This standard specifies the power function characterization method for particle size distribution. This standard is applicable to the cumulative distribution of particle size of a particle system. GB/T 16742.1-1997 Functional Characterization of Particle Size Distribution Power Function GB/T16742.1-1997 Standard Download Decompression Password: www.bzxz.net
This standard specifies the power function characterization method for particle size distribution. This standard is applicable to the cumulative distribution of particle size of a particle system.

GB/T 16742.1—1997
This standard is equivalent to the German standard DIN66143-1974 "Graphical representation of particle size distribution by power function". This standard specifies the power function representation method for particle size distribution. This standard is applicable to the cumulative distribution of particle system size. The standard also derives the calculation formula for the surface area of ​​the particle system under various power function characteristic parameters, and demonstrates the calculation in Appendix A and Appendix B. Appendix C uses the screening composition data obtained by particle size measurement to perform linear regression processing to obtain the characteristic parameters of the power function distribution, and then obtains the specific surface area of ​​the particle system. Other functions that represent particle size distribution include normal distribution, lognormal distribution and RR distribution, and their standards will be formulated separately. Appendix A, Appendix B and Appendix C of this standard are all suggestive appendices. This standard was proposed by the Chinese Academy of Sciences.
This standard is under the jurisdiction of the National Sieve Screening Standardization Technical Committee. The drafting unit of this standard: Institute of Chemical Metallurgy, Chinese Academy of Sciences. The drafter of this standard: Shen Tianlin.
1 Scope
National Standard of the People's Republic of China
Function representation of particle size distributionPower-function
This standard specifies the power function representation method of particle size distribution. This standard is applicable to the cumulative distribution of particle size of a particle system. 2 Vocabulary and symbols
2.1 Vocabulary
2.1.1 Particle
Discrete monomer of a material.
2.1.2 Particle size
The size of a particle material, generally expressed in equivalent diameter. 2.1.3 Equivalent diameterequivalent diameterThe diameter of a sphere that has the same geometric or physical properties as the particle in some aspect. 2.1.4 Particle size distributionParticle size distributionThe percentage of particles of different size grades in a material. 2.1.5 Cumulative undersize distribution The percentage of particles below a certain specified size in the material. 2.1.6 Cumulative oversize distribution The percentage of particles above a certain specified size in the material. 2.1.7 Density distribution The ratio of the relative cumulative percentage of a fraction to the particle size range of that fraction. 2.1.8 Particle surface shape factor The ratio of the surface area of ​​a particle to that of a sphere of the same volume. 2.2 Symbols
The symbols used in this standard are listed in Table 1.
Approved by the State Administration of Technical Supervision on March 4, 1997 GB/T 16742.1--1997
Implementation on September 1, 1997
3 Functional representation of particle size distribution
GB/T 16742.1--1997
Table 1 Standard symbols
Intercept of power function line in double logarithmic coordinates
Slope of power function line in double logarithmic coordinates
Cumulative distribution under sieve
Cumulative distribution over sieve
Specific surface area of ​​particle mass
Specific surface area of ​​particle volume
Particle size
Lower limit particle diameter
Upper limit particle diameter
Maximum particle equivalent diameter
Particle surface area shape coefficient
Particle density
Various particle systems have different particle size distributions, so there are many types of functions used to characterize particle size distribution. The power function of this standard is one of the most common particle size distribution functions. It is more suitable for the middle particle size range of most particle systems, but there is a certain error at the two ends of the particle size distribution.
3.1 Screen function
The power function is defined as:
In the particle size range: 0≤≤zma
Cumulative distribution under the sieve:
Q(r) = 1 - R(α):
For ease of calculation, the power function can be linearly processed: (1) Taking the logarithm on both sides of the equation, we can get:
IgQ(r) = m Igt + C
Where: C= -m Ig max
（2）
Therefore, on the double logarithmic graph with Q(z) as the ordinate and I as the abscissa, the two are linear, and the slope of the straight line is m, and the intercept is C=-mlgEmar.
Therefore, m and 2mx can be used as two characteristic parameters of the power function of particle size distribution. In some cases, the particle system has different m values ​​in each particle size distribution interval, which is a broken line composed of several straight lines with different slopes on the double logarithmic graph. When three ≤ 1, the particle size distribution can also be expressed by RR distribution, that is, the function or RR distribution can be used for function expression at the same time.
3.2 Specific surface area of ​​particle system
The particle surface area is also an important basic characteristic of the particle, which can be used to measure the reactivity of the particle system. It is generally characterized by specific surface area. The specific surface area is the ratio of the particle surface area to its volume or mass, which is called volume specific surface area or mass specific surface area respectively. The relationship between the two is:
Sm = S/ps
Where: Sm—mass specific surface area of ​​the particle, S. Volume specific surface area of ​​the particle;
Ps—-density of the particle.
GB/T 16742.1-1997
The specific surface area of ​​a single particle is related to the particle size and particle shape. The smaller the particle size, the larger the specific surface area. The volume specific surface area of ​​a non-porous particle is s.=
Where: r-
Particle size;
——-Particle surface area shape coefficient, defined as the ratio of the surface area of ​​the particle to the surface area of ​​a spherical particle of the same volume. Obviously, spherical particles are more than 1, and non-spherical particles are ≥1.
Particle systems are mostly composed of many particles of different sizes, and their specific surface area is also related to the particle size distribution. The specific surface area of ​​a particle system can be measured experimentally, and the commonly used method is the BET method. It can also be calculated from its particle size distribution. When its particle size distribution can be characterized by a function, an analytical solution can be obtained. Formula (4) is the specific surface area of ​​single-size particles, while the specific surface area of ​​a particle system with a size distribution can be obtained by integration: r dQ()
S,(TA+T) --
Q(Xr) -Q(TA)JQA)
When the relationship between Q(r) and can be characterized by the curtain function of formula (1), formula (5) can be expressed as: 6dm
S,(ra.x) =二
[Q() = Q(aA)Jma:
3.2.1 The whole particle size distribution interval m is a constant
When m≠1, the volume specific surface area of ​​any particle size interval can be obtained by integration of formula (6): 6mQ(r)
S,(aA,) = (m - 1) TQ()=Q(A))
Where: A--—lower limit of particle size interval; 2B——upper limit of particle size interval;
S(A,B)--—volume specific surface area within the particle size interval from a to Z. m-3d.a
If the volume specific surface area of ​​the entire particle system is required, just take Q(rA)=0,Q(g)=1. From (1), we can get: =0=mn
Substituting the above data into (5), we can get:
S, which is the volume specific surface area of ​​the entire particle system. 6m
(m = 1)xmar
When m is 1, integrating (6) can get the volume specific surface area of ​​particles in the particle size range: 64Q()
S(raTg) =
[Q(T) - Q(A)JXR
3.2.2 Different m values ​​in different particle size ranges (5)
Some particle systems have different m values ​​in different particle size ranges. The specific surface area of ​​each interval can be first obtained by (7), and then the volume specific surface area of ​​the particle system in the entire particle size distribution range can be obtained by weighting. When m≠1, S.(TA.iXy.n) -
3.2.3 Square root distribution
In the power function distribution shown in formula (1), when m is:
（10）
(11) is called square root distribution.
GB/T 16742.1-1997
Similarly, taking the logarithm of both sides of equation (11), we can obtain: ig + lg
IgQ(α) =
On the double logarithmic graph with Q(z) as the ordinate and Q(α) as the abscissa, it is a straight line with a slope of and an intercept of lg
Substituting into equation (7), we can obtain the volume specific surface area of ​​the particle size distribution range from zA to: zn: m=
60Q(xg)
S(A,&)=
[Q(）-Q(A)(V
（12）
*（13）
GB/T 16742.1—1997
Appendix A
(Suggested Appendix)
Particle system with constant m
The particle size distribution of a certain particle system can be characterized by the power function Q(z)= rmg
, with characteristic parameters Tmx8mm, m=3.34. Particle density Ps2.60g/cm2, particle surface area shape relationship coefficient g=1.4, calculate the volume specific surface area and mass specific surface area of ​​particle size 1.00~3.00mm, 5.00~7.00mm and full particle size segment. In Table A1, the 4th column Q(rA.) and the 5th column Q(rB) are obtained by formula (1). The 6th column S.. is obtained by formula (7).
The 7th column Sm is obtained by formula (3) .
Appendix B
(Suggested Appendix)
Calculation of specific surface area of ​​particle systems with different m values ​​in different particle size intervals The m values ​​of a particle system in three particle size intervals are shown in Table B1. Table B1
The particle surface area shape coefficient of this particle system is 1.4, and the particle density ps = 2.6g/cm. Calculate the volume specific surface area and mass specific surface area in each particle size interval and the entire system. Substituting the above known data into formula (7) can obtain the volume specific surface area of ​​each particle size segment, and the total particle size The specific surface area can be obtained by formula (10) and then by formula (3) to obtain the mass specific surface area. The results are listed in Table B2. Table B2
Particle size range
430～1100
0～1100
GB/T16742.11997
Appendix C
(Suggested Appendix)
Calculate the specific surface area from the particle size analysis results Table C1 is the screening data of the particle system, and the surface area shape coefficient of the particle system is measured to be 1.4, dense The density is 2.6g/cm. Calculate the volume specific surface area and mass specific surface area of ​​the particle system. Table C1
Q(1)(%)
Figure C1 Cumulative distribution under the sieve
Put the data points of Table C1 on a double logarithmic graph with Q(r) as the ordinate and x as the abscissa to obtain Figure C1. It can be seen from the figure that the Q(αx) and α of the particle system on the double logarithmic coordinate graph are close to a linear relationship and can be characterized by a power function distribution. The data of Table C1 are passed through the least squares: 368
GB/T 16742.1--1997
Squared for logarithmic linear regression, the equation of the line can be obtained: lgQ(x) = 1.619 Igr -- 1.214 Correlation coefficient: r=0.995bZxz.net
From (C1) formula: m=1.619, cmx=4.930 Therefore, the particle size distribution function of the particle system is: Q(α)=
（C1）
As shown in the straight line in Figure C1. It can also be seen from the figure that the experiment and the straight line have a large deviation at the larger particle size end, and the other particle size ranges are relatively close. Therefore, the linear correlation coefficient is large, reaching 0.995. Substituting rA0, B==4.930 into (8), we can obtain the volume specific surface area of ​​the particle coefficient in the whole particle size distribution area: S.
6 × 1.4 × 1.619
（1.619=1)× 4.930
The mass specific surface area is:
=.4.456mm144.56 cm-1
17.14 cm2/g
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