WO2012002493A1 - 光学ガラスの仮想温度の測定方法 - Google Patents
光学ガラスの仮想温度の測定方法 Download PDFInfo
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- WO2012002493A1 WO2012002493A1 PCT/JP2011/065053 JP2011065053W WO2012002493A1 WO 2012002493 A1 WO2012002493 A1 WO 2012002493A1 JP 2011065053 W JP2011065053 W JP 2011065053W WO 2012002493 A1 WO2012002493 A1 WO 2012002493A1
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
- G01N29/22—Details, e.g. general constructional or apparatus details
- G01N29/30—Arrangements for calibrating or comparing, e.g. with standard objects
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N25/00—Investigating or analyzing materials by the use of thermal means
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01K—MEASURING TEMPERATURE; MEASURING QUANTITY OF HEAT; THERMALLY-SENSITIVE ELEMENTS NOT OTHERWISE PROVIDED FOR
- G01K11/00—Measuring temperature based upon physical or chemical changes not covered by groups G01K3/00, G01K5/00, G01K7/00 or G01K9/00
- G01K11/22—Measuring temperature based upon physical or chemical changes not covered by groups G01K3/00, G01K5/00, G01K7/00 or G01K9/00 using measurement of acoustic effects
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
- G01N29/04—Analysing solids
- G01N29/07—Analysing solids by measuring propagation velocity or propagation time of acoustic waves
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
- G01N29/44—Processing the detected response signal, e.g. electronic circuits specially adapted therefor
- G01N29/4472—Mathematical theories or simulation
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2291/00—Indexing codes associated with group G01N29/00
- G01N2291/02—Indexing codes associated with the analysed material
- G01N2291/023—Solids
- G01N2291/0232—Glass, ceramics, concrete or stone
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2291/00—Indexing codes associated with group G01N29/00
- G01N2291/02—Indexing codes associated with the analysed material
- G01N2291/028—Material parameters
- G01N2291/02881—Temperature
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2291/00—Indexing codes associated with group G01N29/00
- G01N2291/04—Wave modes and trajectories
- G01N2291/042—Wave modes
- G01N2291/0423—Surface waves, e.g. Rayleigh waves, Love waves
Definitions
- the present invention relates to glass used for optical applications such as lenses, prisms, and photomasks, and more particularly to a method for measuring a virtual temperature that affects the refractive index, transmittance, ultraviolet resistance, and expansion coefficient of optical glass.
- quartz glass has three major characteristics: extremely high light transmittance, excellent heat resistance, and extremely low metal impurities, and is indispensable as a material for manufacturing semiconductor devices and cable materials for optical communication. It is a material that can not be.
- Silica-titania glass TiO 2 —SiO 2 glass
- EUVL extreme ultraviolet lithography
- Quartz glass manufacturing methods are roughly classified into two types: fused quartz glass obtained by melting natural quartz powder, and synthetic quartz glass that is chemically synthesized.
- a gel body is formed by hydrolysis and polycondensation reaction in a solution obtained by adding water, alcohol or hydrochloric acid to silicon alkoxide such as Si (OC 2 H 5 ) 4, and after drying this There is a sol-gel method for vitrification by heating.
- synthetic quartz glass with less metal impurities of 10 ppb or less is used.
- Optical applications generally require uniformity of refractive index, high transmittance, no defects that cause light scattering, and the like for lenses for reduction projection exposure devices (steppers).
- the refractive index, transmittance, and UV resistance of synthetic quartz glass and silica / titania glass vary depending on the concentration of OH groups, other impurities, and F and Ti added as additives.
- the OH concentration mixed during the manufacturing process is usually 500 to 2000 [wtppm] in the synthetic quartz glass of the direct method (type III), and is produced by the vapor phase axial (VAD) method, which is one of the soot methods. Since synthetic quartz glass has a concentration of 50 to 200 [wtppm], it is important to control the concentration of impurities such as OH during the manufacturing process in addition to the concentration control of additives.
- Non-Patent Document 1 As a method for measuring the virtual temperature, a method using Raman spectroscopy or a method using infrared spectroscopy is used.
- the method shown in Non-Patent Document 1 For the measurement of the fictive temperature by infrared spectroscopy, the method shown in Non-Patent Document 1 is well known.
- the method shown in Non-Patent Document 2 As a method for measuring a fictive temperature by Raman spectroscopy, the method shown in Non-Patent Document 2 is well known.
- Non-Patent Document 3 a method for obtaining a virtual temperature from a measured value of density using the relationship between the density of synthetic quartz glass and a virtual temperature is also known.
- Non-Patent Document 4 reports that there is a linear relationship between the virtual temperature obtained from the density and the longitudinal wave velocity using the relationship between temperature and density.
- Non-Patent Document 3 reports that the gradient of the fictive temperature dependence of density varies with the chlorine concentration.
- Non-Patent Document 5 reports that the gradient of the virtual temperature dependence of density does not change depending on the OH concentration. As a result of further investigation, it was found that the coefficient fluctuates depending on the OH concentration contained in quartz glass, and it is difficult to introduce density measurement into the production line. This has led to the present invention.
- the present invention solves the conventional problems related to the virtual temperature measurement method for optical glass, and does not require the preparation of a special sample for virtual temperature measurement, and is capable of measuring the virtual temperature with higher accuracy than before. It is an object to provide a method for measuring the fictive temperature of glass.
- the method of measuring the fictive temperature of the optical glass according to the second aspect of the present invention (2-A) a step of performing heat treatment at different heat treatment temperatures for a plurality of calibration curve preparing glass samples having the same composition; (2-B) For the sample obtained in the step (2-A), one of the longitudinal wave velocity, the LSAW velocity, and the transverse wave velocity and the other one are set to the first acoustic characteristic AP 1 and the second acoustic wave, respectively.
- the present invention it is possible to measure a virtual temperature with an accuracy one digit higher than that of a conventional virtual temperature measurement method, and it is possible to measure a virtual temperature of a material to be a product in a production line. It is possible to provide a method for measuring the virtual temperature of an optical glass capable of measuring the in-plane distribution of the virtual temperature of the sample to be measured.
- the basic concept of the “virtual temperature measurement method” of the present invention is to improve the characteristics by adding not only synthetic quartz but also additives (fluorine, germanium, phosphorus, boron, etc.) according to the application.
- concentration of a synthetic quartz glass sample, a strain point, a slow cooling point, and its preparation method It is a figure which shows the relationship between the heat processing temperature with respect to synthetic quartz glass # 1 and # 2, and an acoustic characteristic, A is a figure which shows the relationship between heat processing temperature and longitudinal wave sound velocity, B shows the relationship between heat processing temperature and LSAW velocity. It is a figure, C is a figure which shows the relationship between heat processing temperature and a shear-wave sound speed, D is a figure which shows the relationship between heat processing temperature and a density. It is a figure which shows the relationship between the longitudinal wave sound velocity and density with respect to synthetic quartz glass # 1 and # 2.
- A is a figure which shows the relationship between virtual temperature and longitudinal wave sound velocity
- B shows the relationship between virtual temperature and LSAW velocity
- C is a figure which shows the relationship between heat processing temperature and a sound wave velocity
- D is a figure which shows the relationship between fictive temperature and density.
- Table 2 which shows the sensitivity with respect to virtual temperature of the acoustic characteristic of synthetic quartz glass, and resolution
- Table 1 shown in FIG. 1 shows the specifications of the sample used in the examination experiment in carrying out the present invention.
- the OH concentration was determined based on the method shown in Reference Document 1.
- Synthetic quartz glass sample # 1 and sample # 2 have different OH concentrations and different glass characteristic temperatures (strain point and annealing point) because of different manufacturing processes. The values of strain point and annealing point are based on the data of the quartz glass manufacturer.
- Samples prepared to create a calibration curve are # 1 cut out from one glass ingot and # 2 cut out from another glass ingot, each sample size is 60mm x 60mm ⁇ 15mm. Four samples cut from the same ingot are considered to have the same composition.
- the samples shown in Table 1 were heat-treated in air using a high temperature electric furnace. First, in order to erase the thermal history of the sample, it was raised to a temperature about 50 ° C. higher than the annealing point of each sample, and then held for 5 hours (hereinafter, time is represented by h). Then, after the desired heat treatment temperature T A at a cooling rate of 5-10 ° C. / h, the samples were held for a long time in consideration of the structural relaxation time of each sample, release in the furnace by turning off the heater Chilled. Each sample was placed in a furnace with two 70 mm x 70 mm x 10 mm quartz glass plates sandwiched so that the fictive temperature distribution during heat treatment was small. The holding temperature of each sample was 1050, 1100, 1150, 1200 ° C. for the four samples # 1, respectively, 900, 1000, 1050, 1100 ° C. for the four samples # 2.
- the sample was shaped into a size of 50 mm x 35 mm x 10 mm, and the 50 mm x 35 mm surface was optically polished on both sides.
- the LSAW velocity was measured for the prepared sample using a linearly focused beam ultrasonic material analysis (LFB-UMC) system with an ultrasonic frequency of 225 MHz.
- LLB-UMC linearly focused beam ultrasonic material analysis
- the measurement principle and method of LSAW speed are detailed in Reference 2 and Reference 3.
- longitudinal wave velocity and shear wave velocity were measured at an ultrasonic frequency of 50-250 MHz using a bulk planar ultrasonic material analysis (PW-UMC) system.
- PW-UMC bulk planar ultrasonic material analysis
- the measurement principle and method of longitudinal wave velocity and shear wave velocity are detailed in Reference Document 4.
- the density ⁇ was measured based on Archimedes' principle. The measurement was performed based on Reference 5.
- the system is calibrated using standard samples with longitudinal wave velocity, shear wave velocity, and density measurement. (Reference 6).
- Figure 2 shows the results obtained, the relationship of the sample # 1 and # each four heat treatment temperature for 2 (retention temperature) T A and the acoustic properties of the synthetic quartz glass of the measurement.
- the relationship between the heat treatment temperature and each acoustic characteristic was linear at temperatures below about 50 ° C below the annealing point (see Fig. 1). Deviated from its linearity. This is because the structural relaxation time is shortened when the heat treatment temperature is increased, and the fictive temperature becomes lower than the heat treatment temperature in the cooling process of the sample. In addition, when the cooling is performed in a time sufficiently shorter than the structure relaxation time, the fictive temperature becomes equal to the heat treatment temperature. From the results of FIG. 2, with respect to the heat treatment temperature T A, the change in longitudinal wave sound velocity it was found to be greatest.
- FIG. 3 shows the result of determining the relationship between the longitudinal wave sound velocity and the density with the largest change with respect to the heat treatment temperature.
- a linear relationship between longitudinal wave velocity and density was obtained for both synthetic quartz glass # 1 and # 2.
- an approximate line is obtained by the least square method in data in a temperature range in which the heat treatment temperature and the virtual temperature can be regarded as being equal to each other, and on each approximate line corresponding to the longitudinal wave sound velocity of each sample in FIG.
- FIG. 3 shows the least square method in data in a temperature range in which the heat treatment temperature and the virtual temperature can be regarded as being equal to each other, and on each approximate line corresponding to the longitudinal wave sound velocity of each sample in FIG.
- FIG. 4A shows the result of plotting the corrected heat treatment temperature on the approximate line as the virtual temperature. That is, the two approximate lines are obtained from the data excluding the data of sample # 1 with heat treatment temperature of 1200 ° C. and sample # 2 with heat treatment temperatures of 1050 ° C. and 1100 ° C. in FIG. 2A.
- the corrected heat treatment temperature is obtained as shown in FIG. 4A by plotting the longitudinal wave sound speeds of the four samples # 1 and the longitudinal wave sound speeds of the four samples # 2.
- the LSAW speed in FIG. 2B, the transverse wave speed in FIG. 2C, the density in FIG. 2D are plotted, and these approximate lines are shown in FIGS. 4B and 4C. , 4D respectively. It can be seen that both characteristics have good linearity.
- Table 2 in Fig. 5 shows the sensitivity and resolution of the acoustic characteristics with respect to the virtual temperature. From this result, it can be seen that the resolution of longitudinal sound velocity is very high at 0.3-0.4 ° C against the virtual temperature. Conventionally, the fictive temperature is measured by infrared spectroscopy or Raman spectroscopy, but the resolution is ⁇ 15 ° C. [Non-Patent Document 1] and ⁇ 60 ° C. [Non-Patent Document 2], respectively. For this reason, the measurement of the virtual temperature by the longitudinal wave velocity is 40 to 150 times higher than the conventional method and is extremely useful as a virtual temperature measurement method.
- the approximate straight line in FIG. 4A is obtained as shown in Equation (1).
- the longitudinal acoustic wave velocity V L is measured for the synthetic quartz glass to be measured having the same composition as the sample # 1 or # 2
- the virtual temperature T f can be obtained using the equation (1).
- the LSAW velocity or shear wave sound velocity data shown in FIGS. 2B and 2C the LSAW velocity or shear wave velocity of the synthetic quartz glass to be measured having the same composition is measured by directly determining the approximate heat treatment temperature as a virtual temperature.
- the virtual temperature can be calculated from the approximate straight line.
- an approximate linear expression (1) indicating the relationship between the virtual temperature and the longitudinal wave sound velocity shown in FIG. 4A by the longitudinal wave sound velocity with high sensitivity to the virtual temperature is obtained.
- the virtual temperatures of Samples # 1 and # 2 plotted in the approximate straight line are obtained by correcting the heat treatment temperatures of Samples # 1 and # 2 in FIG. 2.
- the corrected heat treatment temperatures are the virtual temperatures.
- FIG. 4B obtained by plotting the LSAW speed of FIG. 2B
- an approximate linear expression represented by the following equation is obtained in the same manner as FIG. 4A.
- the virtual temperature T f of the sample can be calculated by measuring the LSAW speed V LSAW of the sample to be measured.
- the virtual temperature at each position may be obtained from the approximate linear equation (2) shown in FIG. 4B using the measurement result of the LSAW velocity V LSAW at each position in the plane.
- the virtual temperature may be obtained from the measured LSAW speed at each position as follows from the virtual temperature obtained from the equation (1) by measuring the longitudinal wave velocity at one point in the plane, for example, the center position.
- T f (x, y) T f ⁇ V LSAW (x, y) ⁇ -T f (V LSAW-Std ) (3)
- T f (x, y) T f ⁇ V LSAW (x, y) ⁇ -T f (V LSAW-Std )
- T f (x, y) T f (V L-Std ) + ⁇ T f (x, y) (4) It is also possible to calibrate using the longitudinal wave sound velocity of the sample. Longitudinal wave acoustic velocity V LC and LSAW velocity V LSAW-C at the center of the sample, as well as a point on the sample surface (x, y) LSAW velocity V LSAW (x, y) in the measurement of performing. From equation (1), the precise value T f (V LC ) of the fictive temperature at the center of the sample is determined from the longitudinal sound velocity V LC .
- the virtual temperature may be calculated from the transverse wave sound velocity of the sample to be measured using an approximate linear equation representing the relationship between the transverse wave sound velocity and the virtual temperature shown in FIG. 4C.
- the reason why the gradient of the density ⁇ with respect to the virtual temperature T f of the sample # 1 and the sample # 2 is different is due to the difference in the OH concentration.
- the longitudinal wave velocities V L and LSAW velocities V LSAW are measured and substituted into equations (1) and (2) using the above coefficients.
- the virtual temperature T f can be obtained.
- Non-Patent Document 5 the dependence of density ⁇ and fictive temperature T f on OH concentration is studied. Although the change in absolute value of density due to the difference in OH concentration was captured, the difference in slope with respect to the virtual temperature was not captured. For this reason, it has been found that the measurement error increases when the virtual temperature is obtained from the measured value of the density ⁇ using the relationship obtained in the past.
- the ranges in which the heat treatment temperature and the acoustic characteristics are linear are 1150 ° C. or lower for sample # 1 and 1000 ° C. or lower for sample # 2.
- the temperature was about 50 ° C. lower than the annealing point, and the temperatures were about 40 ° C. and about 110 ° C. higher than the strain point, respectively.
- the structural relaxation time is shortened when the heat treatment temperature is increased, and the fictive temperature becomes lower than the heat treatment temperature in the cooling process of the sample.
- the structural relaxation times at 1150 ° C. and 1000 ° C. are estimated to be 11 minutes and 16 minutes for samples # 1 and # 2, respectively.
- the corresponding viscosity ⁇ is estimated to be 10 13.5 poise and 10 13.7 poise, respectively.
- This result means that glass having a small fictive temperature distribution can be produced by lowering the heat treatment temperature in the heat treatment in the glass ingot production process.
- the viscosity ⁇ is 10 14.5 poise, and the structure relaxation time is 47 minutes for sample # 1 and 14 hours for sample # 2.
- the heat treatment temperature lower than the strain point, the virtual temperature distribution in the ingot resulting from the temperature distribution during the heat treatment cooling is reduced, and it is possible to produce a homogeneous large glass ingot.
- the longitudinal sound velocity and the density are proportional. 4B and 4D, the LSAW speed and density are also proportional.
- the resolution for longitudinal sound velocity density is 0.003 (kg / m 3 ) and 0.002 (kg / m 3 ), respectively, and the resolution for LSAW velocity density is 0.09 (kg / m 3 ), respectively. ), 0.08 (kg / m 3 ). From this, it is possible to measure the local density and its distribution by measuring longitudinal sound velocity and LSAW velocity.
- the longitudinal wave sound velocity of the sample to be measured is only measured as in the first embodiment, and the hypothesis is obtained using the equation (1).
- the temperature may be determined.
- the longitudinal wave velocity is generally obtained from the propagation time of the longitudinal wave propagating in the thickness direction of the sample to be measured and the thickness of the sample to be measured. Longitudinal sound velocity has high resolution with respect to virtual temperature.
- a parallel polishing process for the front and back surfaces of the sample to be measured is required. By reducing the measurement ultrasonic frequency (for example, about ⁇ 10 MHz), polishing required for the sample to be measured is required. The processing conditions are relaxed and it can be introduced into the mass production process.
- the LSAW speed can be measured if the surface of the sample to be measured is flat by performing calibration using a standard sample, although the sensitivity to the virtual temperature is lower than the longitudinal wave sound speed.
- the linearly focused beam device (LFB device) used in the above can be easily moved along the sample surface, the two-dimensional distribution, that is, the virtual temperature distribution on the sample surface can be measured. In particular, it can be introduced at an early stage of a mass production process in a mass production line with a stable production process.
- the sensitivity of shear wave velocity to virtual temperature is lower than that of longitudinal wave velocity, and it is effective at the time of R & D because it is necessary to bond the sample to be measured to the ultrasonic device for measurement. It is difficult to introduce to LSAW speed.
- Step S1 A plurality of synthetic quartz glass samples having the same composition as the sample to be measured are heat-treated at different temperatures, and calibration curve creation samples having different virtual temperatures are created.
- Step S2 measuring longitudinal wave acoustic velocity for a plurality of calibration curve samples obtained in step S1, LSAW speed of sound, one of the shear wave velocity as the acoustic characteristics AP 1.
- Step S3 From the measurement result in step S2, the heat treatment temperature as the virtual temperature T f in the linear range relationship between the heat treatment temperature T A and the acoustic characteristics AP l, as an approximate linear equation the relationship between virtual temperature and acoustic characteristics AP 1 Ask for.
- Step S4 measuring the acoustic properties AP 1 of the measured sample.
- Step S5 calculate the virtual temperature by substituting the acoustic characteristics AP 1 measured in the approximate linear equation.
- step S1, S2, S3 are the same as in the first embodiment, longitudinal wave acoustic velocity, LSAW speed, yet another one acoustic characteristics in addition to any one acoustic characteristic AP 1 of shear wave velocity in the step S2 Measure AP 2 .
- Step S3A in step S3 obtains another approximate linear equation representing the relationship between the acoustic characteristics AP 2 as measured by the virtual temperature T f and Step S2 obtained from acoustic characteristics AP l.
- Step S4 ' measuring the acoustic characteristics AP 2 of the measured sample.
- Step S5 ' determining the fictive temperature by using the measured approximate linear equation from the acoustic characteristics AP 2 obtained in step S3A.
- step S4 If an approximate linear equation of equation (1) or equation (2) is obtained in advance for a calibration curve preparation sample manufactured under the same conditions as the sample to be measured, step S4, S5 or step S4 ′ , S5 ′, the virtual temperature can be obtained.
- the fictive temperature of the optical glass and its distribution can be determined with higher accuracy than the conventional method, so that the glass manufacturer can use the fictive temperature of the produced glass and its distribution. It is possible to evaluate and evaluate the glass production process. By using this evaluation result, it can be used to improve glass manufacturing process conditions for manufacturing a glass whose virtual temperature and its distribution are controlled so as to have desired characteristics (for example, optical characteristics).
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Abstract
Description
(1) 仮想温度の測定精度が赤外分光分析法の場合に±15℃、ラマン分光分析法の場合に±60℃程度であり、不十分である。
(2) 仮想温度測定用の試料を準備する必要があり、製造ラインへの導入が困難である。
(3) 基板表面の仮想温度分布の測定が困難である。
(4) 密度による仮想温度評価では、試料の平均的な値しか得られない。
などの欠点があった。
(1-A) 同一の組成をもつ複数の検量線作成用ガラス試料に対し、それぞれ異なる熱処理温度で熱処理を行う工程と、
(1-B) 前記工程(1-A)で得られた試料に対して縦波音速、漏洩弾性表面波(LSAW)速度、横波音速のいずれか1つを音響特性AP1として測定する工程と、
(1-C) 前記熱処理温度を仮想温度とし、前記工程(1-B)で得られた音響特性AP1との関係を近似する次式
Tf=a×AP1+b
で表される近似直線式を決める工程と、Tfは仮想温度、aとbは定数であり、
(1-D) 前記検量線作成用ガラス試料と同一の組成をもつ被測定用光学ガラス試料に対して音響特性AP1を測定し、前記近似直線式を用いて仮想温度Tfを計算により求める工程、
とを含む。
(2-A) 同一の組成をもつ複数の検量線作成用ガラス試料に対し、それぞれ異なる熱処理温度で熱処理を行う工程と、
(2-B) 前記工程(2-A)で得られた試料に対して縦波音速、LSAW速度、横波音速のいずれか1つと他の1つをそれぞれ第1音響特性AP1及び第2音響特性AP2として測定する工程と、
(2-C) 前記熱処理温度を仮想温度とし、前記第1音響特性AP1との関係を近似する次式
Tf=a×AP1 + b
で表される第1近似直線式を決める工程と、Tfは仮想温度、aとbは定数であり、
(2-D) 前記工程(2-C)で得られた仮想温度Tfと前記第2音響特性AP2との関係を表す次式
Tf=c×AP2 + d
で表される第2近似直線式を決める工程と、cとdは定数であり、
(2-E) 前記検量線作成用ガラス試料と同一の組成をもつ被測定用の光学ガラス試料に対して前記第2音響特性AP2を測定し、その測定した第2音響特性AP2から前記第2近似直線式を用いて仮想温度Tfを求める工程、
とを含む。
[準備]
以下にまず光学ガラスとして合成石英ガラスの仮想温度の測定について説明する。
図1に示す表1は、本発明を行うに当たり検討実験に用いた試料の仕様を示している。OH濃度は、参考文献1に示されている方法に基づき求めた。合成石英ガラス試料#1および試料#2は、製造プロセスが異なるため、含有されるOH濃度が異なっており、異なるガラス特性温度(歪点、徐冷点)を有している。なお、これら歪点と徐冷点の値は石英ガラスメーカの資料による。検量線を作成するために用意した試料は、#1が1つのガラスインゴットから切り出した4枚、#2がもう1つのガラスインゴットから切り出した4枚であり、各試料の大きさは60mm×60mm×15mmである。同一のインゴットから切り出された4つの試料は同一の組成であるとみなす。
Tf=a×VL+b (1)
ここで、a、bは、合成石英ガラスに含まれるOH濃度によって定まる定数であり、図4Aに示す試料#1、#2のデータに対し近似直線の定数はそれぞれ以下のようになる。
試料#1:a=7.294、b=-42295
試料#2:a=6.549、b=-37871
前述の説明から、縦波音速、LSAW速度、横波音速のいずれか1つ、例えば縦波音速を音響特性として使用し、図4Aの近似直線を式(1) のように求めておくことにより、試料#1又は#2と同じ組成の被測定合成石英ガラスに対し、その縦波音速VLを測定すれば、式(1) を使って仮想温度Tfを求めることができる。同様に、図2B,2Cに示すLSAW速度又は横波音速のデータから熱処理温度を仮想温度とみなして直接近似直線を求めることにより、同じ組成の被測定合成石英ガラスのLSAW速度又は横波音速を測定して近似直線から仮想温度を計算することができる。
第2実施例では、まず仮想温度に対する感度の高い縦波音速による図4Aに示した仮想温度と縦波音速の関係を示す近似直線式(1) を求める。この近似直線状にプロットされた試料#1, #2の仮想温度は図2における試料#1, #2の熱処理温度を補正したものであり、前述のようにこの補正された熱処理温度を仮想温度として図2BのLSAW速度をプロットして得られた前述の図4Bから、図4Aと同様に次式で表される近似直線式を得る。
Tf=c×VLSAW+d (2)
ここで、c、dも、合成石英ガラスに含まれるOH濃度によって定まる定数であり、試料#1、#2、それぞれに関して式(2)の定数cおよびdの値は、それぞれ、以下のようになる。
試料#1:c=144、d=-4.922×105
試料#2:c=187、d=-6.395×105
ΔTf(x, y)=Tf{VLSAW(x, y)}-Tf(VLSAW-Std) (3)
として、測定試料の点(x, y)における仮想温度Tf(x, y)は、以下の式を用いて求めることが可能である。
また、試料の縦波音速を用いて校正することも可能である。試料の中心において縦波音速VL-CとLSAW速度VLSAW-C、ならびに試料表面上の点(x, y)におけるLSAW速度VLSAW (x, y)の測定を行う。式(1)より縦波音速VL-Cから試料中心における仮想温度の精密値Tf(VL-C)を求める。また、LSAW速度VLSAW-CおよびVLSAW(x, y) から、式(2)により、試料中心における仮想温度Tf(VLSAW-C)、試料面内の仮想温度分布Tf{VLSAW(x, y)}を求める。これらの結果から、
ΔTf(x, y)= Tf{VLSAW(x, y)}- Tf(VLSAW-C) (5)
として次式(6)を用いて、試料表面上の仮想温度の面内分布Tf(x, y)を求めることができる。
Tf(x, y)= Tf(VL-C)+ ΔTf(x, y) (6)
同様にして求めた図4Cに示した横波音速と仮想温度の関係を表す近似直線式を使って、被測定試料の横波音速から仮想温度を計算してもよい。
上述では合成石英ガラスを例に仮想温度の測定方法を説明したが、次にこの測定原理をシリカ・チタニアガラスの仮想温度測定に適用した例を簡単に説明する。
TiO2-SiO2超低膨張ガラスに対して本発明を適用した。市販のTiO2-SiO2超低膨張ガラスに対して均質化処理を行い、900℃~1100℃の温度でSiO2ガラスの場合と同様に熱処理を行った。用いた試料のTiO2濃度を蛍光X線分析法[参考文献8]により測定した結果、7.02-7.14 wt%であった。TiO2-SiO2超低膨張ガラスの縦波音速は、TiO2濃度、仮想温度、OH濃度に依存するため、TiO2濃度と縦波音速の間の関係[参考文献9]を利用して、縦波音速を7.00 wt%の値に補正した。熱処理温度と7.00 wt%における縦波音速との間の関係を図6に示す。TiO2-SiO2超低膨張ガラスの場合、式(1) の定数a、bは、以下のように求められる。
a= 7.388、b= -41567
以上のように説明した第1及び第2実施例に基づいて、この発明による合成石英ガラスの仮想温度を評価するための基本的な処理手順を図7に示すフローチャートを参照にして以下に説明する。
ステップS1:被測定試料と同じ組成の複数の合成石英ガラス試料に対してそれぞれ異なる温度で試料の熱処理を行い、異なる仮想温度の検量線作成用試料を作成する。
ステップS2:ステップS1で得られた複数の検量線作成用試料に対して縦波音速、LSAW音速、横波音速のいずれか1つを音響特性AP1として測定する。
ステップS3:ステップS2の測定結果から、熱処理温度TAと音響特性APlとの関係が線形な範囲において熱処理温度を仮想温度Tfとして、仮想温度と音響特性AP1の関係を近似直線式としてを求める。音響特性AP1として縦波音速VLを使用する場合は式(1) を得ることになる。
ステップS4:被測定試料の音響特性AP1を測定する。
ステップS5:測定した音響特性AP1を近似直線式に代入して仮想温度を計算する。
ステップS1、S2,S3は第1実施例の場合と同じであるが、ステップS2において縦波音速、LSAW速度、横波音速のいずれか1つの音響特性AP1に加えてさらに他の1つの音響特性AP2を測定する。ステップS3以降は、
ステップS3A:ステップS3で音響特性APlから求めた仮想温度TfとステップS2で測定した音響特性AP2との間の関係を表すもう1つの近似直線式を求める。音響特性AP2としてLSAW速度を使用する場合は、式(2) を得ることになる。
ステップS4’:被測定試料の音響特性AP2を測定する。
ステップS5’:測定された音響特性AP2からステップS3Aで求めた近似直線式を用いて仮想温度を求める。
[参考文献2]J. Kushibikiand N. Chubachi, "Material characterization by line-focus-beam acoustic microscope," IEEE Trans. Sonics Ultrason., Vol. SU-32, pp. 189-212 (1985).
[参考文献3]J. Kushibiki, Y. Ono, Y. Ohashi, and M. Arakawa, "Development of the line-focus-beam ultrasonic material characterization system," IEEE Trans. Ultrason., Ferroelect., Freq. Contr., Vol. 49, pp. 99-113 (2002).
[参考文献4]J. Kushibiki, and M. Arakawa, "Diffraction effects on bulk-wave ultrasonic velocity and attenuation measurements," J. Acoust. Soc. Am., Vol. 108, pp. 564-573 (2000).
[参考文献5]H. A. Bowman, R. M. Schoonover, and M. W. Jones, "Procedure for high precision density determinations by hydrostatic weighing," J. Res. Natl. Bur. Stand., Vol. 71C, pp. 179-198 (1967).
[参考文献6]J. Kushibikiand M. Arakawa, "A method for calibrating the line-focus-beam acoustic microscopy system," IEEE Trans. Ultrason., Ferroelect., Freq. Contr., Vol. 45, pp. 421-430 (1998).
[参考文献7]K. Saito and A. Ikushima, ”Structural relaxation enhanced by impurities in silica glasses,” AIP Conf. Proc., pp. 507-512 (1999).
[参考文献8]M. Arakawa, J. Kushibiki, Y. Ohashi, and K. Suzuki, "Accurate calibration line for super-precise coefficient of thermal expansion evaluation technology of TiO2-doped SiO2 ultra-low-expansion glass using the line-focus-beam ultrasonic material characterization system," Jpn. J. Appl. Phys., Vol. 45, pp. 4511-4515 (2006).
[参考文献9]PCT/JP2011/054192.
Claims (6)
- 光学ガラスの仮想温度を測定する方法であり、
(1-A) 同一の組成をもつ複数の検量線作成用ガラス試料に対し、それぞれ異なる熱処理温度で熱処理を行う工程と、
(1-B) 前記工程(1-A)で得られた試料に対して縦波音速、LSAW速度、横波音速のいずれか1つを音響特性AP1として測定する工程と、
(1-C) 前記熱処理温度を仮想温度とし、前記工程(1-B)で得られた音響特性AP1との関係を近似する次式
Tf=a×AP1+ b
で表される近似直線式を決める工程と、Tfは仮想温度、aとbは定数であり、
(1-D) 前記検量線作成用ガラス試料と同一の組成をもつ被測定用光学ガラス試料に対して音響特性AP1を測定し、前記近似直線式を用いて仮想温度Tfを計算により求める工程、
とを含む光学ガラスの仮想温度の測定方法。 - 光学ガラスの仮想温度を測定する方法であり、
(2-A) 同一の組成をもつ複数の検量線作成用ガラス試料に対し、それぞれ異なる熱処理温度で熱処理を行う工程と、
(2-B) 前記工程(2-A)で得られた試料に対して縦波音速、LSAW速度、横波音速のいずれか1つと他の1つをそれぞれ第1音響特性AP1及び第2音響特性AP2として測定する工程と、
(2-C) 前記熱処理温度を仮想温度とし、前記第1音響特性AP1との関係を近似する次式
Tf = a×AP1 + b
で表される第1近似直線式を決める工程と、Tfは仮想温度、aとbは定数であり、
(2-D) 前記工程(2-C)で得られた仮想温度Tfと前記第2音響特性AP2との関係を表す次式
Tf=c×AP2 + d
で表される第2近似直線式を決める工程と、cとdは定数であり、
(2-E) 前記検量線作成用ガラス試料と同一の組成をもつ被測定用の光学ガラス試料に対して前記第2音響特性AP2を測定し、その測定した第2音響特性AP2から前記第2近似直線式を用いて仮想温度Tfを求める工程、
とを含む光学ガラスの仮想温度の測定方法。 - 請求項1記載の光学ガラスの仮想温度の測定方法において、
前記第1音響特性AP1は縦波音速であり、前記工程(1-D)は縦波速度の測定を前記被測定用試料の表面上の2点以上で測定を行うことにより、仮想温度の面内分布を求める工程を含む。 - 請求項2記載の光学ガラスの仮想温度の測定方法において、
前記工程(2-B)において前記第1音響特性AP1として縦波音速、前記第2音響特性AP2としてLSAW速度を測定し、前記工程(2-E)は前記被測定ガラス試料の縦波音速の測定により仮想温度の精密な値を、LSAW速度を試料表面上の複数点の測定を行うことにより仮想温度の面内分布を求めることを含む。 - 請求項1乃至4のいずれか記載の測定方法において、光学ガラスは、OH濃度が0から2000 [wtppm]、金属不純物濃度が10 [wtppb]以下の合成石英ガラスである光学ガラスの仮想温度の測定方法。
- 光学ガラスの仮想温度の測定方法であり、
(3-A)光学ガラスからなる被測定試料の縦波音速、LSAW速度、横波音速のいずれか1つを音響特性APとして測定する工程と、
(3-B) 測定した前記音響特性APから、被測定試料と同一の組成をもつ検量線作成用ガラス試料に対して予め作成した音響特性APに対する仮想温度の近似直線式を用いて、仮想温度Tfを求める工程
とを含む光学ガラスの仮想温度の測定方法。
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