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Article(id=1226462300371071210, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1226462293408531329, articleNumber=null, orderNo=null, doi=null, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1732636800000, receivedDateStr=2024-11-27, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1770340998975, onlineDateStr=2026-02-06, pubDate=1761321600000, pubDateStr=2025-10-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1770340998975, onlineIssueDateStr=2026-02-06, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1770340998975, creator=13701087609, updateTime=1770340998975, updator=13701087609, issue=Issue{id=1226462293408531329, tenantId=1146029695717560320, journalId=1225396423026438145, year='2025', volume='45', issue='10', pageStart='1', pageEnd='288', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1770340997315, creator=13701087609, updateTime=1770341205851, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1226463168155792201, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1226462293408531329, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1226463168155792202, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1226462293408531329, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=242, endPage=250, ext={EN=ArticleExt(id=1226462300681449723, articleId=1226462300371071210, tenantId=1146029695717560320, journalId=1225396423026438145, language=EN, title=First-Principles Calculations for Flotation Separation of Magnesite and Hornblende, columnId=null, journalTitle=Mining Research and Development, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Based on the first-principles of density functional theory, quantum chemical calculations were performed using the CASTEP module of Materials Studio (MS) software to simulate and optimize the crystal structure, cleavage surface, and adsorption models of magnesite and hornblende in adsorption with reagents. On this basis, the band structure and density of states of magnesite and hornblende were analyzed. The adsorption energies of dodecylamine and the novel collector KDLX on the magnesite (104) and amphibole (110) surfaces were obtained, respectively. The results show that the band gap widths of magnesite and hornblende are 4.920 eV and 3.962 eV. The optimized crystal structure has a better stability. The ammonium hydrogen atoms in dodecylamine and KDLX undergo hydrogen bonding and physical adsorption with the oxygen atoms of minerals. Compared with dodecylamine, KDLX has a stronger adsorption capacity for hornblende and it is predicted that the collector can be used for flotation removal of silica-containing gangue minerals in magnesite ore. This study has revealed the surface characteristics of minerals and the adsorption mechanism of reagents, which has a guiding significance for the flotation separation of magnesite and hornblende and the selection of flotation reagents.

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基于密度泛函理论的第一性原理，利用软件Materials Studio(MS)的CASTEP模块进行量子化学计算，模拟优化了菱镁矿和角闪石的晶体结构、解理面和与药剂发生作用的吸附模型，在此基础上分析了菱镁矿和角闪石的能带结构、态密度，并求得十二胺、新型捕收剂KDLX分别与菱镁矿(104)面和角闪石(110)面的吸附能。结果表明：菱镁矿和角闪石的禁带宽度分别为4.920 eV和3.962 eV，优化后的晶体结构具有更好的稳定性；十二胺、KDLX中的铵根氢原子与矿物的氧原子发生氢键作用和物理吸附作用，相比于十二胺，KDLX对角闪石具有更强的吸附能力，预测该捕收剂可用于浮选脱除菱镁矿石中的含硅脉石矿物。研究揭示了矿物的表面特性和药剂的吸附机理，对菱镁矿与角闪石的浮选分离和浮选药剂选择具有指导意义。

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李鹏程（1993一），男，辽宁海城人，博士，讲师，主要从事菱镁矿选矿提纯与应用。E-mail:
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董丽鑫（1998一），女，辽宁丹东人，硕士研究生，主要从事菱镁矿选矿及浮选药剂研究。E-mail:

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董丽鑫（1998一），女，辽宁丹东人，硕士研究生，主要从事菱镁矿选矿及浮选药剂研究。E-mail:

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董丽鑫（1998一），女，辽宁丹东人，硕士研究生，主要从事菱镁矿选矿及浮选药剂研究。E-mail:

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Minerals Engineering, 2021, 171:107123., articleTitle=Computational modeling of cetyl phosphate adsorption on magnesite (104) surface, refAbstract=null), Reference(id=1226462317299282540, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462300371071210, doi=null, pmid=null, pmcid=null, year=2022, volume=null, issue=4, pageStart=13, pageEnd=22, url=null, language=null, rfNumber=[22], rfOrder=36, authorNames=迟晓鹏, 叶子涵, 衷水平, journalName=金属矿山, refType=null, unstructuredReference=迟晓鹏，叶子涵，衷水平，等.能带理论在铜冶炼渣浮选中的应用及展望[J].金属矿山，2022(4):13-22., articleTitle=能带理论在铜冶炼渣浮选中的应用及展望, refAbstract=null), Reference(id=1226462317500609149, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462300371071210, doi=null, pmid=null, pmcid=null, year=2022, volume=null, issue=4, pageStart=13, pageEnd=22, url=null, language=null, rfNumber=[22], rfOrder=37, authorNames=CHI Xiaopeng, YE Zihan, ZHONG Shuiping, journalName=Metal Mine, refType=null, unstructuredReference=CHI Xiaopeng, YE Zihan, ZHONG Shuiping, et al. Application and prospect of band theory in the flotation of copper smelting slag[J]. 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Lattice parameters and errors of magnesite obtained by exchange-correlation functional calculations

, figureFileSmall=null, figureFileBig=null, tableContent=
泛函a/nmb/nmc/nm误差/%
试验值0.463 60.463 61.502 6—
GGA-PBE0.473 70.473 71.543 52.720
GGA-RPBE0.477 50.477 51.576 14.891
GGA-PW910.473 70.473 71.539 22.435
GGA-WC0.470 90.470 91.514 41.585
GGA-PBESOL0.470 70.470 71.515 71.524
LDA-CA-PZ0.464 80.464 81.477 11.697
), ArticleFig(id=1226462312152871174, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462300371071210, language=CN, label=表1, caption=

交换相关泛函计算菱镁矿晶格参数与误差

, figureFileSmall=null, figureFileBig=null, tableContent=
泛函a/nmb/nmc/nm误差/%
试验值0.463 60.463 61.502 6—
GGA-PBE0.473 70.473 71.543 52.720
GGA-RPBE0.477 50.477 51.576 14.891
GGA-PW910.473 70.473 71.539 22.435
GGA-WC0.470 90.470 91.514 41.585
GGA-PBESOL0.470 70.470 71.515 71.524
LDA-CA-PZ0.464 80.464 81.477 11.697
), ArticleFig(id=1226462312257728782, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462300371071210, language=EN, label=Table 2, caption=

Lattice parameters and errors of hornblende obtained by exchange-correlation functional calculations

, figureFileSmall=null, figureFileBig=null, tableContent=
泛函a/nmb/nmc/nm误差/%
试验值0.990 81.798 80.527 1—
GGA-PBE1.054 01.865 40.528 26.381
GGA-RPBE1.068 51.886 10.532 67.843
GGA-PW911.052 71.864 70.527 86.254
GGA-WC1.022 21.860 10.526 13.410
GGA-PBESOL1.043 11.849 60.524 35.283
LDA-CA-PZ1.020 11.818 10.514 92.961
), ArticleFig(id=1226462312362586389, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462300371071210, language=CN, label=表2, caption=

交换相关泛函计算角闪石晶格参数与误差

, figureFileSmall=null, figureFileBig=null, tableContent=
泛函a/nmb/nmc/nm误差/%
试验值0.990 81.798 80.527 1—
GGA-PBE1.054 01.865 40.528 26.381
GGA-RPBE1.068 51.886 10.532 67.843
GGA-PW911.052 71.864 70.527 86.254
GGA-WC1.022 21.860 10.526 13.410
GGA-PBESOL1.043 11.849 60.524 35.283
LDA-CA-PZ1.020 11.818 10.514 92.961
), ArticleFig(id=1226462312488415519, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462300371071210, language=EN, label=Table 3, caption=

Surface energy of magnesite (104) surface and hornblende (110) surface with different atomic layer thicknesses

, figureFileSmall=null, figureFileBig=null, tableContent=
矿物晶面原子层厚度/nm表面能/(J/m2)
菱镁矿(104)面0.276 30.302
0.552 60.296
0.828 90.295
1.105 20.294
1.381 50.294
角闪石(110)面0.859 41.493
1.289 21.492
1.718 91.490
2.148 61.491
2.578 31.490
), ArticleFig(id=1226462312568107302, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462300371071210, language=CN, label=表3, caption=

不同原子层厚度的菱镁矿(104)面、角闪石(110)面的表面能

, figureFileSmall=null, figureFileBig=null, tableContent=
矿物晶面原子层厚度/nm表面能/(J/m2)
菱镁矿(104)面0.276 30.302
0.552 60.296
0.828 90.295
1.105 20.294
1.381 50.294
角闪石(110)面0.859 41.493
1.289 21.492
1.718 91.490
2.148 61.491
2.578 31.490
), ArticleFig(id=1226462312660382000, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462300371071210, language=EN, label=Table 4, caption=

Surface energy of magnesite (104) surface and hornblende (110) surface with different vacuum layer thicknesses

, figureFileSmall=null, figureFileBig=null, tableContent=
矿物晶面真空层厚度/nm表面能/(J/m2)
菱镁矿(104)面4.00.294
4.50.293
5.00.293
5.50.293
6.00.295
角闪石(110)面4.01.489
4.51.483
5.01.483
5.51.483
6.01.484
), ArticleFig(id=1226462312752656697, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462300371071210, language=CN, label=表4, caption=

不同真空层厚度的菱镁矿(104)面、角闪石(110)面的表面能

, figureFileSmall=null, figureFileBig=null, tableContent=
矿物晶面真空层厚度/nm表面能/(J/m2)
菱镁矿(104)面4.00.294
4.50.293
5.00.293
5.50.293
6.00.295
角闪石(110)面4.01.489
4.51.483
5.01.483
5.51.483
6.01.484
), ArticleFig(id=1226462312861708615, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462300371071210, language=EN, label=Table 5, caption=

Adsorption energies of reagents on magnesite (104) surface and hornblende (110) surface

, figureFileSmall=null, figureFileBig=null, tableContent=
矿物晶面药剂Ecomplex/eVEmineral/eVEadsorbate/eVΔEads/(kJ·mol-1)
菱镁矿(104)面十二胺—80 501.44—77 932.50—2 567.35—152.78
KDLX—90 253.65—77 932.50—12 288.69—3 131.78
角闪石(110)面十二胺—170 574.57—168 003.12—2 567.35—395.13
KDLX—180 354.90—168 003.12—12 288.69—6 087.23
), ArticleFig(id=1226462312991732050, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1226462300371071210, language=CN, label=表5, caption=

药剂在菱镁矿(104)面、角闪石(110)面的吸附能

, figureFileSmall=null, figureFileBig=null, tableContent=
矿物晶面药剂Ecomplex/eVEmineral/eVEadsorbate/eVΔEads/(kJ·mol-1)
菱镁矿(104)面十二胺—80 501.44—77 932.50—2 567.35—152.78
KDLX—90 253.65—77 932.50—12 288.69—3 131.78
角闪石(110)面十二胺—170 574.57—168 003.12—2 567.35—395.13
KDLX—180 354.90—168 003.12—12 288.69—6 087.23
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菱镁矿和角闪石浮选分离的第一性原理计算
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董丽鑫 1 , 代淑娟 1 , 李鹏程 1 , 周晓蕾 2 , 周滨 3
矿业研究与开发 | 选矿与资源综合利用 2025,45(10): 242-250
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矿业研究与开发 | 选矿与资源综合利用 2025, 45(10): 242-250
菱镁矿和角闪石浮选分离的第一性原理计算
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董丽鑫1 , 代淑娟1, 李鹏程1 , 周晓蕾2, 周滨3
作者信息
  • 1.辽宁科技大学 矿业工程学院，辽宁　鞍山市　114051
  • 2.辽宁省工业和信息化厅，辽宁　沈阳　110032
  • 3.辽宁华子玉科技有限公司，辽宁　海城市　114200

    • 董丽鑫（1998一），女，辽宁丹东人，硕士研究生，主要从事菱镁矿选矿及浮选药剂研究。E-mail:

通讯作者:

李鹏程（1993一），男，辽宁海城人，博士，讲师，主要从事菱镁矿选矿提纯与应用。E-mail:
First-Principles Calculations for Flotation Separation of Magnesite and Hornblende
Lixin DONG1 , Shujuan DAI1, Pengcheng LI1 , Xiaolei ZHOU2, Bin ZHOU3
Affiliations
  • 1.School of Mining Engineering, University of Science and Technology Liaoning, Anshan, Liaoning 114051, China
  • 2.Department of Industry and Information Technology of Liaoning Province, Shenyang Liaoning 110032, China
  • 3.Liaoning Huaziyu Technology Co., Ltd., Haicheng, Liaoning 114200, China
出版时间: 2025-10-25
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摘要
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基于密度泛函理论的第一性原理，利用软件Materials Studio(MS)的CASTEP模块进行量子化学计算，模拟优化了菱镁矿和角闪石的晶体结构、解理面和与药剂发生作用的吸附模型，在此基础上分析了菱镁矿和角闪石的能带结构、态密度，并求得十二胺、新型捕收剂KDLX分别与菱镁矿(104)面和角闪石(110)面的吸附能。结果表明：菱镁矿和角闪石的禁带宽度分别为4.920 eV和3.962 eV，优化后的晶体结构具有更好的稳定性；十二胺、KDLX中的铵根氢原子与矿物的氧原子发生氢键作用和物理吸附作用，相比于十二胺，KDLX对角闪石具有更强的吸附能力，预测该捕收剂可用于浮选脱除菱镁矿石中的含硅脉石矿物。研究揭示了矿物的表面特性和药剂的吸附机理，对菱镁矿与角闪石的浮选分离和浮选药剂选择具有指导意义。

菱镁矿  /  角闪石  /  第一性原理  /  MS模拟  /  吸附机理

Based on the first-principles of density functional theory, quantum chemical calculations were performed using the CASTEP module of Materials Studio (MS) software to simulate and optimize the crystal structure, cleavage surface, and adsorption models of magnesite and hornblende in adsorption with reagents. On this basis, the band structure and density of states of magnesite and hornblende were analyzed. The adsorption energies of dodecylamine and the novel collector KDLX on the magnesite (104) and amphibole (110) surfaces were obtained, respectively. The results show that the band gap widths of magnesite and hornblende are 4.920 eV and 3.962 eV. The optimized crystal structure has a better stability. The ammonium hydrogen atoms in dodecylamine and KDLX undergo hydrogen bonding and physical adsorption with the oxygen atoms of minerals. Compared with dodecylamine, KDLX has a stronger adsorption capacity for hornblende and it is predicted that the collector can be used for flotation removal of silica-containing gangue minerals in magnesite ore. This study has revealed the surface characteristics of minerals and the adsorption mechanism of reagents, which has a guiding significance for the flotation separation of magnesite and hornblende and the selection of flotation reagents.

Magnesite  /  Hornblende  /  First-principles  /  MS simulation  /  Adsorption mechanism
董丽鑫, 代淑娟, 李鹏程, 周晓蕾, 周滨. 菱镁矿和角闪石浮选分离的第一性原理计算. 矿业研究与开发, 2025 , 45 (10) : 242 -250 .
Lixin DONG, Shujuan DAI, Pengcheng LI, Xiaolei ZHOU, Bin ZHOU. First-Principles Calculations for Flotation Separation of Magnesite and Hornblende[J]. Mining Research and Development, 2025 , 45 (10) : 242 -250 .
正文
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0　引言
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菱镁矿属于碳酸盐矿物，根据其结晶状态可分为晶质和非晶质两类，其中以晶质菱镁矿为主。菱镁矿是优质耐火材料的主要原料，应用的范围极为广泛[1]。随着高品质菱镁矿资源的紧缺，通过选矿技术实现菱镁矿的提质除杂已成为我国菱镁矿行业发展的重点[2]。菱镁矿浮选主要处理堆存的低品位菱镁矿粉矿，其目的是除去其中的含硅脉石矿物，镁硅分离一直是菱镁矿浮选的研究重点之一。角闪石是复杂的硅酸盐矿物，天然可浮性较菱镁矿差，是菱镁矿石中常见的含硅脉石矿物之一[3-4]。
近年来，借助日益发展的计算机技术，通过计算模拟方法深入探究矿石的表面特性和结构特征，可以精准、高效地选择合适的浮选药剂。Materials Studio (MS)是基于量子化学、分子动力学等理论的模拟软件，可以在原子尺度上对矿物晶体表面化学特性、浮选药剂分子结构和浮选药剂与矿物表面作用机理进行深入研究[5-7]。其CASTEP模块采用基于密度泛函理论（Density Functional Theory, DFT)的平面波赝势法，可以对矿物浮选分离进行第一性原理计算[8]。目前，已被广泛应用于研究浮选药剂在矿物表面作用机理上。张多阳等[9]通过MS软件对菱镁矿、方解石和白云石的晶胞参数和不同的解理面进行了模拟，计算分析了矿物的重要性质和药剂与矿物的吸附机理。韩聪等[10]通过第一性原理进行了菱镁矿与白云石表面性质的计算并分析了其对二者浮游性的影响。此外，李鹏程[11]和孙文翰等[12]对菱镁矿与白云石的溶解特性和可浮性进行了模拟计算与分析。同时，部分学者进行了菱镁矿与石英的表面性质计算和浮选药剂研究[13-14]。LIU Wenbao等[15]研究了异丙醇胺作为新型捕收剂在菱镁矿与石英浮选中的应用，通过计算模拟在分子尺度上揭示了引入异丙醇基团的作用机理，为浮选药剂分子选择提供了重要依据。TANG Yuan等[16]采用分子动力学模拟与实际检测相结合，研究了十六烷基膦酸钾(PCP)作为菱镁矿新型捕收剂的作用机理。YANG Bin等[17]通过模拟计算研究了十乙氧基硬脂酰胺(DSA)在角闪石和菱铁矿浮选分离中的应用，发现DSA的氨基能与角闪石表面产生强烈的氢键和静电吸附作用。目前，关于菱镁矿与角闪石浮选分离的分子动力学模拟研究尚未见报道。
本文基于密度泛函理论的第一性原理，采用MS软件的CASTEP模块，对菱镁矿和角闪石的晶体结构和解理面进行优化并选取最佳的计算参数。通过计算不同原子层厚度和真空层厚度条件下的表面能，分析菱镁矿和角闪石的能带结构、电子态密度等性质，在此基础上，对弛豫后的菱镁矿(104)面和角闪石(110)面分别与十二胺及新型组合捕收剂KDLX构建吸附模型，并计算相应的吸附能。研究结果在微观尺度上为菱镁矿与角闪石的浮选分离和浮选药剂的选择提供了理论依据。
1　计算模型与方法
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1.1　计算模型
菱镁矿是三方晶系，其空间群符号为；当晶胞为菱面体时，晶胞棱长为0.566 nm，晶胞的面间夹角为48°10′，每个菱面体晶胞中包含的化学式单元数为2；晶胞为六方体时，底面棱长为0.462 nm，六方体晶胞的高为1.499 nm，每个六方晶胞中包含的化学式单元数为6。角闪石属于单斜晶系，空间群符号为C2/m，单科晶胞沿a轴的棱长为0.979 nm，单斜晶胞沿b轴的棱长为1.790 nm，单斜晶胞沿c轴的棱长为0.528 nm, a轴与c轴的夹角为105°31′，每个单斜晶胞中包含的化学式单元数为2[18]。菱镁矿、角闪石的原胞模型如图1所示。
1.2　计算方法
分别对菱镁矿、角闪石晶胞模型进行几何优化，并对其态密度、能带结构进行计算分析。计算所用的初始模型由软件自带的数据库引入，基本参数为：基于第一性原理的超软赝势平面波法，结构优化计算使用的算法为BFGS，晶体内应力不大于0.1 GPa。所有计算都在倒易空间中进行，以选取最佳的计算参数[19]。
2　模型优化与表面模型的建立与优化
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2.1　模型结构优化
采用CASTEP模块中的Geometry Optimization功能对菱镁矿、角闪石进行结构优化计算，主要对交换相关泛函、k点取样密度和截断能三个参数进行计算。通过对矿物晶胞的结构优化，选取最佳的计算参数，从而获得最稳定和精确的矿物晶体结构。
2.1.1　菱镁矿结构优化
首先，考察交换相关泛函对菱镁矿晶体结构参数计算结果的影响，晶胞优化结果见表1。
由表1可知，采用广义梯度近似泛函GGA-PBESOL计算得到的晶格参数与试验值误差最小，此时体系的总能量为—14615.98 eV。因此，后续计算采用GGA-PBESOL泛函。
考察k点选取对菱镁矿晶胞总能和晶格常数误差的影响，结果如图2所示。
由图2可知，k点取4×4×2时，晶格常数误差最小，为1.533%，此时体系能量为—14 615.98 eV，能量最稳定，故后续计算取k点为4×4×2。
考察截断能的选取对菱镁矿晶胞总能和晶格常数误差的影响，如图3所示。
由图3可知，随着截断能的增大，体系的总能量先迅速降低后逐渐趋于平缓，当截断能取560 eV时，体系总能量为—14 617.55 eV，晶格常数误差最小为1.179%。
综上，最终选取GGA-PBESOL泛函、4×4×2的k点网格及560 eV截断能为后续计算的最优参数。在此设置下，菱镁矿晶胞结构趋于稳定。
2.1.2　角闪石结构优化
首先，考察交换相关泛函对角闪石晶体结构参数计算结果的影响，晶胞优化结果见表2。
由表2可知，不同方法计算得到的角闪石晶体结构参数不同，在选取局部密度近似泛函LDA-CA-PZ时，可以获得与试验值误差最小的结果，此时体系的总能量为—41 952.27 eV。因此，后续计算采用LDA-CA-PZ泛函。
考察k点选取对角闪石晶胞总能和晶胞常数误差的影响，结果如图4所示。
由图4所示，k点取3×1×5时，晶格常数误差最小，为2.910%，晶胞总能量趋于稳定，因此后续计算取k点为3×1×5。
考察截断能的选取对角闪石晶胞总能和晶胞常数误差的影响，如图5所示。
从图5可知，随着截断能逐渐增加，体系的总能量呈逐渐降低的趋势，当截断能取400 eV时，晶格常数的误差最小，为2.67%，此时体系的总能量为—42 011.88 eV。
综上，最终选取LDA-CA-PZ泛函，3×1×5的k点网格及400 eV截断能为后续计算的最优参数。在此设置下，角闪石晶胞趋于稳定。
优化后的菱镁矿与角闪石晶体结构如图6所示，用于后续对能带结构和态密度计算分析。
2.2　表面模型建立与表面能计算
表面能是衡量表面稳定性的重要定量参数。矿物破碎过程的化学本质是破坏原子(或离子)与相邻原子(或离子)之间的化学键，在该过程中，外力所做功的一半（因形成两个新生表面）被称为表面能。由于新生表面上的原子(或离子)失去了朝外的配位原子(或离子)，因此，表面层上的原子(或离子)获得了不稳定的额外的化学反应活性，使得表面质点具有比体相质点更高的能量，这种能量差异即为表面能。表面能以式(1)所示公式计算。
式中：Esurf为表面能，J/m2；Eslab为表面模型总能量，eV；Ebulk为原胞模型总能量，eV；Nslab为表面模型包含的总原子数，个；Nbulk为原胞模型包含的总原子数，个；A为表面模型沿轴向的面积，m2[20]。
菱镁矿（104）面[21]、角闪石（110）面[17]分别为菱镁矿和角闪石的完全解理面。本文以此为基础，对结构优化后的矿物晶体进行表面建模：首先采用Cleave surface工具进行切表面，再通过Build vacuum slab添加真空层，构建表面结构并进行结构优化，最终计算其表面能。在固定真空层厚度为4.0 nm的条件下，分别计算不同原子层厚度的菱镁矿(104)面、角闪石(110)面的表面能，结果见表3。
当连续的原子层厚度计算得到的表面能之差小于0.05 J/m2时，可以判断此时矿物的表面能趋于稳定。由表3可以看出，当菱镁矿(104)面原子层厚度为1.105 2 nm时，表面能为0.294 J/m2；当角闪石(110)面原子层厚度为1.718 9 nm时，表面能为1.490 J/m2。此时，两种矿物的表面能均趋于稳定。
固定菱镁矿(104)面原子层厚度为1.105 2 nm，角闪石(110)面原子层厚度为1.718 9 nm，分别计算不同真空层厚度的菱镁矿(104)面、角闪石(110)面的表面能，结果见表4。
真空层的选取判定标准与原子层一致。由表4可以看出，菱镁矿(104)面的真空层厚度取5.0 nm时，表面能为0.293 J/m2；角闪石(110)面的真空层厚度取5.0 nm时，表面能为1.483 J/m2。此时两种矿物的表面能均趋于稳定。
综上，菱镁矿（104）面原子层厚度为1.105 2 nm，真空层厚度为5.0 nm时，表面能为0.293 J/m2；角闪石(110)面的原子层厚度为1.718 9 nm，真空层厚度为5.0 nm时，表面能为1.483 J/m2。此时，两种矿物表面模型的精度较高，表面能趋于稳定。优化后的表面模型将用于后续弛豫计算。
3　计算结果与讨论
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3.1　菱镁矿与角闪石晶胞的能带结构分析
能带结构通常可分为导带、价带和禁带三部分，其横坐标为各个k点[22]。通过分析能带结构，可以揭示矿物的电子学与光学性质。本研究对优化后的菱镁矿和角闪石的能带结构进行计算分析，结果如图7所示。
取费米能级(Ef)为能量零点。禁带宽度是指价带顶和导带底间的能量差，可用于判断固体材料属于半导体还是绝缘体。通常禁带宽度小于2.00 eV为半导体，大于3.00 eV为绝缘体。由图7可知，菱镁矿的禁带宽度为4.920 eV，角闪石的禁带宽度为3.962 eV，两者禁带宽度均大于3.00 eV，可见菱镁矿和角闪石都属于绝缘体。
3.2　菱镁矿与角闪石晶胞的态密度分析
电子态密度是描述材料电子态的基本物理量[19]。分别对优化后的菱镁矿和角闪石晶胞的态密度进行计算分析，结果如图8所示。
从图8(a)可以看出，菱镁矿的能带结构主要分为4部分：—40~—25 eV之间的价带主要由Mg的p轨道贡献；—25~—15 eV之间的价带由为O的s轨道和C的p轨道贡献；—10~2.5 eV之间的价带主要由为O和C的p轨道贡献，并以O的p轨道贡献为主；导带能级部分主要由Mg的s、p轨道及C的p轨道贡献。在费米能级处，贡献最大的为O的2p轨道，由于费米能级附近的电子最为活跃，表明O可能是与药剂发生物理化学作用的活性位点。
由图8(b)可以看出，角闪石的能带结构主要分为5部分：—52~—45 eV之间的价带主要由Na的s轨道贡献；—43~—25 eV之间的价带主要由Mg的p轨道贡献，其次是Ca的s轨道；—25~—14 eV之间的价带主要由Ca、Na和Si的p轨道贡献，同时存在Ca、Si、O、Mg的s轨道参与，以Ca的p轨道贡献为主；—12~1 eV之间的价带主要由O的p轨道，Si的p轨道，Ca的s、p和d轨道贡献，其中O的p轨道贡献最大；2~20 eV之间的价带以Si的p轨道为主要贡献，其次为Si的s轨道、Ca的s、p、d轨道，Na、Mg和O的p、s轨道也有轻微贡献。在费米能级处，同样以O的2p轨道贡献最大，因此，O可能是与药剂发生物理化学作用的活性位点。
3.3　弛豫
表面附近原子层的间距通常与体相内部存在差异，这一现象称为表面弛豫现象。弛豫后的表面能量低于初始表面能量，通过对系统能量最小化，可以得到弛豫后的表面几何构型。分别对菱镁矿 (104)面和角闪石 (110) 面进行弛豫，弛豫前后的结果如图9所示。
由图9可知，菱镁矿（104)面和角闪石（110)面经过弛豫后，表面结构均发生了明显变化，主要表现为沿Z轴方向的调整。两种矿物弛豫后的表面能量均低于初始状态，表面结构更加的稳定。因此，将弛豫后的菱镁矿(104)面、角闪石(110)面用作后续药剂吸附模型构建。
3.4　捕收剂在矿物表面的相互作用模型
吸附能又称作相互作用能，是指吸附后的总体系能量与吸附前矿物的能量和药剂能量之和的差值。在吸附过程中，吸附能为负值表示在矿药吸附时体系对外释放能量，此时吸附过程可以自发进行。释放的能量越多，矿药相互作用效果越明显，吸附状态也越稳定，更容易发生吸附作用。吸附能计算见式（2）。
式中：ΔEads为吸附能；Ecomplex为药剂与矿物吸附后的总体系能量；Eadsorbate为吸附前药剂的总能量；Emineral为弛豫后矿物表面的总能量[20]。
将弛豫后的菱镁矿(104)面和角闪石(110)面作为吸附体，十二胺、新型捕收剂KDLX作为吸附物，分别计算矿物的能量、矿物与药剂发生吸附后的总相互作用能和优化后的药剂的能量。十二胺、新型捕收剂KDLX分别与菱镁矿(104)面和角闪石(110)面作用的吸附模型如图10所示，吸附能计算结果见表5。
由表5可知，十二胺在菱镁矿(104)面和角闪石(110)面的吸附能分别为—152.78 kJ/mol、—395.13 kJ/mol，新型捕收剂KDLX在菱镁矿(104)面和角闪石(110)面的吸附能分别为—3 131.78 kJ/mol、—6 087.23 kJ/mol。吸附能越低，发生反应作用越强烈，因此，相比于十二胺，新型捕收剂KDLX与角闪石(110)面发生了更强烈的吸附作用。
由图10可知，十二胺与菱镁矿(104)面和角闪石(110)面发生吸附时，N—H⋯O的距离分别为0.266 7 nm和0.336 5 nm；新型捕收剂KDLX与菱镁矿(104)面和角闪石(110)面发生吸附时，N—H⋯O的距离分别为0.378 5 nm和0.098 7 nm。十二胺和新型捕收剂KDLX均属于阳离子胺类捕收剂，其吸附均以铵根中的氢原子为“触点”，菱镁矿(104)面和角闪石(110)面均以氧原子为反应的活性位点与之发生吸附行为。新型捕收剂KDLX在菱镁矿(104)面的作用效果较弱，在角闪石(110)面的表现出更强的吸附效果。两种胺类捕收剂在矿物表面的吸附行为均以N—H⋯O氢键作用和物理吸附作用为主。
结合吸附模型与吸附能数据分析可知，新型捕收剂KDLX与角闪石(110)面发生了强烈的吸附作用，体系的相互作用能更低，吸附作用效果尤为显著，而对菱镁矿(104)面的吸附作用相对较弱。这表明KDLX对硅酸盐类矿物角闪石具有良好的选择性，有望实现菱镁矿与角闪石的有效浮选分离，有利于脱除菱镁矿石中的含硅脉石矿物。
4　结论
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（1）对菱镁矿和角闪石晶胞的结构进行优化，确定了菱镁矿(104)面和角闪石(110)面原子层厚度分别为1.105 2 nm和1.718 9 nm，真空层厚度均为5.0 nm，表面能分别为0.293 J/m2和1.483 J/m2。对构建好的两种矿物的表面结构进行弛豫，弛豫后的两种矿物表面能量均低于初始状态，矿物的晶胞结构稳定性好。
（2）菱镁矿和角闪石的能带结构和态密度分析结果表明，菱镁矿和角闪石的禁带宽度分别为4.920 eV和3.962 eV，二者均为绝缘体。两种矿物在费米能级处的价带均以O的2p轨道贡献为主，因此，O可能是与药剂发生物理化学作用的活性位点。(3)结合捕收剂在矿物表面的吸附模型和吸附能数据分析可知，十二胺、KDLX中的铵根氢原子与矿物的氧原子发生N—H…O氢键作用和物理吸附作用。其中，KDLX能与角闪石(110)表面发生强烈的吸附作用，预测该捕收剂可对硅酸盐类矿物尤其是角闪石具有良好的选择性，有利于脱除菱镁矿石中的含硅脉石矿物。
基金
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  • 辽宁省科技计划重点研发项目(2024JH2/102400013)
  • 国家自然科学基金项目(51874168)
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  • 接收时间：2024-11-27
  • 首发时间：2026-02-06
  • 出版时间：2025-10-25
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  • 收稿日期：2024-11-27
基金
辽宁省科技计划重点研发项目(2024JH2/102400013)
国家自然科学基金项目(51874168)
作者信息
    1.辽宁科技大学 矿业工程学院，辽宁　鞍山市　114051
    2.辽宁省工业和信息化厅，辽宁　沈阳　110032
    3.辽宁华子玉科技有限公司，辽宁　海城市　114200

通讯作者:

李鹏程（1993一），男，辽宁海城人，博士，讲师，主要从事菱镁矿选矿提纯与应用。E-mail:
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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