-1

/ ,

1. (sampling) . , -, . - , - 1 g, , (10.000 - 100.000 1010 - 1011 g) 1013 -1015 g/. M . 1 mL - . , - , , . , : , . (segregations) / - , . , . ( ) / ( ) . : : , , -

, .. . ( 0,001 - 1 g). -

.

-2

, .. , .

. , , .. , , , - , .. . , . . , , . 1.1. (object) . - (.. - ). , , . , . , . (sample) . - , : , . 1.1 1.2. 1.2 1-2: (sample): (portion) .

. (increment): -

, / . - () - .

-3

(gradient)

1-1. ( ) (laboratory sample): -

, . - - .

(test portion). : (specimen), (test unit), (aliquot).

(bulk sample): Y , , , , . .. , , - .

(reduction): H .

(subsample): .

. , .

(homogeneity): . . - 1 g, mg .

( -

)

- -

- -

-4

S

1-2. . (lot):

. (population):

. - .

(stratum): T .

(segment): , . (gross sample): M

(record) ( ).

/ /

(object / lot / population)

(increment)

(increment)

(sample)

(sample)

(sample)

/ (Gross sample / Bulk sample)

(subsample)

(subsample)

(subsample)

(subsample)

(test portion)

-5

1.2 . . . (representativeness). - (size), (stability) (cost). , (discriminating power) (speed). H - ( ) , . ( - ). . ( ) -, . : . 1.2.1 - : 1. ,

(bias). . 2.

. .. , . - , . , .

3. . .. , , , , , ( : ).

4. . .. , -, , , (, , ).

5. . - , . , - , . - (.. - ) . -, , .

-6

2. 2.1 , .. , , (test portion), (.. % (material vari-ance), m2. () , - , - , , (x1, x2, , xN), . ( m), - o . : , m. H -. ( , ). , , , . . - . (s), A (.. ) (. m )1.

2.2. Ingamells - O ngamells2 , :

sKRW2 = (2-1)

W , R (R = 100ss /x) s . - (sampling constant) , R 1% 68% () - 1%. s W a . s , W , - R%. 2.2., a24

1 (.. 1,0 - 1,5 g) . 2 C.O. Ingamells, P. Switzer, Talanta, 20, 547 (1973); C.O. Ingamells, Talanta, 21, 141 (1974); 23, 263 (1976).

-7

, - NBS 3.

2-1. ( ) (.. %

) : ) , ) ) , W1, W2 (W2>>W1). , - - .

2-2. ( / ) -

. 2-2 , 1% (. 2,4 g1 s1) 35 g. 1 g, 5%. 2.3. Visman O Visman -. -, (homogeneity constant) , Ingamell (segregation constant) B, :

ss

2s n

Bnw

As += (2-2)

3 S. H. Harrison and R. Zeisler, NBS Internal Report 80-2164, C. W. Reimann, R. A. Velapoldi, L. B. Hagan, and J. K. Taylor, Eds, U.S. National Bureau of Standards, Washington, D.C., 1980, p 66.

-8

w ns ns . = 0, (2-2) - Ingamells. R = 100 ss /x, Ingamells Visman :

s24 Kx10A = (2-3)

-, . - ss2 , (, ) (2-2), ( - -) . , , . 2.4. . , , . (.. , , , ). ns, - ss2 x R, :

22

2s

2theor

sxR

stn = (2-4)

ns , ns . , - ( ) ss2 >> sa2 (sa2 : ). , - . ss2 x . ttheor - t (Students t) ns 1 4. (2-4) , ttheor ns. : - (.. 95%) 1,960, . [ ttheor = 1,645 2,576 - 90% 99%, ( t)]. (2-4) -

4 , , - . ( ) - (finite population correction), (2-4) (1n/N)1/2.

-9

ns. ttheor ns. H - (iterative) ns. (2-4) (Gauss) , . _____________________________

2-1. 10 mg/g. H 0,1 mg/g 1 g. 1 g -, 1% (R=0,01) 95%. . ns (2-4) ttheor = 1,96 : = : ns = (1,9620,12) / (0,012102) = 3,84 4 = 4 1 ns = (3,18220,12) / (0,012102) = 10,12 10 = 10 1 ns = (2,26220,12) / (0,012102) = 5,12 5 = 5 1 ns = (2,77620,12) / (0,012102) = 7,71 8 = 8 1 ns = (2,36520,12) / (0,012102) = 5,59 6 = 6 1 ns = (2,57120,12) / (0,012102) = 6,61 7 = 7 1 ns = (2,44720,12) / (0,012102) = 5,98 6 . 6 . [: n=6 : ttheors / ns = 2,5710,1 / 6 = 0,105 (0,105100/10) = 1,05% ( ns = 7 : 0,89%]. 2.2 , M. H , . , . (.. ). , - . , (pseudorandom) . -. 1 m 100 .. 2 . - , - .., ( / - . ( ) . - , Nyquist ( ): , - , -

-10

. ( f), - ( (2f).

2.3 f fS.

- fS/f

-11

(2-6) -. ,

2s

2a = (2-7)

(2-6) :

+=

s

2

as

2s2

o n

n

n

s (2-8)

(2-8) : 1. , ns na , -

s2. 2. , nans ,

, ns. 12 , 6 2 , 4 - 3 .

3. . , -

, (/na)(s2/ns) s2/ns . - a2. :

1/3 , .

, , , . - . . (2-8) / (cost/benefit). ( + , ..) Cs Ca , C ns na , :

aCnnCnC asss += (2-9)

, (2-8), (2-9) :

( t - , .. 95%) , - e2. A - (2-8).

-12

( )aasa

2

2a

2

2s CnC

n

C +

+= (2-10)

(2-10) na dC/dna , , - (). , :

2/1

a

s

s

aa C

Cn

= (2-11)

2

s

2a2

s

s n

n+

= (2-12) _____________________________

2-1. 2,7% 1 kg. T - . - 0,7%. - - - : ) 3 ( ) 8 . ) 12 ( ) 2 . ) ( , , , ) 500 EU/ 10 EU/, 1,0%; ) ; . ( ) : ) (2-8) : = [ (2,7)2 / 3 + 0,72 / (38) ]1/2 = 1,56% ) : = [ (2,7)2 / 12 + 0,72 / (122) ]1/2 = 0,792% ) (2-11) : na = (0,7 / 2,7)(500 / 10)1/2 = 1,83 2 (2-12) : ns = [ 2,72 + (0,72 / 2) ] / 1,22 = 5,23 5 E : 5 - 2 / ( 10 ). [: (2-8) : = [ (2,7)2 / 5 + 0,72 / (52) ]1/2 = 1,23% . , 1,2% - na ns ]

-13

) : C = (5 )(500 EU/ ) + (10 )(10 EU/) = 2600 EU _____________________________ 2.3. ( ) (stratified sampling) . . 2-8:

asb

2a

sb

2s

b

2b2

o nnn

nn

n

++= (2-13) nb , b2 - (between strata variance), ns s2 (within strata variance). E , . (2-13) ns, nb na. Cb, Cs Ca , :

aasbssbbb CnnnCnnCnC ++= (2-14)

, nb, ns na C : ( )

2/1b

2/1aa

2/1ss

2/1bbb

b C

CCCn

++= (2-15)

2/1

s

b

b

ss C

C

n

= (2-16)

2/1

a

s

s

aa C

C

n

= (2-17)

3. Bene-detti-Pichler, , - : 3.1. Benedetti-Pichler u . wA wB, . xA . A w . ( ) s2.

-14

. - 2 npq, n - , p A q - ( : p + q = 1). , w n = w/u3, : p% = wA % q% = wB % = (100 wA)%, s2 (s() : ) :

10000u)w(100ww

3AA2

s() = (3-1)

:

100w/u

3

s()s = (3-2)

, ( ) (: wA = x), :

x)(100xwu

32s = (3-3)

, , . , . 3.2. Benedetti-Pichler , , , . , , xA xB. , (3-3) :

2BA

AA

32

s 100xx

)w(100wwu

= (3-4) , /. [(xA xB)/100]2 xA = xB . (3-4) , . :

2

BA2/1

2

2B2

s xxx

np)p(1

= (3-5) - :

-15

2

8

ABAAABBB

3AB

2AABB2

s x10

)x)(xx(x)xx)(x(xu)xx)(x(x)x(x

wRK

+== (3-6)

- () . m i (i = 1, 2, , m) wi , xi , Wilson:

= =

= m

1i

3

ji

ji2m

1j

jjii2s w

uww

100xx

21 (3-7)

i, j m , xi xi x. - . Wilson s. 3.3. - Gy H Gy - . (3-3) , Gy:

lgf

=W1

w1x)(100u 32s (3-8)

1/w (3-3) (1/w 1/W). A - W, w ( 4). w W. E w = W, ( ), w

-16

g (.. g 0,50 0,75, ). (liberation factor), l. , . (3-3) - wA = x (. ). , - , . . - :

21

2

1/

=

uu

l (3-9)

, , u1 - u2 . u2u1, l = 1, . l - . 1. P. M. Gy, Sampling of Particulate Materials: Theory and Practice, Elsevier, Amsterdam,

1979. 2. C. O. Ingamells, New Approaches to Geochemical Analysis and Sampling, Talanta, 21,

141-155, 1974. 3. A. A. Benedetti-Pichler, Physical Methods in Chemical Analysis, W. G. Berl, Ed.,

Vol. 3, pp. 183-194, New York Academic Press, 1956, A. A. Benedetti-Pichler, Essentials of Quantitative Analysis Chapter 19, New York, Ronald Press, 1956.

4. B. Kratochvil and J. K. Taylor, Sampling for Chemical Analysis, Analytical Chemistry, 53, 954A-938A, 1981.

5. H. A. Laitinen and W. E. Harris, Sampling in Chemical Analysis, 2nd Ed., Chap. 27, pp 565-582, McGraw-Hill, New York, 1975.

6. R. Smith and G. V. James, The Sampling of Bulk Materials, Royal Society of Che-mistry, London, 1987.

7. J. K. Taylor, Quality Assurance of Chemical Measurements, pp 55-74, Lewis, Michigan, 1987.

8. R. Q. Yu, Analytical Sampling Theory in Introduction to Chemometrics, chap. 3, pp 26-48, Hunan Education Publishing House, Changsha, 1991.

9. R. Q. Yu, Sampling: Overview and Theory in Encyclopedia of Analytical Science, 4518-4525, Academic Press Limited, 1995.