Birch-Murnaghani võrrandi lähenduse tuletamine: Difference between revisions
From Intelligent Materials and Systems Lab
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<math> E(V) = E_0 + \frac{9 V_0 B_0 }{16} \left\{ \left[ \left(\frac{V_0}{V}\right)^{\frac{2}{3}} -1 \right]^3 B_0^' + \left[ \left( \frac{V_0}{V}\right)^{\frac{2}{3}} -1 \right]^2 \left[ 6 - 4 \left( \frac{V_0}{V} \right)^{\frac{2}{3}} \right] \right\} \;\; (1) </math> | <math> E(V) = E_0 + \frac{9 V_0 B_0 }{16} \left\{ \left[ \left(\frac{V_0}{V}\right)^{\frac{2}{3}} -1 \right]^3 B_0^' + \left[ \left( \frac{V_0}{V}\right)^{\frac{2}{3}} -1 \right]^2 \left[ 6 - 4 \left( \frac{V_0}{V} \right)^{\frac{2}{3}} \right] \right\} \;\; (1) </math> | ||
Gruppeerides võrrandis (1) liikmed < | Gruppeerides võrrandis (1) liikmed <math> \frac{V_0}{V}</math> astmete järgi saame järgmise võrrandi: | ||
<math> E(V) = a + b \cdot \left(\frac{V_0}{V}\right)^2 + c \cdot \left(\frac{V_0}{V}\right)^\frac{4}{3} + d \cdot \left(\frac{V_0}{V}\right)^\frac{2}{3} \;\; (2) | <math> E(V) = a + b \cdot \left(\frac{V_0}{V}\right)^2 + c \cdot \left(\frac{V_0}{V}\right)^\frac{4}{3} + d \cdot \left(\frac{V_0}{V}\right)^\frac{2}{3} \;\; (2) | ||
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<math>a = </math> | <math>a = E_0 + \frac{9}{16} \cdot V_0 \cdot B_0 ( 6 - B_0+^') \;\;(3)</math> | ||
<math>b = </math> | <math>b = \;\;(4)</math> | ||
<math>c = </math> | <math>c = \;\;(5)</math> | ||
<math>d = </math> | <math>d = \;\;(6)</math> | ||
Revision as of 11:42, 28 November 2008
Vaatleme võrrandit:
[math] E(V) = E_0 + \frac{9 V_0 B_0 }{16} \left\{ \left[ \left(\frac{V_0}{V}\right)^{\frac{2}{3}} -1 \right]^3 B_0^' + \left[ \left( \frac{V_0}{V}\right)^{\frac{2}{3}} -1 \right]^2 \left[ 6 - 4 \left( \frac{V_0}{V} \right)^{\frac{2}{3}} \right] \right\} \;\; (1) [/math]
Gruppeerides võrrandis (1) liikmed [math] \frac{V_0}{V}[/math] astmete järgi saame järgmise võrrandi:
[math] E(V) = a + b \cdot \left(\frac{V_0}{V}\right)^2 + c \cdot \left(\frac{V_0}{V}\right)^\frac{4}{3} + d \cdot \left(\frac{V_0}{V}\right)^\frac{2}{3} \;\; (2) \;\; , kus [/math]
[math]a = E_0 + \frac{9}{16} \cdot V_0 \cdot B_0 ( 6 - B_0+^') \;\;(3)[/math]
[math]b = \;\;(4)[/math]
[math]c = \;\;(5)[/math]
[math]d = \;\;(6)[/math]