Phosphogypsum(PG)is a potential resource for rare earth elements(REEs).Several studies have been carried out on REE leaching from PG.However,few in-depth studies have investigated the kinetics of this leaching process...Phosphogypsum(PG)is a potential resource for rare earth elements(REEs).Several studies have been carried out on REE leaching from PG.However,few in-depth studies have investigated the kinetics of this leaching process.In this study,the leaching kinetics of REEs from PG in nitric acid at different temperatures were explored in depth.The experiments show that the maximum leaching recovery for ΣREE was 58.5%,75.9%and 83.4%at 30,60 and 80℃,respectively.Additionally,among La,Ce,Y and Nd,Y had the highest leaching rate.A new shrinking core model(SCM)based on the dissolution reaction of a cylindrical solid particle with interfacial transfer and diffusion across the product layer as the rate-controlling step was deduced and could well fit the leaching process of REEs from PG.The activation energies for the leaching of La,Ce,Y and Nd were determined on the basis of the new cylindrical SCM.In summary,the cylindrical SCM was a more suitable fitting model than the spherical SCM,and the interfacial transfer and diffusion across the product layer were the rate-controlling step for REE leaching from the PG sample.展开更多
The matrix least squares （LS） problem minx ｜｜AXB^T--T｜｜F is trivial and its solution can be simply formulated in terms of the generalized inverse of A and B. Its generalized problem minx1,x2 ｜｜A1X1B1^T ＋ A2X2...The matrix least squares （LS） problem minx ｜｜AXB^T--T｜｜F is trivial and its solution can be simply formulated in terms of the generalized inverse of A and B. Its generalized problem minx1,x2 ｜｜A1X1B1^T ＋ A2X2B2^T - T｜｜F can also be regarded as the constrained LS problem minx=diag（x1,x2） ｜｜AXB^T -T｜｜F with A = [A1, A2] and B = [B1, B2]. The authors transform T to T such that min x1,x2 ｜｜A1X1B1^T＋A2X2B2^T -T｜｜F is equivalent to min x=diag（x1 ,x2） ｜｜AXB^T - T｜｜F whose solutions are included in the solution set of unconstrained problem minx ｜｜AXB^T - T｜｜F. So the general solutions of min x1,x2 ｜｜A1X1B^T ＋ A2X2B2^T -T｜｜F are reconstructed by selecting the parameter matrix in that of minx ｜｜AXB^T - T｜｜F.展开更多
基金Project(51904104) supported by the National Natural Science Foundation of ChinaProject(2020JJ5174) supported by the Natural Science Foundation of Hunan Province,China+2 种基金Project(2019M662780) supported by China Postdoctoral Science FoundationProject(19C0746) supported by Scientific Research Fund of Hunan Provincial Education Department,ChinaProject(2021-2843) supported by College Student Innovation and Entrepreneurship Training Program of Hunan Province,China。
文摘Phosphogypsum(PG)is a potential resource for rare earth elements(REEs).Several studies have been carried out on REE leaching from PG.However,few in-depth studies have investigated the kinetics of this leaching process.In this study,the leaching kinetics of REEs from PG in nitric acid at different temperatures were explored in depth.The experiments show that the maximum leaching recovery for ΣREE was 58.5%,75.9%and 83.4%at 30,60 and 80℃,respectively.Additionally,among La,Ce,Y and Nd,Y had the highest leaching rate.A new shrinking core model(SCM)based on the dissolution reaction of a cylindrical solid particle with interfacial transfer and diffusion across the product layer as the rate-controlling step was deduced and could well fit the leaching process of REEs from PG.The activation energies for the leaching of La,Ce,Y and Nd were determined on the basis of the new cylindrical SCM.In summary,the cylindrical SCM was a more suitable fitting model than the spherical SCM,and the interfacial transfer and diffusion across the product layer were the rate-controlling step for REE leaching from the PG sample.
基金supported in part by the Social Science Foundation of Ministry of Education(07JJD790154)the National Science Foundation for Young Scholars (60803076)+2 种基金the Natural Science Foundation of Zhejiang Province (Y6090211)Foundation of Education Department of Zhejiang Province (20070590)the Young Talent Foundation of Zhejiang Gongshang University
文摘The matrix least squares （LS） problem minx ｜｜AXB^T--T｜｜F is trivial and its solution can be simply formulated in terms of the generalized inverse of A and B. Its generalized problem minx1,x2 ｜｜A1X1B1^T ＋ A2X2B2^T - T｜｜F can also be regarded as the constrained LS problem minx=diag（x1,x2） ｜｜AXB^T -T｜｜F with A = [A1, A2] and B = [B1, B2]. The authors transform T to T such that min x1,x2 ｜｜A1X1B1^T＋A2X2B2^T -T｜｜F is equivalent to min x=diag（x1 ,x2） ｜｜AXB^T - T｜｜F whose solutions are included in the solution set of unconstrained problem minx ｜｜AXB^T - T｜｜F. So the general solutions of min x1,x2 ｜｜A1X1B^T ＋ A2X2B2^T -T｜｜F are reconstructed by selecting the parameter matrix in that of minx ｜｜AXB^T - T｜｜F.
