المسألة المعاكسة للمعادن السائلة البسيطة دراسة حالة الألمنيوم السائل عند درجة الإنصهار
Abstract
In an attempt to test the possibility of solving the inverse problem for liquid metals i.e. obtaining the effective pair potential from the experimental structure factor, we solve the modified Hypernetted-Chain Integral equation for liquid aluminum at melting temperature to obtain the effective pair potential starting from the experimental structure factor and compare it with the potential obtained from theoretical considerations. Then we use the potential obtained by solving the inverse problem in Monte Carlo simulation to test it, and the calculated structure factor of the liquid aluminum is compared with experiment. We show that the solution of the inverse problem in such cases gives reasonable quantitative results, and reproduces the general features of the pair potential and the results for the structure factor are not far from the experimental measurements.
في محاولة لإختبار إمكانية حل المسألة المعاكسة للمعادن السائلة أي الحصول على كمون التأثير المتبادل بين الجزيئات انطلاقا من عامل البنية المقاس تجريبيا، نقوم في هذا العمل بحل معادلة الـ Modified Hypernetted Chain التكاملية من أجل الألمنيوم السائل عند درجة الإنصهار للحصول على كمون التأثير المتبادل بدءاً من قيم عامل البنية المأخوذة من قياسات الأشعة السينية التجريبية. و قد قمنا بمقارنة النتيجة مع الكمون المحسوب من طرق نظرية، ثم قمنا باستخدام الكمون الذي حصلنا عليه من حل المسألة المعاكسة في طريقة مونتي كارلو لحساب عامل البنية و مقارنته مع التجربة.
نبين في هذا العمل أن حل المسألة المعاكسة في مثل هذه الحالات يعطي نتائج عددية مقبولة و ينتج عنه كمون قريب من الكمون المحسوب نظريا كما أن نتائج حساب عامل البنية بالإعتماد على الكمون المستنتج كانت قريبة من القيم التجريبية.
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