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How Certain Are the Reported Ionic Conductivities of Thiophosphate-Based Solid Electrolytes? An Interlaboratory Study
ACS Energy Letters ( IF 19.3 ) Pub Date : 2020-02-28 , DOI: 10.1021/acsenergylett.9b02764 Saneyuki Ohno 1, 2 , Tim Bernges 1, 2 , Johannes Buchheim 3 , Marc Duchardt 4 , Anna-Katharina Hatz 5, 6, 7 , Marvin A. Kraft 1, 2 , Hiram Kwak 8 , Aggunda L. Santhosha 9 , Zhantao Liu 10 , Nicolò Minafra 1, 2 , Fumika Tsuji 11 , Atsushi Sakuda 11 , Roman Schlem 1, 2 , Shan Xiong 10 , Zhenggang Zhang 9 , Philipp Adelhelm 9 , Hailong Chen 10 , Akitoshi Hayashi 11 , Yoon Seok Jung 8 , Bettina V. Lotsch 5, 6, 7, 12 , Bernhard Roling 4 , Nella M. Vargas-Barbosa 5 , Wolfgang G. Zeier 1, 2
ACS Energy Letters ( IF 19.3 ) Pub Date : 2020-02-28 , DOI: 10.1021/acsenergylett.9b02764 Saneyuki Ohno 1, 2 , Tim Bernges 1, 2 , Johannes Buchheim 3 , Marc Duchardt 4 , Anna-Katharina Hatz 5, 6, 7 , Marvin A. Kraft 1, 2 , Hiram Kwak 8 , Aggunda L. Santhosha 9 , Zhantao Liu 10 , Nicolò Minafra 1, 2 , Fumika Tsuji 11 , Atsushi Sakuda 11 , Roman Schlem 1, 2 , Shan Xiong 10 , Zhenggang Zhang 9 , Philipp Adelhelm 9 , Hailong Chen 10 , Akitoshi Hayashi 11 , Yoon Seok Jung 8 , Bettina V. Lotsch 5, 6, 7, 12 , Bernhard Roling 4 , Nella M. Vargas-Barbosa 5 , Wolfgang G. Zeier 1, 2
Affiliation
Owing to highly conductive solid ionic conductors, all-solid-state batteries attract significant attention as promising next-generation energy storage devices. A lot of research is invested in the search for and optimization of solid electrolytes with higher ionic conductivity. However, a systematic study of interlaboratory reproducibility of measured ionic conductivities and activation energies is missing, making the comparison of absolute values in the literature challenging. In this Viewpoint, we perform an uncertainty evaluation via a round-robin approach using different Li-argyrodites exhibiting orders of magnitude different ionic conductivities as reference materials. Identical samples are distributed to different research laboratories, and the conductivities and activation barriers are measured by impedance spectroscopy. The results show large ranges of up to 4.5 mS cm–1 in the measured total ionic conductivity (1.3–5.8 mS cm–1 for the highest conducting sample, relative standard deviation 35–50% across all samples) and up to 128 meV for the activation barriers (198–326 meV, relative standard deviation 5–15% across all samples), presenting the necessity of a more rigorous methodology including further collaborations within the community and multiplicate measurements. Fast ionic conductors such as lithium and sodium thiophosphates are currently being investigated for their possible application in all-solid-state batteries.(1,2) Recent research efforts have found a variety of Li+- and Na+-based materials such as the thiophosphates Li10+xM1–xP2+xS12 (M = Si, Ge, Sn),(3−8) Li2S–P2S5 glasses,(9−15) Li6PS5X (X = Cl, Br, I),(16−22) Na3PS4,(23−27) and Na11Sn2PS12.(11,28,29) These materials can exhibit ionic conductivities >1 mS cm–1, making them viable for solid-state battery applications. Throughout the literature, however, we can find a spread in the reported ionic conductivity and activation barrier values, even within the same class of materials. Whereas significant variations in the Li+ ionic transport has been reported as a function of batch variation, particle size, and synthesis procedure, and even due to local sample inhomogeneity,(30,31) to date, no rigorous study on the interlaboratory reproducibility of the ionic conductivity measurement via impedance spectroscopy has been performed. Inspired by the standardization and benchmarking efforts in other communities, e.g., photovoltaics,(32) in this Viewpoint we report a round robin study that considers the reproducibility of ionic conductivity measurements in superionic lithium thiophosphate solid electrolytes. In this Viewpoint, we chose the lithium argyrodite Li6PS5X as an exemplary class of materials because it provides the possibility to establish statistical trends over several orders of magnitude in the ionic conductivity, ranging from 10–4 mS cm–1 up to a few millisiemens per centimeter. All test samples, namely, Li6.6P0.4Ge0.6PS5I, Li6PS5Cl, Li6PS5Br0.75I0.25, Li6PS5Br0.25I0.75, and Li6PS5I, here identified as samples 1, 2, 3, 4, and 5, respectively, were synthesized by the organizing group according to previous reports.(18,20) To obtain a sufficient amount of homogeneous powder (10 g), each composition was synthesized in multiple batches, followed by X-ray diffraction of each batch to confirm the sample purities (see Figure S1). The resulting sample powders were mixed and homogenized, such that each participating group received 1 g of identical test sample for each composition. Prior to the distribution, the ionic conductivity of all homogenized samples was measured by the organizing group to make sure that the values obtained were similar to previously reported values. All samples were supplied as powders to capture the influence of sample-preparation procedures (i.e., densification procedure, relative density, applied pressure during measurement, and pellet contacting method) on the reported ionic conductivities. Each group was asked to measure temperature-dependent impedance spectra on the supplied samples, including at room temperature (25 °C), using the standard measuring procedure within each lab. All groups were asked to provide the measured impedance spectra and Arrhenius behaviors upon heating (see Figures S2–S10) as well as report the calculated room-temperature conductivities and the activation barriers for all samples, without providing the fitting procedure in order to avoid revealing the identity of the different groups. Further details on the sample preparation and the methodology reported of each group (labeled A–H) are given in the Supporting Information (Tables S2–S10), which include applied pressure upon densification (pelletizing pressure) and during measurement, contacting method, contacting material (Au sputtered and stainless steel pressed), impedance analyzer, excitation voltage, temperature and frequency ranges, the cell constants, and employed powder masses. Hence, the statistical analysis presented here includes the measurement uncertainty of the employed impedance spectroscopy, the uncertainty in the cell constants, as well as the differences in sample preparation for the measurement itself and data analysis procedure. Under ideal conditions, the impedance spectrum in a Nyquist representation of a polycrystalline solid electrolyte is characterized by two well-resolved semicircles and an electrode polarization. The higher-frequency semicircle would then describe the ionic transport in the grains, whereas the lower-frequency semicircle describes grain boundary contributions to the ionic transport. As is typically observed for Li+ conducting thiophosphates, bulk and grain boundary contributions in Li-argyrodites cannot be deconvoluted at room temperature (see Figures S2 – S10).(18,20) Therefore, in line with the different preparation and measurement procedures, the here-reported ionic conductivity values correspond to the total ionic conductivities of all samples and their corresponding activation barriers. Table S11 summarizes all of the reported values used for this statistical analysis. The obtained room-temperature conductivities are statistically analyzed using the interquartile range (IQR) method, and the results are shown in Figure 1a as a box plot. Although we observe a large spread in the reported ionic conductivities for all samples (e.g., up to 4.5 mS cm–1 range for sample 1), we were not able to detect any outliers in any of the samples with the IQR method. In the case of samples 1 and 2, the median shows a skewness to lower and higher conductivity values, respectively, whereas for the lower-conducting samples 3, 4, and 5 we observe that the mean and the median are closer to one another. Moreover, the calculated median for the lower-conducting samples is close to the center of the IQR box, which suggests that the spread in the conductivity can be viewed as following a normal distribution. In the particular case of samples 1 and 2, based on this statistical analysis, the samples have very similar median total ionic conductivities, showing the difficulty in comparing different materials across laboratories. Figure 1. (a) Box plots for the room-temperature total ionic conductivity for all samples in the study. (b) Percentile standard deviations and relative median error percentage for all samples. The relative median error was calculated assuming that the median represents the true total conductivity value, using 
Because we do not know what the “true” total ionic conductivity of these samples is, it is challenging to assess the best-practice procedure for the statistical analysis. We can, however, use the different measures of central tendency (median and average) as reasonable estimates for the “true” total ionic conductivity, as well as the standard deviation of the ionic conductivity as the representative expected spread in these samples for the following discussion. It needs to be mentioned that the term “true” total ionic conductivity serves only as a statistical descriptor here; it does not imply that measured values of an individual group represent a “false” ionic conductivity. Note that although the ionic conductivities of all samples range over several orders of magnitude, the calculated average values are close to the median values, and high, but similar, percentages of the standard deviation are found within all samples (see Figure 1b). As the median of any data set is less influenced by extreme values, we take it as the better estimate for the “true” total ionic conductivity and use the calculated average to determine relative median errors for all samples (see Figure 1b). In doing so we observe that for samples with ionic conductivities <1 mS cm–1 this error is less than 10%, whereas in the case of the fastest conductor, the Li6.6P0.4Ge0.6PS5I sample, we obtain a much greater error of 22%. In the case of the calculated activation barriers, we observe a similar spread in the reported values (see Figure 2). The IQR analysis reveals that in the case of the highest and lowest conducting samples, samples 1 and 5, respectively, one of the values with higher activation barrier is an outlier. Here, the median values for samples 3, 4, and 5 show a skewness to lower activation energies. Only in samples 1 and 2 do we observe that the mean and the median are closer to one another and more centered in the IQR box, again suggesting a normal distribution of the data. In spite of the spread, the percentile standard deviations and relative median errors are much smaller than those for the ionic conductivities, likely because the activation barrier is a parameter that is extracted from the slope of the Arrhenius plot and is therefore less sensitive to extreme values at specific temperatures. Nonetheless, even with the small deviation from the average, the values can correspond to a statistical range of up to 128 meV (198–326 meV). This large range of the activation barriers is significant considering that often values of the activation barriers are reported with a large number of significant figures and changes in series of solid solutions are often within this value of the spread. Moreover, these results suggest that direct comparisons between experimental and theoretically calculated activation barriers are not straightforward and similar values between them do not validate the theory or experimental results. Figure 2. (a) Box plots for the activation barrier of all samples in the study. (b) Percentile standard deviations and relative median error percentage for all samples. The relative median error was calculated assuming that the median represents the true conductivity value, using 
. Because the reported conductivities correspond to total conductivities, one may expect an influence of the densification behavior or resulting relative pellet densities. While nearly 100% relative densities can be achieved in oxide ceramic-based materials via sintering, the mechanical soft nature of the thiophosphate-based electrolytes often leads to densities between 80 and 90% by pressing at ambient temperature. In this study a comparison of the reported ionic conductivities against the densification (pelletizing pressure) pressure, the relative pellet density, the excitation voltage, the cell constant, and pellet thickness show no strong apparent trend in all samples (Figures S11–S20). As an example, Figure 3 shows the absence of clear trends for the ionic conductivity and the activation barrier of sample 2 as a function of pelletizing pressure and cell constant. Although there is no apparent trend as a function of cell constants, a qualitative trend of increasing conductivity with the relative density of the pellet can be observed. However, the trend seen as a function of relative density is not correlated to the pelletizing pressure; that is, a higher relative density is not obtained at higher pelletizing pressures. In addition, whereas no clear influence of the contacting material was identified, an increasing conductivity with increasing applied pressure during measurement was found. This trend does not hold for the Au sputtered samples that were measured without external pressure, indicating the influence of the pressing conditions for pellet preparation on the measured ionic conductivity. These results highlight the effect of sample preparation to the microstructure of the sample and its influence on the measured conductivity. However, it should be noted that the trend with relative densities is not universally observed for all the samples and is less prominent in lower-conducting samples as seen in Figures S11–S20, adding the difficulty of assessing the underlying mechanism of the here-observed variations. Figure 3. Spread in the total ionic conductivities and activation barriers of sample 2 as a function of various experimental parameters. The dashed line represents the average value and the shaded area the standard deviation from the average. The absence of universal trends among all the samples on one of the experimental parameters suggests a convolution of influences due to the differences in measurement setups and measurement approaches. One potential reason for the larger discrepancies at high ionic conductivities is the lack of a well-resolved semicircle. In this study, only the samples with a lower ionic conductivity show well-resolved semicircles. An experimental approach for modulating the overall resistance is to change the cell constant (thickness of the pellet divided by the area of the electrode) and with it using enough amount of sample. Note that although changing the cell constant may help to resolve the relevant features in the impedance spectra, the cell constant itself has no influence on the intrinsic conductivity of the material; that is, when normalizing the impedance spectra to the cell constant, the same intercept in the real impedance axis will be obtained. In other words, larger thicknesses will change only the total resistance but not the time constant and frequency range of the occurring transport processes, and a deconvolution of bulk and grain boundaries may be possible only at low temperatures.(33) This may be particularly important in highly conducting samples that lead to low measured resistances in which the influence of the microstructure and resulting grain resistances and microstructure may be more prominent, in comparison to the highly resistive samples. The increasing conductivity with pressure of the stainless-steel contacts, as well as the observed variation as a function of relative densities, in contrast to the values obtained by the Au sputtered samples that do not exhibit any external pressure during measurement, additionally underscores the importance of proper contact between particles, as well as with the electrodes. To show the influence and beneficial approach of low-temperature measurements, one of the participating groups has the experimental capabilities to perform impedance measurements at temperatures down to −120 °C. At these much lower temperatures it is often possible to separate the grain impedance from the total ionic conductivity.(33)Figure S21 shows the conductivity versus inverse temperature behavior for a representative sample 2 measured to such low temperatures as well as a representative impedance spectrum of sample 2 measured at −100 °C. At temperatures below −75 °C, it is possible to resolve the grain conductivity contributions to the impedance spectrum. Upon fitting and extrapolating the data of grain conductivity versus inverse temperature, the extrapolated line of best fit can estimate the upper-bound values of the reported room-temperature total ionic conductivities in this study. These results underscore, again, the effects of sample microstructure on the ionic conductivity and how under the right measurement conditions it is possible to discriminate between bulk and microstructure effects. Considering the spread in the obtained conductivities and activation barriers, a few conclusions may be drawn. A larger relative median error can be clearly seen in the samples that exhibit high ionic conductivities >1 mS cm–1 likely due to the convergence of different occurring processes that lead to unresolved processes, which cannot be deconvoluted without a low-temperature measurement. Additionally, these lithium thiophosphate electrolytes are highly sensitive to atmosphere and, while structurally and chemically comparable, differences in glovebox atmospheres (H2O and O2 content, as well as solvents present) as well as during measurement may interfere with a comparability between groups. Furthermore, pressing in these materials is needed, and a certain degree of microstructural relaxation may occur after pellet consolidation and contacting, making the “sample history” a possible factor in the observed spread. Nevertheless, the large range and uncertainty in the reproducibility of the conductivity and activation barriers suggest the need to adopt a more rigorous approach in the field, as often minor improvements in activation barriers and conductivities are deemed significant. First, it seems reasonable that for future studies showing changing conductivities and activation barriers, e.g. as a result from isovalent and aliovalent substitutions, measurements in triplicate are necessary, and an accurate description of sample consolidation, contacting, and measurement conditions is needed. Here, three different samples of the same composition should be measured with different cell constants (changing thicknesses as the diameter is often restricted in the cell setup), in order to change the overall cell resistance and report an average value and their respective standard deviations. Measurements at low temperatures to deconvolute processes seems crucial;(33) however, this is often restricted by experimental setups. While the recommendation of triplicate measurements seems trivial, it is not often reported in the literature despite the fact that these triplicates may help to produce more realistic uncertainties in obtained ionic conductivities and activation barriers. While the measurement of triplicates does not fully alleviate the large range that was found throughout the groups, it can provide more meaningful information on qualitative changes in the ionic transport within studies for solid solutions. In the future, measurement standards and standard materials for measurement setup validation may be needed. Second, especially within this mechanically soft class of materials, there seems to be an influence of the pressure under measurement when measured in press cells (see Figure 3). Therefore, it may be needed to report ionic conductivities as a function of the external pressure applied. Third, when novel electrolytes with high ionic conductivities >1 mS cm–1 are reported, we suggest sending samples to a collaborative group to corroborate the obtained ionic conductivities. Fourth, a comparison of experimental conductivity values with diffusion coefficients obtained by nuclear magnetic resonance and with it calculations of Haven ratios may be subject to a large uncertainty based on the experimental range in obtained conductivities. While Haven ratios are often used to explain correlation effects,(34) comparing different measurement techniques may not be very meaningful in extracting information about correlation effects in these systems. Fifth, often theoretical calculations are internally validated by reproduction of experimental activation barriers. Despite a smaller relative median error, the larger range of up to 128 meV in the experimentally obtained activation barriers suggests that a direct comparison between experiment and theory alone should not be used to validate theoretical nor experimental results. Overall, within the field of superionic conductors a more rigorous approach for reporting results, including the experimental conditions and triplicate measurements, will be needed to better understand and reliably design solid electrolytes for the use in solid-state batteries. The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsenergylett.9b02764.
中文翻译：
基于硫代磷酸盐的固体电解质的报告电导率如何确定？实验室间研究
由于具有高导电性的固体离子导体，全固态电池作为有前途的下一代储能设备备受关注。已投入大量研究来寻找和优化具有较高离子电导率的固体电解质。但是，对实验室间可重复性的系统研究缺少测量的离子电导率和活化能，这使得文献中绝对值的比较具有挑战性。在这种观点下，我们使用具有不同数量级不同离子电导率的不同锂杂香锂作为参考材料，通过循环法进行不确定性评估。将相同的样品分配给不同的研究实验室，并通过阻抗光谱法测量电导率和活化势垒。结果表明，测得的总离子传导率范围高达4.5 mS cm –1（1.3–5.8 mS cm –1对于导电性最高的样品，所有样品的相对标准偏差为35–50％），对于激活势垒，最高为128 meV（198–326 meV，所有样品的相对标准偏差为5–15％），因此有必要严格的方法，包括社区内的进一步合作和重复测量。目前正在研究快速离子导体，例如锂和硫代磷酸钠在全固态电池中的可能应用。（1,2）最近的研究工作已经发现了多种基于Li +和Na +的材料，例如硫代磷酸盐Li 10+ x M 1– x P 2+ x S 12（M = Si，Ge，Sn），（3-8）Li 2 S–P 2 S 5玻璃，（9−15）Li 6 PS 5 X（X = Cl，Br，I），（16-22） Na 3 PS 4，（23−27）和Na 11 Sn 2 PS 12。（11,28,29）这些材料的离子电导率> 1 mS cm –1，使其在固态电池应用中可行。但是，在整个文献中，即使在同一类材料中，我们也可以发现所报告的离子电导率和活化势垒值的差异。锂+的显着差异据报道离子迁移是批次变化，粒度和合成程序的函数，甚至由于局部样品的不均匀性，（30,31）迄今为止，还没有对通过阻抗谱法测量离子电导率的实验室间重现性进行严格的研究。已执行。受其他观点（例如光伏行业）的标准化和基准化工作的启发（32），我们报告了一项轮循研究，该研究考虑了超离子硫代磷酸锂固体电解质中离子电导率测量的可重复性。在这个观点上，我们选择了锂银辉石Li 6 PS 5X是一种示例性的材料，因为它提供了建立离子电导率几个数量级（从10 –4 mS cm –1到几毫米/厘米）的统计趋势的可能性。所有测试样品，即Li 6.6 P 0.4 Ge 0.6 PS 5 I，Li 6 PS 5 Cl，Li 6 PS 5 Br 0.75 I 0.25，Li 6 PS 5 Br 0.25 I 0.75和Li 6 PS 5I由组织小组根据以前的报告合成，分别确定为样品1、2、3、4和5.（18,20）为获得足够量的均质粉末（10 g），每种组合物批量合成了三氧化二砷，然后每批进行X射线衍射以确认样品纯度（见图S1）。将所得的样品粉末混合并均质化，以使每个参与组针对每种组合物接受1 g相同的测试样品。在分配之前，由组织小组测量所有均质样品的离子电导率，以确保获得的值与先前报告的值相似。所有样品均以粉末形式提供，以捕获样品制备程序（即致密化程序，相对密度，在测量过程中施加的压力，以及颗粒接触方法）上报告的离子电导率。要求每组使用每个实验室中的标准测量程序测量所提供样品的温度相关阻抗谱，包括在室温（25°C）下。要求所有小组提供测量的阻抗谱和加热时的阿伦尼乌斯行为（见图S2-S10），并报告所有样品的计算出的室温电导率和活化势垒，但不提供拟合程序以避免暴露。不同群体的身份。支持信息（表S2-S10）中提供了有关每组样品制备和方法学（标记为AH）的更多详细信息，其中包括在致密化（造粒压力）和测量过程中施加的压力，接触方法，接触材料（Au溅射和不锈钢压制），阻抗分析仪，激励电压，温度和频率范围，电池常数以及使用的粉末质量。因此，此处介绍的统计分析包括所用阻抗谱的测量不确定度，电池常数的不确定度以及测量本身和数据分析程序的样品制备方面的差异。在理想条件下，多晶固体电解质的奈奎斯特表示中的阻抗谱的特征是两个分辨良好的半圆和电极极化。高频半圆将描述颗粒中的离子迁移，而低频半圆描述了晶界对离子迁移的贡献。正如Li所观察到的+室温下不能解卷积锂-香精岩中的硫代磷酸盐，块体和晶界贡献（见图S2-S10）。（18,20）因此，根据不同的制备和测量程序，此处报道的离子电导率值对应于所有样品的总离子电导率及其相应的活化势垒。表S11汇总了用于此统计分析的所有报告值。使用四分位间距（IQR）方法对获得的室温电导率进行统计分析，结果在图1a中以箱形图的形式显示。尽管我们观察到所有样品的报告离子电导率分布很大（例如，高达4.5 mS cm –11）的范围，我们无法使用IQR方法检测到任何样本中的异常值。在样本1和2的情况下，中位数分别显示出较低和较高电导率值的偏斜度，而对于低导电性样本3、4和5，我们观察到平均值和中位数彼此接近。而且，计算出的低导电率样本的中值接近IQR框的中心，这表明电导率的扩展可以看作是服从正态分布。在样品1和2的特定情况下，基于此统计分析，样品的总离子电导率中位数非常相似，这显示了在实验室之间比较不同材料的困难。图1。（a）研究中所有样品的室温总离子电导率的箱形图。（b）所有样本的百分比标准偏差和相对中值误差百分比。假设中位数代表真实的总电导率值，则使用以下公式计算相对中位数误差：由于我们不知道这些样品的“真实”总离子电导率是什么，因此评估最佳实践程序进行统计分析具有挑战性。但是，我们可以使用集中趋势的不同度量（中值和平均值）作为“真实”总离子电导率的合理估计，以及离子电导率的标准偏差作为这些样品中以下样品的代表性预期扩散讨论。需要指出的是，术语“真实的”总离子电导率在这里仅用作统计描述；这并不意味着单个基团的测量值代表“假”离子电导率。请注意，尽管所有样品的离子电导率范围都在几个数量级上，但计算出的平均值却接近中值，并且很高，但是相似的是，在所有样品中都发现了标准偏差的百分比（见图1b）。由于任何数据集的中位数受极值的影响较小，因此我们将其作为“真实”总离子电导率的更好估计，并使用计算出的平均值来确定所有样品的相对中位数误差（见图1b）。这样，我们观察到离子电导率<1 mS cm的样品–1此误差小于10％，而对于最快的导体，Li 6.6 P 0.4 Ge 0.6 PS 5我进行采样，得出的误差要大得多，为22％。在计算出的激活势垒的情况下，我们观察到报告值的分布相似（见图2）。IQR分析表明，在导电性最高和最低的样品（分别为样品1和5）的情况下，具有较高活化势垒的值之一是异常值。在此，样品3、4和5的中值显示出偏斜，以降低活化能。仅在样本1和2中，我们观察到平均值和中位数彼此更接近，并且在IQR框中居中，这再次表明数据呈正态分布。尽管存在差异，但百分数标准偏差和相对中值误差比离子电导率小得多，可能是因为激活势垒是从Arrhenius曲线的斜率提取的参数，因此对特定温度下的极端值不太敏感。尽管如此，即使与平均值的偏差很小，该值仍可以对应高达128 meV（198–326 meV）的统计范围。考虑到经常会用大量有效数字报告活化势垒的值，并且一系列固溶体的变化通常都在该扩散值范围内，因此活化势垒的这一大范围非常重要。此外，这些结果表明，在实验和理论上计算出的激活势垒之间无法直接进行比较，而且它们之间的相似值也无法验证理论或实验结果。图2。（a）研究中所有样品的激活屏障的箱形图。（b）所有样本的百分比标准偏差和相对中值误差百分比。假设中位数代表真实电导率值，则使用以下公式计算相对中位数误差：。因为报告的电导率对应于总电导率，所以可以预期致密化行为或所产生的相对颗粒密度的影响。尽管可以通过烧结在基于氧化物陶瓷的材料中获得近100％的相对密度，但是通过在环境温度下加压，硫代磷酸盐基电解质的机械柔软特性通常导致密度在80％到90％之间。在这项研究中，所报告的离子电导率与致密化（造粒压力）压力，相对颗粒密度，激发电压，细胞常数和颗粒厚度的比较在所有样品中均未显示出明显的趋势（图S11-S20）。举个例子，图3显示了没有明显的离子电导率和样品2的活化势垒随制粒压力和细胞常数变化的趋势。尽管没有明显的趋势作为细胞常数的函数，但是可以观察到随着颗粒的相对密度电导率增加的定性趋势。但是，被视为相对密度的函数的趋势与造粒压力无关。即，在较高的造粒压力下不能获得较高的相对密度。另外，虽然没有确定接触材料的明显影响，但是发现在测量过程中电导率随施加的压力的增加而增加。对于没有外部压力测量的金溅射样品，这种趋势不成立，表明制粒条件对样品中离子电导率的影响。这些结果突出了样品制备对样品微观结构的影响及其对测得的电导率的影响。但是，应该注意的是，并非所有样品都普遍观察到相对密度的趋势，如图S11-S20所示，在低导电率样品中这种趋势不太明显，这增加了评估本文观察到的潜在机理的难度。变化。图3.样品2的总离子电导率和活化势垒随各种实验参数的变化分布。虚线表示平均值，阴影区域表示平均值的标准偏差。由于一个测量参数的不同，在所有样品之间都没有普遍趋势，这表明影响的卷积。高离子电导率差异较大的一个潜在原因是缺乏良好解析的半圆。在这项研究中，只有具有较低离子电导率的样品显示出良好分辨的半圆形。调节总电阻的实验方法是改变电池常数（药丸的厚度除以电极的面积），并使用足够量的样品。请注意，尽管更改单元常数可以帮助解决阻抗谱中的相关特征，但是单元常数本身对材料的本征电导率没有影响。那是，当将阻抗谱归一化为单元常数时，将在实际阻抗轴上获得相同的截距。换句话说，较大的厚度只会改变总电阻，而不会改变发生的传输过程的时间常数和频率范围，并且只有在低温下才可能使体和晶界解卷积。（33）这可能尤其重要在高导电性样品中会导致测得的电阻较低，与高电阻样品相比，微结构的影响以及由此产生的晶粒电阻和微结构的影响可能会更加突出。不锈钢触点的导电性随压力的增加而增加，并且观察到的变化是相对密度的函数，与通过Au溅射的样品获得的值相反，该值在测量过程中不显示任何外部压力，另外还强调了粒子之间以及与电极之间适当接触的重要性。为了显示低温测量的影响和有益的方法，与会的一个小组具有实验能力，可以在低至-120°C的温度下进行阻抗测量。在这些低得多的温度下，通常可以将晶粒阻抗与总离子电导率分开。（33）图S21显示了在如此低的温度下测量的代表性样品2的电导率与逆温度行为的关系，以及样品2在−100°C下测量。在低于-75°C的温度下，可以解决晶粒电导率对阻抗谱的影响。在拟合和外推谷物电导率与逆温度的数据后，最佳拟合的外推线可以估算本研究中报告的室温总离子电导率的上限。这些结果再次强调了样品微结构对离子电导率的影响，以及在正确的测量条件下如何区分体积和微结构的影响。考虑到所获得的电导率和激活势垒的扩散，可以得出一些结论。在显示高离子电导率> 1 mS cm的样品中可以清楚地看到较大的相对中值误差 在拟合和外推谷物电导率与逆温度的数据后，最佳拟合的外推线可以估算本研究中报告的室温总离子电导率的上限。这些结果再次强调了样品微结构对离子电导率的影响，以及在正确的测量条件下如何区分体积和微结构的影响。考虑到所获得的电导率和激活障碍的扩散，可以得出一些结论。在显示高离子电导率> 1 mS cm的样品中可以清楚地看到较大的相对中值误差 在拟合和外推谷物电导率与逆温度的数据后，最佳拟合的外推线可以估算本研究中报告的室温总离子电导率的上限。这些结果再次强调了样品微结构对离子电导率的影响，以及在正确的测量条件下如何区分体积和微结构的影响。考虑到所获得的电导率和激活势垒的扩散，可以得出一些结论。在显示高离子电导率> 1 mS cm的样品中可以清楚地看到较大的相对中值误差 最佳拟合的外推线可以估算本研究中报告的室温总离子电导率的上限。这些结果再次强调了样品微结构对离子电导率的影响，以及在正确的测量条件下如何区分体积和微结构的影响。考虑到所获得的电导率和激活势垒的扩散，可以得出一些结论。在显示高离子电导率> 1 mS cm的样品中可以清楚地看到较大的相对中值误差 最佳拟合的外推线可以估算本研究中报告的室温总离子电导率的上限。这些结果再次强调了样品微结构对离子电导率的影响，以及在正确的测量条件下如何区分体积和微结构的影响。考虑到所获得的电导率和激活势垒的扩散，可以得出一些结论。在显示高离子电导率> 1 mS cm的样品中可以清楚地看到较大的相对中值误差 考虑到所获得的电导率和激活势垒的扩散，可以得出一些结论。在显示高离子电导率> 1 mS cm的样品中可以清楚地看到较大的相对中值误差 考虑到所获得的电导率和激活势垒的扩散，可以得出一些结论。在显示高离子电导率> 1 mS cm的样品中可以清楚地看到较大的相对中值误差–1可能是由于不同的发生过程的收敛导致未解决的过程，如果不进行低温测量，则无法对它们进行反卷积。此外，这些硫代磷酸锂电解质对气氛高度敏感，并且在结构和化学上可比，但手套箱气氛（H 2 O和O 2含量以及存在的溶剂）以及在测量期间可能会干扰组之间的可比性。此外，需要压入这些材料，并且在丸粒固结和接触后可能会发生一定程度的微结构松弛，从而使“样品历史记录”成为观察到的扩散的可能因素。然而，电导率和活化势垒的可再现性的大范围和不确定性表明需要在该领域中采用更严格的方法，因为通常认为活化势垒和电导率的微小改进。首先，对于将来显示电导率和激活障碍发生变化的研究（例如由于等价和异价取代）的结果，有必要一式三份进行测量，这似乎是合理的，并且需要对样品合并，接触和测量条件的准确描述。在这里，应使用不同的样品池常数（由于在样品池设置中通常会限制直径而改变厚度）来测量具有相同成分的三个不同样品，以便更改总体样品池电阻并报告平均值和各自的标准偏差。在低温下进行解卷积过程的测量似乎至关重要;（33）但是，这通常受到实验装置的限制。尽管一式三份测量的建议看似微不足道，但尽管这些一式三份可能有助于在获得的离子电导率和活化势垒方面产生更现实的不确定性，但在文献中却很少报道。虽然一式三份的测量不能完全缓解整个组中发现的较大范围，但它可以提供有关固溶体研究中离子迁移质变的更有意义的信息。将来，可能需要用于测量设置验证的测量标准和标准材料。其次，尤其是在这种机械上柔软的材料类别中，在压力室中进行测量时似乎受到测量压力的影响（见图3）。因此，可能需要根据所施加的外部压力报告离子电导率。第三，当新型电解质具有高离子电导率> 1 mS cm 它可以为固溶体研究提供有关离子迁移质变的更有意义的信息。将来，可能需要用于测量设置验证的测量标准和标准材料。其次，尤其是在这种机械上柔软的材料类别中，在压力室中进行测量时似乎受到测量压力的影响（见图3）。因此，可能需要根据所施加的外部压力报告离子电导率。第三，当新型电解质具有高离子电导率> 1 mS cm 它可以为固溶体研究提供有关离子迁移质变的更有意义的信息。将来，可能需要用于测量设置验证的测量标准和标准材料。其次，尤其是在这种机械上柔软的材料类别中，在压力室中进行测量时似乎受到测量压力的影响（见图3）。因此，可能需要根据所施加的外部压力报告离子电导率。第三，当新型电解质具有高离子电导率> 1 mS cm 在压力室中进行测量时，似乎会对测量压力产生影响（请参见图3）。因此，可能需要根据所施加的外部压力报告离子电导率。第三，当新型电解质具有高离子电导率> 1 mS cm 在压力室中进行测量时，似乎会对测量压力产生影响（请参见图3）。因此，可能需要根据所施加的外部压力报告离子电导率。第三，当新型电解质具有高离子电导率> 1 mS cm–1据报道，我们建议将样品发送到一个合作小组，以证实获得的离子电导率。第四，基于获得的电导率的实验范围，将实验电导率值与通过核磁共振获得的扩散系数进行比较，以及通过计算得出的避风港比率，可能会有很大的不确定性。虽然避风港比率通常用于解释相关效应，[34]在这些系统中，比较不同的测量技术对提取有关相关效应的信息可能并不十分有意义。第五，通常通过重现实验性激活障碍来对理论计算进行内部验证。尽管相对中位数误差较小，在实验中获得的激活势垒中高达128 meV的较大范围表明，不应单独使用实验与理论之间的直接比较来验证理论或实验结果。总体而言，在超离子导体领域，需要一种更加严格的方法来报告结果，包括实验条件和三次测量值，以更好地理解和可靠地设计用于固态电池的固体电解质。可从https://pubs.acs.org/doi/10.1021/acsenergylett.9b02764免费获得支持信息。为了更好地理解和可靠地设计用于固态电池的固体电解质，将需要包括实验条件和一式三份测量。可从https://pubs.acs.org/doi/10.1021/acsenergylett.9b02764免费获得支持信息。为了更好地理解和可靠地设计用于固态电池的固体电解质，将需要包括实验条件和一式三份测量。可从https://pubs.acs.org/doi/10.1021/acsenergylett.9b02764免费获得支持信息。
更新日期：2020-02-28
Because we do not know what the “true” total ionic conductivity of these samples is, it is challenging to assess the best-practice procedure for the statistical analysis. We can, however, use the different measures of central tendency (median and average) as reasonable estimates for the “true” total ionic conductivity, as well as the standard deviation of the ionic conductivity as the representative expected spread in these samples for the following discussion. It needs to be mentioned that the term “true” total ionic conductivity serves only as a statistical descriptor here; it does not imply that measured values of an individual group represent a “false” ionic conductivity. Note that although the ionic conductivities of all samples range over several orders of magnitude, the calculated average values are close to the median values, and high, but similar, percentages of the standard deviation are found within all samples (see Figure 1b). As the median of any data set is less influenced by extreme values, we take it as the better estimate for the “true” total ionic conductivity and use the calculated average to determine relative median errors for all samples (see Figure 1b). In doing so we observe that for samples with ionic conductivities <1 mS cm–1 this error is less than 10%, whereas in the case of the fastest conductor, the Li6.6P0.4Ge0.6PS5I sample, we obtain a much greater error of 22%. In the case of the calculated activation barriers, we observe a similar spread in the reported values (see Figure 2). The IQR analysis reveals that in the case of the highest and lowest conducting samples, samples 1 and 5, respectively, one of the values with higher activation barrier is an outlier. Here, the median values for samples 3, 4, and 5 show a skewness to lower activation energies. Only in samples 1 and 2 do we observe that the mean and the median are closer to one another and more centered in the IQR box, again suggesting a normal distribution of the data. In spite of the spread, the percentile standard deviations and relative median errors are much smaller than those for the ionic conductivities, likely because the activation barrier is a parameter that is extracted from the slope of the Arrhenius plot and is therefore less sensitive to extreme values at specific temperatures. Nonetheless, even with the small deviation from the average, the values can correspond to a statistical range of up to 128 meV (198–326 meV). This large range of the activation barriers is significant considering that often values of the activation barriers are reported with a large number of significant figures and changes in series of solid solutions are often within this value of the spread. Moreover, these results suggest that direct comparisons between experimental and theoretically calculated activation barriers are not straightforward and similar values between them do not validate the theory or experimental results. Figure 2. (a) Box plots for the activation barrier of all samples in the study. (b) Percentile standard deviations and relative median error percentage for all samples. The relative median error was calculated assuming that the median represents the true conductivity value, using . Because the reported conductivities correspond to total conductivities, one may expect an influence of the densification behavior or resulting relative pellet densities. While nearly 100% relative densities can be achieved in oxide ceramic-based materials via sintering, the mechanical soft nature of the thiophosphate-based electrolytes often leads to densities between 80 and 90% by pressing at ambient temperature. In this study a comparison of the reported ionic conductivities against the densification (pelletizing pressure) pressure, the relative pellet density, the excitation voltage, the cell constant, and pellet thickness show no strong apparent trend in all samples (Figures S11–S20). As an example, Figure 3 shows the absence of clear trends for the ionic conductivity and the activation barrier of sample 2 as a function of pelletizing pressure and cell constant. Although there is no apparent trend as a function of cell constants, a qualitative trend of increasing conductivity with the relative density of the pellet can be observed. However, the trend seen as a function of relative density is not correlated to the pelletizing pressure; that is, a higher relative density is not obtained at higher pelletizing pressures. In addition, whereas no clear influence of the contacting material was identified, an increasing conductivity with increasing applied pressure during measurement was found. This trend does not hold for the Au sputtered samples that were measured without external pressure, indicating the influence of the pressing conditions for pellet preparation on the measured ionic conductivity. These results highlight the effect of sample preparation to the microstructure of the sample and its influence on the measured conductivity. However, it should be noted that the trend with relative densities is not universally observed for all the samples and is less prominent in lower-conducting samples as seen in Figures S11–S20, adding the difficulty of assessing the underlying mechanism of the here-observed variations. Figure 3. Spread in the total ionic conductivities and activation barriers of sample 2 as a function of various experimental parameters. The dashed line represents the average value and the shaded area the standard deviation from the average. The absence of universal trends among all the samples on one of the experimental parameters suggests a convolution of influences due to the differences in measurement setups and measurement approaches. One potential reason for the larger discrepancies at high ionic conductivities is the lack of a well-resolved semicircle. In this study, only the samples with a lower ionic conductivity show well-resolved semicircles. An experimental approach for modulating the overall resistance is to change the cell constant (thickness of the pellet divided by the area of the electrode) and with it using enough amount of sample. Note that although changing the cell constant may help to resolve the relevant features in the impedance spectra, the cell constant itself has no influence on the intrinsic conductivity of the material; that is, when normalizing the impedance spectra to the cell constant, the same intercept in the real impedance axis will be obtained. In other words, larger thicknesses will change only the total resistance but not the time constant and frequency range of the occurring transport processes, and a deconvolution of bulk and grain boundaries may be possible only at low temperatures.(33) This may be particularly important in highly conducting samples that lead to low measured resistances in which the influence of the microstructure and resulting grain resistances and microstructure may be more prominent, in comparison to the highly resistive samples. The increasing conductivity with pressure of the stainless-steel contacts, as well as the observed variation as a function of relative densities, in contrast to the values obtained by the Au sputtered samples that do not exhibit any external pressure during measurement, additionally underscores the importance of proper contact between particles, as well as with the electrodes. To show the influence and beneficial approach of low-temperature measurements, one of the participating groups has the experimental capabilities to perform impedance measurements at temperatures down to −120 °C. At these much lower temperatures it is often possible to separate the grain impedance from the total ionic conductivity.(33)Figure S21 shows the conductivity versus inverse temperature behavior for a representative sample 2 measured to such low temperatures as well as a representative impedance spectrum of sample 2 measured at −100 °C. At temperatures below −75 °C, it is possible to resolve the grain conductivity contributions to the impedance spectrum. Upon fitting and extrapolating the data of grain conductivity versus inverse temperature, the extrapolated line of best fit can estimate the upper-bound values of the reported room-temperature total ionic conductivities in this study. These results underscore, again, the effects of sample microstructure on the ionic conductivity and how under the right measurement conditions it is possible to discriminate between bulk and microstructure effects. Considering the spread in the obtained conductivities and activation barriers, a few conclusions may be drawn. A larger relative median error can be clearly seen in the samples that exhibit high ionic conductivities >1 mS cm–1 likely due to the convergence of different occurring processes that lead to unresolved processes, which cannot be deconvoluted without a low-temperature measurement. Additionally, these lithium thiophosphate electrolytes are highly sensitive to atmosphere and, while structurally and chemically comparable, differences in glovebox atmospheres (H2O and O2 content, as well as solvents present) as well as during measurement may interfere with a comparability between groups. Furthermore, pressing in these materials is needed, and a certain degree of microstructural relaxation may occur after pellet consolidation and contacting, making the “sample history” a possible factor in the observed spread. Nevertheless, the large range and uncertainty in the reproducibility of the conductivity and activation barriers suggest the need to adopt a more rigorous approach in the field, as often minor improvements in activation barriers and conductivities are deemed significant. First, it seems reasonable that for future studies showing changing conductivities and activation barriers, e.g. as a result from isovalent and aliovalent substitutions, measurements in triplicate are necessary, and an accurate description of sample consolidation, contacting, and measurement conditions is needed. Here, three different samples of the same composition should be measured with different cell constants (changing thicknesses as the diameter is often restricted in the cell setup), in order to change the overall cell resistance and report an average value and their respective standard deviations. Measurements at low temperatures to deconvolute processes seems crucial;(33) however, this is often restricted by experimental setups. While the recommendation of triplicate measurements seems trivial, it is not often reported in the literature despite the fact that these triplicates may help to produce more realistic uncertainties in obtained ionic conductivities and activation barriers. While the measurement of triplicates does not fully alleviate the large range that was found throughout the groups, it can provide more meaningful information on qualitative changes in the ionic transport within studies for solid solutions. In the future, measurement standards and standard materials for measurement setup validation may be needed. Second, especially within this mechanically soft class of materials, there seems to be an influence of the pressure under measurement when measured in press cells (see Figure 3). Therefore, it may be needed to report ionic conductivities as a function of the external pressure applied. Third, when novel electrolytes with high ionic conductivities >1 mS cm–1 are reported, we suggest sending samples to a collaborative group to corroborate the obtained ionic conductivities. Fourth, a comparison of experimental conductivity values with diffusion coefficients obtained by nuclear magnetic resonance and with it calculations of Haven ratios may be subject to a large uncertainty based on the experimental range in obtained conductivities. While Haven ratios are often used to explain correlation effects,(34) comparing different measurement techniques may not be very meaningful in extracting information about correlation effects in these systems. Fifth, often theoretical calculations are internally validated by reproduction of experimental activation barriers. Despite a smaller relative median error, the larger range of up to 128 meV in the experimentally obtained activation barriers suggests that a direct comparison between experiment and theory alone should not be used to validate theoretical nor experimental results. Overall, within the field of superionic conductors a more rigorous approach for reporting results, including the experimental conditions and triplicate measurements, will be needed to better understand and reliably design solid electrolytes for the use in solid-state batteries. The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsenergylett.9b02764.- Synthesis procedure of all samples and X-ray diffraction results; all experimental measurement conditions of the different data sets along with their statistical analysis; measured impedance spectra and Arrhenius plots as well as the comparison of the transport properties against possible sample preparation and measurement influences (PDF)
中文翻译：
基于硫代磷酸盐的固体电解质的报告电导率如何确定？实验室间研究
由于具有高导电性的固体离子导体，全固态电池作为有前途的下一代储能设备备受关注。已投入大量研究来寻找和优化具有较高离子电导率的固体电解质。但是，对实验室间可重复性的系统研究缺少测量的离子电导率和活化能，这使得文献中绝对值的比较具有挑战性。在这种观点下，我们使用具有不同数量级不同离子电导率的不同锂杂香锂作为参考材料，通过循环法进行不确定性评估。将相同的样品分配给不同的研究实验室，并通过阻抗光谱法测量电导率和活化势垒。结果表明，测得的总离子传导率范围高达4.5 mS cm –1（1.3–5.8 mS cm –1对于导电性最高的样品，所有样品的相对标准偏差为35–50％），对于激活势垒，最高为128 meV（198–326 meV，所有样品的相对标准偏差为5–15％），因此有必要严格的方法，包括社区内的进一步合作和重复测量。目前正在研究快速离子导体，例如锂和硫代磷酸钠在全固态电池中的可能应用。（1,2）最近的研究工作已经发现了多种基于Li +和Na +的材料，例如硫代磷酸盐Li 10+ x M 1– x P 2+ x S 12（M = Si，Ge，Sn），（3-8）Li 2 S–P 2 S 5玻璃，（9−15）Li 6 PS 5 X（X = Cl，Br，I），（16-22） Na 3 PS 4，（23−27）和Na 11 Sn 2 PS 12。（11,28,29）这些材料的离子电导率> 1 mS cm –1，使其在固态电池应用中可行。但是，在整个文献中，即使在同一类材料中，我们也可以发现所报告的离子电导率和活化势垒值的差异。锂+的显着差异据报道离子迁移是批次变化，粒度和合成程序的函数，甚至由于局部样品的不均匀性，（30,31）迄今为止，还没有对通过阻抗谱法测量离子电导率的实验室间重现性进行严格的研究。已执行。受其他观点（例如光伏行业）的标准化和基准化工作的启发（32），我们报告了一项轮循研究，该研究考虑了超离子硫代磷酸锂固体电解质中离子电导率测量的可重复性。在这个观点上，我们选择了锂银辉石Li 6 PS 5X是一种示例性的材料，因为它提供了建立离子电导率几个数量级（从10 –4 mS cm –1到几毫米/厘米）的统计趋势的可能性。所有测试样品，即Li 6.6 P 0.4 Ge 0.6 PS 5 I，Li 6 PS 5 Cl，Li 6 PS 5 Br 0.75 I 0.25，Li 6 PS 5 Br 0.25 I 0.75和Li 6 PS 5I由组织小组根据以前的报告合成，分别确定为样品1、2、3、4和5.（18,20）为获得足够量的均质粉末（10 g），每种组合物批量合成了三氧化二砷，然后每批进行X射线衍射以确认样品纯度（见图S1）。将所得的样品粉末混合并均质化，以使每个参与组针对每种组合物接受1 g相同的测试样品。在分配之前，由组织小组测量所有均质样品的离子电导率，以确保获得的值与先前报告的值相似。所有样品均以粉末形式提供，以捕获样品制备程序（即致密化程序，相对密度，在测量过程中施加的压力，以及颗粒接触方法）上报告的离子电导率。要求每组使用每个实验室中的标准测量程序测量所提供样品的温度相关阻抗谱，包括在室温（25°C）下。要求所有小组提供测量的阻抗谱和加热时的阿伦尼乌斯行为（见图S2-S10），并报告所有样品的计算出的室温电导率和活化势垒，但不提供拟合程序以避免暴露。不同群体的身份。支持信息（表S2-S10）中提供了有关每组样品制备和方法学（标记为AH）的更多详细信息，其中包括在致密化（造粒压力）和测量过程中施加的压力，接触方法，接触材料（Au溅射和不锈钢压制），阻抗分析仪，激励电压，温度和频率范围，电池常数以及使用的粉末质量。因此，此处介绍的统计分析包括所用阻抗谱的测量不确定度，电池常数的不确定度以及测量本身和数据分析程序的样品制备方面的差异。在理想条件下，多晶固体电解质的奈奎斯特表示中的阻抗谱的特征是两个分辨良好的半圆和电极极化。高频半圆将描述颗粒中的离子迁移，而低频半圆描述了晶界对离子迁移的贡献。正如Li所观察到的+室温下不能解卷积锂-香精岩中的硫代磷酸盐，块体和晶界贡献（见图S2-S10）。（18,20）因此，根据不同的制备和测量程序，此处报道的离子电导率值对应于所有样品的总离子电导率及其相应的活化势垒。表S11汇总了用于此统计分析的所有报告值。使用四分位间距（IQR）方法对获得的室温电导率进行统计分析，结果在图1a中以箱形图的形式显示。尽管我们观察到所有样品的报告离子电导率分布很大（例如，高达4.5 mS cm –11）的范围，我们无法使用IQR方法检测到任何样本中的异常值。在样本1和2的情况下，中位数分别显示出较低和较高电导率值的偏斜度，而对于低导电性样本3、4和5，我们观察到平均值和中位数彼此接近。而且，计算出的低导电率样本的中值接近IQR框的中心，这表明电导率的扩展可以看作是服从正态分布。在样品1和2的特定情况下，基于此统计分析，样品的总离子电导率中位数非常相似，这显示了在实验室之间比较不同材料的困难。图1。（a）研究中所有样品的室温总离子电导率的箱形图。（b）所有样本的百分比标准偏差和相对中值误差百分比。假设中位数代表真实的总电导率值，则使用以下公式计算相对中位数误差：
由于我们不知道这些样品的“真实”总离子电导率是什么，因此评估最佳实践程序进行统计分析具有挑战性。但是，我们可以使用集中趋势的不同度量（中值和平均值）作为“真实”总离子电导率的合理估计，以及离子电导率的标准偏差作为这些样品中以下样品的代表性预期扩散讨论。需要指出的是，术语“真实的”总离子电导率在这里仅用作统计描述；这并不意味着单个基团的测量值代表“假”离子电导率。请注意，尽管所有样品的离子电导率范围都在几个数量级上，但计算出的平均值却接近中值，并且很高，但是相似的是，在所有样品中都发现了标准偏差的百分比（见图1b）。由于任何数据集的中位数受极值的影响较小，因此我们将其作为“真实”总离子电导率的更好估计，并使用计算出的平均值来确定所有样品的相对中位数误差（见图1b）。这样，我们观察到离子电导率<1 mS cm的样品–1此误差小于10％，而对于最快的导体，Li 6.6 P 0.4 Ge 0.6 PS 5我进行采样，得出的误差要大得多，为22％。在计算出的激活势垒的情况下，我们观察到报告值的分布相似（见图2）。IQR分析表明，在导电性最高和最低的样品（分别为样品1和5）的情况下，具有较高活化势垒的值之一是异常值。在此，样品3、4和5的中值显示出偏斜，以降低活化能。仅在样本1和2中，我们观察到平均值和中位数彼此更接近，并且在IQR框中居中，这再次表明数据呈正态分布。尽管存在差异，但百分数标准偏差和相对中值误差比离子电导率小得多，可能是因为激活势垒是从Arrhenius曲线的斜率提取的参数，因此对特定温度下的极端值不太敏感。尽管如此，即使与平均值的偏差很小，该值仍可以对应高达128 meV（198–326 meV）的统计范围。考虑到经常会用大量有效数字报告活化势垒的值，并且一系列固溶体的变化通常都在该扩散值范围内，因此活化势垒的这一大范围非常重要。此外，这些结果表明，在实验和理论上计算出的激活势垒之间无法直接进行比较，而且它们之间的相似值也无法验证理论或实验结果。图2。（a）研究中所有样品的激活屏障的箱形图。（b）所有样本的百分比标准偏差和相对中值误差百分比。假设中位数代表真实电导率值，则使用以下公式计算相对中位数误差：。因为报告的电导率对应于总电导率，所以可以预期致密化行为或所产生的相对颗粒密度的影响。尽管可以通过烧结在基于氧化物陶瓷的材料中获得近100％的相对密度，但是通过在环境温度下加压，硫代磷酸盐基电解质的机械柔软特性通常导致密度在80％到90％之间。在这项研究中，所报告的离子电导率与致密化（造粒压力）压力，相对颗粒密度，激发电压，细胞常数和颗粒厚度的比较在所有样品中均未显示出明显的趋势（图S11-S20）。举个例子，图3显示了没有明显的离子电导率和样品2的活化势垒随制粒压力和细胞常数变化的趋势。尽管没有明显的趋势作为细胞常数的函数，但是可以观察到随着颗粒的相对密度电导率增加的定性趋势。但是，被视为相对密度的函数的趋势与造粒压力无关。即，在较高的造粒压力下不能获得较高的相对密度。另外，虽然没有确定接触材料的明显影响，但是发现在测量过程中电导率随施加的压力的增加而增加。对于没有外部压力测量的金溅射样品，这种趋势不成立，表明制粒条件对样品中离子电导率的影响。这些结果突出了样品制备对样品微观结构的影响及其对测得的电导率的影响。但是，应该注意的是，并非所有样品都普遍观察到相对密度的趋势，如图S11-S20所示，在低导电率样品中这种趋势不太明显，这增加了评估本文观察到的潜在机理的难度。变化。图3.样品2的总离子电导率和活化势垒随各种实验参数的变化分布。虚线表示平均值，阴影区域表示平均值的标准偏差。由于一个测量参数的不同，在所有样品之间都没有普遍趋势，这表明影响的卷积。高离子电导率差异较大的一个潜在原因是缺乏良好解析的半圆。在这项研究中，只有具有较低离子电导率的样品显示出良好分辨的半圆形。调节总电阻的实验方法是改变电池常数（药丸的厚度除以电极的面积），并使用足够量的样品。请注意，尽管更改单元常数可以帮助解决阻抗谱中的相关特征，但是单元常数本身对材料的本征电导率没有影响。那是，当将阻抗谱归一化为单元常数时，将在实际阻抗轴上获得相同的截距。换句话说，较大的厚度只会改变总电阻，而不会改变发生的传输过程的时间常数和频率范围，并且只有在低温下才可能使体和晶界解卷积。（33）这可能尤其重要在高导电性样品中会导致测得的电阻较低，与高电阻样品相比，微结构的影响以及由此产生的晶粒电阻和微结构的影响可能会更加突出。不锈钢触点的导电性随压力的增加而增加，并且观察到的变化是相对密度的函数，与通过Au溅射的样品获得的值相反，该值在测量过程中不显示任何外部压力，另外还强调了粒子之间以及与电极之间适当接触的重要性。为了显示低温测量的影响和有益的方法，与会的一个小组具有实验能力，可以在低至-120°C的温度下进行阻抗测量。在这些低得多的温度下，通常可以将晶粒阻抗与总离子电导率分开。（33）图S21显示了在如此低的温度下测量的代表性样品2的电导率与逆温度行为的关系，以及样品2在−100°C下测量。在低于-75°C的温度下，可以解决晶粒电导率对阻抗谱的影响。在拟合和外推谷物电导率与逆温度的数据后，最佳拟合的外推线可以估算本研究中报告的室温总离子电导率的上限。这些结果再次强调了样品微结构对离子电导率的影响，以及在正确的测量条件下如何区分体积和微结构的影响。考虑到所获得的电导率和激活势垒的扩散，可以得出一些结论。在显示高离子电导率> 1 mS cm的样品中可以清楚地看到较大的相对中值误差 在拟合和外推谷物电导率与逆温度的数据后，最佳拟合的外推线可以估算本研究中报告的室温总离子电导率的上限。这些结果再次强调了样品微结构对离子电导率的影响，以及在正确的测量条件下如何区分体积和微结构的影响。考虑到所获得的电导率和激活障碍的扩散，可以得出一些结论。在显示高离子电导率> 1 mS cm的样品中可以清楚地看到较大的相对中值误差 在拟合和外推谷物电导率与逆温度的数据后，最佳拟合的外推线可以估算本研究中报告的室温总离子电导率的上限。这些结果再次强调了样品微结构对离子电导率的影响，以及在正确的测量条件下如何区分体积和微结构的影响。考虑到所获得的电导率和激活势垒的扩散，可以得出一些结论。在显示高离子电导率> 1 mS cm的样品中可以清楚地看到较大的相对中值误差 最佳拟合的外推线可以估算本研究中报告的室温总离子电导率的上限。这些结果再次强调了样品微结构对离子电导率的影响，以及在正确的测量条件下如何区分体积和微结构的影响。考虑到所获得的电导率和激活势垒的扩散，可以得出一些结论。在显示高离子电导率> 1 mS cm的样品中可以清楚地看到较大的相对中值误差 最佳拟合的外推线可以估算本研究中报告的室温总离子电导率的上限。这些结果再次强调了样品微结构对离子电导率的影响，以及在正确的测量条件下如何区分体积和微结构的影响。考虑到所获得的电导率和激活势垒的扩散，可以得出一些结论。在显示高离子电导率> 1 mS cm的样品中可以清楚地看到较大的相对中值误差 考虑到所获得的电导率和激活势垒的扩散，可以得出一些结论。在显示高离子电导率> 1 mS cm的样品中可以清楚地看到较大的相对中值误差 考虑到所获得的电导率和激活势垒的扩散，可以得出一些结论。在显示高离子电导率> 1 mS cm的样品中可以清楚地看到较大的相对中值误差–1可能是由于不同的发生过程的收敛导致未解决的过程，如果不进行低温测量，则无法对它们进行反卷积。此外，这些硫代磷酸锂电解质对气氛高度敏感，并且在结构和化学上可比，但手套箱气氛（H 2 O和O 2含量以及存在的溶剂）以及在测量期间可能会干扰组之间的可比性。此外，需要压入这些材料，并且在丸粒固结和接触后可能会发生一定程度的微结构松弛，从而使“样品历史记录”成为观察到的扩散的可能因素。然而，电导率和活化势垒的可再现性的大范围和不确定性表明需要在该领域中采用更严格的方法，因为通常认为活化势垒和电导率的微小改进。首先，对于将来显示电导率和激活障碍发生变化的研究（例如由于等价和异价取代）的结果，有必要一式三份进行测量，这似乎是合理的，并且需要对样品合并，接触和测量条件的准确描述。在这里，应使用不同的样品池常数（由于在样品池设置中通常会限制直径而改变厚度）来测量具有相同成分的三个不同样品，以便更改总体样品池电阻并报告平均值和各自的标准偏差。在低温下进行解卷积过程的测量似乎至关重要;（33）但是，这通常受到实验装置的限制。尽管一式三份测量的建议看似微不足道，但尽管这些一式三份可能有助于在获得的离子电导率和活化势垒方面产生更现实的不确定性，但在文献中却很少报道。虽然一式三份的测量不能完全缓解整个组中发现的较大范围，但它可以提供有关固溶体研究中离子迁移质变的更有意义的信息。将来，可能需要用于测量设置验证的测量标准和标准材料。其次，尤其是在这种机械上柔软的材料类别中，在压力室中进行测量时似乎受到测量压力的影响（见图3）。因此，可能需要根据所施加的外部压力报告离子电导率。第三，当新型电解质具有高离子电导率> 1 mS cm 它可以为固溶体研究提供有关离子迁移质变的更有意义的信息。将来，可能需要用于测量设置验证的测量标准和标准材料。其次，尤其是在这种机械上柔软的材料类别中，在压力室中进行测量时似乎受到测量压力的影响（见图3）。因此，可能需要根据所施加的外部压力报告离子电导率。第三，当新型电解质具有高离子电导率> 1 mS cm 它可以为固溶体研究提供有关离子迁移质变的更有意义的信息。将来，可能需要用于测量设置验证的测量标准和标准材料。其次，尤其是在这种机械上柔软的材料类别中，在压力室中进行测量时似乎受到测量压力的影响（见图3）。因此，可能需要根据所施加的外部压力报告离子电导率。第三，当新型电解质具有高离子电导率> 1 mS cm 在压力室中进行测量时，似乎会对测量压力产生影响（请参见图3）。因此，可能需要根据所施加的外部压力报告离子电导率。第三，当新型电解质具有高离子电导率> 1 mS cm 在压力室中进行测量时，似乎会对测量压力产生影响（请参见图3）。因此，可能需要根据所施加的外部压力报告离子电导率。第三，当新型电解质具有高离子电导率> 1 mS cm–1据报道，我们建议将样品发送到一个合作小组，以证实获得的离子电导率。第四，基于获得的电导率的实验范围，将实验电导率值与通过核磁共振获得的扩散系数进行比较，以及通过计算得出的避风港比率，可能会有很大的不确定性。虽然避风港比率通常用于解释相关效应，[34]在这些系统中，比较不同的测量技术对提取有关相关效应的信息可能并不十分有意义。第五，通常通过重现实验性激活障碍来对理论计算进行内部验证。尽管相对中位数误差较小，在实验中获得的激活势垒中高达128 meV的较大范围表明，不应单独使用实验与理论之间的直接比较来验证理论或实验结果。总体而言，在超离子导体领域，需要一种更加严格的方法来报告结果，包括实验条件和三次测量值，以更好地理解和可靠地设计用于固态电池的固体电解质。可从https://pubs.acs.org/doi/10.1021/acsenergylett.9b02764免费获得支持信息。为了更好地理解和可靠地设计用于固态电池的固体电解质，将需要包括实验条件和一式三份测量。可从https://pubs.acs.org/doi/10.1021/acsenergylett.9b02764免费获得支持信息。为了更好地理解和可靠地设计用于固态电池的固体电解质，将需要包括实验条件和一式三份测量。可从https://pubs.acs.org/doi/10.1021/acsenergylett.9b02764免费获得支持信息。- 所有样品的合成程序和X射线衍射结果；不同数据集的所有实验测量条件及其统计分析；测得的阻抗谱和Arrhenius图，以及传输特性与可能的样品制备和测量影响之间的比较（PDF）
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