] This embodiment illustrates the application of the present invention in the electrochemical treatment process sequence of TC11 titanium alloy bulk samples.

[0091] (1) Sample preparation: TC11 titanium alloy cuboid block samples from the same batch were selected as test objects. Among them, untreated samples or samples in the reference treatment state were used as standard samples S, and the remaining samples treated with different electrical treatment parameters were used as test samples X. i Each test sample X i The standard sample S preferably has the same material grade, similar or identical dimensions, identical test surface orientation, and identical four-probe placement. Before testing, record the sample number, electrical treatment parameters, sample length, sample width, sample thickness, test surface orientation, adjacent probe spacing, and ambient temperature for each sample. During the surface pretreatment stage, the standard sample S and each test sample X are... i The test surfaces are uniformly wet-ground, fine-polished, cleaned, and dried to reduce the impact of surface oxide film and local rough contact on low resistance comparison measurements.

[0092] (2) Four-probe clamping: clamp the standard sample S and the sample to be tested X. i The standard sample is loaded into a linear four-probe holder, and the sample to be tested is loaded into a linear four-probe holder. Each holder has four elastically loaded probes arranged in a straight line, with the two outer probes serving as current terminals and the two inner probes serving as voltage terminals. In this embodiment, the probe spacing is preferably 1 mm; the probe contact pressure can be set to 0.2 N to 1 N and should remain consistent throughout the batch testing process; the probe material can be tungsten carbide conductive alloy. The holder leads are coaxial and are wired using an isothermal wiring method to reduce environmental noise and thermoelectric potential effects.

[0093] (3) Temperature gating and repeatability determination: The sample temperature T is collected simultaneously. X Standard sample S temperature T S and base temperature T BWhen the temperature satisfies equations (10) to (13), it enters the effective sampling window; where θ T 0.05℃, θ R It is 0.001℃ / s.

[0094] (4) Positive current bridge balancing: During the bridge connection stage, the standard sample S and the test sample X are connected. i The four-probe clamps are connected to a double-arm bridge. A bipolar constant current source is directed towards the standard sample S and the test sample X. i A test current +I is applied to the outer current probe. The test current +I can be selected based on the equivalent resistance, allowable temperature rise, and zero-position detector sensitivity of the TC11 titanium alloy sample, and is preferably 0.2 A. After the temperature stabilizes, the main ratio arms A and B and the inner ratio arms a and b of the ratio bridge are adjusted so that A / B and a / b satisfy equation (4) or equation (5); at the same time, the output voltage U of the zero-position detector G is observed. G To make it satisfy |U G |≤U0, where U0 is 1 μV. When the bridge reaches the zero-position condition and is within the effective temperature sampling window, the control and calculation unit records the main comparison arm ratio, the inner comparison arm ratio, the zero-position detector output, temperature data, and sampling time, and obtains the resistance ratio k of the i-th test sample relative to the standard sample under forward current. i+ In this embodiment, k i+ It can be expressed by the bridge-road balance relationship (3).

[0095] (5) Reverse current bridge balancing: Switch the test current from +I to -I, keep the current amplitude constant, and repeat the above bridge balancing and temperature gating judgment process after the temperature stabilizes. When A / B and a / b meet the matching condition and the zero-position detector G output satisfies |U G When |≤U0, record the resistance ratio k under reverse current. i- .

[0096] (6) Average ratio of forward and reverse resistance: The control and calculation unit follows the following:

[0097]

[0098] It is used to calculate the i-th test sample X. i The resistance ratio relative to the standard sample S. Since thermoelectric potential, contact thermoelectric potential, and zero-point drift are usually independent of the test current direction, while the sample resistance voltage drop changes in the opposite direction with the current, averaging the forward and reverse currents can reduce the influence of the above bias errors on the measurement of small resistivity changes.

[0099] (7) Calculation and geometric correction of resistivity formula for block four-probe material: According to the resistivity formula of linear four-probe block material:

[0100]

[0101] Where ρ is the sample resistivity, s is the distance between adjacent probes, U is the voltage between the two inner voltage probes, I is the test current between the two outer current probes, and F is the geometric correction factor, which consists of a thickness correction factor F1 and an edge correction factor F2. Based on the standard sample S and the test sample X... i Geometric corrections are made based on the geometry, probe spacing, or boundary conditions.

[0102]

[0103] Where s S and s Xi The two samples are the standard sample S and the test sample X, respectively. i The spacing between adjacent probes, F S and F Xi These are the geometric correction factors for the corresponding samples. The geometric correction factors can be obtained through publicly available four-probe correction tables, standard sample calibration, analytical approximations, or finite element calculations.

[0104] (8) Result output: The control and calculation unit outputs the result based on the resistivity ratio K under the effective sampling window. i Calculate the percentage change in resistivity of the i-th electrically treated sample relative to the standard sample:

[0105]

[0106] Simultaneously record the sample number, test current I, probe spacing s, probe pressure, main comparison arm A / B, inner comparison arm a / b, zero threshold U0, and positive result k. i+ Reverse result k i- Temperature T S T Xi T B Geometric correction factor F S and F Xi , and the standard deviation of repeated measures.

[0107] (9) Batch testing: Keep the standard sample S, ratio bridge, leads, temperature sensor positions and test parameters unchanged, and change the test sample X under different electrical processing parameters in sequence. i Each test sample X i The measurement can be repeated 10 times. Ultimately, K is obtained under different electrical processing times or parameters. i Δ i And repeatability indicators, and output Δ iThe curves showing the change of electrical treatment time parameters are used to evaluate the influence of electrical treatment parameters on the resistivity and microstructure of TC11 titanium alloy.

[0108] The above embodiments are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make several improvements and equivalent substitutions without departing from the principle of the present invention. All such improvements and equivalent substitutions to the claims of the present invention fall within the protection scope of the present invention.

Claims

1. A two-arm four-probe method for comparing the resistivity of low-resistivity metals, characterized in that, Includes the following steps: Step 1: The standard sample S, a regular cylindrical or cuboid block used for the comparative measurement of resistivity of low-resistivity metals, and the sample X to be tested are respectively clamped in the first straight four-probe fixture and the second straight four-probe fixture. The four probes of each fixture are arranged along the same straight line. The two outer probes are used as current terminals and the two inner probes are used as voltage terminals. Record the sample geometry, test surface orientation, spacing between adjacent probes, and temperature. Step 2, measure the equivalent resistance R across the four terminals of the standard sample S. S The equivalent resistance R of the four terminals of the test sample X X As the low-resistance arm being compared is connected to the dual-arm ratio bridge via a straight four-probe shielded wire, the dual-arm ratio bridge includes main arms A and B, inner arms a and b, and a zero-position detector G. Step 3: Apply test current I to the two outer probes through a bipolar constant current source, adjust the main comparison arms A and B and the inner comparison arms a and b so that A / B and a / b meet the preset matching conditions, and adjust the output voltage U of the zero-position detector G. G The preset zero position condition is met; Step 4: Perform zero-point balance under both forward current +I and reverse current -I to obtain the ratio of the equivalent resistances of the four terminals under forward bias, k. + Find the ratio of the reverse four-terminal equivalent resistance k-, and calculate the four-terminal equivalent resistance ratio: ； Where k represents R X / R S ; Step 5: Calculate the resistivity ratio K of the test sample X relative to the standard sample S according to the resistivity formula and geometric correction factor formula for linear four-probe bulk materials, and output the percentage change in resistivity: 。 2. The dual-arm four-probe method for comparing the resistivity of low-resistivity metals according to claim 1, characterized in that, In step 2, the dual-arm ratio bridge is configured as follows: the main arms A and B establish the main potential ratio between the standard sample S and the test sample X; the inner arms a and b proportionally compensate for the potential drop of the low-resistance connection link connecting the lower-resistance arm being compared; the balance formula is: ； Among them, the low-resistance connection link between the resistor under test and the standard resistor has a weakened first-order influence on the resistance ratio when A / B and a / b meet the preset matching conditions.

3. The dual-arm four-probe method for comparing the resistivity of low-resistivity metals according to claim 2, characterized in that, The preset matching conditions satisfy the following: Main comparison arms A and B and inner comparison arms a and b: ； Or it satisfies: ； This reduces the first-order effect of low-resistance connection links on the resistance ratio.

4. The dual-arm four-probe method for comparing the resistivity of low-resistivity metals according to claim 1, characterized in that, In step 3, the preset zero-position condition specifically refers to: ； Among them, U G U0 is the output voltage of the zero-position detector G, ranging from 10 nV to 1 μV. When the output voltage of the zero-position detector G does not meet the preset zero-position condition, the main comparison arms A and B and the inner comparison arms a and b are readjusted, or the current and temperature are stabilized before sampling is performed again.

5. The dual-arm four-probe method for comparing the resistivity of low-resistivity metals according to claim 1, characterized in that, In step 4, when zero-point balance is achieved under forward current +I and reverse current -I, the amplitudes of the forward current and reverse current are the same; k + With k - The bridge balance ratio A / B is determined based on the corresponding forward current +I and reverse current -I, respectively. When A / B and a / b meet the preset matching conditions, k + With k - It is approximately equal to the A / B value under the corresponding current polarity; the thermoelectric potential, contact thermoelectric potential and zero drift, which are independent of the test current direction, are weakened as bias terms through the processing of equation (1).

6. The dual-arm four-probe method for comparing the resistivity of low-resistivity metals according to claim 2, characterized in that, In step 5, the resistivity formula for the linear four-probe bulk material is: ； Where ρ is the sample resistivity, s is the distance between adjacent probes, U is the voltage between the two inner voltage probes, I is the test current between the two outer current probes, and F is the geometry correction factor, which is equal to the product of the thickness correction factor F1 and the edge correction factor F2. ； Once k is calculated using equation (3) that satisfies the preset matching condition, the resistivity ratio K is calculated using the following formula: ； Among them, s S s X F represents the distance between adjacent probes of the standard sample S and the test sample X, respectively. S F X These are the corresponding geometric correction factors; when the geometric dimensions, boundary conditions, and probe spacing of the standard sample S and the test sample X are the same, no geometric correction is required, therefore K=k.

7. The dual-arm four-probe method for comparing the resistivity of low-resistivity metals according to claim 6, characterized in that, The geometric correction factor F is used to correct the current field boundary effect caused by the finite thickness, finite width, finite length and probe-to-boundary distance of the bulk sample; the geometric correction factor F is obtained by four-probe correction table, standard sample calibration, analytical approximation or finite element calculation.

8. The dual-arm four-probe method for comparing the resistivity of low-resistivity metals according to claim 1, characterized in that, The method further includes a temperature gating step: synchronously acquiring the temperature T of the standard sample. S Temperature T of the sample to be tested X and base temperature T B The sample enters the valid sampling window when the following conditions are met simultaneously: ； ； ； ； ； Where θ T The temperature ranges from 0.05℃ to 0.5℃, θ R The range is 0.001℃ / s to 0.1℃ / s; when the temperature gating condition is not met, the corresponding sampling window is marked as invalid, and the process waits for thermal equilibrium, rebalancing of the bridge, or correction to the reference temperature based on the material resistance temperature coefficient.

9. The dual-arm four-probe method for comparing the resistivity of low-resistivity metals according to claim 1, characterized in that, The spacing between adjacent probes of the linear four-probe fixture is 0.5 mm to 2 mm; the probe contact pressure is 0.2 N to 1 N; and the probe material is tungsten, tungsten steel, gold-plated tungsten needle, platinum-iridium alloy, or hard conductive alloy.

10. A dual-arm four-probe device for comparing the resistivity of low-resistivity metals, used to implement the method as described in any one of claims 1-9, characterized in that, The system includes a dual-sample linear four-probe fixture for a standard sample and a test sample, a bipolar constant current source meter, a dual-ratio bridge, a zero-point detector G, a temperature monitoring module, and a control and calculation unit. The dual-sample linear four-probe fixture includes an insulating base, a standard sample support position, a test sample support position, a first elastically loaded four-probe corresponding to the standard sample support position, a second elastically loaded four-probe corresponding to the test sample support position, a contact pressure adjustment knob, shielded leads, and a temperature sensor near the test surface. It is used to fix the standard sample S and the test sample X and measure their four-terminal equivalent resistance R. S R X The dual-arm ratio bridge includes main ratio arms A and B and inner ratio arms a and b, and is configured to compare R... S With R X Zero-point ratio comparison is performed; the control and calculation unit is used to control current reversal, bridge circuit balancing, temperature gating, geometric correction, and resistivity change percentage output. The control and calculation unit stores a calculation program, which performs the following operations when executed: acquiring U... G A / B, a / b, T S T X and T B Determine the zero-point condition and temperature gating condition, and record k. + and k - Calculate k, K, and Δ, and generate a result table and variation curves for a batch of samples.

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