Upload
others
View
1
Download
0
Embed Size (px)
Citation preview
(
4 (
0 1
2
: 7
8 7 6 : :
6 8 6
3 6
7
6
6
( 6
)
7 5 , 0
1 , 2 5
I 6
I I 6
( , , , )
1 ! " = 1 − !
& ' ()
() = *)+ !)"+,) = +!
)! +,) ! !)"+,) (1)
*)+ (Combination) . . = &!
. (1) & → ∞
(('|.)
(()|4) = 5,4
46
)! (2)
(2) 5 '
lim+→:
(1 − !)+,) = 5,4 (3)
! = 0.4 5
1 5 2 (2 (1) (2
! "
2 (2
(1) & → ∞ (2)
1
lim+→:
{&(& − 1)(& − 2)… (& − ' + 2)(& − ' + 1)!)} = &! ) = .)
2 1 (3) (1) (2)
mî÷� ¹°]�(('|.)!O× {�ñØ .n�' ����!l1�.� 1 �.óSJ!m� À�+ó
m 1� 5A1B = 0!'0-�93AF}ä�+ó m 2� m 1!Æ�1`³��ñSJ!��-¾� �1º�ó
(()|4)
:
)CD
= 1
A
F =5 36 2
(1)
1 A
2 1
3 2 G
G,1
4 3 A
O-XYZ Q N ', P, Q
X α
S) T
S) T =1 0 00 cosT −sinT
0 sinT cosT
(2)
Q N '′, P′, Q′ S) T Q
1 Z [ S\ [
2 Q N ', P, Q = N 1,3,5 ]T 1
N '′, P′, Q′
3 T = [ = ^ 2 2
I
_ ` , a(`)
ℱ _(`) ≡ _ ` 5defg`,:
,:
ℒ a(`) ≡ a ` 5,ifg`:
j a ` = 0, ` < 0 m Rem > 0
_ ` , a(`)
_ ` qg` < ∞:
,:
_ ` = r5,sfcos(jD`) _ ` = 0, ` < 0 At, jD > 0 , ℱ _(`)
ℱ _′(`) ℒ a′(`) ℱ _(`) , ℒ a(`)
ℱ _′′(`) ℒ a′′(`)
a(`) u(`) ≡ a(v)gvf
D ℒ u(`)
1 ℒ u(`) t t t t
t t 2 1 t
t 1 t t
3 2 a(`) ℒ u(`) ℒ a(`)
I –
w B 0 ≤ ' ≤ B) y ', ` ∂y
∂`= w
∂qy
∂'q
` = 0 y ', 0 = _ ' ' =
0, B y{, yq
y ', `
yi(')
y ', ` ≡ yi ' + Θ(', `)
Θ(', `) Θ(', `)
Θ ', ` = 0
Θ(', `) ≡ } ' ∙ �(`) Θ(', `)
' t } ' , �(`) A,
B, C Ä
} ' = r sin Ä' +Åcos Ä' ,� ` = *exp −wÄq`
Θ ', ` = 0 } ' , �(`) Å = 0 ÄB = &^ & = 1,2,⋯
. Θ ', `
*+
Θ(', `) = *+exp −w&q^q
Bq` sin
&^
B'
:
+C{
y ', 0 = yi ' + Θ ', 0 = _(')
*+ _(') y ', ` .
( , , , )
1 Vp A B B C
C A 1Cp Cv
1 A B ΔU
2 1 Cp Cv R
3 A B ΔS
4 1 dQT!∫ T Q
1) 2) 1) D H
d , D >>d
z r gv = (a)
z r D, H z = (b)
Q1 Q2 zu = (c)
1 1) (a) (c)
2 1) Te
2) θ
H M rz (< H)
v I ω gMgH = (a) ω v = (b) ω Mgz = (c)
s s sinθ= (d) v = ds/dt = (e) ×(dz/dt)
3 2) (a) (e)
4 I (2/5)Mr2
dv/dt g, θ
�ġĥĞĉ¡ğ ÕæĖÁ I ���Ġy(a) Ø�,� ÕæĖÁ�-ÿĕ R Vé�/Ėî q!¹!îĖâ�ą� v �Ùi�/�q�Ġy(b) Ø�,� ģă!ď� L !¹¬�!�WwĀ ABCD ą� v �Ùi�/�q2ê�/Ģ��-!�q�)ĠÕæĖÁ!r�ą� v!r"ÕQ���/ĢTN!uě ôá�,Ģ��ÖÜ!Ą×Î"µ0��/Ģ
uě 1 ÕæĖÁ IĠÿĕ Rĕ0�}É ��/×±�� B!��2½(,Ģ uě 2 y(a)!�qĠÕæĖÁÑ'c�×� ,.ĠîĖâ� ]�IKHJ?
g!��2ĠI� R2Ò��ð�Ģ uě 3 y(b) ���ÕæĖÁ�ă AD!ÿĕ2 R��ĠTN!u� á�,Ģ u 1� ÕæĖÁÑ'c�×� ,.ă AD Ñ�/ø�þĖg!��2½(,Ģ u 2� pă�!ø�þĖg!t2½(/ ��-ĠÕæĖÁÑ'c�×� ,/
wĀ`W�!ø�þĖg2½(,Ģ u 3� ÕæĖÁÑ'c�×� ,/wĀ ABCDa�!×±Φ2½(,Ģ u 4� wĀ ABCDa!×±!Đ�j�-ĠÕæĖÁÑ'c�×� ,/wĀ`
W�!ø�þĖg2½(Ġu 2�½(�[�Lí�/ �2Ø�Ģ
1) 2) 1)
10-3 10-2 cm/s ( )
ρ g Vp, p0 z
(a) M (b) Z (c) P M, Z, P
(d) (e)
1 (a) (e)
2 V = 10-2 cm/s z =300 m p = 4.0×105 Pa, p0 = 1.0×105 Pa
( )ρ = 1,000 kg/m3 g = 9.8 m/s2
2)
A L
QΔL a b 2 z1 z2
�1 �2 “ q2 ( + ) 2 ΔL
” Ks
3 2)
4 2)q
( + )
1 1 3
N2 °C
1
2
3
2
3 60
wt% 1.37 g cm-3 100 cm3
4 60 wt% 1.37 g cm-3 100
cm3 1.0 mol L-1 cm3
IIIó÷ð�ìñXR"uí�$�!ÚÈ�*ô
uí 1�д¼"0FBå#PÑ!ow"¤â��×�-,ô���òR# HòCòOòNòS ��+�,l~v�,ôR×"ð0ñúð;ñ#�-)0FBå�,ô14
2.t/�,"#ð5ñ���,ôÓî�¤â.�
��,"#ð7ñ���,ôð9ñ�ð;ñ#¤â
¾�Z�,ôHòCòOòNòS "l~æ.�-�- 1ò12ò16ò14ò32��,ôд¼"0FBå!è�,XR"u!È�*ô
u 1 0FBåð3ñòð4ñòð5ñòð9ñ �-�- 15ò10ò13ò12 b~Ìq��>NC9à.¤�����ò�">NC9à"b~æ.È�*ô
u 2 ê£�"T�0FBåð0ñ"¤â�.È�*ô
u 3 £�"T�0FBåð1ñ"¤â�.È�*ô
u 4 zy�0FBåð2ñ"¤â�.È�*ô
u 5 å�0FBåð3ñ"¤â�.È�*ô
u 6 142.t'0FBåð5ñ"¤â�.È�*ô
u 7 Óî�¤â.t'0FBåð7ñ"¤â�.È�*ô
u 8 0FBåð9ñ!#ö�"S�²Ë ,ô�"¤â�.È�*ô
u 9 0FBåð;ñ!#÷�"S�²Ë ,ô�"¤â�.È�*ô
u 10 0FBåð;ñ"ÆZ¾�Z. Fischer���!*���$�È�*ô
u 11 S�²Ë.�� 0FBå"¤â���ºs.ö�È�*ô
1 −74.40 kJ mol-1
2 716.68 kJ mol-1
217.97 kJ mol-1
3 CH
1 2
4 8.180 kJ mol-1 111.67 K 4
5 Na Al300
IV ®Ħľ¿ I� pi,Ƭ¨ƥIVƨ1ƧIVƨ2ƧIVƨ3Ʀ�2%*ŭŅ�9Ʃ IVƨƪƥàƝƦ� pi,¨Ơ*Ņ�9Ʃ ¨Ơ 1� œģƌƍÔƥBanded Iron Formation; BIFƦ,Ī�ƟÖ,Óo�Ð?Ľ�
«?�Ř*�%Ƨpi,¨�*Ņ�9Ʃ
�« œģƌƍÔ,Óo�ÐƥKlein, C. and Beukes, N.J. (1992)Proterozoic crustal evolution (Condie, K.J., ed.)ElsevierƧHolland, H.D. (1994)Early life on Earth (Bengtson, S., ed.) Columbia Univ. Press*±$�%xãƦƩ
¨ 1 BIF,Úã-Ƨ�FdX`Aûo*��<®ĦĨ´,�İ)¶�'Ãê
*ƒ>"%�<'Ř�:=%�<Ʃ(,9 )Ĩ´¶�'ƒ>"%�<
,�Ƨ�,ĩã]FSL\?¦6% 100½ŀÖ&Ųú�9Ʃ ¨ 2 BIF-¤Ŀ,'�;œģĈƂ?Ģß'�<�Ƨ)��,9 )ĈƂ?)
�,� 100½ŀÖ&Ųú�9Ʃ ¨ 3 27�Ó�9;��ûo, BIF-H`fdKQfdÑ&Ī��%�%ƧŪ
ċ��4;·��)�NBY&�<�'�>�"%�<Ʃ�=pƓ,
BIF-Ƨ·ƕą&²ł� ·Ūċ)NBY')<Ʃ�=:,�'?ż4�%Ƨh«�: BIF,Úã*ƒ><®ĦĨ´,¶�*#�%Ƨ150½ŀÖ&Ųú�9Ʃ
¨ 4 8Ƴ6�Ó�*Úã�= BIF-Ƨ�,Ùû*�Ħİ*Ż�" Ĩ´ğ¶
,BZdQ'ƒƃ�%�<'Ř�:=%�<Ʃ�,Ĩ´ğ¶� BZd
Q-w'§.=%�<�ƧŅ�9Ʃ
2
1
2
3 30
4
2
5 34S 50
H2S SO42-(�)
(�)
FeS2(�)
�ƨƫƥàƝƦ� pi,óń?ų5Ƨ¨ƠƪƳƭ*Ņ�9Ʃ �<®°?āŧ*ź<ĕÒ)ưŵ,�Í&Ƨl#,ƙƞ�ŴĄOf\*9"%
ūÄ�= Ʃƙƞ�*-ŹŝÉģO^fQ�:)<®ÉƮ�ƙ��%�;Ƨť
Ɨ)ŦüĈƂ?Ľ�%� ƩO^fQ�:-Ƨ[a\ʼn�þ,ïðŠ
Pseudoalbaillella�å��= Ʃƙƞ�*-Ƨ��÷¥,ź¥'ā1 60Ö,~ô?æ#®ÉƯ�ƙ��%�;Ƨŧ}�:ƧļÌƧ�ÉķÌƧķÌ'ĘÌ,mÉƧ
,Ɯ*Ɗ)"%� Ʃ�Éķ
Ì�:ƧlĂŶBTM_\K
ƥInoceramusƦ,�Ķ�ũ��= Ʃl#,ƙƞ,Ƒ*-
>��)ƙ�,č¸��;Ƨ
®ÉƮ'Ư,êŮƒz?ūÄ
�<�'-&�)�" Ʃ ¨Ơ 1� ŴĄOf\-Ƨ®ÉƮ'®ÉƯ,IJmƒz'�%jò¢ƒz�¹
Ù'�õ� Ʃ�,ħĬ'�%Ř�:=<�'? 100 ½ŀÖ&Ųú�9Ʃ
¨Ơ 2� ưŵ,�÷,Ʊ®ĠeƲ®Ġ&Ƨ
£ĉ*®ÉƮ'®ÉƯ,´ĭ�¾
�<�'�ĻŰ�= Ʃ�,Ċ
Ƣ-Ʊ®Ġ�ưŵ9; 100 mƢ�ƧƲ®Ġ�ưŵ9; 50 mu�ƩāŧtŖ-ƧƱ®Ġ�ưŵ,´ĭ9;
7 58 mŧƧƲ®Ġ� 29 mā!" Ʃ
®ÉƮ'®ÉƯ,´ĭ�Òƛ&�,ź¥���'qÁ�%Ƨ´ĭƛ,
~ô'~ô÷¥?Ė69ƩÆ�,ƅŀ7Ľ�Ʃ
��
���
���
N
���������
58 m
29 m
S
W E
����� ������
¨Ơ 3� ®ÉƯ,ķÌ'ĘÌ,mÉk*è4=<ķÌ�É,JdYa?é�
��õĊÿ*�%ūÄ�<'Ƨ¡
«,9 )�ƈĈƂ�Ű6:= Ʃ
)�«-ƧJdYa?��:ũ
Ńƛ«&�<Ʃpi,¨�*Ņ�
9Ʃ ¨ 1� � �,ūÄŐă�:®ÉƮ'®ÉƯ
,ƒz?ũı�àŨ�ĩ� Ʃ)
�ũı�=)�=.):)��Ƨ
4 ũı� Őă�:(,9 )
řâ�Ř�:=<�Ƨ120 ½ŀÖ&Ųú�9Ʃ
¨ 2� � «,ķÌ�É,�vİ)�ƈĈƂ-Ƨw'§.=<�Ƨ�,ãª''
7*Ņ�9Ʃ ¨ 3� � pi,óń,� � � *�<ű?Ņ�9Ʃ
®ÉƯ,ķÌÉ*ũ:=<9 )Ƨ�É�&ŇÛ�hi÷¥*¶��
<ĈƂ?� ƥ�Ʀ� '§0ƩgŜ*ƧĸÇŇ¼�ėƓ�<Ɩ,ƁÖÏ
*9;Úã�= 7,'�=<Ʃ»Ÿk,Ň¼,ýōİ)ėƓƁÖ-Ƨ
Ň¼Û,� ƥ�Ʀ� 'ƧŇ¼'»Ÿ,� ƥ Ʀ� Ï*ƧĔy�<Ʃ ¨Ơ 4� ƙƞ�?ůŌ*ūÄ�<'Ƨ®ÉƮ,k*ŷ��<ş�ÀËÌŚ�į
ũ�= Ʃ�,ÀËÌ,őÅÓo'�% řâ��<7,?i�:�
2%Ƈ2Ʃ 1000 MaƧ500 MaƧ250 MaƧ125 MaƧ60 MaƧ30 Ma
��
����
�����
�
10 cm
�
�
����
1 simple shear
2 pure shear30
3 °
τ, τc, σn, µC °
20 km150
4
30 km
0 kbar ( MPa) 0 °C
1 10 °C/km 30 km° 3 g/cm3
10 m/s2
2 25 °C/km15 km
°
ACF
3 kbar MPa °C
30
ACF
A=Al2O3, C=CaO, F=MgO+FeO
!"#$%&'
!"#$%&'()*'(+*'(,*'($-./0123456 '()&78-9:;<#=>#?;@ABCDEFG*?;#HIJ 3K#LMNO1PQRSD6TD*?;UVW1XYZ@[\]5^_`#abcde/D
EFG*!"#5fgFEhijkD6!"#%l13m56 !"#$%&!"#$%&!"#$%&!"#$%& LMNO 1n;o5p?qrhstuvC0swx 15 km1yC*z#W*{
jR|}h~"C0�tXYCD6 LMNO 2n?qrh=���C0*;��h��@�Q"kD6 LMNO 3n?qrh�TkDW*;ojR��h�"CD6
!'()*+,-./012&!'()*+,-./012&!'()*+,-./012&!'()*+,-./012&
1) LMNO 1#XYZ@ABCDEFG*��Z�J�0|}d9kD6��CD|}1J*��}*}�*����}*���h���ZEC0�
TS0�D6���`P�#� *SiO2 = 66 ¡¢%d9kD6 2) LMNO 2#;��h�"CDEFG@e£C*�¤¥ m#XYZ@¦§
CD6zFjR��Z�EC0LMNO 1E¨©|}#ª1«¢#¬®¯E*°±h²©p9kD³´|}@µ¶CD6|}JLMNO 1E¨©d9kDh*¬®¯1J��}E·¸¹¸}h��EC0�TS0�D6
���`P�#� *SiO2 = 51¡¢ºd9kD6 3) ���#»�JN¼¬´#½¾d¿iS0]p*���ÀÁ#»�ÂÃ
ÄhÅÆd9kD6��1J*��}*}�*����}*jÇRÇ}]
5^���h��EC0�TS0�D6���`P�#� *SiO2 = 56¡¢ºd9kD6
%l 1È LMNO 1#?;ÉÊ@3m56 %l 2È LMNO 2#;��dJ*�"Ë1;<Ì@�ÍÌÎÏEÐÑS:
ash-cloudhÒÓ.:6F#ÌÎÏhÒÓ.:Ô·ÕOÖ1K�0 80×ØwdÙÅ456
%l 3È LMNO 3#���#ÚÛÜ@3m56TD=ÝÞg���#»�ÂÃÄ
EC0ß»Þgà#@ 2K3m56
!" 4# $%&' 1($%&' 2)*+,)*+-.)/0(12)345678
9:;<=(>)/0:?0@1ABC@ 150DEFGHIJK !" 5# $%&' 1)LM($%&' 2)NOPQ)RMS5HIJK !" 6# $%&' 3)TUT)VWXYZN512)J[:\I=]^((_: 50
DEFGHIJK
!"#$%&' ()*+,-./01234567 89:;<=>?@A@B08);CDEFGHI>JKLMG0$ N 'GOPQR*STBUVWM7X*YZB[*6P3\]LM^0_XPS`@A@*a
bKcUd-e3f5g/6P7X*@A@h0SiO2"NaAlSi3O8"KAlSi3O8 * 3=ij;kl;mMn*G>0hophqr*/^VsMG>6P7)*thu*
rabt;vM7tw*x= X *@A@BCDEFHILMG0yz$ { '|;$ } 'Bc~-��>0q*x=B��>hopM7u>g0�6u$ � '|y;��B)BMG$ � 'nc~>hopM7�V3��B�)>$ � '|3sMG$ � 'nc~LM6P3sM7����-�LX*�h$ � 'G��WM7u>g0(a)@A@*Kc�B��LMG0�V3��B�)LM6P3sM7
KcUdB\��0�^3h�B!XM"�P^7@A@3h H2O -#=iGLM$�%=iB��>gOM7(b)H2Oh0T�&�T*Kc3h�G�[ F'yWsO?p0Kc�B\�Gqr3()>gCE7u>g0q* H2O (�B*+���3¡LMG0H2O-#=iGLM¢,$-,y?h./0¢,'B£~LM7>?BDg0Kc�*\�"@A@h0J,1q,1¢,B23LM 3rj;vM7X*6Ps¤4;h0¥`56B¦7;!XM?p0$ 8 'G��WM09>E:;sKc$§ cm<§ m'^VsMSTB>�>�¨=�WM7Kc�=>*qr3h©ª?@n()>gOM?p0$ 8 '3h0uWV-#=i3n«(c)A¬
T&B-Ts[0CDE*¦O®¥B¨=�WMXGnvM7
SiO2!NaAlSi3O8!KAlSi3O8"#$%&'( )*+#,-./0123456( !"# 500 MPa$Johannes & Holtz (1996) %&'(
!" 1 # $ %!# " %&#'()*$%)+(,-.&/0 !" 2 1'2(a)&34'5# 6 %7(5898:;<&=>?@AB:(CD
E4F)GHI:1:JE40KLKM.5B*.N4' 100-OI7PQRS0
!" 3 1'2(b)&34'5AB:=>?@'TUMV5+AL H2O,I:WL
SX&Y?Z*F5[1L! 1!! 47-@U\]'^SX0+.@5H2O(=>&(_/`aRb5+A&L^,0Z*cLMZ*0
! 1 de MLA:fG5gL H2O,I. C0#hei1%MZ*0KLA&j
)D* H2OLde. M5C0.N4'kR0 ! 2 KLAFJ5de m#+.@ m < M%L=>:lm@+MZ*0+AL
H2O,I. C#hei1%MZ*MV5+AnL H2OLde. M, m, C.N4'kR0
! 3 ! 15! 2L=o.cM&=>?2p7L H2OLde34q.5'5C.
C0, m, M.N4'kR0 ! 4 67 H2O,I: 4her#hei1 0.04%LA:=>Z*KM.\]*0
s8:lm@(tu*L(5m/M#=>?I%:4UJ&v@+MVF9:RS0+.@ H2OL;<`aI. 10herMZ*0
!" 4 1'2(c)&34'5f*wKXx8.yz@+MK{5=> 10 cm, |}
63 cmL?~E@��#Be3Al2Si6O18%L=>:��}D+0KLA��L
@��=>(5BCXW 100 mol&B#Z*0KL=>.�*&(� m3
LAFJ Be.0uE/D�EJE4F9:RS0+.@5[1L 43LDE.N4S0
FABLGI �2000 kg/m3 FABL Be,I �0.005her#50he ppm% FBeLHIe �9.0 FABnL Be(Z�'@��L=>?&JK}D*
!"#$%&'()*)+,!-."/012*34.5678 34 1 90:*();<=#*>[email protected].$C%/D!-E908F*!-
GHIDJK<5678LM<F*!-G&N();<O*>?PQ.R
*7JS='E90K<40TUVW5678 34 2 (XYZG)[\<**(1)+(4)*,-W()*.V !MG/#]M8
(1) ^*(XYZ*X_ W0G`[M8 (2) (XYZ.0`*()12G3C<X_ W1G`[M8 (3) (XYZG/#aV.bc0.V ! *d4G5]\6M]<X_
W2G`[M8 (4) (XYZKe12Gfgh]<.V ! *d47cW6M]<X_
W3G`[M8 /#]M()12*.V !MG !<W0<W1<W2<W3G)[\ijk8
34 3l ()*m.;<89Sn:W;;<=oW90E<>pq`*?r@A
GstFI.7[\B]pC<]<DuI]\EX_C0v*E908
Du*FGwIHxIyz;<()I]\;{|v*W90E<J<*
v*GFGw<OC1}*<*v*GHxIyzI~K8FGwIHx
Iyz*()�I89Sn:*����G5678LM<FGw*J<
*LMI�6eC0?r@Ay��GN�IIv.5678 34 4l ()*<;<>?�G�/I�IOP.]MI�W�p�J<G�/F
IE908Q��yR$Fe2O3';<>?�G�/I�;STUVG�/
FIE90E<OP.]MI�;H<G�/K<5678LM<()G
OP.]MI��/<GHIDJK<5678 34 5l ()*W_Gi/XVI]\Yw�WVE908Yw�WVI;R*7
JSv*K<40TUVW�ok78 34 6 =oS()>?;<>?�.7[\U�,Z[4IU�,\[4.jc
eC08U�,Z[4W90>?�G5678LM<U�,Z[4IU
�,\[4;<]U^q_��WR*7J.`a/0FIEW�0K<
70TUVW�ok78 34 7 ��.<U�,\[4*mWU;<[email protected]<g_*\S
0hN*]U.jKC\�t8F*ijGHIDJK<5678
!" 8 #$%!"#&$'()*+,-%./01234./56&'789
#$:;5(<=>3?@A6B2=C6DB:)E%F2GHI4J
K8DL14B:)E%;5MN%440OPQ'JK8D !" 9 RS:TUV4TU%*+019,W-W19562X.56DB:)
E%F2GHI4JK8D
!!"#$%&'()*+,-./0123456 7 89)":)9;)<#/=>)$?@A:)%&BCD'D(E2)F@*+,
-,G:9;H/./0I19;2JKLDMNO6PDH/GJGJ89)QR
BST)UV25WMXFDMYO3Z2/P)9;24[@5\)89)6]7
8])TB7 ^7 _`@PJabc9dbDOG))5<_`@6C)e, fZ89gBh:iM;<89jklmBn./P)9;)*+,-H(1=T_`@J
>DOB/c>)1HST2o/[@0I12,C)pp?Y@dMNO6C)O
qAr89gBHCD89E_`@ 2014E,F2/P)9;)cGJiM/(Hs2Fat7[Y0(19;#I19;&2,?<5<2IJiMY@6 01 1 0(19;#I19;&224[@892H/(110), (1 10), ( 110), ( 1 10)]
,u]#c&2vX?]&J[@ST,K:G)B5\wbD@6#a&)=>&x#b&)=>&= 2x1)JN/P)5<?89) c&2L(?])T,yz{56pOP)8|5t/ ^ 2`MHp@MN,3456
01 2 a}b}~JI1O~H/JG2P)9;24[@P�QR��_`@B
SiO4S]=)8T��H$?@6SiO4S]=)8T��_QRiO3/C
D'D�JY<�U��24[@a/3456pO/SiO4S]=)8T�
�H/a}b}~JI1O~_�)5<2$?@a/�YBFa@5<2, 60���_V�56
01 3 O~2H/�W2V�O0(19;#I19;&224[@I1O~Xd
_H?\/*I9;24[@*IO~GYZ[@6[\]�^,�YM/
I1O~J*IO~,_`[@1a,/40���_bc2V�56
! ! ! ! ! ! ! !
!
"# 4 $%&'(!)*+,-./01"2#$3 CaCO3%%42+*5CaCO3
(67*8&9(:;<0=>%";(?@A5
" 1! 'B'"2#$3 CaCO3%%4C A8D)*DE0A8%FGHC?@A5
" 2 (I(67*)*(a)D(b)/0+
,-.D A8%0+JK,-.L G %'B(67*"/MNCOPQR%2+*5+,-.
%+JK,-.LMNCSP<
;*%/(a)T(b)T0?@A5! ! " 3 +*8%+JK,-.L G %
U$BVWTX(67*"/YZ/0[%8%0\ VCS).
VPG
T
=⎟⎠
⎞⎜⎝
⎛
∂
∂
$%$DC1]P<0^8_2
3)*"/ P0(67*4V/0
+,-.DA8%`5,_aE;TC0120 bcV%dJC:7<?@A5