阅读说明：本技术 静态热机械分析仪测试木质文物线膨胀系数的方法及系统 (Method and system for testing linear expansion coefficient of wooden cultural relic by using static thermomechanical analyzer ) 是由 韩向娜 韩刘杨 秦振芳 吴梦若 黄琦钧 于 2021-09-23 设计创作，主要内容包括：本发明公开一种静态热机械分析仪测试木质文物线膨胀系数的方法及系统,属于分析测试技术方法领域。该方法包括：从木质文物裁切出木质文物试样并干燥,将干燥后的木质文物试样表面加工平整；将所述木质文物试样放置于静态热机械分析仪上并固定住,测量记录测试方向上的初始试样长度；设置静态热机械分析仪的升温程序并开始实验,记录所述木质文物试样的形变随温度变化的曲线；在静态热机械分析仪数据分析软件中处理试验得到的形变随温度变化的曲线,计算所述木质文物在该温度区间内的平均线膨胀系数。本方法用于木质文物线膨胀系数测试,适用于轻度、中度、重度降解木质文物在温度变化下的尺寸稳定性评估。(The invention discloses a method and a system for testing linear expansion coefficient of a wooden cultural relic by using a static thermal mechanical analyzer, belonging to the technical field of analysis and testing. The method comprises the following steps: cutting a wood cultural relic sample from the wood cultural relic, drying the wood cultural relic sample, and processing the surface of the dried wood cultural relic sample to be flat; placing the wood cultural relic sample on a static thermomechanical analyzer and fixing, and measuring and recording the length of the initial sample in the testing direction; setting a temperature rise program of a static thermomechanical analyzer, starting an experiment, and recording a curve of the deformation of the wood cultural relic sample along with the change of temperature; and (3) processing the curve of the deformation changing along with the temperature obtained by the test in data analysis software of a static thermomechanical analyzer, and calculating the average linear expansion coefficient of the wooden cultural relic in the temperature interval. The method is used for testing the linear expansion coefficient of the wooden cultural relics, and is suitable for evaluating the dimensional stability of the slightly, moderately and severely degraded wooden cultural relics under the temperature change.)

1. A method for testing linear expansion coefficient of wooden cultural relics by using a static thermomechanical analyzer is characterized by comprising the following steps:

(1) a sample preparation step: cutting a wood cultural relic sample from the wood cultural relic, drying the wood cultural relic sample, and processing the surface of the dried wood cultural relic sample to be flat;

(2) lofting: placing the wood cultural relic sample on a static thermomechanical analyzer and fixing, and measuring and recording the length of the initial sample in the testing direction;

(3) the test steps are as follows: setting a temperature rise program of a static thermomechanical analyzer, starting an experiment, and recording a curve of the deformation of the wood cultural relic sample along with the change of temperature;

(4) and (3) data processing: and (3) processing the curve of the deformation changing along with the temperature obtained by the test in data analysis software of a static thermomechanical analyzer, and calculating the average linear expansion coefficient of the wooden cultural relic in the temperature interval.

2. The method according to claim 1, wherein the sample preparation step is specifically: selecting a proper position from the wooden cultural relic, cutting and taking off the wooden cultural relic sample, drying, processing and flattening the surface of the dried wooden cultural relic sample, cutting off the uneven part on the surface of the dried wooden cultural relic sample, and slowly and lightly polishing the upper surface and the lower surface of the dried wooden cultural relic sample by using sand paper, wherein the upper surface and the lower surface are parallel and vertical to the testing direction.

3. The method of claim 1, wherein the wood cultural relic sample is nitrogen-purged and oven dried.

4. The method as claimed in claim 1, wherein in the lofting step, after drying, sample preparation and introduction of dry nitrogen for 12 hours, the length of the wood cultural relic sample is recorded as the initial length l₀。

5. The method of claim 1, wherein the probe of the static thermomechanical analyzer is a quartz compression probe, the probe loading range is 0-1.8N, the loading resolution is 9.8 μ η ι, and the displacement resolution is 0.01 μ η ι.

6. The method according to claim 1, wherein the lofting step is embodied as: placing the wood cultural relic sample on a compression clamp base of a static thermomechanical analyzer, fixing the wood cultural relic sample by a probe of the static thermomechanical analyzer with a proper constant load, and measuring and recording the initial sample length in the testing direction; and lightly pressing the tip of the probe at the central position of the wooden cultural relic sample during testing, repeatedly lifting the probe after compaction, and confirming that the tip of the probe is stably contacted with the wooden cultural relic sample without shaking the wooden cultural relic sample.

7. The method according to claim 1, characterized in that the test steps are in particular: setting a temperature rise program of a static thermomechanical analyzer, starting a test, measuring the relation between the deformation and the temperature of the wood cultural relic sample in a dry nitrogen environment at a program control temperature rising at a constant speed, and recording a curve of the deformation along with the change of the temperature; when the temperature program of the temperature raising program is set, the test temperature interval comprises an effective data temperature interval, the test starting temperature is lower than the lower limit of the effective data interval by 30 ℃, and the test finishing temperature is higher than the upper limit of the data acquisition temperature interval by 20 ℃.

8. The method according to claim 1, wherein the data processing steps are in particular: and opening a curve of deformation changing along with temperature obtained by the test in data analysis software of a static thermomechanical analyzer, selecting a target temperature interval, and automatically calculating by the data analysis software to obtain the average linear expansion coefficient of the measured wooden cultural relic in the temperature interval.

9. Method according to claim 8, characterized in that during the calculation the temperature interval (t) is calculated₁,t₂) Inner mean linear expansion coefficient alpha_lIs calculated by the formulaWherein l_tThe real-time sample length corresponding to the temperature at this point,/₀Is the initial sample length.

10. A system for testing the coefficient of linear expansion of a wooden cultural relic by using a static thermomechanical analyzer, characterized in that the system operates based on the method according to any one of claims 1 to 9, and in particular comprises:

the sample preparation unit is used for cutting a wooden cultural relic sample from the wooden cultural relic, drying the wooden cultural relic sample and processing the surface of the dried wooden cultural relic sample to be smooth;

the lofting unit is used for placing and fixing the wood cultural relic sample on a static thermomechanical analyzer, and measuring and recording the length of an initial sample in the testing direction;

the test unit is used for setting a temperature rise program of the static thermomechanical analyzer, starting an experiment and recording a curve of the deformation of the wood cultural relic sample along with the change of temperature;

and the data processing unit is used for processing the curve of the deformation along with the temperature change obtained by the test in the data analysis software of the static thermomechanical analyzer and calculating the average linear expansion coefficient of the wooden cultural relic in the temperature interval.

Technical Field

The invention belongs to the technical field of analysis and test, and particularly relates to a method and a system for testing linear expansion coefficient of a wooden cultural relic by using a static thermal mechanical analyzer.

Background

The wooden cultural relics are usually buried in an underground environment or an underwater environment for a long time, and the wooden cultural relics have the problem of unstable size after archaeological excavation. The natural anisotropy of the wood causes different size variation in the axial direction, the radial direction and the chord direction, and the mismatching of linear expansion coefficients in the three directions easily causes deformation and distortion of the wooden cultural relics, so that the safety risk is increased. The wood cultural relics are nonuniformly degraded in the burying process, the physical and chemical properties of the wood cultural relics are greatly changed compared with those of modern healthy wood, and the linear expansion rule of the wood cultural relics is different from that of the modern healthy wood. The temperature fluctuation of the wooden cultural relics in the cultural relic storeroom and the like can cause the size of the wooden cultural relics to change, so that the accurate measurement of the linear expansion coefficients of the wooden cultural relics in the axial direction, the radial direction and the chord direction has important significance for mastering the change rule of the size of the wooden cultural relics along with the temperature and evaluating the storage safety of the wooden cultural relics.

The linear expansion coefficient is the ratio of the change in length of a solid substance per 1 ℃ change in temperature to its length at the initial temperature. The existing method for detecting the linear expansion coefficient of the archaeological material only comprises a thermal expansion instrument, generally the temperature is increased to more than 800 ℃ from room temperature, the size is required to be 25mm multiplied by 5mm, the method is mainly used for detecting the firing temperature of pottery and porcelain, and the method is not used in wooden cultural relics. The wood cultural relics are generally large in nonuniformity and limited in large-size sampling, and the linear expansion coefficient measurement in storage is carried out in a cold winter and a hot summer, and the measurement of the linear expansion coefficient comprises a general environment temperature range of a storehouse, such as-10-50 ℃, and a thermal expansion instrument is not suitable for low-temperature region measurement, so that the measurement of the linear expansion coefficient of the wood cultural relics cannot be used for detecting the linear expansion coefficient of the wood.

Static Thermomechanical analysis (TMA) is a technique for precisely measuring the relationship between the deformation and temperature of a sample under the conditions of program temperature control and non-vibration load, and is suitable for the linear expansion test of materials such as plastics. The method has the advantages of small sample amount (the height of the sample in the testing direction is larger than 2 mm), high sensitivity (the load resolution is 9.8 mu N and the deformation resolution is 0.01 mu m), temperature control range of-98-600 ℃, meeting the testing requirement of the actual storage environment of the cultural relics, and continuously introducing nitrogen into the sample furnace to keep the sample in a dry state and avoid the influence of humidity change. Therefore, the coefficient of linear expansion of the wooden cultural relics is expected to be tested by utilizing static thermomechanical analysis, and no patent and literature report of a related method is found at present.

Disclosure of Invention

The invention provides a method and a system for testing linear expansion coefficient of a wooden cultural relic by using a static thermomechanical analyzer. The method is used for testing the linear expansion coefficient of the wooden cultural relics, and is suitable for evaluating the dimensional stability of the slightly, moderately and severely degraded wooden cultural relics under the temperature change.

According to the first aspect of the technical scheme, the invention provides a method for testing the linear expansion coefficient of a wooden cultural relic by using a static thermomechanical analyzer, which comprises the following steps:

(1) a sample preparation step: cutting a wood cultural relic sample from the wood cultural relic, drying the wood cultural relic sample, and processing the surface of the dried wood cultural relic sample to be flat;

(2) lofting: placing the wood cultural relic sample on a static thermomechanical analyzer and fixing, and measuring and recording the length of the initial sample in the testing direction;

(3) the test steps are as follows: setting a temperature rise program of a static thermomechanical analyzer, starting an experiment, and recording a curve of the deformation of the wood cultural relic sample along with the change of temperature;

(4) and (3) data processing: and (3) processing the curve of the deformation changing along with the temperature obtained by the test in data analysis software of a static thermomechanical analyzer, and calculating the average linear expansion coefficient of the wooden cultural relic in the temperature interval.

Preferably, the sample preparation step specifically comprises: selecting a proper position from the wooden cultural relic, cutting and taking off the wooden cultural relic sample, drying, processing and flattening the surface of the dried wooden cultural relic sample, cutting off the uneven part on the surface of the dried wooden cultural relic sample, and slowly and lightly polishing the upper surface and the lower surface of the dried wooden cultural relic sample by 600-mesh abrasive paper in a direction parallel to the testing direction.

Preferably, the wood cultural relic sample has a moisture state of absolutely dry.

Preferably, the wood cultural relic sample is in a nitrogen-blown dry state, so that errors caused by moisture absorption of the sample in the testing process are avoided.

Preferably, the drying method in a nitrogen-blowing oven-dry state is as follows: and placing the wooden cultural relic sample in a pricking hole sealing bag, slowly drying at a speed of slowing down water evaporation (drying time is 3-10 days), then transferring the wooden cultural relic sample into a 50 ℃ oven for drying, placing the wooden cultural relic sample into a static thermal mechanical analyzer furnace body before testing, and introducing dry nitrogen for 12 hours to ensure that the wooden cultural relic is absolutely dry.

Preferably, the side length of the wooden cultural relic sample is 5.00-10.00 mm.

Preferably, in the lofting step, after drying, sample preparation and introduction of dry nitrogen for 12 hours, the length of the wood cultural relic sample at the moment is recorded as the initial length l₀。

Preferably, in the testing step, the temperature control assembly is arranged in the static thermomechanical analyzer, and in order to achieve low temperature below zero and ensure high temperature test safety, an external cold machine is used for refrigeration, the temperature control range of the cold machine is-98-600 ℃, and the cooling method is an electronic cooling mode.

Preferably, in the testing step, the protective gas in the sample furnace of the static thermomechanical analyzer is normal nitrogen, and is provided by an external compressed gas cylinder, and the flow rate is 200 mL/min.

Preferably, a probe of the static thermomechanical analyzer is a quartz compression probe, the load range of the probe is as low as 0-1.8N, the load resolution is 9.8 μ N, the displacement resolution is 0.01 μm, the test precision condition can meet the requirement that extremely fragile archaeological wood samples are not damaged, the micro deformation of small-size samples can be accurately measured, and the precision is extremely high.

Preferably, the lofting step specifically comprises: placing the wood cultural relic sample on a compression clamp base of a static thermomechanical analyzer, fixing the wood cultural relic sample by a probe of the static thermomechanical analyzer with a proper constant load, and measuring and recording the initial sample length in the testing direction; and lightly pressing the tip of the probe at the central position of the wooden cultural relic sample during testing, repeatedly lifting the probe after compaction, and confirming that the tip of the probe is stably contacted with the wooden cultural relic sample without shaking the wooden cultural relic sample.

Preferably, in the lofting step, the probe applies a constant load of 50 μ N to the wood relic sample; when the sample is extremely fragile, the constant load applied by the probe to the wood cultural relic sample is 20 mu N, so that the wood cultural relic sample is completely contacted with the probe without damage or deformation influenced by the load in the test process.

Preferably, the testing steps are specifically: setting a temperature rise program of a static thermomechanical analyzer, starting a test, measuring the relation between the deformation and the temperature of the wood cultural relic sample in a dry nitrogen environment at a program control temperature rising at a constant speed, and recording a curve of the deformation along with the change of the temperature.

Preferably, the temperature rise program is set by adopting a constant-speed temperature rise method, and the temperature rises at a speed not exceeding 5 ℃/min, so that the size of the sample linearly changes along with the temperature in a relatively stable state, and the test error and the fragile sample damage caused by too fast temperature rise are avoided.

Preferably, when the temperature program of the temperature program is set, in order to eliminate the influence of the initial temperature rise process and the continuous temperature rise process before the end of the instrument, and improve the data accuracy, the test temperature interval should include an effective data temperature interval, the test start temperature is lower than the lower limit of the effective data interval by 30 ℃, and the test end temperature is higher than the upper limit of the data acquisition temperature interval by 20 ℃.

The temperature change interval of the environment of a common cultural relic storehouse of the wooden cultural relics is-10 ℃ to 50 ℃, and the testing temperature interval is set to-40 ℃ to 70 ℃.

Preferably, the data processing step specifically includes: and opening a curve of deformation changing along with temperature obtained by the test in data analysis software of a static thermomechanical analyzer, selecting a target temperature interval, and automatically calculating by the data analysis software to obtain the average linear expansion coefficient of the measured wooden cultural relic in the temperature interval.

Preferably, in the calculation procedure, the temperature interval (t) is calculated₁,t₂) Inner mean linear expansion coefficient alpha_lIs calculated by the formula Wherein l_tThe real-time sample length corresponding to the temperature at this point,/₀Is the initial sample length.

Preferably, the linear expansion coefficients of the wood cultural relics in the three anatomical directions of the axial direction, the radial direction and the chord direction are respectively tested by adopting the method.

According to a second aspect of the technical solution of the present invention, there is provided a system for testing linear expansion coefficient of wooden cultural relics by using a static thermo-mechanical analyzer, wherein the system is operated based on the method according to any one of the above aspects, and specifically comprises:

the sample preparation unit is used for cutting a wooden cultural relic sample from the wooden cultural relic, drying the wooden cultural relic sample and processing the surface of the dried wooden cultural relic sample to be smooth;

the lofting unit is used for placing and fixing the wood cultural relic sample on a static thermomechanical analyzer, and measuring and recording the length of an initial sample in the testing direction;

the test unit is used for setting a temperature rise program of the static thermomechanical analyzer, starting an experiment and recording a curve of the deformation of the wood cultural relic sample along with the change of temperature;

and the data processing unit is used for processing the curve of the deformation along with the temperature change obtained by the test in the data analysis software of the static thermomechanical analyzer and calculating the average linear expansion coefficient of the wooden cultural relic in the temperature interval.

Compared with the prior art, the invention has the advantages that:

(1) the test can be carried out only by using small wooden cultural relic samples with the side length of 2 mm-10 mm, the data efficiency is high, and massive sampling and large-size sampling of the cultural relics are avoided.

(2) The temperature change range of the environment of the cultural relic storehouse in the preservation process of the wooden cultural relics is covered, and the test from low temperature to room temperature can be carried out.

(3) The static thermomechanical analyzer can provide 50mN micro load, is suitable for wooden cultural relic samples with low archaeological unearthing strength, has extremely high displacement sensitivity, can be accurate to 0.01 mu m, and has high data accuracy and good repeatability.

Drawings

FIG. 1 is a flow chart of the method for testing linear expansion coefficient of wooden cultural relics by using the static thermomechanical analyzer.

FIG. 2 is a schematic diagram of the structure and testing principle of the static thermomechanical analyzer of the present invention.

Fig. 3 is a schematic diagram showing the arrangement of a compression probe, a clamp and a sample of a static thermo-mechanical analyzer in the method for testing the linear expansion coefficient of the wood cultural relic.

Fig. 4 is an actual view of a wood relic sample in the method for testing linear expansion coefficient of the wood relic, which is disclosed by the embodiment 4 of the method for testing linear expansion coefficient of the wood relic.

FIG. 5 is a graph showing the three-dimensional length of a wooden relic sample according to the temperature change in the example 4 of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.

The following detailed description of specific embodiments of the invention refers to the accompanying drawings.

As shown in fig. 1, the method for testing linear expansion coefficient of wooden cultural relics provided by the technical scheme of the invention comprises the following steps:

step 101: selecting a proper position from the wooden cultural relic, cutting and taking a sample with the side length of about 5.00-10.00 mm, drying the sample, and processing the surface of the dried wooden cultural relic sample to be smooth;

step 102: placing on a compression fixture base of a static thermomechanical analyzer, holding the sample with a probe under a suitable constant load, and measuring at room temperature the initial length of the recorded sample in the test direction;

step 103: setting a temperature rise program of a static thermomechanical analyzer, starting a test, and recording a curve of deformation along with temperature change;

step 104: and (3) processing the deformation-temperature curve obtained by the test in data analysis software of a static thermomechanical analyzer, and calculating to obtain the average linear expansion coefficient of the measured wooden cultural relic in the temperature interval.

The method comprises the steps of sample preparation and drying, sample initial length data measurement and other pretreatment steps, and the test method comprises the steps of placing a wood cultural relic sample to be tested on a compression clamp base of a static thermomechanical analyzer, fixing the sample by a probe under a proper constant load, measuring the functional relation of the vertical deformation of the wood cultural relic sample along with the temperature change under the program control temperature of uniform speed rise in a dry nitrogen environment, and obtaining the linear expansion coefficient of the wood cultural relic sample according to a deformation-temperature curve. The method has the advantages of small needed wood sample amount, small size and high sensitivity, is suitable for the wood cultural relics with low, medium and high degradation degrees, can accurately measure the linear expansion coefficient of the wood cultural relics under the condition of micro-damage sampling, and effectively evaluates the storage stability of the wood cultural relics.

Example 1

The average linear expansion coefficient of a sample of the sinking ship board No. I in south China sea at the temperature of-10-50 ℃ is tested by the thermo-mechanical analysis method, the wood species are identified to be hardwood pine, the wood species are severely degraded, and the maximum water content is 242.77%. The sample is cut into cuboid test blocks, and the initial lengths in the axial direction, the radial direction and the chord direction are respectively 4.141mm, 4.605mm and 6.722mm after drying and polishing. As shown in fig. 2 to 3, the fitting for volume expansion of the static thermomechanical analyzer comprises a compression probe and a compression clamp base, a test is started by placing a sample on the compression clamp base and closing a sample furnace, a temperature change is controlled by a temperature control component arranged in the thermomechanical analyzer and an external cold machine, a load is provided by the compression probe and displacement change is recorded, a constant load is set to be 50mN, a test temperature range is set to be-40 ℃ to 70 ℃, the temperature is controlled to rise at a rate of 5 ℃/min, and a curve of deformation along with temperature change is recorded. Processing the test in data processing software of a static thermomechanical analyzerThe three-way average linear expansion coefficients of the sample at-10 ℃ to 50 ℃ are calculated to be 4.331 multiplied by 10 respectively according to the obtained deformation-temperature curve^-5 1/℃、4.387×10^-5 1/℃、3.124×10^-5 1/℃。

Example 2

The average linear expansion coefficient of the Nanhai No. I wood member sample at-10-50 ℃ is tested by the thermo-mechanical analysis method, the tree species of the wood is identified as cypress, the cypress belongs to moderate degradation, and the maximum water content is 315.73%. The sample is cut into cuboid test blocks, and the initial lengths in the axial direction, the radial direction and the chord direction are respectively 6.064mm, 4.743mm and 3.462mm after drying and polishing. Placing the sample on a compression clamp base and starting a test, setting a constant load to be 50mN, setting a test temperature range to be-40-70 ℃, controlling the temperature to rise at a speed of 5 ℃/min, and recording a curve of deformation along with temperature change. The deformation-temperature curve obtained by the test is processed in the data processing software of the static thermomechanical analyzer, and the three-way average linear expansion coefficient of the sample at-10 ℃ to 50 ℃ is calculated to be 3.857 multiplied by 10^-5 1/℃、3.890×10^-5 1/℃、5.545×10^-5 1/℃。

Example 3

The average linear expansion coefficient of a Nanhai No. I ship wood sample at the temperature of between 10 ℃ below zero and 50 ℃ is tested by the thermo-mechanical analysis method, the tree species of the wood is identified to be liquidambar formosana, the wood is severely degraded, and the maximum water content is 511.42%. The sample is cut into cuboid test blocks, and the initial lengths in the axial direction, the radial direction and the chord direction are respectively 3.635mm, 4.789mm and 2.473mm after drying and polishing. Placing the sample on a compression clamp base and starting a test, setting a constant load to be 50mN, setting a test temperature range to be-40-70 ℃, controlling the temperature to rise at a speed of 5 ℃/min, and recording a curve of deformation along with temperature change. The deformation-temperature curve obtained by the test is processed in the data processing software of the static thermomechanical analyzer, and the three-way average linear expansion coefficient of the sample at-10 ℃ to 50 ℃ is calculated to be 3.968 multiplied by 10^-5 1/℃、3.641×10^-5 1/℃、3.248×10^-5 1/℃。

Example 4

The average linear expansion coefficient of a Nanhai No. I sunken ship scattered wood sample at the temperature of-10-50 ℃ is tested by the thermo-mechanical analysis method, the tree species of the wood is identified to be persimmon wood, the persimmon wood is severely degraded, and the maximum water content is 561.82%. The sample is cut into cuboid test blocks, and the initial lengths in the axial direction, the radial direction and the chord direction are respectively 5.035mm, 5.068mm and 2.037mm after the test blocks are dried and polished. Placing the sample on a compression clamp base and starting a test, setting a constant load to be 50mN, setting a test temperature range to be-40-70 ℃, controlling the temperature to rise at a speed of 5 ℃/min, and recording a curve of deformation along with temperature change. The test was repeated three times as shown in fig. 3, and the deformation-temperature curves obtained from the test were processed in a static thermomechanical analyzer data processing software as shown in fig. 4. The three-way average linear expansion coefficients of the sample at-10 ℃ to 50 ℃ are calculated to be 3.744 multiplied by 10 respectively^-51/℃、3.914×10^-5 1/℃、3.894×10^-5 1/℃。

Example 5

The average linear expansion coefficient of a sample of the 'south sea I' sunken ship plank floor at-10-50 ℃ is tested by the thermo-mechanical analysis method, the tree species of the wood is identified as banyan, the banyan belongs to severe degradation, and the maximum water content is 710.03%. The sample is cut into cuboid test blocks, and the initial lengths in the axial direction, the radial direction and the chord direction are respectively 6.138mm, 4.821mm and 4.119mm after drying and polishing. Placing the sample on a compression clamp base and starting a test, setting a constant load to be 20mN, setting a test temperature range to be-40-70 ℃, controlling the temperature to rise at a speed of 5 ℃/min, and recording a curve of deformation along with temperature change. The test is repeated three times, the deformation-temperature curve obtained by the test is processed in the data processing software of the static thermomechanical analyzer, and the three-way average linear expansion coefficient of the sample at minus 10 ℃ to 50 ℃ is calculated to be 3.413 multiplied by 10 respectively^-5 1/℃、4.322×10^-5 1/℃、3.205×10^-5 1/℃。

The foregoing embodiments and description have been presented only to illustrate the principles and preferred embodiments of the invention, and various changes and modifications may be made therein without departing from the spirit and scope of the invention as hereinafter claimed.