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Article(id=1193534739173835472, tenantId=1146029695717560320, journalId=1190260162528112641, issueId=1193513023760466128, articleNumber=1672-0636（2025）01-0211-07, orderNo=null, doi=10.3969/j.issn.1672-0636.2025.01.019, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1734278400000, receivedDateStr=2024-12-16, revisedDate=1735401600000, revisedDateStr=2024-12-29, acceptedDate=null, acceptedDateStr=null, onlineDate=1762490456622, onlineDateStr=2025-11-07, pubDate=1738944000000, pubDateStr=2025-02-08, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1762490456622, onlineIssueDateStr=2025-11-07, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1762490456622, creator=13701087609, updateTime=1762490456622, updator=13701087609, issue=Issue{id=1193513023760466128, tenantId=1146029695717560320, journalId=1190260162528112641, year='2025', volume='42', issue='1', pageStart='1', pageEnd='217', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=0, articleOrder=1, issueType=-1, specialIssue=null, createTime=1762485279264, creator=13701087609, updateTime=1762498836216, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1193569885797184010, tenantId=1146029695717560320, journalId=1190260162528112641, issueId=1193513023760466128, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1193569885797184011, tenantId=1146029695717560320, journalId=1190260162528112641, issueId=1193513023760466128, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=211, endPage=217, ext={EN=ArticleExt(id=1193534739467436753, articleId=1193534739173835472, tenantId=1146029695717560320, journalId=1190260162528112641, language=EN, title=The measurement of 232Th in slag with high-purity germanium γ spectrometer, columnId=1190343834849607834, journalTitle=World Nuclear Geoscience, columnName=RESEARCH ARTICALS, runingTitle=null, highlight=null, articleAbstract=

In order to accurately measure 232Th in the waste residues of associated radioactive mines, especially for the measurement of slag samples under non-equilibrium conditions, and to provide data support for radiation environment supervision, a method for measuring 232Th in slag using a high-purity germanium γ spectrometer was established. The method involves indirect measurement by selecting the characteristic γ rays of the daughter nuclides in the decay chain of 232Th, and calculating its specific activity by the relative comparison method. The slag samples in a non-equilibrium state are sealed for 20 days to enable 228Ra and 228Ac to reach equilibrium, and 228Th, 224Ra and subsequent daughter nuclides to reach equilibrium. Then, the specific activity of the parent nuclide 232Th is obtained through conversion relationships. This method is accurate and efficient, with a detection limit of 1.1 Bq・kg-1, a precision better than 5 %, and a relative error lower than 5 %. The method of measuring 232Th in slag using a high-purity germanium γ spectrometer does not require complex chemical treatment, which makes up for the deficiencies of inductively coupled plasma mass spectrometry. The calculation method under non-equilibrium conditions is also more reliable than using the average value of a single characteristic peak or multiple characteristic peaks.

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HUANG Yuqi，male，born in 1992，engineer，focusing on physical analysis. E-mail：

, authorsList=HUANG Yuqi, ZHONG Chunming), CN=ArticleExt(id=1193534834766217980, articleId=1193534739173835472, tenantId=1146029695717560320, journalId=1190260162528112641, language=CN, title=高纯锗γ谱仪测量矿渣中的232Th, columnId=1190343834992214173, journalTitle=世界核地质科学, columnName=研究论文, runingTitle=null, highlight=null, articleAbstract=为了准确测量伴生放射性矿废渣中的232Th，尤其是针对处于不平衡条件下的矿渣样品的测量，给辐射环境监管提供数据支持。建立了利用高纯锗γ谱仪测量矿渣中232Th的方法。通过选择232Th衰变链子体的特征γ射线进行间接测量，采用相对比较法计算其比活度。把处于不平衡状态的矿渣样品封存20 d，使228Ra与228Ac达到平衡，228Th与224Ra及后续子体达到平衡，再利用换算关系求得母体核素232Th的比活度。方法准确高效，检出限为 1.1 Bq・kg-1，精密度优于5 %，相对误差低于5 %。高纯锗γ谱仪测量矿渣中232Th的方法不用进行复杂的化学处理，弥补电感耦合等离子体质谱法的不足；不平衡条件下的计算方法也比利用单一特征峰或多个特征峰的平均值更可靠。, correspAuthors=null, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=QPhoWG87RU4TnMwpq2th9A==, magXml=9ygBFJuhVDg7jPxviEQIZw==, pdfUrl=null, pdf=l1NlAGRhnP+J9HjrAfKg3Q==, pdfFileSize=1474156, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=kWa94WA/WiQQukqeTk/+wg==, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=uZitXGeXgJYeIqWm0Rjfcg==, mapNumber=null, authorCompany=null, fund=null, authors=

黄宇琦，男，1992年生，工程师，主要从事物理分析。E-mail：

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黄宇琦，男，1992年生，工程师，主要从事物理分析。E-mail：

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黄宇琦，男，1992年生，工程师，主要从事物理分析。E-mail：

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Types and energies of 232Th radiation

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射线类型 能量/keV 分支比/%
α射线 4 012.3 78.2
α射线 3 947.2 21.7
α射线 3 811.1 0.069
γ射线 63.8 0.263
γ射线 140.9 0.021
), ArticleFig(id=1193534837010170666, tenantId=1146029695717560320, journalId=1190260162528112641, articleId=1193534739173835472, language=CN, label=表1, caption=

232Th射线类型和能量

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射线类型 能量/keV 分支比/%
α射线 4 012.3 78.2
α射线 3 947.2 21.7
α射线 3 811.1 0.069
γ射线 63.8 0.263
γ射线 140.9 0.021
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The characteristic ray peaks of the selected 232Th daughter

, figureFileSmall=null, figureFileBig=null, tableContent=
子体核素 半衰期 能量/keV 分支比/%
208Tl 3.053 min 583.1 84.5
212Pb 10.64 h 238.2 43.3
212Bi 60.55 min 727.3 6.58
228Ac 6.13 h 911.2 25.8
), ArticleFig(id=1193534837144388396, tenantId=1146029695717560320, journalId=1190260162528112641, articleId=1193534739173835472, language=CN, label=表2, caption=

选用的232Th子体特征射线峰

, figureFileSmall=null, figureFileBig=null, tableContent=
子体核素 半衰期 能量/keV 分支比/%
208Tl 3.053 min 583.1 84.5
212Pb 10.64 h 238.2 43.3
212Bi 60.55 min 727.3 6.58
228Ac 6.13 h 911.2 25.8
), ArticleFig(id=1193534837219885869, tenantId=1146029695717560320, journalId=1190260162528112641, articleId=1193534739173835472, language=EN, label=Table 3, caption=

Precision and trueness of the method

, figureFileSmall=null, figureFileBig=null, tableContent=
标准物质编号 性质 测定值/（Bq·kg-1） 平均值/（Bq·kg-1） 精密度RSD/% 相对误差/% 参考值/（Bq·kg-1）
GBW04110 矿石 108.3、107.2、100.1、106.4、
103.4、106.5、95.4、97.8		 103.1 4.4 2.0 101.1±8.1
GBW04115 矿石 1 225.6、1 234.8、1 229.4、1 288.0、
1 276.3、1 245.7、1 240.6、1 239.0		 1 247.4 1.7 -1.4 1 265.8±56.6
GBW04116 矿石 8 062.4、8 066.9、8 210.5、8 023.8、
8 092.1、8 180.4、8 124.7、8 032.7		 8 099.2 0.8 -0.9 8 168.9±161.8
), ArticleFig(id=1193534837307966254, tenantId=1146029695717560320, journalId=1190260162528112641, articleId=1193534739173835472, language=CN, label=表3, caption=

方法精密度及正确度

, figureFileSmall=null, figureFileBig=null, tableContent=
标准物质编号 性质 测定值/（Bq·kg-1） 平均值/（Bq·kg-1） 精密度RSD/% 相对误差/% 参考值/（Bq·kg-1）
GBW04110 矿石 108.3、107.2、100.1、106.4、
103.4、106.5、95.4、97.8		 103.1 4.4 2.0 101.1±8.1
GBW04115 矿石 1 225.6、1 234.8、1 229.4、1 288.0、
1 276.3、1 245.7、1 240.6、1 239.0		 1 247.4 1.7 -1.4 1 265.8±56.6
GBW04116 矿石 8 062.4、8 066.9、8 210.5、8 023.8、
8 092.1、8 180.4、8 124.7、8 032.7		 8 099.2 0.8 -0.9 8 168.9±161.8
), ArticleFig(id=1193534837375075119, tenantId=1146029695717560320, journalId=1190260162528112641, articleId=1193534739173835472, language=EN, label=Table 4, caption=

Results of measurements on mining slags

, figureFileSmall=null, figureFileBig=null, tableContent=
样品编号 性质 A 4测定值/（Bq·kg-1） A 2测定值/（Bq·kg-1） A 1计算值/（Bq·kg-1）
1 中和渣 314.0 33.9 319.6
2 优溶渣 1 035.6 8 355.7 889.2
3 优溶渣 2 214.8 335.6 2 252.4
4 酸溶渣 460.1 6 102.1 347.3
5 尾矿渣 55.4 680.5 42.9
6 浸出渣 1 406.8 673.6 1 421.5
), ArticleFig(id=1193534837433795376, tenantId=1146029695717560320, journalId=1190260162528112641, articleId=1193534739173835472, language=CN, label=表4, caption=

矿渣样品的测量结果

, figureFileSmall=null, figureFileBig=null, tableContent=
样品编号 性质 A 4测定值/（Bq·kg-1） A 2测定值/（Bq·kg-1） A 1计算值/（Bq·kg-1）
1 中和渣 314.0 33.9 319.6
2 优溶渣 1 035.6 8 355.7 889.2
3 优溶渣 2 214.8 335.6 2 252.4
4 酸溶渣 460.1 6 102.1 347.3
5 尾矿渣 55.4 680.5 42.9
6 浸出渣 1 406.8 673.6 1 421.5
), ArticleFig(id=1193534837509292849, tenantId=1146029695717560320, journalId=1190260162528112641, articleId=1193534739173835472, language=EN, label=Table 5, caption=

Results of the ICP-MS

, figureFileSmall=null, figureFileBig=null, tableContent=
样品编号 性质 ICP-MS测定值/（Bq·kg-1） 与 A 1的比值
1 中和渣 342.5 1.07
2 优溶渣 819.7 0.92
3 优溶渣 2 354.2 1.05
4 酸溶渣 313.9 0.90
5 尾矿渣 45.9 1.07
6 浸出渣 1 563.7 1.10
), ArticleFig(id=1193534837597373234, tenantId=1146029695717560320, journalId=1190260162528112641, articleId=1193534739173835472, language=CN, label=表5, caption=

电感耦合等离子体质谱法的测量结果

, figureFileSmall=null, figureFileBig=null, tableContent=
样品编号 性质 ICP-MS测定值/（Bq·kg-1） 与 A 1的比值
1 中和渣 342.5 1.07
2 优溶渣 819.7 0.92
3 优溶渣 2 354.2 1.05
4 酸溶渣 313.9 0.90
5 尾矿渣 45.9 1.07
6 浸出渣 1 563.7 1.10
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高纯锗γ谱仪测量矿渣中的232Th
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黄宇琦 1, 2, 3 , 钟春明 1, 2, 3
世界核地质科学 | 研究论文 2025,42(1): 211-217
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世界核地质科学 | 研究论文 2025, 42(1): 211-217
高纯锗γ谱仪测量矿渣中的232Th
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黄宇琦1, 2, 3 , 钟春明1, 2, 3
作者信息
  • 1 核工业二三○研究所，湖南 长沙 410007
  • 2 湖南中核环保科技有限公司，湖南 长沙 410007
  • 3 湖南省伴生放射性矿产资源评价与综合利用工程技术研究中心，湖南 长沙 410007

    • 黄宇琦，男，1992年生，工程师，主要从事物理分析。E-mail：

The measurement of 232Th in slag with high-purity germanium γ spectrometer
HUANG Yuqi1, 2, 3 , ZHONG Chunming1, 2, 3
Affiliations
  • 1 Research Institute No. 230，CNNC，Changsha 410007，China
  • 2 Hunan Zhonghe Nuclear Environmental Protection Technology Co., Ltd.，Changsha 410007，China
  • 3 Hunan Engineering Technology Research Center for Evaluation and Comprehensive Utilization of Associated Radioactive Mineral Resources，Changsha 410007，China
出版时间: 2025-02-08 doi: 10.3969/j.issn.1672-0636.2025.01.019
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摘要
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为了准确测量伴生放射性矿废渣中的232Th，尤其是针对处于不平衡条件下的矿渣样品的测量，给辐射环境监管提供数据支持。建立了利用高纯锗γ谱仪测量矿渣中232Th的方法。通过选择232Th衰变链子体的特征γ射线进行间接测量，采用相对比较法计算其比活度。把处于不平衡状态的矿渣样品封存20 d，使228Ra与228Ac达到平衡，228Th与224Ra及后续子体达到平衡，再利用换算关系求得母体核素232Th的比活度。方法准确高效，检出限为 1.1 Bq・kg-1，精密度优于5 %，相对误差低于5 %。高纯锗γ谱仪测量矿渣中232Th的方法不用进行复杂的化学处理，弥补电感耦合等离子体质谱法的不足；不平衡条件下的计算方法也比利用单一特征峰或多个特征峰的平均值更可靠。
高纯锗  /  矿渣  /  232Th  /  伴生放射性  /  放射性平衡  /  环境  /  固体废物

In order to accurately measure 232Th in the waste residues of associated radioactive mines, especially for the measurement of slag samples under non-equilibrium conditions, and to provide data support for radiation environment supervision, a method for measuring 232Th in slag using a high-purity germanium γ spectrometer was established. The method involves indirect measurement by selecting the characteristic γ rays of the daughter nuclides in the decay chain of 232Th, and calculating its specific activity by the relative comparison method. The slag samples in a non-equilibrium state are sealed for 20 days to enable 228Ra and 228Ac to reach equilibrium, and 228Th, 224Ra and subsequent daughter nuclides to reach equilibrium. Then, the specific activity of the parent nuclide 232Th is obtained through conversion relationships. This method is accurate and efficient, with a detection limit of 1.1 Bq・kg-1, a precision better than 5 %, and a relative error lower than 5 %. The method of measuring 232Th in slag using a high-purity germanium γ spectrometer does not require complex chemical treatment, which makes up for the deficiencies of inductively coupled plasma mass spectrometry. The calculation method under non-equilibrium conditions is also more reliable than using the average value of a single characteristic peak or multiple characteristic peaks.

high-purity germanium  /  slag  /  232Th  /  associated radioactivity  /  radioactive equilibrium  /  environment  /  solid waste
黄宇琦, 钟春明. 高纯锗γ谱仪测量矿渣中的232Th. 世界核地质科学, 2025 , 42 (1) : 211 -217 . DOI: 10.3969/j.issn.1672-0636.2025.01.019
HUANG Yuqi, ZHONG Chunming. The measurement of 232Th in slag with high-purity germanium γ spectrometer[J]. World Nuclear Geoscience, 2025 , 42 (1) : 211 -217 . DOI: 10.3969/j.issn.1672-0636.2025.01.019
正文
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伴生放射性矿是指含有较高水平天然放射性核素浓度的非铀矿。这类矿产资源中不仅包含有经济价值的主要元素（如稀土元素、钽、铌、锆和磷酸盐等），同时也含有一定量的天然放射性物质，主要是铀(U)和钍(Th)系列的放射性核素。这些放射性物质在矿产开采、加工过程中可能会释放出来，对环境和人体健康造成潜在的影响[1]。
由于伴生放射性矿在开采和利用过程中可能产生放射性污染，因此对于这类矿产的开发需要遵循严格的环境保护标准和措施，确保辐射安全[2]。生态环境部等相关部门已经制定相关法律法规和技术指南，用于指导和规范伴生放射性矿的开发利用活动，减少对环境和公众健康的潜在风险。根据生态环境部相关规定，含超过1 000 Bq·kg-1 的放射性核素的伴生放射性矿及其废渣需要被纳入监管范围，而准确测量放射性核素活度浓度是有效监管的前提[3]。
232Th是伴生放射性固体废物环境风险监管的重要项目之一，常用的分析方法有γ能谱法[4]、电感耦合等离子体质谱法[5]、X射线荧光光谱法[6]和化学比色法等[7]。伴生放射性矿渣成分复杂，干扰元素多，化学前处理难，因此不用复杂前处理的γ能谱法常作为232Th测量的推荐方法。由于232Th的衰变链长且复杂，在实际工作中，用γ能谱法测量伴生放射性矿废渣中时也面对诸多难题，比如特征峰之间的互相干扰、低能端探测器的能量响应限制、自吸收与散射效应、环境本底与宇宙射线干扰和仪器的稳定性与校准问题等[8]。另外对比一般矿产，伴生放射性矿有着更为特殊的开采技术和复杂的工艺流程，从而更容易打破232Th的衰变链，导致232Th与其子体处于放射性不平衡状态，给测量带来更大的难度和不确定性。
1 实验部分
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1.1 实验原理
232Th是一种长寿命的放射性核素，其半衰期约为140亿年。232Th通过一系列衰变最终转化为稳定的208Pb。在这个衰变链中，会产生多个放射性核素，其中一些会发射γ射线。例如，232Th衰变链中的重要中间产物包括228Ac、208Tl等，这些同位素在衰变过程中会发射特定能量的γ射线。每个核素发射的γ射线具有特定的能量，这些能量值是唯一的，可以用来识别特定的核素。
γ能谱法通常使用高纯锗（HPGe）探测器，其具有极高的能量分辨率，可以准确区分不同能量的γ射线，适用于实验室高精度分析。探测器接收到的γ射线信号会被转换为电信号，经过放大和数字化处理后，形成能谱图。能谱图显示不同能量γ射线的强度分布。通过分析能谱图中的峰位置和强度，可以确定样品中232Th及其衰变产物的含量[9]。其构成和原理示意如图1。
1.2 仪器与工作参数
高纯锗γ能谱仪：ORTEC GEM100-95型，美国阿美特克有限公司；分析天平：LQ-C5001型，浙江乐祺公司。高纯锗γ能谱仪工作参数：运行高压：4 160 V；工作温度：25 ℃；工作湿度：<65 %；测量时间：30 000 s；样品盒：聚乙烯塑料圆柱盒φ75 mm×70 mm。能量响应范围：40 keV至10 MeV。能量分辨率：在1.332 MeV（Co-60源）处为1.8 keV。监测效率校准源：7NTR/70-805 φ75 mm×70 mm，中国计量科学研究院。
1.3 样品处理方法
样品经烘干和破碎后，研磨成粉状。预先把样品盒称重，随即称取大约350 g样品装入样品盒，装样过程中用铁勺逐步压实，表面用薄板刮平，不留空隙并盖紧盖子，最后再次称量总重，计算得出样品的净质量。严格控制装样过程，目的是使样品与标准源在密度和几何形状上接近一致，如果两者相差较大，需要进行自吸收校正。实验表明：样品粒度、密度、紧实度和均匀度等都对自吸收产生一定影响[10]。虽然前处理没有化学处理过程，回收率可以视为100 %，但是也需要重视装样过程，以免产生额外误差。
1.4 上机测量
将封装好的样品置于探测器上测量，室内保持恒温、恒湿。测量前后都应该测量仪器的本底值，计算时取平均值。测量时间可以由特征峰峰面积判断，其统计误差应小于10 %，最长不超过24 h，本文选择测量时间为30 000 s。
2 结果与讨论
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2.1 特征射线峰的确定
232Th自身发射的γ射线能量有63.8和 140.8 keV，但是发射率极低，如表1所示。
想要直接测量232Th的γ射线来确定其比活度是不可行的，通常需要通过其衰变链中子体核素的γ射线来间接推算。间接测量的前提条件是232Th和其衰变链中的子体达到放射性平衡。232Th的衰变链是一系列连续的放射性衰变过程，最终达到稳定的208Pb，又被称为钍系或4n+0系[11]，其衰变链图如图2。
虽然232Th的子体众多，但是并非都可以用于间接测量。一个理想的特征γ射线峰应该具有高分支比、较高的能量和较低的背景干扰等条件[12]。表2列出几个常用于232Th测量的特征γ射线峰。
2.2 比活度的计算
232Th的比活度计算方法有核素全吸收峰探测效率法、γ射线全吸收峰探测效率法和相对比较法等。本文采用易于理解的相对比较法进行计算[13]。其计算公式如式（1）：
A 1 = A 0 ( N 1 - N b ) ( N 0 - N b )
式（1）中： A 1—待测样品232Th的比活度，Bq·kg-1；A0—校准源中232Th的比活度，Bq·kg-1； N 1—待测样品中特征γ射线峰的净计数率，cps； N 0—校准源中特征γ射线峰的净计数率，cps； N b—本底计数率，cps。
在γ核素测量中，相对比较法是一种常用方法，它通过与已知标准源进行比较，可以有效减少由于仪器响应特性或环境条件变化引起的系统误差；可以通过选择与待测样品物理性质相似的标准源来进一步提高测量的准确性。而且校准过程较为简单，可以通过与该标准源的比较来确定其他样品的比活度或其他相关参数。伴生放射性矿及其废渣的样品经过一段时间的测量后，得到表2中特征峰的净计数率，代入式（1）计算后得出相应结果。
2.3 方法检出限
高纯锗γ谱仪测量矿渣中的232Th的检出限可以用式（2）计算[14]：
L L D = 4.66 E ∙ m N b T b
式（2）中： L L D—方法检出限，Bq·kg-1； N b—特征峰的本底计数率，cps； T b—本底测量时间，s；E—特征峰处的探测效率，无量纲； m—样品质量，kg。
上式是基于9 5 %置信度下的简化算法，所选特征峰、测量时间和装样质量都会影响计算结果。当上式选取232Th 在911.2 keV处的特征射线峰， N b、 T b、E和 m分别取值0.003 93 cps、300 00 s、0.004 56和0.35 kg，计算得到方法检出限为1.1 Bq·kg-1。
2.4 方法精密度与正确度
按照上述实验流程和测量方法，对不同比活度的放射性标准物质GBW04110、GBW04115和GBW04116进行实验，并选择911.2 keV为特征射线峰来计算，结果如表3。由表3可见，该方法精密度良好，小于5 %（n=8），准确度较高，相对误差都低于±5 %，测定结果均落在参考值范围内。
2.5 232Th在非平衡条件下的测量
放射性平衡是指在放射性衰变链中，当母核素的衰变速率与子体核素的产生速率相等时所达到的一种动态平衡状态。在这种状态下，虽然母核素不断衰变成子体核素，但由于子体核素也在不断地衰变成其他核素或稳定同位素，因此子体核素的数量保持恒定，即其浓度不再随时间变化[15]，其动力学方程可表述为式（3）：
A i ( t ) = ∑ k - 1 i A k , i
式(3)中： A i ( t )—衰变链中第 i种核素经过时间 t后的比活度，Bq·kg-1； A k , i—第 k种核素的初始放射性比活度 A k 0对第 i中核素的放射性比活度 A i ( t )的贡献，Bq·kg-1。
伴生放射性矿的矿渣中232Th时常出现不平衡现象。矿石经过物理分离、化学提取等处理过程中，如酸浸、碱浸等，不同的放射性核素由于化学性质的不同，可能表现出不同的溶解性和反应活性。这意味着某些放射性核素更容易被提取或留在矿渣中，从而破坏原有的放射性平衡。例如，232Th及其衰变产物在不同pH值下的溶解度差异可能导致它们在处理过程中分布不均。此外，还有时间因素、环境污染和人为干预等，也可能影响放射性核素的分布，进而影响放射性平衡[16]。
放射性平衡一旦被打破，需要等待10个半衰期（按各子体中最长半衰期计算）才能被视为再次达到平衡。在非平衡情况下，232Th及其衰变子体之间没有固定的比例关系，这时很难通过一个特征 γ 射线峰的计数来计算232Th的含量[17]。由图2可见，232Th的衰变子体中长半衰期的核素有228Ra(5.75 a）和228Th（1.91 a），因此将样品封存20 d后，232Th的子体228Ra和228Th会形成2个独立的衰变链，228Ra与228Ac达到平衡，228Th与224Ra及后续子体达到平衡，通过式（3）和衰变定律式（4）可进一步推导出232Th、228Ra和228Th的比活度关系，表述为式（5）：
A = A 0 e - λ t
A 1 = 1.02 A 4 - 0.02 A 2
式（4）和（5）中： A 0—某一特定核素的初始比活度，Bq·kg-1； A—经过衰变时间 t后的比活度，Bq·kg-1； λ—核素的衰变常数，s-1； A 1—待测样品中232Th的比活度，Bq·kg-1； A 2—待测样品中228Ra的比活度，Bq·kg-1； A 4—待测样品228Th的比活度，Bq·kg-1。
综上所述，利用高纯锗γ能谱仪，可以通过 212Pb 的 特征射线238.2 keV 得到 A 4，通过 228Ac 的特征射线 911.2 keV 得到 A 2，进而计算出母核素232Th的比活度。
2.6 实际矿渣样品测量
根据上述实验方法，对某稀土公司的矿渣样品封存20 d后进行测量，选用238.2和911.2 keV的特征峰进行测量，并将结果代入式（5）进行计算得到232Th的比活度值 ( A 1 )，结果列于表4。
由表4可见，所选矿渣测试样品中232Th和其衰变子体处于不平衡状态，因而用某一个子体的特征峰并不能代表232Th的真实比活度。但是将样品封存20 d后，根据式（5）进行计算可以得到232Th的比活度值 ( A 1 )。并且当 A 4远小于 A 2时， A 2对结果的影响才能体现出来，否则 A 1约等于 A 4。为进一步验证实验结果，利用电感耦合等离子体质谱法（ICP-MS）对上述矿渣样品中的Th进行测量，并将测量结果换算为比活度单位，列于表5。
通过表5中的对比可以看出，表4中 A 1的计算值与电感耦合等离子体质谱法（ICP-MS）所测得的Th的值十分接近，很好地验证了用上述方法计算得出的232Th的值更接近真实值，比用某一个特征峰或多个特征峰的平均值更加可靠。
3 结论
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1）利用高纯锗γ能谱仪测量矿渣中的232Th，选择子体的特征γ射线进行间接测量，并采用相对比较法计算，是一种准确且高效的方法，能为伴生放射性矿的辐射环境监管提供有力支持。
2）实验结果表明：方法具有检出限低和精密度高等优点，方法检出限为1.1 Bq·kg-1，精密度优于5 %，可适用于实际矿渣样品的测量。
3）将处于不平衡状态的矿渣样品封存20 d后测量子体核素228Ra和228Th的比活度，进而换算出232Th的比活度更接近真实值，可以避免因放射性不平衡导致测量不准的问题。
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2025年第42卷第1期
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doi: 10.3969/j.issn.1672-0636.2025.01.019
  • 接收时间：2024-12-16
  • 首发时间：2025-11-07
  • 出版时间：2025-02-08
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  • 收稿日期：2024-12-16
  • 修回日期：2024-12-29
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    1 核工业二三○研究所，湖南 长沙 410007
    2 湖南中核环保科技有限公司，湖南 长沙 410007
    3 湖南省伴生放射性矿产资源评价与综合利用工程技术研究中心，湖南 长沙 410007
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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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