利用小角中子核磁散射分离研究AerMet100钢中纳米析出相的形貌和成分

图1 CoNi_454样品透过率曲线的Bragg边，及沿0°和90°方向按10°角进行积分和规约

Fig.1 Transmission curve and Bragg-edge feature of CoNi_454 sample (a), integration and normalization within 10° azimuth angle along the 0° and 90° orientations (b) (Q_x, Q_y —scattering vector moduli in x and y axes, repectively)

1.3 XRD和TEM实验方法

采用线切割截取尺寸为10 mm × 10 mm × 1 mm的片状试样，依次使用320、800、1000和1500号水砂纸进行研磨，最后用2.5 μm的金刚石研磨膏抛光。利用D/MAX-2500型高能XRD对抛光后的试样进行物相分析(Cu靶，扫描速率6°/min，电压40 kV，电流200 mA)。

抛光后的试样经过冲片、电解双喷制备TEM样品。实验设备为RL-I电解双喷仪，实验条件为：温度-15℃，10% (体积分数)高氯酸无水乙醇溶液，恒定电流200 mA，电解液流量和穿孔尺寸控制参数均设置为50。采用2100F场发射TEM观察样品微观组织。

2 实验结果及分析

2.1 电子显微成像结果

图2是AerMet100钢经过回火处理后的显微组织TEM像及SAED花样。在马氏体基体中可以发现大量的针状析出相(白色箭头所示)，在马氏体板条边界出现逆转奥氏体薄膜(黑色箭头所示)。当回火温度为486℃时，马氏体板条间存在厚度为2.5 nm的不连续的逆转奥氏体薄膜；当回火温度提高至498℃时，板条间的逆转奥氏体薄膜发生明显的长大，厚度达到3 nm，同时逆转奥氏体形成连续的薄膜。

图2

图2 486和498℃回火5 h的AerMet100钢显微组织的TEM像及选区电子衍射(SAED)花样

Fig.2 TEM images and SAED patterns (insets) of AerMet100 steel samples tempered at 486^oC (a) and 498^oC (b) for 5 h (White and black arrows indicate precipitates and reverted austenite films (RAFs), respectively)

图3为AerMet100钢回火处理后的XRD谱。经486℃回火处理后，衍射峰主要由(110) _α 、(200) _α 和(211) _α 3个马氏体衍射峰组成，未发现额外的碳化物或奥氏体衍射峰。然而，经498℃回火处理后，XRD谱中出现了额外的(111) _γ 、(200) _γ 和(220) _γ 奥氏体衍射峰。对比2种热处理状态(110) _α 衍射峰位置可以看出，回火温度不同可导致(110) _α 衍射峰出现位移。相较于486℃回火试样，498℃回火试样的(110) _α 衍射峰向左移动了0.05°，对应的(100)晶面间距大约相差0.0004 nm。

图3

图3 AerMet100回火钢的XRD谱

Fig.3 XRD spectra of the AerMet100 steel tempered at different temperatures

图4所示为AerMet100钢回火后针状M₂C析出相形貌的TEM像和SAED花样。图4a和b分别为486℃回火5 h后，沿基体[001] _α 以及[011] _α 方向观察的析出相形貌(白色箭头所示)。沿[001] _α 方向观察可以发现针状析出相沿着<010>方向析出，从[011] _α 方向可以观察到针状析出相的长轴与基体的<011>方向平行。针状析出相的平均长度为10 nm，平均直径为1~2 nm。图4c和d为498℃回火5 h后，沿基体[001] _α 以及[011] _α 方向观察到的析出相形貌。针状析出相平均长度为16 nm，平均直径仍保持在1~2 nm。

图4

图4 AerMet100钢回火处理后沿基体不同晶体学取向的针状M₂C析出相形貌的TEM像及SAED花样

Fig.4 TEM images and SAED patterns (insets) of the needle-like M₂C precipitates in tempered AerMet100 steel along different crystallographic orientations of the matrix phase (White arrows indicate the needle-like precipitates)

(a) 486^oC, [001] _α (b) 486^oC, [011] _α (c) 498^oC, [001] _α (d) 498^oC, [011] _α

2.2 SANS数据及拟合策略分析

为了进一步分析AERMET100钢中析出相的尺寸分布及其随时效温度的演化，分别对454、482、486及498℃回火5 h的样品开展了SANS实验观测，实验结果如图5所示。由图5a中4种回火状态AERMET100钢的磁滞回线可以看出，施加1.1 T磁场，样品基本处于饱和磁化状态，随着磁矩的转动，0.2 nm^-1处所探测的磁畴结构被消除。从图5b可以看出，在Q为0.2和1.5 nm^-1处，散射曲线均存在明显的“隆起”特征，表明合金中存在尺寸不同的纳米结构。其中，1.5 nm^-1处的散射特征在5 mT和1.1 T磁场下均存在，且随磁场变化很小，表明其主要结构来源为析出相的核散射。然而，在0.2 nm^-1处散射曲线仅在5 mT磁场下存在明显“隆起”特征，随着加载至1.1 T磁场，所有样品在该处的散射特征均消失，说明该处的结构来源为合金中的磁不均匀结构。

图5

图5 不同温度回火处理AerMet100钢的磁滞回线，及无磁场(电磁铁5 mT剩磁)和1.1 T磁场条件下AerMet100钢小角中子散射(SANS)一维散射曲线

Fig.5 Magnetic hysteresis curves (a) and the 1D SANS scattering curves measured under no field application (5 mT remanence) and 1.1 T magnetic field of AerMet100 steel tempered at different temperatures (b) (SANS—small-angle neutron scattering; Q—scattering vector modulus)

在采用中子散射技术观测材料微观结构时，主要需要考虑2个方面的因素：结构的尺度和结构的中子散射衬度。根据TEM结果可知，在AERMET100钢的组成相中，马氏体板条尺寸粗大(300 nm~3 μm)，不在SANS的探测尺度范围(1~100 nm)。而低温回火产生的Fe₃Mo₃C (尺寸约50 nm)和高温时效的(Cr, Mo)₂C析出相(尺寸为1~20 nm)均在SANS探测范围内。表1所示为对合金组成相的中子散射长度密度的计算结果，其中，ρ_N和ρ_M分别为AERMET100钢组成相的中子核散射长度密度和磁散射长度密度。Fe₃Mo₃C低温相以及逆转奥氏体薄膜与基体马氏体板条之间的衬度，即中子散射长度密度差的平方 ${(Δ ρ)}^{2}$ ，都小于0.15 × 10²⁰ cm^-4。因此在SANS数据中，Fe₃Mo₃C和逆转奥氏体薄膜的核散射密度差别非常微小，在对核散射数据进行分析拟合时可以忽略，仅需考虑针状碳化物相。对于磁散射数据，由于针状碳化物相和逆转奥氏体薄膜均为非磁性相，2者的磁散射长度密度可视为0，其与铁磁性的马氏体板条之间的磁散射长度密度差别为4.43 × 10¹⁰ cm^-2，拟合时均需予以考虑。

表1 AerMet100钢组成相的成分、密度及中子散射长度密度

Table 1 Chemical compositions, densities and neutron scattering length densities of phases in AerMet100 steel

Phase	Chemical composition	Density / (g·cm^-3)	ρ_N / (10¹⁰ cm^-2)	ρ_M / (10¹⁰ cm^-2)
Martensite lath matrix	Fe_70.92Co_13.4Ni_11.1Cr_3.1Mo_1.2C_0.23Ti_0.05	7.62	6.84	4.43
Reverse austenite film	Fe_70.92Co_13.4Ni_11.1Cr_3.1Mo_1.2C_0.23Ti_0.05	7.59	6.74	0
Needle-like carbide	(Cr _x Mo _y )C	Unknown	5.21	0
Tempered particle	Fe₃Mo₃C	9.17	6.52	-

Note: ρ_N—nuclear neutron scattering length density, ρ_M—magnetic neutron scattering length density; the chemical composition and density of nano-scale needle-like carbide is to be determined in this study

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基于上述分析，对于核散射数据，本工作采用圆柱标准模型来对合金中存在的针状纳米析出相的形状和尺寸进行拟合，对低Q区采用power-law模型来分析相界面的散射。此外，引入硬球(hardsphere)的结构因子模型对针状纳米相的有序分布和排列进行拟合^[20]。而对磁散射数据，在上述模型基础上，本工作增加了一个不依赖于形状的unified-level模型，来拟合出逆转奥氏体薄膜的厚度标准模型，细节参见文献[21,22]。核与磁散射强度 $I_{N} (Q)$ 、 $I_{M} (Q)$ 的数学表述如下^[23]：

I_{N} (Q) = N_{0} {(Δ ρ_{N})}^{2} V^{2} \int_{0}^{\infty} f (R) F^{2} (Q) S (Q) d R +

k Q^{- γ} + b g

(1)

I_{M} (Q) = N_{0} {(Δ ρ_{M})}^{2} s i n^{2} α \cdot V^{2} \int_{0}^{\infty} f (R) F^{2} (Q) d R +

k Q^{- γ} + b g

(2)

其中，携带析出相的形状和尺寸分布等形貌信息的圆柱模型形状因子(form factor，F)表述如下^[24]：

F (Q) = \frac{s i n (\frac{1}{2} Q L c o s β)}{\frac{1}{2} Q L c o s β} \frac{J_{1 (Q R s i n β)}}{Q R s i n β}

(3)

采用对数正态分布函数来进行描述析出相的尺寸分布f(R)^[23]：

f (R) = \frac{1}{\sqrt[]{2 π} σ R} e x p (- \frac{(l n R - l n R_{m})^{2}}{2 σ^{2}})

(4)

代表针状纳米相之间相对位置干涉对散射曲线的调制作用的结构因子(structure factor，S)表述如下^[20]：

S (Q) = 1 + n 4 π \int (g (R_{H S}) - 1) \frac{s i n (Q R_{H S})}{Q R_{H S}} R_{H S}^{2} d R_{H S}

(5)

式中， $Δ ρ_{N}$ 和 $Δ ρ_{M}$ 分别是针状纳米相与基体之间的中子核散射和磁散射衬度； $N_{0}$ 为Avogadro常数； $k 为拟合得到的常数因子; b g$ 代表样品的中子散射背底，对特定的样品为常数； $V$ 是针状纳米相的体积；L为圆柱状析出相的长度；n为析出相的数密度； $g (R_{H S})$ 为径向分布函数或对关联函数；R代表针状相的半径；R_m为对核、磁散射曲线拟合得到的名义半径；σ为R_m的标准偏差； $α$ 为Q与外磁场的夹角；β为圆柱轴向与Q的夹角； $γ$ 为衰减系数，核散射一般在(0, 4.2)之间取值；磁散射在(0, 8)之间取值；J₁为一阶Bessel方程；R_HS为根据硬球模型结构因子拟合得到的硬球半径。

2.3 核磁散射分离及散射曲线拟合分析

2.3.1 不同磁场下SANS二维散射花样

图6为分别在无磁场(5 mT)及50 mT、0.1 T和1.1 T横向磁场加载下采集的二维SANS散射花样。可以看出，在低磁场下(图6a和b)，由于在析出相-基体界面和缺陷(如孔洞、夹杂和位错等)附近均存在自旋错排^[25]，使得散射花样表现出各向同性的特征。

图6

图6 不同磁场加载下498℃回火AerMet100钢的二维SANS散射花样

Fig.6 2D SANS patterns of 498^oC-tempered AerMet100 steel under different magnetic field strengths (I—integral intensity)

(a) no field application (5 mT) (b) 50 mT (c) 0.1 T (d) 1.1 T

根据前文分析，图6a中Q = 0.1 nm^-1处轻微的各向异性主要源于合金中磁畴结构的散射。在0.1 T和1.1 T横向磁场加载条件下(图6c和d)，二维散射花样具有明显的各向异性，沿与外磁场垂直方向呈现出倒“8”字特征，预示着磁矩沿外磁场方向的重排。尤其是在1.1 T磁场下，磁矩完全沿外磁场方向排列，呈现饱和特征。此时，散射花样具有显著的“蝴蝶”形状，这是由于中子与磁矩的磁偶极相互作用所致^[26]。

2.3.2 饱和磁场下SANS核磁散射比值

如前所述，由于并不知道Cr取代Mo元素的比例，从而无法确定(Cr, Mo)₂C相的具体成分。为此将该碳化物相的成分标记为(Cr _x Mo _y )C，并尝试通过对该相SANS数据的核磁散射分离来获得其核磁散射长度密度的比值。根据表1的计算，可以知道(Cr, Mo)₂C针状相为非磁性相，其与基体相的中子磁散射衬度为： $(Δ ρ_{M})^{2}$ = 19.62 $\times 10^{20}$ cm^-4。而饱和磁化状态下，析出相SANS核磁散射的比值(I_mag / I_nuc)符合以下关系式^[27]：

\frac{I_{m a g}}{I_{n u c}} = \frac{(Δ ρ_{M})^{2}}{(Δ ρ_{N})^{2}}

(6)

对样品施加横向磁场，在饱和磁化状态下，对二维散射花样分别在平行和垂直于磁场方向(< 20°散射角内)分别进行积分(如图7所示)，得到2个方向的散射强度 $I_{⊥} (H) 和 I_{∥} (H)$ 。其中，垂直于磁场方向的数据 $I_{⊥} (H)$ 是核散射和磁散射强度之和，而平行于磁场方向的数据 $I_{∥} (H)$ 则仅仅包含核散射强度^[24]。对2者运算可实现样品的磁散射和核散射的分离^[26]：

图7

图7 1.1 T磁场加载下AerMet100回火钢的SANS实验观测结果，核散射和拟合曲线，磁散射和拟合曲线，以及核磁散射比值曲线

Fig.7 SANS results of AerMet100 tempered steel under magnetic field application

(a) total SANS 1D scattering data

(b, c) experimental and fitted nuclear (b) and magnetic (c) SANS results

(d) observed ratio between SANS nuclear scattering intensity (I_N) and magnetic scattering intensity (I_M)

I_{n u c} = I_{∥} (H)

(7)

I_{m a g} = I_{⊥} (H) - I_{∥} (H)

(8)

根据分离出的SANS实验核磁散射强度可以计算出2者的核散射衬度平均值为 $(Δ ρ_{N})^{2} = 2.66 \times$ $10^{20}$ cm^-4，于是得到(Cr _x Mo _y )C的中子核散射长度密度 $ρ_{N_(C r_{x} M o_{y} C)} = (6.84 - \sqrt[]{2.66}) \times 10^{10} c m^{- 2} = 5.21 \times$

$10^{10} c m^{- 2}$ 。另一方面， $ρ_{N_(C r_{x} M o_{y} C)}$ 的理论计算式如下：

ρ_{N_(C r_{x} M o_{y} C)} = \frac{1}{3} (ρ_{N_C r} x + ρ_{N_M o} y) + \frac{1}{3} ρ_{N_C}

(9)

x + y = 2

(10)

通过查询各元素的中子散射长度 $ρ_{N_i}$ (i = Cr、Mo、C)数据可知， $ρ_{N_C r} = 3.01 \times 10^{10} c m^{- 2}$ ， $ρ_{N_M o} = 4.31 \times 10^{10} c m^{- 2}$ ， $ρ_{N_C} = 7.53 \times 10^{10} c m^{- 2}$ ，将其带入式(9)中，联立式(9)和(10)方程组可得到：(Cr _x Mo _y )C的成分为：(Cr_0.4Mo_1.6)C。根据该成分碳化物相的核散射长度密度值可以反推出其密度为8.55 g/cm³。

这种通过纳米异质相与基体之间理论核、磁散射衬度比值与实验核、磁散射强度比值测得的散射衬度对比计算的方法可以对纳米异质相的化学成分进行推测。对于磁矩和成分与基体合金存在差别的纳米异质相，采用该方法推断其化学组成具有通用性。然而，所获得的纳米相的化学成分可能与其实际成分存在一定的偏差，除了受SANS数据统计误差影响外，其可能的影响因素还包括：(1) 由于在热处理过程中的元素扩散，基体相的成分可能发生变化；(2) 当合金中存在多种纳米析出相，不同组成的纳米相体积分数也可能出现相对变化^[28]，使得根据原有单一基体相成分计算的核磁散射长度密度与实际值存在偏差；(3) 当纳米异质相含有“杂质”时，例如空位，也会使得推测的纳米相成分存在偏差^[29]。尽管如此，SANS核磁散射分离为细小纳米相成分的确定提供了新思路，该技术可以弥补传统SANS仅能测试形貌尺寸的不足。

2.3.3 SANS核散射与磁散射拟合结果

根据表1的SLDs计算数据，对平行于磁场方向的I(Q $∥$ H)-Q曲线拟合时，析出相(中子散射长度密度为 $ρ_{(C r_{x} M o_{y} C)}$ )与基体(中子散射长度密度为 $ρ_{M - s t e e l}$ )之间的中子散射衬度为 ${(Δ ρ)}^{2} = (ρ_{(C r_{x} M o_{y} C)} - ρ_{M - s t e e l})^{2} = 2.66$ 。SANS核散射数据拟合出的析出相的结构参数如表2所示。4种温度回火样品中针状相直径均在1.2~2.5 nm，长度在6~16 nm之间，析出相尺寸随回火温度升高呈增长趋势。按照圆柱体积与硬球模型体积之比计算出的针状碳化物相的体积分数随回火温度的升高逐渐增大，由454℃回火态的0.54%增加到498℃回火态的5.19%。

表2 AerMet100钢SANS核散射拟合结果

Table 2 Fitted structural parameters of nanoprecipitates from the nuclear SANS data of AerMet100 steel

Sample	D / nm	L / nm	R_HS / nm	f_V / %
CoNi_454	1.15 ± 0.76	6.00 ± 1.27	5.95 ± 1.05	0.54 ± 0.15
CoNi_482	2.02 ± 1.04	9.63 ± 0.87	6.68 ± 0.92	2.47 ± 0.34
CoNi_486	2.37 ± 0.75	10.6 ± 1.72	6.75 ± 0.78	3.25 ± 0.38
CoNi_498	2.48 ± 0.99	15.9 ± 2.94	7.07 ± 0.93	5.19 ± 0.68

Note: D—diameter of needle-like carbide, L—length of needle-like carbide, R_HS—radius of hard sphere model, f_V—volume fraction of needle-like carbide

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表3为SANS磁散射数据拟合出的纳米畴的结构参数。与表2对比可以看出，由磁散射数据拟合得到的针状相的直径和长度均大于核散射数据的拟合结果，这是由于在针状相与马氏体板条基体间磁矩急剧“跳变”，使得在相界面处存在磁偶极杂散场作用，并使得该区域自旋会偏离周围基体错排，形成纳米磁畴结构，从而导致拟合的结构参数偏大。可见这些纳米畴结构既包含了非磁性针状相碳化物和逆转奥氏体相在铁磁性基体中形成的“磁洞”，又包含了析出相与基体间相界面处磁偶极杂散场引起的自旋错排区。这也正是表3中磁散射数据拟合得到的逆转奥氏体厚度要大于TEM观测厚度的原因。

表3 AerMet100钢SANS磁散射拟合结果 (nm)

Table 3 Fitted structural parameters of nanodomains from the magnetic SANS data of AerMet100 steel

Sample	D	L	R_HS	t
CoNi_454	1.80 ± 0.74	6.51 ± 0.42	5.01 ± 0.47	0
CoNi_482	2.46 ± 0.75	13.70 ± 1.24	18.50 ± 0.41	2.59 ± 0.47
CoNi_486	2.60 ± 0.86	13.40 ± 1.50	18.00 ± 0.35	5.56 ± 1.60
CoNi_498	2.62 ± 0.40	19.07 ± 1.61	18.57 ± 0.46	5.57 ± 1.56

Note: t—thickness of the reverse austenite

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由本工作的示范性研究可以看出：与TEM技术的微观形貌分析特点相比，结合核-磁散射分离的SANS技术能够对较大块体样品(探测体积范围mm³~cm³)中纳米析出相的形貌、尺寸和成分进行定量分析。通过统计平均获得的结构参数可靠性更高，也更能代表整块样品的结构和成分特征。此外，中子的穿透性也使得人们能够在复杂外场环境下对材料的纳米结构进行原位观测，更易于实现对制备加工和服役条件下样品微观结构演化的原位观测。然而，SANS技术的观测结果不如TEM成像直观和易于解读，散射数据的解析依赖于模型拟合，相对更为复杂，这也是该技术未来发展需要重点突破的研究方向。

3 结论

(1) TEM和SANS实验结果均显示回火处理后AerMet100合金钢中针状析出相平均长度为6~16 nm，平均直径为1~2 nm。SANS测定合金中针状碳化物相的体积分数随回火温度升高，由0.54%逐渐提高至5.19%。

(2) 随着磁场的加载，SANS散射花样逐渐由各向同性演变成各向异性的倒“8”字特征。磁散射拟合得到的碳化物直径均大于核散射结果，说明在碳化物与马氏体基体相界面处存在自旋错排的纳米磁畴区。

(3) 饱和磁化状态下，纳米析出相SANS核磁散射的比值存在2个峰值。通过对碳化物和基体相中子核磁散射长度密度的对比计算，推断出针状碳化物的可能化学组成及密度分别为：(Cr_0.40Mo_1.60)C和8.55 g/cm³。

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