晶界破裂會對粉碎後礦石的粒度分佈與品位變化產生影響，並且是造成粒度與品位異常分佈的主要原因，這是早在1939年的高汀 「選礦學」教科書中所明確指出的。歷經六十餘年，卻仍然沒有數量化的研究出現。本論文就是要將礦石粉碎時，晶界破裂的比例P作為量化之基礎，應用以往發展出來的暴露與單離模式，導出粉碎礦石的粒度及品位分佈的量化數值，並且經由實驗結果驗證，證明這個量化計算模式的正確性。

　　本研究是根據徐與溫（1995-1998）的單離模式以及暴露模式作為基礎，來進行礦石粉碎後的粒度分佈與品位變化的探討。驗證理論的推演，是以顎碎機進行粉碎礦石，得到的粉碎礦石產品進行篩分析以獲得顆粒大小分佈，每個篩徑範圍進行品位分析，以得到不同顆粒大小的品位數值。同時分析獲得樣品的組成、礦物晶粒大小分佈，配合不同程度的晶界破裂係數，來推算粉碎礦石中有價礦物之品位變化，和實驗分析的結果比對驗證，最後得到理論推演正確與否之結論。驗證樣品有不銹鋼電爐渣、碳化矽廢磨石與含磁鐵礦的滑石片岩等，都是國內資源回收項目的原料。

　　從粉碎實驗得到粉碎礦石的顆粒大小分佈、各粒徑區間的品位、晶粒大小分佈等數據，應用暴露模式的公式，來推算粉碎後爐渣、磨石與滑石片岩中的有價礦物之品位變化，發現在特定的晶界破裂係數之下，實驗分析的粒度分佈及品位變化都與經由公式推算的結果十分吻合，本論文推演的模式應用在這些物質的粉碎產品粒度分佈及品位變化應是獲得實證。經過計算得到的爐渣晶界破裂係數為0.30，碳化硅磨石的晶界破裂係數為0.35，滑石片岩的晶界破裂係數為0.70。採用不同的顎式碎礦機閉口間隙，將會造成有價礦物不同的品位變化，也可以據此訂定出較為有利於後續分選作業的粉碎作業條件。

　　本研究推導了一個品位計算模式，來估算粉碎礦石中的有價礦物的品位隨著顆粒大小而變化的狀況。由於可以實際測得粉碎礦石的粒度分佈、結晶粒度分佈、品位，並以晶界破裂係數算出品位變化值，因此可以應用在粉碎工程中的產品品質控管的流程中，作為提升粉碎作業效率的一種有效評估工具。確實改善了目前過於龐雜繁複的估算粉碎產品之品位變化的方式，具有簡便且真正實用的價值，這也是本研究最大的貢獻。

　　Grain boundary fracturing, proposed by Gaudin in 1939 in his textbook “Principles of mineral dressing”, is a major influencing factor that makes the abnormal distribution in the particle size and the grade of comminuted ores. But there is no other quantified research presented for about 60 years since then. This study is based on the quantified factor, intergranular fracturing factor P, in comminuted ores and uses the exposure model and the liberation model to infer the quantified values of particle size distribution and grade distribution of crushed ores. By the experimental results, the accuracy of the quantified calculation model based on the models is proved.

　　This study is based on the exposure model and liberation model of Hsih and Wen (1995-1998) that are utilized to study the abnormal distribution of particle size distributoin and grade variation in comminuted ores. Experiment is applied to put to the proof of the inferred model. The experimental procedure is conducted by jaw crushing and the comminuted ores sieved to gain the particle size distribution and analyzes the grade distribution in each size interval. The components and grain size distribution of samples are also obtained by experimental analysis. With different intergranular fracturing factors put into the model to calculate the grade variation of valuables in comminuted ores, the results of right or wrong for the model inference is obtained. Samples utilized to test are arc steel slag, waste SiC grinding stone and talc schist that are recycling material in Taiwan.

　　Particle size distribution, grain size distribution and grade variation in each size interval, obtained from experimental and calculation, are utilized in the formulae of grade variations of the exposure model to compute the variation of grade in valuables of slag, grinding stone and talc schist. It’s found that in a specific value of intergranular fracturing factor the calculated results of formulae are matched well with experimental results. The inferred model in this study puts to proof by the good coincidence with the experimental data. After the calculation, the intergranular fracturing factor, P, in slag is 0.30, in grinding stone is 0.35 and in talc schist is 0.70. Different closed sets at a jaw crusher make the variations of grade in valuables and the comparatively better condition of comminution and liberation can be chosen.

　　This research derives a useful calculational model to evaluate the variations of grade at different size ranges in comminuted ores. The evaluated method applied in the quality control of comminuted products promotes the efficiency of comminution procedure. It indeed improves the numerous and jumbled calculation works conducted by other researchers. The grade variation model is proved to be simple and practical and it is also the greatest contribution of this study.

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