JP3491042B2 - How to measure liquid diffusion coefficient - Google Patents

Description

Description: BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for measuring a liquid diffusion coefficient based on a novel algorithm. [0002] Many materials, from metals and semiconductors to proteins, are produced by crystal growth from a liquid phase.
In order to produce high-quality crystals, it is important to control the concentration distribution in the liquid phase, and it is essential to optimize the growth conditions by numerical calculations. In numerical calculations, the diffusion coefficient is an extremely important physical property value. However, the conventional diffusion coefficient measurement method analyzes a solution concentration distribution formed by a diffusion pair experiment based on Fick's second law. However, this method does not provide sufficient measurement accuracy. This is because high-precision measurement of the concentration distribution in a solution is not only technical, but also very difficult in principle, so there is no way to overcome this difficulty at present and even in anticipation of future technological developments No further improvement in accuracy can be expected with the conventional method. SUMMARY OF THE INVENTION [0004] The present invention has been made in view of the above circumstances, and an object of the present invention is to provide a general industry for performing crystal growth from a liquid phase, particularly, a metal / semiconductor. It is an object of the present invention to provide a measurement method capable of easily and accurately obtaining a liquid diffusion coefficient as an indispensable tool for obtaining basic physical property values for crystal production in the industry and the pharmaceutical industry for producing protein crystals. [0005] In order to achieve the above object, the present invention has the following arrangement. [0008] (1) A diffusion cell in which two solution reservoirs are connected by a capillary tube is prepared, and solutions having different concentrations are respectively placed in first and second solution reservoirs, and a first solution is supplied. A step of putting a solute replenishing crystal for keeping the solution concentration constant in the reservoir, and allowing the components of each solution reservoir to mutually diffuse through a capillary tube, and measuring a change in solution weight and a change in solution concentration caused by the diffusion, From these measurements, the diffusion flux J and the concentration gradient dc / d
x, the obtained diffusion flux J and the concentration gradient dc /
dx, the diffusion coefficient D based on Fick's first law
A method for measuring a liquid diffusion coefficient, wherein In summary, the present invention measures the time change of the concentration in a solution by using an in-situ method for measuring the concentration of a solution during a diffusion experiment, which has been difficult so far, and provides a new algorithm for deriving a diffusion coefficient. Used to measure the liquid diffusion coefficient. According to the present invention, there are the following structural features not found in the conventional method. Measuring the diffusion flux;・ Perform analysis based on Fick's first law. The following effects are obtained by the method of the present invention. -In this method, the measurement accuracy depends on the in-situ measurement technology. This is extremely easy compared with the improvement of the accuracy of the conventional concentration distribution measuring method. -It is possible to acquire the mutual diffusion coefficient, the intrinsic diffusion coefficient, and the self diffusion coefficient at the same time. -The in-situ measurement method and the material of the diffusion cell can be freely designed depending on the material to be measured. DETAILED DESCRIPTION OF THE INVENTION In the present invention, an experiment is performed using a special diffusion cell. The diffusion cell is composed of two solution reservoirs (reservoirs) and a capillary section connecting them. When the solution and the solute replenishing crystal S are put into the first solution reservoir 10 as shown in FIG. 1A, the solution component is diffused through the capillary tube 20 through the capillary tube 20 as shown in FIG. 1B. Thereby, the solution concentration and the weight of the respective solution reservoirs 10 and 30 change. The flux J and the concentration gradient dc / dx are obtained by measuring the weight change and the concentration change of the solution concentration of the second solution reservoir 30, and the diffusion coefficient is calculated from these values based on Fick's first law shown in the following equation. Find D. (C)
Indicates that both solutions have the same concentration and diffusion has been completed. In the figure, C1 is the concentration of the solution in the first solution reservoir,
C2 indicates the concentration in the second solution reservoir, and t indicates time. [Equation 1] Here, it is assumed that the solution in each of the solution reservoirs 10 and 30 is homogeneous, and that the diffusion in the capillary tube 20 is steady. Further, the cell and the in-situ measurement technique in the figure can be freely designed according to the material to be measured, and the present invention does not depend on these measurement methods and cell materials. The present invention seeks the flux, which is unique to the present invention. In addition, the measurement accuracy of the diffusion coefficient
Equivalent or better than conventional methods have been obtained. Further, since the accuracy of the measured value according to the present invention depends only on the in-situ measurement technique, further improvement in the in-situ measurement technique can be expected in the future. This is the greatest advantage over the conventional method. Further, as shown in FIG. 4, the diffusion coefficient can be measured without adding the solute replenishing crystal S.
That is, the solution whose diffusion coefficient is to be measured is put into each of the first solution reservoir 10 and the second solution reservoir 30. At this time, solutions having different concentrations are stored in the respective solution reservoirs. Then
As shown in (b), the solution component diffuses through the capillary tube 20. Thereby, the solution concentration and the weight of the respective solution reservoirs 10 and 30 change. The flux J and the concentration gradient dc / dx are obtained by measuring the weight change and the concentration change of the solution concentration in the second solution reservoir 30, and the diffusion coefficient is calculated from these values based on Fick's first law shown in the above equation. Find D. EXAMPLE The diffusion coefficient of GaZn was measured using the apparatus shown in FIG. For the in-situ measurement method, a method by X-ray fluorescence analysis is used, and for the diffusion cell, a dedicated cell made of graphite is used. FIG. 2 shows the results. (A) shows a diffusion flux J, and (b) shows an actual measurement example of a concentration gradient dc / dx in a capillary tube. The horizontal axis indicates the measurement time, and the vertical axis indicates the respective values. Diffusion coefficient D is determined by dividing the flux by the value of the concentration gradient. In order to confirm the accuracy of the diffusion coefficient measured in the examples, the change in the concentration of the solution reservoir was obtained by numerical calculation and compared with the experimental value. This is shown in FIG. It can be seen that the calculation results using the diffusion coefficient values obtained in the figure show good agreement with the experimental values. Also, when the apparatus shown in FIG. 4 was used, good agreement with the experimental values was similarly observed. Note that the present inventors are not limited to GaZn,
The mutual diffusion coefficient, intrinsic diffusion coefficient, and self-diffusion coefficient of the binary aGe solution were measured, and the usefulness of the present invention was confirmed. As described above, according to the present invention, in all industries which carry out crystal growth from a liquid phase, particularly in the metal / semiconductor industry and the pharmaceutical industry for producing protein crystals,
As a tool indispensable for obtaining basic physical property values of crystal production, it is possible to provide a measurement method capable of easily and accurately obtaining a liquid diffusion coefficient.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a schematic explanatory view of a diffusion coefficient measurement, wherein (a) is a state at the beginning of an experiment, (b) is a state in the middle of diffusion, and (c) is the same concentration in both solutions. This shows a state where the diffusion has been completed. FIGS. 2A and 2B show the results of an example in which the diffusion coefficient of GaZn was measured. FIG.
FIG. 4 is a view showing an example of actual measurement of a concentration gradient in a capillary. FIG. 3 is a diagram in which a change in the concentration of a solution reservoir is obtained by numerical calculation and is compared with an experimental value. FIG. 4 is a schematic explanatory view of a diffusion coefficient measurement different from FIG. 1;
(A) is the state at the beginning of the experiment, (b) is the state during diffusion,
(C) shows a state in which both solutions have the same concentration and the diffusion has been completed. [Description of Signs] . . First solution reservoir 20. . . Capillary 30. . . Second solution reservoir S. . . . Crystal for solute supply

──────────────────────────────────────────────────続 き Continuation of the front page (56) References JP-A-55-121130 (JP, A) JP-A-61-226637 (JP, A) Dictionary of Physical and Chemical Sciences, Iwanami Shoten, Japan, January 10, 1991 4th edition, p. 1077 (58) Fields investigated (Int. Cl. ⁷ , DB name) G01N 13/00 G01N 9/32

Claims (1)

(57) [Claims 1] A diffusion cell in which two solution reservoirs are connected by a capillary is prepared, and solutions having different concentrations are respectively put into first and second solution reservoirs, and A step of putting a solute replenishing crystal for keeping the solution concentration constant in the solution reservoir and diffusing the components of each solution reservoir through a capillary tube, and measuring the change in the solution weight and the solution concentration caused by the diffusion. A step of obtaining a diffusion flux J and a concentration gradient dc / dx from these measured values, and a diffusion coefficient D based on Fick's first law from the obtained diffusion flux J and concentration gradient dc / dx. A method for measuring a liquid diffusion coefficient, characterized in that: