JPH11281599A - Method for measuring linear expansion coefficient - Google Patents
Method for measuring linear expansion coefficientInfo
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- JPH11281599A JPH11281599A JP7977898A JP7977898A JPH11281599A JP H11281599 A JPH11281599 A JP H11281599A JP 7977898 A JP7977898 A JP 7977898A JP 7977898 A JP7977898 A JP 7977898A JP H11281599 A JPH11281599 A JP H11281599A
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- change
- temperature
- linear expansion
- expansion coefficient
- measuring
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Abstract
Description
【０００１】[0001]
【発明の属する技術分野】本発明は、セラミックスやガ
ラス等の絶縁体材料の線膨張係数を測定するための測定
方法に関するものである。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a measuring method for measuring a coefficient of linear expansion of an insulating material such as ceramics and glass.
【０００２】[0002]
【従来の技術】一般に、線膨張係数測定法としては、押
棒式やＴＭＡ（Ｔｈｅｒｍｏ−Ｍｅｃｈａｎｉｃａｌ
Ａｎａｌｙｚｅｒ）、レーザー干渉法、さらに静電容量
法等が知られている。しかしながら、上記測定方法は、
測定装置が複雑、高価になる欠点がある。2. Description of the Related Art In general, as a method for measuring a coefficient of linear expansion, a push rod method or a TMA (Thermo-Mechanical) is used.
(Analyzer), a laser interferometry, a capacitance method, and the like. However, the above measurement method is
There is a disadvantage that the measuring device is complicated and expensive.
【０００３】そこで、最近、小林、佐藤等による" Ｉｍ
ｐｒｏｖｅｄ ｃａｖｉｔｙ ｒｅｓｏｎａｎｃｅ ｍ
ｅｔｈｏｄ ｆｏｒ ｎｏｎｄｅｓｔｒｕｃｔｉｖｅ
ｍｅａｓｕｒｅｍｅｎｔ ｏｆ ｃｏｍｐｌｅｘ ｐｅ
ｒｍｉｔｔｉｖｉｔｙ ｏｆｄｉｅｌｅｃｔｒｉｃ ｐ
ｌａｔｅ" （ＣＰＥＭ Ｄｉｇｅｓｔ，ｐｐ．１４７〜
１４８，１９８８）や、加屋野, 榊原, 小林らによる "
空洞共振器法による誘電体平板材料の複素誘電率の温度
特性の自動測定”（信学技法、ＭＷ９１〜７５、ｐｐ．
１１７〜１２４、Ｓｅｐ．１９９１）において、誘電体
基板の誘電定数の温度特性測定法に関する研究の中で、
金属製の円筒空洞共振器における共振周波数の温度変化
から円筒空洞共振器を構成する金属の線膨張係数を測定
することが提案されている。この方法は測定装置が簡単
でかつ絶対測定が可能であり、金属材料の新たな線膨張
係数の測定方法として注目されている。[0003] Therefore, recently, "Im" by Kobayashi, Sato et al.
Proven Cavity resonance m
method for nondestructive
measurement of complex pe
rmity ofdieelectric p
rate "(CPEM Digest, pp. 147-
148, 1988), Kayano, Sakakibara, Kobayashi et al.
Automatic Measurement of Temperature Characteristics of Complex Permittivity of Dielectric Plate Material by Cavity Resonator Method "
117-124, Sep. 1991), in a study on a method for measuring the temperature characteristics of the dielectric constant of a dielectric substrate,
It has been proposed to measure the linear expansion coefficient of the metal constituting the cylindrical cavity resonator from the temperature change of the resonance frequency in the metal cylindrical cavity resonator. This method has a simple measuring device and can perform absolute measurement, and is attracting attention as a new method for measuring a linear expansion coefficient of a metal material.
【０００４】さらに、最近では、超電導体を用いた素子
の開発に伴い、室温から数１０Ｋまでの低温領域におけ
る絶縁体材料、より具体的には回路基板や誘電体共振器
材料の線膨張係数を評価する方法が望まれている。Further, recently, with the development of devices using superconductors, the linear expansion coefficient of an insulator material, more specifically, a circuit board or a dielectric resonator material in a low temperature range from room temperature to several tens of K has been increased. An evaluation method is desired.
【０００５】[0005]
【発明が解決しようとする課題】しかしながら、上記文
献に開示された方法によれば、金属材料の線膨張係数を
測定することは可能であっても、セラミックス、ガラ
ス、有機材料などの絶縁体材料の線膨張係数を測定する
ことはできないものであった。However, according to the method disclosed in the above document, it is possible to measure the linear expansion coefficient of a metal material, but it is difficult to measure the insulating material such as ceramics, glass and organic material. Could not be measured.
【０００６】また、一般の測定方法あるいは測定器によ
って、室温から数１０Ｋまでの線膨張係数を測定するた
めには、岡路による「低温領域での変位測定技術」（計
測技術、９１年４月）においても述べられているよう
に、装置構成上、特別の工夫が必要であった。In order to measure the coefficient of linear expansion from room temperature to several tens of kilograms using a general measuring method or measuring instrument, it is necessary to use "Displacement measurement technology in low temperature region" by Okaji (measurement technology, April 1991). As described in (2) above, a special device was required for the device configuration.
【０００７】従って、本発明の目的は、簡単な装置構成
でセラミックスやガラス等の絶縁体材料の線膨張係数を
高精度に測定でき、しかも室温から数１０Ｋまでの温度
領域で測定可能な測定方法を提供することにある。Accordingly, an object of the present invention is to provide a measuring method capable of measuring the linear expansion coefficient of an insulating material such as ceramics or glass with high accuracy with a simple device configuration and capable of measuring in a temperature range from room temperature to several tens of K. Is to provide.
【０００８】[0008]
【課題を解決するための手段】本発明者等は、上記の課
題に対して検討を重ねた結果、セラミックス等の絶縁体
材料で作製した中空体内壁に導体膜を形成するととも
に、該中空体の両端面を２つの導体板で挟持した空洞共
振器を形成し、この空洞共振器の共振周波数の温度に対
する変化を測定することにより、中空体を構成するセラ
ミックス等の絶縁体材料の膨張係数を算出できることを
見いだしたものである。Means for Solving the Problems As a result of repeated studies on the above problems, the present inventors have formed a conductor film on a hollow body wall made of an insulating material such as ceramics, By forming a cavity with both end faces sandwiched between two conductor plates, and measuring the change of the resonance frequency of the cavity with respect to temperature, the expansion coefficient of the insulator material such as ceramics constituting the hollow body is determined. It has been found that it can be calculated.
【０００９】即ち、本発明の線膨張係数の測定方法は、
絶縁体材料で作製され、内壁に導体膜が被着形成された
中空体の両端面を導体板で挟持して空洞共振器を構成
し、該共振器における共振周波数の温度に対する変化を
測定し、その共振周波数の変化から前記中空体の寸法変
化を求め、その寸法変化から前記絶縁体材料の線膨張係
数を算出することを特徴とするものである。That is, the method for measuring the linear expansion coefficient of the present invention is as follows.
A hollow resonator is formed by sandwiching both end faces of a hollow body formed of an insulating material and having a conductive film adhered to the inner wall with a conductive plate, and a change in the resonance frequency of the resonator with respect to temperature is measured. A dimensional change of the hollow body is obtained from the change in the resonance frequency, and a linear expansion coefficient of the insulating material is calculated from the dimensional change.
【００１０】特に、前記空洞共振器の２種類のモードの
共振周波数の温度に対する変化を測定し、その共振周波
数の変化から、前記中空円筒の内径の寸法変化を計算
し、該内径の寸法変化から、前記中空円筒を構成する絶
縁体材料の線膨張係数を算出すること、さらには、前記
１対の導体板に、マイクロ波励振及び検波用のループア
ンテナが設けられていることが望ましい。In particular, a change in the resonance frequency of the two modes of the cavity resonator with respect to temperature is measured, and a change in the inner diameter of the hollow cylinder is calculated from the change in the resonance frequency. It is desirable that the linear expansion coefficient of the insulator material constituting the hollow cylinder be calculated, and that the pair of conductor plates be provided with a loop antenna for microwave excitation and detection.
【００１１】[0011]
【発明の実施の形態】まず、本発明の線膨張係数の測定
方法とその原理について説明する。一般に、電磁場の空
洞共振器の共振周波数は、空洞共振器の寸法と空洞共振
器内の物質の誘電率だけに依存するが、本発明によれ
ば、空洞共振器内を真空にした場合や、誘電率の温度変
化が極めて小さい空気等の気体で満たした場合には、共
振周波数の温度に対する変化が、空洞共振器の熱膨張に
よる寸法変化のみに依存することを利用し、共振周波数
の温度に対する変化を測定することにより、共振器を構
成する絶縁体材料の線膨張係数を算出するものである。DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS First, a method of measuring a linear expansion coefficient according to the present invention and its principle will be described. In general, the resonance frequency of a cavity in an electromagnetic field depends only on the dimensions of the cavity and the dielectric constant of the substance in the cavity. According to the present invention, when the inside of the cavity is evacuated, If the temperature change of the dielectric constant is filled with a gas such as air, which is extremely small, the change of the resonance frequency with respect to the temperature depends on only the dimensional change due to the thermal expansion of the cavity resonator. By measuring the change, the coefficient of linear expansion of the insulator material constituting the resonator is calculated.
【００１２】図１は、本発明の測定方法における測定シ
ステムの全体構成の一実施例を示すブロック図である。
図１によれば、シンセサイズドスイーパー１から出力さ
れたマイクロ波信号は、２つに分割され、一方は基準用
としてネットワークアナライザ２に入力される。他方
は、線膨張係数測定用の空洞共振器３に入力され、透過
した信号がネットワークアナライザ２に入力されるよう
に構成される。FIG. 1 is a block diagram showing one embodiment of the overall configuration of a measuring system in the measuring method of the present invention.
According to FIG. 1, the microwave signal output from the synthesized sweeper 1 is divided into two, and one is input to the network analyzer 2 as a reference. The other is configured to be input to the cavity resonator 3 for measuring the linear expansion coefficient and to transmit a transmitted signal to the network analyzer 2.
【００１３】線膨張係数測定用の空洞共振器３は、図２
に示すように、セラミックス等の絶縁体材料で作製した
中空円筒体あるいは中空方形体からなる中空体４の内壁
に導体膜５を形成し、中空体４の両端面を導体板６、７
で挟持してなる。The cavity 3 for measuring the linear expansion coefficient is shown in FIG.
As shown in FIG. 2, a conductor film 5 is formed on the inner wall of a hollow body 4 made of a hollow cylindrical body or a hollow rectangular body made of an insulating material such as ceramics.
In between.
【００１４】また、この空洞共振器３を、市販の高温槽
やクライオスタット（低温発生装置）内に設置すること
によって共振器３を所定の温度に設定できる。そして、
上記の構成に基づき、所定の温度に設定された空洞共振
器３は、共振器３の一対の導体板６、７に設けられた一
対のループアンテナ９を経由してネットワークアナライ
ザー２に接続されており、共振器３のその温度における
共振周波数を測定できるように構成されている。なお、
共振器３内の空洞部８は、真空あるいは大気等の誘電率
が１に近い気体が封入されるが、取り扱い及び装置の簡
略化の点から大気であることがよい。The cavity 3 can be set at a predetermined temperature by installing the cavity 3 in a commercially available high-temperature bath or cryostat (low-temperature generator). And
Based on the above configuration, the cavity resonator 3 set at a predetermined temperature is connected to the network analyzer 2 via a pair of loop antennas 9 provided on a pair of conductor plates 6 and 7 of the resonator 3. The configuration is such that the resonance frequency of the resonator 3 at that temperature can be measured. In addition,
The cavity 8 in the resonator 3 is filled with a gas having a dielectric constant close to 1 such as a vacuum or the atmosphere. However, it is preferable that the cavity 8 be the atmosphere from the viewpoint of handling and simplifying the apparatus.
【００１５】また、本発明によれば、図２に示すよう
に、上記一対の導体板６、７に、ループアンテナ９を設
けることが望ましい。このループアンテナ９は、空洞部
８の電磁場を励振及び検波するためのものである。ま
た、ループアンテナ９は、セミリジッドケーブル１０と
接続され、セミリジッドケーブル１０の一方は、シンセ
サイズドスイーパー１と接続され他方はネットワークア
ナライザ２と接続される。According to the present invention, as shown in FIG. 2, it is desirable to provide a loop antenna 9 on the pair of conductor plates 6 and 7. The loop antenna 9 is for exciting and detecting the electromagnetic field in the cavity 8. The loop antenna 9 is connected to a semi-rigid cable 10, one of the semi-rigid cables 10 is connected to the synthesized sweeper 1, and the other is connected to the network analyzer 2.
【００１６】本発明によれば、上記の測定装置を用い、
空洞共振器３の共振周波数ｆ0 の温度に対する変化が、
中空体４を構成するセラミックス等の絶縁体材料の温度
変化に伴う寸法変化だけに依存することを利用して線膨
張係数を算出する。According to the present invention, using the above measuring device,
The change of the resonance frequency f 0 of the cavity resonator 3 with respect to the temperature is
The linear expansion coefficient is calculated by utilizing only the dimensional change of the insulator material such as ceramics constituting the hollow body 4 due to the temperature change.
【００１７】具体的な測定方法として、まず、単一モー
ドの共振周波数の温度変化より、線膨張係数を算出する
場合について述べる。一般に、円筒空洞共振器のＴＥ
nml モードの共振周波数ｆ0 は下記数１の式（１）で与
えられる。ただし、ｎは円筒の回転方向における電磁界
の変化の数、ｍは円筒の径方向における電磁界の変化の
数、ｌは円筒の軸方向における電磁界の変化の数であ
り、式（１）中、ｃは光速、ｊ' nmはＪn '(x)＝０のｍ
番目の解、Ｊn '(x)はＮ次のベッセル関数の微分であ
る。Ｄは共振器の内径、Ｈは共振器の高さである。First, as a specific measuring method, a case where a linear expansion coefficient is calculated from a temperature change of a single mode resonance frequency will be described. In general, the TE of a cylindrical cavity resonator
The resonance frequency f 0 in the nml mode is given by the following equation (1). Here, n is the number of changes in the electromagnetic field in the rotational direction of the cylinder, m is the number of changes in the electromagnetic field in the radial direction of the cylinder, l is the number of changes in the electromagnetic field in the axial direction of the cylinder, and equation (1) Where c is the speed of light, j ′ nm is m of J n ′ (x) = 0
The second solution, J n '(x), is the derivative of the Nth order Bessel function. D is the inside diameter of the resonator, and H is the height of the resonator.
【００１８】[0018]
【数１】 (Equation 1)
【００１９】ここで、内径Ｄと高さＨとの比Ｓ＝Ｄ／Ｈ
は温度によらず一定であると仮定すると、式（１）から
共振器の内径Ｄが下記数２の式（２）で与えられる。Here, a ratio S = D / H between the inner diameter D and the height H
Assuming that is constant irrespective of the temperature, the inner diameter D of the resonator is given by the following equation (2) from equation (1).
【００２０】[0020]
【数２】 (Equation 2)
【００２１】さらに、基準温度（室温）での共振器の内
径Ｄ、共振周波数ｆ0 をＤ0 、ｆ00とすると、熱膨張に
よる寸法変化ΔＤ＝Ｄ−Ｄ0 をＤ0 で除した値であるΔ
Ｄ／Ｄ0 は下記数３の式（３）で与えられる。Further, assuming that the inner diameter D of the resonator at the reference temperature (room temperature) and the resonance frequency f 0 are D 0 and f 00 , the dimensional change ΔD = D−D 0 due to thermal expansion is divided by D 0. Some Δ
D / D 0 is given by the following equation (3).
【００２２】[0022]
【数３】 (Equation 3)
【００２３】実際には、ｆ00と温度Ｔにおけるｆ0(T)を
測定し、上記式（３）によりΔＤ／Ｄ0 を温度の関数と
して求める。線膨張係数はΔＤ／Ｄ0 −温度データの回
帰曲線を温度で微分して求める。In practice, f 0 (T) at f 00 and temperature T is measured, and ΔD / D 0 is obtained as a function of temperature by the above equation (3). The linear expansion coefficient is obtained by differentiating the regression curve of ΔD / D 0 -temperature data with temperature.
【００２４】さらに、高精度な測定結果を求めるために
は、２種類のモードの共振周波数の温度に対する変化を
測定することが、中空体４の両端面と２つの導体板６、
７の接触状態の変化による線膨張係数の測定誤差の発生
を抑制する上で望ましい。Further, in order to obtain a highly accurate measurement result, it is necessary to measure the change in the resonance frequency of the two modes with respect to the temperature.
It is desirable to suppress the occurrence of the measurement error of the linear expansion coefficient due to the change in the contact state of No. 7.
【００２５】そこで、２種類のモード、特にＴＥ011 モ
ードと、ＴＥ012 モードの共振周波数の温度に対する変
化の測定に基づく線膨張係数の算出方法について述べ
る。A method for calculating the coefficient of linear expansion based on the measurement of the change in the resonance frequency of the two modes, that is, the TE011 mode and the TE012 mode, with respect to the temperature will be described.
【００２６】ＴＥ011 、ＴＥ012 モードの共振周波数を
それぞれｆ1 、ｆ2 とすると，数１から次の数４中の式
（４）、式（５）が与えられる。 Assuming that the resonance frequencies of the TE 011 and TE 012 modes are f 1 and f 2 , respectively, Equations (4) and (5) in Equation 4 are given from Equation 1 below.
【００２７】[0027]
【数４】 (Equation 4)
【００２８】ただし、Ｊ' 01は、Ｊ0 '(x)＝０の１番目
の解、Ｊ0 '(x)は０次のベッセル関数の微分である。従
って、数４中の式（４）、式（５）から、共振器におけ
る円柱体の内径Ｄ、高さＨは、次の数５中の式（６）
（７）で与えられる。Here, J ′ 01 is the first solution of J 0 ′ (x) = 0, and J 0 ′ (x) is the derivative of the zero-order Bessel function. Therefore, from the equations (4) and (5) in the equation (4), the inner diameter D and the height H of the cylindrical body in the resonator are calculated by the following equation (6) in the equation (5).
Given by (7).
【００２９】[0029]
【数５】 (Equation 5)
【００３０】さらに基準温度（室温）における円柱体の
内径Ｄ、高さＨ、共振周波数ｆ1 、ｆ2 をＤ0 、Ｈ0 、
ｆ01、ｆ02とすると、温度変化に伴う熱膨張による内径
寸法変化ΔＤ＝Ｄ−Ｄ0 をＤ0 で除した値であるΔＤ／
Ｄ0 、および高さ寸法変化ΔＨ＝Ｈ−Ｈ0 をＨ0 で除し
た値であるΔＨ／Ｈ0 は下記数６の式（８）、式（９）
によって与えられる。Further, the inner diameter D, height H, and resonance frequencies f 1 , f 2 of the cylindrical body at the reference temperature (room temperature) are represented by D 0 , H 0 ,
Assuming f 01 and f 02 , a change in inner diameter dimension due to thermal expansion due to a temperature change ΔD = D−D 0 divided by D 0 ΔD /
D 0 and ΔH / H 0, which is a value obtained by dividing the height dimension change ΔH = H−H 0 by H 0 , are represented by the following equations (8) and (9).
Given by
【００３１】[0031]
【数６】 (Equation 6)
【００３２】つまり、基準温度における共振周波数
ｆ01、ｆ02と、温度Ｔにおける共振周波数ｆ1(T)、ｆ
2(T)を測定し、前記式（８）（９）によりΔＤ／Ｄ0 と
ΔＨ／Ｈ0を温度の関数として求める。このうち、ΔＨ
／Ｈ0 には、中空体４の両端面と２つの導体板６，７の
接触状態の変化による誤差が含まれている可能性があ
る。That is, the resonance frequencies f 01 and f 02 at the reference temperature and the resonance frequencies f 1 (T) and f
2 (T) is measured, and ΔD / D 0 and ΔH / H 0 are obtained as a function of temperature by the equations (8) and (9). Among them, ΔH
/ H 0 may include an error due to a change in the contact state between both end surfaces of the hollow body 4 and the two conductor plates 6 and 7.
【００３３】従って、正確な線膨張係数は、ΔＤ／Ｄ0
−温度データの回帰曲線を温度で微分することによって
求めることができる。Therefore, the exact coefficient of linear expansion is ΔD / D 0
-It can be determined by differentiating the regression curve of the temperature data with the temperature.
【００３４】[0034]
【実施例】上記の測定方法に基づき具体的にＡｌ2 Ｏ3
セラミックスの線熱膨張係数を２種類のモードを用いた
方法によって測定した。純度９９．５％Ａｌ2 Ｏ3 セラ
ミックスを被測定試料として、本発明に基づき共振周波
数の温度に対する変化の測定を測定し、熱膨張係数を算
出した。測定にあたり先ず中空体を作製した。中空体の
サイズは、空洞共振器の共振周波数を比較的測定しやす
い１０〜２０ＧＨｚとするため、内径Ｄ0 ＝３０ｍｍ、
高さＨ0＝２６ｍｍ（いずれも２５℃における寸法）の
円筒体とした。さらに、この円筒体の内面に銀ペースト
を塗布し、６５０℃で焼成した。焼結した銀の厚さは２
０〜３０μｍであった。そして、この円筒体の上下端面
を、純銅からなる厚さ２ｍｍの金属板で挟持して空洞共
振器を構成した。なお、金属板の一部には、図１に示し
たように、マイクロ波を励起，検波するためのループア
ンテナを挿入する２〜３ｍｍ径の結合口を設けた。EXAMPLE Based on the above measuring method, Al 2 O 3
The linear thermal expansion coefficient of the ceramic was measured by a method using two types of modes. Using a 99.5% pure Al 2 O 3 ceramic as a sample to be measured, a measurement of a change in resonance frequency with respect to temperature was measured based on the present invention, and a coefficient of thermal expansion was calculated. Upon measurement, a hollow body was first prepared. The size of the hollow body, for relatively easily measured 10~20GHz the resonant frequency of the cavity resonator, the inner diameter D 0 = 30 mm,
The cylindrical body had a height H 0 = 26 mm (all dimensions at 25 ° C.). Further, a silver paste was applied to the inner surface of the cylindrical body and fired at 650 ° C. The thickness of the sintered silver is 2
It was 0 to 30 μm. Then, upper and lower end surfaces of the cylindrical body were sandwiched between metal plates made of pure copper and having a thickness of 2 mm to form a cavity resonator. As shown in FIG. 1, a part of the metal plate was provided with a coupling port having a diameter of 2 to 3 mm for inserting a loop antenna for exciting and detecting microwaves.
【００３５】上記の構成からなる空洞共振器をクライオ
スタット（低温発生装置）に挿入して、１０Ｋ（ケルビ
ン）まで冷却し、その後、温度上昇させながら、各温度
におけるＴＥ011 モードの共振周波数ｆ1 とＴＥ012 モ
ードの共振周波数ｆ2 を随時測定した。なお、測定で
は、空洞共振器を組み直して２回の測定（ｆｉｒｓｔ，
ｓｅｃｏｎｄ）を行い、その結果を図３に示した。The cavity resonator having the above configuration is inserted into a cryostat (low-temperature generator), cooled to 10 K (Kelvin), and then, while the temperature is increased, the resonance frequency f 1 of the TE 011 mode at each temperature is increased. It was at any time measured the resonance frequency f 2 of the TE 012 mode. In the measurement, the cavity resonator was reassembled and the measurement was performed twice (first,
second), and the results are shown in FIG.
【００３６】最後に到達した２９３Ｋ（ケルビン）を基
準温度とし、２９３Ｋでの共振周波数ｆ1 とｆ2 をｆ01
とｆ02とした。次に、式（８）（９）により、ΔＤ／Ｄ
0 、ΔＨ／Ｈ0 を計算し、その結果を図４に示した。こ
のうち、円筒体の両端面と導体板の接触状態の変化によ
る誤差が含まれにくいΔＤ／Ｄ0 −温度のデータの回帰
曲線を温度の４次関数として求め、このΔＤ／Ｄ0 −温
度の回帰曲線を温度で微分することにより、線膨張係数
を温度の関数として求めた。その結果を図５に示した。
また、図５には文献値（ｒｅｆｅｒｅｎｃｅ）も示し
た。Using the last temperature of 293 K (Kelvin) as a reference temperature, the resonance frequencies f 1 and f 2 at 293 K are expressed as f 01
And it was set to f 02. Next, according to equations (8) and (9), ΔD / D
0 and ΔH / H 0 were calculated, and the results are shown in FIG. A regression curve of data of the temperature as a quartic function of temperature, the ΔD / D 0 - - Of these, both end faces and the conductor plate errors contained hardly [Delta] D / D 0 due to the change in the state of contact of the cylinder temperature The coefficient of linear expansion was determined as a function of temperature by differentiating the regression curve with temperature. The results are shown in FIG.
FIG. 5 also shows reference values (reference).
【００３７】図５中の文献値（ｒｅｆｅｒｅｎｃｅ）
の、線膨張係数は「Guy K White, Ronald B Roberts:
"Thermal expansion of reference material: tungst
en andα−Al2O3 ", High Temperature-High Pressure,
Vol.15, pp.321-328 (1983)」によるものであって、図
５の結果から明らかなように、本発明による算出値は、
文献値と良く一致している。また、共振器を組み直して
２回の繰り返し測定を行っても高い再現性が確認され
た。Reference values in FIG. 5 (reference)
Has a coefficient of linear expansion of "Guy K White, Ronald B Roberts:
"Thermal expansion of reference material: tungst
en andα−Al 2 O 3 ", High Temperature-High Pressure,
Vol.15, pp.321-328 (1983) ", and as is clear from the results of FIG. 5, the calculated value according to the present invention is:
Good agreement with literature values. High reproducibility was confirmed even when the resonator was reassembled and the measurement was repeated twice.
【００３８】以上の結果より、本発明の測定装置を用い
た熱膨張係数の測定精度として、文献値との差に基づけ
ば、０．１〜０．２ｐｐｍ／Ｋ程度が期待されることが
わかった。From the above results, it can be understood that the accuracy of measuring the thermal expansion coefficient using the measuring apparatus of the present invention is expected to be about 0.1 to 0.2 ppm / K based on the difference from the literature value. Was.
【００３９】[0039]
【発明の効果】以上詳述した通り、本発明の線膨張係数
の測定方法及び測定装置によれば、従来は複雑で高価な
測定装置が必要であった室温から数１０Ｋにおける絶縁
体材料の線膨張係数の測定を簡単な装置構成で且つ高精
度に行うことができる。As described above in detail, according to the method and the apparatus for measuring the coefficient of linear expansion of the present invention, the line of the insulator material from room temperature to several tens of K has conventionally required a complicated and expensive measuring apparatus. The expansion coefficient can be measured with a simple device configuration and with high accuracy.
【図１】本発明における線膨張係数の測定システムの全
体構成を説明するためのブロック図である。FIG. 1 is a block diagram illustrating an overall configuration of a system for measuring a linear expansion coefficient according to the present invention.
【図２】本発明における線膨張係数測定用の共振器構造
を示す図である。FIG. 2 is a diagram showing a resonator structure for measuring a linear expansion coefficient according to the present invention.
【図３】本発明の実施例における空洞共振器の共振周波
数ｆ1 、ｆ2 の測定結果を示す図である。FIG. 3 is a diagram showing measurement results of resonance frequencies f 1 and f 2 of the cavity resonator in the example of the present invention.
【図４】本発明に実施例における円筒体の内径Ｄと高さ
Ｈの寸法変化の算出結果を示す図である。FIG. 4 is a diagram showing a calculation result of a dimensional change of an inner diameter D and a height H of a cylindrical body according to an example of the present invention.
【図５】本発明に実施例における円筒体の線熱膨張係数
の算出結果を示す図である。FIG. 5 is a diagram showing a calculation result of a linear thermal expansion coefficient of a cylindrical body according to an example of the present invention.
１ シンセサイズドスイーパー ２ ネットワークアナライザー ３ 共振器 ４ 中空体 ５ 導体膜 ６，７ 導体板 ８ 空洞部 ９ ループアンテナ １０ セミリジッドケーブル DESCRIPTION OF SYMBOLS 1 Synthesized sweeper 2 Network analyzer 3 Resonator 4 Hollow body 5 Conductor film 6,7 Conductor plate 8 Cavity part 9 Loop antenna 10 Semi-rigid cable
Claims (3)
れ、内壁に導体膜が被着形成された中空体の両端面を導
体板で挟持して空洞共振器を構成し、該共振器における
共振周波数の温度に対する変化を測定し、その共振周波
数の変化から前記中空体の寸法変化を求め、該寸法変化
から線膨張係数を算出することを特徴とする線膨張係数
の測定方法。A hollow resonator is formed by sandwiching both end surfaces of a hollow body made of a sample to be measured made of an insulator material and having a conductor film adhered to an inner wall thereof with a conductor plate. A method of measuring a linear expansion coefficient, comprising: measuring a change in a resonance frequency with respect to a temperature; obtaining a dimensional change of the hollow body from the change in the resonance frequency; and calculating a linear expansion coefficient from the dimensional change.
波数の温度に対する変化を測定し、その共振周波数の変
化から、前記中空円筒の内径の寸法変化を計算し、該内
径の寸法変化から、前記中空円筒を構成する絶縁体材料
の線膨張係数を算出することを特徴とする請求項１記載
の線膨張係数の測定方法。2. A method for measuring a change in the resonance frequency of the two modes of the cavity with respect to temperature, calculating a change in the inner diameter of the hollow cylinder from the change in the resonance frequency, and calculating the change in the inner diameter of the hollow cylinder from the change in the inner diameter. 2. The method for measuring a linear expansion coefficient according to claim 1, wherein the coefficient of linear expansion of an insulating material forming the hollow cylinder is calculated.
けられていることを特徴とする請求項１記載の線膨張係
数の測定方法。3. The method according to claim 1, wherein a loop antenna is provided on the pair of conductor plates.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP07977898A JP3561141B2 (en) | 1998-03-26 | 1998-03-26 | Measurement method of linear expansion coefficient |
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP07977898A JP3561141B2 (en) | 1998-03-26 | 1998-03-26 | Measurement method of linear expansion coefficient |
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| Publication Number | Publication Date |
|---|---|
| JPH11281599A true JPH11281599A (en) | 1999-10-15 |
| JP3561141B2 JP3561141B2 (en) | 2004-09-02 |
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ID=13699675
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106610389A (en) * | 2015-10-22 | 2017-05-03 | 中国科学院深圳先进技术研究院 | Method for determining thermal expansion coefficient of hydrogen-containing diamond-like coating layer at low temperature |
| JP2017201840A (en) * | 2012-05-01 | 2017-11-09 | ナノトン， インコーポレイテッド | Radio frequency (rf) conductive medium |
| CN111175341A (en) * | 2019-12-10 | 2020-05-19 | 南京玻璃纤维研究设计院有限公司 | Optical test system and test method for low-temperature linear expansion coefficient of material |
| WO2020254698A1 (en) * | 2019-06-20 | 2020-12-24 | Grindosonic Bvba | Method and system for analysing a test piece using a vibrational response signal |
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1998
- 1998-03-26 JP JP07977898A patent/JP3561141B2/en not_active Expired - Fee Related
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2017201840A (en) * | 2012-05-01 | 2017-11-09 | ナノトン， インコーポレイテッド | Radio frequency (rf) conductive medium |
| CN106610389A (en) * | 2015-10-22 | 2017-05-03 | 中国科学院深圳先进技术研究院 | Method for determining thermal expansion coefficient of hydrogen-containing diamond-like coating layer at low temperature |
| CN106610389B (en) * | 2015-10-22 | 2019-10-08 | 中国科学院深圳先进技术研究院 | A method of measuring the thermal expansion coefficient of hydrogeneous diamond-like coating at low temperature |
| WO2020254698A1 (en) * | 2019-06-20 | 2020-12-24 | Grindosonic Bvba | Method and system for analysing a test piece using a vibrational response signal |
| US12061177B2 (en) | 2019-06-20 | 2024-08-13 | Grindosonic Bv | Method and system for analysing a test piece |
| CN111175341A (en) * | 2019-12-10 | 2020-05-19 | 南京玻璃纤维研究设计院有限公司 | Optical test system and test method for low-temperature linear expansion coefficient of material |
Also Published As
| Publication number | Publication date |
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