is not suited to
Optical spectral holeburning is the selective bleaching of an inhomogeneously broadened absorption line by a narrow band laser.
The Sm2+ ions occupy sites of cubic (Oh) symmetry.
In such a situation, it is highly probable that


  1. It is possible to envisage that photoinduced reduction of Eu3+ to Eu2+ in Sr2SiO4 may be induced by....
    envisage [ɪnˈvɪzɪdʒ] 想象; 设想; 展望;
  2. S is then often referred to as a sensitizer of the luminescence from A, although it may itself also act as activator.
    be referred to as 被称作
    the IBM tools referred to in this paper refer to xx中提到的
  3. In what follows I shall attempt to convey the reasons for these beliefs.
    In what follows, 在下文中
  4. Research on these phosphors in particular has considerably advanced the understanding of characteristic luminescence, since the properties of these phosphors can be studied on simple model compounds.
  5. by the dissipation of the excitation energy in the form of heat
  6. Luminescent materials rely on electronic “traps” to store energy that is subsequently released in the form of light.
    in the form of  以....的形式
  7. Rare earth ions, for example Eu3+ or Tb3+, are now substituted for a small proportion of the host lattice ions.
    Substitute A for B 用A替换B A is substituted for B A(被用来)替换B
  8. virtually  adv. 事实上,几乎;实质上 in a virtually random distribution.
  9. we will illustrate how the ideas presented in xxx work in the case of
  10. It may find technical applications in xx.
  11. The characteristic properties of the R ions are attributable to the presence in the ion of a deep-lying 4f shell which is not entirely filled. The electrons of this shell are screened by the outer electron shells, and as a result they give rise to a number of discrete energy levels. Since the presence of the crystal lattice scarcely affects the positions of these levels, there is a close resemblance between the energy-level diagram of the free ion and that of the incorporated ion.
  12. They are the representative of all the types encountered.
  13. The number of XXX is fairly large, except in.
  14. As the number of electrons increases, there is in general a rapid increase in the number of possible states.
  15. depend to a great extent on
  16. One electron is raised to the higher 5d level, strongly influenced by the lattice.
    The answer to this question is bound up with the fact that a state with a completely or half-filled electron shell is very stable.
  17. Can readily accept an electron and thus xxx
  18. In the latter case, apart from xxx,  xxx is nevertheless frequently observed.
  19. varies considerably from one lattice to another, so does xxxx
  20. decays stepwise from A state to B  state
  21. returns to the ground state, thereby emitting radiation.
  22. The situation as far as the Ce3+ ion is concerned is entirely different.
    As far as, adv 至于,直到,远到;就…而言
    They may be there forever as far as any one of us is concerned.就我们任何一个人来说,它们也许会永远存在
  23. Contrary to the case of Tb3+
  24. Unlike XX, however, there is  no no distinct splitting in xx
  25. In the emission process of the Eu3+ ion the charge-transfer level plays no part, since the ion decays from the charge-transfer level via a number of 4f levels to the 5D levels, from which the ground state is reached by the emission of radiation.
  26. More will be said about this in Section V
  27. Electric-dipole transitions between 4f levels of rare earth ions are strictly forbidden, because the parity does not change (Laporte's selection rule).
  28. Let us now consider the situation where the Eu3+ ion occupies a crystallographic site that does not coincide with a centre of symmetry.
    Coincide with符合;与...相一致
  29. are similarly subject to selection rules
  30. a site which is not a centre of symmetry.
  31. This seemingly minor difference in structure has a considerable influence on the relative intensities of the Eu3+ emission lines.
    seemingly 看来似乎;表面上看来
  32. The relevant transitions occur because the ions of the host lattice vibrate. These vibrations can cause a deviation from pure inversion symmetry, which means that the electric-dipole transitions are no longer forbidden.
  33. This is approximately 1000 times longer than xx.
  34. Xxx can be well understood.
  35. The conversion efficiency of a phosphor can be numerically expressed in various ways.
    Numerically, adv.  数字上;用数字表示 in number; with regard to numbers
  36. Various models have been proposed to explain the presence or absence of luminescence
  37. are based on what is termed the configurational-coordinate diagram
    be termed XXX. 被称作XXX.
  38. it is too early for a full account of the long-term impact.现在详细说明长期影响还太早
    a full account 详细说明
  39. She was granted a divorce on the grounds of unreasonable behavior by her husband.
    on the grounds of 基于……理由,根据
  40. When drawing the configurational-coordinate diagram it is assumed (on not unreasonable grounds  基于合理的理由) that we need only take this symmetric valence vibration into account.
  41. Configurational-coordinate diagram of a luminescent centre. The potential energy E of the centre in the lattice is plotted as a function of the configurational coordinate r for the ground state and the first excited state. Vibrational states are represented schematically by horizontal lines in the parabola. In the region where the two parabola intersect, the curve is marked by dashes since the situation is actually more complicated than is indicated here.
    parabola [pə‘ræb(ə)lə] 抛物线 horizontal line 水平线 Intersect vi. 相交,交叉
  42. In the symmetric vibrational mode the Mn+  ion remains stationary, while the O2- ions vibrate in phase along the M-O bonding axis.
  43. At absolute zero the luminescent centre will occupy the lowest vibrational level of the ground state.   absolute zero 绝对零度
  44. The ions surrounding the central ion vibrate about their equilibrium positions situated at a distance r0 from the central ion.
    situated at  位于….
  45. Since the equilibrium distance re of the excited state will not in general be equal to that of the ground stare, and since the centre may be at different vibrational levels, this transition will correspond to a fairly broad absorption band.
  46. is attributable to the rapid nature of electronic transitions as compared to vibrational movements,
  47. the system will relax towards the equilibrium state (of the excited level) by dissipating heat.
  48. Line emission is found in the case of small △r.
  49. The emission generally lies at a lower energy than the absorption.
  50. This displacement of emission with respect to absorption is known as the Stokes shift.displacement  n. 位移,取代
  51. the centre will return non-radiatively to the equilibrium configuration of the ground state, dissipating heat in the process
  52. the luminescence decreases with rising temperature.
  53. the temperature dependence of the emission
  54. In the preceding parts of
    preceding adj. 在前的;前述的
  55. As already mentioned
  56. We also pointed out that there is in fact no fundamental difference between these two kinds of centre.
  57. There are various methods that can be used to demonstrate the occurrence of energy transfer. One can, for example, measure xx
  58. This is illustrated in
  59. As a result  τs will become shorter and so will the decay time of the luminescence from S.
  60. measure the decay time of the luminescence from S as a function of the concentration of A.
  61. This case is seldom of importance in the phosphors of interest to us.
  62. we need an interaction that can be of two essentially different types.
    essentially, adv. 本质上;本来
  63. In the first place the transfer can be brought about by the Coulomb interaction between S and A. If S and A are so far apart that their charge clouds do not overlap, this form of energy transfer is the only one possible.
     far apart  离得很远
  64. If the charge clouds of S and A do overlap, however, another transfer process is possible by exchange interaction between the electrons of S and A. The essential difference between the previous process and this one is that here electrons are exchanged between S and A, whereas in the Coulomb interaction process the electrons remain with their respective ions or ionic groups.
  65. we can disregard the contributions of the latter.
  66. It is possible to determine experimentally whether the levels involved are in resonance with one another by comparing the emission band of S with that of the relevant absorption band of A. The more these bands overlap, the better the resonance condition is fulfilled.
  67. an appreciable distance
    An appreciable amount or effect is large enough to be important or clearly noticed.
    appreciable adj. 可感知的;可评估的;相当可观的;
  68. Significant overlapping of the charge clouds of two cations in a crystal lattice is found only between cations that are nearest neighbours (separation 3 to 4 埃). Exchange interaction is therefore limited to neighbouring cations in the lattice. The critical distance for this transfer will never be much greater than 4 埃.
  69. We note that Psa(ex) does not comprise the optical properties of S and A (apart from the overlap integral). Exchange transfer, then, unlike transfer by Coulomb interaction, is not dependent on the oscillator strength or transition probability of the relevant transitions, and may even take place to a level from which a return to the ground state is strictly forbidden.
  70. The hopping time is the reciprocal of the transfer rate P mentioned above. reciprocal 互为倒数的 [rɪ'sɪprək(ə)l] 
  71. In many cases, however, it is found that the emission efficiency decreases if the activator concentration exceeds a specific value known as the critical concentration.
  72. may be explained in a number of cases as follows.
  73. If the concentration of the activator becomes so high that the probability of energy transfer exceeds that from emission, the excitation energy starts migrating through the lattice. Now the host lattice is not perfect: it contains all kinds of sites where the excitation energy may, in some obscure way, be lost, such as at the surface, at dislocations, impurities, etc. The efficiency then decreases, in spite of the increase of the activator concentration.
  74. At room temperature the luminescence of the VO4 group in YVO4, for example, is concentration quenched. The vanadate emission can be observed by either Iowering the temperature, so that the energy migration through the lattice is stopped (Palilla et al., 1965) or by diluting the vanadate groups with phosphate groups (system YP1-xVxO4) so that the energy migration is stopped because of the increasing V-V distance.
  75. broad-band emitting R ions
    In case
    given xxx
    For the sake of
    be concerned with
    followed by
    a fairly constant emission
    regardless of
  76. Absorption is the process by which a photon is absorbed by the atom, causing an electron to jump from a lower energy level to a higher one.
  77. thermodynamic equilibrium will be valid universally.
  78. The above equation must hold at any temperature.
  79. The aim of xx is to distill this information, providing readers with xxx.
  80. The current attention to energy saving and reduction of CO2 emission in the atmosphere, should therefore give an additional boost to the development of LEDs for lighting.
  81. The present review is focused on six main performance requirements for state-of-art color conversion phosphors.
  82. XX remains unchanged at elevated temperature.
  83. This paper is reviewed as follows.
  84. However, we will specifically aim for white light only, as this is the type of light with the most universal applications.
  85. Xxxx is the highest xx that can ever be obtained.
  86. At very low light level, typically below 1 cd/m2, the rods of the retina, responsible for night vision, starts to play a role.
  87. Conversion losses with the use of phosphors are eliminated.
  88. XXX, as will be shown/discussed further on.
  89. This goes at the cost of efficiency, and vice versa.
  90. This choice is motivated by the fact that XX.
  91. It is therefore advisable to have a relatively flat excitation for the phosphor near the peak emission of the LED.
  92. There exists a trade-off between the increasing absorption and a decrease in the internal quantum efficiency.
  93. The failure in one aspect in principle renders the phosphors useless for commercial applications.
  94. This is of course very interesting from a fundamental point of view, care must be taken to asses these properties in conditions mimicking the pumping LED behavior.
  95. Xxx are related to the interplay between host and dopant.
  96. When looking at the data compiled in Table 1, it is clear that .
  97. Xxx makes them less suited as dopant for LED phosphors.
  98. Long decay time for Mn2+(typically being several to tens of millisecond)
  99. Especially the temperature dependency should be carefully investigated, to rule out temperature dependent color shifts.
  100. The peak wavelength of the red emission is situated beyond 650 nm.
  101. Depending on the emission spectrum aimed for.
  102. Resist the elevated temperature.
  103. Fulfill certain requiremnts
  104. XX is shorthand for
  105. It is well established that BaFX materials are ubiquitously contaminated with oxygen impurities.33−35 This is corroborated by the fact that Tm2+ can be generated in nanocrystalline BaFCl:Tm3+ also by exposure to UV radiation at ∼200 nm (not illustrated here) where oxide impurities render strong absorbance.
  106. as time progresses
  107. The approach used in this paper is easily transferable to other new persistent phosphors for better practical applications.

  108. This model is not sustained by ab initio calculations.
    sustain v. 维持,保持;维持……的生命;遭受,经受;(在体力或精神方面)支持,支撑;承受住……的重量;证实,证明;认可,赞成,确认;(演员)充分表演(角色,人物),扮演

  109. which is in excellent agreement with the tabulated value in the literature.
    Results for the test program haven't been tabulated. 试验的结果还没有制成表格。
    tabulated 列成表格的,列表显示的
  110. The elucidation of the Ba3MgSi2O8 structure has also been in the center of much discussion.
    elucidation [ɪˌluːsɪˈdeɪʃn] n. 说明;阐明
  111. To circumvent this issue.
    circumvent [ˌsɜːkəmˈvent] v. 设法回避; 规避; 绕过; 绕行; 绕道旅行;
  112. From the XRD data of pristine phosphor SrAl2O4:Eu2+.
    pristine 原始的,未开发的
  113. Similarly, it is a common misconception among laymen that radioactive compounds show glow-in-the-dark persistent luminescence.
    laymen 非专业人员,外行,门外汉;
    misconception 误解;错觉;错误想法
  114. In the course of the years, several review papers, book chapters, and entire books have been published on persistent luminescence.
  115. Ultimately, some traps are not emptied at room temperature for months, making them useful for personal dosimetry, or for thousands of years, rendering them into excellent materials for geological dating.
  116. , this particle size reduction is is far from obvious.
    is far from obvious 无从知晓
  117. While this kind of top-down approach to the synthesis of nanoparticles is successful in a number of cases, it is more obvious to opt for a bottom-up synthesis method, starting from liquid precursors.
    opt for 选择
  118. In this fashion it was found that xxxx.
    in this fashion 用这种方式; 以这种方式; 照这样;
  119. The quantum efficiency is a parameter which is used to indicate to which extent non-radiative pathways dominate the decay of the luminescence activator. 
  120. This work helps to elucidate the mechanisms of the non-thermal excitation quenching process that has long been overlooked and most importantly explores the uncharted realms of the thermal-optical quenching of rare-earth doped phosphors.
    uncharted 人迹罕至的; 无人涉足的; 陌生的; 地图上未绘出(或未标明)的;
  121. Hitherto, the discovery of phosphor materials has largely taken place through painstaking experiments.
    hitherto  [ˌhɪðəˈtuː] 今为止; 迄今; 直到某时;
  122. By virtue of the close correlation of the quantum yield with the rigidity of molecules, it seems rational to state that the rigidity of the host lattice could be viewed as an ideal indicator for efficient photoluminescence.
    by virtue of 凭借,依靠,因为,由于;
  123. Considering that the Stokes shift varies from nearly zero to a value as large as 1.3 eV, the host effect on 5d-4f emission color through changes in Stokes shift also merits special consideration.
    merit [ˈmerɪt] v. 值得,应受;应受赏(或罚)
  124. Self-healing phosphor: New paradigm for high-power LED lighting.
    paradigm [ˈpærədaɪm] n. 典范,范例;样板,范式;词形变化表;纵聚合关系语言项
  125. Commercially used LED phosphors are often inorganic crystals doped with lanthanide ions, which still outcompete rapidly developing alternatives like quantum dots and perovskites.
    outcompete vt. 超过;胜出
  126. The search for new materials and new mechanisms for hole burning is stimulated both by the desire to understand the breadth of the applicability of spectral hole burning as a powerful tool in high-resolution optical spectroscopy of solidsand by the need for materials with the properties required for frequency-domain optical storage.
  127. In a recent review article devoted exclusively to the coloration of WO3 films, Bange did an admirable job in compiling the vast amount of work that has been done in this field. It would be instructive at this point to recapitulate what we know about the coloration phenomena in WO3.
  128. displaying tailorable optical properties
  129. In particular, we show that, by rational control of different combinations of dopants and dopant concentration, a wealth of color output can be generated under single-wavelength excitation.
  130. Importantly, we demonstrate that an inert-shell coating provides the particles with stable emission against perturbation in surrounding environments, paving the way for their applications in the context of biological networks.
  131. The introduction of lanthanides into these solid materials laid the foundation for many modern applications, such as lighting, photonic communication, and battery devices.
  132. considerable interest had arisen in screening various dopant/host combinations for improved optical properties
  133. Although the optical transitions in lanthanide-doped nanoparticles essentially resemble those in bulk materials, the nanostructure amenable to surface modifications provides new opportunities for research.
  134. have enabled them to rival conventional luminescent probes in challenging tasks including
  135. one urgent task that confronts materials chemists lies in the synthesis of nanoparticles with tunable emissions
  136. lanthanide-doped nanoparticles are generally characterized by the emission of optical centers.
  137. exerts a strong influence on
  138. e control over doping concentration and host lattices.
  139. It is worth noting that although each lanthanide behaves differently and has different optical properties from all of the others, the lanthanides of different types can combine with one another to impart desired optical properties.
  140. This attribute, together with the lack of fully matched absorption bands between different lanthanide ions, impedes effective excitation of different lanthanide activators under a single wavelength.
  141. In a parallel effort, Wang demonstrated downshifting multicolor tuning in NaGdF4 particles doped with Tb3+, Eu3+, Dy3+, and Sm3+ as the activator, in conjunction with Ce3+ as the sensitizer.
  142. In search of dual emitters that do not cause deleterious cross relaxations
  143. The selection of dopants for multicolor tuning in conventional bulk materials needs to meet stringent criteria because the extensive dopant−dopant interactions in the host lattice may induce luminescence quenching.
  144. xxx is stable within the measurement error.
  145. Co-doping a material with several activators exhibiting emissions centered at specific wavelengths is a widely used approach to target the desired color of emission.
  146. It is highly desirable to understand and mitigate photodarkening to prevent the associated deterioration of laser performance and secure reliability over several years.
  147. Although some KSF:Mn4+-containing LED devices are on the market, it remains unclear to what extent the application potential of this phosphor is limited by its relatively poor saturation behavior.
  148. With the exception of YAG:Ce phosphor and some organic luminescent materials, however, there are no reports on yellow phosphor that has significant emission in the 450–470 nm excitation range.
  149. Notably strontium aluminate, SrAl2O4, doped with europium and dysprosium, has been discovered over two decades ago and since then the phosphor has transcended its popular use in watch dials, safety signage, or toys with more niche applications such as stress sensing, photocatalysis, medical imaging, or flicker-free light-emitting diodes.
    transcend — v. 超出,超越;胜过(某人),超过(某项成就)
    niche market — 利基市场,也称利益市场、小众市场,是指由已有市场占有率绝对优势的企业所忽略之某些细分市场,并且在此市场尚未完善供应服务。一般由较小的产品市场并具有持续发展的潜力中,一些需要但尚未被满足的族群消费者所组成。
    at play — 在玩
  150. Phenomena such as persistent luminescence are often the result of a subtle balance between hard-to-assess microscopic properties such as bond lengths and vibrational frequencies or the presence of defects in the vicinity of the active centers.
    hard-to-assess — 难以评估的
  151. It was first reported over two decades ago, in 1996, by Matsuzawa et al., and really kickstarted persistent phosphor research.
    kickstart —vt. 启动(摩托);开始,重启;振兴(同kick start)
  152. Nanoparticles of SrAl2O4 do not appear to be cytotoxic, which is an important condition for potential biological applications.
    cytotoxic — / ˌsaɪtəʊˈtɒksɪk /  [细胞] 细胞毒素的  Cytotoxicity is the quality of being toxic to cells.
  153. This can partly be attributed to a poor reproducibility in material synthesis and seemingly conflicting experimental results, but is also a consequence of drawing too far-going conclusions from experiments that can be explained in multiple ways.
    far-going adj. 范围广泛的
  154. Except for some coarse mechanistic insights, the hidden variables that drive the persistent luminescence are still largely unknown as is apparent from literature.
  155. As such, we approach the topic from another angle compared to existing related overview articles on synthesis, the relation between host stoichiometry and Eu2+ emission characteristics and applications of persistent phosphors.
    approach the topic — 切入话题。另外的例句:They had obviously been hoping to approach the topic with more subtlety. 他们显然一直在希望更巧妙地切入这个话题。
    as such — 像这样的
  156. Finally, based on these experimental findings, requirements for an adequate model for the persistent luminescence mechanism are drafted.
    adequate model — 适当的模型
    draft — v. 起草
  157. However, this argument tacitly assumes that there is no preferential occupation of the dopants in the crystal which is not necessarily the case.
    tacitly — adv.肃静地;沉默地;心照不宣地    (understand tacitly 心领神会 ; 心照不宣地理解)
  158. However, given the large similarity between these hosts, it is plausible that many conclusions drawn for SrAl2O4 are transferable to other phases.
    plausible — 似乎合理/可信的
    transferable — 可转让的; 可转移的  (Use the transferable skills acquired from your previous working background. 利用你以前工作经历中获得的可转移性技能)
  159. Based on charge-neutrality arguments it was initially postulated that these trivalent lanthanides occupy Al3+ sites.
    postulate  — vt 假定
  160. Especially for non-isovalent substitutions, that is, when charge-compensating defects are generated, a stochastic distribution of dopants is an unjustified assumption.
    stochastic — adj. [数] 随机的;猜测的
    unjustified assumption — 不合理的假设
  161. The ions in SrO, Al2O3, and rare earth oxide precursors interdiffuse during calcination at high temperature.
    interdiffuse — 互扩散
  162. Unfortunately, SrAl2O4:Eu2+ suffers from degradation when exposed to water with the luminescence intensity decreasing over time. To counter this effect, post-synthesis, atomic layer deposition of a thin Al2O3 or TiO2 coating has been applied to increase the moisture resistance of the phosphor as required for outdoor applications.
    To counter this effect — 为了消除(应对)这种影响
  163. However, quite often the detection is achieved using photomultiplier tubes or photodiodes and only some rudimentary spectral information is obtained through the use of bandpass filters.
    rudimentary — 简陋的,最基本的(略带贬义)
  164. In contrast, it would be a good practice to simultaneously fit a mathematical model to a complete set of independent thermoluminescence, afterglow and fading measurements obtained under different conditions to obtain a consistent set of trapping parameters.
    a set of parameters — 一组参数
  165. Optical stimulation is often limited to illumination with infrared light while there is no a priori reason to exclude higher-energy light.
    a priori — adj.先天的;演绎的,推理的  adv.先天地;演绎地;推理地
  166. We will not describe these models in detail as this has already been done by, for example, Van den Eeckhout et al. or Vitola et al. but we will rather try to identify the requirements to which a model describing the afterglow process in SrAl2O4:Eu2+,Dy3+,B3+ should adhere.
    adhere to — 坚持;粘附;拥护,追随
  167. The size of this effect depends, however, on which site Eu2+ is incorporated: excitation with wavelengths higher than 420 nm, exclusively exciting EuSr2
    exclusively — 仅仅,单独地,专门地;作为唯一的(消息)来源
  168. Models such as the one by Aitasalo et al. that conjecture an energy transfer from trapping defects (other than Eu2+) to Eu2+ are unable to explain the similarity between persistent luminescence and photoluminescence excitation spectra.
    conjecture — v.<正式>猜测,推测;
  169. Following this reasoning, the hole trapping model quickly lost its initial popularity in favor of an electron trapping model.
    Following this reasoning — 按照这个推理
  170. It should however be stressed that some caution should be exercised when interpreting the results in Figure 10.
    caution should be exercised — 应谨慎行事
  171. Interestingly, no intermediate electronic state is required and the initial (Eu2+-Sm3+) and final (Eu3+-Sm2+) states are bridged directly.
    bridge — vt 克服 (障碍),结合  (bridge the gap/difference)
  172. The most important requirement for a defect to qualify as a trap is that it can adopt at least two charge states, that is, it can undergo a (photo)redox reaction with the Eu2+ activator.
    qualify as — 取得……资格;作为……合适
    I hope to qualify as a doctor. 我希望取得医生资格。
  173. Particularly, hydrogen (H) is a notorious impurity in semiconductor physics where its amphoteric character is known to strongly impact charge carrier dynamics.
    notorious — 声名狼藉的,臭名昭著的
  174. These hypothetical states are reminiscent of impuritytrapped exciton states, originally hypothesized by McClure and Pedrini in a different context,[276] that is, xxx
    reminiscent of — 使人联想的;怀旧的,缅怀往事的;与……相像的
  175. This assumption has not been verified and it cannot be excluded a priori that an intermediate state is formed where the transferred electron is temporarily localized at an auxiliary defect that bridges between the Eu activator and the (Dy) trap.
    auxiliary — / ɔːɡˈzɪliəri / 辅助的;备用的,后备的
  176. however it is thinkable that interstitial hydrogen can play a similar role.
    thinkable — 辅助的;备可想像的; 可能的; 可行的
  177. Nonetheless, models involving delocalized conduction band (CB) electrons or valence band (VB) holes are ubiquitous in literature and delocalized (i.e., global) models beat local models in terms of popularity by far.
    ubiquitous — / juːˈbɪkwɪtəs /  普遍存在的,无所不在的
  178. For cases where the number of carriers are much less than the number of band states, the carrier concentrations can be approximated by using Boltzmann statistics, giving the results below.
  179. The above equation holds true even for lightly doped extrinsic semiconductors as the product np is independent of doping concentration.
  180. This beautiful old building has been restored to its former glory. 这座美丽的老建筑物已恢复了昔日的壮观。
  181. Figure 16a shows an n-type semiconductor in which excess carriers are injected from one side as a result of illumination.
  182. The experimental results can be approximated by the empirical expression.

Leave a Reply