查看“︁居里点”︁的源代码

{{translating|[[:en:Curie temperature]]|time=2019-04-07}}
{{NoteTA
|G1 = Chemistry
}}

'''居里点'''（{{lang-en|Curie point}}），又作'''居里温度'''（Curie temperature，'''Tc'''）或'''磁性转变点'''。是指磁性材料中[[磁化強度|自发磁化强度]]降到零时的温度，是[[铁磁性]]或[[亚铁磁性]]物质转变成[[顺磁性]]物质的临界点。低于居里点温度时该物质成为[[铁磁体]]，此时和材料有关的[[磁场]]很难改变。当温度高于居里点时，该物质成为[[順磁性|顺磁体]]，磁体的磁场很容易随周围磁场的改变而改变。这时的[[磁化率|磁敏感度]]约为10<sup>-6</sup>。居里点由物质的化学成分和[[晶体结构]]决定。居里温度是以[[皮埃尔·居里]]命名的，他表明在临界温度下磁性材料会失去磁性。

居里點的溫度可以用平均場理論估計。

{| class="wikitable sortable" style="float:right; clear:right; margin-left:1em;"
|+ style="font-size: 88%"|材料的居里温度<ref>{{harvnb|Buschow|2001|loc=p5021, table 1}}</ref><ref name="table 3.1">{{harvnb|Jullien|Guinier|1989|p=155}}</ref><ref name=Kitteltable>{{harvnb|Kittel|1986|pp=}}</ref>
|-
! 材料
! 居里 <br />温度 (K)
|-
| [[铁]] (Fe)
| 1043
|-
| [[钴]] (Co)
| 1400
|-
| [[镍]] (Ni)
| 627
|-
| [[钆]] (Gd)
| 292
|-
| [[镝]] (Dy)
| 88
|-
| [[铋化锰]] (MnBi)
| 630
|-
| 锑化锰(Mn[[锑|Sb]])
| 587
|-
| [[二氧化铬]] (CrO<sub>2</sub>)
| 386
|-
| [[砷]]化锰
| 318
|-
| [[氧化铕]]
| 69
|-
| [[氧化铁]] (Fe<sub>2</sub>O<sub>3</sub>)
| 948
|-
| [[四氧化三铁]] (FeOFe<sub>2</sub>O<sub>3</sub>)
| 858
|-
| 氧化镍-氧化铁NiO–Fe<sub>2</sub>O<sub>3</sub>
| 858
|-
| 氧化铜-氧化铁CuO–Fe<sub>2</sub>O<sub>3</sub>
| 728
|-
| 氧化镁-氧化铁MgO–Fe<sub>2</sub>O<sub>3</sub>
| 713
|-
| 氧化锰-氧化铁MnO–Fe<sub>2</sub>O<sub>3</sub>
| 573
|-
| [[钇铁石榴石]] (Y<sub>3</sub>Fe<sub>5</sub>O<sub>12</sub>)
| 560
|-
| [[釹磁鐵|钕磁铁]]
| {{convert|310|-|400|C|K|disp=number}}
|-
| [[鋁鎳鈷合金|铝镍钴合金]]
| {{convert|700|-|860|C|K|disp=number|comma=off}}
|-
| [[釤鈷磁鐵|钐钴磁铁]]
| {{convert|720|-|800|C|K|disp=number|comma=off}}
|-
| [[铁氧体|锶铁氧体]]
| {{convert|450|C|K|disp=number}}
|}

== 磁矩 ==
磁矩是原子内的永久[[偶极矩]]，包含电子的角动量和自旋<ref name=Hall>{{harvnb|Hall|Hook|1994|p=200}}</ref>，他们之间的关系是 <math>\mu_l = \frac{el}{2m_e}</math>, m<sub>e</sub> 是电子质量, μ<sub>l</sub> 是磁矩, l是角动量; 这个比例被称作 '''gyromagnetic ratio'''（[[旋磁比]]）.

原子中的电子从它们自己的[[角动量]]和它们围绕原子核的轨道动量贡献[[磁矩]]。与来自电子的磁矩相比，来自原子核的磁矩是微不足道的。<ref name=Jullien136>{{harvnb|Jullien|Guinier|1989|pp=136–38}}</ref> 热作用在更高能量的电子上结果就是扰乱了秩序，并破坏了偶极子之间的对齐。 

[[铁磁性]]、[[顺磁性]]、[[亚铁磁性]]和[[反铁磁性]]材料有不同的固有磁矩结构。在材料特定的居里温度({{math|''T''<sub>C</sub>}})下，这些属性会发生变化。从反铁磁性到顺磁性（或反之亦然）的过渡发生在[[奈尔温度]]({{math|''T''<sub>N</sub>}}), 这与居里温度类似。

{|
|-
!   低于{{math|''T''<sub>C</sub>}} !!        高于{{math|''T''<sub>C</sub>}}
|-
| [[铁磁性]] ||↔ [[顺磁性]]
|-
| [[亚铁磁性]] ||↔ [[顺磁性]]
|-
!   低于{{math|''T''<sub>N</sub>}} !!        高于{{math|''T''<sub>N</sub>}}
|-
| [[反铁磁性]] ||↔ [[顺磁性]]
|}
<gallery caption="材料中磁矩的方向" heights="120" mode="packed">
File:Diagram of Ferromagnetic Magnetic Moments.png|'''[[铁磁性]]''': 铁磁性材料中的磁矩。在没有施加磁场的情况下，磁矩是有序的且具有相同的大小。
File:Diagram of Paramagnetic Magnetic Moments.png|'''[[顺磁性]]''': 顺磁性材料中的磁矩。在没有施加磁场的情况下，这些磁矩是无序的，并且在施加的磁场的情况下有序。
File:Diagram of Ferrimagnetic Magnetic Moments.png|'''[[亚铁磁性]]''': 亚铁磁性材料中的磁矩。由于由两种不同的离子组成，磁矩相反地对齐并且具有不同的大小。 这是在没有施加磁场的情况下。
File:Diagram of Antiferromagnetic Magnetic Moments.png|'''[[反铁磁性]]''': 反铁磁性材料中的磁矩。这些磁矩是相反的，并且具有相同的大小。 这是在没有施加磁场的情况下。
</gallery>

==在居里温度下改变特性的具有磁矩的材料 ==

铁磁性，顺磁性，亚铁磁性和反铁磁性结构由固有磁矩组成。 如果结构中的所有电子都配对，则由于它们的相反自旋和角动量，这些力矩会抵消。 因此，即使施加磁场，这些材料也具有不同的性质，并且没有居里温度。<ref name=Ibach/><ref name=Levy>{{harvnb|Levy|1968|pp=236–39}}</ref>

===顺磁性===
{{main|顺磁性}}
当一些材料的温度高于居里点时，材料会表现出顺磁性，这样的材料叫顺磁性材料。当没有受到外部[[磁场]]的影响时，顺磁性材料不会表现磁性；反之则会表现磁性。没有受到外部磁场影响时，材料内部的[[磁矩]]是无序排列的。也就是说，材料内部的粒子不整齐且没有顺[[磁力线]]方向排列。当受到磁场影响时，这些磁矩会顺磁场线整齐排列<ref name=Dekker1>{{harvnb|Dekker|1958|pp=217–20}}</ref><ref name=Levy4>{{harvnb|Levy|1968|pp=}}</ref><ref name=Fan>{{harvnb|Fan|1987|pp=164–65}}</ref>，并且产生感应磁场<ref name=Fan/><ref name=Dekker>{{harvnb|Dekker|1958|pp=454–55}}</ref>。

对于顺磁性，这种对外加磁场的响应是正的，称为[[磁化率]]。<ref name=Ibach>{{harvnb|Ibach|Lüth|2009}}</ref> 磁化率仅适用于居里温度以上的无序状态。<ref name=Mendelssohn3>{{harvnb|Mendelssohn|1977|p=162}}</ref>

顺磁性的来源（具有居里温度的材料）包括：<ref name=Levy1>{{harvnb|Levy|1968|pp=198–202}}</ref>
* 所有含未配对电子的原子；
* 内电子层未被填满的原子；
* [[自由基]]；
* 金属。

超過居禮溫度後，原子被激發， 旋轉的方向變成隨機的<ref name=Levy/> ，这种方向可以被作用場重新調整，此时即变为顺磁性。在居里温度以下，材料的固有结构经历了一次[[相变]]，<ref name=Cusack>{{harvnb|Cusack|1958|p=269}}</ref> 原子变为有序，材料具有铁磁性。<ref name=Fan/> 与铁磁性材料的磁场相比，顺磁性材料的感应磁场非常弱。<ref name=Cusack/>


===铁磁性===
{{main|铁磁性}}

材料仅在其相应的居里温度以下具有铁磁性。在没有外加磁场的情况下，铁磁材料具有磁性。

当没有外加磁场时，材料具有{{En-link|自发磁化|Spontaneous magnetization}}，这是有序磁矩的结果；也就是说，对于铁磁性材料，原子具有某种对称性并且在同一方向上排列，从而产生永久磁场。

磁性相互作用通过[[交换作用|交换相互作用]]结合在一起；否则，热无序将克服磁矩的弱相互作用。交换相互作用的平行电子占据同一时间点的可能性为零，这意味着材料中会有一个倾向的平行排列。<ref name="Hall1">{{harvnb|Hall|Hook|1994|pp=220–21}}</ref> 在这个过程中，玻尔兹曼因子贡献很大，因为它倾向于使相互作用的粒子在同一方向上排列。<ref name="Palmer">{{harvnb|Palmer|2007|pp=}}</ref> 这会导致[[铁磁体]]具有较强的磁场和较高的居里温度，约 1000K（730℃）<ref name="Hall3">{{harvnb|Hall|Hook|1994|p=220}}</ref>

在居里温度以下，原子有序排列，从而导致自发磁性，材料具有铁磁性。在居里温度以上，该材料是顺磁性的，因为当该材料经历相变时，原子会失去其有序的磁矩。<ref name="Cusack" />

===亚铁磁性===
{{main|亚铁磁性}}材料仅在其相应的居里温度以下具有亚铁磁性。在没有外加磁场的情况下，亚铁磁材料具有磁性，并由两种不同[[离子]]组成。<ref name=":0">{{harvnb|Jullien|Guinier|1989|pp=158–59}}</ref>

当没有外加磁场时，材料具有自发磁化，这是有序磁矩的结果；也就是说，对于亚铁磁性材料，一种离子的磁矩对准一个方向，有一个大小，另一种离子的磁矩对准相反方向，有一个不同的大小。因为磁矩在相反的方向有着不同的大小，所以仍然有自发磁化，存在磁场。<ref name=":0" />

和铁磁性材料相似，磁性相互作用通过[[交换作用|交换相互作用]]结合在一起。但是，磁矩的方向是反平行的，导致净势是一个减另一个。<ref name=":0" />

低于居里点时，每个离子的原子都反平行对齐，有着不同的磁矩，造成自发磁化；材料具有亚铁磁性。高于居里点时，该材料是顺磁性的，因为当该材料经历相变时，原子会失去其有序的磁矩。<ref name=":0" />

=== 反铁磁性与奈尔温度 ===
{{Main|反铁磁性}}
材料仅在其相应的[[奈尔温度]]以下具有反铁磁性。这与居里温度相似，高于奈尔温度时，该材料经历[[相变]]，变成顺磁性。也就是说，热能变得足够大，足以破坏材料内的微观磁有序性。 <ref>{{cite book|last1=Spaldin|first1=Nicola A.|title=Magnetic materials : fundamentals and device applications|date=2006|publisher=Cambridge Univ. Press|location=Cambridge|isbn=9780521016582|pages=89&ndash;106|edition=Repr.}}</ref>它以[[路易·奈爾|路易·奈尔]]（Louis Néel，1904-2000 年）的名字命名，他因在该领域的工作而获得了 1970 年的[[诺贝尔物理学奖]]。

材料有方向相反的相等磁矩，导致在奈尔温度以下磁矩为零和净磁性为零。反铁磁性材料在有或没有外加磁场的情况下有很弱的磁性。

与铁磁性材料相似，磁性相互作用通过交换相互作用结合在一起；否则，热无序将克服磁矩的弱相互作用。<ref name="Hall1" /><ref name=":1">{{harvnb|Jullien|Guinier|1989|pp=156–57}}</ref>奈尔温度时无序出现。<ref name=":1" />

下面列表中有几种物质的奈尔温度：<ref>{{cite book|first=Charles|last=Kittel|title=[[Introduction to Solid State Physics]]|edition=8th|location=New York|publisher=John Wiley & Sons|year=2005|isbn=978-0-471-41526-8}}</ref>
{| class="wikitable sortable"
|-
! Substance
! Néel temperature ([[开尔文|K]])
|-
| [[一氧化锰|MnO]]
| 116
|-
| [[硫化锰|MnS]]
| 160
|-
| [[碲化锰|MnTe]]
| 307
|-
| [[氟化锰|MnF<sub>2</sub>]]
| 67
|-
| [[氟化亚铁|FeF<sub>2</sub>]]
| 79
|-
| [[氯化亚铁|FeCl<sub>2</sub>]]
| 24
|-
| [[碘化亚铁|FeI<sub>2</sub>]]
| 9
|-
| [[氧化亚铁|FeO]]
| 198
|-
| {{En-link|氧基氯化铁|Iron oxychloride|FeOCl}}
| 80
|-
| [[氯化亚铬|CrCl<sub>2</sub>]]
| 25
|-
| [[碘化亚铬|CrI<sub>2</sub>]]
| 12
|-
| [[一氧化钴|CoO]]
| 291
|-
| [[氯化镍|NiCl<sub>2</sub>]]
| 50
|-
| [[碘化镍|NiI<sub>2</sub>]]
| 75
|-
| [[一氧化镍|NiO]]
| 525
|-
| KFeO<sub>2</sub>
| 983<ref>{{cite journal |last1=Ichida |first1=Toshio |title=Mössbauer Study of the Thermal Decomposition Products of K2FeO4 |url=https://archive.org/details/sim_bulletin-of-the-chemical-society-of-japan_1973-01_46_1/page/79 |journal=Bulletin of the Chemical Society of Japan |date=1973 |volume=46 |issue=1 |pages=79–82 |doi=10.1246/bcsj.46.79|doi-access=free }}</ref>
|-
| [[铬|Cr]]
| 308
|-
| [[三氧化二铬|Cr<sub>2</sub>O<sub>3</sub>]]
| 307
|-
| Nd<sub>5</sub>Ge<sub>3</sub>
|50
|}

{{TransH}}

==居里 - 韦斯定律==
{{main|居里-韦斯定律}}
居里-韦斯定律是[[居里定律]]的修正版本，是基于[[平均场论]]近似的简单模型，在材料温度{{mvar|T}}远高于其对应居里温度{{math|''T''<sub>C</sub>}}（即{{math|''T'' ≫ ''T''<sub>C</sub>}}）时较为适用，但却因原子间的局部波动作用无法在居里点附近对[[磁化率]]{{mvar|χ}}进行描述<ref name=Jullien153>{{harvnb|Jullien|Guinier|1989|pp=153}}</ref>。而{{math|''T'' < ''T''<sub>C</sub>}}的情况下，在居里定律和居里-韦斯定律均不成立。

Curie's law for a paramagnetic material:<ref name=Hall205>{{harvnb|Hall|Hook|1994|pp=205–06}}</ref>

:<math>\chi = \frac{M}{H} =\frac{M \mu_0}{B} =\frac{C}{T} </math>

{|
|-
! Definition !!
|-
| {{mvar|χ}} ||the magnetic susceptibility; the influence of an applied [[magnetic field]] on a material
|-
| {{mvar|M}} ||the [[magnetic moments]] per unit volume
|-
| {{mvar|H}} || the macroscopic magnetic field
|-
| {{mvar|B}} ||the magnetic field
|-
| {{mvar|C}} ||the material-specific [[Curie constant]]
|}

:<math>C = \frac{\mu_0 \mu_\mathrm{B}^2}{3 k_\mathrm{B}}N_A g^2 J(J+1)</math><ref name=Levy201>{{harvnb|Levy|1968|pp=201–02}}</ref>
{|
|-
| <math>N_A</math>
|[[阿伏伽德罗常数|Avagadro常数]]
|-
| {{math|''µ''<sub>0</sub>}} || the [[permeability of free space]]. Note: in [[CGS]] units is taken to equal one.<ref name=Kittel1996>{{harvnb|Kittel|1996|p=444}}</ref>
|-
| {{mvar|g}} || the [[Landé g-factor|Landé ''g''-factor]]
|-
| {{math|''J''(''J'' + 1)}} || the eigenvalue for eigenstate J<sup>2</sup> for the stationary states within the incomplete atoms shells (electrons unpaired)
|-
| {{math|''µ''<sub>B</sub>}} || the [[Bohr Magneton]]
|-
| {{math|''k''<sub>B</sub>}} || [[Boltzmann's constant]]
|-
| total magnetism || is {{mvar|N}} number of magnetic moments per unit volume
|}

The Curie–Weiss law is then derived from Curie's law to be:

:<math>\chi = \frac{C}{T-T_\mathrm{C}}</math>

where:

:<math>T_\mathrm{C} = \frac{C \lambda }{\mu_0}</math>

{{mvar|λ}} 是Weiss分子场常数。<ref name=Levy201/><ref name=Myers>{{harvnb|Myers|1997|pp=334–45}}</ref>

For full derivation see [[居里-外斯定律|居里-韦斯定律]].

==物理==

===从上方接近居里温度===

As the Curie–Weiss law is an approximation, a more accurate model is needed when the temperature, {{mvar|T}}, approaches the material's Curie temperature, {{math|''T''<sub>C</sub>}}.

Magnetic susceptibility occurs above the Curie temperature.

An accurate model of critical behaviour for magnetic susceptibility with [[critical exponent]] {{mvar|γ}}:

:<math>\chi \sim \frac{1}{(T - T_\mathrm{C})^\gamma}</math>

The critical exponent differs between materials and for the [[mean field theory|mean-field]] model is taken as {{mvar|γ}}&nbsp;=&nbsp;1.<ref name=Hall227>{{harvnb|Hall|Hook|1994|pp=227–28}}</ref>

As temperature is inversely proportional to magnetic susceptibility, when {{mvar|T}} approaches {{math|''T''<sub>C</sub>}} the denominator tends to zero and the magnetic susceptibility approaches [[infinity]] allowing magnetism to occur. This is a spontaneous magnetism which is a property of ferromagnetic and ferrimagnetic materials.<ref name=Kittel>{{harvnb|Kittel|1986|pp=424–26}}</ref><ref>{{harvnb|Spaldin|2010|pp=52–54}}</ref>

===从下方接近居里温度===

Magnetism depends on temperature and spontaneous magnetism occurs below the Curie temperature. An accurate model of critical behaviour for spontaneous magnetism with critical exponent {{mvar|β}}:

:<math>M \sim (T - T_\mathrm{C})^\beta</math>

The critical exponent differs between materials and for the mean-field model as taken as {{mvar|β}}&nbsp;=&nbsp;{{sfrac|1|2}} where {{math|''T'' ≪  ''T''<sub>C</sub>}}.<ref name=Hall227/>

The spontaneous magnetism approaches zero as the temperature increases towards the materials Curie temperature.

===接近绝对零度（0开尔文）===

The spontaneous magnetism, occurring in ferromagnetic, ferrimagnetic and antiferromagnetic materials, approaches zero as the temperature increases towards the material's Curie temperature. Spontaneous magnetism is at its maximum as the temperature approaches 0&nbsp;K.<ref name=Hall4>{{harvnb|Hall|Hook|1994|p=225}}</ref> That is, the magnetic moments are completely aligned and at their strongest magnitude of magnetism due to no thermal disturbance.

In paramagnetic materials temperature is sufficient to overcome the ordered alignments. As the temperature approaches 0&nbsp;K, the [[熵]] decreases to zero, that is, the disorder decreases and becomes ordered. This occurs without the presence of an applied magnetic field and obeys the [[热力学第三定律]].<ref name=Hall1/>

Both Curie's law and the Curie–Weiss law fail as the temperature approaches 0&nbsp;K. This is because they depend on the magnetic susceptibility which only applies when the state is disordered.<ref name=Mendelssohn1>{{harvnb|Mendelssohn|1977|pp=180–81}}</ref>

[[硫酸钆]] continues to satisfy Curie's law at 1&nbsp;K. Between 0 and 1&nbsp;K the law fails to hold and a sudden change in the intrinsic structure occurs at the Curie temperature.<ref name=Mendelssohn2>{{harvnb|Mendelssohn|1977|p=167}}</ref>

===Ising相变模型===

The [[Ising model]] is mathematically based and can analyse the critical points of [[phase transitions]] in ferromagnetic order due to spins of electrons having magnitudes of ±{{sfrac|1|2}}. The spins interact with their neighbouring [[dipole]] electrons in the structure and here the Ising model can predict their behaviour with each other.<ref name=Bertoldi>{{harvnb|Bertoldi|Bringa|Miranda|2012}}</ref><ref name=Brout>{{harvnb|Brout|1965|pp=6–7}}</ref>

This model is important for solving and understanding the concepts of phase transitions and hence solving the Curie temperature. As a result, many different dependencies that affect the Curie temperature can be analysed.

For example, the surface and bulk properties depend on the alignment and magnitude of spins and the Ising model can determine the effects of magnetism in this system.

===Weiss磁畴和表面和体积居里温度===

<!-- 檔案不存在 [[File:Weiss domains in a ferromagnetic material.png|thumb|right|'''Figure 3.''' The Weiss domains in a ferromagnetic material; the magnetic moments are aligned in domains.]] ，可從英文維基百科取得 -->
Materials structures consist of intrinsic magnetic moments which are separated into domains called [[Weiss domains]].<ref name=Jullien160>{{harvnb|Jullien|Guinier|1989|p=161}}</ref> This can result in ferromagnetic materials having no spontaneous magnetism as domains could potentially balance each other out.<ref name=Jullien160/> The position of particles can therefore have different orientations around the surface than the main part (bulk) of the material. This property directly affects the Curie temperature as there can be a bulk Curie temperature {{math|''T''<sub>B</sub>}} and a different surface Curie temperature {{math|''T''<sub>S</sub>}} for a material.<ref name=Rau>{{harvnb|Rau|Jin|Robert|1988|pp=}}</ref>

This allows for the surface Curie temperature to be ferromagnetic above the bulk Curie temperature when the main state is disordered, i.e. Ordered and disordered states occur simultaneously.<ref name=Bertoldi/>

The surface and bulk properties can be predicted by the Ising model and electron capture spectroscopy can be used to detect the electron spins and hence the [[magnetic moments]] on the surface of the material. An average total magnetism is taken from the bulk and surface temperatures to calculate the Curie temperature from the material, noting the bulk contributes more.<ref name=Bertoldi/><ref name=Skomski>{{harvnb|Skomski|Sellmyer|2000|pp=}}</ref>

The [[angular momentum]] of an electron is either +{{sfrac|{{mvar|ħ}}|2}} or −{{sfrac|{{mvar|ħ}}|2}} due to it having a spin of {{sfrac|1|2}}, which gives a specific size of magnetic moment to the electron; the [[Bohr magneton]].<ref name=Jullien138>{{harvnb|Jullien|Guinier|1989|p=138}}</ref> Electrons orbiting around the nucleus in a current loop create a magnetic field which depends on the Bohr Magneton and [[magnetic quantum number]].<ref name=Jullien138/> Therefore, the magnetic moments are related between angular and orbital momentum and affect each other. Angular momentum contributes twice as much to magnetic moments than orbital.<ref name=Hall1994>{{harvnb|Hall|Hook|1994|pp=}}</ref>

For [[terbium]] which is a [[rare-earth metal]] and has a high orbital angular momentum the magnetic moment is strong enough to affect the order above its bulk temperatures. It is said to have a high [[anisotropy]] on the surface, that is it is highly directed in one orientation. It remains ferromagnetic on its surface above its Curie temperature while its bulk becomes ferrimagnetic and then at higher temperatures its surface remains ferrimagnetic above its bulk Néel Temperature before becoming completely disordered and paramagnetic with increasing temperature. The anisotropy in the bulk is different from its surface anisotropy just above these phase changes as the magnetic moments will be ordered differently or ordered in paramagnetic materials.<ref name=Rau/>

===更改材料的居里温度===

==== Composite materials ====

[[Composite materials]], that is, materials composed from other materials with different properties, can change the Curie temperature. For example, a composite which has [[silver]] in it can create spaces for oxygen molecules in bonding which decreases the Curie temperature<ref name=Hwang>{{harvnb|Hwang et al.|1998|pp=}}</ref> as the crystal lattice will not be as compact.

The alignment of magnetic moments in the composite material affects the Curie temperature. If the materials moments are parallel with each other the Curie temperature will increase and if perpendicular the Curie temperature will decrease<ref name=Hwang/> as either more or less thermal energy will be needed to destroy the alignments.

Preparing composite materials through different temperatures can result in different final compositions which will have different Curie temperatures.<ref name=Paulsen>{{harvnb|Paulsen et al.|2003|pp=}}</ref> [[Doping (semiconductor)|Doping]] a material can also affect its Curie temperature.<ref name=Paulsen/>

The density of nanocomposite materials changes the Curie temperature. [[Nanocomposites]] are compact structures on a nano-scale. The structure is built up of high and low bulk Curie temperatures, however will only have one mean-field Curie temperature. A higher density of lower bulk temperatures results in a lower mean-field Curie temperature and a higher density of higher bulk temperature significantly increases the mean-field Curie temperature. In more than one dimension the Curie temperature begins to increase as the magnetic moments will need more thermal energy to overcome the ordered structure.<ref name=Skomski/>

==== Particle size ====

The size of particles in a material's crystal lattice changes the Curie temperature. Due to the small size of particles (nanoparticles) the fluctuations of electron spins become more prominent, this results in the Curie temperature drastically decreasing when the size of particles decrease as the fluctuations cause disorder. The size of a particle also affects the [[anisotropy]] causing alignment to become less stable and thus lead to disorder in magnetic moments.<ref name=Bertoldi/><ref name=Lopez-Dominguez>{{harvnb|López Domínguez et al.|2013|pp=}}</ref>

The extreme of this is [[superparamagnetism]] which only occurs in small ferromagnetic particles and is where fluctuations are very influential causing magnetic moments to change direction randomly and thus create disorder.

The Curie temperature of nanoparticles are also affected by the [[crystal lattice]] structure, [[body-centred cubic]] (bcc), [[face-centred cubic]] (fcc) and a [[hexagonal]] structure (hcp) all have different Curie temperatures due to magnetic moments reacting to their neighbouring electron spins. fcc and hcp have tighter structures and as a results have higher Curie temperatures than bcc as the magnetic moments have stronger effects when closer together.<ref name=Bertoldi/> This is known as the [[coordination number]] which is the number of nearest neighbouring particles in a structure. This indicates a lower coordination number at the surface of a material than the bulk which leads to the surface becoming less significant when the temperature is approaching the Curie temperature. In smaller systems the coordination number for the surface is more significant and the magnetic moments have a stronger affect on the system.<ref name=Bertoldi/>

Although fluctuations in particles can be minuscule, they are heavily dependent on the structure of crystal lattices as they react with their nearest neighbouring particles. Fluctuations are also affected by the exchange interaction<ref name=Lopez-Dominguez/> as parallel facing magnetic moments are favoured and therefore have less disturbance and disorder, therefore a tighter structure influences a stronger magnetism and therefore a higher Curie temperature.

==== Pressure ====

Pressure changes a material's Curie temperature. Increasing [[pressure]] on the [[crystal lattice]] decreases the volume of the system. Pressure directly affects the [[kinetic energy]] in particles as movement increases causing the vibrations to disrupt the order of magnetic moments. This is similar to temperature as it also increases the kinetic energy of particles and destroys the order of magnetic moments and magnetism.<ref name=Bose>{{harvnb|Bose et al.|2011|pp=}}</ref>

Pressure also affects the [[density of states]] (DOS).<ref name=Bose/> Here the DOS decreases causing the number of electrons available to the system to decrease. This leads to the number of magnetic moments decreasing as they depend on electron spins. It would be expected because of this that the Curie temperature would decrease however it increases. This is the result of the [[exchange interaction]]. The exchange interaction favours the aligned parallel magnetic moments due to electrons being unable to occupy the same space in time<ref name=Hall1/> and as this is increased due to the volume decreasing the Curie temperature increases with pressure. The Curie temperature is made up of a combination of dependencies on kinetic energy and the DOS.<ref name=Bose/>

The concentration of particles also affects the Curie temperature when pressure is being applied and can result in a decrease in Curie temperature when the concentration is above a certain percent.<ref name=Bose/>

==== Orbital ordering ====

[[Atomic orbital|Orbital ordering]] changes the Curie temperature of a material. Orbital ordering can be controlled through applied [[Deformation (mechanics)|strains]].<ref name=Sadoc>{{harvnb|Sadoc et al.|2010|pp=}}</ref> This is a function that determines the wave of a single electron or paired electrons inside the material. Having control over the [[probability]] of where the electron will be allows the Curie temperature to be altered. For example, the [[delocalised]] electrons can be moved onto the same [[lattice plane|plane]] by applied strains within the crystal lattice.<ref name=Sadoc/>

The Curie temperature is seen to increase greatly due to electrons being packed together in the same plane, they are forced to align due to the [[exchange interaction]] and thus increases the strength of the magnetic moments which prevents thermal disorder at lower temperatures.

== 铁电材料中的居里温度 ==

In analogy to ferromagnetic and paramagnetic materials, the term Curie temperature ({{math|''T''<sub>C</sub>}}) is also applied to the temperature at which a [[ferroelectric]] material transitions to being [[paraelectric]]. Hence, {{math|''T''<sub>C</sub>}} is the temperature where ferroelectric materials lose their spontaneous polarisation as a first or second order phase change occurs. In case of a second order transition the Curie Weiss temperature {{math|''T''<sub>0</sub>}} which defines the maximum of the dielectric constant is equal to the Curie temperature. However, the Curie temperature can be 10 K higher than {{math|''T''<sub>0</sub>}} in case of a first order transition.<ref name=Webster>{{harvnb|Webster|1999|pp=}}</ref>
{{multiple image|direction=vertical
| image1 =Ferroelectric polarisation.svg|caption1='''Figure 4.''' (Below {{math|''T''<sub>0</sub>}}) Ferroelectric polarisation {{math|'''P'''}} in an applied electric field {{math|'''E'''}}
| image2 =Paraelectric polarisation.svg|caption2='''Figure 5.''' (Above {{math|''T''<sub>0</sub>}}) Dielectric polarisation {{math|'''P'''}} in an applied electric field {{math|'''E'''}}
}}
{|
|-
! Below {{math|''T''<sub>C</sub>}} !! Above {{math|''T''<sub>C</sub>}}<ref name=Kovetz>{{harvnb|Kovetz|1990|p=116}}</ref>
|-
| Ferroelectric ||↔ Dielectric (paraelectric)
|-
| Antiferroelectric ||↔ Dielectric (paraelectric)
|-
| Ferrielectric ||↔ Dielectric (paraelectric)
|-
| Helielectric ||↔ Dielectric (paraelectric)
|}

=== Ferroelectric and dielectric ===

Materials are only ferroelectric below their corresponding transition temperature {{math|''T''<sub>0</sub>}}.<ref name=Myers404>{{harvnb|Myers|1997|pp=404–05}}</ref> Ferroelectric materials are all [[pyroelectric]] and therefore have a spontaneous electric polarisation as the structures are unsymmetrical.

Ferroelectric materials' polarization is subject to [[hysteresis]] (Figure 4); that is they are dependent on their past state as well as their current state. As an electric field is applied the dipoles are forced to align and polarisation is created, when the electric field is removed polarisation remains. The hysteresis loop depends on temperature and as a result as the temperature is increased and reaches {{math|''T''<sub>0</sub>}} the two curves become one curve as shown in the dielectric polarisation (Figure 5).<ref name=Pascoe1>{{harvnb|Pascoe|1973|pp=190–91}}</ref>

=== 相对介电常数  ===

A modified version of the Curie–Weiss law applies to the dielectric constant, also known as the [[relative permittivity]]:<ref name=Webster/><ref>{{harvnb|Webster|1999|pp=6.55–6.56}}</ref>

:<math>\epsilon = \epsilon_0 + \frac{C}{T-T_\mathrm{0}}.</math>

==应用==
A heat-induced ferromagnetic-paramagnetic transition is used in [[magneto-optical]] storage media, for erasing and writing of new data. Famous examples include the [[Sony]] [[Minidisc]] format, as well as the now-obsolete [[CD-RW#CD-MO|CD-MO]] format. Curie point electro-magnets have been proposed and tested for actuation mechanisms in passive safety systems of [[Breeder_reactor|fast breeder reactors]], where [[Control_rod|control rods]] are dropped into the reactor core if the actuation mechanism heats up beyond the material's curie point.<ref name="Takamatsu">{{cite journal |last1=Takamatsu |title=Demonstration of Control Rod Holding Stability of the Self Actuated Shutdown System in Joyo for Enhancement of Fast Reactor Inherent Safety |journal=Journal of Nuclear Science and Technology |volume=44 |issue=3 |url=https://doi.org/10.1080/18811248.2007.9711316}}</ref> Other uses include temperature control in [[soldering iron]]s,<ref>{{harvnb|TMT-9000S}}</ref> and stabilizing the magnetic field of [[tachometer]] generators against temperature variation.<ref>{{harvnb|Pallàs-Areny|Webster|2001|pp=262–63}}</ref>
{{TransF}}

== 参见 ==
* [[铁电性]]
* [[居里定律]]

== 参考资料 ==
=== 引用 ===
{{reflist|20em}}

=== 来源 ===
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{{refend}}

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