Experimental measurements of the enhancement factors for mixtures of water vapor and CO2-free air have been made at -20, -10, and +70 °C. The results, coupled with previous experimental enhancement data, have been used to calculate the second interaction virial coefficients, Baw , for water vapor air mixtures from -50 to +90 °C. Within this temperature range, an error analysis shows that the uncertainties in Baw are between 6 and 10 percent. The calculated Baw· values are used in deriving enhancement factors at 10 °C intervals for -50<t<90 °C, at varying pressure intervals from 0.25 to 100 bar. The associated uncertainties are shown as a function of pressure and temperature. The enhancement factors are extrapolated to -80 °C.
{"title":"A Correlation for the Second Interaction Virial Coefficients and Enhancement Factors for Moist Air.","authors":"R W Hyland","doi":"10.6028/jres.079A.017","DOIUrl":"10.6028/jres.079A.017","url":null,"abstract":"<p><p>Experimental measurements of the enhancement factors for mixtures of water vapor and CO<sub>2</sub>-free air have been made at -20, -10, and +70 °C. The results, coupled with previous experimental enhancement data, have been used to calculate the second interaction virial coefficients, <i>B</i> <sub><i>aw</i></sub> , for water vapor air mixtures from -50 to +90 °C. Within this temperature range, an error analysis shows that the uncertainties in <i>B</i> <sub><i>aw</i></sub> are between 6 and 10 percent. The calculated <i>B</i> <sub><i>aw</i></sub> <i>·</i> values are used in deriving enhancement factors at 10 °C intervals for -50<<i>t</i><90 °C, at varying pressure intervals from 0.25 to 100 bar. The associated uncertainties are shown as a function of pressure and temperature. The enhancement factors are extrapolated to -80 °C.</p>","PeriodicalId":17018,"journal":{"name":"Journal of Research of the National Bureau of Standards. Section A, Physics and Chemistry","volume":"79A 4","pages":"551-560"},"PeriodicalIF":0.0,"publicationDate":"1975-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6565410/pdf/jres-79A-551.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37747701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
There are several glasses and glass-ceramics available today which have low coefficients of thermal expansion - some near zero. For this reason they often serve as substrates for massive mirrors in orbit. In order for such a mirror to enjoy a lifetime of 5 years or more of diffraction-limited service, the substrate must be dimensionally stable and thereby preserve the original figure. Early in l967, it was decided that the National Bureau of Standards and Corning Glass Works would undertake a joint effort to measure the lengths of small samples of such materials over a period of years. These measurements were completed in 1971. The average length changes in parts per million of the four materials selected are as follows: Corning Code 9623 a glass ceramic- 0.30Corning Code 7971 a titanium silicate- 0.37Corning Code 7940 a vitreous silica- 0.47Corning Code 9622 a glass-ceramic- 1.03.
{"title":"Precision Measurements of the Dimensional Stability of Four Mirror Materials.","authors":"B Justice","doi":"10.6028/jres.079A.016","DOIUrl":"https://doi.org/10.6028/jres.079A.016","url":null,"abstract":"<p><p>There are several glasses and glass-ceramics available today which have low coefficients of thermal expansion - some near zero. For this reason they often serve as substrates for massive mirrors in orbit. In order for such a mirror to enjoy a lifetime of 5 years or more of diffraction-limited service, the substrate must be dimensionally stable and thereby preserve the original figure. Early in l967, it was decided that the National Bureau of Standards and Corning Glass Works would undertake a joint effort to measure the lengths of small samples of such materials over a period of years. These measurements were completed in 1971. The average length changes in parts per million of the four materials selected are as follows: Corning Code 9623 a glass ceramic- 0.30Corning Code 7971 a titanium silicate- 0.37Corning Code 7940 a vitreous silica- 0.47Corning Code 9622 a glass-ceramic- 1.03.</p>","PeriodicalId":17018,"journal":{"name":"Journal of Research of the National Bureau of Standards. Section A, Physics and Chemistry","volume":"79A 4","pages":"545-550"},"PeriodicalIF":0.0,"publicationDate":"1975-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6565407/pdf/jres-79A-545.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37747702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
An analysis of Cu iii based on observations from 500 to 6900 Å is presented. The low structures 3d9 and 3d84s are complete, including the rarely, if ever before, found 3d8(1S)4s2S. The 3d74s2 includes 4F, 2F, 2G, and 2H but the 4P, 2P, a2D, b2D have eluded all attempts to find them. The ionization potential calculated from 4s, 5s, 6s4 is 296 980 cm-1 but by a comparison with Ni II which has a longer series an approximate value of 297 140 can be estimated. The 3d84d group is complete, except for one level, as is 5dbased on 3F and 1G, the other 5d groups being incomplete. 3d8(3F)4f is complete and 26 levels based on 1D, 3P, 1G are known. 3d8(3F)5g is incomplete and a few levels based on 1D and 1G have been found. A discussion of the validity of the analysis of Cu iv by J. F. Schröder and Th. A. M. Van Kleef is given.
{"title":"The Third Spectrum of Copper (Cu iii).","authors":"A G Shenstone","doi":"10.6028/jres.079A.014","DOIUrl":"10.6028/jres.079A.014","url":null,"abstract":"<p><p>An analysis of Cu iii based on observations from 500 to 6900 Å is presented. The low structures 3<i>d</i> <sup>9</sup> and 3<i>d</i> <sup>8</sup>4<i>s</i> are complete, including the rarely, if ever before, found 3<i>d</i> <sup>8</sup>(<sup>1</sup>S)4<i>s</i> <sup>2</sup>S. The 3<i>d</i> <sup>7</sup>4<i>s</i> <sup>2</sup> includes <sup>4</sup>F, <sup>2</sup>F, <sup>2</sup>G, and <sup>2</sup>H but the <sup>4</sup>P, <sup>2</sup>P, <i>a</i> <sup>2</sup>D, <i>b</i> <sup>2</sup>D have eluded all attempts to find them. The ionization potential calculated from 4<i>s</i>, 5<i>s</i>, 6<i>s</i> <sup>4</sup> <math> <mrow><msup><mrow></mrow> <mn>4</mn></msup> <msub><mtext>F</mtext> <mrow><msup><mn>4</mn> <mrow><mn>1</mn> <mo>/</mo> <mn>2</mn></mrow> </msup> </mrow> </msub> </mrow> </math> is 296 980 cm<sub>-1</sub> but by a comparison with Ni II which has a longer series an approximate value of 297 140 can be estimated. The 3<i>d</i> <sup>8</sup>4<i>d</i> group is complete, except for one level, as is 5<i>d</i>based on <sup>3</sup>F and <sup>1</sup>G, the other 5<i>d</i> groups being incomplete. 3<i>d</i> <sup>8</sup>(<sup>3</sup>F)4<i>f</i> is complete and 26 levels based on <sup>1</sup>D, <sup>3</sup>P, <sup>1</sup>G are known. 3<i>d</i> <sup>8</sup>(<sup>3</sup>F)5<i>g</i> is incomplete and a few levels based on <sup>1</sup>D and <sup>1</sup>G have been found. A discussion of the validity of the analysis of Cu iv by J. F. Schröder and Th. A. M. Van Kleef is given.</p>","PeriodicalId":17018,"journal":{"name":"Journal of Research of the National Bureau of Standards. Section A, Physics and Chemistry","volume":"79A 3","pages":"497-521"},"PeriodicalIF":0.0,"publicationDate":"1975-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6589410/pdf/jres-79A-497.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37747698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The enthalpies of combustion and formation of one sample of ortho- and two samples of parafluorobenzoic acids have been determined by combustion in an oxygen-bomb calorimeter. The data obtained by other investigators are discussed briefly. The values obtained and their estimated uncertainties are as follows: [Table: see text] where ΔHc° corresponds to the reaction: .
{"title":"The Enthalpies of Combustion and Formation of Ortho- and Parafluorobenzoic Acid.","authors":"Walter H Johnson, Edward J Prosen","doi":"10.6028/jres.079A.011","DOIUrl":"https://doi.org/10.6028/jres.079A.011","url":null,"abstract":"<p><p>The enthalpies of combustion and formation of one sample of ortho- and two samples of parafluorobenzoic acids have been determined by combustion in an oxygen-bomb calorimeter. The data obtained by other investigators are discussed briefly. The values obtained and their estimated uncertainties are as follows: [Table: see text] where Δ<i>Hc</i>° corresponds to the reaction: <dispformula> <math> <mrow><msub><mtext>C</mtext> <mn>7</mn></msub> <msub><mtext>H</mtext> <mn>5</mn></msub> <msub><mtext>O</mtext> <mn>2</mn></msub> <mtext>F</mtext> <mo>(</mo> <mtext>c</mtext> <mo>)</mo> <mo>+</mo> <mn>7</mn> <msub><mtext>O</mtext> <mn>2</mn></msub> <mo>(</mo> <mtext>g</mtext> <mo>)</mo> <mo>+</mo> <mn>48</mn> <msub><mtext>H</mtext> <mn>2</mn></msub> <mtext>O</mtext> <mo>(</mo> <mtext>liq</mtext> <mo>)</mo> <mo>→</mo> <mn>7</mn> <msub><mrow><mtext>CO</mtext></mrow> <mn>2</mn></msub> <mo>(</mo> <mtext>g</mtext> <mo>)</mo> <mo>+</mo> <mrow><mo>[</mo> <mrow><mtext>HF</mtext> <mo>+</mo> <mn>50</mn> <msub><mtext>H</mtext> <mn>2</mn></msub> <mtext>O</mtext></mrow> <mo>]</mo></mrow> <mo>(</mo> <mtext>liq</mtext> <mo>)</mo> <mo>.</mo></mrow> </math></dispformula>.</p>","PeriodicalId":17018,"journal":{"name":"Journal of Research of the National Bureau of Standards. Section A, Physics and Chemistry","volume":"79A 3","pages":"481-486"},"PeriodicalIF":0.0,"publicationDate":"1975-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6589408/pdf/jres-79A-481.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37746775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The enthalpy of combustion of cholesterol was measured in an adiabatic, rotating-bomb calorimeter capable of high precision with relatively small samples. The random error for the experimental measurements was 0.006 percent which may be compared with approximately 0.3 percent for prior investigations on this substance. The results obtained for the enthalpy of combustion and the derived enthalpy of formation together with the estimated overall uncertainties are: The results of prior investigations are discussed briefly.
用绝热式旋转弹量热计测量了胆固醇的燃烧焓,该量热计在相对较小的样品下具有高精度。实验测量的随机误差为0.006%,相比之下,对该物质的先前调查的随机误差约为0.3%。得到的燃烧焓和生成焓的计算结果以及估计的总体不确定度为:Δ H c°(25°c) = - 16524.0±3.9 kJ/mol Δ H f°(25°c) = - 674.8±4.1 kJ/mol。
{"title":"The Enthalpies of Combustion and Formation of Cholesterol [cholest-5-en-3-ol (3 <sub><i>β</i></sub> )].","authors":"Walter H Johnson","doi":"10.6028/jres.079A.013","DOIUrl":"https://doi.org/10.6028/jres.079A.013","url":null,"abstract":"<p><p>The enthalpy of combustion of cholesterol was measured in an adiabatic, rotating-bomb calorimeter capable of high precision with relatively small samples. The random error for the experimental measurements was 0.006 percent which may be compared with approximately 0.3 percent for prior investigations on this substance. The results obtained for the enthalpy of combustion and the derived enthalpy of formation together with the estimated overall uncertainties are: <dispformula> <math><mrow><mi>Δ</mi> <mi>H</mi> <msup><mi>c</mi> <mo>°</mo></msup> <mrow><mo>(</mo> <mrow> <msup><mrow><mn>25</mn></mrow> <mo>°</mo></msup> <mtext>C</mtext></mrow> <mo>)</mo></mrow> <mo>=</mo> <mo>-</mo> <mn>16524.0</mn> <mo>±</mo> <mn>3.9</mn> <mspace></mspace> <mtext>kJ/mol</mtext></mrow> </math> </dispformula> <dispformula> <math><mrow><mi>Δ</mi> <mi>H</mi> <msup><mi>f</mi> <mo>°</mo></msup> <mrow><mo>(</mo> <mrow> <msup><mrow><mn>25</mn></mrow> <mo>°</mo></msup> <mtext>C</mtext></mrow> <mo>)</mo></mrow> <mo>=</mo> <mo>-</mo> <mn>674.8</mn> <mo>±</mo> <mn>4.1</mn> <mspace></mspace> <mtext>kJ/mol</mtext></mrow> </math> </dispformula> The results of prior investigations are discussed briefly.</p>","PeriodicalId":17018,"journal":{"name":"Journal of Research of the National Bureau of Standards. Section A, Physics and Chemistry","volume":"79A 3","pages":"493-496"},"PeriodicalIF":0.0,"publicationDate":"1975-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6589411/pdf/jres-79A-493.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37746777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The enthalpies of combustion of acetanilide and urea have been determined in an oxygen-bomb calorimeter. The following values and their estimated uncertainties were obtained. [Table: see text].
在氧弹热量计中测定了乙酰苯胺和尿素的燃烧热。得出了以下数值及其估计不确定性。[表:见正文]。
{"title":"The Enthalpies of Combustion and Formation of Acetanilide and Urea.","authors":"Walter H Johnson","doi":"10.6028/jres.079A.012","DOIUrl":"10.6028/jres.079A.012","url":null,"abstract":"<p><p>The enthalpies of combustion of acetanilide and urea have been determined in an oxygen-bomb calorimeter. The following values and their estimated uncertainties were obtained. [Table: see text].</p>","PeriodicalId":17018,"journal":{"name":"Journal of Research of the National Bureau of Standards. Section A, Physics and Chemistry","volume":"79A 3","pages":"487-491"},"PeriodicalIF":0.0,"publicationDate":"1975-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6589409/pdf/jres-79A-487.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37747699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Accurate measurements of the thermal conductivities of Ar and He agree with the theoretical value of 2.5 ϕηcv (η = viscosity, cv = specific heat capacity at constant volume ϕ is a number slightly greater than 1 depending upon the intermolecular potential). Measurements of the thermal conductivities of N2 at 9.6 and 75 °C as a function of pressure up to 2.53 × 107 Pa help to appraise the validity of other measurements of the thermal conductivities of dense gases. The excess conductivity of nitrogen (the additional conductivity resulting from pressure) is shown to be a function of only the density of the nitrogen from 0 to 700 °C and pressures up to 1.3 × 108 Pa.
对Ar和He的热导率的精确测量与2.5 μ d ηc v的理论值一致(η =粘度,c v =定容时的比热容φ是一个略大于1的数字,取决于分子间势)。氮气在9.6℃和75℃下的热导率随压力达2.53 × 107 Pa的函数的测量有助于评估致密气体热导率的其他测量的有效性。氮气的超导电性(由压力产生的额外导电性)显示为仅在0至700°C和高达1.3 × 108 Pa的压力下氮气密度的函数。
{"title":"Thermal Conductivity of Gases. III. Some Values of the Thermal Conductivities of Argon, Helium, and Nitrogen from 0 °C to 75 °C at Pressures of 1 × 10<sup>5</sup> to 2.5 × 10<sup>7</sup> Pascals.","authors":"Leslie A Guildner","doi":"10.6028/jres.079A.005","DOIUrl":"https://doi.org/10.6028/jres.079A.005","url":null,"abstract":"<p><p>Accurate measurements of the thermal conductivities of Ar and He agree with the theoretical value of 2.5 <i>ϕηc</i> <sub><i>v</i></sub> (<i>η</i> = viscosity, <i>c</i> <sub><i>v</i></sub> = specific heat capacity at constant volume <i>ϕ</i> is a number slightly greater than 1 depending upon the intermolecular potential). Measurements of the thermal conductivities of N<sub>2</sub> at 9.6 and 75 °C as a function of pressure up to 2.53 × 10<sup>7</sup> Pa help to appraise the validity of other measurements of the thermal conductivities of dense gases. The excess conductivity of nitrogen (the additional conductivity resulting from pressure) is shown to be a function of only the density of the nitrogen from 0 to 700 °C and pressures up to 1.3 × 10<sup>8</sup> Pa.</p>","PeriodicalId":17018,"journal":{"name":"Journal of Research of the National Bureau of Standards. Section A, Physics and Chemistry","volume":"79A 2","pages":"407-413"},"PeriodicalIF":0.0,"publicationDate":"1975-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6565413/pdf/jres-79A-407.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37746768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Heat capacities of two polyethylene samples, one linear with a density of 0.973 g cm-3 and one branched with a density of 0.91 g cm-3, have been determined by adiabatic calorimetry from 5 to 360 K in a different experimental arrangement then employed for studies of other polyethylene samples in this series. The heat capacity behavior of these two samples confirms expectations for samples with corresponding densities.
在不同的实验安排中,通过5至360K的绝热量热法测定了两个聚乙烯样品的热容,一个是密度为0.973 g cm-3的线性样品,另一个是0.91 g cm-3密度的支链样品,然后用于研究该系列中的其他聚乙烯样品。这两个样品的热容行为证实了对具有相应密度的样品的期望。
{"title":"Heat Capacities of Polyethylene III. One Linear and One Branched Sample from 5 to 350 K.","authors":"Shu-Sing Chang, Edgar F Westrum, H Gary Carlson","doi":"10.6028/jres.079A.010","DOIUrl":"10.6028/jres.079A.010","url":null,"abstract":"<p><p>Heat capacities of two polyethylene samples, one linear with a density of 0.973 g cm<sup>-3</sup> and one branched with a density of 0.91 g cm<sup>-3</sup>, have been determined by adiabatic calorimetry from 5 to 360 K in a different experimental arrangement then employed for studies of other polyethylene samples in this series. The heat capacity behavior of these two samples confirms expectations for samples with corresponding densities.</p>","PeriodicalId":17018,"journal":{"name":"Journal of Research of the National Bureau of Standards. Section A, Physics and Chemistry","volume":"79A 2","pages":"437-441"},"PeriodicalIF":0.0,"publicationDate":"1975-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6565414/pdf/jres-79A-437.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37746774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A formal formulation of the differential cross section for x-ray inelastic scattering is given for a real solid, in particular, in terms of the polarization propagator and the inverse dielectric function. The differential cross section is related to the causal functions of electron properties rather than those retarded functions.
{"title":"On the Differential Cross Section for X-Ray Inelastic Scattering.","authors":"Masao Kuriyama","doi":"10.6028/jres.079A.006","DOIUrl":"https://doi.org/10.6028/jres.079A.006","url":null,"abstract":"<p><p>A formal formulation of the differential cross section for x-ray inelastic scattering is given for a real solid, in particular, in terms of the polarization propagator and the inverse dielectric function. The differential cross section is related to the causal functions of electron properties rather than those retarded functions.</p>","PeriodicalId":17018,"journal":{"name":"Journal of Research of the National Bureau of Standards. Section A, Physics and Chemistry","volume":"79A 2","pages":"415-417"},"PeriodicalIF":0.0,"publicationDate":"1975-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6565416/pdf/jres-79A-415.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37746770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The coefficients in van der Poel's equation for calculating the shear modulus of a particulate composite have been greatly simplified, making the calculation much less unwieldy. Approximate solutions of van der Poel's equation are also derived, and it is shown that one of the low order approximations is Kernels equation, or Mashin and Shtrikman's equation for the highest lower hound. The Kerner approximation is often too low in value when the volume fraction of filler exceeds 0.2, but it can he used to provide further simplification in van der Poel's equation, or it can be used as a first approximation in a Newton's method of solution.
范德波尔方程中用于计算颗粒复合材料剪切模量的系数已经大大简化,使计算变得不那么麻烦。文中还导出了van der Poel方程的近似解,并证明低阶近似之一是Kernels方程,或最高下猎犬的Mashin和Shtrikman方程。当填料的体积分数超过0.2时,Kerner近似值通常过低,但它可以用于进一步简化范德波尔方程,也可以用作牛顿解法中的第一近似值。
{"title":"Simplification of van der Poel's Formula for the Shear Modulus of a Particulate Composite.","authors":"Jack C Smith","doi":"10.6028/jres.079A.007","DOIUrl":"10.6028/jres.079A.007","url":null,"abstract":"<p><p>The coefficients in van der Poel's equation for calculating the shear modulus of a particulate composite have been greatly simplified, making the calculation much less unwieldy. Approximate solutions of van der Poel's equation are also derived, and it is shown that one of the low order approximations is Kernels equation, or Mashin and Shtrikman's equation for the highest lower hound. The Kerner approximation is often too low in value when the volume fraction of filler exceeds 0.2, but it can he used to provide further simplification in van der Poel's equation, or it can be used as a first approximation in a Newton's method of solution.</p>","PeriodicalId":17018,"journal":{"name":"Journal of Research of the National Bureau of Standards. Section A, Physics and Chemistry","volume":"79A 2","pages":"419-423"},"PeriodicalIF":0.0,"publicationDate":"1975-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6565412/pdf/jres-79A-419.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37746776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}