Reading the title, one might ask what exactly is a Polaron? “A polaron is a quasi particle that is used in condensed matter physics to understand the interactions between electrons and atoms in a solid material. The polaron concept was first proposed by Lev Landau in 1933 to describe an electron moving in a dielectric crystal where the atoms move from their equilibrium positions to effectively screen the charge of an electron, known as a phonon cloud. This lowers the electron mobility and increases the electron’s effective mass.” In addition, “Experimentally, polarons are important to the understanding of a wide variety of materials. The electron mobility in semiconductors can be greatly decreased by the formation of polarons. Organic semiconductors are also sensitive to polaronic effects, which is particularly relevant in the design of organic solar cells that effectively transport charge. Polarons are also important for interpreting the optical conductivity of these types of materials.” This wiki goes in greater detail on Polaron theory if one is interested in further reading on the topic. [1]
References
- “Polaron Theory,” Polaron – Wikipedia
- Burak Guzelturk et al, Visualization of dynamic polaronic strain fields in hybrid lead halide perovskites, Nature Materials (2021). DOI: 10.1038/s41563-020-00865-5 :PDF 2011.03103.pdf (arxiv.org)
Recently scientists have published work on the visualization of dynamic polaronic strain fields in hybrid lead halide perovskites in the Journal Nature Materials. [2] Polarons operate on very short timescales (trillions of a second) as distortions in a materials atomic lattice form around a moving electron. This distortion very quickly forms and then disappears. Scientists have theoretically predicted this effect of the polaron years ago, as fleeting as they are, may affect a materials behavior and may even be the reason that solar cells made with hybrid perovskite material achieve extraordinarily high efficiencies in the lab. Researchers at the Department of Energy SLAC National accelerator Laboratory and Stanford University have used an X-ray laser to measure the formation of polarons for the first time. [2] Again, this idea of Polarons has been around for many years, as Lev Landau proposed this phenomenon as early as 1933. These experiments are the first to observe the formation of the local distortions including their size, shape, and how they are formed.
A Perovskite is a calcium titanium oxide mineral composed of calcium titanate (CaTiO3). Its name is also applied to the class of compounds which have the same type of crystal structure as CaTiO3 (ABX3), known as the perovskite structure. Many different cations can be exchanged in this structure, allowing the development of a very diverse set of engineered materials. The material used in this study [2] was a lead halide perovskite. In the application to solar cells, this material is both easy to make and cheaper than using silicon. The down side is this material is much more unstable when exposed to air than silicon based cells. In addition, there is the problem of environmental concerns if these materials are put in a landfill as the leaching of the cations may be toxic to the environment. Previous studies from the DOE SLAC facility looked into the structure of Perovskites using an electron camera with X-ray laser. These studies revealed that the EM energy whirls atoms around in perovskites and they were able to measure the lifetimes of the acoustic phonons (sound waves) that carry heat through the material. In the present study, [2] researchers used their laboratory Linac Coherent Light Source (LCLS) to take X-ray snapshots of atoms and molecules at work, revealing these fundamental processes in materials. Researchers used a powerful X-ray free-electron laser and the resulting scattering / diffraction to study the materials at the atomic level in order to simultaneously capture atomic motions occurring in millionths of a billionth of a second. They looked at single crystals of the perovskite synthesized by a research group from Stanford University. In this study, they used a standard optical laser to interact with the perovskite material, and used the X-ray laser to experimentally measure the material response on the order of tens of trillionths of a second.
We note from history, Einstein was awarded the 1921 Nobel Prize in Physics for “his discovery of the law of the photoelectric effect,” and Robert Millikan was awarded the Nobel Prize in 1923 for “his work on the elementary charge of electricity and on the photoelectric effect.” The photoelectric effect is a phenomenon where electrons are emitted from the metal surface when the light of sufficient frequency is incident upon the material. The concept of photoelectric effect was first documented in 1887 by Heinrich Hertz and later by Lenard in 1902. Essentially, impinging an optical laser on the material resulted in the liberation of free electrons on the surface to move around the material. What occurs in the material is these electrons are engulfed in a sort of bubble of local distortion which is the polaron that travels with the electron. Some researchers believe the polaron bubble protects the scattering effects due to defects in the material, and claim this explains why perovskites are so efficient in the solar cell application. The study revealed that the distortions in the crystal lattice are on the order of a few angstroms which are within the length scales of the spacing between atoms in a solid. These distortions then expand in all directions to a diameter of about 5 billionths of a meter which is a 50-fold increase. This leads to 10 layers of atoms being slightly nudged outward with spherical radius over the course of 10ps, or a 10−12 of a second. This new finding shows the distortion to be very large which is something that was not known before. The study demonstrates how this phenomenon is real, it does exist, but this does not explain the perovskite efficiency in the solar cell application. There is a lot more work that needs to be conducted in order to fully understand how polarons affect the properties of materials and this is the current effort being made for future publications.
The Spiritual Insights that we receive from this type of research draws out the effects of sin in our lives. We can observe this using the story of Achan in the Tanakh according to Joshua 7.
ספר יהושע פרק ז
א וַיִּמְעֲלוּ בְנֵי-יִשְֹרָאֵל מַעַל בַּחֵרֶם וַיִּקַּח עָכָן בֶּן-כַּרְמִי בֶן-זַבְדִּי בֶן-זֶרַח לְמַטֵּה יְהוּדָה מִן-הַחֵרֶם וַיִּחַר-אַף יְהֹוָה בִּבְנֵי יִשְֹרָאֵל: ב וַיִּשְׁלַח יְהוֹשֻׁעַ אֲנָשִׁים מִירִיחוֹ הָעַי אֲשֶׁר עִם-בֵּית אָוֶן מִקֶּדֶם לְבֵית-אֵל וַיֹּאמֶר אֲלֵיהֶם לֵאמֹר עֲלוּ וְרַגְּלוּ אֶת-הָאָרֶץ וַיַּעֲלוּ הָאֲנָשִׁים וַיְרַגְּלוּ אֶת-הָעָי: ג וַיָּשֻׁבוּ אֶל-יְהוֹשֻׁע וַיֹּאמְרוּ אֵלָיו אַל-יַעַל כָּל-הָעָם כְּאַלְפַּיִם אִישׁ אוֹ כִּשְׁלֹשֶׁת אֲלָפִים אִישׁ יַעֲלוּ וְיַכּוּ אֶת-הָעָי אַל-תְּיַגַּע-שָׁמָּה אֶת-כָּל-הָעָם כִּי מְעַט הֵמָּה: ד וַיַּעֲלוּ מִן-הָעָם שָׁמָּה כִּשְׁלֹשֶׁת אֲלָפִים אִישׁ וַיָּנֻסוּ לִפְנֵי אַנְשֵׁי הָעָי: ה וַיַּכּוּ מֵהֶם אַנְשֵׁי הָעַי כִּשְׁלֹשִׁים וְשִׁשָּׁה אִישׁ וַיִּרְדְּפוּם לִפְנֵי הַשַּׁעַר עַד-הַשְּׁבָרִים וַיַּכּוּם בַּמּוֹרָד וַיִּמַּס לְבַב-הָעָם וַיְהִי לְמָיִם: ו וַיִּקְרַע יְהוֹשֻׁעַ שִֹמְלֹתָיו וַיִּפֹּל עַל-פָּנָיו אַרְצָה לִפְנֵי אֲרוֹן יְהֹוָה עַד-הָעֶרֶב הוּא וְזִקְנֵי יִשְֹרָאֵל וַיַּעֲלוּ עָפָר עַל-רֹאשָׁם: ז וַיֹּאמֶר יְהוֹשֻׁעַ אֲהָהּ | אֲדֹנָי יְהֹוִה לָמָה הֵעֲבַרְתָּ הַעֲבִיר אֶת-הָעָם הַזֶּה אֶת-הַיַּרְדֵּן לָתֵת אֹתָנוּ בְּיַד הָאֱמֹרִי לְהַאֲבִידֵנוּ וְלוּ הוֹאַלְנוּ וַנֵּשֶׁב בְּעֵבֶר הַיַּרְדֵּן: ח בִּי אֲדֹנָי מָה אֹמַר אַחֲרֵי אֲשֶׁר הָפַךְ יִשְֹרָאֵל עֹרֶף לִפְנֵי אֹיְבָיו: ט וְיִשְׁמְעוּ הַכְּנַעֲנִי וְכֹל יֹשְׁבֵי הָאָרֶץ וְנָסַבּוּ עָלֵינוּ וְהִכְרִיתוּ אֶת-שְׁמֵנוּ מִן-הָאָרֶץ וּמַה-תַּעֲשֵֹה לְשִׁמְךָ הַגָּדוֹל: י וַיֹּאמֶר יְהֹוָה אֶל-יְהוֹשֻׁעַ קֻם לָךְ לָמָּה זֶּה אַתָּה נֹפֵל עַל-פָּנֶיךָ: יא חָטָא יִשְֹרָאֵל וְגַם עָבְרוּ אֶת-בְּרִיתִי אֲשֶׁר צִוִּיתִי אוֹתָם וְגַם לָקְחוּ מִן-הַחֵרֶם וְגַם גָּנְבוּ וְגַם כִּחֲשׁוּ וְגַם שָֹמוּ בִכְלֵיהֶם: יב וְלֹא יֻכְלוּ בְּנֵי יִשְֹרָאֵל לָקוּם לִפְנֵי אֹיְבֵיהֶם עֹרֶף יִפְנוּ לִפְנֵי אֹיְבֵיהֶם כִּי הָיוּ לְחֵרֶם לֹא אוֹסִיף לִהְיוֹת עִמָּכֶם אִם-לֹא תַשְׁמִידוּ הַחֵרֶם מִקִּרְבְּכֶם:
Joshua 7:1-12
7:1 But the sons of Israel acted unfaithfully in regard to the things under the ban, for Achan, the son of Carmi, the son of Zabdi, the son of Zerah, from the tribe of Judah, took some of the things under the ban, therefore the anger of the Lord burned against the sons of Israel. 7:2 Now Joshua sent men from Jericho to Ai, which is near Beth-aven, east of Bethel, and said to them, ‘Go up and spy out the land.’ So the men went up and spied out Ai. 7:3 They returned to Joshua and said to him, ‘Do not let all the people go up; only about two or three thousand men need go up to Ai; do not make all the people toil up there, for they are few.’ 7:4 So about three thousand men from the people went up there, but they fled from the men of Ai. 7:5 The men of Ai struck down about thirty-six of their men, and pursued them from the gate as far as Shebarim and struck them down on the descent, so the hearts of the people melted and became as water. 7:6 Then Joshua tore his clothes and fell to the earth on his face before the ark of the Lord until the evening, both he and the elders of Israel; and they put dust on their heads. 7:7 Joshua said, ‘Alas, O Lord God, why did You ever bring this people over the Jordan, only to deliver us into the hand of the Amorites, to destroy us? If only we had been willing to dwell beyond the Jordan! 7:8 ‘O Lord, what can I say since Israel has turned their back before their enemies? 7:9 ‘For the Canaanites and all the inhabitants of the land will hear of it, and they will surround us and cut off our name from the earth. And what will You do for Your great name?’ 7:10 So the Lord said to Joshua, ‘Rise up! Why is it that you have fallen on your face? 7:11 ‘Israel has sinned, and they have also transgressed My covenant which I commanded them. And they have even taken some of the things under the ban and have both stolen and deceived. Moreover, they have also put them among their own things. 7:12 ‘Therefore the sons of Israel cannot stand before their enemies; they turn their backs before their enemies, for they have become accursed. I will not be with you anymore unless you destroy the things under the ban from your midst. (NASB)
We read specifically that Achan and his family were punished for this sin according to Joshua 7:15 and 7:24. Joshua 7:15, טו וְהָיָה הַנִּלְכָּד בַּחֵרֶם יִשָּׂרֵף בָּאֵשׁ אֹתוֹ וְאֶת-כָּל-אֲשֶׁר-לוֹ כִּי עָבַר אֶת-בְּרִית יְהֹוָה וְכִי-עָשָֹה נְבָלָה בְּיִשְֹרָאֵל: 7:15 ‘It shall be that the one who is taken with the things under the ban shall be burned with fire, he and all that belongs to him, because he has transgressed the covenant of the Lord, and because he has committed a disgraceful thing in Israel.’‘ (NASB) Joshua 7:24, כד וַיִּקַּח יְהוֹשֻׁעַ אֶת-עָכָן בֶּן-זֶרַח וְאֶת-הַכֶּסֶף וְאֶת-הָאַדֶּרֶת וְאֶת-לְשׁוֹן הַזָּהָב וְאֶת-בָּנָיו וְאֶת-בְּנֹתָיו וְאֶת-שׁוֹרוֹ וְאֶת-חֲמֹרוֹ וְאֶת-צֹאנוֹ וְאֶת-אָהֳלוֹ וְאֶת-כָּל-אֲשֶׁר-לוֹ וְכָל-יִשְֹרָאֵל עִמּוֹ וַיַּעֲלוּ אֹתָם עֵמֶק עָכוֹר: 7:24 Then Joshua and all Israel with him, took Achan the son of Zerah, the silver, the mantle, the bar of gold, his sons, his daughters, his oxen, his donkeys, his sheep, his tent and all that belonged to him; and they brought them up to the valley of Achor. (NASB) וַיֹּ֤אמֶר יְהוֹשֻׁ֙עַ֙ מֶ֣ה עֲכַרְתָּ֔נוּ יַעְכֳּרְךָ֥ יְהוָ֖ה בַּיּ֣וֹם הַזֶּ֑ה וַיִּרְגְּמ֨וּ אֹת֤וֹ כָל־יִשְׂרָאֵל֙ אֶ֔בֶן וַיִּשְׂרְפ֤וּ אֹתָם֙ בָּאֵ֔שׁ וַיִּסְקְל֥וּ אֹתָ֖ם בָּאֲבָנִֽים׃ 7:25 And Joshua said, “Why have you brought disaster on us? The Lord will bring disaster on you this day.” And all Israel stoned them with stones; and they burned them with fire [n]after they had stoned them with stones. (NASB) Reading these scriptures, the problem is when Achan committed this crime, which was a capital offence against God, we are told in the Scriptures that it was not just Achan who was killed. The stolen items, his children (וְאֶת-בָּנָיו וְאֶת-בְּנֹתָיו, sons and daughters) his oxen, donkeys, sheep, even his tent, and all that he owns was taken to the valley of Achor, and were stoned and then burned with fire. The key phrase here is וַיִּשְׂרְפ֤וּ אֹתָם֙ בָּאֵ֔שׁ where the word אֹתָם֙ “them” is written as a plural pronoun, the text is stating that “they” were all stoned and burned in the context of the list given in Joshua 7:24. One of the issues with this is the Scriptures state that God does not punish the children for the sins of their parents. (Ezekiel 18:20) and that God does not destroy the righteous with the wicked. (Bereshit / Genesis 18:23).
The issue with sin is that sin affects others. This is what the scientific research is drawing out for us on how there are distortions in the crystal lattice that occur due to the formation of a polaron. The lattice distortion is on the order of a few angstroms which are within the length scale of the spacing between atoms in a crystalline solid. These distortions then expand in all directions to a diameter of about 5 billionths of a meter which is a 50-fold increase. This leads to 10 layers of neighboring atoms being slightly nudged outward with spherical radius over the course of 10ps, or a 10−12 of a second. This new finding shows the distortion to be very large which is something that was not known before. The presence of a polaron leads to this distortion affecting the neighboring atoms and moving them from their equilibrium crystalline positions. Notice how this presents for us a fantastic picture on how sin functions in our lives affecting others!
A Crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter. The crystalline structure of materials parallels the family unit which is also structured, the Messiah Yeshua is head over the family, the father is head over the wife, and both are head over the children, etc. (1 Corinthians 11:3) There is a structured design to the family according to the Scriptures, and this is the danger of allowing sin to run its course without repentance, and seeking the Lord God of Israel and His Messiah Yeshua. Here reading the book of Joshua, we learn how the guilt of the family was also implied in their punishment. Since God is Just, the family must have sinned along with Achan or else they would not have been punished with him. We note that there was no reference to small children in the family as it lists simply “sons and daughters” (וְאֶת-בָּנָיו וְאֶת-בְּנֹתָיו). Another disturbing issue with this story is how the Lord God judges the collective by the sin of an individual. Achan had sinned in this way, and the result was 36 men died at the hands of the men of Ai (אַנְשֵׁ֣י הָעַ֗י). This parallels the polarons spherical influence, a 50-fold radius of influence on the crystalline structure. The Scientific researchs helps us to understand the impact of sin in our lives! These are reasons why sin is not something to be ignored and why repentance is so important. In Hebrew, Teshuvah (תשובה) has a critically important meaning. In Hebrew, the word Teshuvah translates literally as “turn / return,” and describes the return to God and with our fellow human beings that is made possible through repentance of our sins. In Judaism Teshuvah is most frequently associated with the High Holy days such as the ten days of repentance prior to Yom Kippur. Teshuvah however is not restricted to the holy days, men, women, and children can repent of their sins at any time. There are several stages of repentance, (i) one must recognize their wrongs and feel remorse for doing them and the damage that had been done, (ii) the sin must be confessed before God with a request for forgiveness in the name of Yeshua the Messiah. A sin against another person is more complicated as this requires reconciliation or making right what was wrong and there are times this may not be possible. The Torah goes to great lengths explaining how to make restitution. Without repentance and drawing near to the Lord God of Israel and Yeshua for our forgiveness, there is the danger of our sins affecting others, just as the polaron affects the crystalline structure distorting the crystalline atomic positions of materials. Our sins in parallel fashion can nudge others in the wrong direction, away from the way of God and the path of righteousness, holiness, and truth. We should also not neglect the intimate nature of repentance, as “forsaking the sin” requires the help of God to overcome and to not become a habitual repeat offender. In the case of the habitual sinner this is more complex. If the habitual sinner regrets his or her sin at all, that regret alone clearly does not translate into a change in behavior. In such a case, Rabbi Nosson Scherman recommends devising “a personal system of reward and punishment” and to avoid circumstances which may cause temptation toward the relevant sin. In the case of habitual sin one must create new habits that are holy and righteous that take the place of the sin. Rabbi Judah taught, “Who is the penitent whose repentance ascends until the Throne of Glory? one who is tested and emerges guiltless” (Talmud Bavli Yoma 86b and Yoma, 65). Maimonides interpreted this statement to mean that the sign of a true penitent is one who commits a sin and is later given the opportunity to commit exactly the same sin, yet one chooses not to (Maimonides “Laws of Repentance” 2:1). When we go to the Lord asking in the name of Yeshua the messiah, the Lord gives us the ability to overcome sin, and most significantly, as being weak, He is the One who is the enabler as we are totally reliant upon him! These are the things that the scientific research draws out according to the Scriptures!
