1
`
`EX 1015
`IPR of U.S. Pat. No. 7,829,595
`
`

`
`174
`
`Lantz
`
`..
`
`FERET'S DIAM.__..
`
`Martin's diameter = mean length of line paralleling the direction of measure(cid:173)
`ment bisecting the particle, and terminating at the particle boundaries
`Faret's diameter = mean length of line paralleling the direction of measure(cid:173)
`ment and terminating at two tangents to the outer-most boundaries of
`the particle
`
`Figure 50
`
`Statistical diameters.
`
`1. Sampling the material to be analyzed (discussed earlier in this
`chapter
`2. Preparing the sample for analysis (see Sec. IV)
`3. Generating the data
`4. Treatment and presentation of the data
`
`F. Particle Size Statistics
`
`In generating the data, individual or groups of particles from each sample
`are sized and counted. The sizing and counting follow a particular pattern
`in order to put this data into an orderly, meaningful form which can be
`statistically analyzed for interpretive and comparative purposes. For ex(cid:173)
`ample, it will be assumed that initial microscopic observation of a sample
`reveals a size range between 0. 5 to 60 µm. To begin the statistics, this
`range is divided into convenient equal parts known as class intervals and
`the mean of each class interval is determined. For convenience of calcula(cid:173)
`tion, the lower limit of the first class interval is assumed to be zero. The
`particles are sized, counted, and tallied under their proper class interval
`as shown in Table 10.
`For the statistical calculation all the particles counted in each class
`interval are assumed to be equal to the mean of their respective class
`interval. This data can now be put into bar graph or histogram form as
`If the means of each class interval are connected by
`shown in Figure 51.
`a smooth line, a distribution curve results as shown in Figure 52. This
`frequency curve is bell-shaped and is known as a Gaussian curve if sym(cid:173)
`metrical. The sample represented by the curve is said to have a
`Gaussian distribution. To normalize the data, the percentage of particles
`can be calculated in each class interval (Table 11), added cumulatively,
`and plotted to give the number distribution curve seen in Figure 53.
`
`l
`
`2
`
`

`
`Size Reduction
`
`Table 10 Microscopic Count Data
`
`175
`
`Class interval
`(µm)
`
`Mean of the
`class interval
`(µm)
`
`Number of particles
`counted in each
`class interval
`
`2.5
`
`7.5
`
`12.5
`
`17.5
`
`22.5
`
`27.5
`
`32.5
`
`37.5
`
`42. 5
`
`47.5
`
`52.5
`
`57.5
`
`96
`
`105
`
`116
`
`129
`
`150
`
`212
`
`148
`
`127
`
`114
`
`101
`
`93
`
`88
`
`~MEAN OF CLASS INTERVAL
`
`r-cLASS INTERVAL
`..--
`
`0-5
`
`5-10
`
`10-15
`
`15-20
`
`20-25
`
`25-30
`
`30-35
`
`35-40
`
`40-45
`
`45-50
`
`50-55
`
`55-60
`
`> u
`2 w
`::>
`0
`w
`a:
`u.
`
`250
`
`200
`
`150
`
`100
`
`50
`
`..J
`<{
`
`> ex:
`w
`1-
`2
`~
`<{
`..J
`tJ
`:i:
`~
`
`UJ
`~
`<I)
`UJ
`..J
`()
`
`i== ex:
`<{
`c..
`u.
`0
`a:
`w
`CXl
`::::
`::>
`2
`
`0
`
`10
`
`20
`
`30
`40
`CLASS INTERVAL IN MICRONS
`
`50
`
`60
`
`70
`
`Figure 51
`
`Histogram.
`
`l
`
`3
`
`

`
`- - - - - - - - - · - - · - - . - - · · - -
`
`Lantz
`
`176
`
`250
`
`200
`
`Cl)
`
`w _,
`
`(.)
`
`~ 150
`cl:
`0..
`u.
`0
`
`>-(.) z
`~ 100
`d
`w
`er:
`u.
`
`50
`
`~ l STD.---+-~ l STD.~
`DEV.
`DEV.
`
`MEAN
`
`Figure 52
`
`Frequency curve.
`
`PARTICLE SIZE IN MICRONS
`
`Table 11
`
`Calculations of Cumulative Percent
`
`Class interval
`(µm)
`
`Means
`(µm)
`
`No. of
`particles
`
`% of
`particles
`
`Cumulative
`%
`
`0-5
`
`5-10
`
`10-15
`
`15-20
`
`20-25
`
`25-30
`
`30-35
`
`35-40
`
`40-45
`
`45-50
`
`50-55
`
`55-60
`
`2.5
`
`7.5
`
`12.5
`
`17.5
`
`22.5
`
`27.5
`
`32.5
`
`37.5
`
`42. 5
`
`47.5
`
`52.5
`
`57.5
`
`96
`
`105
`
`116
`
`129
`
`150
`
`212
`
`148
`
`127
`
`114
`
`101
`
`92
`
`88
`
`Total = N = 1478
`
`6.5
`
`7.1
`
`7.8
`
`8.7
`
`10.1
`
`14.3
`
`10.0
`
`8.6
`
`7.7
`
`6.8
`
`6.2
`
`5.6
`
`6.5
`
`13.6
`
`21. 4
`
`30.1
`
`40. 2
`
`54.5
`
`64.5
`
`73.1
`
`80.8
`
`87.6
`
`93.8
`
`99.4
`
`4
`
`

`
`Size Reduction
`
`100
`
`177
`
`I-
`
`..J
`
`w
`N
`<ii
`0
`w
`I-
`<t
`I-
`(/)
`z
`<t :c
`~ w
`... z w
`
`u
`a:
`w
`~
`w
`>
`~
`<t
`..J
`::::>
`:E
`:::>
`(.)
`
`90
`
`80
`
`70
`
`60
`
`50
`
`40
`
`30
`
`20
`
`10
`
`oo~~~~~..._~~~--1.~~~~-'-~~~~"---~~~--1.~~~_J
`10
`20
`30
`40
`50
`60
`PARTICLE SIZE IN MICRONS
`
`Figure 53 Cumulative distribution curve.
`
`5
`
`

`
`Lantz
`
`0
`
`178
`
`99.8
`
`99.5
`
`99
`
`98
`
`95
`
`90
`
`80
`
`70
`
`60
`
`50
`
`40
`
`30
`
`20
`
`LU
`N
`Cl)
`0
`LU
`I-
`<(
`I-
`Cl)
`z
`<(
`::c
`I-
`Cl)
`Cl)
`LU
`.....
`I-
`z
`LU
`0
`a:
`LU
`Cl..
`
`LU > 10
`
`I-
`<(
`...J
`::>
`~
`:::> u
`
`5
`
`2
`
`1
`
`0.5
`
`0.2
`
`0.1
`
`0.05
`
`0.01 0
`
`10.7
`
`10
`
`28
`
`44.8
`
`20
`30
`40
`PARTICLE SIZE IN MICRONS
`
`50
`
`60
`
`Figure 54 Normal-probability plot.
`
`6